THE EFFECTS OF LONG CHAIN BRANCHING ON THE RHEOLOGICAL PROPERTIES OF POLYMERS

Transcription

1 THE EFFECTS OF LONG CHAIN BRANCHING ON THE RHEOLOGICAL PROPERTIES OF POLYMERS by RADU GIUMANCA Bachelor of Engineering (Chem. Eng.), City College of New York, 1999 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in the Faculty of Graduate Studies Department of Chemical and Biological Engineering We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA June Radu Giumanca

2 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of HFM-tlAL- & MVjodtCA^ WEE* «^3 The University of British Columbia Vancouver, Canada Date OC \2G lo?- DE-6 (2/88)

3 ABSTRACT Long chain branching (LCB) is a very important feature in polymer science due to its influence on the rheological properties of polymers. It has been shown that long chain branching causes strain hardening behavior in the extensional flow of polymer, feature which is not seen in linear species. A great industrial interest has been shown in a method which would detect long chain branching by a simple, yet robust method. Fifteen different samples of polypropylene (PP) of varying molecular weights (MW) and branching structures were studied. The aim was to obtain linear viscoelastic measurements using a Rheometrics System IV rheometer and compare the results to determine the effects of backbone MW, branch MW, and number of branches on the polymers' viscoelastic properties. It was discovered that the samples exhibit drastic thermal degradation, even under inert atmosphere. An antioxidant (Irganox 1010) was found to have no effect. A comparison of linear viscoelastic data yielded questionable results, perhaps suggesting a higher than expected polydispersity. Samples of comb-structure polystyrene were also studied. Linear viscoelastic data was obtained for two different series of PS, differing in MW and branch MW. By comparing with previously obtained data, it was discovered that time (-20 years) has had a small effect for most of the samples. Non-linear measurements were also obtained, and the results for the most part agree with published data. The differences, especially an extended plateau feature previously unpublished, are discussed. it

4 TABLE OF CONTENTS Abstract List of Figures List of Tables Acknowledgements Chapter 1: Introduction Chanter 2: Long Chain Branching: General Review 2.1 Introduction 2.2 Viscoelasticity 2.3 The Relaxation Modulus of Molten Polymers 2.4 Small Amplitude Oscillatory Shear 2.5 Non-Linear Viscoelasticity 2.6 Effects of LCB on the Rheology of Polymers 2.7 Effects of Comb Structure on the Rheology of Polymers Chapter 3: Scope of Work 1.1 Introduction 1.2 Thesis Objectives 1.3 Thesis Organization Chapter 4: Experimental Work 4.1 Introduction 4.2 Experimental Equipment in

5 4.2.1 Parallel Plate Geometry Cone and Plate Geometry Sources of Error Operating Procedure Linear Measurements Non-Linear Measurements 28 Chapter 5: Rheology of LCB Polypropylenes Introduction Samples Used Results Obtained Effect of Prolonged Exposure to Temperature; Degradation A Effect of Temperature B Effect of Stabilizer Irganox 1010 [CD3A Chemicals] C Temperature History Effect Effect of Molecular Weight Increase Effect of Increasing Number of Branches Overall Conclusions 43 Chanter 6: Rheology of Comb Polystyrenes Introduction Samples Used Results Obtained Linear Viscoelastic Measurements Non-Linear Stress Relaxation Experiments 57 Chapter 7: Conclusions and Recommendations Introduction Findings & Suggestions for Future Work on PP Project Findings & Suggestions for PS Project 68 References 70 iv

6 LIST OF FIGURES Chapter 1 Figure 1.1 (pg. 2): Comparison of Polymer Branching States Figure 1.2 (pg. 3): Comparison of LCB vs. Linear Polymer Behavior in Shear and Extensional Flows Figure 1.3 (pg. 5): Reptation Mechanism; Restricted motion in a Tube Figure 1.4 (pg. 6): Comparison of Various LCB Architectures Chapter 2 Figure 2.1 (pg. 9): Comparison of Viscoelastic to Liquid and Solid Behavior Figure 2.2 (pg. 9): Illustration of Boltzmann Superposition Principle Figure 2.3 (pg. 10): A Typical Stress Relaxation Spectrum for a High and a Low MW Polymer Figure 2.4 (pg. 13): Dynamic Moduli Spectrum for sample c652, tested at Fo.R.T.H. Figure 2.5 (pg. 14): Stress Relaxation for a Comb Polystyrene Solution 30% in DEP, at various strains Figure 2.6 (pg. 15): Stress Relaxation Curves shown in Figure 2.5 shifted to determine the separation time Figure 2.7 (pg. 15): Damping Function for Data Shown in Figure 2.5 Chapter 4 Figure 4.1 (pg. 25): Setup for Parallel - Plate Geometry Figure 4.2 (pg. 26): Setup for Cone and Plate Geometry

7 Chapter 5 Figure 5.1 (pg. 30): Illustration of PP Sample Structures Figure 5.2 (pg. 32): Effect of Prolonged Exposure to High Temperature for Sample Figure 5.3 (pg. 33): Thermal Degradation for Sample 13 Figure 5.4 (pg. 33): Differences between UBC and Fo.R.T.H. Data, Sample 13 Figure 5.5 (pg. 34): Decrease in Zero-Shear Rate Viscosity with Exposure Time Figure 5.6(a) (pg. 35): Effect of Stabilizer Irganox 1010 over Storage Modulus Figure 5.6(b) (pg. 37): Effect of Irganox 1010 over Complex Viscosity Figure 5.7 (pg. 37): Comparison of Degradation with or Without Irganox 1010 for Sample 3 Figure 5.8 (pg. 38): Comparison of Different Strategies Used for Sample 13 Figure 5.9 (pg. 40): Chain Length Increase Effect on Complex Viscosity, Linear Polymers Figure 5.10 (pg. 41): Effect of Backbone MW Increase for Branched PP's Figure 5.11 (pg. 41): Effect of Backbone MW Increase on Samples 11, 12 and 13 Figure 5.12 (pg. 42): Effect of Increasing Number of Branches Chapter 6 Figure 6.1 (pg. 46): Illustration of Comb PS Samples Figure 6.2(a) (pg. 47): C6 Series Storage Moduli Figure 6.2(b) (pg. 47): C6 Series Loss Moduli Figure 6.3(a) (pg. 48): C7 Series Storage Moduli Figure 6.3(b) (pg. 48): C 7 Series Loss Moduli Figure 6.4(a) (pg. 49): C6 Series Complex Viscosities vi

8 Figure 6.4(b) (pg. 49): C7 Series Complex Viscosities Figure 6.5 (pg. 51): Comparison of Zero-Shear Viscosities for C612 and C712 Figure 6.6(a) (pg. 52): Comparison of G\ G" curves from Roovers and at Fo.R.T.H., Series C612 Figure 6.6(b) (pg. 52): Comparison of G\ G" curves from Roovers and at Fo.R.T.H., C622 Figure 6.6(c) (pg. 53): Comparison of G', G" curves from Roovers and at Fo.R.T.H., C632 Figure 6.6(d) (pg. 53): Comparison of G', G" curves from Roovers and at Fo.R.T.H., C642 Figure 6.6(e) (pg. 54): Comparison of G', G" curves from Roovers and at Fo.R.T.H., C652 Figure 6.6(f) (pg. 54): Comparison of G\ G" curves from Roovers and at Fo.R.T.H., C722 Figure 6.6(g) (pg. 55): Comparison of G\ G" curves from Roovers and at Fo.R.T.H., C732 Figure 6.6(h) (pg. 55): Comparison of G', G" curves from Roovers and at Fo.R.T.H., C742 Figure 6.7(a) (pg. 58): Stress Relaxation for sample C752, 30% wt. in DEP Figure 6.7(b) (pg. 59): Shifted Curves from Figure 6.7(a), C752 30%wt. in DEP Figure 6.7(c) (pg. 59): Damping Function for C752, 30% wt. in DEP Figure 6.8(a) (pg. 60): Stress Relaxation for Sample C742, 30% wt. in DEP Figure 6.8(b) (pg. 60): Shifted Curves from Figure 6.8(a) Figure 6.9 (pg. 61): Comparison of C742 and C752 Damping Functions Figure 6.10(a) (pg. 62): Stress Relaxation for C652 20% in DEP Figure 6.10(b) (pg. 63): Shifted Curves for Figure 6.7(a) Figure 6.11 (pg. 63): Stress Relaxation for C642 20% wt. in DEP, Shifted Curves Vll

9 Figure 6.12 (pg. 64): Comparison of C652 and C642 Damping Functions Figure 6.13 (pg. 65): Comparison of C642 30% and C642 20% solutions damping functions Figure 6.14 (pg. 66): Comparison of Linear PS Damping Function to Comb to Doi- Edwards Prediction Figure 6.15 (pg. 66): Stress Relaxation Curves for a Linear Polystyrene 30% wt. in viii

10 LIST OF TABLES Chapter 5 Table 5.1 (pg. 30): Description of the 15 PP Samples used Chapter 6 Table 6.1 (pg. 45): Specifics of Comb PS Samples Table 6.2 (pg. 57): Comparison of GN values IX

11 ACKNOWLEDGEMENTS I wish to express my most heartfelt gratitude to my supervisor, Prof. Savvas G. Hatzikiriakos, for his guidance and utmost support during the course of this study. I sincerely thank Dr. Dimitris Vlassopoulos for his mentorship, his many valuable suggestions during the course of my study and for inviting me to spend eight months to work on my thesis at the Foundation for Research and Technology - Hellas, in Crete, Greece. I am grateful to Dr. Vlassopoulos for the excellent hospitality that was extended to me during my stay in Crete, and for his financial support. Thanks also to Ms. Eirini Chira for her invaluable support with the use of the rheometer, her expertise was appreciated. To Ms. Chira and everyone at Fo.R.T.H. who have aided me, I extend a heartfelt " V)(aplotco TT OXv". My colleagues, both at the U.B.C. RheoLab and at Fo.R.T.H., have helped me in various ways. I wish to thank Alfonsius Budi Ariawan, Philip Servio, and Peter Holmqvist for their helpful discussions and exchange of ideas. Finally, I wish to extend a special note of thanks to my family. I would like to thank my mother for her never-ending love and support and for her faith in me, and my sisters, Ruxandra and Doina, who have been a source of strength and motivation for success. Thanks also go out to my father for his belief in me and perpetual pep talks. x

12 CHAPTER 1 INTRODUCTION Polymers are generally recognized as long chains of carbon atoms with varying architectures and molecular weights. A linear chain is one in which any carbon atom is chemically bonded to at most two other carbon atoms. Such a chain is known as a linear chain (see Figure 1.1). Any chains of carbon atoms which stem from carbon atoms that are already part of another chain, are known as branches. Long chain branches (as opposed to short ones) are those whose length is close to that of the distance between chain intersections in a polymer network. On the basis of diffusion measurements, Jordan et. al (1989) have indicated that polymers with branches of the order of 2M_ (average molecular weight between entanglements) behave as long-chain branched molecules. A lot of polymers contain what is known as side branches. Such structures influence to a great extent various aspects of the polymer rheology (Larson, 1999). The length of the branches is the primary factor that decides the extent of the differences. Branches can be introduced deliberately in order to alter the processability and/or mechanical properties of a certain polymer. Often times, however, they can occur as an undesired side reaction during polymerization in industrial processes. In such cases, even small changes in the reaction conditions can lead to great differences in the rheological behavior of the product. Metallocene catalysts are known to be able to synthesize polymers with relatively narrow molecular weight and comonomer distributions, which, combined with controlled amounts of long chain branching is claimed to lead to improved processability and enhanced mechanical properties (Hatzikiriakos, 2000). 1

13 Long Chain Branching Short Chain Branching Linear Chain (no branching) Figure J.J: Comparison of Branching States For polymer melts used in commercial applications, large differences in their processability and rheological behavior have been noticed between long-chain branched (LCB) polymers and linear ones. The differences are most clearly evident in flows involving extensional elements. Certain melts, such as low density polyethylene (LDPE), which are known to have an extensive amounts of irregularly spaced side long chain branches, exhibit a distinct "strain hardening" phenomenon in uniaxial extensional flows that is in direct contrast with results obtained in a similar experiment for linear polymers. In shearing flows, nevertheless, the behavior of long-chain branched polymers is qualitatively similar to that of linear ones, both exhibiting a highly "strain softening" behavior (McLeish, Larson et al, 1998). The only difference is that the presence of LCB increases the extent of the shear thinning or "shear softening". Strain softening and strain hardening behavior is illustrated by the relationship between the viscosity and strain rate. Figure 1.2 shows a typical schematic to illustrate this type of behavior. For example, in this situation, strain hardening behavior is equivalent to the fact that, for strains in the 2

14 nonlinear region, the viscosity values rise above those of the linear values of viscosity. Such behavior would certainly be of great interest to industrial applications that use extensive amounts of extensional flows, such as fiber spinning or film blowing. In addition, the viscosity at very low shear rates, known as zero-shear viscosity, has been discovered to grow exponentially with molecular weight. Berry and Fox (1968) performed a study of several nearly monodisperse polymers and found that their viscosity scales linearly with molecular weight up to a certain molecular weight they defined as critical (Mc), from which point viscosity scales as a power law, n - MW 34. o Shear Rate (radls) Figure 1.2: AdaptedfromMcLeish & Larson, 1997, comparison of LCB vs. Linear polymer behavior in extensional and shear flows A plausible explanation for the above behavior exists in literature (Rouse, 1953). Rouse proposed a model that works well for unentagled polymers that emphasizes the friction between polymer chains as they glide past each other. The steeper slope above Mc. is caused by entanglements, which are restrictions to flow for a chain due to the physical presence of other chains, i.e. chains cannot pass through other chains. Due to 3

15 entanglements, a chain has only a limited path to go, and it is restricted in its motions perpendicular to its own molecular contour. Such constraints can be summed up as a restrictive tube that encapsulates each chain. As such, a molecule can only perform a snake-crawl-like motion along its tube, which is known as reptation (de Gennes, 1971). In the case of entangled chains, the Rouse theory needs to be supplemented by a model that takes into account the severe topological restrictions that are caused by the tight vicinity of the other molecules. The tube model of Doi and Edwards (1986) provides for such constraints. A molecule that is confined to a tube can only perform a reptative motion along its tube, the free chain ends being free to explore the melt without the constraints of this tube, as seen in Figure 1.3. The presence of branching brings about additional constraints for which new models have been created, the most significant of which is the Pom-Pom Model (McLeish, Larson 1998). All these peculiarities exhibited by LCB polymers lead to an increased industrial interest in the subject. More importantly, it is a challenging task to find a straightforward and effective means of detecting whether a polymer contains even small amounts of LCB. Rheology provides a good means for detecting even small amounts of LCB. The tell-tale signs that alert us to the presence of LCB, are as discussed above, an increase in zero-shear viscosity over linear chains, the onset of shear thinning behavior at smaller shear rates and also the ratio of the loss modulus over the storage modulus is reduced significantly (Yan, 1999). 4

16 Figure 1.3: Reptation Mechanism in a Tube (adapted from de/iff/personen/g. Schuetz/pictures/tube.jpg) A likely reason for this, as discussed above, is because a branched polymer finds it a lot more difficult to navigate in a polymer network because of the additional constraints offered by the existence of the branches. We thus have the grounds for further investigation of LCB-containing polymers. Though a lot is known about these types of polymers, more insight is needed to be able to predict more accurately the presence and extent of branching. In addition, since polydispersity acts in the same direction as branching, only reasonably monodisperse samples need to be studied in order to single out solely the effect of long chain branching. In order to further investigate the effects of LCB, and how to detect their presence using linear viscoelastic measurements, a study of polypropylenes might be worthwhile. To this effect, nearly monodisperse samples of polypropylene were synthesized, with 5

17 varying molecular weights of the backbone, and of the arms. The samples' rheological behavior was analyzed, and the results are outlined in this thesis. A series of comb polystyrenes was also studied, in order to deepen our understanding of the effects of morphology and branching on the rheological behavior of polymers. A comb constitutes a special type of architecture for a LCB molecule, which is carefully synthesized in the laboratory, in order, to observe its behavior, and draw appropriate conclusions. Combs are used as an intermediary step, a "stepping stone" between "star" polymers and linear polymers, and can also be designed to test the effect of LCB. Figure 1.4 illustrates the differences between the aforementioned structures, as well as compares it to theoretical models such as the POM-POM and H-polymers. Figure 1.4: Comparison of Various LCB Polymer Architectures and Theoretical Models Thus, carefully prepared nearly monodisperse comb polystyrenes of various molecular weights and arm lengths were tested Theologically. The aim of this particular study is to obtain linear and nonlinear measurements in order to find the effect of comb structure on their rheology. The larger purpose of studying comb polymers is to bridge the structure gap between randomly branched commercial polymers and model stars (Roovers, 1981). The results obtained are outlined in this thesis. 6

18 CHAPTER 2 LONG CHAIN BRANCHING: GENERAL REVIEW 2.1 Introduction Beginning as early as the first two decades of the 20 th century, due to their industrial usefulness, a great amount of attention has been paid to polymers in general. The industry's primary motivation was to optimize the quality of their product, and reduce costs, and to that effect they became very interested in polymers' physical and chemical properties. In this section, the key theoretical concepts behind polymer rheology are outlined. In addition, the latest outstanding research published in the literature is analyzed. 2.2 Viscoelasticity Polymers are materials which exhibit a behavior that lies between those of a fluid or a solid. Hooke's law accurately describes solid behavior, where the tensile stress in extension is directly proportional to the strain, or the relative length change. o E (t) = G-y(t) (2.1a) The corresponding form of Hooke's law for simple shear is: c = G-y (2.16) where G is the shear modulus or modulus of rigidity. For fluids, Newton's law of viscosity accurately predicts that the force is directly proportional to the rate of strain. (0 = TI-YW ( 2-2 ) 7

19 In these equations, a represents the shear stress, y(t) and y (t) the shear strain and strain rate, respectively, whereas n represents the viscosity of the fluid. An appropriate visual example that illustrates both types of behavior is "silly putty". When bounced against a hard surface, it rebounds, much like a solid, but when allowed to stand on a solid surface for an extended period of time, shows a liquid-like tendency to flow. For a viscoelastic substance, such as a polymeric one, the stress history becomes important. As pointed out in the "silly putty" example, the response varies from that of a solid-like behavior at very short times to that of a liquid-like behavior at long times. Such behavior is called viscoelasticity and fluids that follow it are referred to as viscoelastic fluids. Viscoelasticity can be demonstrated by several different simple experiments. For example, a stress relaxation experiment implies imposing a small shear strain yo at time 0, and then monitoring the stress while the strain is held fixed. The difference in response between a liquid, a solid and a viscoelastic fluid is shown in Figure 2.1. The ratio of stress to strain is then a linear viscoelastic property, G(t), called the shear stress relaxation modulus. G{t) = a{t)/y 0 (2.3) When the imposed strain and strain rates are small enough, so that the molecules are not disturbed far away from their equilibrium state, the relaxation modulus is independent of the imposed strain or strain rate. Such behavior is called linear viscoelasticity. For such stresses, in the linear regime, the Boltzmann superposition principle states that the stress at any point is simply a sum of all previous stresses resulting from a series of N small strains. For example, Figure 2.2 illustrates a series of 8

20 strains imposed at different times. To calculate the shear stress at time t, one can use Equation 2.4: i3 00 ^5 Time 0 (A) Liquid-like (B) Solid-like (C) Viscoelastic Figure 2.1: Liquid-like, solid-like and, respectively, viscoelastic response for a material with a structural time dependency G(0= G('-O-5Y(O (2.4) In such a case, the viscosity of a viscoelastic material is related to the relaxation modulus: r) 0 =]G{t)-dt (2.5) Fig 2.2: Sequence of Step Strains - Boltzmann Superposition Principle 9

21 2.3 The Relaxation Modulus ofmolten Polymers The primary characteristics of a typical G(t) plot are shown in Figure 2.3. As can be seen, G(t) exhibits a plateau region. The value of this plateau is a function of the polymeric structure. The plateau modulus GN is a constant for a particular polymer species, and increasing the length of the chain (i.e. the molecular weight) only increases the width of the plateau region, but not the value at which it occurs. The plateau region separates the short time relaxation region, where the large scale chain architecture has little effect and the long-time relaxation region where factors like molecular weight, molecular weight distribution and long chain branching influence the values of G(t) greatly (Graessley, 1993). Time Figure 2.3: Typical Stress Relaxation Modulus Features for a High Molecular Weight Polymer The reason why the plateau region exists is due to the entanglements that occur in the polymer network. At high polymer concentrations, individual polymer chains have a hard time returning to their initial equilibrium orientations due to the physical presence of many other neighboring polymer chains, which restrict its range of movement. As shown 10

22 in Figure 2.3 and mentioned in the previous chapter, polymer chains are forced to undertake a snake-crawl like motion around the physical constraints offered by the presence of other chains through a restrictive tube, called reptation (De Gennes, 1971, Doi & Edwards, 1986). Naturally, the lower the molecular weight, the less constrictive the tube is. The molecular weight at which entanglements first occur is an important material property which is known asmc, the entanglement critical molecular weight. 2.4 Small Amplitude Oscillatory Shear - Relaxation Moduli Another important experiment which is employed for the characterization of polymers and was of great use for the development of this thesis is the small-amplitude oscillatory shear stress experiment. In such an experiment, the liquid is strained sinusoidally, and the in-phase and out-of-phase components of shear stress at steady state are measured as a function of the frequency, co. y(/) = y 0 -sin(co/) (2.6) In this equation, y 0 represents the strain amplitude. By differentiating, we obtain the shear rate as a function of time: y(0 = Y 0 cos(co^) = y 0 cos(co^) (2.7) For the case of sufficiently small yo we can calculate the stress by using the Boltzmann superposition principle. Thus, it can be shown that the stress is sinusoidal in time and has the same frequency as the strain: c(t)=o 0 -sin(co/+ 5) (2.8) where go is the stress amplitude and S is a phase shift called the "mechanical loss angle". 11

23 In order to simplify things, it is customary to write Equation 2.8 as: o (0/Yo = G'(co ) sin (co r)+g"(o) cos(co t) (2.9) G'(co) is known as the dynamic storage modulus, and is the component of G that is in phase with the strain. G"(a>) is known as dynamic loss modulus and it is the component of stress that is out of phase with the strain, but in phase with the rate of strain. For a low enough initial strain, these measurements can all be performed in the linear region. Thus, the behaviors of both G'(ou) and G"(co) are linked to G(t) through the Boltzmann superposition principle and the values for the zero-shear viscosity can be obtained from their properties in the low-frequency limit: T io = lim G "(»)/ f f l ( 2 1 ) 0)~>0 In addition, it is perhaps noteworthy to mention that the G(t) curve can also be obtained from G\ G" data simply by performing an inverse Fourier transform that converts G'(co) and G"(co) vs. co to G(t) vs. / data. A typical dynamic moduli spectrum is shown in Figure 2.4 for a nearly monodisperse polystyrene sample. The dynamic moduli, as seen in Figure 2.4, span over several orders of magnitude in the frequency domain. Unfortunately, no single experiment can cover this whole area, due to apparatus limitations. In fact, Figure 2.4 represents what is known as a master curve, which can be obtained based on the fact that the polymers used obey the timetemperature superposition principle. The time-temperature superposition principle states that a change in temperature shifts the viscoelastic functions along the modulus axis without changing their shape. Thus, measurements at many different temperatures can be 12

24 put together, spanning many more orders of magnitude than can be obtained by any single experiment (Dealy, 1990). C652 Tref MasterCurve T ' Q4 Freq [rad/s] Figure 2.4: Dynamic Moduli Spectrum for Polystyrene sample number C652, Master curve (from experiments performed by Giumanca at Fo.RT.H., Greece) 2.5 Non-Linear Viscoelasticity So far we have only discussed the behavior of fluids in the linear regime, where deformations are small and slow enough to allow the material to return to its equilibrium state. However, this is not the case when dealing with large deformations, the chains are displaced significantly from their equilibrium conformations and the Boltzmann superposition principle no longer applies. Furthermore, the relaxation modulus, G(t), is no longer independent of the strain: o(/,y) = y-g(/,y) (2.11) 13

25 However, for many polymeric liquids, stress relaxation following a sudden imposition of shear is factorizable into strain-dependent and time-dependent functions: o(t,y) = yh(y)-g(t) (2.12) where h(y) is known as the damping function. This is not normally observed at ALL times following step strain (Archer, 1999). Instead time-strain separability is only found after a characteristic separability time Ik that varies with polymer molecular weight, architecture, concentration, and temperature (Osaki, 1982). A plot of relaxation modulus vs. time is shown in Figure 2.5, at different stresses, for a solution of nearly monodisperse comb-architecture polystyrene in diethylphthalate (DEP). r h i i i i i i i n i i i i * i i i 10" 2 10" t(s) Fig 2.5: Stress Relaxation for a Comb Polystyrene Solution 30% wt in DEP, at Different Strains Figure 2.6 represents the same data in Figure 2.5, but the data is shifted up to indicate the separation time. 14

26 10 b- C752 30% Solution in DEP Dashed Line represents Linear Data from DFS 10' fe- Separation time X ~ t- i 1 1 i i i i i * i _i i tti i i i 11 i 10"' ' 10' Figure 2.6: Shifted Curvedfor Stress Relaxation, Comb Polystyrene, from experiments by Giumanca. Vertical line indicates separation time, Xk. t(s) A plot of the damping function is shown in Figure 2.7: i 1 I i j i i i i i i i i ' i ' Figure 2.7 Damping Function for Comb Polystyrene 15

27 2.6 Effects of LCB on the Rheology of Polymers Due to increased interest in the rheological behavior of polymers, extensive work has been done on this subject and these results have been reported in the literature. Polyethylene (PE) has been a polymer that's been studied quite extensively in the past few decades. Vega et al. (1996) studied the rheological behavior of metallocene catalyzed HDPE's and compared to that of conventional HDPE's. The differences found for metallocene HDPE's include higher viscosities than their conventional counterparts, the existence of a power law dependence on MW with a power of 4.2, a lower crossover value for the storage and loss moduli, and a reported difficulty to process due to sharkskin and slip-stick effects. In a subsequent article, Vega et al (1998) studied the viscoelastic behavior of 23 noncommercial metallocene-catalyzed PE's in order to find a correlation between rheological behavior and small amounts of long-chain branching. Results point to the fact that the samples which they believe to contain LCB exhibit higher values for zero-shear viscosities, higher relaxation times, higher values of elastic modulus and a higher Arrhenius activation energy all when compared to other PE's of similar MW, polydispersity and amount of short-chain branching (SCB). Wood-Adams and Dealy (2000) investigated the effect of polydispersity, SCB and LCB on the linear viscoelastic behavior of polyethylenes. They found out that for metallocene polyethylene, LCB increased the zero-shear rate viscosity and also broadened the relaxation spectrum by adding a long time relaxation mode when compared to linear PE's of the same molecular weight. Hatzikiriakos (2000) investigated a means of detecting the presence of LCB from linear viscoelastic measurements. He discovered that, after plotting 16

28 atan(g'vg') vs. G* (Van Gurp plots), the area below the Van Gurp curves correlates with the extent of LCB and polydispersity. The rheological behavior of LCB polypropylene has also been studied, though significantly less extensively than PE. Kurzbeck et al. (1999) investigated two polypropylenes (PP) with different molecular structures, in shear and elongational flow. He confirmed the no strain-hardening behavior for the linear species, yet for the LCB species he found a more pronounced strain-hardening behavior than any other polyolefin studied up to date. He appropriates this behavior to the coexistence of a long chain branched structure and a high molecular weight component. Tsenoglou et al. (2001) studied the effect of introducing long chain branching on an initially linear PP. They developed a simple rheological method for estimating the degree of long chain branching (the fraction of branched chains or the average number of branches per chain) in a polymer melt undergoing the early stages of cross-linking. Due to the fact that polypropylene is less prominent than PE as far as industrial interest is concerned, it has been studied less extensively. However, due to its attractive physical properties (high melting point, low cost, high tensile stress, low density) and the inception of some novel methods of producing narrow molecular weight species, such as the metallocene catalyzed method, there has lately been an increased interest in PP. As such, a comprehensive rheological study that analyzes the effect of the number of branches, branch length and backbone length on a series of model polypropylenes would perhaps be of great interest. Such a study is attempted here. The degradation of polypropylene, which is related to this thesis, as will be evident below, has also been studied extensively. Tzoganakis (1988) studied the 17

29 controlled degradation of polypropylene. He splits degradative processes into two general categories: thermal degradation and peroxide promoted degradation. Thermal degradation is reported to occur over relatively long periods of time (1-24 hrs) at very high temperatures (>240 C), and to achieve relatively low degrees of MW reduction. Peroxide promoted degradation is described as a deliberate process, and it involves mixing an amount of peroxide into the PP melt before feeding it to an extruder. A description of the degradation mechanism is also provided. Curry and Jackson (1988) have studied the effects of controlled degradation. They had developed a control loop around the degradation system in order to maximize the desired results. Ibrahim and Seehra (1997) reported on sulphur as being a promoter of degradation in a PE/PP system. They employed electron spin resonance (ESR) spectroscopy in order to investigate the thermal and catalytic degradation of a sample of commingled plastics (CP) containing about 95% PE and 5% PP. They reported significant reductions in the depolymerization temperature of CP with added catalysts, which include sulphur, NiMo/Al 2 03, and zeolite HZSM-5. Schoenberg (1996) reported on a process for increased peroxide efficiency in controlled rheology polypropylene resin. He has reported a decrease in MW and an increase in melt flow index of a controlled rheology polypropylene resin without exceeding a limit of 100 parts per million of tertiary butyl alcohol as a peroxide decomposition product. This is accomplished by adding small amounts of hexane and thioester. Watson et al (1975) reported on the economical and convenience benefits of injecting air (oxygen) into a melted polymer as it is processed within an extruder, towards the purpose of achieving controlled degradation of C?+ polyolefins, in particular polypropylene. In all these references, degradation of a polyolefin is meant to create a product of lower molecular 18

30 weight, but with more desirable rheological properties, such as viscosity and melt flow index, and lower polydispersity. In our case, degradation is an undesired side effect, and it occurs at much lower temperatures than what has been reported. Initially, it was not the purpose of this thesis to study the thermal degradation of polymers. However, as I proceeded with my study, it became evident that our samples degraded with temperature, to the point that they even hindered it. The results outlined above portray the benefits of a controlled degradation of polymers, whereas in our case degradation is an unintended and undesired side effect. In addition, none of the results report significant degradation at relatively low temperatures (~ C), as is our case. Even more surprisingly, as discussed below, is that significant thermal degradation of the samples occurs despite adding an anti-oxidant (Irganox CIBA Chemicals) and operating in an inert nitrogen atmosphere. 2.7 Effects of Comb Structure on the Nonlinear Rheology of Polymers A great range of literature is also available on the properties of model comb polymers. Comb architecture is a carefully produced model meant to be a link between linear polymers and randomly branched industrial polymers. Daniels et al. (2001) presented experiments and theory on the melt dynamics of monodisperse entangled comb polymers. They found data to be in good agreement with a tube-model theory which combines star polymer melt behavior at high frequency with modified linear polymer reptation at low frequencies. Qualitatively distinct features of comb polymers were then compared to simpler star and H-topologies. Roovers (1981) performed a study on two series of narrow molecular weight polystyrenes. He found the plateau modulus to be the 19

31 same for linear, star and comb polystyrenes of same backbone MW. The frequency dependence of the dynamic moduli was interpreted to be consistent with three relaxation mechanisms: movement of the whole molecule (reptation) at long times, movement of branches at intermediate times and the high frequency is identified with that found in the transition zone of linear and star polymers. Several nonlinear stress relaxation studies are also available. In a series of papers, Watanabe et al. (1996) examined the nonlinear stress relaxation behavior for blends of styrene-isoprene diblock copolymers in a homopolyisoprene matrix. For sufficiently small strains, he found G(y,t) to agree with linear values of G(t). He also found two distinct relaxation processes, a fast and a slow one, and he attributed the fast process to the relaxation of the individual corona blocks. Islam et. al (2001) studied non-linear step shear relaxation moduli in a series of polystyrene/diethylphtalate solutions in order to understand whether the shear damping function is universal for fluids in the class entangled liquids, and got a clear answer in the negative. They also found that with increasing entanglement densities, the damping function becomes progressively softer, and they explained these results through the prism of a tube model. Vrentas and Graessley (1982) obtained shear stress relaxation data for a range of shear strains on a series of entangled polymer liquids (linear and star polybutadienes of narrow MWD) in order to test time-strain factorability and the Doi-Edwards predictions about strain dependence. They observed some departures from time-strain factorability, but nonsystematic and uncorrelated. They also observed some departures from Doi-Edwards behavior at higher entanglement densities, the causes of which they deemed to be unknown. Osaki (1993) reviewed published data on the damping function of the shear 20

32 relaxation modulus. He found most of the data to be in good agreement with the Doi- Edwards prediction. He associated weaker damping with (1) comb branching, (2) lack of entanglement and (3) bimodal molecular weight distribution. For highly entangled systems (more than 50 entanglement points per molecule) he discovered the strain dependence to be stronger than predicted by Doi-Edwards, which he deemed possible to be due to slip, or an instability or deformation within the material. The aim of our thesis is to obtain the linear viscoelastic data for comb polymers, then run stress relaxation experiments and see how data compare for low strains. In addition, the shear damping function will be analyzed and compared to previous results and the Doi-Edwards prediction. 21

33 CHAPTER 3 SCOPE OF WORK 3.1 Introduction Although there is a great commercial interest in the effect of long-chain branching on the rheological properties of a polymer, there is still much to be discovered about the properties of LCB polymers. In the long run, more knowledge on the subject will lead to process optimization, improved products and increased profits. Lately, there has been an increased interest in polypropylene, due to its attractive physical properties. However, a comprehensive rheological study of LCB propylene has yet to be published. Likewise, there is a need for a unifying theory that describes nonlinear rheology. Although much progress has been made lately, for example, the Pom- Pom theory, more work needs to be done on nearly monodisperse model architectures, such as the comb structures. 3.2 Thesis Objectives This research project is fundamental in nature. Its scope is two-fold. First, a series of polypropylene samples are studied. The objectives of this work were: 1. To obtain linear viscoelastic measurements for 15 samples of nearly monodisperse polypropylene, of different molecular weights and branching architectures. 2. To analyze the effect of molecular weight, branch length, and number of branches on the rheological properties of the polymers. 22

34 3. To attempt to rationalize the results through the prism of a complex theoretical model, i.e. the Pom-Pom model. Secondly, a series of comb polystyrenes were studied. The objectives of this study can be summarized as: 1. To obtain linear viscoelastic measurements on two series of nearly monodisperse comb-architecture polystyrenes and compare results to data obtained by Roovers et al. (1976). 2. To perform non-linear stress relaxation measurements, and compare the results obtained to the linear data in order to obtain the damping function. 3. To use a comprehensive theory, such as that of Daniels and McLeish (2001) to analyze the results obtained. 3.3 Thesis Organization The first chapter provides an introduction, a set of fundamental information on the features and importance of long-chain branching in polymers. The chapter also introduces the concept of comb architecture, and discusses its features. Chapter 2 presents a brief overview of the key theoretical concepts. In addition, it reviews the latest advances in the long-chain branched polymer field published in the literature. Chapter 4 provides a basic analysis of the equipment used. The rheology of 15 samples of polypropylene is discussed in Chapter 5. A through description of the samples is given, and the rheological results obtained for the 15 samples are also discussed in Chapter 5. Chapter 6 relates linear and non-linear viscoelastic experiments on 10 samples of monodisperse, combstructure polystyrenes. Chapter 7 presents the most important conclusions of the results presented in Chapters 5 and 6. Recommendations for future work are also given. 23

35 CHAPTER 4 EXPERIMENTAL WORK 4.1 Introduction This chapter describes the means by which the experimental results were obtained. The main equipment used in our quest is a parallel-plate rheometer. The concepts and design of such an apparatus are explained. Two sets of samples were used towards our goals, a set of 15 samples of LCB polypropylene, with varying molecular weights and architecture, and a set of comb polystyrene of increasing arm molecular weight. A detailed description of the two sets of samples is also given. Finally, a brief overview of the experimental procedure is presented here. 4.2 Experimental Equipment For the purpose of analyzing the rheological properties of polymers, a rheometer is a very useful piece of equipment. For the purpose of this study, two different parallelplate rheometers were used, located at UBC and Fo.R.T.H. (Greece). The non-linear stress-relaxation measurements were performed by means of cone-and plate geometry Parallel-Plate Geometry The parallel plate geometry utilized by a rheometer is shown schematically in Figure 4.1. For this type of geometry, the fluid is placed between the parallel plates, one of which rotates with a user-defined angular velocity. In order to determine the linear viscoelastic properties, one plate is oscillated with angular amplitude, <po, the torque amplitude is 24

36 measured, Mo, as well as its phase lag, 6, which is calculated from the stress signal. Then, the following relations can be used to calculate the linear viscoelastic moduli of polymer melts and solutions (Dealy, 1982): Sample Fixed Plate Figure 4.1: Parallel Plate Geometry G = ~ coso ( %-R -<p 0 2-M a -h. G = sin 5 ( n R (p 0 The software provided with the rheometer (Rheometric Scientific) performs these calculations automatically and outputs a set of G', G" vs. frequency (of) data Cone-and-Plate Geometry A different geometry that is used to determine viscoelastic properties is known as cone-and-plate. A sketch of this geometry is shown in Figure 4.2. The principal advantages of such geometry are that loading and cleaning are relatively easy, and the 25

37 shear rate is uniform for small angles. Thus, differentiation of data is not necessary to compute the relevant material functions. Fixed Plate Figure 4.2: Cone and Plate Geometry Sources of Error in both Parallel-Plate and Cone-and-Plate Flows Viscous heating and temperature fluctuations within the sample can introduce significant errors into the measurements. This effect is, however, very small in comparison with the variations of temperature with time resulting from the operation of the temperature control system. These variations results in fluctuations in system geometry and sample density, which will be most severe in the case of highly viscous fluids. Another important source of error is edge effects. One of the assumptions used to derive the rheometrical equations is that the free surface is spherical with a radius of curvature equal to the cone radius. At large rotational speeds, the fluid deformation can cause a pronounced change in the shape of the free surface. The fluid tends to flow outwards near the walls of the plates. The torque decreases markedly and then fluctuates. 26

38 As speed is further increased, air bubbles may be entrapped when the speed is reduced again, making it impossible to reproduce low shear rate data when the shear rate is subsequently reduced. "Edge failure", as this phenomenon has come to be known, governs the maximum shear rate at which cone-and-plate can be used in the study of molten polymers (Hutton, 1963). Deviations in the flow geometry from that for a perfectly shaped, aligned and positioned plates will also lead to errors in the measured properties. First, for cone-and plate, the apex of the cone is assumed to be just touching the surface of the lower plate, and there are several mechanisms that can cause deviations from this ideal situation, for example, lack of care in calibrating the gap between the plates, or failure to account for plate expansion due to temperature. In addition, another mechanism that can alter the gap spacing once the rheometer has been put into operation is a deflection of the rheometer frame in response to a large imposed stress. To minimize this, the rheometer has to be sturdy enough and firmly set into the floor. 4.3 Operating Procedure Linear Measurements The operating procedure we used consists of a series of different tests using a rheometer. Initially, a Dynamic Time Sweep (DTS), at a relatively low frequency (5 s" 1 ) and using a relatively low strain of 0.1 strain units, in the linear regime, at the initial starting temperature, which was between 150 and 170 C. The tests were run for anywhere 27

39 between 4 hours to 10 hours. This is done in order to test the chemical stability of the sample under the operating conditions. In case the DTS yielded positive results (no significant change in the viscoelastic functions with time), we moved on to what's known as a Dynamic Strain Sweep (DSS), where the frequency is held constant and strain is increased, typically from 0.1 strain units to 10 strain units, in order to determine the limits of the linear region. We ran several DSS's at various constant frequencies, to ensure that the linear region is determined for the whole frequency range of interest. At low strains, as previously discussed, the viscoelastic functions are not a function of the strain. As such, when the viscoelastic functions begin to decrease with increasing strain, its critical strain marks the onset of non-linear viscoelasticity. The ensuing test was a Dynamic Frequency Sweep (DFS) at constant strain, which was picked to be as high as possible, but well within the linear regime. This type of test was run at several temperatures, and the results were superimposed to yield a master curve (an example is given in Figure 2.4) using the time-temperature superposition principles already discussed Non-Linear Measurements Non-linear stress relaxation tests were also performed, on a series of comb polystyrenes. Stress relaxation tests were run for strains increasing in magnitude from 0.1 stress units (linear regime) up to 100 strain units. A typical set of results, plotted on the same set of axes, is shown in Figure

40 CHAPTER 5 RHEOLOGY OF LCB POLYPROPYLENES 5.1 Introduction In this section, the main results obtained on the rheology of long chain branched polypropylenes are outlined. Overall, the results differ greatly from expectations, but still, valuable conclusions can be drawn. An attempt is made to rationalize the results, and analyze the reasons why expectations were not met. The effects of molecular weight, number of branches and thermal degradation upon the linear viscoelastic properties of polypropylene are analyzed. 5.2 Samples Used Since the effects of polydispersity and LCB have similar effects on the rheological properties of polymers, it was of paramount importance for this study to obtain samples having the narrowest possible molecular weight distribution. To this end, polypropylene samples were synthesized by Tzoganakis et al. (2001), with reportedly well defined LCB structures and low polydispersities. Samples used in this work are listed in Table 5.1. The zero-shear viscosities are obtained from the RSI Orchestrator software, which fits the viscosity curves using a mathematical model (Ellis model) and then extrapolates the curves to low shear rate values. The values are based on data obtained at UBC, when samples were tested Theologically for the first time. In order to illustrate the strategy behind studying the rheology of the samples, and the aim of this study, Figure 5.1 shows a schematic of how the samples were expected to 29

41 look like, in order to thoroughly test the effects of molecular weight, arm length (MW), and number of arms, on the rheological properties of polypropylene. Comonomer Nominal (label) MWn MW from GPC(x1000) M. Temp # 1(DSC) (deg.c) Melt Temp #2 (DSC) (deg. C) Zero Shear Rate Viscosity Sample 1 Homo PP -110K Sample 2 Homo PP -170K Sample 3 Homo PP -210K Sample 4 0.5% C8-110K Sample 5 0.8% C8-110K Sample 6 0.8% C8-170K Sample 7 0.8% C8-210K NA Sample 8 2% C8-170K Sample 9 2% C8-210K Sample % C16-110K Sample % C16-110K Sample % C16-170K Sample % C16-210K Sample 14 2% C16-170K Sample 15 2% C16-210K Table 5.1: Polypropylene Samples Synthesized by Tzoganakis et al. (2001) Figure 5.1: Structures of PP Samples 30