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1 This article was downloaded by: [TIB & Universitaetsbibliothek] On: 14 February 2015, At: 03:42 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: Registered office: Mortimer House, Mortimer Street, London W1T 3JH, UK Soft Materials Publication details, including instructions for authors and subscription information: Polymer-Filler Interphase Dynamics and Reinforcement of Elastomer Nanocomposites F. Fleck a, V. Froltsov a & M. Klüppel a a Deutsches Institut für Kautschuktechnologie e. V. (DIK), Hannover, Deutschland Accepted author version posted online: 06 Oct 2014.Published online: 18 Nov Click for updates To cite this article: F. Fleck, V. Froltsov & M. Klüppel (2014) Polymer-Filler Interphase Dynamics and Reinforcement of Elastomer Nanocomposites, Soft Materials, 12:sup1, S121-S134, DOI: / X To link to this article: PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the Content ) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at

2 Soft Materials (2014) 12, S121 S134 Copyright Taylor & Francis Group, LLC ISSN: X print / online DOI: / X Polymer-Filler Interphase Dynamics and Reinforcement of Elastomer Nanocomposites F. FLECK, V. FROLTSOV, and M. KLÜPPEL* Deutsches Institut für Kautschuktechnologie e. V. (DIK), Hannover, Deutschland Received May 7, 2014; Accepted August 13, 2014 Downloaded by [TIB & Universitaetsbibliothek] at 03:42 14 February 2015 The effect of polymer-filler interaction on interphase dynamics between filler particles in elastomer nanocomposites and the mechanisms of rubber reinforcement by carbon black (CB) are investigated with different techniques. To determine how polymer-filler interface influences the properties of the system, CB black was modified with the ionic liquid (IL) 1-allyl-3-methylimidazolium chloride (AMIC) and mixed with different, more or less, polar elastomers. For typical diene-elastomers (EPDM, SBR), this modification leads to a decreased polymer-filler coupling strength due to the coverage of active sites at the CB surface by AMIC. This is demonstrated by evaluating the energy site distribution from static gas adsorption isotherms with the polymer analogues gas 1-Butene. However, an improvement of polymer filler coupling was determined in the case of saturated, polar rubbers (HNBR) due to attractive dipolar interactions between the polar units of the polymer and the strongly adsorbed IL at the CB surface. The different couplings affect the polymer-filler interphase dynamics between filler particles, which determines the properties of the filler network and filler-filler bonds. To describe the effect of CB surface modification quantitatively, the Dynamic Flocculation Model (DFM) has been used to calculate polymer- and filler-specific material parameters from cyclic stress-strain measurements. The fitted data deliver a coherent picture of filler-filler- and polymer-filler couplings showing a characteristic dependence on rubber polarity. A confirmation of the effect of surface modification on the strength of filler-filler bonds is obtained by nonequilibrium molecular dynamics (MD) simulations of bond rupture under tension. They also provide indications for a glassy-like behavior of strongly confined polymer layers between attractive walls. Keywords: Filler networking, Ionic liquids, MD simulations, Polymer-filler interphase dynamics, Reinforcement, Static gas adsorption Introduction Reinforcement of elastomers by nanostructured fillers, such as carbon black or silica, is essential for obtaining a sufficiently tough material for applications of rubber goods. Without reinforcing fillers, dynamically excited rubber products, such as tires or seals, could rupture or wear off rapidly (1, 2). In addition to making the elastomer stiffer and tougher, the incorporation of fillers leads to a nonlinear dynamic-mechanical response. An example is the Payne effect, referring to the pronounced amplitude dependence of the dynamic moduli (3, 4). With increasing strain amplitude, one observes an increasing loss angle and a decreasing storage modulus. These effects will be more pronounced, the higher the amount of filler in the elastomer. A related effect is stress softening under quasi-static cyclic deformation, which was intensively studied by Mullins (5). A drop in stress usually occurs after the loading history has gone beyond *Address correspondence to: Prof. Dr. M. Klüppel, Deutsches Institut für Kautschuktechnologie e. V. (DIK), Eupener Str. 33, D Hannover, Germany. Manfred.Klueppel@ DIKautschuk.de Color versions of one or more of the figures in the article can be found online at the previous maximum. Most of the stress drop at a certain strain occurs in the first cycle, and in the following cycles the specimen approaches a steady-state stress-strain curve. An example for a carbon black (CB) filled ethylene-propylene-diene monomer rubber (EPDM) is depicted in Fig. 1. A second characteristic effect caused by fillers is the pronounced hysteresis that is related to the dissipation of mechanical energy. All these effects are interrelated due to their common origin, often denoted filler networking, whereas the filler itself consists of relatively stiff particles that do not significantly participate in the deformation. Structure and properties of reinforced filler networks in elastomers are strongly influenced by the polymer-filler interphase dynamics. Thus far, this is not fully understood, though the interaction between polymer and filler and filler networking are the main factors for designing technical properties of rubber goods, for example, wet traction and wear of tires. Special emphasize lies in a better understanding of the microscopic mechanisms affecting the polymer-filler interphase dynamics and filler networking at elevated temperature (6 10). The behavior of the polymers close to adsorbing interface is largely determined by the interplay between the loss of configuration entropy due to presence of the solid surface and interactions of the chain with the filler and other chains in the bulk. By using different experimental techniques, it has been shown that a thin layer of confined, glassy-like polymer is formed at the filler

3 S122 Fleck et al strain strain history: multi hysteresis time t [s] Downloaded by [TIB & Universitaetsbibliothek] at 03:42 14 February 2015 nomin. stress strain Fig. 1. Uniaxial multi-hysteresis measurement in tension of a CB-filled EPDM sample; the inset shows the strain history. surface due to attractive interactions between elastomer chains and fillers (11 15). If these layers overlap, a glassy-like polymer bridge is formed between adjacent filler particles transmitting the stress by a mechanically flexible bridge (13 15). At moderate temperature, the bonds between adjacent filler particles represent a specific filler-polymer-filler interphase with significantly increased glass transition temperature. To describe these fillerfiller bonds quantitatively, a micromechanical material model [i.e. the Dynamic Flocculation Model (DFM)], can be used to evaluate the strength of filler-filler bonds from cyclic stress-strain measurements (16 18). In the present paper we will study the effect of polymer-filler interaction strength on the interphase dynamics and rupture stress of glassy-like polymer bridges between filler particles in strained elastomers by applying different experimental and numerical techniques. In particular, we will perform nonequilibrium MD simulations of filler-filler bond rupture, which allows for a direct evaluation of rupture stress in dependence of polymer-filler interaction strength for different bond lengths and temperatures. This is compared to experimental data of model composites of more or less polar elastomer systems filled with an original, highly active CB and the surface modified counterpart. This has been deactivated with the ionic liquid 1-allyl-3-methylimidazolium chloride (AMIC), which has also been investigated in a previous paper (19). The effect of surface modification is quantified by estimating the surface energy distribution from static gas adsorption measurements at low pressure. The tensile strength or yield stress of filler-filler bonds of the model composites will be obtained from fits of measured stress-strain cycles with the DFM. We will briefly describe the basic assumptions of this material model and the possibility to evaluate micro-mechanical material parameters from measured stress-strain cycles. We are mainly interested in the question how the material parameters are affected by the coupling of polymer chains to the filler surface. We will demonstrate that a systematic variation of material parameters occurs in dependence of polarity of the polymer and surface activity of the filler. This will be shown to be the key factor for understand the interphase dynamics and rupture mechanism of filler-filler bonds in strained elastomers. Theoretical Dynamic Flocculation Mode of Rubber Reinforcement The Dynamic Flocculation Model describes the physical mechanisms that lead to the stress-strain behavior of filled elastomers and is depicted in Fig. 1. It combines well-established concepts of rubber elasticity with a micro-mechanical approach of dynamic filler flocculation in strained rubbers at different elongations. The entropy-elastic behavior of elastomers (rubber) constituting the matrix is well understood and may be described, for example, by the extended nonaffine tube model (20 23). The presence of stiff filler particles or clusters leads to increased stress values due to strain amplification of the rubber matrix, also denoted hydrodynamic reinforcement. This term has been introduced in 1944 by Smallwood (24) who found a close relationship between the Einstein equation for the viscosity of a suspension of nonaggregated hard spheres and the shear modulus of an elastomer filled with the same hard spheres (1, 10). The stress response of filled rubbers as a function of strain can be derived from the following mesoscopic phenomena. A successive breakdown of filler clusters takes place upon increasing the strain of an unconditioned virgin rubber sample. This process begins with the largest filler clusters and continues up to a minimum cluster size. Upon decreasing the strain, complete re-aggregation of the filler particles takes place. However, the filler-filler bonds,

4 Polymer-Filler Interphase of Elastomer Nanocomposites which are formed again after once being broken, are significantly weaker than in the virgin sample. At subsequent stress-strain cycles of a prestrained, reinforced sample, two micro-mechanical mechanisms can be distinguished. 1. Hydrodynamic reinforcement of the rubber matrix by a fraction of rigid filler aggregates with strong virgin filler-filler bonds, which have not been broken during previous deformations. 2. Cyclic breakdown and re-aggregation of the remaining fraction of more soft filler clusters with damaged and hence weaker filler-filler bonds. The fraction of rigid (unbroken) filler clusters decreases with increasing strain, whereas the fraction of soft filler-clusters increases. The mechanical action of the soft filler clusters refers primarily to a viscoelastic effect, as any type of cluster that is stretched in the stress field of the rubber stores energy that is dissipated when the cluster breaks. This mechanism leads to a filler-induced viscoelastic hysteresis contribution to the total stress, which significantly affects the internal friction of the filled rubber samples. Note that this kind of hysteresis response is present also in the limit of quasi-static deformations, where no explicit time dependency of the stress-strain cycles is taken into account. A sketch of the two basic micro-mechanical mechanisms giving rise to stress softening and filler-induced hysteresis of elastomer nanocomposites is shown in Fig. 2. According to the DFM, the apparent stress of filled elastomers consists of two contributions: the stress of the rubber matrix, which is amplified due to the presence of rigid filler particles and clusters with virgin filler-filler bonds, and the stress of the strained (and broken) soft filler clusters with damaged fillerfiller bonds. The free energy density of filler reinforced rubber is shown as: W(ε μ ) = ( 1 Φ eff ) WR (ε μ ) + Φ eff W A (ε μ ) (1) where ε μ are the principal strains for μ = 1,.., 3 and Φ eff is the effective filler volume fraction of the structured filler particles, S123 for example, primary carbon black aggregates. The first addend considers the equilibrium energy density stored in the strained rubber matrix, which includes hydrodynamic strain amplification effects varying with the fraction of relatively stiff filler clusters with strong virgin filler-filler bonds. The second addend considers the energy stored in the residual fraction of more soft filler clusters with damaged bonds that are deformed in the stress field of the rubber matrix. The free energy density of the strained rubber matrix is described by a nonaffine tube model of rubber elasticity (20 23): ( ) G c W R εμ = 2 + ln 1 T 3 e n e ( 3 )( ) μ=1 λ2 μ 3 1 T e n e μ=1 ( 1 T 3 ) e n e μ=1 λ2 μ 3 λ 2 μ 3 + 2G e 3 λ 1 μ=1 μ 3 The first bracket term of Eq. (2) considers the inter-chain junctions, with an elastic modulus G c proportional to the density of cross-links or network junctions. The second addend is the result of tube constraints, whereby the tube constraint modulus G e is proportional to the entanglement density of the rubber. The parenthetical expression in the first addend corresponds to a non-gaussian extension of the tube model taking into account the finite chain extensibility of the polymer network. The finite extensibility parameter is chosen as the ratio n e /T e with n e being the number of statistical chain segments between two successive entanglements and T e is the trapping factor characterizing the portion of elastically active entanglements. As T e increases with the number of cross-links in the system (0 <T e <1), the finite extensibility parameter decreases with increasing cross-linking density. The presence of rigid filler clusters, with bonds in the virgin, unbroken state of the sample, give rise to hydrodynamic reinforcement of the rubber matrix. This is specified by the strain (2) Fig. 2. Schematic drawing of micro-mechanical mechanisms giving rise to stress softening and filler-induced hysteresis of elastomer nanocomposites. The inset on the right side represents the mechanical connection of filler particles by confined polymer forming glassy-like polymer bridges.

5 S124 amplification factor X, which relates the external strain ε μ of the sample to the internal strain ratio λ μ of the rubber matrix: λ μ = 1 + X ε μ (3) In the DFM, the strain amplification factor depends on the preconditioning of the sample and gives rise to the well-known stress softening effect of filler reinforced rubbers. In the case of preconditioned samples and for strains smaller than the previous straining (ε μ <ε μ,max ), the strain amplification factor X is independent of strain and determined by ε μ,max: X = X (ε μ,max ). For the first deformation of virgin samples, it depends on the external strain X = X (ε μ ). For fractal clusters, X (ε μ,max )orx (ε μ ) can be evaluated by averaging over the size distribution of rigid clusters in all space directions. In the case of preconditioned samples, this yields: X (ε μ,max ) = 1 + c Φ eff 2 3 d f 3 μ=1 φ ( ξ μ) dξ μ + 1 d ξ μ,min ξ μ,min 0 ( ξ ) dw d f μ d (4) ( ) φ ξ μ dξ μ where c is a constant of order one, Φ eff is the effective filler volume fraction, ξ μ is the cluster size, d is the particle size, d f 1.8 is the mass fractal dimension, and d w 3.1 is the anomalous diffusion exponent on cluster-cluster aggregation. The φ(ξ μ ) is the normalized size distribution that can be derived from the Smoluchowski equation of the kinetics of cluster-cluster aggregation of colloids. With the abbreviation x μ ξ μ /d and the normalized mean cluster size x 0 ξ 0 /d, it reads: φ (x μ ) = 4 x μ x 0 exp ( 2 x ) μ x 0 μ = 1, 2, 3 (5) We point out that with this distribution function the integrals in Eqs. (4) and (6) can be solved analytically. The second addend in Eq. (1) considers the energy stored in the substantially strained filler clusters. It delivers a filler induced hysteresis due to cyclic stretching, breakdown, and reaggregation, which is described by an integral over the soft filler clusters in stretching direction ( ε μ > 0) with strain dependent upper boundary: W A (ε μ ) = ε μ >0 μ 1 2 d ξ μ (ε μ ) ξ μ,min ( ) ( ) ( ) G A ξ μ ε 2 A,μ ξ μ, ε μ φ ξ μ dξ μ where the dot denotes time derivative. The sum over stretching directions with ( ε μ > 0) implies that clusters store energy by being stretched and re-aggregate upon contraction. The G A is the elastic modulus and ε A,μ is the strain of the soft filler clusters in spatial direction μ. The dependency of these quantities on cluster size ξ and external strain ε μ can be derived from basic (6) Fleck et al. micro-mechanical considerations regarding elasticity and fracture mechanics of tender filler clusters imbedded into a strained rubber matrix (13). This analysis has shown that the cluster strain under a certain load rises stronger with cluster size than the failure strain does. Accordingly, with rising load, large clusters break first followed by smaller ones. The critical size of currently breaking clusters ξ μ (ε μ ) entering into the upper integration limit of Eq. (6) is derived as: x μ (ε) = Q d ε d,b d 3 ˆσ R,μ (ε) s d ˆσ R,μ (ε) This involves the tensile strength of damaged bonds s d, which can be expressed by their failure strain ε d,b and elastic modulus Q d /d 3, and the stress of the rubber matrix relative to the start of the cycle where ε μ / t = 0: (7) ˆσ R,μ (ε) := σ R,μ (ε) σ R,μ ( ε μ / t = 0) (8) In a similar way the tensile strength of virgin bonds s v governs the minimum size of damaged clusters ξ μ min (ε μ,max ) appearing in the integration boundaries of Eqs. (4) and (6): x μ,min = Q v ε v,b d 3 ˆσ R,μ (ε max ) s v ˆσ R,μ (ε max ) The two parameters s d and s v will be treated as fitting parameters. A more detailed physical description of the DFM and the various experimental tests of the model can be found in the existing literature (13, 16 18). It should be noted that the consideration of filler induced hysteresis, described by Eq. (6), does not allow for a constitutive formulation of the DFM, as both concepts are restricted to the principal axis system. Nevertheless, by applying the concept of representative directions, introduced by Ihlemann (17), an implementation of the model into the Finite Element Method (FEM) has been achieved (17, 18). Evaluation of Surface Energy Distribution from Static Gas Adsorption Isotherms Measuring a static adsorption isotherm of the filler particles provides information regarding the amount of adsorbed gas as a function of pressure. From a BET-Plot, it is possible to evaluate the smallest amount of gas that covers the surface completely, which is the volume of a monolayer of gas V m. By dividing the total Volume V by the monolayer volume V m, the surface coverage is obtained. As the surface is, in most cases, not homogeneous, it is important to obtain information regarding the energetic heterogeneity. Therefore, the following integral equation can be used (25, 26): (9) (p, T) = ϑ (p, Q, T) f (Q) dq. (10) 0 Here, the left side of the equation represents the overall global isotherm that is actually measured. On the left side is an integral over all interaction energies Q present on the surface. Here, the model isotherm ϑ(p, Q, T) needs to be chosen in a sensible way and the energy distribution f(q) has to be obtained. For the

6 Polymer-Filler Interphase of Elastomer Nanocomposites model isotherm, usually a modified Langmuir isotherm can be used. In this work the model isotherm had the following form: ϑ(p, Q, T) = b2 BET b FGb L p 1 + b BET b FG b L p. (11) This modified Langmuir isotherm equation consists of a Fowler- Guggenheim correction term, b FG, that takes lateral interactions between the gas molecules into account, a BET correction for multilayer adsorption, b BET, and the classical Langmuir constant, b L : b L = N { } Aστ 0 Q exp. (12) 2πMRT RT Here, the cross-section of the gas molecules σ, the adsorption time τ 0, and the molar mass M is of importance in the prefactor. In the exponential, the heat of adsorption Q is present. Multilayer adsorption is corrected with a factor of the following form: b BET = 1 1 p p 0. (13) where p 0 is the saturation vapor pressure at measuring temperature T. Additionally, the lateral interaction is described by the exponential: { } zωθ b FG = exp. (14) RT If z is the number of neighbors for each molecule, zω can be approximated as 1 / 4 of the enthalpy of vaporization (25). The probability for gas molecules to occupy a site on the surface is equal to θ. Ifforθ one chooses the global isotherm, the sites are randomly occupied; if on the other hand, the model isotherm is chosen, this will represent a patch-wise distribution of surface-sites, which is in most cases closer to reality (25). Molecular Dynamics Simulation of Filler-Filler Bond Rupture As the computational capabilities of modern computers have improved drastically over the last decade, molecular modelling and simulations have become indispensable in explaining various phenomena in many areas of physics. Recent computational and theoretical advances of rubber reinforcement have been reviewed in existing literature (10, 27). Due to its relevance to experiments and applications, a special interesting aspect to examine by computer simulations is deformation and rupture in dense glassy polymer systems confined between surfaces of fillers. A series of molecular dynamics (MD) simulations to study microstructural changes, energy dissipation, and crazing during rupture of adhesive polymer films confined between atomic walls have been performed by Baljon and Robbins (28 30). In addition, the failure of polymer nanocomposites and the role of chain breakup in polymer adhesives have been investigated with MD simulations by Gersappe (31) and Sides et al. (32). Further relevant work concerning the role of boundary conditions in MD simulation under tensile stress has been provided by Makke S125 et al. (33). Analytical theories of the breakup of stretched polymer chains have also been developed and tested by simulation (34 36). Nonequilibrium dissipative particle dynamics (DPD) simulations have provided further evidence for the importance of finite chain extensibility and the polymer-filler interface to the nonlinear response of rubbers reinforced with nanofillers (37, 38). Furthermore, Liu et al. (39) studied dispersion and aggregation mechanisms of nanoparticles in polymer melts by applying MD simulations. A recent review article of Rottler (40) discusses general fracture mechanical features of glassy polymers from a molecular simulation perspective. Herein, we performed extensive nonequilibrium molecular dynamics (MD) simulations (41 43) to investigate the rupture mechanisms of glassy-like polymer bridges confined between surfaces of filler aggregates (see Fig. 3). Approximating the surfaces as atomic walls, it is possible to assign the realistic filler surface energy distribution (compare Fig. 4) by defining specific interaction strength at each wall atom (25). This will be a task of future work. In the present study, we have restricted ourselves to homogeneous wall energy distribution and have performed MD simulations of rupture at constant temperature, which is usually the case in experiments. Starting from different sample thicknesses and temperature conditions, which strongly Fille r Filler Fig. 3. Schematic drawing of filler-filler bonds, representing a filler polymer filler interphase, where red chains describe polymer chains and blue circles are the particles building the walls. The arrow indicates the direction of mechanical deformation. Potential [ε 0 ] LJ FENE LJ+FENE r/σ [ ] Fig. 4. Coarse-grained model: all monomers interact pairwise via the Lennard-Jones potential U LJ to prevent chains from crossing each other as well as self-crossing. The potential U FENE ensures chain connectivity.

7 S126 affect mechanical properties of such polymer system, we have monitored the rupture process by observing the structure (configurational snapshots) and thermodynamics (tensile stress, energy, temperature) during the simulation run. In our simulations we adopt a coarse-grained polymer model, which is widely used for a qualitative explanation of polymer physics phenomena. Within this so called bead-spring model (42), the polymers are represented as chains of connected monomers (beads), each of which interacts with its neighbors through the Lennard-Jones (LJ) potential (43). U LJ (r) = 4ε 0 [ (σ r ) 12 ( σ r ) 6 ] and finite extensible nonlinear elastic (FENE) potential (42): (15) ( ) ] r 2 U FENE = 0.5kR 2 0 [1 ln. (16) R 0 where ε 0 and σ are the characteristic energy and length scales and the distance between interacting particles is r. The finite extended length R 0 = 1.5 σ and the spring constant k = 30 ε 0 /σ 2.This model does not allow the chains to break. In addition, all unconnected monomers, whether belonging to the same or different chains, interact via the LJ potential in order to prevent chains from (self-) crossing. The interaction potentials are plotted in Fig. 5. We point out that in this coarse grained model, the connected beads of a chain are (almost) free to rotate around each other, indicating that a random walk statistics of chain segments is more or less realized. This implies that the consideration of bending and torsion potentials is not necessary. Accordingly, the size of the beads corresponds to the statistical segment length also denoted Kuhn s step length. As the real filler particles are much (up to hundred times) larger than the monomers of polymer molecules, the straight walls consisting of LJ atoms are a good approximation of filler surfaces as shown in Fig. 3. The beads interact pairwise with the upper and lower wall atoms by means of the LJ potential: U wall (r) = 4ε wall [ (σ r ) 12 ( σ r ) 6 ] Fleck et al. (17) with the interaction strength ε wall. The wall atoms are placed on a square lattice with the particle density equal to one. We point out that the exponents 12 and 6 in the LJ potential of Eq. (17) are used because the monomers interact with the single atoms of the walls. The integrated LJ potential with exponents 9 and 3 must be used when the monomers interact with a continuous solid wall. All physical quantities are expressed in LJ units of length σ, energy ε 0, and time τ = (mσ 2 /ε 0 ) 1/2. In these units the reduced temperature T = k B T/ε 0 (with k B being Boltzmann s constant), the reduced stress P = Pσ 3 /ε 0, and the reduced time t = t/τ. Standard periodic boundary conditions in the x- and y-directions parallel to the walls have been applied. Temperature control was maintained by using Kremer-Grest thermostat (44) with the friction coefficient 0.5τ 1. Newton s equations of motion are integrated with velocity-verlet algorithm (43), where the time step t = 0.01τ. Our simulations were carried out using MD code COGNAC of the OCTA package (45). All samples consist of 500 polymer molecules, each linear chain having 16 monomers, such that the entanglement length limit is not exceeded (42). The simulation box, confined by the walls in the z-direction, has equal sizes in the x- and y-directions derived from the requirement to obtain the desired average bead density n = 0.85σ 3 inside the simulation box. Experimental Section Materials The sample pool was prepared from three amorphous rubber types of different polarity: (i) ethylene-propylene-diene rubber (EPDM, Keltan 512) purchased from DSM (Geleen, Holland), which is a nonpolar rubber with few double bonds in side groups; (ii) solution-styrene-butadiene rubber (SBR, VSL HM) purchased from Lanxess (Leverkusen, Germany), which contains a high amount of polarizable units (50 vol.% vinyl and 25% styrene); and (iii) hydrogenated nitrile-rubber (HNBR, Therban 10 1 N339 (65 m 2 /g) 10 0 N339 + AMIC (55 m 2 /g) V/ V m p/p 0 (a) (b) Fig. 5. (a): 1-Butene adsorption isotherms (T = 267 K, p 0 = 101 kpa) of the CB N339 with and without treatment by AMIC; Inset: Schematic drawing showing the coverage of active sites by IL. (b) Energy distribution of N339 (±AMIC); Inset: Magnification of energy distribution at high energies demonstrating the reduction of high energy sites due to AMIC.

8 Polymer-Filler Interphase of Elastomer Nanocomposites C3446) also from Lanxess, which is a saturated, polar rubber with 34 vol.% acryl-nitrile units. The EPDM and SBR samples were cross-linked semi-efficiently by sulfur together with the vulcanization accelerators N-yclohexyl-2-benzthiazylsulfenamid (CBS) and Diphenylguanidin (DPG). The HNBR was crosslinked by peroxide (Luporox 101). As filler material the carbon black (CB) Corax N339 delivered from Orion Engineered Carbons (Cologne, Germany) was applied. For modification of the carbon black, the ionic liquid 1-allyl-3-methylimidazolium chloride (AMIC) from Sigma Aldridge (Hamburg, Germany) was used. The modification was done by pre-mixing 50 parts by weight of CB with 1 part by weight of AMIC together with an excess of ethanol in an ultrasonic bath for one hour. Afterward, the AMIC-coated CB was dried in an oven at 105 C. The modification technique of CB with AMIC and the obtained mechanical and dielectric properties of EPDM composites is described in more detail in literature (19). Static Gas Adsorption Techniques Volumetric static gas adsorption experiments were performed with the adsorption apparatus BELsorp max from BEL Inc. Japan. To get information about the surface, to which the polymer chain is attached, the polymer analogues gas 1-Butene was used as adsorptive. The samples were pretreated in a vacuum at 120 C for at least 2 hours. Stress-Strain Measurements Uniaxial multi-hysteresis tensile tests under quasistatic conditions with small strain rate ε 0.01/s at22 C were carried out with dumbbells using a Zwick 1445 universal testing machine. For the strain measurement, two reflection marks were placed in a distance of l 0 15 mm. Multi-hysteresis means: at constant velocity up and down -cycles between certain minimum and maximum strains, ε min and ε max, are carried out. This is done 5 times each step, and after every of such steps the boundaries of deformation are successively raised (ε max ) or lowered (ε min ), respectively. An example of uniaxial multi-hysteresis measurement with dumbbell is shown in Fig. 1. For the fitting procedure, every 5th up and down -cycle are considered, which can be regarded as being steady-state in a good approximation. For the uniaxial measurements engineering (nominal) stress σ 1 is determined by dividing the measured force by the initial cross-section area. To determine the nominal strain, ε 1, the displacement between two reflection marks glued onto the surface is measured and divided by the initial distance. Results and Discussion Characterization of Surface Energy Distribution To get an idea of how the surface influences the properties of the system, carbon black has been modified with the ionic liquid (IL) 1-allyl-3-methylimidazolium chloride (AMIC). Details concerning the characterization of surface modification by Raman-spectroscopy are found in literature (19). For a quantitative analysis of the change in surface activity, the surface of S127 the unmodified and modified filler particles has been characterized by static gas adsorption techniques down to low pressure. To obtain information about the interaction strength between typical diene-elastomers and the filler, the gas adsorption measurements were carried out with the polymer analogues gas 1-Butene, allowing for an estimation of the energetic heterogeneity of the surface. Fig. 4(a) shows the 1-Butene adsorption isotherms of the original CB N339 and the surface modified sample with the ionic liquid AMIC. By using an iterative formalism to solve Eq. (10), the energy distribution function f (Q) has been calculated from the adsorption isotherms. Fig. 4(b) shows that the treatment of carbon black with AMIC reduces the amount of high energy sites as well as drastically reduces the energetic heterogeneity. Previous research (19) drew conclusions from Raman spectroscopic data that the origin of the activity reduction is due to the adsorption of the IL at the crystallite edges at the CB surface, representing the highly active sites. This is shown schematically in the inset of Fig. 4(a). It implies that the polymer-filler interaction strength of the modified CB with nonpolar diene-elastomers is decreased because strong coupling of the polymer chains is mainly obtained by interactions of the double bonds with the crystallite edges (25). However, for more polar and saturated rubbers, we expect that the interaction strength with the modified CB might be increased due to attractive dipolar interactions with the strongly adsorbed IL. Effect of Filler Surface Modification on Stress-Strain Behavior From cyclic stress-strain experiments with cured samples information regarding the nature of the polymer and filler network can be extracted. Fig. 6 shows the 5 th cycles of the experimental stress-strain data (black lines) for EPDM samples with 40 phr CB (N339) with and without AMIC, which are fitted with the DFM (red lines). Obviously, the fitting is reasonable in both cases. The fitting parameters are shown in the inset of each plot. They are summarized in Table 1 and will be discussed later in detail. Obviously, simply by looking at the experimental data we can conclude that the stress values of the sample with modified CB are significantly smaller and the hysteresis is increased due to the modification of CB with AMIC. Fig. 7 shows the 5 th cycles of multi-hysteresis measurements (black lines) for the SBR samples filled with 40 and 50 phr CB (N339) with and without AMIC. Again, they are fitted with the DFM (red lines) delivering reasonable agreement between theory and experiment in all cases. The observed effects are similar as for the EPDM samples: The stress values are reduced, slightly, the hysteresis is increased and the setting behavior (i.e., the remaining negative stress at zero strain) is more pronounced. Finally, Fig. 8 shows the 5 th cycles of multi-hysteresis measurements (black lines) and the fits (red lines) for the polar HNBR samples filled with 20 and 40 phr CB (N339) with and without AMIC. Herein, the effects of surface modification are quite different from the EPDM and SBR samples: the stress values are significantly higher and the hysteresis as well as the set behavior seems to be more or less unaffected. This indicates that the reinforcement of HNBR by CB can be improved by the surface modification with AMIC, which might be of technical importance for applications of conducting fillers like CB in polar

9 S128 Fleck et al. 2,1 1,8 EPDM 40 phr N339 2,1 1,8 EPDM 40 phr N339 + AMIC 1,2 1,2 0,9 0,6 0,3 0,3 G_e ± G_c ± n ± s_d ± s_v ±1.258 x ± phi_eff ± sset ± ,9 0,6 G_e ± G_c ± ,3 n ±28.43 s_d ± s_v ± x ± ,3 phi_eff ± sset ± Downloaded by [TIB & Universitaetsbibliothek] at 03:42 14 February 2015 Fig. 6. Fitting of 5 th cycles of stress strain measurements with the DFM for EPDM samples filled with 40 phr N339 with and without AMIC, as indicated. Table 1. Micro-mechanical material parameters obtained from the fits of Figures 6 8 with the DFM for EPDM SBR and HNBR samples filled with variable amount of CB (N339) with and without AMIC (IL) G e G c n s v s d x 0 Φ eff s set Sample (MPa) (MPa) (-) (MPa) (MPa) (-) (-) (MPa) EPDM/40CB EPDM/40CB+IL SBR/40CB SBR/40CB+IL SBR/50CB SBR/50CB+IL HNBR/20CB HNBR/20CB+IL HNBR/40CB HNBR/40CB+IL rubbers. It seems that the strongly adsorbed IL at the CB surface increases the polymer-filler coupling due to attractive dipolar interactions between the IL and the ACN-units of the HNBR. Alternatively, the cross-linking process or the flocculation behavior of CB might be affected by the IL. We will see in the following section that a detailed analysis of the fitting parameters can answer these questions for the different rubbers used in this study. An adaptation of the multi-hysteresis stress-strain cycles in Figs. 6 8 with the DFM [Eqs. (1) to (9)] delivers microscopic material parameters characterizing the effect of CB surface modification by AMIC on the polymer and the filler network structure. The fitting parameters are summarized in Table 1. The polymerspecific parameters, G e,g c, and n, are shown in the left three columns followed by the fitting parameters describing the filler network, s v,s d,x 0, and Φ eff.thesetstresss set in the right column is an additional empirical parameter, which considers the remaining (negative) stress at zero strain after retraction. Hence, it is not a fitting parameter of the DFM, but has been adapted prior to the fitting procedure (16-18). Prior to the discussion of the effect of surface modification, we note that all micro-mechanical material parameters related to the filler network show a systematic dependence on filler concentration in agreement with previous observations (18). Accordingly, the tensile strength of virgin and damaged filler-filler bonds, s v and s d, both increase with filler loading, which can be related to a more pronounced filler flocculation. As expected, also the effective filler volume fraction Φ eff increases with filler concentration. The same behavior was determined for the set stress s set demonstrating that it was strongly affected by filler networking. Due to the fact that the parameters have a physical meaning, the reproducibility of the fits is high, indicating that there exists a unique solution for all fitting parameters. The errors for the single fitting parameters are shown in the inset of the plots in Figs. 6 8 behind the fitted values. Apart from a view, exceptions where the polymer or filler networking effects are not sufficiently marked, the errors are smaller than 5%. We will next discuss the effect of surface modification on the polymer-specific material parameters. If the samples with the original and modified CB are compared, the nonpolar EPDM and the slightly polar SBR, on the one side, and the polar HNBR, on the other side, show the same qualitative behavior

10 Polymer-Filler Interphase of Elastomer Nanocomposites S129 3,5 SBR 40 phr N339 G_e ± G_c ± n ± s_d ± s_v ±1.086 x ± phi_eff ± sset ± ,5 SBR 40 phr N339 + AMIC G_e ± G_c ± n ± s_d ± s_v ± x ± phi_eff ± sset ± Downloaded by [TIB & Universitaetsbibliothek] at 03:42 14 February ,5 SBR 50 phr N339 G_e ± G_c ± n ± s_d s_v ± ± x ± phi_eff ± sset ± ,5 SBR 50 phr N339 + AMIC G_e ± G_c ± n ± s_d ±1.207 s_v ±1.055 x ± phi_eff ± sset ± Fig. 7. Fitting of 5 th cycles of stress strain measurements with the DFM for SBR samples filled with 40 and 50 phr N339 with and without AMIC, as indicated. 3,5 HNBR 20 phr N339 G_e ± G_c ± n ± s_d ± s_v ± x ± phi_eff ± sset ± HNBR 40 phr N339 G_e ± G_c ± n ± s_d ± s_v ± x ± phi_eff ± sset ±0 3,5 HNBR 20 phr N339 + AMIC G_e ± G_c ± n ± s_d ± s_v ±1.435 x ± phi_eff ± sset ± HNBR 40 phr N339 + AMIC G_e ± G_c ± n ± s_d ± s_v ±1.065 x ± phi_eff ± sset ± Fig. 8. Fitting of 5 th cycles of stress strain measurements with the DFM for HNBR samples filled with 20 and 40 phr N339 with and without AMIC, as indicated.

11 S130 with opposite trends. In particular, for all EPDM and SBR samples, one observes a decrease of the tube constraint modulus G e and an increase of the cross-link modulus G c for the samples with modified CB, demonstrating that the entanglement density as well as the cross-linking density is affected by the presence of the IL. Both effects are more pronounced for the nonpolar EPDM. The influence of AMIC on the cross-linking process with sulfur is not surprising, as the IL may interact with the vulcanization accelerators. The reduction of the entanglement density of the sample with modified CB indicates that the number of surface-induced entanglements due to chain adsorption at the CB surface is decreased. This implies that the polymer filler interaction strength for the diene-elastomers EPDM and SBR, which are mainly coupled to the CB surface via dispersive interactions of the double bonds with highly active crystallite edges (25), is decreased by the treatment with AMIC. This correlates with the evaluated lower adsorption energy of the polymer analogues gas 1-Butene at the modified CB surface due to the coverage of active sites by IL (Fig. 4). Contrary, for the HNBR samples with modified CB the tube constraint modulus G e increases. This can be related to the attractive, dipolar polymer filler interaction due to the presence of strongly bonded ionic groups at the CB surface, which interact with the polar ACN-groups. The cross-link modulus G c remains almost constant though it decreases slightly, indicating that the peroxide cross-linking system is not affected by the IL. The number of chain segments between two trapped entanglements, n = n e /T e, with n e being the number of chain segments between two entanglements and T e the trapping factor, respectively, increases for the EPDM- and SBR samples with modified CB, which can primary be related to the reduced entanglement density, i.e. an increase of n e (G e 1/n e ). For the same reason, n is determined to decrease for the HNBR samples with modified CB as G e is increasing due to more surface induced entanglements. Note that the unexpected high value of n for the EPDM sample with modified CB exhibits a high error (see inset of Fig. 6) as the upturn behavior of the stress-strain cycles due to finite chain extensibility is mostly not visible. In the following discussion, we will consider the micromechanical material parameters reflecting the filler-filler interaction and filler networking listed in the right columns of Tab. 1. From our physical understanding of filler networking and reinforcement we expect a characteristic correlation of these parameters with the polymer-filler interaction strength as specified by the value of G e in the left column. Indeed, we observe an increase of the set stress s set, as well as the effective filler volume-fraction Φ eff for the modified EPDM- and SBR samples, and a decrease for the HNBR sample. The behavior of the set stress is intuitively clear, as it results from a viscos flow of filler particles during deformation. Obviously, a weaker coupling between polymer and filler supports this viscos flow while a stronger coupling suppresses it. The reduced polymerfiller interaction of the modified EPDM- and SBR samples is also reflected by the systematic increase of the effective filler volume-fraction Φ eff. The ratio between this parameter and the real filler volume-fraction is a measure for the more or less ramified structure of primary CB aggregates which is determined to be higher for the sample modified with AMIC. This indicates Fleck et al. that due to the weaker polymer-filler interaction the rupture of primary CB aggregates during mixing is less pronounced for the EPDM- and SBR samples, whereas it is more pronounced for the HNBR samples, respectively. The related mean cluster size x 0, representing the ratio between the cluster size and the particle (primary aggregate) size, is determined to be almost constant and not affected by AMIC. Nevertheless, there seems to be a small trend for an increased cluster size with decreasing polymer-filler interaction. Two further important parameters of filler networking are the tensile strength of virgin and damaged filler-filler bonds, s v and s d, respectively, delivering direct access to the strength of the filler clusters under external deformation. For these parameters, the expected correlation with polymer-filler interaction strength is not found for all systems. Only the nonpolar EPDM and the polar HNBR show this correlation if the samples with the original and modified CB are compared. However, for the slightly polar SBR systems the tensile strength of damaged filler-filler bonds, s d, increase significantly upon surface modification and the tensile strength of virgin filler-filler bonds, s v, increases slightly, though the polymer-filler interaction strength decreases, as indicated by a slightly decreasing tube constraint modulus G e. Contrary, for the EPDM- and HNBR samples, all three parameters (G e,s v, and s d ) show the same trend; that is, upon surface modification they all respond synchronic and decrease or increase, respectively. This appears reasonable if the morphological structure of filler-filler bonds, consisting of a fillerpolymer-filler interphase, is taken into account (compare Fig. 2). Accordingly, on the one side a weaker adsorption of EPDM chains at the CB surface due to the covering of active sites by IL supports adhesive failure of filler-filler bonds at the polymer-filler interface. On the other side, an enhanced adsorption of HNBR chains at the CB surface due to attractive dipolar interactions between the ACN-units and the strongly adsorbed IL suppresses adhesive failure of filler-filler bonds. At the moment, it remains unclear why this picture is not working for the SBR samples. A possible reason could be that in these systems the gap distance between filler particles, corresponding to the length of filler-filler bonds, is relatively large (13, 14). This could support cohesive failure of the bonds that might be less sensitive to changes in polymer-filler interaction. To obtain more insight into this question regarding different rupture modes of filler-filler bonds, the effect of gap distance and polymer-filler interaction strength on the strength of filler-filler bonds will be analyzed in detail in the next section by performing MD-simulations of filler-filler bond rupture under tension. Molecular Dynamics Simulations of Filler-Filler Bond Rupture In this section, we will address the systematic variation of tensile strength of virgin and damaged filler-filler bonds obtained from the fits with the DFM. We will attempt to confirm the developed picture regarding polymer-filler interaction and failure of fillerfiller bonds for the different polymer systems by performing a series of nonequilibrium molecular dynamics simulations, where the upper wall is pulled with the constant velocity v = 0.01σ/τ (compare Fig. 3) during the total fracture time τ.the

12 Polymer-Filler Interphase of Elastomer Nanocomposites S131 tensile stress P * T * = 0.3 T * = 0.4 T * = 0.5 T * = 0.6 T * = 0.7 T * = δ 0 = 5 Deformation rate ε tensile stress P * 4 δ 0 = 5 3 δ 0 = 8 δ 0 = 10 2 δ 0 = 12 δ 0 = 15 1 δ 0 = 20 0 T * = 0.3 Deformation rate ε (a) (b) Downloaded by [TIB & Universitaetsbibliothek] at 03:42 14 February 2015 Fig. 9. Tensile stress P during rupture of filler-filler bonds as a function of strain ε: in (a) the curves are for a thin polymer layer (bond length) with δ 0 = 5.0 at various temperatures, in (b) curves correspond to the polymer layers of various initial thicknesses δ 0 at fixed temperature T = 0.3. rupture process has been monitored in details for various gap distances between filler particles (initial thickness of polymer layer between walls) and temperatures. Stretching has been carried out with the Poisson ratio equal to zero. This takes reference to the strong constraints of a thin polymer layer confined between two attractive walls implying that the lateral contraction under tension is strongly suppressed. Instead, cohesive failure and cavity formation is expected to appear when the chains are strongly bonded to the surface. The relevant quantities (tensile stress, temperature, energy, etc.) describing the rupture process have been averaged over the interval of 500 steps. The rupture can occur either at the polymer-wall interface or within the polymer layer forming the filler-filler bonds [adhesive or cohesive failure (28), respectively]. As we are interested in strongly adsorbed elastomer chains at the filler surface, the pair interaction with the walls U wall should be stronger than U LJ within the polymers; therefore, we define ε wall > ε 0. In general, we choose ε wall = 2.0 and ε 0 = 1.0 similar to the literature (28). As we are interested in the effect of polymer-filler interaction strength, we also made simulations for a stronger coupling with ε wall = 3.0 and ε wall = 4.0. The polymer layers used in our simulations are of various thicknesses, starting from very thin with the distance between the walls δ = 5.0σ and increasing to δ = 8.0σ and δ = 15.0σ. The film thickness δ is represented in units of σ as δ 0 = δ/σ. More details of the simulation procedure are found in literature (46). We start the analysis of structural and mechanical processes inside the polymer layer undergoing rupture by first examining behavior of the force needed to displace the top wall with constant velocity. Fig. 9 shows the tensile stress as a function of strain. First, the polymer layer deforms elastically and stress increases linearly with time. The density in the simulation box decreases. The stress continues to rise until it reaches a yield stress. Then the layer becomes unstable and one or more small cavities begin to form. This allows the rest of the layer return to equilibrium density and tensile stress drops sharply. As we observe in Figs. 9(a, b) the height of the stress peak depends on temperature and layer thickness. Such behavior of the yield stress is related to the interplay of internal and external energy contributions. It must be noted that it was not possible to bring all samples to an equilibrium state prior to wall separation, even after an equilibration time of several days. This implies that the samples are not initially stress free; that is, the stress-strain curves in Fig. 9 are not going through the origin in all cases. Nevertheless, we think that the stress-strain curves at larger strains and the estimated maximum stress values are not strongly affected by this discrepancy because a systematic dependence on temperature T and layer thickness δ 0 was observed. Separation of the walls beyond the yield point causes plastic deformation inside the polymer layer. In this stage, small peaks on the stress-strain curves showed up, which correspond to structural rearrangements of polymers leading to an increase of cavity size. As stress drops, the cavities grow and merge until just a few polymers connect the walls by attaching their ends to the wall surfaces. The remaining bridge chains become almost completely oriented perpendicular to the walls. As rupture progresses, the fully stretched polymers detach their ends from one wall and collapse on the opposite side until no more polymers exist connecting the walls. Such failure mechanism, typical for dense polymeric systems at low temperatures (28 30), isstrongly affected by different confinements and temperatures. In Fig. 10 three typical snapshots representing different types of film rupture behavior are shown. In rupture mode A (Fig. 10a), (a) (b) (c) Fig. 10. Rupture modes A, B and C: in (a) many single polymer bridges are formed between the walls in thin samples (δ 0 = 5.0); in (b) few cavities separated by bridges develop in intermediate samples (δ 0 = 8.0), which grow and merge as rupture progresses; in (c) only one large bridge is formed in thick samples (δ 0 = 15.0), that stretches until the walls are completely separated.