UvA-DARE (Digital Academic Repository) Comprehensive characterization of branched polymers Edam, R. Link to publication

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1 UvA-DARE (Digital Academic Repository) Comprehensive characterization of branched polymers Edam, R. Link to publication Citation for published version (APA): Edam, R. (2013). Comprehensive characterization of branched polymers General rights It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. UvA-DARE is a service provided by the library of the University of Amsterdam ( Download date: 01 Jan 2019

2 Comprehensive Characterization of Branched Polymers Rob Edam Comprehensive Characterization of Branched Polymers Rob Edam

3 Comprehensive Characterization of Branched Polymers

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5 Comprehensive Characterization of Branched Polymers ACADEMISCH PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Universiteit van Amsterdam op gezag van de Rector Magnificus prof. dr. D.C. van den Boom ten overstaan van een door het college voor promoties ingestelde commissie, in het openbaar te verdedigen in de Agnietenkapel op donderdag 21 februari 2013, te 14:00 uur door Rob Edam geboren te Avenhorn

6 Promotor: Prof. Dr. Ir. P.J. Schoenmakers Overige leden: Prof. Dr. Ir. J.G.M. Janssen Prof. Dr. Sj. van der Wal Prof. Dr. A.M. van Herk Dr. W.Th. Kok Dr. W. Radke Dr. F.A. van Damme Faculteit der Natuurwetenschappen, Wiskunde en Informatica Comprehensive characterization of branched polymers; R. Edam Printed by Universal Press, Veenendaal, The Netherlands This research is part of the research program of the Dutch Polymer Institute (DPI), project #509. ISBN

7 Contents Chapter 1: General introduction An introduction to polymers Macromolecules Early characterization of polymers Polymer structure Branched polymers Characterization and separation of branched polymers TREF, Crystaf and DSC Rheology Spectroscopy Size-exclusion chromatography with selective detection SEC separation of branched polymers SEC with on-line (micro-)viscometry SEC with multi-angle laser-light-scattering detection Application and challenges of existing methodology Scope of the thesis Chapter 2: Hydrodynamic chromatography of macromolecules using polymer monolithic columns Introduction Experimental Chemicals and materials Instrumentation Column preparation Results and discussion Preparation and characterization of monoliths for HDC HDC separation of polymers Flow-rate dependence in polymer separations Conclusions Appendix Mercury intrusion and extrusion SEC separation of alkylbenzenes and solvents on monolith Deborah numbers... 66

8 Chapter 3: Branched-Polymer Separations using Comprehensive Two-Dimensional Molecular-Topology Fractionation Size-Exclusion Chromatography Introduction Experimental Samples and materials Instrumentation and methods Results and discussion Calibration curve for molecular-topology-fractionation column Branched-polymer separations Conclusions Appendix Chapter 4: Branched Polymers Characterized by Comprehensive Two-Dimensional Separations with fully Orthogonal Mechanisms Introduction Theory Separation techniques based on size Deformation of polymers in solution Reptation Calibration curves and separation of deformed-polymers Experimental Chemicals and materials Instrumentation and operating conditions Columns and experimental conditions Results and discussion Flow-rate effect for columns with different pore size Branched-polymer separations Selectivity for branched polymers Effect of flow rate on migration of branched polymers Effect of temperature on migration of polymers in MTF Conclusions Appendix Comprehensive HDC SEC experiment Second-dimension calibration for MTF SEC Flow-rate effect in MTF SEC MTF SEC at orthogonal conditions

9 4.6.5 MTF SEC-UV/MALLS on long-chain-branched polystyrene Selectivity in MTF as a function of flow rate Effect of temperature on MTF SEC separations Chapter 5: Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using Size-Exclusion Chromatography Introduction Experimental Section Chemicals Instrumentation RAFT agent synthesis Polymerizations Results and Discussion Conclusion Summary Samenvatting Acknowledgements Publications

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11 Chapter 1: General introduction Abstract In this chapter the objective of the PhD study is introduced. Theory, concepts, instruments and technologies for the analysis of branched polymers are presented. Also different ways to achieve branching in the polymer structure and the impact on the polymer properties are reviewed. 9

12 Chapter An introduction to polymers The ability to characterize polymers has been of critical importance for progress in the field of macromolecular chemistry. It allows one to understand how a material behaves, how it was made and how to make it better. Continuous development of polymers has resulted in materials that are highly optimized and in the rapid proliferation of polymers into everyday life of the 21 st century. Polymers with a very wide range of physical properties can now be produced, often at low cost. They cover an incredible application space that continues to expand. The traditional applications, such as simple molded items, fibers and disposable items, are still present today. More recent is the introduction of functionalized and smart materials. Modification of the polymers can be used to increase durability, conduct electricity or even provide self-healing properties. These specialty materials provide higher added value and are, therefore, of great interest for production in a commercial setting. An overview of common synthetic polymers and their applications is presented in Table 1. Table 1. Synthetic polymers and their application in traditional and functional materials Material Polystyrene Polyvinylchloride Polyethylene Polypropylene Polyester Polyamide Application example Coffee cups Envelope window film Insulation foam Piping Window lining Wire & cable insulation Bags Garbage containers Artificial ice-skating floors Fishing lines Joint replacement Automotive bumpers Heat-resistant food packaging Soda bottles (polyethylene terephthalate) Clothing / fibers Nylon stockings 10

13 Introduction Macromolecules A landmark in history has been the discovery of covalent bonding between smaller molecules (monomers) [1] to form polymers or macromolecules of high molar mass [2]. These concepts were introduced in the 1920 s by Hermann Staudinger, for which he was awarded the Nobel Prize in 1953 [3].The term polymerization was introduced already in 1863 by Berthelot, who recognized the ability of unsaturated compounds to react with themselves and yield high-boiling oligomers [4]. His work did not comprise the formation of higher polymers. The idea of higher polymers was opposed by the ruling misconception from crystallography that molecules had to fit in a single unit cell. It was not until the late 1920 s that the concept of higher polymers became accepted. Before this time the mechanism of polymerization was not well understood and was attributed to self-assembly of small molecules by colloidal interactions [5]. Poor understanding of molecular structure did not withhold Baekeland from producing the first fully synthetic polymer already in 1907 [6,7] Early characterization of polymers The difficulty in obtaining experimental proof for higher polymers was one of the reasons that it took a long time for macromolecules to become accepted. Many methods for determining the molar mass of macromolecules were published in the years following the introduction of the macromolecular concept [8]. This is not strange, considering that the interpretation of most measurement techniques depends on (assumptions about) the structure of the analyte. Colligative properties of polymers in dilute solution can be used to determine molar mass. The response of such properties corresponds to the mole fraction in solution as pointed by Johannes van t Hoff (Nobel Prize in Chemistry, 1901) and may be used to obtain number-averaged molar-mass (M n ) data. Membrane osmometry has historically been favored over other techniques, such as freezing-point-depression and vaporpressure measurements, because it is more practical to measure and offers better accuracy. End-group determination may also yield M n, provided that a selective detection of terminal groups is possible and the polymer molecules are known to be linear. Other techniques available for molar-mass determination are light scattering and 11

14 Chapter 1 ultracentrifugation [9]. Both techniques may be used to provide accurate ( absolute ) molar masses, as is the case for the colligative properties described before. Viscosity of polymer solutions has been recognized as a readily accessible and sensitive property for molar-mass determination by so-called viscometry. It is due to the expanded nature of the molecules in solution that viscosity is increased by most polymers. The empirical relation between intrinsic viscosity ([η]) and relative molar mass (M r ) was introduced by Staudinger [10] (Eq. 1). [η] = KM r a (1) This equation has become known as the Mark-Houwink relation after their efforts to improve the theory of this relation and their documentation of constants K and a for different polymer-solvent systems at given temperatures [11,12,13]. The simplicity of capillary viscometry for determining molar mass resulted in a high popularity of this method and documentation of Mark-Houwink constants for many polymer-solvent systems [14]. Viscometric methods are relative measurements, because the relation between molar mass and viscosity needs to be determined for each different polymer at each set of conditions (solvent and temperature). Relations between polymer melt viscosity and molar mass were also investigated. Determination of molar mass with much better precision was possible due to the higher viscosity of the pure polymer than of a polymer-containing solution, but the empirical relations were found only to hold for relatively low molar masses [15,16,17]. The macromolecular structure of polymers was supported by published work on the application of these techniques for polymers. Polymer science and related analytical capabilities expanded rapidly once the scientific community accepted the existence of macromolecules. Research into polymerization reactions and mechanisms thereof increased throughout the 1930 s. This revolutionized polymer synthesis and quickly resulted in the first commercial production of polystyrene, polyesters, polyvinylchloride, polyethylene and polyamides. Development of polymercharacterization techniques was driven by the need to support polymer production and studies into new synthesis routes and application fields. In 1953 Flory wrote Principles of polymer chemistry, an overview of both polymer chemistry, as well as 12

15 Introduction characterization methods for polymers, which is still considered an important reference work [8]. Flory s contributions to the theory of polymers in solution (Flory-Huggins solution theory and excluded volume) earned him the Nobel Prize in Chemistry in According to IUPAC the modern definition for macromolecule or polymer is: "A molecule of high relative molecular mass, the structure of which essentially comprises the multiple repetition of units derived, actually or conceptually, from molecules of low relative molecular mass [18]. Different types of polymer may be identified depending on their origin. Most common are synthetic polymers and natural- or biopolymers. Examples of natural polymers include proteins, starch, cellulose and DNA. The emphasis throughout the work presented in this thesis will be on synthetic polymers. Table 2. Different levels of polymer structure Micro- level (molecular) Meso-level (morphology) Macro-level (polymer properties) Polymer Relative molar mass (MMD) (Relative) Monomer content (CCD) Functionality (end groups) Branching / Topology Crystallinity Self-assembly Particle size distribution Mixing and compatibilization Orientation Density Glass transition temperature Melting point Optical properties Solubility Strength Viscosity (melt) Additives Structure and concentrations Spatial distribution Migration behavior Effects of additives, such as plasticizers, fillers, reinforcing agents, stabilizers, anti-static agents, colorants, on polymer properties Polymer structure The characteristics of polymeric materials are the results of many structural features (Table 2). It is for this reason that characterization is not straightforward and that understanding of the material properties requires information on more than a single structural feature. The basic structure of a polymer is determined by the chemistry of the repeat units and how they are linked together (micro-level). Structural features at the 13

16 Chapter 1 meso- and macro-level depend on the molecular features, but also on the processing conditions of the material. Polymers are heterogeneous materials and so the distribution of micro-structural features is important as well. A very important parameter is the number of repeat units in a chain, which is also known as the degree of polymerization. It has a large impact on polymer properties (macro-level) and is typically expressed as the relative molar mass (M r ). A molar-mass distribution (MMD) is invariably present in synthetic polymers due to the stochastic nature of polymerization reactions. This does result in molecules with different M r being formed even when reaction conditions are kept identical. A common metric for the MMD in polymers is the polydispersity index (Eq. 2), which is defined as the ratio of weight averaged to number-averaged molar mass (M w and M n respectively). PDI = M w M n (2) Optimization of polymerization conditions makes it possible to control M r and MMD and obtain polymers with targeted properties. Reversely, measuring M r and MMD may provide information on the polymerization conditions, in particular the termination reactions [19]. Details on various types of polymerization reactions can be found in textbooks on polymer chemistry [e.g. 8,20]. Chemistry is the broadest variable in polymer structure. Polymers with different monomer chemistries have vastly different properties and application areas. Copolymers can be created with monomers of different chemistry, which are appropriately referred to as co-monomers. The chemical-composition distribution (CCD) may deal with overall composition (inter-chain composition), as well as distribution within chains (intra-chain distribution). Examples include randomness and block-length distribution. Tacticity is an intra-molecular form of stereochemistry and may therefore also be considered part of the CCD. When the chemistry of individual repeat units has affects reactivity or structure this is classified as functionality. Typical examples are reactive end groups and pendant groups on the backbone. 14

17 Introduction Fig. 1. Schematic representation of various types of chain structures, including linear, long-chain-branched, short-chain-branched, cyclic, network, comb, brush, dendritic and star polymers Branched polymers Branching and topology are other important aspects of the polymer structure. Polymers with branching may be obtained through the addition of (multi-functional) comonomers, post-reaction processing or back-biting side-reactions taking place during polymerization [21]. There are many variations possible to the linear structure, resulting in branched polymers with many different forms (Fig. 1). The most common applications of branched polymers take advantage of the melt rheology and solid-state material properties that are unique for these materials. These macro-level effects can be explained by the characteristics at the meso- and micro-structural level. Especially the level of (inter-molecular) chain entanglement and crystallinity are affected by branching properties, which affects material properties related to stretching, deformation or flow of the polymer. Changes on the molecular level as a result of branching include a higher number of end groups, shorter back-bone length and a more compact structure relative to linear polymers. Branched polymer with chemically different or modified end groups can be used as highly effective functional materials. The compact molecular structure of branched molecules gives rise to the melt and material properties corresponding to a 15

18 Chapter 1 combination of shorter chain length but higher molar mass. It is also an important handle in the characterization of branched polymers using dilute-solution techniques, which will be explained later. The main classes of branched polymers are presented in Table 3. Table 3. Different types of branched polymers and the properties Type Effects and applications Chemical pathways Examples Long-chain branching Melt rheology modification Increased toughness Back-biting in ethylene and acrylate polymerization Co-polymerization LDPE, polypropylene, polycarbonate [23], polystyrene, nylon, PMMA [24] Light Cross-linking [22] Short-chain branching Reduction in crystallinity Improved material properties Back-biting in ethylene polymerization Co-polymerization Polyolefins, LLDPE Star Model component in rheology research Multi-functional macromonomers Functional materials Core-first Multi-functional initiator Thermo-responsive polymer [25] Low-viscosity inkjet ink [26] Light-switchable coatings [27] Combs/brush Model component in rheology research Functional materials Macro-monomer polymerization [28] Polyelectrolites [29] Biomimetic materials [30] Dendrimers / Hyperbranched polymers Multi-functional macromonomers Functional materials [31] Drug delivery [32] OLEDs [33] Short-chain branching (SCB) is a property that is almost exclusively associated with polyolefins. This is because in other polymers the functionality of pendant groups is different from the backbone and it is reflected in the CCD. Unlike other forms of branching, the impact of short-chain branches on polymer properties is mainly a result of interference with crystallinity at the microscopic level (meso scale). The most common application of SCB is in the modification of linear high-density polyethylene. With Ziegler-Natta catalysts linear low-density polyethylene may be produced by copolymerization of ethylene with alpha-olefins, ranging from propylene to 1-hexadecene, 16

19 Introduction to introduce SCB. With contemporary single-site and metallocene catalysts it is possible to precisely control the degree and distribution of SCB in LLDPE polymers and, thus, to produce materials with highly optimized properties. An increase in SCB density results in lower crystallinity and lower density of the material. These are important characteristics of linear low-density polyethylene, where linear in the name refers merely to the absence of long-chain branching (LCB). It is generally accepted that very short branching introduces rubber-like behavior (e.g. ethylene-propylene rubbers), whereas longer chains as obtained by copolymerizing 1-hexene or 1-octene provides elasticity and other properties beneficial for LLDPE films [34]. Low-density polyethylene (LDPE) is produced by free-radical polymerization at high pressure and contains both SCB and LCB as a result of back-biting. This is a side-reaction where in a propagation step the free radical at a terminal methylene group is transferred to a methylene group somewhere in the chain by hydrogen abstraction. Branches of random length and at random position are created in this way. LDPE combines the distinct advantages of LCB polymers with a lower density than linear high-density polyethylene (HDPE). Advantages of LCB polymers are higher zero-shear viscosity, improved melt strength, reduced melt fracture, reduced melt viscosity at high shear rates (i.e. shear thinning) and extensional thickening. Polymers with LCB have superior processing properties and they can be used for demanding applications such as blow molding, blown-film formation and closed-cell foam production. Long-chain branching has an effect on viscosity through entanglement of the polymer molecules. Above the critical molecular weight M c, which marks the onset of chain entanglement, the melt viscosity of polymers increases no longer linearly with mass but with M 3.4 r [35,36]. The average length of the chain segments between entanglements M e can be determined using experimental techniques [37,38]. An overview of M e values for many polymers has been established based on rheology and small-angle neutron scattering (SANS) measurements on linear and short-chain-branched model compounds [39]. For amorphous polymers the critical molecular weight M c 2 M e. The chemical composition of the polymer backbone has a large effect on the onset of entanglement. Therefore, the effects of LCB may differ for polymers with different chemistries through the effect on M e. Branches in LCB-polymers should be longer than M e to affect 17

20 Chapter 1 the rheology of the material. In practice long-chain branches will have a significant chain length relative to the backbone of the polymer. Polyolefins with LCB are created using free-radical polymerization, but may also be obtained in metallocene catalyzed polymerization. Using constraint geometry catalysts (CGC) it is possible to produce and incorporate chains with vinyl terminal groups into the final polymer [40,41,42]. The typical branching frequency for CGC and other metallocene polyethylenes is less than 1 long chain branch per polymer [43], while in LDPE between 3 and 7 long chain branches are common. LCB in CGC polyethylene will be longer ( carbon atoms) than LCB in LDPE, which has branches with carbon atoms in the backbone [44,45,46,47,48]. Other pathways for the introduction of LCB are the use of multi-functional co-monomers [24] or multi-functional initiators. Cross-linking after reaction can also be used to introduce LCB, for instance by addition of peroxides or irradiation. Treatment of HDPE and LLDPE with gamma-irradiation has been performed to induce LCB successfully [22]. A too high degree of cross-linking will result in network or gel formation, which will compromise the melt behavior of the material. LCB is introduced in most commercially produced polymers by chemistry that adds branches at random locations on the backbone. The polymerization processes for polymers with controlled and regular LCB (star, comb and brush polymers) are usually not cost effective for the production of commodity plastics, because of the need for high-purity monomers or expensive reactants. These materials are typically produced using multi-step reactions, in which macro-monomers or multi-functional cores are coupled using anionic polymerization or controlled polymerization reactions, such as atom-transfer radical-polymerization (ATRP) [49], nitroxide mediated polymerization (NMP) [50] or reversible addition-fragmentation chain-transfer polymerization (RAFT) [51]. Only the use for specialty applications or functional materials justifies the cost involved in producing these materials (Table 3). The ability to create polymers with well-defined branching topologies and branch lengths is important for studies into the rheological behavior of polymers [37,38,52]. In this way the effect of increased branching frequency and branch length on various rheological and material properties can be determined. Results from this type of research are used to design new materials with optimized properties. 18

21 Introduction In dendrimers and hyperbranched polymers the branching functionality is included in the main polymerization process, rather than a variation to linear polymerization. Most often such polymers are produced using condensation polymerizations. The emphasis is on chemical functionality of the material and most dendrimers are used as functional materials [31]. 1.2 Characterization and separation of branched polymers Nowadays several techniques are available for the characterization of branched polymers. The effectiveness generally depends on the type of branching, as well as the impact on the measurement by other structural properties of the polymer and the distribution thereof. In certain cases it is therefore desirable or even necessary to add a separation step before measurements are performed on the polymer TREF, Crystaf and DSC Measurements on crystallization behavior and rheological properties of polymers are common in quality control, production and application-related testing. These tests are highly sensitive towards the impact of branching on the macro level properties. The impact of branching on crystallinity and melt-behavior was described in the section on polymer structure above. Techniques that are often applied are differential scanning calorimetry (DSC), temperature-rising elution fractionation (TREF) and crystallization analysis fractionation (Crystaf). In TREF the polymer is first loaded on a stationary phase and subsequently eluted as temperature is increased [53]. The loading step is performed by having the polymer crystallize slowly out of solution. The polymer eluting from the stationary phase upon temperature increase may either be fractionated or subject to concentration detection for characterization of the redissolution behavior. TREF was developed in the early 1980 s and has been widely applied to characterize the short-chain-branching distribution (SCBD) and tacticity, but it may also be used to fractionate by chemical composition for certain polyolefins. In more recent applications the analysis of TREF fractions by, for instance, size-exclusion chromatography (SEC) has been automated [54]. Crystaf was developed in the 1990 s and is used to monitor the crystallization of polymer in solution when the temperature is decreased [55]. Crystaf is preferred over TREF, because the analysis can generally be performed at higher cooling rates, provided the desired information on polymer composition can still 19

22 Chapter 1 be obtained. The suitability of either technique depends on specific crystallization behavior. It is known that the crystallization and dissolution delays for ethylene and propylene polymers are different, which implies that the separation of polyethylene and polypropylene is only possible with TREF. Another complication is the supercooling of crystallizable materials in solution when the solution is cooled down faster than nucleation in solution occurs [56,57]. Crystallization steps should be performed at sufficiently slow so as to prevent co-crystallization. These effects have been illustrated in a comparison between TREF, Crystaf and DSC for the analysis of LLDPE and blends with polypropylene [58]. Results for Crystaf analysis of an LDPE and an LLDPE resin are compared in Fig. 2 [59]. Crystaf and TREF results are typically presented in the same way with differential polymer concentrations in solution on the y-axis and temperature on the x-axis. For Crystaf analysis the results have been measured starting at 95 C down to 30 C in 1,2,4- trichlorobenzene (TCB). For LLDPE a typical bi-modal distribution is observed. The mode near 80 C corresponds to crystalline polyethylene segments in the polymer, whereas the broad mode below 75 C represents the amorphous material. Only one single mode is observed for LDPE in the amorphous region as a result of both SCB and LCB. Crystallization behavior is influenced not only by the amount of co-monomer (i.e. degree of branching), but also by the distribution and block-length of segments with different crystalline properties. Therefore, crystallization techniques are the method of choice for characterizing modern LLDPE polymers. These may be prepared using multiple metallocene catalysts or in a multi-stage reactions, resulting in complex distribution of SCB. Crystaf and related techniques are the first choice for monitoring catalyst efficiency in production processes or for investigating unexpected changes in polymer performance Rheology Measurements of viscosity and the behavior of polymer melts are among the most sensitive methods known for characterizing LCB in polymers. Rheological experiments allow for direct characterization of macro-level properties. Different types of measurements are performed, depending on the shear-rate regime of interest [60]. 20

23 Introduction Fig. 2. CRYSTAF results for typical LDPE (1) and LLDPE (2) materials [59] Dynamic-mechanical analysis (DMA) can be performed to obtain detailed information on stress-strain relations typically in the range between 0.1 and 100 s -1 using rotational viscometers. Zero-shear viscosity is obtained from the viscosity value at an arbitrary low shear value, typically 0.1 s -1. Elastic properties (e.g. shear storage- and loss modulus) and dampening (tan δ) may be investigated by oscillatory viscometry in frequency-sweep experiments. All these parameters have been compared against structural properties for polyethylene and were found to be affected by SCB and LCB in distinct ways [37,61]. Measurements with an extensional rheometer are used to test for strain-hardening behavior, and uniaxial and biaxial elongation [62]. Branching often improves strain-hardening and biaxial-elongational properties of polymers. Therefore, extensional rheology can be used for quality control of LLDPE and other branched polymers. DMA at shear rates < 0.1 s -1 is rarely used for purposes other than studies on creep behavior of polymers. Capillary viscometers are used for measurement at shear rates > 100 s -1. Applications include the measurement of polymer melt-flow-rate (MFR, also referred to as melt flow index in case of polyethylenes) and determination of intrinsic viscosity of polymers in dilute solution. Solution measurements using capillary viscometry will be described in more detail later (see section Size-exclusion chromatography with selective detection). 21

24 Chapter 1 Fig. 3. Trends in shear-dependence of melt viscosity for polyethylene polymers with different degrees of branching by DMA [45] The effect of long-chain branching on viscosity is demonstrated in a comparison of rheology curves for polyethylenes with different LCB frequency (Fig. 3) [45]. These materials were prepared using a constrained-geometry catalyst, which is a metallocenetype catalyst that allows for accurate control of LCB in the polymer [61,63]. An increased zero-shear viscosity and a shear-thinning effect at high shear rate are observed for polymers with higher branching frequencies. A metric that is used to express shearrate sensitivity is the ratio of melt-flow indices obtained with two different loads. The measurement of melt-flow indices is performed at standardized conditions (ASTM D- 1238), where the melt flow through a capillary is measured with either 2.18 or 10 kg of load on the piston driving the polymer. For polyethylene this measurement is typically performed at 190 C. Investigation of LCB using rheology curves is complicated, because the viscosity and the shear-rate dependence thereof are also influenced by other properties of the polymer. Comparing polymers with different MMDs is difficult. An increase in the molar mass will result in a higher viscosity, irrespective of the shear rate. Changes in the polydispersity will affect shear-rate-dependent viscosity, with an increase in PDI resulting in changes comparable to those observed for polymers with increased LCB frequency. The presence of additives (Table 2) will also affect rheology curves. It is known that additives can have an unexpected impact on rheology that interferes with the 22

25 Introduction measurement. Rheological measurements, therefore, are most useful when performed on pure polymers with comparable characteristics. Access to a number of comparable pure reference materials with known architecture is highly desirable for interpretation of the results in terms of relative differences. Comparison of molar-mass data and zero-shear viscosity for such a set of data provides very sensitive detection of LCB in the polymer [43] Spectroscopy Information obtained from spectroscopic techniques can be used to elucidate the microlevel structure of polymers. Infrared detection is traditionally used for monitoring the chemical composition and it can be used to discriminate between repeat units and branch points. It was used already in 1940 by Fox and Martin to prove branching in polyethylene polymers [64]. The only common application for branching-selective detection with IR today, however, is for the determination of SCB in polyolefins by selective detection of C-H bonds on secondary and primary carbon atoms [65]. Shortchain-branching frequency is reported as the number of methyl groups per 1000 carbon atoms. Most often information on the SCB distribution of a polymer rather than an average SCB frequency is desired. Such information can be obtained by infrared analysis of the fractionated polymer or by using a hyphenated technique, such as SEC- FTIR. Deslauriers et al. demonstrated SEC-FTIR with a precision of ±0.5 Methyl/1000C under optimized conditions for ethylene 1-olefin copolymers with ethyl and butyl branches [65]. Partial least squares regression was used to build a calibration between a selected spectral region and reference data on SCB frequency. Precision of FTIR detection depends on the training set used to build a model. Either levels of ethyl en butyl branches beyond that of the training set or inclusion of different functionality will reduce the accuracy of the model. On-line coupling with chromatographic techniques reduces the sensitivity of FTIR, because of the dilute solutions inherent to most forms of chromatography [66,67]. An alternative to dilute-solution detection in flow cells is available in the form of on-line polymer deposition on a germanium disk using an LC-transform interface [68]. Polymer composition may be detected more sensitively in this way without interference by the solvent, but the precision and accuracy of the method leave to be desired [69]. 23

26 Chapter 1 Both SCB and LCB may be studied by NMR spectroscopy. In case of 13 C NMR quantitative results well below 1 in 10 4 carbon atoms have been reported for polyolefins with good precision using modern techniques [61]. It is possible to distinguish between branches of different length up to hexyl side-groups and report their frequency independently [48,70]. Branching frequency may be reported per molecule or an arbitrary number of carbon atoms, provided molar-mass information is available. Most quantitative results have been obtained by measurement of polymer solutions, but melt analysis by magic-angle spinning NMR has also been reported [66]. Unfortunately, measurement of the backbone atoms near or at low-abundance branch points requires very long measurement times in 13 C NMR. Fractionation and even on-line coupling with HPLC or SEC is possible, but this is only practical for 1 H NMR for reasons of sensitivity and speed [71]. LC-NMR is used more often for screening of chemical composition [72] than for characterizing LCB. Mass-spectrometric characterization of branched polymers is limited to a specific number of applications, despite its proliferation for polymer characterization in general [73]. Soft ionization techniques, such as matrix-assisted laser/desorption ionization (MALDI) and electrospray ionization (ESI), in combination with high-resolution mass spectrometry (e.g. time-of-flight mass spectrometry, ToF-MS) are most useful for the analysis of dendrimers [74]. These techniques are not applicable for polyolefins and traditional random LCB polymers, because their molar mass is too high and branching does not induce distinct mass differences of fragments. Mass spectrometry can be applied successfully for branched polymers with moderate molecular weight and sufficient ionizability. Products of condensation polymerization, including dendrimers and hyperbranched polymers, are often amenable for characterization using mass spectrometry [75,76]. Most mass-spectrometry applications for polymers deal with the analysis of chemical-composition distributions, which includes the use of multifunctional initiators and repeat units ultimately resulting in branched polymers. Hyphenation of various types of liquid chromatography with ESI-ToF-MS provides a strong combination for these polymers [77]. 24

27 Introduction 1.3 Size-exclusion chromatography with selective detection Separations are important in many techniques for the characterization of polymer microstructure and are essential when studying the distribution in polymer properties. Size-exclusion chromatography (SEC) is one of the most-common techniques in the characterization of polymers. Since its introduction the 1960 s [78,79] SEC has been used for the characterization of molar mass and MMD of polymers. In combination with selective-detection techniques, such as on-line laser-light scattering and viscometry, the degree of branching may be studied as a function of molar mass. The sensitivity of these techniques is highest for LCB polymers, but other types of branching may be investigated as well. A general requirement is that the polymers under consideration are well dissolved and do not significantly differ from random-coil behavior in solution. Different configurations of SEC with selective detection may be applied to obtain comparable information of branched polymers. Preference for any separation or detector configuration depends on specific strengths and tolerances. Separation and different forms of detection are presented in the following sections to introduce the considerations for common configurations of SEC with selective detection SEC separation of branched polymers Separation in SEC is achieved through size-selective migration of polymers in dilute solution through a column packed with porous particles [80]. The separation is entropic in nature and interactions between the polymer and the column packing should be negligible. Large polymer molecules are selectively excluded from pore space in the SEC column. Their reduced access to the stagnant mobile phase in the pores results in elution before materials that can enter the pore volume driven by random diffusion. The relevant size parameter is that of the free molecule in solution and is referred to as the hydrodynamic size or volume of the polymer [81]. Separation in SEC is an indirect result of molar mass and branching through their impact on hydrodynamic size. It is therefore important to understand how experimental and molecular properties affect the relation between size and mass. The theory for solution behavior of flexible-chain linear polymers has been described in detail by Flory and Casassa [8, 82]. They found that random-coil statistics could be used to describe the relation between molar mass and coil dimensions in solution (simply referred to as 25

28 Chapter 1 polymer size from here on) for ideal polymers. Application of random-coil statistics can be used to describe many other structure-property relations of real polymers appropriately using scaling laws [83]. The relation between polymer size r and molar mass may be described using the general scaling law shown as Eq. 3, with empirical constants a and b correcting for polymer-solvent specific behavior (with b = 0.5 for a random coil). r = a M b (3) Scaling laws can be used, for instance, to describe mass dependency of intrinsic viscosity using the Mark-Houwink relation (Eq. 1) over a molar-mass range of several orders in magnitude [84]. Branching in polymers will interfere with the scaling behavior between hydrodynamic size r h and molar mass M (Fig. 4) [85,86]. Identical M different topology Identical r h different topology Fig. 4. Schematic representation of polymer structure in solution An increasing level of (long-chain) branching will result in a reduced freedom of the chain and therefore a smaller size in solution. Another effect is the increase in segment density, which generally results in a lower intrinsic viscosity. The differences in scaling behavior between linear and branched polymers i.e. different relation between molar mass and polymer size, may result in co-elution of polymers with different molar mass when linear and branched molecules are present. Branched polymers will generally elute from the SEC column together with linear polymers with lower molar mass (but identical hydrodynamic size) due to their more compact coil structure. Local polydispersity in SEC [87,88,89] as a result of branching has been studied by several experts. Its presence was proven experimentally by careful consideration of the results from on-line detection techniques that provide either number- or weight-average molar mass at each elution increment. The calculation of local polydispersity is typically not 26

29 Introduction included in the workflow of multi-detector SEC techniques and only possible with the additional effort of setting up a universal calibration. This highlights one of the fundamental limitations of multi-detector SEC and supports the need for better separation techniques that can resolve linear and branched materials SEC with on-line (micro-)viscometry Capillary viscometry has been used for calculation of molar mass since the early discovery of the Mark-Houwink relation for polymers. Before the advent of on-line detectors in the 1980 s, Mark-Houwink relations had to be established by measurement of solution viscosity using, for instance, Ubbelohde viscometers. With the introduction of differential viscometry it became possible to hyphenate viscometers with separation techniques [80]. Viscometers based on the Wheatstone-bridge design have been commercialized and have become widely available for viscosity measurement in SEC [90]. Most commercial detectors use a Wheatstone bridge constructed made with four steel capillaries with matched restriction. For the work presented in the rest of this section a novel micro-sized viscometer has been used. This detector was made available by Polymer Laboratories and Micronit in an effort to address the challenges experienced with traditional commercial viscometers [91]. The Wheatstone bridge of this detector has a total volume of only 8 µl and has been created on a glass chip, which allows for tight engineering specifications and a perfectly balanced bridge. At a flow rate of 100 µl/min the viscometer operates at a shear rate of 3000 s -1, which is the standard for commercial capillary viscometers. With the reduced detector bridge volume this detector can match cell volumes encountered in contemporary light scattering and concentration detectors. A complete set of miniaturized detectors allows also for miniaturized separations. Therefore, SEC columns with dimensions of 4.6 mm ID 250 mm were used. With differential viscometry the specific viscosity can be measured on-line. In combination with on-line concentration detection it will allow calculation of intrinsic viscosity at each elution volume (Fig. 5). For polymers with known Mark-Houwink constants the molar mass can also be calculated at each elution volume. This approach is not practical for the analysis of branched polymers, because the Mark-Houwink parameters change with branching properties and frequency. However, other approaches 27

30 Chapter 1 that do not require Mark-Houwink parameters may be used to characterize branched polymers using SEC with viscometry. Fig. 5. Instrument configuration for SEC with on-line viscometry as used for universal calibration Universal calibration Regular molar-mass calibrations, prepared using narrow standards, have limited applicability. Corrections for other polymer systems can only be made when Mark- Houwink constants are known for both calibrant and analyte. A universal calibration method was introduced by Grubistic [92]. Knowledge on Mark-Houwink parameters of the analyte is no longer required for molar-mass calculation when an on-line viscometer is used. Intrinsic viscosity may be used to calculate molar mass directly when a column calibration is available in terms of hydrodynamic volume (V h ). This is possible because of the direct proportionality between V h and the product of intrinsic viscosity [η] and molar mass (M) (Eq. 4). V h [η]m (4) Validity of the universal calibration for polymers of different architecture and composition has been demonstration by the good correlation for all polymers in a plot of [η]m against elution volume [84,92]. Accuracy of the results obtained by universal calibration is challenged by the sensitivity of this calibration principle to experimental imperfections. For samples with narrow MMD the incomplete separation is incorrectly interpreted, resulting in a higher PDI and anomalies in Mark-Houwink plots. Better results are obtained using the concentration and viscometer signals from the setup in Fig. 6. For samples with broad MMD acceptable results could be obtained. Also these results were extremely sensitive to changes in absolute retention time (correction using flow-marker possible) and inter-detector delay volume. Changes in the room 28

31 Introduction temperature suffice to compromise the accuracy of universal calibration for systems that are not fully thermostatted, such as the setup used in this study. Good results with acceptable accuracy may be obtained using universal calibration performed under wellcontrolled conditions. Fig. 6. Instrument configuration for triple-detection SEC Triple detection SEC With on-line light-scattering detection the molar mass of polymers can be measured directly. For polymers in dilute solution the weight-average molar mass may be calculated from the intensity of the scattered light using the Rayleigh-Gans-Debye approximation [80,86]. A practical complication is the angular dependence of scattering as a result of destructive interference of scattered light from molecules in solution larger than roughly 1/20 times the wavelength of the light. The applicable size is the rootmean-square radius of the polymer, also referred to as radius of gyration (r g ). A correction is generally applied to obtain corrected values for M and r g through iterative calculations [93]. In triple-detection SEC both a light scattering and viscometer are added to the detector array. In the original configuration of triple detection SEC a right-angle laser-lightscattering detector is used [93]. With measurement of light scattering at 90 the traditional problems with signal noise at low angles are avoided, but a correction for angular dependence is required. This is achieved using an estimate of r g calculated using the viscometer data, estimated M and the Flory-Fox equation. The detector 29

32 Chapter 1 configuration allows for calculation of both M and [η] at every elution volume without the need for column calibration. This prevents issues and limitations inherent to the universal calibration with respect to absolute elution-volume differences. The sensitivity to errors in inter-detector delay or band broadening remains. In Fig. 7 the effect of interdetector band broadening in a non-optimized setup is demonstrated for the analysis of six-arm star polystyrenes with narrow MMD [94]. Broadening in the detector signals for the RALLS and viscochip was caused by splitting of the flow towards the differential refractive index (dri) detector before the RALLS detector (in contrast to the configuration in Fig. 6). This resulted in an unrealistic increase in both M and [η] at higher elution volumes. The RALLS signal was found to be broadened by 2 seconds for a narrow-standard peak with a width at half height of 36 seconds on the dri signal. With the appropriate detector configuration as displayed in Fig. 6 good results have been obtained without artifacts resulting from inter-detector band broadening. Z-RAFT six-arm star polystyrenes were analyzed using triple-detection SEC with UV absorption for concentration detection (Fig. 8 and Fig. 9). The extent of inter-detector band broadening was minimal due to the small UV detector-cell volume of only 2.5 µl. Most of the polystyrene polymers were found to have an extremely narrow MMD (i.e. PDI < 1.1), with the exception of polymerization products obtained at very high levels of conversion. Absolute molar-mass results obtained using triple detection were used for confirmation in studies into the molar-mass offset in conventionally calibrated SEC by polymers with known branching topology [94,95]. The results of this work are treated in more detail in Chapter 5. The traditional strength of triple-detection SEC lies in the possibility of absolute molarmass detection for polymers with relatively low molar mass. A RALLS detector is simpler by design (less expensive) and can be built with a smaller detector-cell volume relative to the more complex forms of light-scattering detection. In modern applications the uncertainties introduced by angular correction and estimation of r g using the Flory- Fox equation may be alleviated by using a dual-angle detector. Above an arbitrary mass or estimate of r g the low-angle signal is used, which is much less sensitive to angular dependence. 30

33 Introduction Fig. 7. Mark-Houwink plot; example of triple-detector data subject to inter-detector band broadening. (a) linear PS1683, (b) 6-arm star polystyrene polymers with different molar mass but uniform arm length Fig. 8. Chromatograms of narrow-mmd six-arm star polymers and a broad-mmd reference; (a) linear PS1683, (b) 6-arm star PS polymers, (c) 6-arm star PS polymer obtained at high monomer conversion Fig. 9. Mark-Houwink plot for narrow-mmd six-arm star polymers and a broad-mmd reference 31

34 Chapter SEC with multi-angle laser-light-scattering detection The different relation between molar-mass and intrinsic viscosity of branched polymers is clearly observable in the Mark-Houwink plot. Six-arm star polymers have higher molar mass and lower intrinsic viscosity than linear polystyrene with an identical hydrodynamic size. The difference in solution properties of branched polymers relative to those of linear polymers can be detected using SEC with selective detectors. Multiangle laser-light scattering (MALLS) is another selective detector that was not introduced yet, but is commonly used in the characterization of branched polymers. Due to the added information of scattering at multiple angles relative to the incident light the angular dependence may be solved to obtain r g directly at every elution volume, provided that the particle is large enough to yield appreciable angular dependence. Calculation of r g does not require any other detector signal and is therefore not affected by the experimental imperfections of multi-detector arrays, such as inter-detector volumes and inter-detector band-broadening. Relative differences in solution behavior of polymers are often expressed as contraction ratios based on either MALLS detection (Eq. 5) or viscometry (Eq. 6). The subscripts B and L indicate data for branched and linear reference polymer respectively, comparing data of identical molar mass as indicated as the subscript M. g = r 2 g B 2 r g L M (5) g = [η] B [η] L M (6) Differences in r g and [η] between linear and branched polymers may be small and hard to observe in log-plots in comparison with plots of contraction ratio vs. molar mass. Theoretical models for long-chain-branching frequency based on the relative changes compared to linear polymers were derived for random-coil polymers even before SEC with on-line detection became available [96]. Nowadays contraction ratios have been tabulated for many branched polymers under different solvent conditions [86]. Plots of contraction factors, r g or [η] as a function of molar mass provide important information on the branching distribution and are often indicative of the polymerization mechanism 32

35 Introduction related to the inclusion of branching. The relation between the parameters g and g has been of great interest, because the models for branching frequency are based on g. The relation between both parameters is not straightforward and varies within polymers as a function of molar mass. SEC-MALLS and triple-detection SEC with a MALLS detector may be used to investigate this relation on-line [97,98] Application and challenges of existing methodology Measurement of differences in r g and intrinsic viscosity with SEC in combination with selective detection techniques is particularly useful for polymers with a low degree of long-chain branching. Branched polystyrenes that have been used throughout this thesis were analysed using triple-detection SEC (Fig. 10 and Fig. 11) and SEC-MALLS-dRI (Fig. 12). Both techniques demonstrate good signal quality for high-molar-mass polymers, because of the high light-scattering intensity. Contraction is observed in r g and intrinsic viscosity measurements of the branched materials and increases towards increasing molar mass, which indicates an increase in long-chain branching. At the low molar-mass end the data quality is not so good, in particular for the MALLS data. Data for the low-lcb polymer is of similar quality as the linear reference and the scatter in r g is caused by the small angular dependence of the light scattered by the smaller molecules. Anomalous results are observed for the polystyrene with high LCB. The material that is eluting later from the SEC columns is responsible for the upward curvature in the conformation plot (Fig. 12). A change of the curve for LCBps in the Mark-Houwink plot towards higher molar mass is observed at the low-mass end, which is indicative of SCB in case of a good SEC separation [99].This phenomenon is known as anomalous late elution or late elution in SEC and occurs specifically for branched materials. Detailed investigation of the experimental parameters in the SEC separation and comparison with field-flow fractionation (FFF) was performed for polystyrenes and acrylates [100] as well as for LDPE [101]. It was concluded that the high molar-mass tail of branched polymers is retained in the SEC column and slowly elutes together with the molecules of low molar mass. 33

36 Chapter 1 Fig. 10. Chromatograms of broad-mmd linear and branched polystyrene samples. (a) linear PS1683, (b) low-lcb PS , (c) LCB PS PA / PSbranch Fig. 11. Mark-Houwink plot for broad-mmd linear and branched polystyrene samples Fig. 12. Conformation plot of linear and branched polystyrene samples 34

37 Introduction The separation of this high-lcb polystyrene was performed using FFF, which separates also the large molecules in solution very well [102] (Fig. 13). In the same figure an overlay is provided of the SEC and asymmetrical flow field-flow fractionation (AF4) results. It is clear that the material on the high molar-mass end is not separated by SEC. As a result of the incomplete separation in SEC the eluent fractions will be polydisperse. Overestimation of r g is promoted by the higher sensitivity of the MALLS for larger polymers, as the calculated value over the average population is a z-average. Polymers with very-high molar mass fractions that are not well separated using SEC are preferably separated using FFF or another technique that does not suffer from problems with late-elution of branched or high-molar-mass materials. Separation techniques that do include light scattering will provide the end user with data that makes it possible to recognize problems with late elution, whereas in universal calibration this is not observed unless significant material is observed to elute after the column void volume using the concentration detector. In practice the amount of late-eluting material is very small and it is unlikely that this is detected using a concentration detector. A broader overview of complications in SEC with on-line light scattering and viscometry has been provided by Mourey [103] Rg (nm) E E E E E E+09 Molar Mass (g/mol) LCBps SEC PS1683 AF4 LCBps AF4 Fig. 13. SEC-MALS and AF4-MALS of the same highly branched polystyrene 35

38 Chapter Scope of the thesis The aim of this work is to explore new technology for the characterization of branched polymers, not limited by the traditional boundaries of common applied analytical techniques. Initial results on molecular topology fractionation [104] served as an inspiration to explore this separation further. The mechanism behind this fractionation was still open for multiple explanations, because separation conditions could often not be defined or studied systematically. Monolithic columns were prepared specifically to address this issue. Columns for MTF were applied in a two-dimensional separation with a size-based separation to study and optimize a true separation by topological properties of the polymer. Chapter 2 deals with the preparation of monolithic columns and their optimization for polymer separations. Monolithic stationary phases have received much attention as an alternative for packed beds for interaction chromatography. The highly interconnected network of channels in polymeric monoliths provides an excellent environment for hydrodynamic separations. Monoliths with different macropore sizes were prepared and the materials were studied in an effort to understand the porous structure. It was concluded that hydrodynamic chromatography was the prevailing separation mechanism based on the confirmation of a unimodal pore-size distribution and a continuous flowthrough nature of the pores. Chapter 3 details the application of multi-dimensional separations with selectivity based on topology. The idea to separate a polymer based on its hydrodynamic size and topology in a comprehensive two-dimensional separation is demonstrated for the first time. A star polymer was used for the branching-selective separation. This serves as a model compound for LCB polymers. In Chapter 4 the application of MTF is considered in more detail and the mechanism of separation is discussed. A systematic study on the selectivity is conducted using columns with different channel sizes. Knowledge obtained in Chapter 2 on the pore structure and separation characteristics of the columns was taken into account. Columns used in this study provided better efficiency compared to previously used MTF columns, which were short in length and were packed with polydisperse silica. The 36

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43 Chapter 2: Hydrodynamic chromatography of macromolecules using polymer monolithic columns Abstract The selectivity window of size-based separations of macromolecules was tailored by tuning the macropore size of polymer monolithic columns. Monolithic materials with pore sizes ranging between 75 nm and 1.2 μm were prepared in-situ in large I.D. columns. The dominant separation mechanism was hydrodynamic chromatography in the flow-through pores. The calibration curves for synthetic polymers matched with the elution behavior by HDC separations in packed columns with analyte-to-pore aspect ratios (λ) up to 0.2. For large-macropore monoliths, a deviation in retention behavior was observed for small polystyrene polymers (M r < 20 kda), which may be explained by a combined HDC-SEC mechanism for λ < The availability of monoliths with very narrow pore sizes allowed investigation of separations at high λ values. For highmolecular weight polymers (M r > 300,000 Da) confined in narrow channels, the separation strongly depended on flow rate. Flow-rate dependent elution behavior was evaluated by calculation of Deborah numbers and confirmed to be outside the scope of classic shear deformation or slalom chromatography. Shear-induced forces acting on the periphery of coiled polymers in solution may be responsible for flow-rate dependent elution. 41

44 Chapter Introduction Liquid chromatography (LC) is an invaluable analytical separation technique for the characterization of synthetic polymers and bio-macromolecules. Large molecules with relative molecular weights up to several millions can be separated, provided that they are well dissolved in the mobile phase [1,2]. Size-exclusion chromatography (SEC), hydrodynamic chromatography (HDC) and flow field-flow fractionation (F 4 ) are often used in the analysis of macromolecules. The separation conditions are typically mild (moderate temperatures and shear stress), leaving the molecules intact for further characterization (e.g. light scattering, viscometry, spectroscopy), separation, or collection of fractions. Each of these techniques separates the analytes by size in solution and enthalpic interactions between analytes and stationary surfaces must be negligible. When this is the case, the physical properties of the stationary phase, rather than the surface chemistry, are of paramount importance in creating a suitable hydrodynamic environment for separation. As opposed to SEC, HDC separations are based on partitioning within the transient mobile phase [3,4,5]. The separation is a result of partitioning induced by surfaceexclusion in flow-through pores and hydrodynamic forces on the polymer in laminar flow. Small analyte molecules can sample the low-velocity flow regions near the stationary-phase surface that cannot be sampled by larger analytes. The latter are excluded from the channel surface, because of both steric and hydrodynamic effects. An overview of conditions and requirements of separations techniques for macromolecule characterization is provided in Table 1. Hydrodynamic separations are ideally performed in very narrow open (tubular) channels, because of their well-described geometry, which allows rigorous theoretical description and calibration [6], and the absence of eddy diffusion. The selectivity in HDC depends on the aspect-ratio (λ = r / R) that relates the size of the analyte molecule (radius r) to the size of the flow-through channel (radius R). For solutes moving through open-tubular channels with laminar (Poiseuille) flow (i.e. a parabolic flow profile), the migration rate can generally be expressed as the residence time of an analyte polymer or particle (t p ) relative to the migration time of a small-molecule marker (t m ) as defined in Eq. 1 where τ is the relative retention (with τ = 1 for a flow marker). In the basic form with C = 1 Eq.1 42

45 Hydrodynamic chromatography of macromolecules using polymer monolithic columns describes solute migration based on surface exclusion only. This is the dominant effect for low values of λ. C is a variable used for including hydrodynamic effects. Its value varies between 1 and 5.3 depending on solute type and model assumptions [7]. τ = t p t m = 1 1+2λ Cλ 2 (1) Table 1. Description and boundary conditions for selected size-based macromolecule separations. SEC HDC MTF Principal requirements Stagnant pore volume. Transient mobile phase + inhomogeneous flow profile (e.g. Poiseuille flow). Obstructed flow for analyte molecules. Critical dimensions Stagnant-pore size related to size of analyte molecules in solution. Channel diameter 5 to 50 times the diameter of analyte molecules in solution. Channel diameter less than 2.5 times the diameter of analyte molecules in solution < λ < 0.2 λ > 0.4 Implementation Porous particles; monoliths with bimodal pore-size distributions. Open-tubular columns ( 2 µm inner diameter); packed columns (nonporous particles; 2 µm particle diameter), monoliths 1 µm channel diameter). Columns packed with sub-micron (non-porous) particles; monoliths (ca. 0.1 µm channel diameter). Selectivity Molecular size (flow-rate independent). Molecular size (largely flow-rate independent). Molecular size, branching (flow-rate dependent). Stationary-phase characterization Particle-size measurement (Coulter counter, SEM, FFF); MIP; Inverse SEC Particle-size measurement; MIP MIP, permeability Linear (interstitial) velocity 0.5 mm/s 1 to 2 mm/s 0.05 mm/s Typical column dimensions mm a mm (packed columns) b mm Volumetric flow rate 1 ml/min 1 ml/min (packed columns) b 10 µl/min Typical analysis time 10 min a 4 min 180 min a b Often several columns are used in series. Typical dimensions of open columns for HDC would be 500 mm 1 µm I.D. and the flow rate would be of the order of 10 nl/min. Such experiments are highly impractical. 43

46 Chapter 2 Separations of particles in open-tubular columns are extremely difficult to perform, due to the exceptionally narrow column diameters needed (internal diameter of the order of 1 µm) and the resulting brutal requirements on injection, detection and other aspects of the instrumentation [8]. HDC can more conveniently be performed on columns packed with non-porous particles. In such columns, the inter-particle space serves as a network of narrow channels where the hydrodynamic separation takes place [9]. For packed beds, the dimensions of R scale with the particle size. Columns with narrow and uniformly sized flow-through channels require homogeneous packing of very small particles, which is notoriously difficult. Packing capabilities for small particles dictate the lower limit of selectivity attainable in packed-column chromatography. HDC has been demonstrated using 1-µm non-porous particles where a value of R = 213 nm was obtained [10]. Alternative stationary phases that provide suitable flow-through characteristics may be applied to perform HDC. As a result of advances in micro fabrication, chips and pillar-structured micro channels have been used with increasing success to perform hydrodynamic separations [11,12]. However, R values suitable for the separation of synthetic polymers are difficult to realize even with the most-advanced contemporary fabrication technologies. Monolithic columns, which have become increasingly popular as separation media for LC [13], can also be considered for HDC. Hydrodynamic separations can be performed in the macropores, which offer a highly interconnected network of flow-through pores in the monolith. In contrast to the well-defined structure of packed beds with uniform particles, the structure and porous properties of monoliths may vary with the type of material and the preparation conditions. Although many different formulations and preparation techniques for monoliths have been presented in recent years [14], silica monoliths [15] and organic-polymer monoliths [16,17] have become most wide-spread in liquid chromatography. Separations of polystyrenes with low dispersity based on SEC-type partitioning have been demonstrated using silica monoliths featuring a bimodal pore-size distribution (PSD) [18]. However, the small volume of stagnant mobile phase in mesopores in comparison with the much larger external volume in the flow-through pores (ε i /ε e << 1) limits the resolution and sample capacity for SEC separations on this type of monolith. The ratio ε i /ε e is even more unfavorable for 44

47 Hydrodynamic chromatography of macromolecules using polymer monolithic columns polymeric monoliths due to the absence of mesopores (microglobules in the polymeric material) and thus the absence of stagnant zones in the column [19]. Separations of synthetic polymers by HDC using organic-polymer monoliths have been investigated in this work. Polystyrene-co-divinylbenzene (PS-DVB) was selected as the material of the monoliths based on its mechanical strength, solvent compatibility and low susceptibility for enthalpic interactions with synthetic polymers. Due to the low degree of dimensional shrinkage during polymerization, PS-DVB columns can be prepared successfully in-situ in wide-bore stainless steel columns [20], which allows usage in a manner analogous to contemporary high-performance SEC. We will attempt to elucidate the separation mechanism by relating the observed selectivity to the morphology and the pore-size distribution. 2.2 Experimental Chemicals and materials Styrene (PS, >99.5%), divinylbenzene (DVB, ~80%), dodecanol (98%), and azodiisobutyrodinitrile (AIBN, 98%) were purchased from Sigma-Aldrich (Zwijndrecht, The Netherlands). Tetrahydrofuran (THF, 99.8% unstabilized HPLC grade), diethyl ether (99.5%), and toluene (99.7%) were obtained from Biosolve (Valkenswaard, The Netherlands). Ethanol (99.7%) was obtained from BDH Chemicals (Poole, England). 2,6-di-tert-butyl-4-methylphenol (ionol, 99%) was acquired at Acros (Geel, Belgium). Polystyrene and poly(methyl methacrylate) standards with low dispersity and relative molecular weights (M r ) ranging between 580 Da and 3.7 MDa were obtained from Polymer Laboratories (Church Stretton, UK). The monomers were purified by passing them over activated basic alumina followed by a distillation under reduced pressure. AIBN was refluxed in diethylether for 30 min, recrystallized, and dried under vacuum before use. Helium 5.0 (99,999% Praxair, Vlaardingen, The Netherlands) was used to degas the HPLC mobile phase prior to use. The polymer standards were dissolved in THF. 45

48 Chapter 2 Stainless-steel column hardware (100 mm 4.6 mm I.D. and mm I.D.; SS grade 316), including end fittings, and 2-μm frits was purchased from Restek (Bellefonte, PA, USA) Instrumentation HPLC experiments were performed on a Shimadzu LC system ( s Hertogenbosch, The Netherlands) consisting of a system-controller (SCL10a), a micro-pump (LC10Advp), a column oven (CTO7), and a UV detector (SPD10AVvp). Data acquisition was performed using ClassVP software. Separations were performed applying 5-μL injections, with the column placed in the oven thermostatted at 50 C. The flow rate was varied between 10 and 500 μl/min to record calibration curves on different monolithic materials. UV detection was performed at 260 nm or 280 nm. Porosity data were obtained by using Pascal 140 and 440 mercury-intrusion porosimeters (CE Instruments, Milan, Italy) for low- and high-pressure analysis, respectively. The pore-size distribution was calculated using Pascal software using a model based on the Washburn equation [21] assuming cylindrical pores and a surfacecontact angle of 140 for mercury with the monolith. The samples for mercury-intrusion porosimetry (MIP) were obtained by extruding the monolithic columns from their steel cladding by removing one end fitting of the column and applying a flow. The monolith was cut into coarse pieces and dried overnight under vacuum Column preparation Monolithic columns were prepared in-situ in 4.6-mm I.D. stainless-steel columns. The composition of the polymerization mixture was 20% styrene, 20% divinylbenzene (w/w). The percentage of toluene was varied in between 10 and 24% (w/w) to control the pore size; dodecanol was used to make up to the composition (60% w/w minus the toluene content). After purging the polymerization mixture with Helium for 10 min. it was transferred into the column, closed by stainless-steel disks in lieu of porous frits. Polymerization was performed in a water bath (with Neslab RTE-140 water circulator, Thermo, Waltham, MA, USA) for 24 hours at 80 C. After completion of the polymerization reaction, the stainless-steel disks were replaced by porous frits and the columns were flushed with at least 50 column volumes of THF at 50 C and 10 µl/min. 46

49 2.3 Results and discussion Hydrodynamic chromatography of macromolecules using polymer monolithic columns Preparation and characterization of monoliths for HDC To make the polymer HDC separations compatible with conventional detectors for the characterization of macromolecules, such as refractive-index detection, viscometry, and static light-scattering, the monoliths were developed in wide-bore (4.6 mm I.D.) columns. No covalent bonding of the monolith with the wall was required since the cross-linked polymer was significantly more swollen in the SEC mobile phase (THF). For a small molecule (ionol) symmetric peak shapes were observed, indicating the absence of channeling effects. To create monoliths with macropores that give inter-particle space of comparable dimensions to columns packed with sub-3 μm particles [7], the porogen ratio in the polymerization mixture was adjusted while the monomer composition was kept constant. A detailed description of pore formation and the effect of porogen composition on the phase separation and consequently on pore and globule size is provided by Eeltink et al. [22]. Figure 1 shows the intrusion curves (A) and the volume distributions (B) of the monolithic materials as determined with mercury-intrusion porosimetry (MIP). The macropore size of the monolithic materials decreased with increasing toluene content in the reaction mixture. Remarkably, the monoliths with the smallest mode pore size (< 500 nm) appear to have a bimodal pore-size distribution. This is probably an artifact of the MIP measurements, due to compression effects of the semi-flexible monoliths during the intrusion process. In the MIP experiment dried monolith (under vacuum) is immersed in mercury and subsequently pressurized. At initial conditions mercury does not protrude the pores. During the intrusion process the macropores are filled with mercury at the pressure required to overcome the surface tension of mercury to enter the pores. For the material with the largest pores (sample 1 with a macropore diameter of 1200 nm) this occurs at approximately 1.2 MPa. For monoliths with smaller pores higher pressures are required, because the intrusion pressure is inversely related to the pore size. However, these materials are compressed before the onset of pore intrusion, as shown in Fig. 1a, and this will result in an increasing bias to smaller pore size and even an apparent bimodal pore size (Fig. 1b). 47

50 Chapter 2 Fig. 1. (a) Intrusion curves and (b) pore-size distributions of monoliths with different macropore size as determined with mercury-intrusion porosimetry. Numbers correspond to materials depicted in Table 2. 48

51 Hydrodynamic chromatography of macromolecules using polymer monolithic columns In the Appendix (section 2.5) it is discussed how extrusion data obtained by MIP may be used to confirm sample compression during intrusion measurements. Caution should be exercised in interpretation of the PSD from Fig. 1b, because this may be influenced by the extent of compression at the moment of mercury intrusion. This may result in the apparent narrow distribution, particularly for pores larger than the mode of PSD, as observed for materials 6 and 7. Flow-restriction measurements with THF were used to compare macropore sizes for monolithic columns without errors introduced by compression of the monolith. The Hagen-Poiseuille equation (Eq. 2) can be used to relate changes in flow resistance to macropore-size, under the assumption that the monoliths have narrow pore-size distributions. It relates backpressure ( P) and average linear mobile-phase velocity (u 0 ) in cylindrical channels to solvent viscosity (η), column length (L), and channel radius (r). This relationship has been demonstrated to hold for the pores in acrylic and styrenic monoliths [23]. P = 8ηL u 0 r 2 (2) The P/u 0 ratio was determined for material 4, which was selected as reference for its balance between pore size and compression effects. Under the assumption that the morphology remains the same, Eq. 2 was used to convert the changes in P/u 0 ratio to macropore size (diameter D P ) for the other materials with r = D P /2. Table 2 summarizes mode pore sizes as determined with mercury-intrusion porosimetry (D mip ) and flowresistance measurements (D P ). The deviation between D mip and D P becomes larger for monoliths with smaller pores. This is indicative for compression effects in MIP. The microscopic images obtained with scanning electron microscopy (SEM; see Fig. 2) show the typical globular structures of the monoliths prepared with different porogen composition. It was observed that monoliths with sub-micron pores have the same globular structure as their highly-permeable counterparts, but the domain size (i.e. the length scale of both pore and globular support) is different. Surface roughness of the fused globular structure for sample 1 provides some void space with dimensions significantly smaller than the through pores of 1.2 µm. Exclusion from such pores may 49

52 Chapter 2 contribute to the separation (SEC mechanism), but because the void volume is obviously low compared to ε e this contribution will be small. For monoliths with submicron pores no large through pores were observed. Therefore, the mobile phase must be flowing through the sub-micron pores, thereby providing a suitable environment for HDC of polymers. Fig. 2. Scanning electron micrographs of polymer monoliths prepared with different porogen ratios. (a) material 1: 10% toluene, 50% dodecanol, 20% PS, 20% DVB, (b) material 6: 18% toluene, 42% dodecanol, 20% PS, 20% DVB. Table 2. Porous properties of monolithic materials as obtained with mercury-intrusion porosimetry and pressure measurements. Monolithic material Wt% toluene in polymerization mixture Mode pore size (nm) MIP D mip Mode pore size correction using Poiseuille, D P * *reference value in D P calculation 50

53 Hydrodynamic chromatography of macromolecules using polymer monolithic columns HDC separation of polymers Polystyrene (PS) and polymethylmethacrylate (PMMA) standards were used to study the separation performance of PS-DVB monoliths with different pore sizes. Figure 3 shows overlaid chromatograms obtained for individual PS standards obtained on a 100 mm 4.6 mm I.D. monolithic column with D P of 258 nm (material 4) operating at flow rates of 300 μl/min and 100 µl/min. Good peak symmetry, A s = b / a < 1.24 (with b = the peak width of the tail at 10% of peak height and a = the peak width at the front at 10% of the peak height) was observed. The peak width at half height for 20 kda PS was 6.1 s for the 300 µl/min separation, yielding a (minimum) plate height of 18 µm. Backpressure over the monolith was 120 bar for THF at 50 C at 300 µl/min. Fig. 3. Hydrodynamic chromatographic separation of polystyrene standards on a 100 mm 4.6 mm I.D. polymer monolithic column with 260 nm macropores. Peak identification: 1 = ionol, 2 = 20 kda PS, 3 = 200 kda PS, 4 = 1120 kda PS. Flow rates: a = 300 μl/min, b = 100 µl/min. Mobile phase: 100% THF at 50 C. Compared to the best plate-height values, about 6 µm for HDC separations reported on columns packed with 2.7-µm particles at a linear velocity of 0.5 mm/s or higher, the peaks are significantly broader [7]. Since the mass-transfer contribution to the total peak width can be neglected in HDC, peak dispersion for polymers can be attributed to the 51

54 Chapter 2 large eddy-diffusion contribution induced by the column inhomogeneity. No significant changes in polymer separation efficiency have been observed with changes in the mobile-phase velocity (Fig. 3) or macropore size of the different monolithic materials. Ionol is commonly used as a marker for the mobile-phase volume and its dimensionless retention was defined as τ = 1. Different elution volumes were observed for other lowmolecular-weight flow markers, such as benzene, toluene, and alkylbenzenes. Alkylbenzenes were found to elute earlier with increasing molecular weight, supporting a separation based on size rather than a separation based on (adsorption) interactions. Similar behaviour was observed for commercially available SEC columns with PS-DVB cross-linked porous packings (Appendix, section 2.5.2). Low-molecular-weight nonpolar markers can adsorb onto or diffuse into the cross-linked PS-DVB phase. In case of the ionol both processes are unfavourable, because of its polarity. Different behavior of the flow marker may cause an offset, which should be taken into account when comparing phases with different cross-link densities or permeabilities. Monolithic columns compared in this work were all prepared with the same monomer-to-crosslinker ratio and they all behaved comparably. High flow-rates could not be used on all monolithic materials, because of the high backpressures generated in the narrow macropores and the concomitant risk of phase compression. Separations of polystyrene standards were obtained with flow rates ranging from 300 µl/min (material 2 and 3) down to 20 µl/min for material 9. The effect of macropore size on the retention behaviour and on the selectivity window is demonstrated by the calibration curves depicted in Figure 4. Monoliths with different macropore sizes show selectivity across different molecular-weight ranges. Columns with narrower macropores (and thus lower permeabilities) separate smaller polymers. This concurs with the expectation of HDC being the dominating retention mechanism as postulated in the introduction. Selectivity for the different monolithic materials is very similar between 0.75 < τ < 0.95, but the corresponding molecular-weight ranges differ by more than one order of magnitude. For each monolith the effective range of separation covers at least 2 orders of magnitude in polystyrene molecular weight. For values of τ < 0.75 differences in the shapes of the calibration curves were observed. For the materials with larger macropores (materials 3 through 6) the separation window 52

55 Hydrodynamic chromatography of macromolecules using polymer monolithic columns extended down to τ = 0.65, which is extraordinary for HDC-type separations. Separations at the upper end of the calibration curve have been observed to be flow-rate dependent in previous studies in which packed columns were used [7,10]. Comparison of the calibration curves in a universal format provides a better means to evaluate this hypothesis using monolithic columns. In a universal calibration graph the aspect ratio λ is displayed on the y-axis, which allows for a direct comparison of HDC-type separations irrespective of macropore size or molecular weight of the analyte polymer. Fig. 4. Effect of macropore size of monolithic columns on HDC selectivity for polymers with M r ranging between 990 Da and 3.7 MDa. Numbers correspond to materials depicted in Table 2. Monolith materials 2 and 3 were operated at 300 µl/min, materials 5 through 8 at 50 µl/min. and material 9 at 20 µl/min. The size of the flow-through channel and that of the solute molecules in solution must be known to calculate λ. Neither is obvious in the case of monolithic columns and dissolved synthetic polymers. Irregular shapes of the macropores and uncertainties about the morphology prevent a straightforward calculation of the hydraulic radius (i.e. the surface-to-volume ratio), which has been successfully used to calculate the equivalent capillary size for packed beds with non-porous particles [7]. The mode of pore size from MIP is expected to be less accurate when either the pore-size distribution in the monolith is broad or when compression occurs during MIP before the mode of 53

56 Chapter 2 pore size is reached. Therefore macropore size D P as determined from flow-restriction measurements was used in calculation of λ (Table 2). This is appropriate, because backpressure depends on the restriction in the flow-through pores where HDC takes place by definition. Polymers in solution do not behave as hard spheres, but as flexible chains following random coil statistics. Excluded volume of the polymer chain contributes to the coil size and varies with solvent and polymer chemistry [24]. The distance of exclusion near a surface has been used successfully in modeling retention behavior. This size is commonly referred to as the effective size and is conveniently defined relative to the radius of gyration for linear random-coil polymers [25] as r eff = π 2 r g (3) The relation between molecular weight (M) and radius of gyration (r g ) in THF as obtained using light scattering [26] was substituted in Eq. 3. The effective size (r eff ) of PS and PMMA polymer standards was calculated using Eq. 4 and Eq. 5. r eff,ps = π M0.600 (4) r eff,pmma = π M0.596 (5) The same calibration curves for columns with various pore sizes in Fig. 4 are presented in the form of a universal HDC calibration plot in Fig. 5a. A theoretical curve for HDC on packed columns (calculated using Eq. 1 and C = 2.7) is provided for reference purposes [9]. Experimental data match the theoretical curve for HDC separation best for solutes in the center of the selectivity window of the columns (around λ = 0.1). The slope in this central region is identical for all curves, which suggests that the balance between size exclusion and hydrodynamic effects is identical to that encountered with HDC in capillaries and packed beds. The experimental curves do not coincide with the theoretical curve, with an offset towards lower elution volumes that increases with macropore size. This offset is 54

57 Hydrodynamic chromatography of macromolecules using polymer monolithic columns believed to result from additional size-exclusion effects. For λ < 0.1 size exclusion of the polymer from the walls of flow-through channels is the main mechanism of separation [6]. Modeled retention assumes surface exclusion in cylindrical channels. Globular morphology and a distribution of the pore sizes (PSD) of the monolith, however, provide an increased volume for SEC effects. For macropores with a large average diameter this may result in increased selectivity at low λ. The broad PSD for materials 1 and 2 (Fig. 1B) and increased selectivity of material 2 for λ < 0.02 (Fig. 5a) illustrate this effect on monolithic columns. Size-exclusion effects other than wall exclusion in flow-through pores observed for λ < 0.02 decrease with macropore size and account for < 5% in elution volume for all monoliths. This effect is different from exclusion in HDC using columns packed with non-porous particles, which is limited to the geometric exclusion volume of spheres and scales with particle size [27]. It is dependent on the morphology of the monolith and may, therefore, be reduced further by optimization of the column-preparation process Flow-rate dependence in polymer separations Flow-rate dependent elution behavior was observed for polymers separated at λ ~ 0.2 and above (Figs. 5 and 6). Hydrodynamic interactions (particle rotation, drag, flowinduced radial force, etc.) become significant for solutes approaching the flow-through channel size and depend on both flow rate and solute characteristics [9]. Only when these contributions hold universally, retention will scale with λ and a single constant can be used to account for hydrodynamic interactions in Eq. 1 (e.g. C = 2.7, assuming rotating, non-draining behaviour of polymers in cylindrical channels according to Dimarzio & Guttman [28]). However, this universality fails for λ > 0.4 and the selectivity becomes dependent on either macropore or polymer size (Fig. 5a). For materials 5 through 8 the calibration curve for monoliths with smaller macropores demonstrates stronger reversal due to stronger retardation by hydrodynamic effects. The same calibration curves acquired at 20 µl/min (Fig. 5b) closely resemble the theoretical curve, which predicts strong retardation at λ > 0.2 after the assumption of non-draining polymer coils. At λ = 0.4 reversal of the calibration curves towards higher τ values is observed. Both PS and PMMA polymers are present as random coils under goodsolvent conditions and their flow-rate dependent elution behaviour is identical (Fig. 6). 55

58 Chapter 2 Fig. 5. Universal retention plot showing the calibration curves on monoliths with different macropore size. (a) Materials and LC condition similar as in Fig. 4. (b) Reversal of calibration curves for material 5 through 8 when operating at a flow rate of 20 μl/min. 56

59 Hydrodynamic chromatography of macromolecules using polymer monolithic columns Fig. 6. Flow-rate dependent calibration curves of PS and PMMA polymers on monolith material 7 (a) and corresponding chromatograms for PS standards 1.1 MDa, 523 kda, 200 kda, 71 kda, 20 kda, 7 kda and 2 kda at a flow rate 50 μl/min (b). Column dimensions: 250 mm 4.6 mm I.D. monolithic column. 57

60 Chapter 2 Flow-rate dependent elution of high-molecular weight polymers has been observed for separations under wall-exclusion (HDC-like) conditions in other studies [7,10,29,30,31]. It has been attributed to either deformation or elongation of the polymer coil. The time-averaged coil size measured perpendicular to the flow direction will decrease when the polymer molecules are subjected to shear stress. To describe these effects the Deborah number (De) can be introduced [29]. De expresses the ratio of hydrodynamic (elongation) forces to Brownian (relaxation) forces. For dilute polymer migrating through packed beds it can be described as follows De = K deb ν 6.12 Φ η r3 g d p R T (6) where K deb is a constant (with a typical value of 6 [29]), ν is the superficial solvent velocity, d p the particle size of the packing, Φ the Flory-Fox parameter, η the solvent viscosity, r g the radius of gyration of the polymer, R the gas constant and T the absolute temperature. Application of Eq. 6 for monoliths is complicated, because reference data only exist for packed beds [29,32]. In the elongation factor in Eq. 6 (K deb ν /d p ) the particle size can be replaced by the hydrolic radius (i.e. the radius of a capillary with an identical surface-to-volume ratio). For a packed bed of non-porous monodisperse particles R h = 2/9 d p assuming a porosity of 0.4 [5,7]. This relation was used successfully in comparing HDC selectivity between packed beds and capillary columns, but may be used for monoliths as well. For monoliths R h = D P / 2 was used. K deb is a constant that accounts for the effect of pore structure on elongation. It is determined semi-empirically by matching selectivity changes in HDC for well characterized systems with De = 0.5 [32]. Since K deb could not be established accurately for monoliths, the typical value for particle-packed beds was used. Random spherical coils prevail at low values of De. The onset of polymer deformation is commonly assumed to occur around a value of De of 0.1. At still higher values (De > 0.5) the chains become completely elongated, resulting in a separation mechanism termed slalom chromatography to picture the migration of flexible, stretched polymer chains through the interstitial channels of the support [31]. Liu et al. describe a system 58

61 Hydrodynamic chromatography of macromolecules using polymer monolithic columns with λ values on the order of 0.1 (d p = 15 µm, R h = 3.3 µm, polystyrene r g = 125 to 450 nm). On the 4.6-mm I.D. column used the onset of slalom chromatography was observed for flows in excess of 0.1 ml/min. The present separations on monoliths differ significantly from those described by Liu on packed columns in terms of analyte molecular weight (De r 3 g ) and aspect ratio (λ). Uliyanchenko et al. reported on slalom chromatography for polymers in the same molecular-weight range as used in the present study. They used contemporary HPLC conditions (d p = 1.7 µm, R h = 0.38 µm) [30] with a flow rate of 1 ml/min on 4.6-mm I.D. columns, which corresponded to De = 0.6 for the 2.0-MDa PS. Deborah values were calculated for separations on monoliths with different macropore sizes (see Appendix, section 2.5.3). At the point where the calibration curves in Fig. 5 show a reversal towards higher elution volumes the De values were almost always much lower than 0.1. Thus, the present observations are not akin to the slalom chromatography described elsewhere [31]. Conventionally, De numbers are calculated for channels much larger than the diameter of the polymer coil (λ < 0.2). In that case the elongation (K deb ν /d p ) can be assumed not to depend on the coil size. In the present study we consider phenomena that occur for much higher λ values. Clearly, the straightforward calculation of De values does not suffice to describe the observations in such narrow channels, where the shear stress caused by the Poiseuille flow profile only affect the periphery of the polymer coil and rotation of the coil is largely prohibited. Very large polymers with λ 1 elute faster than the average fluid velocity (τ = 1; see Fig. 5). This suggests that the polymer coils are reptating [33,34] through the stationary-phase channels without significant restriction. Higher flow rates cause an increase in the migration rate, which suggests that chain segments of the reptating coil move towards the faster-moving central part of the Poiseuille flow profile (assuming that the non-draining assumption holds). It appears that they no longer possess the spherical coil geometry that prevails under equilibrium conditions at De < 0.1 in the absence of constriction. The chromatographic selectivity arising from coil-reptationbased elution is large and expected to cover the complete elution window of HDC. This is supported by calibration curves obtained at different flow rates for materials 5 through 8 (cf. λ > 0.4 range in Fig. 5). It is not expected that a fully flexible polymer such as polystyrene will uncoil at conditions of moderate constriction (λ 1), because 59

62 Chapter 2 of fast relaxation by Brownian motion under the conditions used here. In reptation or translocation of charged polymers and biomaterials, however, complete elongation may readily occur as a result of reduced flexibility in the polymers, highly constricted pores or conditions featuring much slower relaxation due to Brownian motion [35, 36, 37, 38]. A different mechanistic explanation is therefore desired for flow-rate sensitive polymer separation in monoliths. A useful concept from the theory of flow-rate-dependent migration in HDC is stressinduced diffusion (SID) [9,39]. This concept implies that polymers in Poiseuille flow migrate away from the channel walls, driven by the lower entropy as a result of elongation and reduced orientation by shear stress in this region. Migration towards the channel center (and avoiding the elongating shear forces) leads to an increase in entropy [40]. This effect is strongest at high shear rates and for high molecular weights. The same arguments can be applied to reptating coiled polymers in confined channels. Relaxation towards a spherical coil sampling the full channel diameter (natural trend to increased entropy) will result in strong internal forces near the channel walls (induced decrease in entropy). This effect is in agreement with the results for polymers eluted from confined channels in monoliths in Fig. 5. Higher M r polymers eluting at identical λ from larger macropores get stronger deformed by SID due to their longer relaxation times and the calibration curve demonstrates less reversal. The mechanism described here is also in agreement with topology based separation by MTF [41,42]. Branched polymers with identical hydrodynamic size but increased segment may exhibit stronger resistance to SID compared to linear polymers under identical conditions. The mechanism of an entropy-barrier was postulated before [41], but emphasized the role of migration through orifices as compared to SID which takes place in continuous narrow channels. 60

63 2.4 Conclusions Hydrodynamic chromatography of macromolecules using polymer monolithic columns Monolithic columns for separations of macromolecules were successfully prepared insitu in wide bore (4.6-mm I.D.) stainless-steel columns. The selectivity window depended strongly on the size of the macropores tuned by the ratio of porogens. HDC is the dominant mechanism of separation, since the mesoporous volume required for SEC was too small. Also, calibration curves match with elution behavior as expected for HDC separation up to λ = 0.2. Only for large-macropore monoliths, a deviation in retention behavior is observed for small polymers (M r < 20 kda), which may be explained by a combined HDC-SEC mechanism for λ < Macropores with much smaller hydrolic radii relative to packed columns were obtained and therefore selectivity for lower-m r macromolecules can be obtained. Our approach allowed the preparation of monoliths with a pore size as small as 75 nm and a selectivity window in HDC corresponding to a theoretical column packing with 0.17 µm particles (D P = 4/9 d p ). These monoliths have limited applicability for fast size-based separations due to their low permeability. Monoliths with 258 nm macropores yielded polymer separations in the molecular weight-range common for SEC separations. Selectivity equivalent to 0.6 µm particles was demonstrated on this material with only 120 bar for THF at 0.5 mm/s on a 100 mm column (Fig. 3). Size-based separations featuring selectivity beyond what is possible with contemporary column-packing techniques are readily obtained. The efficiency of polymers monoliths for HDC may be improved further by optimization of the column heterogeneity. For high-molecular weight polymers (M r > 300,000 Da) the separation in monoliths with confining channels strongly depended on flow rate. This situation differs from other flow-rate dependent in that the shear rate is not identical throughout mobile phase sampled by the coil. Response to the high shear rate experienced in the polymer-coil periphery was suggested to result in departure from thermodynamic equilibrium geometry and flow-rate dependent elution. This hydrodynamic-based explanation was found to be in semi-quantitative agreement with experimental results for linear polystyrene polymers. 61

64 Chapter Appendix In this supporting information extrusion data is provided from mercury intrusion porosimetry. It is explained how this information may be helpful to confirm compression of monolithic samples during porosimetry measurements. Separation of alkylbenzenes on cross-linked polystyrene-co-divinylbenzene monoliths and SEC-particles is presented to demonstrate the absence of adsorption effects and diffusion of small molecules into the stationary phase compared to non-porous silica columns. The calculation of Deborah numbers is explained for polymer separations on monolithic columns. Threshold values for molecular weight and λ are presented for the separation conditions that were used in obtaining calibration curves for monolithic columns with various macropore sizes Mercury intrusion and extrusion Mercury extrusion data for two monoliths is presented in support of the discussion on compression of monoliths. During the intrusion measurement the pressure was increased up to 300 MPa. At this pressure porosity in pores with a diameter down to 5 nm can be measured. Porosity data for monolithic materials 7 and 8 (Table 2) was obtained during both pressure increase and decrease and is presented in Fig. S-1. Once the pressure is decreased, mercury will be extruded from pores again driven by its surface tension. The pressure where extrusion will always be somewhat lower compared to the intrusion pressure. Compression of the material during intrusion measurement will result in a higher pressure required for mercury intrusion, because the pores become smaller when the material is compressed. If the compression is a reversible process, the sample will reassume its equilibrium dimensions once it has been intruded by the mercury under high pressure. Little or no effect of compression is expected for the extrusion pressure. The higher pressure difference between intrusion and extrusion pressure for material 8 supports the assumption that this material suffers more compression compared to material 7 at the moment of mercury intrusion. The recovery may depend on actual pore geometry as well as the rate at which pressure was reduced. For the results presented here pressure was decreased at a faster rate 62

65 Hydrodynamic chromatography of macromolecules using polymer monolithic columns compared to the pressure increase. A study of mercury extrusion under well controlled conditions can reveal useful information with respect to sample compression during the intrusion measurement. Unfortunately, such data was not acquired for the work here, because the hypothesis of compression was formed after most of the measurements were completed. Fig. S-1. Mercury intrusion during pressure increase and decrease 63

66 Chapter SEC separation of alkylbenzenes and solvents on monolith The elution for ionol, benzene, toluene and alkylbenzenes was measured to confirm that absence of adsorption effects. Ionol, benzene, toluene, ethylbenzene, propylbenzene, butylbenzene and hexylbenzene were diluted in THF before injection at a concentration of about 1 mg/ml. Detection was performed by UV at 260 nm. All separations were performed at room temperature to minimize axial diffusion. Column dimensions were mm I.D. in each case. (A) Monolithic material 4, D P 258 nm, 100 µl/min THF (B) 10 6 Å PLgel, d p 10 µm, 200 µl/min THF (C) Non-porous silica, d p 1.0 µm, 100 µl/min THF The elution order in Fig. S-2 and S-3 was, from left to right, ionol, hexylbenzene, butylbenzene, propylbenzene, ethylbenzene, toluene/benzene with the lowest peak height for benzene. In Fig. S-4 all elute at the same volume, because the samples do not diffuse into or adsorb onto the non-porous silica. Fig. S-2. Separation of small molecules on cross-linked PS-DVB monolith (A) 64

67 Hydrodynamic chromatography of macromolecules using polymer monolithic columns Fig. S-3. Separation of small molecules on cross-linked PS-DVB SEC particles (B) Fig. S-4. Separation of small molecules on non-porous silica (C) 65

68 Chapter Deborah numbers The polystyrene molecular weight corresponding to a Deborah value of 0.1 was calculated using Eq. 6. This specific value of De = 0.1 was used, because it provides the lower limit where the effects of polymer deformation may be observed. For each monolith the flow rate that was used to obtain its calibration curve in Fig. 5a was used. Common variables used in calculating De were a viscosity of Cp for THF at 50 C, a Flory-Fox parameter of mol -1 and fictive particle size of d p = 4/9 D P. The results are presented in Table S-1 and Fig. S-5. The onset of deformation is reached at increasingly lower molecular weight with smaller macropore size. However, it was not reached within the classic HDC selectivity range for separations on monolithic columns. The mobile phase flow-rate directly impacts the expected onset of deformation. Deborah scales linear with both particle size (channel size) and average linear mobilephase velocity u 0. In practice the flow rate and thus u 0 are a result from backpressure limitations and permeability of the column. According to Hagen-Poiseuille (Eq. 2) u 0 scales quadratic with increasing pore size at identical backpressure. Therefore, deformation of analytes is more commonly observed for highly permeable stationary phases with large interstitial pores. De > 0.1 is reached at much lower backpressure, within the range of common separation conditions. Table S-1. Lower-limits for polymer deformation according to Deborah-number calculation, expressed in PS molecular weight and λ. Monolithic material D P (nm) Flow rate (µl/min) De = 0.1 PS M r (MDa) De = 0.1 λ

69 Hydrodynamic chromatography of macromolecules using polymer monolithic columns Fig. S-5. Calibration curves on monoliths with different macropore size with diamonds indicating De = 0.1 for conditions described in Table S-1. References [1] A.M. Striegel, W.W.Yau, J.J.Kirkland and D.D.Bly, Modern Size-Exclusion Liquid Chromatography, Second edition, Wiley, New York, [2] T. Chang, Adv. Polym. Sci., 163 (2003) 1. [3] K.O. Pedersen, Arch. Biochem. Biophys., Suppl., 1 (1962) 157. [4] E.A. DiMarzio, C.M. Guttman, J. Polym. Sci., Part B, 7 (1969) 267. [5] A.J. McHugh, CRC Crit. Rev. Anal. Chem., 15 (1984) 63. [6] R. Tijssen, J. Bos, M.E. Van Kreveld, Anal. Chem. 58 (1986) [7] G. Stegeman, R. Oostervink, J.C. Kraak, H. Poppe, K.K. Unger, J. Chromatogr. 506 (1990) 547. [8] J. Bos, R. Tijssen, M.E. van Kreveld, Anal. Chem. 61 (1989) [9] G. Stegeman, J.C. Kraak, H. Poppe, R. Tijssen, J. Chromatogr. A 657 (1993)

70 Chapter 2 [10] E. Venema, J.C. Kraak, H. Poppe, R. Rijssen, J. Chromatogr. A 740 (1996) 159. [11] E. Chmela, R. Tijssen, M.T. Blom, J.G.E. Gardeniers, A. Van den Berg, Anal. Chem. 74 (2002) [12] M. De Pra, W. De Malsche, G. Desmet, P.J. Schoenmakers, W. Th. Kok, J. Sep. Sc. 30 (2007) [13] G. Guiochon, J. Chromatogr. A 1168 (2007) 101. [14] D. Sykora, F. Svec, in: F. Svec, T.B. Tennikova, Z. Deyl (Eds.), Monolithic materials: preparation, properties and applications, Chapter 20, Elsevier, Amsterdam, [15] K. Nakanishi, N. Soga, J. Am. Ceram. Soc. 74 (1991) [16] S. Hjertén, J.-L. Liao, R. Zhang, J. Chromatogr. 473 (1989) 273. [17] F. Svec. J.M.J Fréchet, Anal. Chem. 64 (1992) 820. [18] K. Ute, S. Yoshida, T. Kitayama, T. Bama, K. Harada, E. Fukusaki, A. Kobayashi, N. Ishizuka, H. Minakuchi, K. Nakanishi, Polym. J. 38 (2006) [19] J. Urban, S. Eeltink, P. Jandera, P.J. Schoenmakers, J. Chromatogr. A (2008) 161. [20] M. Petro, F. Svec, I. Gitsov, J.M.J. Fréchet, Anal. Chem. 68 (1996) 315. [21] E.W. Washburn, Physical Rev., 17 (1921) 273. [22] S. Eeltink, J.M. Herrero-Martinez, G.P. Rozing, P.J. Schoenmakers, W. Th. Kok, Anal. Chem. 77 (2005) [23] C. Viklund, K. Irgum, F. Svec, J.M.J. Fréchet, Chem. Mater. 8 (1996) 744. [24] P.J. Flory, Principles of Polymer Chemistry, Cornell University Press, Ithaca, NY, [25] M.E. van Kreveld, N. Van den Hoed, J. Chromatogr., 83 (1973) 111. [26] C. Jackson, Y.-J. Chen, J.W. Mays, J. Appl. Pol. Sci., 61 (1996) 865. [27] W. Cheng, J. Chromatogr. 362 (1986) 309. [28] E.A. DiMarzio, C.M. Guttman, J. Chromatogr. 55 (1971) 83. [29] D.A. Hoagland, R.K. Prud homme, Macromolecules 22 (1989) 775. [30] E. Uliyanchenko, P.J. Schoenmakers, S. van der Wal, J. Chromatogr. A 1218 (2011) [31] Y. Liu, W. Radke, H. Pasch, Macromolecules 38 (2005) [32] R. Haas, F. Durst, Rheol. Acta 21 (1982) 566. [33] R. Tijssen and J. Bos, in: F. Dondi and G. Guiochon (eds.), Theoretical Advancement in Chromatography and Related Separation Techniques, Kluwer, Dordrecht, 1992, pp [34] P.G. De Gennes, J. Chem. Phys. 55 (1971) 572. [35] P.G. De Gennes, Science 276 (1997) [36] W. Reisner, K.J. Morton, R. Riehn, Y.M. Wang, Z. Yu, M. Rosen, J.C. Sturm, S.Y. Chou, E. Frey, R.H. Austin, Phys. Rev. Lett. 94 (2005) [37] T. Su, P.K. Purohit, Phys. Rev. E 83 (2011) [38] C.T.A. Wong, M. Muthukumar, J. Chem. Phys. 133 (2010) [39] A.B. Metzner, Y. Cohen, C. Rangel-Nafaile, Non-Newtonian Fluid Mech. 5 (1979) 449. [40] M. Muthukumar, A. Baumgartner, Macromolecules 22 (1989) [41] D.M. Meunier, P.B. Smith, S.A. Baker, Macromolecules 38 (2005) [42] R. Edam, D.M. Meunier, E.P.C. Mes, F.A. Van Damme, P.J. Schoenmakers, J. Chromatogr. A 1201 (2008)

71 Chapter 3: Branched-Polymer Separations using Comprehensive Two-Dimensional Molecular-Topology Fractionation Size-Exclusion Chromatography Abstract Branching has a strong influence on the processability and properties of polymers. However, the accurate characterization of branched polymers is genuinely difficult. Branched molecules of a certain molecular weight exhibit the same hydrodynamic volumes as linear molecules of substantially lower weights. Therefore, separation by size-exclusion chromatography (SEC), will result in the co-elution of molecules with different molecular weights and branching characteristics. Chromatographic separation of the polymer molecules in sub-micron channels, known as molecular-topology fractionation (MTF), may provide a better separation based on topological differences among sample molecules. MTF elution volumes depend on both the topology and molar mass. Therefore co-elution of branched molecules with linear molecules of lower molar mass may also occur in this separation. Because SEC and MTF exhibit significantly different selectivity, the best and clearest separations can be achieved by combining the two techniques in a comprehensive two-dimensional (MTF SEC) separation system. In this work such a system has been used to demonstrate branching-selective separations of star branched polymers and of randomly long-chain branched polymers. Star-shaped polymers were separated from linear polymers above a column-dependent molecular weight or size. 69

72 Chapter Introduction Knowledge of the relationships between polymerization conditions and functional properties of the polymers being formed enables polymer chemists to make materials that are largely optimized for their application. High-performance polymers meet specific needs in the market place. The desired properties of such polymers are typically achieved by optimizing the parameters of the polymerization process. Such an optimization can be performed much more efficiently when key structural parameters affecting polymer properties are understood. Meaningful structure-property relationships can only be developed if the key structural parameters can be measured. In the case of branched polymers, a more detailed description of branching, beyond a basic estimate of the average number of branch points per molecule, is required. Distributions of the molecular properties must be revealed, which requires that the molecules with different degrees of branching be separated, ideally in combination with selective detection techniques. Knowledge of detailed molecular characteristics and their effect on functional properties will ultimately allow the design of high-performance polymers. Spectroscopic techniques (e.g. Fourier-transform infrared, FTIR, or nuclear magnetic resonance, NMR) and physical measurements (e.g. light scattering or viscometry) are used on a routine basis to characterize the overall (or average) molecular structure of polymers. Using hyphenated techniques (typically combinations of a chromatographic separation with one or more spectroscopic or physical methods) more information concerning the distributed properties may be obtained. Size-exclusion chromatography (SEC) with light scattering and/or viscometry detection is commonly used to characterize long-chain branching (LCB) in high-molecular-weight polymers [1,2,3]. The characterization of LCB in polymers is of particular interest, because of the influence of LCB on processing properties, such as zero-shear viscosity and melt strength. Branching factors based on the Zimm-Stockmayer theory [4] may be calculated when a linear-polymer (reference) sample with identical chemistry or its Mark-Houwink parameters are available. These can subsequently be converted to branching frequencies if assumptions are made regarding the functionality of the branching points and the average branch length. SEC with selective detection is, however, not able to fully characterize branched polymers. Separation by size of the 70

73 Branched-Polymer Separations using Comprehensive 2D MTF SEC unperturbed chain in solution yields fractions containing molecules with equal hydrodynamic volumes, but with different topologies and molecular weights. This distribution cannot be characterized by selective detection techniques. For example, light scattering only provides the weight-average molecular weight for the ensemble of chains eluting in each SEC fraction. Molecular-weight polydispersity at a given SEC elution volume was recently confirmed by comparing selective-detection techniques that yielded different types of molecular-weight averages (weight average from light scattering and number average from viscometry, [5]). The authors demonstrated that the so-called local polydispersity was affected by the distribution of the degree of branching and the functionality. NMR is an alternative technique for determining the structure and the frequency of branch points, but the technique has some limitations. A high-field instrument is needed to detect and quantify low levels of LCB, but discrimination of different branch lengths is still not possible when branches are longer than a few carbon atoms [6]. Most importantly, NMR provides only an average number of branches per molecule. Multi-dimensional separations can be used to study complex polymers that feature more than one distribution simultaneously. In a comprehensive two-dimensional separation system, denoted by the sign, every part of the sample is subjected to two independent mechanisms and the separation obtained in the first dimension is maintained in the final two-dimensional chromatogram) [7]. The peak capacity is increased substantially by comprehensive operation of multi-dimensional separations. However, the separation power is only used efficiently when different selectivity in each separation dimension allows the sample to be separated among its distributions of interest [8,9]. Only in orthogonal separations the retention times in the different dimensions are by definition completely independent (uncorrelated). Although most multi-dimensional separation systems are not orthogonal, confounded distributions that remain unresolved in a single separation step can be separated using two independent separations with different selectivity. Therefore, complex polymers with distributions in distinct molecular properties can successfully be resolved using multi-dimensional systems. Separations by functionality [10] and chemical composition [11] have, for example, been combined with separations according to size using SEC to fully elucidate two mutually dependent distributions. 71

74 Chapter 3 Branched polymers can also be separated using combinations of independent separations, such as interactive liquid chromatography and SEC, in a comprehensive two-dimensional setup. Selectivity for branched versus linear polymers has resulted from differences in the number of repeat units, number of branch points or size in solution. Star polymers prepared by coupling living polystyrene anions were separated by an off-line combination of temperature-gradient interaction chromatography (TGIC) and SEC [12]. The TGIC separation is thought to be based on molecular weight, while SEC is based on the size of molecules in solution. The relationships between molecular weight and hydrodynamic volume are different for branched and linear polymers allowing separations of differently branched polymers by a combination of both methods. Similar star polymers of lower molecular weights were separated on-line by liquid chromatography at the critical composition in combination with either SEC or TGIC (LCCC SEC or TGIC LCCC [13]). In the LCCC separation, branched polymers were separated by interaction of the apolar side-groups at the coupling agent. The techniques described here yielded good separations for branched homo-polymers with numerous branches and chemically different branch points or end groups. Highmolecular-weight polymers, with very little long-chain branching (LCB), or without functional groups at the branch points or chain ends of different polarity cannot be separated using these techniques. For LCB polymers, complete separation may be obtained when the polymer is also separated based on branching parameters. Such a separation has previously been demonstrated on monolithic columns containing sub-micron macro pores [14] and on columns packed with sub-micron particles [15]. Both separation systems featured submicron flow channels. Polymers above a stationary-phase dependent molecular weight become retained at low flow rates. Branched polymers were found to elute much later than linear ones of the same molecular weight. This separation method was termed molecular-topology fractionation (MTF) and it was thought to result from the topologydependent relaxation-time spectrum of polymers in dilute solution [15]. The word topology reflects the geometrical structure of the polymer molecules, more specifically the branch length, frequency and functionality of the branch points. Separation of branched polymers by MTF can only be applied to samples with very narrow molecular-weight distributions, since the degree of polymerization also affects the 72

75 Branched-Polymer Separations using Comprehensive 2D MTF SEC retention. Off-line fractionation of LCB polymer by SEC and re-injection of the fractions in MTF was used to demonstrate the differences in selectivity of the two techniques for LCB polymers [15]. Similar to the comprehensive two-dimensional separation systems (described in the previous paragraph) for separating star polymers, samples featuring LCB could be resolved when the separation dimensions display significantly different selectivity towards long-chain branching and hydrodynamic size. In this paper, the separation of long-chain branched polymers using MTF SEC will be demonstrated. Knowledge of the relationship between molecular weight, hydrodynamic size and branching will be used to interpret the selectivity in MTF separations. The separation of polymers with similar hydrodynamic size, but different topologies is demonstrated for star polymers with narrow molecular-weight distributions. Results on the separation of randomly long-chain-branched polymers and star polymers will be used to discuss the selectivity of MTF and the applicability MTF SEC for the separation of complex samples of branched polymers. 3.2 Experimental Samples and materials The eluent for MTF and SEC separations was non-stabilized HPLC-grade tetrahydrofuran (THF; Biosolve, Valkenswaard, The Netherlands); it was continuously degassed by purging with helium 5.0 (99,999% Praxair, Vlaardingen, The Netherlands). Sample polymers were dissolved in HPLC-grade THF stabilized with 250 ppm butylhydroxylated toluene to prevent degradation by radicals. Narrowly distributed linear polystyrene standards (Polymer Laboratories, Church Stretton, UK) were used to study retention behaviour. These standards were dissolved at concentrations of 0.5 mg/ml. A nominal three-arm star polystyrene sample was obtained from Polymer Source (Dorval, Canada) and used at a concentration of 1.0 mg/ml. This star polymer was synthesized by coupling of anionically polymerized arms with a tri-functional agent (α,α,α - trichloromesitylene). The manufacturer specified a nominal molar mass of 1,480 kg/mol for the precursor arms. However, thorough analysis using size-exclusion chromatography with low-angle light scattering and differential viscometry revealed an arm molar-mass closer to 1,250 kg/mol. The sample composition was determined from 73

76 Chapter 3 the same experiment. Integration of the concentration signal revealed ~5% to be uncoupled precursor, ~45% linear polymer with double the precursor molecular weight and a remainder of three-arm coupling product. A small amount of higher-coupling products as a result of lithium-halide exchange [16,22] was evident from the overall molecular weight of the star-polymer sample as estimated by SEC with light-scattering detection. A four-arm coupling side-product by lithium-halide exchange is expected to have all arms coupled in one functional centre. The concentration of this large-molecule fraction could not be determined quantitatively by SEC. The reaction scheme of the coupling and analysis results have been presented by Meunier et al. [15]. Polystyrene with a high LCB frequency was obtained from the Dow Chemical Company (Midland, MI, USA). The Mark-Houwink plot and information on the molecular-weight distribution of this material can be found in the supplementary information of this article. Details regarding the preparation of this high-lcb sample can be found elsewhere [17]. A custom-made 150 mm 4.6 mm I.D. column packed with 10-µm 10 6 Å PLgel particles by Polymer Laboratories was used for fast SEC as the second dimension separation at a flow rate of 750 µl/min. The MTF-column packing consisted of a polydisperse mixture of particles in the range of 0.1 to 1 µm (Admatech, Aichi, Japan). Particle-size-distribution data provided by the supplier revealed that the average particle diameter was 0.5 µm and the half-width of the distribution was about 0.3 µm. The particles were functionalized with C 8 chains to facilitate the packing procedure. A 150 mm 4.6 mm I.D. column was packed by Diazem (Midland, MI, USA) using an identical procedure as that used previously for packing columns for MTF [15] Instrumentation and methods Comprehensive two-dimensional MTF SEC was performed on a system assembled inhouse. Basic components of the system were two LC10ADvp pumps (Shimadzu, s Hertogenbosch, The Netherlands) to perform isocratic separations in the two dimensions, along with an SCL10a system controller (Shimadzu) for interfacing with the data-acquisition computer. Either 10 or 20 µl injections of the samples were performed by a SIL9a autosampler and columns were kept at 50 C in a CTO7 column oven (both from Shimadzu). Detection in MTF SEC experiments was performed using 74

77 Branched-Polymer Separations using Comprehensive 2D MTF SEC a Spectroflow 757 (ABI, Ramsey, NJ, USA) UV-absorbance detector equipped with an 8-µl flow cell. Data acquisition was typically performed at 5 Hz, recording the signals of both detectors. A capillary UV detector was used (Linear UVIS 200, Linear Instruments, Reno, NV, USA) to record the data for the calibration curve in Fig. 1. The detector wavelength of UV detectors was set to 260nm, close to the absorption maximum of polystyrene in tetrahydrofuran. Modulation in comprehensive two-dimensional separations was accomplished with an air-actuated VICI two-position 10-port valve (Valco, Schenkon, Switzerland). This valve was operated using a high-speed switching accessory. The digital valve interface (DVI; Valco) was connected to the SCL10a system controller. The 10-port valve was plumbed for symmetrical dual-loop modulation [11]. Two injection loops of equal volume (43 or 92 µl) were used. From the moment of injection on the MTF column, the 10-port valve was switched either every 2, 2.67 or 4 minutes in order to inject 40 µl from the first dimension (running at 20, 15 or 10 µl/min respectively) at the SEC column. Instrument control and data acquisition were achieved with ClassVP v7.4 build15 software (Shimadzu). Exported data were processed in Matlab v7.3 (The Mathworks, Natick, MA, USA) using in-house written software for data folding and visualization of two-dimensional colour plots. 3.3 Results and discussion Calibration curve for molecular-topology-fractionation column Linear polystyrene standards with a well-defined molecular-weight distribution (MWD) are readily available, in contrast to well-characterized branched polymers with high molecular weights. Therefore, linear polystyrenes were used to determine retention behaviour in MTF as a function of molecular weight. The elution volume at the peak maximum is plotted against the logarithm of the peak molecular weight in Fig. 1. Reversal of the curve is observed around 200 kg/mol. The molecular weight where such a reversal occurs will be referred to as the critical molecular weight M crit for reversal. The elution order for polymers below M crit was consistent with that observed for polystyrenes separated on columns packed with 1-µm, non-porous particles and can be explained as hydrodynamic chromatography [18]. The interest in MTF stems from the 75

78 Chapter 3 elution region above M crit, because in this range the selectivity for branching (molecular topology) has been observed [14, 15]. Although branched molecules are more effectively retained than linear ones (section 3.2), the flow-rate effect on retention of linear molecules may be used as a benchmark for the MTF selectivity of the column. Fig. 1. MTF calibration curve for linear polystyrenes; obtained at a flow rate of 20 µl/min, at 10 µl/min. Retention times of linear polymers above M crit were measured at two different flow rates. The influence of flow rate on retention volume is much larger for high molar masses, i.e. above M crit. Elution-order reversal has also been observed for polystyrene standards in hydrodynamic chromatography (HDC) on columns packed with 1-µm nonporous particles [18], but in that case the effect is very much smaller than observed for MTF. In HDC the reversal in the calibration curve has been explained by shear deformation of the polymers in solution [18]. After such a deformation the radius of the polymer molecules perpendicular to the direction of flow is effectively smaller compared to its unperturbed state. As a result the deformed molecules can get closer to the channel walls, where the linear velocity is lower, and elute later from HDC columns. Reversal due to polymer deformation is expected to be observed most strongly at high shear and thus high flow rates. This is indeed observed in HDC, but not in the present MTF system, where the effect is strongest at the lowest flow rates (Fig. 1). Our calibration curves (molecular weight vs. elution volume) are thus not in agreement with HDC data. However, our results are in agreement with observations in previous MTF studies [14]. Thus, the separation mechanisms in HDC and MTF are based on different principles. 76

79 Branched-Polymer Separations using Comprehensive 2D MTF SEC One important difference between the more conventional chromatographic separation techniques (SEC, HDC, or field-flow fractionation, FFF) and MTF is the aspect ratio (λ), defined as the ratio of the effective radius of the polymer in solution and the radius of the channel that it is migrating through. Hydrodynamic separation techniques (such as HDC) are typically operated below λ = 0.2 [19], whereas branching selectivity in MTF is obtained only at values of λ that exceed this value. HDC theory predicts that for large values of λ the forces resulting from rotation and solvent lagging (inertia) will reduce the migration rate of the polymer, ultimately resulting in elution volumes greater than the column volume. Shear alignment or deformation at such high values of λ may be responsible for decreasing retention with increasing flow rate for large polymers (above M crit ). However, this is unlikely in MTF considering that the linear velocity of the mobile phase is several times lower for MTF than in HDC with 1-µm particles [18]. A quantitative comparison of λ values for the different separation systems cannot be made, because absolute values of the average diameter of the flow-through channels are hard to obtain for the column used in this study. The flow path in particle packed beds is much more complex than that in open-tubular channels, for which HDC theory was derived. Successful attempts to relate hydrodynamic retention in particle packed beds with retention in capillaries were made by using the hydraulic radius to define the interstitial channel diameter [18, 20, 21]. However, the polydisperse packing material of the present MTF column complicates the use of the classical concepts. Stationary phases with well-defined channel parameters will have to be used to for a robust comparison of HDC and MTF in terms of the aspect ratio Branched-polymer separations Because branched polymers and linear polymers of the same hydrodynamic size coelute in SEC, triple-detection SEC can only be used to obtain the average number of branches per molecule at any given elution volume. Therefore, branching properties cannot be fully characterized when polymers are separated by hydrodynamic size only. Comprehensive two-dimensional separation by hydrodynamic size and by branching properties will be used to demonstrate this point. MTF is used in the first dimension to fractionate polymers that vary in molecular weight and/or branching properties. This choice for MTF in the first dimension is dictated by the experimental conditions. MTF 77

80 Chapter 3 is operated at flow rates between 10 and 20 µl/min on a 150 mm 4.6 mm I.D. column, resulting in analysis times of one or several hours. Therefore, MTF is convenient as a (slow) first-dimension separation, but it cannot be applied as a (fast) second-dimension separation. In MTF SEC, 120 fractions of 40 µl each were collected using the two-way 10-port switching valve. These fractions were injected and analysed in real time on a fast SEC column. The same number of fractions was collected, irrespective of the first-dimension flow rate. The time used for collection and seconddimension separation was adapted to the first-dimension flow rate. By keeping the number of fractions and the second-dimension flow rate constant, we were able to directly compare the resulting chromatograms in terms of (MTF) resolution in relation to the hydrodynamic size (SEC retention volume) of the molecules. A sample of a star polymer, prepared by coupling anionically polymerized linear polystyrene [22], was used for our studies. Because the PS-precursors possess a very narrow molecular-weight distribution, the sample exhibits a nearly discrete relationship between molecular weight and topology (the number of branches connected to the coupling point in the molecule). The molecular weight of the PS-precursor was determined to be 1,250 kg/mol [15]. In the star synthesis of the star polymers, coupling was performed by reaction of the living ends of the precursor polymers with a trifunctional coupling agent. Besides a three-arm star molecule, some unreacted linear polymer remains and linear two-arm polymers are formed, as well as some higher order coupling products. The presence of a four-arm star was first demonstrated using onedimensional MTF with low-angle-light-scattering detection [15]. More details on the synthesis and composition of the star polymer can be found in the experimental section. Linear polymers with molar masses comparable to the coupling products of the precursor polymer were injected for reference purposes. Coupling of one, two or three precursor polymers (arms) used for the star-polymer sample would result in the peaks as observed in figure 2a, b and c if the MTF separation would be based solely on molecular weight. In the chromatogram of the star sample in Fig. 3a, which was obtained using identical experimental conditions, two peaks (1.60 and 2.68 ml) are observed at MTF elution volumes higher than any of the peaks observed in Fig. 2. The elution volumes corresponding to peak-maxima have been 78

81 Branched-Polymer Separations using Comprehensive 2D MTF SEC summarized in Table 1 for both dimensions. Because retention of branched molecules is expected to be higher in MTF, it can be tentatively concluded that the peak in Fig. 3a at V MTF = 1.6 ml is due to the three-arm star-shaped coupling product. Comparison of V SEC values suggests that the hydrodynamic size of the three-arm star is close to that of the linear polymer of 2,536 kg/mol. Both the increased retention in MTF and the decreased elution volume in size-exclusion chromatography compared to linear polymer of identical mass can be explained by branching. The last peak eluting in Fig. 3a is consistent with a higher order star as the peak has nearly the same SEC retention volume as the three-arm star, but is retained much longer in the MTF column. The probability of such products being formed decreases with increasing functionality, but the presence of a peak corresponding to the four-arm coupling product is clearly visible in Fig. 3a. At lower MTF flow rates the components of the star-polymer sample were better separated. This is illustrated in Fig. 3b and 3c where flow rates of 15 and 10 µl/min were used. At low flow rates the calibration curves in MTF become less steep (Fig.1 ) and branched components are retained much longer. Because of the very slow molecular diffusion of high molecular-weight polymers we do not anticipate increased band broadening at very low flow rates. Indeed, peak broadening is hardly affected by the long residence time in the MTF column (Fig. 3). Comparison of the peak widths in Fig. 3 with those of the linear polystyrene standards (with M w /M n ) in Fig. 2 shows that the peak widths of branched polymers are not significantly greater than those of narrowly distributed linear standards. The observed broadening may be due to the limited efficiency of the column. Furthermore, it is known that overloading occurs easily in HDC. Therefore, overloading may also be a threat when using MTF. The low porosity (ε = 0.3) of the column may well aggravate the loadability issues. To assess whether shear degradation was occurring in the system, polymer elution was studied as MTF flow rate was varied. It was speculated that at relatively high flow rates in MTF shear-induced degradation (i.e. chain scission) of the polymer could occur. Because even partial degradation of the polymer is likely to have a significant effect on the hydrodynamic-size distribution of the polymer, MTF SEC provides information on the likelihood of chain scission. Neither increase in SEC elution volume nor tailing in 79

82 Chapter 3 the SEC dimension towards lower molecular weights was observed as MTF flow rate was increased. Thus, polymer molecules do not appear to be shear degraded as a result of MTF separation. Shear degradation in the SEC separation has been addressed in the supporting information of this article. No significant evidence for shear degradation that might impair the integrity of MTF SEC was found. It is much more difficult to establish whether or not the polymer molecules are deformed during the MTF separation. If they are, it is likely that the molecules relax to their unperturbed shapes before they are analysed by SEC or characterized by light scattering. Table 1. Peak maxima in MTF and SEC for different first-dimension flow rates. MTF 20 µl/min MTF 15 µl/min MTF 10 µl/min V max (ml) MTF SEC MTF SEC MTF SEC 1,373 kg/mol ,536 kg/mol ,742 kg/mol arm linear polymer arm linear polymer arm star polymer > 3.5 > 3.5 Another example of the separation of a branched polymer is presented by the separation of a broadly distributed polystyrene (PDI = 3.3, see supplementary information) with random long-chain branching (LCB) in Fig. 4a. For a sample with a considerable degree of LCB (MTF flow rate 20 µl/min) a low-concentration tail towards higher MTF elution volume is observed which is considerably different from that of the three-arm star polymer sample. However, the star sample contained discrete populations of branched species which could be separated into discrete peaks in the MTF separation. On the other hand, the broadly distributed PS contains a nearly continuous distribution of branched components varying in the number of branch points and branch lengths. The fact that peaks in the MTF separation tail to larger elution volumes, while the SEC separation becomes constants, suggests that this distribution of branching may result in separation in the MTF direction. Elution of this material in the SEC dimension was compared to that of the linear polymers shown in Fig. 2. The peak maximum of the 80

83 Branched-Polymer Separations using Comprehensive 2D MTF SEC branched PS in SEC for an MTF elution volume of 1.24 ml was 1.47 ml. This is considerably different from the 1.35 ml and 1.31 ml that were found for linear polymer (table 1). Fig. 2. (left). Comprehensive two-dimensional MTF SEC of linear polystyrene standards with MTF at 20 µl/min. Nominal molecular weights (a) M p 1373 kg/mol, (b) 2536 kg/mol, (c) 3742 kg/mol, (a)/(b)/(c) kg/mol (internal-reference peak in top-left corner). Fig. 3. (right). Comprehensive two-dimensional MTF SEC of linear and star-branched polymers. (a) MTF at 20 µl/min, (b) MTF at 15 µl/min, (c) MTF at 10 µl/min. 81

84 Chapter 3 Fig. 4. Separations of a polystyrene sample with a broad MWD and a high degree of LCB (a) MTF SEC, (b) SEC SEC An important question is whether or not the samples are fully eluted from the MTF column (featuring sub-µm flow-through channels). Recovery may be negatively affected if the flow rate is decreased in order to increase resolution. At 15 µl/min the four-arm star polymer is no longer observed to elute within about five column volumes (Fig. 2b). The chromatograms in Fig. 2 were integrated over MTF volumes from 0.5 to 3.5 ml and SEC volumes from 1.15 to 1.7 ml. Compared to MTF performed at 20 µl/min, only 89% of the sample was eluted at 15 µl/min in the same retention window. For 10 µl/min this relative recovery drops to 80%. The sample that is not recovered is expected to elute after the elution window as a result of increased retention. The separation was not extended long enough to observe all the branched polymers at flow rates below 20 µl/min. Therefore, the run length was increased in subsequent experiments for recovery studies (Fig. 5a). Furthermore, these experiments were all performed at 20 µl/min. Fig. 5. Separations of the star-polymer sample (a) MTF SEC, (b) SEC SEC 82

85 Branched-Polymer Separations using Comprehensive 2D MTF SEC To assess absolute sample recovery in the MTF SEC system, the MTF column was replaced by a SEC column (V 0 = 1.2 ml; Fig. 4b and 5b). The experimental conditions were equal to those for MTF SEC, except that the first-dimension separation was run until only 1.5 times the total permeation volume had passed through the first-dimension SEC column. No polymer is expected to elute after this point. This showed that in the MTF SEC set-up linear polymers with high molecular weight (Fig. 2) and the LCB polystyrene (Fig. 4) were all recovered quantitatively (> 95%). The star polymer sample was recovered for 92% (average of triplicate MTF SEC measurements) when integrated over MTF volumes from 0.5 to 4.7 ml (Fig. 5a). When the integration was extended to a volume of 7.2 ml the recovery was also found to be quantitative (>95%). 3.4 Conclusions Molecular-topology fractionation (MTF) provides branching-selective separation. The technique can be used to separate molecules according to their degree of long-chain branching, but only for samples with extremely narrow molecular-weight distributions. In all other cases, the effect of branching on retention in MTF is confounded with the effect of molecular weight. A solution to this problem has been found by combining MTF and size-exclusion chromatography into a comprehensive two-dimensional separation system. This MTF SEC technique was used to clearly demonstrate the branching-selective separation obtained by MTF for a sample of (narrowly distributed) star-shaped polystyrenes. MTF SEC was also applied to a broadly distributed polystyrene sample that featured a high degree of long-chain branching (LCB). Although some selectivity was observed, the separation may need to be improved if we are to obtain quantitative measures for LCB. However, even in the present, immature state, the fractionation of LCB polymers may prove to be useful in predicting rheological properties of polymers. Only high-molecular-weight polymers were separated using MTF for this study. The range of applicability of MTF is limited to the range above the reversal molecular weight (M crit ), which in turn depends on the diameter of the flow-through-channels. Several improvements are foreseen in the near future. The presently used MTF column was packed with polydisperse particles. It is difficult to obtain such columns, let alone 83

86 Chapter 3 pack them reproducibly. Even the repeatability of nominally identical columns is poor. It is also difficult to use these columns to perform fundamental studies on MTF, because accurate information regarding the size of the inter-particle (flow-through) channels is cannot be obtained. Because it is difficult to accurately characterize the channel dimensions in these packed columns, the relationship of the former with elution behaviour is challenging to evaluate. Columns packed with mono-disperse particles are needed to sensibly compare hydrodynamic chromatography (HDC) and MTF. However, because the two techniques operate in different regimes of the aspect ratio (size of molecules compared with that of the flow channels) and because the effects of changes in the flow rate were found to be opposite, we believe that HDC and MTF are based on different separation mechanisms. Columns that are well packed with uniform submicron particles are also difficult to obtain. Monolithic stationary phases with wellcharacterized sub-micron flow-through pores may be a viable alternative. The use of such monolithic columns for MTF separations will be reported elsewhere. 3.5 Appendix MTF column parameters The column volume and efficiency were determined by injection of 5 µl of a 1000-ppm solution of ethylbenzene. At a flow rate of 20 µl/min THF and a column-oven temperature of 50 C ethylbenzene eluted at 38.1 minutes. Therefore, the MTF column volume (V 0 ) was 762 µl, the efficiency of the separation was 3400 plates per meter. The porosity of the packing was calculated by dividing the ethylbenzene elution volume by the theoretically calculated volume of the empty column (150 x 4.6 mm) and was ε = Characterization of long-chain-branched polystyrene sample The long-chain-branched (LCB) polystyrene sample was characterized using sizeexclusion chromatography (SEC) with multi-angle light scattering (MALS) and on-line viscometry detection. The SEC columns used were three mixed-b columns (300x7.5 mm each; 10-µm particles) from Polymer Labs (Church Stretton, UK). Stabilized THF 84

87 Branched-Polymer Separations using Comprehensive 2D MTF SEC (J.T. Baker, Deventer, The Netherlands) was used as the mobile phase at a flow rate of 1 ml/min. The weight-average molecular weight of the LCB polymer (measured by SEC-MALS) was 810 kg/mol with a polydispersity of PDI = 3.3. The presence of long-chain branching at high molecular weights is illustrated by the reduction in intrinsic viscosity in the Mark-Houwink plot in Fig. 1. Fig. S1. Mark-Houwink plot for the long-chain branched polystyrene used in this article and a linear reference polystyrene polymer. Verification of SEC at elevated flow rates SEC was performed at two and a half times the recommended flow rate in the MTF SEC experiment. The impact of separation at elevated flow rates was validated by performing SEC separations comparable to those in a two-dimensional experiment at the recommended and elevated flow rates. SEC was performed at 300 and 750 µl/min on a 150 mm x 4.6 mm I.D. column with 10-µm PLgel particles with a pore size of 10 6 Å. The porosity of the frits in this column was 5 µm. The mobile phase was non-stabilized tetrahydrofuran (Biosolve, Valkenswaard, The Netherlands) and separations were performed at 50 C. The injection volume was 5 µl of polymer solution. Four samples and one blank were injected in duplicate. Polystyrenes with peak molecular weights of 7,450, 3,742, 2,536 and 1,373 kg/mol (Polymer laboratories, Church Stretton, UK) were dissolved in tetrahydrofuran individually at a concentration of 0.1 mg/ml. The samples with 3,742, 2,536 and 1,373 85

88 Chapter 3 kg/mol polystyrene were all used with an additional 0.2 mg/ml of kg/mol polystyrene (reference standard). All four samples and the blank contained approximately 250 ppm butyl-hydroxylated toluene to prevent degradation by radicals. Detection was performed using a Spectroflow 757 (ABI, Ramsey, NJ, USA) UVabsorbance detector equipped with an 8-µl flow cell and set for detection at 260 nm. The chromatograms have been overlaid in Fig. S2. An x-axis multiplier was chosen to have this x-axis display the elution volume. Peak assignment for Fig. S2 from left to right: 7,450, 3,742, 2,536, 1,373 and kg/mol linear polystyrene, ionol, injectionsolvent related peak. Fig. S2. UV absorbance of high molecular weight polystyrenes at 750 µl/min (offset 0 mau) and 300 µl/min (offset 15 mau). Retention times are annotated in red for 7,450 kg/mol PS, ionol and an injectionsolvent related peak. For all high-molecular-weight PS polymers a shift towards higher elution volume is observed when separated at 750 µl/min. This shift is small compared to the separation of the individual standards and therefore has a small effect on the separation. The shift in elution volume may possibly be explained by the slow diffusion of high-molecularweight polymers, being responsible for incomplete inclusion of the polymer in the pores of the packing material. If any shear degradation were to occur, this would be expected to result in significant tailing and changes in the peak shape. Only the peak front of the 7,450 kg/mol appears to be deformed at 750 µl/min. Absolute molecular-weight determination techniques, such as low-angle laser light scattering, can be used to discriminate between poor chromatography or shear degradation. Because fast SEC is not used for absolute-molecular-weight determination, this discussion is beyond the 86

89 Branched-Polymer Separations using Comprehensive 2D MTF SEC scope of the present article. Based on the results in Fig. S2 we conclude that peak elution volumes for polystyrene polymers up to a molecular weight of 7,450 kg/mol may be used to compare hydrodynamic size parameters at 750 µl/min. under the conditions used for MTF SEC. References [1] T.H. Mourey, Int. J. Polym. Anal. Charact. 9 (2004) 97. [2] S. Pang, A. Rudin, in T. Provder (Editors), Chromatography of Polymers (ACS Symposium Series, No. 521), American Chemical Society, Washington, DC, 1993, p [3] K.D. Caldwell, in H.G. Barth, J.W. Mays (Editors), Modern Methods of Polymer Characterization, Wiley, New York, 1991, p [4] B.H. Zimm, W.H. Stockmayer, J. Chem. Phys. 17 (1949) [5] M. Gaborieau, J. Nicolas, M. Save, B. Charleux, J.-P. Vairon, R.G. Gilbert, P. Castignolles, J. Chromatogr. A 1190 (2008), 215. [6] P.M. Wood-Adams, J.M. Dealy, A.W. degroot, O.D. Redwine, Macromolecules 33 (2000) [7] P.J. Schoenmakers, P. Marriott, J. Beens, LC-GC Eur. 16 (2003) 335. [8] J.C. Giddings, J. Chromatogr. A 703 (1995) 3. [9] P.J. Schoenmakers, G. Vivó-Truyols, W.M.C. Decrop, J. Chromatogr. A 1120 (2006) 282. [10] X. Jiang, A. v.d. Horst, V. Lima, P.J. Schoenmakers, J. Chromatogr. A 1076 (2005) 51. [11] A. v.d. Horst, P.J. Schoenmakers, J. Chrom. A 1000 (2003) 693. [12] J. Gerber, W. Radke, Polymer 46 (2005) [13] K. Im, Y. Kim, T. Chang, K. Lee, N. Choi, J. Chromatogr. A 1103 (2006) 235. [14] D.M. Meunier, S.A. Baker, P.B. Smith, Macromolecules 38 (2005) [15] D.M. Meunier, T.M. Stokich Jr., D. Gillespie, P.B. Smith, Macromol. Symp. 257 (2007) 56. [16] R. Matmour, A. Lebreton, C. Tsitsilianis, I. Kallitsis, V. Héroguez, Y. Gnanou, Angew. Chem. Int. Ed. 44 (2005) 284. [17] J.L. Hahnfeld, W.C. Pike, D.E. Kirkpatrick, T.G. Bee, in R. Quirk (Editor), Applications of Anionic Polymerization Research (ACS Symposium Series, No. 696), American Chemical Society, Washinton, DC, 1996, p [18] E. Venema, J.C. Kraak, H. Poppe, R. Tijssen, J. Chromatogr. A 740 (1996) 159. [19] R. Tijssen, J. Bos, in F. Dondi, G. Guiochon (Editors), Theoretical Advancement in Chromatography and Related Separation Techniques, Kluwer, Dordrecht, 1992, p [20] G. Stegeman, R. Oostervink, J.C. Kraak, H. Poppe, K.K. Unger, J. Chromatogr. 506 (1990) 547. [21] G. Stegeman, J.C. Kraak, H. Poppe, R. Tijssen, J. Chromatogr. A 657 (1993) 283. [22] T. Altares Jr., D. P. Wyman, V. R. Allen, K. Meyersen, J. Polym. Sci., Part A : Polym. Chem. 3 (1965)

90

91 Chapter 4: Branched Polymers Characterized by Comprehensive Two-Dimensional Separations with Fully Orthogonal Mechanisms Abstract Polymer separations under non-conventional conditions have been explored to obtain a separation of long-chain branched polymers from linear polymers with identical hydrodynamic size. In separation media with very narrow flow-through channels (of the same order as the size of the analyte molecules in solution) the separation and the elution order of polymers are strongly affected by the flow rate. At low flow rates the largest polymers are eluted last. At high flow rates they are eluted first. By tuning the channel size and flow rate, conditions can be found were separation becomes independent of molar mass or size. Other differences between polymer molecules are revealed, such as the extent of long-chain branching. This type of separation is referred to as molecular-topology fractionation (MTF) at critical conditions. MTF involves partial deformation of polymer coils in solution. The increased coil density and resistance to deformation can explain the different retention behavior of branched molecules. Much higher efficiency and selectivity were obtained by MTF in columns than with traditional membrane fractionations. MTF in combination with size-exclusion chromatography (SEC) was applied for the separation of branched polymers. Branching selectivity was demonstrated for three- and four-arm star polystyrenes of 3 to g/mol molar mass. Baseline separation could be obtained between linear polymer, Y- shaped molecules, and X-shaped molecules in a single experiment at constant flow rate. For randomly branched polymers the branching selectivity inevitably results in an envelope of peaks, because it is not possible to fully resolve the huge numbers of different branched and linear polymers of varying molar mass. Separations performed by comprehensive two-dimensional MTF SEC revealed the presence of branched polymers that could not be discerned with one-dimensional SEC in combination with mass-selective detectors, such as light scattering or viscometry. 89

92 Chapter Introduction Branching that is accidentally or purposefully introduced in (high-molar-mass) polymers may be advantageous. Long chain branching in thermoplastics improves melt strength and flow, which allows for faster processing and unique applications [1]. Through the introduction of branching a favorable balance may be obtained between modulus (i.e. stress-strain relation), viscosity, and elongation behavior [2,3,4]. A major challenge up to this day remains the analysis of long-chain-branched (LCB) polymers, because a distribution of different topologies (or qualitative geometries ) [5,6] is confounded with a molar-mass distribution (MMD). In many polymer samples both linear molecules and molecules with various degrees of branching are present, depending on the polymerization conditions. Unequivocally demonstrating the properties of branched-polymeric materials can only be achieved by synthesis and physical testing of model compounds with well-described branching topologies [7]. Branching may also be introduced by post-synthesis blending of linear polymers with LCB molecules. Although the positive effects of branched polymers remain after blending with other polymers, no existing techniques can specifically characterize the properties of branched molecules. Recent theories on structure-property relationships for branched polymers emphasize the role of the intra-molecular structure [8]. For material characterization it is, therefore, important that polymers can be separated according to their structure and that molecules can be discriminated based on their topology. However, conventional polymer-analysis techniques cannot be used to perform such separations for LCB polymers. Separations by either branches or end groups based on interaction chromatography [9,10] may be possible for polymers of low to moderate molecular weight with chemically different end groups [11]. Highmolecular-weight short-chain-branched (SCB) polyolefins may also be analyzed with gradient liquid chromatography [12]. While spectroscopic techniques offer the best possibility to identify functional groups, they only provide information on population averages of the sample. Hyphenation of size-exclusion chromatography (SEC) with NMR or FTIR spectroscopy has been applied successfully to investigate distributions in terms of functionality [13] or SCB frequency [14]. Studying the extent of LCB using this approach is extremely difficult, because the low frequency of functional groups (i.e. branch points) would require an exceptional sensitivity and dynamic range [15]. 90

93 Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms Polymers of high molar mass and moderate to low degree of branching are typically separated based on their hydrodynamic size using SEC or field-flow fractionation (FFF), often followed by selective detection using on-line viscometry and/or light scattering [16,17]. Results for branched polymers are commonly reported as so-called contraction ratios based on radius of gyration (r g, Eq. 1, [18]) or intrinsic viscosity ([η], Eq. 2, [19]). g = r 2 g B 2 r g L M (1) g = [η] B [η] L M (2) where B refers to branched polymers and L to the linear-equivalent reference polymer and the subscript M indicates molecules of equal mass. LCB has a strong impact on the solution properties of macromolecules, such as the relation between hydrodynamic size, molar mass and intrinsic viscosity. Contraction ratios can be used to estimate the branching frequency and to obtain information on the topology [20] when information on polymer chemistry and linear reference polymers are available. This methodology has developed over the years into the most popular method for LCB analysis [21]. Nevertheless, the separation by SEC is based on the hydrodynamic size of the analyte molecules and is only indirectly related to branching and topology. This is a limitation and a source of errors inherent to this method. As in conventional SEC analysis, a significant bias may be accepted in practice, especially when comparing similar polymers (prepared by identical chemistries). Algorithms exist to estimate the branching frequency for tri- and tetra-functional branching based on the Zimm-Stockmayer theory [18], but failure to separate by topology prevents such an approach from successfully discriminating between branching functionality and frequency. The relationship between molar mass and size in solution is affected by the topology and this implies that a fraction of given size will be polydisperse when a branching distribution is present [22,23]. The ability to separate polymers according to their topology and degree of LCB would clearly benefit the characterization of branched polymers. Potentially interesting for this 91

94 Chapter 4 purpose are separations that exploit differences in what has been referred to [24] as polymer dynamics in solution. In this study the application of molecular-topology fractionation (MTF) [25,26] has been explored for the separation of branched polymers. This technique is based on the migration of polymers in dilute solution through chromatographic columns with very narrow flow channels. Unlike fractionation under conditions of strong confinement that require the coil to unwind (e.g. reptation), the separation is based on continuous migration of the coiled polymers. This renders MTF less sensitive to clogging of the pores. The size of the polymer in solution has an effect on MTF as well and, therefore, the separation by branching properties will be confounded with the molar-mass distribution. Therefore, comprehensive twodimensional MTF SEC (after nomenclature in [27]) separations were used to independently study the selectivities due to branching and due to hydrodynamic size [28]. In the present study key variables, such as the pore size and the flow rate, have been optimized in an attempt to obtain orthogonal separation mechanisms. Accurate information on the pore size will be used to provide a better definition of the MTF separation and predict its application range. Flow-rate gradients have been explored to enhance the applicability of the technique. 4.2 Theory Separation techniques based on size Polymers in dilute solution are present as coils. For ideal polymers behaving as perfect random-flight chains the time-averaged coil size scales with the square root of the molar mass. Deviations from this scaling law for real polymers are implied by limited flexibility in the backbone, excluded volume by the chain itself and solvent adsorbed by the coil due to enthalpic interactions [29,30]. A relation where size follows a power law of mass is often still valid across broad molar-mass ranges, provided that composition and structure of the polymer remain constant. The equilibrium size of polymers in solution provides a robust basis for SEC and HDC separations. Wall exclusion from the stationary-phase surface based on coil-size of dissolved polymers is the driving force in both separations (steric exclusion). In SEC smaller polymers selectively populate the stagnant volume in narrow pores by diffusion 92

95 Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms from adjacent convective channels [31,32]. In packed beds with porous particles the porous properties can be optimized to provide selective exclusion and convective transport takes place in the interstitial space between the particles. In HDC large polymers are excluded from the slow-moving solvent layers near the walls in convective pores [33,34,35]. Selectivity scales with the aspect-ratio (λ) that relates the size of the solute molecules (radius r) to the size of the flow-through channel (radius r c ) as λ = r / r c. Besides steric exclusion, which increases the migration rate for larger polymers, hydrodynamic interactions in convective flow will affect the polymer migration rate. For most flexible-chain polymers with M > 10 kg/mol the polymer coil behaves as if impermeable to flow (i.e. non-draining behavior) under the mild conditions of SEC or viscometry [16,36,37]. Friction in shear flow due to non-draining behavior of the analyte will generally result in retardation and counteract the exclusion effect at higher λ values [38,39,40]. Hydrodynamic interaction is specific to the conditions used and depends on both λ and absolute size. A detailed breakdown of hydrodynamic effects for polymers in shear flow has been provided by Tijssen et al. [41] and Stegeman et al. [42]. Migration in HDC can be described using Eq. 3 where migration rate (τ) is defined as residence time of the polymer (t p ) relative to the residence time of a flow marker (t m ) and expressed as a function of λ and a constant C describing hydrodynamic interaction. τ = t p t m = 1 1+2λ Cλ 2 (3) Deformation of polymers in solution Under HDC conditions shear stress on the solute may become significant and result in flow-rate-dependent elution behavior [42]. The effective size (r) may decrease when the molecules are subjected to shear stress above a certain threshold that may be related to the Deborah number (De) [24,43]. De is defined as the product of effective elongation (ε ) and the longest relaxation time of the polymer (τ rel ). The effect of elongation may become detectable in HDC for Deborah numbers exceeding 0.1, while for De > 0.5 severe elongation may occur. Separation in this latter domain does result in elution behavior that differs significantly from that of HDC and is referred to as slalom chromatography (SC) [44]. Deborah numbers can be calculated using either molar mass 93

96 Chapter 4 (Eq. 4) or radius of gyration (Eq. 5), depending on the experimental conditions and available data on the polymer [24,45]. De = ε τ rel = K deb ν d p 0.42 η s [η] M R T (4) De = ε τ rel = K deb ν 6.12 Φ η s r3 g d p R T (5) K deb is a constant related to the geometry of the pores (with a typical value of 6), ν is the superficial solvent velocity, d p the particle size of the packing, Φ the Flory-Fox parameter, η s the solvent viscosity, [η] the polymer intrinsic viscosity, r g the polymer radius of gyration, R the gas constant and T the absolute temperature. The Flory-Fox equation (Eq. 6) is used to transform Eq. 4 into Eq. 5. [η]m = 6 3/2 Φr g 3 (6) It is important to note that the Flory-Fox parameter is a measure of hydrodynamic interaction and depends on solvent conditions, molar mass and branching of the polymer. For example, values ranging from Φ = mol -1 for linear polymers to Φ = mol -1 for branched polymers have been observed, while at θ-conditions (indicated by the subscript 0) a value of Φ 0 = mol -1 is common [46,47]. When studying molecules of varying topology in good solvents we prefer to use Eq. 4, avoiding the assumptions inherent to Eq. 5. A problem with the application of Deborah numbers for branched polymers is in the treatment of polymer relaxation. The polymer relaxation τ rel (Eq. 7) is based on a model by Zimm for a chain of beads connected by ideal springs [48,49]. τ rel = C Z η s [η] M R T (7) The constant C Z corrects for hydrodynamic interaction (e.g. draining behavior) of the polymer. Branching and topology effects are not included in the model and correct treatment should therefore not be assumed. Notice that according to Eq. 7 relaxation for polymers with identical hydrodynamic volumes is identical. Linear and branched 94

97 Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms polymers in dilute solution can be expected to respond differently to stress. It is known that branching leads to increased segment density and reduced internal freedom of motion for random-coil polymers in solution [50,51]. The entropy decrease resulting from deformation of a branched molecule will be greater than that for the deformation of a linear polymer. Therefore, branched polymers are expected to deform less than linear polymers under identical stress. A size-dependent separation may then be applied to achieve branching selectivity, dependent on the level of stress on the molecules (i.e. on the flow rate). The aspect ratio and Deborah number provide convenient metrics to compare separation techniques based on size and dynamic properties of the polymers. In Fig. 1 techniques are indicated at λ and De values corresponding to typical operating conditions. Arrows in the insert indicate how λ and De values respond to changes in the separation conditions, such as increasing the flow rate and decreasing the particle size (d p ). Molar mass has an indirect effect on both λ and De through its impact on the radius. Ultrahigh-pressure SEC separations are by definition operated at higher flow rates and with smaller particles. Complex multi-mode separations result for samples with high molar mass [52]. Some uncertainty is introduced in the assessment of elongation for λ > 0.3 (shaded region in Fig. 1), because shear stress experienced by the polymer is no longer continuous and its elongation character is reduced. In Poiseuille flow shear stress will mainly affect the periphery of the coiled polymer with λ > 0.3 and rotation is largely prohibited. This situation no longer meets the assumptions in calculation of Deborah numbers i.e. steady elongation against relaxation of the entire coil, but it is expected that deformation as a result of shear forces will still occur. Hydrodynamic interaction of polymers is significant for λ > 0.3 and MTF separations can be obtained under these conditions. The upper limit of λ for MTF separations is not strictly defined. The dashed line in Fig.1 puts an approximate limit at λ = 1, but MTF separations with linear polymers up to λ = 2 have been performed. 95

98 Chapter 4 Fig. 1. Classification of separation techniques based on Deborah number and aspect ratio. Arrows in the insert indicate changes implied by variation of experimental conditions Reptation Separation techniques which are performed at conditions associated with MTF are reviewed for similarities that can explain the topology sensitivity obtained at different flow rates. Different mechanisms can be identified for polymer migration through strongly confining media i.e. λ > 1. Sieving, entropic-barrier transport, and reptation can be distinguished based on channel geometry and rigidity of the solute [53]. Random-coil polymers in dilute solution with equilibrium sizes larger than the flow-through channels through which they migrate will be continuously squeezed into a stretched conformation. This condition is most similar to the tube-like diffusion path of molecules as described in the theory of reptation [41,54]. This model finds its origin in the description of the rheological behavior of melted polymers, where it is used to describe motion, diffusion, and viscosity successfully [7,55]. Modifications to the theory have been described for polymers in dilute solution, specifically for the case of separating polymers by their degree of branching [56]. The barrier energy and critical flux required to overcome the osmotic pressure under strong and weak confinement was derived for ideal-star and randomly branched chains. Shortcomings of the theory impose serious 96

99 Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms limitations on its applicability for real chains. For critical-flux calculations the flow needed to overcome diffusion of a polymer segment is considered, while treating the molecule as free-draining (i.e. interaction of each polymer segment with flow is not affected by other segments in the molecule). Because non-draining conditions are more likely for real chains, shear inside the coil domain will be low, resulting in smaller drag forces on the chains in comparison with free-draining conditions. Thus, flow-induced migration through strongly confining pores, resulting in unwinding of the polymer and in molar-mass insensitivity for linear chains, will not take place for real polymers. It was later pointed out that the critical flux for linear and branched chains under strong confinement will be identical and cannot be used to achieve separation, because of the progressive nature of the drag force once the first segments of a chain have entered the pore [57]. In the weak-confinement case deformation and moderate stretching are considered for polymers in solution. Most theoretical work takes into account constriction by the pore walls alone, whereas for real polymers hydrodynamic interactions are present as well. The forces induced by solvent shear on the polymer contribute to deformation and can be controlled externally by adjusting the flow rate. Polycarbonate or mica filtration membranes prepared by fast-atom bombardment and track-etching have been used to study reptation of synthetic polymers. Flow-rate-dependent rejection of polymers with equilibrium dimensions close to or larger than the membrane pores has been described by Long and Anderson [58]. They confirmed that polymer migration through pores in a mica membrane at higher flow rates was due to deformation rather than degradation for the range 1 < λ < 2. Selective rejection of branched-polymers was considered in a follow-up article [59]. A greater rejection of comb and star polymers relative to linear polymers was attributed to deformability of the polymers. Unfortunately, the branched samples used in this study had different molecular weights and high dispersities. Challenges with membrane separations are the limited separation efficiency and low sample capacity (concentrations of 160 ppm w/w had to be used). It was observed that high concentrations (above the overlap limit) were needed for polymers with λ 1 to diffuse through the membrane when using osmotic pressure only [60,61]. Therefore concentration build-up on membranes in flow-driven separations may present a problem, because this would alter the migration behavior of the polymer [62]. The 97

100 Chapter 4 results obtained for flow-rate dependent polymer rejection are most relevant to the separations considered here, since the conditions and findings are in good agreement with the observations for molecular-topology fractionation (MTF) Calibration curves and separation of deformed-polymers The impact of polymer deformation on migration can be very different depending on the separation technique and corresponding conditions. Whether a useful separation may be obtained for polymers with different deformability is assessed by comparing the calibration curves as a function of polymer equilibrium size (Fig. 2). SEC (pore exclusion) and HDC (wall exclusion) separate non-deformed macromolecules and result in decreasing residence times for analyte molecules with increasing size. SEC by definition takes place in pores that are not subject to convective transport. Pores in stationary phases for SEC are typically smaller than the flow-through channels and may be optimized independently from the flow-through-channel size. The channel size (related to the particle diameter) may vary, but λ is generally below 0.1 for polymers separated by SEC. Modern phases offer both high porosity, which ensures a broad separation window (e.g. 0.5 < τ < 1), and a high mechanical strength, which allows separation at higher flow rates. In case high-molar-mass polymers are separated using small particles (i.e. small flow-through channels) λ may be high enough for a seamless transition into HDC to occur [63,64]. A continuous SEC-HDC separation is the result, with the largest polymers eluting first. However, if λ increases beyond about 0.35 a strong reversal of the HDC calibration curve is observed (Fig. 2). Unlike rigid particles, which will be significantly retarded for λ > 0.4, polymers will respond to shear stress either through deformation or degradation. Deformation is broadly defined and may comprise many effects, such as compression, elongation or increased flow draining of the coil periphery. In the MTF region (above λ 0.35; see Fig.2) the behavior of nonrigid polymers may be used to discriminate between different architectures. Deformation of polymers results in departure from the HDC calibration curve, which applies for rigid solutes, with λ corresponding to the non-deformed-polymer. All molecules will be deformed, but linear molecules more so than branched ones. The linear molecules, therefore, elute earlier (indicated by the gray horizontal arrows in Fig. 2). 98

101 Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms Fig. 2. Schematic calibration curves for SEC, HDC, MTF and SC. Arrows indicate the effect of flow-induced polymer deformation. Hydrodynamic interactions of polymers play an important role in flow-induced deformation. This is supported by the observation that linear polymers with equilibrium dimensions of the order of the channel size elute much faster at increased flow rates [65]. In the absence of deformation the polymer lags the solvent in its surrounding due to non-draining behavior (i.e. impermeability to flow). Especially in monoliths or packed beds with highly interconnected flow-through channels this results in τ > 1 for polymers with λ 1. At elevated flow rate τ = 0.7 was observed, which is possible only by depletion of the slower-moving solvent layers near the stationary phase surface (Fig. 3). The effect does not occur for smaller polymers that do not have sufficient hydrodynamic interaction relative to the fast internal relaxation, rotation and translational diffusion. Only for large polymers will a higher shear strain near the surface result in a higher internal stress, thereby making conformations that occupy this region unfavorable. To think of this effect as stress-induced diffusion or stress-induced deformation depends on whether or not migration of the entire coil perpendicular to the direction of flow is achieved. Separation due to stress-induced deformation is a moreaccurate description for the aspect ratios considered in MTF. 99

102 Chapter 4 Fig. 3. Stress-induced deformation presented schematically. (a) Deformation absent at low flow rate; (b) depletion of high-shear region near channel surface at high flow rate. Higher entropic elasticity of branched polymers was suggested as a qualitative explanation for topology selectivity. Different possible interpretations of polymer deformation prevent a more accurate description at this moment. Deformation may be explained as selective population of polymer conformations. After all, the spherical equilibrium dimensions represent the average of many instantaneous aspherical conformations at a time scale longer than the longest relaxation time of the polymer [66,67]. This supports the entropic nature of (stress-induced) deformation. Differences in flow permeability are reflected in the viscosity-shielding ratio [21], the Flory-Fox parameter, and ratios of viscosity radius and radius of gyration [16] in Poiseuille flow under traditional separation conditions. Most published work on deformation under flow conditions focuses on the coil-stretch transition in elongational flow. The shear-rate dependent coil-stretch transition for DNA was found to agree very well with predictions based on Brownian dynamics for random coils [68]. Experiments on polystyrene, however, demonstrated that the extended length under flow conditions did not exceed twice the radius of gyration and was generally lower than predicted [69,70]. Experimental evidence from light scattering and birefringence measurements on the absence of a coil-stretch transition for polystyrene were later suggested to be biased and not selective [68,71]. Furthermore, it was suggested that shear levels were simply too low for the polymers considered and the experiments therefore failed to provide conclusive results. 100

103 Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms In slalom chromatography (SC) coil-stretch transition interferes with the accelerated migration by wall-exclusion of the polymer. Stretched molecules are retarded in the tortuous interstitial space by frequent conformational changes and changes in flow direction through the stationary phase packing. In the SC region, the extent of deformation could potentially result in a different elution volume for linear and branched molecules. Successful application of SC is unlikely, because it is expected that the selectivity (length of the arrows in Fig. 2) is limited. Conditions where wallexclusion and slalom chromatography co-exist and their effects on migration cancel out do not exist. Instead it was observed that flow rate could be used to obtain coil-stretch transition for different molar masses in agreement with Deborah-number calculations. Once this transition was reached elution volumes increased quickly [52]. 4.3 Experimental Chemicals and materials The eluent for MTF and SEC separations was non-stabilized tetrahydrofuran (THF, HPLC-grade, Biosolve, Valkenswaard, The Netherlands). The eluent was degassed by purging with helium 5.0 (99.999% Praxair, Vlaardingen, The Netherlands). Sample polymers were dissolved in THF stabilized with 250 mg/l butyl-hydroxylated toluene to prevent degradation by radicals. Narrowly distributed linear polystyrene standards (Polymer Laboratories, Church Stretton, UK) with molar masses (M) between 1,990 and g/mol with polydispersity indices (PDI) no larger than 1.05 were used to study retention behaviour. These standards were dissolved at concentrations between 0.1 and 1 mg/ml. A nominal three-arm star (or Y-shaped) polystyrene sample was obtained from Polymer Source (Dorval, Canada) and used at a concentration of 1.0 mg/ml. Synthesis of the star polymer was by coupling of anionically polymerized arms with a tri-functional agent (α,α,α -trichloromesitylene). Analysis using SEC with light scattering and viscometry revealed an arm molar-mass of 1,250 kg/mol and a composition of 5% uncoupled precursor, 45% linear two-arm coupling product and a remainder of three-arm coupling product [26]. Suspected side products were a four-arm star polymer formed by lithium-halide exchange with all arms coupled in one functional centre (X-shaped) [72,73]. The concentration of this large-molecule fraction could not be determined quantitatively by SEC. 101

104 Chapter 4 Polystyrenes with broad molar-mass distributions were obtained from the Dow Chemical Company (Midland, MI, USA). Dow polystyrene 1683 (weight-average molar mass (M w ) 250 kg/mol, PDI 2.5) was used as a linear reference material. LCB polystyrene (M w 810 kg/mol, PDI 3.3, SEC-MALLS [28]) and low-lcb polystyrene (M w 310 kg/mol, PDI 5) were used for analysis of branched polymers. Long-chain branching at high-molar mass is confirmed by the reduced intrinsic viscosity in the Mark-Houwink plot (Fig. 7). The LCB polystyrenes were prepared by coupling of polystyryl anions with di- and tri-functional benzyl chlorides as published elsewhere [74]. Comb polystyrene (kindly donated by Dr. C. Fernyhough, University of Sheffield) has a backbone molar mass of around 200 kg/mol and approximately 30 randomly placed branches of 70 kg/mol. The synthesis technique of the comb polymer has been described in [75] Instrumentation and operating conditions HPLC experiments were performed on a Shimadzu LC system ( s Hertogenbosch, The Netherlands) consisting of a system-controller (SCL10a), two micro-pumps (LC10ADvp), a column oven (CTO7), autosampler (SIL9a), UV detector (SPD10AVvp) and right-angle laser light scattering (RALLS) detector model LD600 (Viscotek, Houston, TX, USA). UV detection was performed simultaneously at 260 nm and 214 nm. Modulation for comprehensive two-dimensional separation was performed with a VICI two-position 10-port valve (Valco, Schenkon, Switzerland) with a highspeed switching accessory and digital valve interface. The 10-port valve was plumbed for symmetrical dual-loop modulation [76]. From the moment of injection on the 1 D column, the 10-port valve was switched at regular intervals between 1 and 3 minutes in order to inject first-dimension effluent on the 2 D SEC column. Instrument control and data acquisition were achieved with ClassVP v7.4 build15 software (Shimadzu). Exported data were processed in Matlab v7.3 (The Mathworks, Natick, MA, USA) using in-house written software for data folding and visualization of two-dimensional colour plots. Triple-detection SEC was performed using the Shimadzu LC system plumbed for 1D chromatography. The detection array consisted of a UV detector (SPD10AVvp), RALLS detector (LD 600) and chip-based on-line viscometer (Polymer Laboratories / 102

105 Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms Micronit, Enschede, The Netherlands). Data acquisition and processing was performed with PLCirrus (Polymer Laboratories, v3.0) based on triple-detection SEC principles [1] Columns and experimental conditions Wide-bore columns (4.6-mm I.D.) were used for all separations. The sample volume injected on the 1 D column was between 5 and 25 μl. Monolithic columns with narrow macropore sizes were prepared in columns of 100, 150 and 250 mm length according to the procedure published previously [65]. Custom-made columns (Polymer Laboratories) were used for fast 2 D SEC. A 150-mm long column packed with 10-µm 10 6 Å PLgel particles (V 0 = 1.9 ml) was used at 750 µl/min. Two 100-mm long columns packed with 5-µm 10 5 Å PLgel particles were used in series only for the 2 D separation in HDC SEC at 600 µl/min. Chromatograms in the HDC SEC mode (Fig. 5, Fig. S-1) were acquired with two 150 mm 1 D monolithic column in series (V 0 = 3.1 ml) at 10 µl/min D chromatograms were obtained during a runtime of 480 minutes at 50 C. Flow-rate studies in MTF SEC (Fig. 6) were performed on a 250 mm monolithic 1 D column (V 0 = 2.6 ml) with D pore 126 nm and a 150 mm 10 6 Å 2 D column, with both columns operated at 40 C D chromatograms were obtained by injection of 30 µl 1 D effluent fractions at a modulation interval matched to the 1 D flow rate. MTF SEC at conditions with minimal molar mass selectivity (Fig. 7) was achieved using two 150 mm monolithic columns (D pore = 126 nm, 30 µl/min) and a 150 mm 10 6 Å 2 D column D chromatograms were obtained during a runtime of 120 minutes at 50 C. Light scattering was used in most 2D experiments. It allows for overlapped 2 D injections, because a solvent signal is not present. This is beneficial in experiments where higher 1 D flow rates are used and the time required to complete the 2 D separation is rate limiting. More second-dimension chromatograms can be obtained when using the RALLS signal. Triple-detection SEC was performed at room temperature with a flow rate of 0.3 ml/min. A set of two minimix B (10-µm particles) and one minimix C (5-µm particles) columns (each 250 mm long) was used. 103

106 Chapter Results and discussion Flow-rate effect for columns with different pore size Monolithic columns with well-controlled macropore sizes were prepared by in-situ polymerization of polystyrene and divinylbenzene. In thermodynamically favorable or good solvents, such as tetrahydrofuran for polystyrene, polymers readily dissolve and can be separated free from enthalpic interaction with the column. The selectivity for hydrodynamic separations on monolithic columns has been studied for linear polymers [65]. A flow-rate effect on migration rate was observed and stress-induced diffusion (SID) was presented as the mechanism responsible for this effect when separating synthetic polymers in macropores close to unperturbed-polymer dimensions. The hypothesis of SID playing an important role in MTF separations will be tested with the results obtained in this work on branched-polymer separations. After presenting the results we provide a detailed discussion on the mechanism. Channel dimensions of the columns used in the present work have been optimized for MTF separation. Separation by a HDC mechanism according to unperturbed-polymer dimensions was obtained at low flow rates. This is demonstrated by the calibration curves obtained with narrow-molar-mass polystyrenes for columns with pore sizes (D pore ) ranging from 160 nm down to 75 nm (Fig. 4, Table 1). At 20 µl/min reversal of the calibration curve is observed for high molar masses. This is in agreement with HDC separation of rigid solutes (solid spheres) where hydrodynamic interaction at λ > 0.4 will reduce the migration rate. The retardation for high- molar-mass polymers is generally reduced when the flow rate is increased to 50 µl/min. This was also observed for micro-porous membranes where the rejection of large polymers decreased at higher flow rates [58]. Calibration curves in Fig. 4 indicate that only the hydrodynamic effects for λ approaching 1 are affected, because the selectivity for molecular weights below the point of reversal is maintained. Wall exclusion-effects and coil dimensions that induce these effects apparently have not changed for polymers below the reversal molar mass. Under certain conditions the molar-mass selectivity diminishes above the reversal point. Hydrodynamic interactions and calibration-curve reversal depend on the aspect ratio λ, rather than on the molar mass. Thus, we should preferably speak of a reversal (or critical) size. In practice, we may refer to a critical molar mass. In the present case 104

107 Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms this is a linear-polystyrene-equivalent molar mass. The effective radius for wallexclusion separations [77] is used in calculating λ and is given in Eq. 8 for polystyrene in THF [78]. r eff = π 2 r g = π M0.600 (8) In MTF experiments it has been observed that branched polymers are retained longer than linear polymers for λ > 0.4 [41,28]. At optimized experimental conditions a separation may then be performed where linear polymers above a critical molar mass co-elute, while branched materials elute later from the column and co-elute with linear polymers of lower molecular weight. In a comprehensive MTF SEC separation the coeluting species can be separated and distributions in terms of hydrodynamic size and branching will be obtained. Monolithic columns with three different flow-through-pore sizes were considered for MTF in MTF SEC separations. Small pores are required to obtain λ values high enough to allow MTF separations of polymers below 1000 kg/mol. A special test was designed to establish the molecular weight at the point of reversal in the calibration curve. Broad-MWD polystyrene was analyzed in a comprehensive two-dimensional separation with the monolith in the first dimension ( 1 D) and a regular SEC column in the second dimension ( 2 D). Separation in the HDC SEC-mode was obtained for monolith 7 (see Table 3) with D pore = 126 nm at a flow rate of 10 µl/min (Fig. 5). The ionol peak originating from the sample solvent marks the void volume in both the 1 st and 2 nd dimensions at τ = 1.00 and V sec = 2.4 ml, respectively. The earliest eluting polymeric material from the monolith (τ = 0.69) was used to determine the critical molar mass of reversal. M crit, (Table 1) is the peak molar mass in the 2 D SEC separation of the first fraction containing polymer. Two-dimensional separations for monolith 8 and 9, as well as the calibration curve for the 2 D SEC separation are presented in section of the Appendix. Calibration-curve reversal for separation at 10 µl/min occurs at roughly identical values of λ (Table 1), which are very close to the expected value of 0.37 based on the Dimarzio-Guttman retention model for HDC of unperturbed polymers (Eq. 3 with C = 2.7). 105

108 Chapter 4 Fig. 4. Calibration curves for narrow polystyrene standards obtained on monoliths at 20 µl/min (a) and 50µL/min (b). 106

109 Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms Fig. 5. Calibration plot obtained by MTF SEC for a broad standard 1 F = 10 µl/min (PS1683; M w = 250 kg/mol, PDI = 2.5) using monolith 7 in the first dimension. Table 1. Reversal molar masses for monoliths determined by HDC SEC at 10 µl/min. Monolithic ID D pore (nm) M crit (kg/mol) λ [700]* [0.4]* *Approximate values obtained from calibration curve at 20 µl/min Comprehensive-two-dimensional chromatography is highly useful for exploring the migration behavior in MTF. Not only does it provide more information than a calibration curve based on the injection of narrow-mwd standards, it also allows the characterization of samples with a high polydispersity. The 2D chromatogram gives a qualitative impression of the calibration curve in a single experiment (Fig. 5). Therefore, the flow-rate effect was examined by MTF SEC with 1 D flow rates ( 1 F) between 10 and 75 µl/min. A shorter 2 D column with packing optimized for separation of large polymers was used (supplementary information, S2). Linear polymers with molecular weights above M crit were separated on a monolith with D pore = 126 nm at 10 µl/min (Fig. 6a) and at 30 µl/min (Fig. 6b). A sample of three polystyrene standards of , and g/mol was used, which for this monolith corresponds to aspect ratios in the range 0.80 < λ < Higher flow rates result in a transition from 107

110 Chapter 4 polymers separated under equilibrium conditions (HDC) to polymers separated in a deformed state (MTF) (Fig. 6, Fig. S-4). The three peaks corresponding to the narrow standards merge into a single peak in 1 D and molecular-weight independence is achieved for these high-molecular-weight materials. For the monolith with D pore = 126 nm a flow rate of 1 F = 30 µl/min was used in subsequent experiments to suppress the molar-mass selectivity. A similar suppression of molar-mass selectivity above M crit was obtained with a D pore = 104 nm monolith, but at a higher flow rate. In 2D experiments with this column (L = 100 mm) the lowest degree of molar-mass selectivity was obtained for 1 F = 50 µl/min (Fig. S-6). The calibration curves in Fig. 4b confirm this trend, but do reveal little retention above M crit. The small 1 D column volume is limiting the number of 2 D chromatograms and thus the resolution of the 2D experiment. However, the use of long columns with narrow pores is experimentally challenging. The pressure drop that is required for operating longer monolithic columns with D pore = 104 nm or smaller is so high as to cause irreversible damage by compression of the stationary phase. Additional results on MTF SEC at various flow rates for both column types are presented in the supplementary information, section S3. Fig. 6. A mixture of three narrow-mmd polystyrenes separated on an MTF column with D pore = 126 nm at different flow rates. (a) 10 µl/min (b) 30 µl/min Branched-polymer separations Conditions for MTF separation with minimal molar-mass selectivity for linear polymers above M crit were established. Branched polymers with different topology were analyzed at those conditions using MTF SEC to assess branching-selectivity in MTF (Fig. 7). A linear reference prepared by mixing Dow1683 with the narrow standards from Fig. 6 was used to cover a wide molar-mass range. Only little retardation for the highest 108

111 Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms molar-mass polymers was observed in Fig. 7a. Such small difference may be the result of inaccuracy of the flow or the porous properties of the column (similar columns were used, see section 4.3.3). Star-branched polystyrene prepared by coupling of 1250 kg/mol linear arms was mixed with the linear reference. Base-line separation of the 3- arm (Y-shaped) and 4-arm (X-shaped) branched coupling products from the linear materials is obtained (Fig.7b). The linear 2-arm coupling product and single arm polystyrene elute together with the linear materials. The 4-arm star, which is a byproduct from the coupling reaction, is base-line separated from the 3-arm star. This separation provides a dramatic demonstration of the separation of high molar-mass, branched polymers with only a single branching point from linear polymers with a broad range in molar mass and hydrodynamic size. An overview of the elution volumes in both dimensions is given in Table 2. Calibration of the 2 D separation with linear polymers was used to calculate λ values for the branched material eluting from the MTF column (supplementary information, S2). Retardation of polymers with higher branching frequency was observed already at smaller hydrodynamic size relative to long-chain branched (LCB) star polymer. Random long-chain branched material (LCB PS, Fig. 7c) and a comb polymer with controlled long-chain branching (Fig. 7d) were separated at the same conditions as those used in Fig.7a and 7b. The results of analyses by SEC with triple detection are provided in Fig. 8 for reference. For both the separations of LCB PS and Comb polymers by MTF SEC a tail is observed in the MTF direction. This is the expected result for the LCB PS, because here the degree of branching increases with molecular weight. In case of the comb the tail may reflect a cross-linking byproduct of the synthesis. The comb itself (V MTF = 2.48 ml) is hardly retained, most likely because its aspect ratio (λ) is too low for significant hydrodynamic interactions to occur. In the UV chromatogram a small amount of polystyrene with a smaller hydrodynamic size than the bulk of the sample can also be observed (Fig. S-7). This material is not separated from the bulk in the 2 D SEC separation or in the triple-detection analysis. Most likely this is a uncoupled linear precursor that has remained in the comb sample as a side-product. 109

112 Chapter 4 The branched materials retarded in MTF have different hydrodynamic sizes depending on their topology. In Fig. 9 an overlay with 2 D-SEC peak maxima from Fig. 7 is presented on top of the linear reference polymer. LCB and comb polymers start to be retained at lower hydrodynamic sizes than the star polymers. This implies that stressinduced deformation effects are less effective in counteracting the hydrodynamic effects for polymers with higher degree of branching. A plausible explanation is that polymers with higher segment density are less susceptible to deformation. Segment density in solution is inversely related to intrinsic viscosity, which is given in Fig. 8. Lower intrinsic viscosity for polymers above log M = 6 correlates well with the lower λ for material retarded in MTF (Table 2) Selectivity for branched polymers A better look at the separation conditions is needed to understand the separation selectivity for branched polymers. We will assume that polymers with higher segment densities than linear polymer will deform to a lesser extent under stress and, therefore, resemble HDC behaviour. Material eluting later than linear polymers above M crit at λ > 0.4 will have a higher segment density and/or a larger hydrodynamic size. In the case of 3- and 4-arm star polymers the elution is affected by segment density only, because hydrodynamic size (e.g. λ) is identical. For the randomly branched LCB polymer branching and hydrodynamic size both increase, indicating that molar mass increases for material eluting later from the MTF column. However, when segment density is too high to allow for deformation and hydrodynamic size is large then polymers may elute very late or not at all. The tail for both LCB and comb polystyrene is indicative of very dense polymer (possibly crosslinked) that is not completely eluting. Applicability of the present separation conditions is limited to conditions that allow polymers to elute from the MTF column within reasonable time. This may be achieved by using MTF columns with pore size matched to polymers of interest or by changing the conditions to make also more dense polymers at higher λ elute. While material eluting slowly from the MTF column can be explained as material with exceptional high coil density, it can also be argued that this is the result of polymer degradation. The light-scattering signal from RALLS divided by a concentration signal (UV) was used to estimate molar-mass changes for material eluting from the MTF 110

113 Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms column. High angular dependence of the RALLS signal makes it impossible to quantitatively compare LS/UV ratios without correction for angular dependence, which strongly depends on polymer size. However, it is possible to use the LS/UV ratio for a qualitative comparison when dealing with polymers of identical size (e.g. eluting at identical 2 t r ). The LS/UV ratio for polymers in Fig. 7 is presented in Fig. S-7. In all cases material eluting later from the MTF column was found to have a higher LS/UV ratio, which is indicative of higher molar mass. MTF SEC-MALLS was performed to obtain accurate molar mass following the separation of LCB PS on the monolithic column with D pore = 104 nm (Supplementary Information, S5). The gradual increase in molar mass was confirmed and material up to the highest mass present in this polymer as measured in Fig. 8 was found back in fractions eluting later from the MTF column. Fig. 7. 2D Chromatograms of polystyrene polymers separated by MTF SEC with 1 F 30 µl/min. (a) Linear polymers kg/mol; (b) linear and star polymers; (c) LCB PS; (d) comb PS. 111

114 Chapter 4 Table 2. Elution volume and aspect ratio for polymers of different topology in MTF SEC (V 0,MTF = 3.1 ml). MTF SEC MTF linear reference V max (ml) τ V max (ml) λ τ 3-arm star arm star LCB Comb Fig. 8. Mark-Houwink plot of linear and branched polystyrene samples. Dow PS1683 (1), star [26] (2), low-lcb PS (3), LCB PS (4), comb (5). 112

115 Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms Fig. 9. Linear polymer separated by MTF SEC; overlay of peak maxima in 2 D light-scattering signal for star (+), LCB (o) and comb (x) polymers Effect of flow rate on migration of branched polymers The flow rate applied in MTF separation can be used to change migration behavior for branched polymers in a similar way as it was used to obtain molecular-weight independent elution for linear polymers. MTF SEC experiments were performed with MTF flow rates up to 75 µl/min on the star polymer and two LCB polymers with different degrees of branching (Supplementary information, S6). At 75 µl/min the star polymer and the polymer with a low degree of LCB could be completely eluted within a single column volume. These results support that flow rate can be used to control migration rates for both linear and branched polymers and influence their recovery. Only polystyrene with material that is highly branched or even cross-linked did not readily elute at these conditions. Polymers with a low degree of branching are not well separated in the MTF separation at higher flow rates. In order to obtain good separation for materials subject to much different extent of retardation on the MTF column a flow-rate gradient may be applied. It was observed in experiments at constant flow rate that little separation was obtained for polymers eluting after the column void volume (V 0 ). An MTF SEC experiment was performed in which the flow rate was increased gradually from 10 µl/min to 20 µl/min between 150 and 250 minutes or once the elution volume approached V 0 (Fig. 10). A 113

116 Chapter 4 complete separation resulted, in which well-resolved peaks were observed for the single-arm precursor up to the 4-arm star. Even a high molar-mass coupling product can be discerned, which has a slightly smaller hydrodynamic size. The elution of highlybranched materials with a smaller hydrodynamic size than earlier eluting material was also observed in constant flow rate experiments for three-arm star polymer (Fig. S-9) and LCB polystyrene (Fig. S-10). Fig. 10. MTF SEC separation of star-polymer sample using a flow-rate gradient; (1) unreacted single-arm polymer (2) two-arm linear coupling product (3) 3-arm star polymer (4) 4-arm star polymer (5) higher coupling product. The star polymer separated in Fig. 10 could even be fractionated by topology in a 1D- MTF experiment. Such a separation is unlikely for other branched polymers under the conditions used for this separation, because linear and branched polymers may co-elute as a result of the low flow rate. Operating at conditions with minimal selectivity for linear polymers provides the most powerful application. The optimal experiment would therefore start at conditions with minimal selectivity for linear chains. Once linear materials have eluted the flow rate may be ramped up to elute branched material with higher segment density from the column. 114

117 Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms Effect of temperature on migration of polymers in MTF The effect of flow rate on selectivity in MTF is very clear and can be understood. It provides direct control over the levels of shear and stress that polymers in solution are subjected to. Temperature as a parameter to control deformation was not considered in detail, but it may certainly be used for this purpose considering the low speed of separation. Higher temperatures induce faster polymer relaxation (τ rel, eq. 7) through faster Brownian motion and lower solvent viscosity. The migration of polymer above M crit will be slower at higher temperatures because of less deformation. This trend was confirmed in a comparison of linear and star polymers separated at both 50 C and room temperature. However, the effect of temperature on retention proved rather small, even at low flow rates (Supplementary section S7). Great changes in polymer relaxation times cannot be achieved within the limits of practical separation conditions. Flow rate is a more effective parameter, exerting a greater effect on migration and selectivity. 4.5 Conclusions Molecular-topology fractionation (MTF) is a term used to denote separations of branched and linear polymers as a result of selective deformation. MTF separations combine characteristics of HDC and reptation. Polymers were separated on monolithic column with flow-through channels only slightly larger than the polymer itself. At such conditions polymer molecules experience strong hydrodynamic interactions, resulting in deformation and increased migration rates. MTF separations were used successfully to fractionate polymers by their topology in a comprehensive two-dimensional separation with size-exclusion chromatography (SEC) in the second dimension (MTF SEC). Selectivity based on topology is introduced through faster relaxation of branched polymers subject to shear deformation. At optimized conditions the effects of hydrodynamic interaction and deformation for linear polymers compensate for each other. Such conditions allows for an orthogonal separation of polymers by their hydrodynamic size and branching properties above M crit. Branched polystyrenes with λ between 0.4 and 0.9 were separated from linear polymers with identical hydrodynamic size. A relation was observed between the aspect ratio of branched polymers retarded in MTF and coil density in solution. The absence of migration effects resulting from polymer properties other than topology with an effect 115

118 Chapter 4 on coil density was not rigorously validated in this study. It would be interesting to assess the impact of chemical composition and short-chain branching on migration for application of MTF to polyolefins and polar synthetic polymers. Several results support the hypothesis of molecular relaxation as the decisive property for selectivity in MTF, such as increased retention above M crit at higher temperature or the higher flow rates needed for molar-mass-independent elution from monoliths with narrower flow-through channels. MTF SEC was used to investigate MTF separations preferably on long 1 D columns for better separation efficiency. Lengthy experiments were the result and comprehensive on-line coupling with SEC proved impossible without a significant sacrifice in terms of separation efficiency. For practical purposes off-line fractionation may be used once the separation conditions are known [26]. A simple SEC-MTF experiment with MTF performed at conditions with minimal molar mass selectivity above M crit can be used for a fast and inexpensive screening for branched material. In another approach a short MTF column may be used to obtain the fraction with branched material and linear molecules below M crit. A high-resolution SEC experiment with selective detection may than be used to characterize only the branched material free from co-eluting linear material. A challenge for the application of MTF is still the lack of commercially available stationary phases with suitable flow-through-channel dimensions. High diffusion and fast relaxation of synthetic polymers require an aspect ratio (λ) close to unity for branched molecules. Extension of deformation-selective separation of branched polymers towards either larger polymers or polymers with longer relaxation times may be possible even when using commercially available HDC columns. Starches and biopolymers may satisfy this criterion and provide interesting cases [79]. 116

119 Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms 4.6 Appendix Comprehensive HDC SEC experiment Monolithic columns with different pore sizes were used to obtain chromatograms at identical conditions (see Table 1). The chromatograms obtained using each monolith in the first dimension for HDC SEC are presented in Fig. S-1. Fig. S-1. HDC SEC performed with 1D monolithic phases 7 (a), 8 (b) and 9 (c). The sample was 0.8 mg/ml PS mg/ml 2MDa narrow-standard PS in THF. Two 100 mm 4.6 mm I.D. column packed with 5-µm 10 5 Å PLgel were used in the second dimension. Accurate molar-mass calibration was performed by injection of four mixtures, each with three narrow-mmd PS standards. Calibration samples were injected at 30 min intervals with 1 F = 10 µl/min. Elution volumes corresponding to peak maxima were used to construct a third order polynomial fit (Fig. S-2). This calibration data were used to calculate M crit for each monolithic phase (Table 1). (b) 7 y = -2.5x x x log M 5 4 Fig. S-2. Narrow MMD PS standards separated using HDC SEC (a) and calibration of the second-dimension SEC separation (b) Elution volume (ml) 117

120 Chapter Second-dimension calibration for MTF SEC For MTF SEC experiments a 2 D column with a high exclusion limit (10-µm 10 6 Å PLgel particles, mm I.D.) was used to prevent overloading and anomalouselution behavior in the 2 D-SEC separation. Accurate molar-mass calibration was performed by injection of four mixtures, each with three narrow-mmd PS standards. Peak maxima from the UV signal were used to construct the calibration curve (Fig. S- 3). The polynomial equation fitted to the calibration curve was used to calculate polymer size corresponding to each elution volume in order to calculate λ values (Eq. 8 / Table 2). (b) 7 6 y = -251x 5 + 1,897x 4-5,720x 3 + 8,597x 2-6,443x + 1,933 log M Elution volume (ml) Fig. S-3. Calibration experiment and calibration curve for second-dimension of MTF SEC separations Flow-rate effect in MTF SEC The transition from an HDC to an MTF-type separation at critical conditions is demonstrated in Fig. S-4 using a comprehensive two-dimensional experiment. Linear and star-branched polymers were separated on a 250-mm long monolithic column with D pore = 126 nm at 10, 15, 20 and 30 µl/min (Fig. S-4). A sample containing three linear polystyrene standards of , and g/mol was used, as well as a nominal three-arm star (or Y-shaped) polystyrene sample obtained from Polymer Source (Dorval, Canada; see section 4.3.1). A particularly challenging aspect of studies into flow-rate effects is the transfer of all 1 D effluent to the 2 D separation. The flow rate and injected amount in the 2 D were kept identical to maximize the comparability. 200 Injections of 30 µl each were transferred to the 2 D in all chromatograms, irrespective of the 1 D flow. 118

121 Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms For the chromatogram with 1 F = 30 µl/min only one minute is available for each 2 D chromatogram. An experimental problem is the overlap or wrap-around in the UV signal for these short sampling intervals. Signals near the void volume of the 2 D column interfere with the high-molar-mass peaks in the subsequent 2 D chromatogram. Fig. S-4. Transition of the 1D separation mode from HDC to MTF. Linear polymer at 10 (a), 15 (b), 20 (c) and 30 µl/min 1 F (d); three-arm star polymer at 10 (e), 15 (f), 20 (g) and 30 µl/min 1 F (h). Experiments were performed with RALLS detection using 150 mm 1 D columns to study selectivity at higher flow rates for linear polymers. The sample was a mixture of nine narrow-mmd linear PS standards in the range kg/mol. Separations on monolithic material 7 were performed with 1 F between 75 and 10 µl/min (Fig. S-5). A 1 D flow rate higher than 33 µl/min does not significantly change the selectivity or bring additional advantages other than analysis-time reduction. Such high flow rates are not practical for comprehensive 2D separations, because adjustments to the second dimension are required to deal with the larger 1 D flow. These will result in either a reduced separation efficiency or a lower sensitivity. For 1 F of 50 and 75 µl/min part of the 1D effluent is lost between 2 D injections. 119

122 Chapter 4 Fig. S-5. Flow-rate effect for linear polystyrene on a mm I.D. monolith with D pore = 126 nm. 1 F = 75 (a), 50 (b), 33 (c), 22 (d), 15(e) and 10 (f) µl/min. Flow-rate effects were also investigated for a 100 mm monolith with smaller pores (Fig. S-6). Molar-mass selectivity can be suppressed at comparable or slightly higher flow rates relative to a D p = 126 nm monolith. At a flow rate in between 33 and 50 µl/min a separation can be obtained with minimal molar-mass selectivity. The narrow-pores of this monolith induced higher operating pressures. A backpressure of 13 MPa was measured for separation at 50 µl/min with THF at 50 C. 120

123 Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms Fig. S-6. Flow-rate effect for linear polystyrene on a mm I.D. monolith with D pore = 104 nm. 1 F = 50 (a), 33 (b), 22 (c), 15 (d), and 10 (e) µl/min MTF SEC at orthogonal conditions All detector signals for the separations shown in Fig. 7 (see section 4.4.3) are presented in Fig. S-7. The detector array consisted of a Shimadzu dual-wavelength UV detector and a Viscotek right-angle laser light scattering (RALLS) detector coupled in series. In the bottom row the light-scattering signal divided by the UV absorption signal at 214 nm is presented to give an indication of changes in molar mass. The angular dependence for 90 light scattering is significant for the polymers considered here. Regardless of the reduced scattering intensity for large solutes, the signal is most sensitive for high molarmass polymers. A comparison of the LS/UV ratio at identical 2 t r yields a qualitative indication of molar-mass changes. The ratio is sensitive to inter-detector delay and inter-detector band broadening. 121

124 Chapter 4 Fig. S-7. Polystyrene separated by MTF SEC at 30 µl/min; consecutive detector signals from top to bottom: UV 260nm, UV 214nm, 90 light scattering and light scattering / UV 214nm ratio (indicated near color bar). (a) linear polymers (b) linear and star polymers (c) LCB polymer M w 810 kg/mol (d) comb polymer 122

125 Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms MTF SEC-UV/MALLS on long-chain-branched polystyrene An experiment was performed where the RALLS detector in the MTF SEC- UV/RALLS setup was replaced by a MALLS detector. For the 1 D a 150 mm 4.6 mm I.D. column with D pore = 104 nm monolith (monolith 8) was used with 1 F = 30µL/min. The 2 D was identical to other MTF SEC experiments (150 mm 4.6 mm I.D. 10 µm 10 6 PLgel with 2 F = 750 µl/min). 25 µl of 1 mg/ml LCBps were injected. Fractions of 90 µl each were transferred to the 2 D separation. Results of this experiment are presented in Fig. S-8. (c) 7 1.0x10 Molar Mass vs. Volume LCBps_03 LCBps_04 LCBps_05 LCBps_06 LCBps_07 LCBps_08 LCBps_09 LCBps_10 Molar Mass (g/mol) 6 1.0x x x Volume (ml) Fig. S-8. 2D plots for UV absorption (a) and the 90 light-scattering signal (b), as well as molar mass for MTF fractions from the MTF SEC-UV/MALLS experiment between 1.1 and 1.9 ml in the 1 D (c). 123

126 Chapter 4 The signal from the MALLS detector was sufficient to calculate molar-masses, but not for calculating R g. Therefore, a conformation plot with results of the different fractions could not be created. The increase in molar mass for materials eluting at the same hydrodynamic volume (in the 2 D) supports the hypothesis that material eluting later from the MTF column has an increasing degree of branching Selectivity in MTF as a function of flow rate MTF SEC Experiments were performed with linear (Fig. S-5) and branched polymers (Fig. S-9 through Fig. S-11) at different 1 D flow rates. A 150 mm 4.6 mm I.D. column with D pore 126nm with V 0 = 1.65 ml was used. Experimental conditions are presented in Table S-1. Red +++ was added as a marker for 2 D-peak maxima to 2D chromatograms of branched samples as a visual aid to help establish whether material is still eluting from the 1 D column. Fig. S-9. Star polymer separated at different flow rates in 1 D MTF. 75 (a), 50 (b), 33 (c), 22 (d), 15(e) and 10 µl/min (f) 124

127 Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms Fig. S-10. LCB Polymer separated at different flow rates in 1 D MTF. 75 (a), 50 (b), 33 (c), 22 (d), 15(e) and 10 µl/min (f). Fig. S-11. Polymer with little LCB separated at different flow rates in 1 D MTF. 75 (a), 50 (b), 33 (c), 22 (d), 15(e) and 10 µl/min (f). A problem with the 2 D pump prevented completion of the experiment at 10 µl/min (f). 125

128 Chapter 4 Table S-1.: Experimental conditions for the separations in Fig. S-9, S-10 and S D flowrate (µl/min) 2 D time (min) 2D injection volume (µl) Total time min. ( 2 D chromatograms) Total volume 1 D (ml) * 80 (60) * 120 (90) (135) (200) (200) (200) 6 * Incomplete sampling is expected due to the use of 45 µl transfer loops Effect of temperature on MTF SEC separations Separations of linear and star-branched polystyrene polymers by MTF SEC were performed under identical conditions, but at room temperature and 50 C different temperatures. For the 1 D a 100 mm 4.6 mm I.D. column with D pore = 104 nm (monolith 8) was used with 1 F = 10 µl/min. The 2 D was a 250 mm 4.6 mm I.D., 10 µm Mini-mixed B column with 2 F = 600 µl/min. 25 µl of sample solution were injected. 60 Consecutive fractions of 50 µl were transferred to the 2 D. 2D Chromatograms of the separations are provided in Fig. 12 and Fig. 13. Dimensionless elution volume (τ) is provided for a convenient comparison of elution volumes in the first-dimension (table S-2) and the second-dimension (table S-3). Table S-2.: First-dimension temperature dependence of polymer separations in Fig. S-12 and S-13 Elution volume MTF (ml) τ MTF Label Sample 25 C 50 C 25 C 50 C 1 ionol kg/mol PS kg/mol PS kg/mol PS ionol arm linear PS arm Star PS

129 Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms Table S-3.: Second-dimension temperature dependence of polymer separations in Fig. S-12 and S-13 Elution volume SEC (ml) τ SEC Label Sample 25 C 50 C 25 C 50 C 1 ionol kg/mol PS kg/mol PS kg/mol PS ionol arm linear PS arm Star PS Fig. S-12. Room-temperature separation of narrow-mmd linear standards (a) and a three-arm Star Polymer (b).. Fig. S-13. Separation of narrow-mmd PS standards (a) and a three-arm Star Polymer (b) at 50 C. 127