14TH DRESDEN POLYMER DISCUSSION Meißen, Germany, May 25 to 28, 2014 Understanding of Reinforcement in Polymer Networks and Melts

BOOK OF ABSTRACTS

The 14th Dresden Polymer Discussion is sponsored by

Chairpersons: Gert Heinrich (IPF Dresden and TU Dresden, Germany) Marina Grenzer-Saphiannikova (IPF Dresden, Germany) in co-operation with Rainer Jordan (TU Dresden, Germany) Local organizing committee: Kerstin Wustrack Juliane Jeschke Jan Domurath Contact: Leibniz-Institut für Polymerforschung Dresden e. V. Hohe Str. 6, 01069 Dresden Phone: +49 351 4658-282/367 Fax: +49 351 4658-214 E-Mail: DPD14@ipfdd.de Website: www.ipfdd.de/DPD14

PREFACE The 14th Dresden Polymer Discussion focuses on reinforcement effects in polymer networks and melts on all relevant scales, from molecular to macroscopic, making an attempt to better understanding of those effects and their utilization for material developments by bringing together scientists active in different fields of fundamental as well as applied science. Dresden Polymer Discussions are – nomen est omen – meetings characterized by intensive discussions and therefore held with a strictly limited number of participants in a venue that provides under one roof the conference location and accommodation for all participants. Most of the lectures are invited talks by representatives of groups leading in the field. TOPICS METHODS • hydrodynamic reinforcement • experimental techniques • polymer-filler and filler-filler interactions • statistical physics • percolation and jamming transitions • computer simulations • strain-induced crystallization • continuum modeling GENERAL INFORMATION VENUE AND REGISTRATION/CONFERENCE OFFICE Evangelische Akademie Meißen Freiheit 16, 01662 Meißen tel. +49 (0) 3521 47060 The conference office is located in the foyer of the main entrance. tel. of the conference office 0160 / 97216924 The lecture hall is called “Propsteisaal” (2nd floor). Opening hours: Sun, May 25, 2015: from 17:00 to 22:00 Mon, May 26 to Wed, May 28, 2014: from 8:30 throughout all sessions COFFEE AND LUNCH BREAKS Drinks and snacks during the breaks will be available at buffets close to the lecture hall (2nd floor) and the poster displays in the room “Katharina” (1st floor). Lunch is served at the dining hall “Tonne” in the ground floor (accessible from the foyer of the main entrance). INTERNET WLAN/WiFi access is provided for the participants during the meeting and is free of charge. Access data can be obtained in the conference office. PRESENTATIONS UPLOAD OF PRESENTATIONS Please contact one of our student helpers in the lecture hall to upload your presentations in the break before your presentation at the latest. POSTERS Posters should be mounted by the beginning of the lunch break on Monday and will be up during the entire duration of the meeting.

SOCIAL EVENTS SIGHTSEEING AND CONFERENCE DINNER Tuesday, May 27, 2014, 16:00 to 18:00 Sightseeing in the Staatliche Porzellan-Manufaktur Meissen (Meissen Porcelain Manufactory with museum, the special exhibition and the demonstration workshops). After enjoying the sightseeing we get up to the historic restaurant “Vincenz Richter” which is located at the market square of Meißen – You may expect dinner in an informal and relaxing atmosphere in one of the oldest houses in the historic centre. No special dressing code. Registration is required (no extra charge for active participants, EUR 70 for accompanying persons).

PROGRAM SUNDAY, MAY 25th 17:00 Arrival

Start of registration

19:30 Dinner

Discussions

MONDAY, MAY 26th 8:15 Breakfast page

Chairperson: M. Grenzer-Saphiannikova 9:00

Gert Heinrich Dresden, Germany

Opening Why do we need a well-grounded understanding of the reinforcements in polymers?

9

9:30 Helmut Münstedt Erlangen, Germany

Rheological behaviour of particle-filled polymer melts

10

10:00 Alexander Chervanyov Dresden, Germany

Effects of polymer-mediated interactions on the coagulation-fragmentation of fillers in the presence of shear flow

11

10:30 Break 11:00 Philippe Cassagnau

Lyon, France Viscoelasticity and dynamics of suspensions and nanocomposites filled with nanorods

12

11:30 Julien Férec Lorient, France

Rheological modeling of rod suspensions with interactions: from particles to macroscopic behavior

13

12:00 Vladimir Toshchevikov Dresden, Germany

Relaxation spectrum of a polymer network with included particles: a regular cubic network model

14

12:30 Lunch

Chairperson: F. Ehrburger-Dolle 13:30 Paul Sotta

Lyon, France Discriminating entropic and non-entropic contributions to elastomer reinforcement

15

14:00 Christopher George Robertson Ohio, USA

Flocculation in elastomeric polymers containing nanoparticles: Jamming and the new concept of fictive dynamic strain

16

14:30 James Busfield, London, UK

Rubber reinforcement at small strains 17

15:00 Break

Chairperson: M. Klüppel 15:30 Amit Das

Dresden, Germany

Rubber reinforcement by nanoparticles: Preparation and properties

18

16:00 Wilma Dierkes Twente, Netherlands

The influence of non-rubber constituents on the reinforcement of natural rubber by a silica/silane filler system

19

16:20 Caroline Fayolle Lyon, France

Temperature dependence of the linear and non-linear mechanical response of elastomer nanocomposites

20

16:40 Lewis Tunnicliffe London, UK

Carbon black flocculation effects in natural rubber 21

17:00 Break

17:20 Poster Discussion

18:30 Dinner

TUESDAY, MAY 27th 8:15 Breakfast page

Chairperson: S. Govindjee 9:00 Stefanie Reese

Aachen, Germany Finite element micro-field simulation illustrating the effect of micro-structure morphology on stress softening in filled elastomer networks

22

9:30 Manfred Klüppel Hannover, Germany

The role of polymer confinement between filler particles in rubber reinforcement

23

10:00 Francois Lequeux Paris, France

Mechanical non linearity of elastomers in the glass transition domain

24

10:30 Break

Chairperson: J. L. Valentin 11:00 Françoise Ehrburger-Dolle

Grenoble, France Stress relaxation in strained filled elastomers 25

11:30 Kay Saalwächter Halle, Germany

Filler effects on segmental dynamics and local chain deformation in elastomers: Insights from NMR

26

12:00 Wim Pyckhout-Hintzen Jülich, Germany

Investigations of supramolecular interactions in polymer networks with neutron scattering

27

12:30 Lunch

Chairperson: G. Heinrich 13:30 Michael Rubinstein

North Carolina, USA Nanoparticle dynamics in polymer melts and networks

28

14:00 Kristian K. Müller-Nedebock Stellenbosch, South Africa

Modelling reversible and irreversible polymer networks with variable functionality for reinforcement

29

14:30 Jens-Uwe Sommer Dresden, Germany

Effective interactions of nanoparticles in polymer matrices

30

15:00 Break

16:00 Sightseeing

19:39 Conference Dinner

WEDNESDAY, MAY 28th 8:15 Breakfast page

Chairperson: S. Reese 9:00 Sanjay Govindjee

California, USA A micro-mechanically based continuum for strain-induced crystallization in natural rubber

31

9:30 Karsten Brüning Dresden, Germany

Kinetics of self-reinforcement of natural rubber by strain-induced crystallization: An X-ray diffraction approach

32

9:50 Toshio Tada Kobe, Japan

Stress relaxation behavior of carbon black filled rubber under uni- and biaxial stretching

33

10:10 Stanard Mebwe Pachong Stellenbosch, South Africa

Density fluctuation of reversible cross-links in permanent networks

34

10:30 Break

Chairperson: J. Busfield 11:00 Stephan Westermann

Colmar-Berg, Luxembourg Matrix chain deformation in reinforced networks - a SANS approach

35

11:20 Juan L. Valentin Madrid, Spain

Evaluation of structure of rubber (nano)composites by time-domain NMR

36

11:40 Marina Grenzer-Saphiannikova Dresden, Germany

Closing Approaches to hydrodynamic reinforcement in polymer melts and networks

37

12:00 Lunch

status: as of June 2, 2014

nr. title authors1 Mesoscopic simulations of colloids in polymeric

systems by responsive particle dynamicsW.K. den Otter, I.S. Santos de Oliveira,B. Fitzgerald, S. Luding, W.J. Briels

2 Strain amplification effects in filled elastomers J. Domurath, M. Saphiannikova,T. Horst, G. Heinrich

3 Analysis ofcrack growth in elastomers undermulti-axial load state

S. Gorelova, K. Schneider, G. Heinrich

4 Physically based multi-scale approach to dynamic-mechanical behavior of reinforced rubbers

I. Ivaneiko, V. Toshchevikov,K.W. Stöckelhuber, M. Saphiannikova,G. Heinrich

5 Tuning mechanical properties in magneto-sensitive elastomers

D. Ivaneyko, V. Toshchevikov, M. Saphiannikova, G. Heinrich

6 Order and phase behavior of copolymer/nano-particle mixtures: A molecular dynamicssimulations study

L. S. Shagolsem, J.-U. Sommer

7 Effect of melt mixing conditions on the filler dispersion and rheological properties of PC/SAN polymer blends filled with graphenenanoplatelets

M. Liebscher, P. Pötschke, G. Heinrich

8 Homogenization of slender structures in small-strain regimes

St. Neukamm

9 Reinforcement mechanisms in natural rubber materials: Low-field NMR and X-ray diffraction study

A. Vieyres, K. Schneider, G. Heinrich

10 Polymer dynamics and crosslink density of SBR nanocomposites containing fillers with different surface area

A. Mujtaba, M. Keller, S. Ilisch, H-J. Radusch,T. Thurn-Albrecht, K. Saalwächter, M. Beiner

LIST OF POSTERS

Abstracts of the lectures

WHY DO WE NEED A WELL-GROUNDED UNDERSTANDING OF THE REINFORCEMENT IN POLYMERS? G. Heinrich1,2 1) Leibniz-Institut für Polymerforschung Dresden e. V., Hohe Straße 6, 01069 Dresden, Germany 2) Technische Universität Dresden, Institut für Werkstoffwissenschaft, 01062 Dresden, Germany Relatively few applications of polymer melts or cross-linked polymer networks use the polymer in its unfilled state. In the latter case, reinforcement signifies primarily an inevitable increase in ultimate rubber properties such as modulus, tear and tensile strength and abrasion resistance. Even though rubber reinforcement by carbon (channel) black was already discovered in 1911, it took until 1940 before extensive scientific investigations of the mechanisms of reinforcement were undertaken. Within the last two decades several new aspects came into play, as nanofillers of spherical, non-spherical and layered shape were introduced as reinforcing ingredients. Clearly, reinforcement impacts several features of polymer material processing as well as the performance level of rubbers under different modes of application. However, on the other side reinforcement in rubbery networks or polymer melts led to a long list of interesting and challenging scientific questions which, for example, are attributed to the understanding of hydrodynamic reinforcement polymer-filler interactions, filler-filler interactions below and above critical filler percolations thresholds, filler cluster morphologies and their characterization, flocculation phenomena, depletion interactions, non-linear rheological phenomena, soft glassy rheology and jamming concepts, and self-reinforcing effects due to crystallization. This list could even be extended by some “chemical” keywords, which highlight the role of surface chemistry or surface nano-pattern of the reinforcing particles. The whole puzzle needs support by a spectrum of new adapted experimental methods (e.g. NMR and neutron scattering), models and theories that enable a multi-scale understanding of structure, morphology and mechanical and dynamic-mechanical behaviour of reinforced polymer systems. Support may come, for example, from disciplines such as statistical physics of reinforced polymer networks and polymer melts, spatial statistics as the art to model spatial (fractal) filler cluster structures, etc. Finally, a well-grounded understanding of the reinforcement in polymers provides a physical basis for micromechanical modelling and finite element simulations of reinforced polymer networks and melts on macroscopic length scales as indispensable tools for versatile technical applications.

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RHEOLOGICAL BEHAVIOUR OF PARTICLE-FILLED POLYMER MELTS H. Münstedt Friedrich-Alexander-University Erlangen-Nürnberg, Institute of Polymer Materials, Martensstr. 7, 91058 Erlangen, Germany Rheological properties of particle-filled polymer melts are of interest from two points of view. Regarding processing one would like to know in which way the addition of particles influences the viscosity as a function of shear rate or shear stress and how the elasticity is affected which is the reason for the swelling of extruded items, for example. A short qualitative description of the general effects due to fillers in this predominantly non-linear regime will be given. Linear rheological properties are of interest when structural changes and interactions between particles or between particles and matrix molecules are the aims of research. Rheological measurements at constant stresses are the experimental method preferred for such kind of investigations as the stress is the decisive physical quantity which determines the mechanical behaviour of a material. Such creep experiments can rather easily be performed in shear as the geometry of a sample does not change during deformation. Regarding the samples investigated, the presentation is divided into the two categories of highly filled and sparsely filled systems. For high filler concentrations interactions between particles dominate. It is shown from viscosity measurements on glass beads in a polyisobutylene how a structure builds up under shear at small stresses and how it is destroyed by larger ones. The influences of concentration, size, distribution, and surface properties of particles will be discussed. Additional information on structure break up is obtained from measurements of the recoverable strain after previous deformations of a sample in creep. At lower stresses a remarkable recovery is found, whereas at higher stresses a measurable recoverable portion is not detected Interactions between particles and matrix molecules are investigated on poly- methylmethacrylate filled with low concentrations of various silicates. In the linear range of deformation the viscosity is only weakly affected by the particles. The steady-state elastic compliance, however, exhibits significant increases at small filler concentrations. From the time dependence of the recoverable compliance measured in creep-recovery experiments, retardation spectra are calculated which reveal distinct maxima for the filled samples in comparison to the matrix. They can be explained by assuming interactions between matrix molecules and particles which reduce the mobility of polymer molecules adjacent to the particle surfaces. By a systematic change of the specific surface area of the fillers experimental evidence is added to support the model. Creep-recovery experiments in the non-linear range of deformation show a distinct decrease of the recoverable compliance with growing stress. This result can be interpreted by assuming a detachment of the molecules from the particles at higher stresses.

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EFFECTS OF POLYMER-MEDIATED INTERACTIONS ON THE COAGULATION-FRAGMENTATION OF FILLERS IN THE PRESENCE OF SHEAR FLOW A.I. Chervanyov 1) Centre for BioNano Interactions, University College Dublin, Dublin 4, Ireland 2) Leibniz-Institut für Polymerforschung Dresden e.V., Hohe Straße 6, 01069 Dresden, Germany We investigate the effect of the polymer mediated (PM) interactions on the coagulation-fragmentation of colloids immersed in the sheared polymer system. Our theoretical analysis addresses both cases of fast and slow coagulation of colloids, as is described in what follows. In the case of fast coagulation, the coagulation-fragmentation of colloids is shown to be driven by the competition between the processes of Brownian coagulation and shear induced fragmentation, described by respective collision rates in our model. In order to describe this competition, we have developed the self-consistent mean rate approach that makes it possible to analytically solve the coagulation–fragmentation balance equations subject to the mass conservation constraint. The developed approach is not restricted to a specific form of the coagulation and fragmentation rates, thus being applicable to a variety of different coagulation–fragmentation processes. As an example of the practical applicability of the developed method we have calculated the aggregate size distribution and average aggregate diameter for the above case of shear induced fast coagulation–fragmentation. In the case of slow coagulation, the interactions among colloids must be taken into account, including PM interactions. This effect is calculated by making use of the analytic self-consistent field theory of the PM interactions between nanocolloids developed in our previous work. Specifically, we applied our theory to calculate the potential of the PM force acting between nano-colloids bearing irreversibly adsorbed polymer layers, immersed in a bath of non-adsorbing polymers. On the basis of the obtained results for the PM potential, we have calculated the stability ratio and rate of the coagulation in the presence of adsorbing and non-adsorbing polymers. As a final result of our studies, we constructed the coagulation-fragmentation diagram that quantifies the combined effect of the Van der Waals and polymer-mediated forces on the process of PM colloid coagulation-fragmentation in the presence of shear. Kinetic stability of the material-specific polymer-colloid systems is discussed.

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VISCOELASTICITY AND DYNAMICS OF SUSPENSIONS AND NANOCOMPOSITES FILLED WITH NANORODS Ph. Cassagnau Université de Lyon, Univ Lyon 1, CNRS, Ingénierie des Matériaux Polymères, 15 Boulevard Latarjet, 69622 Villeurbanne Cedex, France philippe.cassagnau@univ-lyon1.fr The development during the past two decades of nano- or sub-micrometer particles with high aspect ratio has led to a significant increase of studies on nanorods and/or nanofibers and on their applications. The most significant feature of nanofibers is obviously their 1D aspect ratio (generally L/d > 10) with typically a diameter below 100 nm. Due to their nanosize, these anisotropic particles have high surface-to-volume ratios resulting in an increase of the interactions with other substrates in different fields of applications. The objective of this communication is to discus on the linear viscoelasticity of suspensions and of polymers filled with nano-size particles of different aspect ratios and aggregation. First of all, it is of importance to point out that the viscoelastic behaviour of nano-filled system must be discussed from the knowledge of the dispersion of nanoparticles in terms of dispersion at different scales (from primary to aggregate particles) and anisotropy (privileged orientation of anisotropic particles). The main question that can be derived from different studies is the following: What we can we learn from the viscoelasticity of suspensions to understand the melt reinforcement of nanocomposites? In other words, we intend to qualitative compare some rheological behaviours of liquid suspensions with some viscoelastic behaviour of molten nanocomposites. We have recently demonstrated1 that carbon nanotubes (CNT), cellulose whiskers and polymer nanofibres in dilute and semi-dilute regimes obey an universal diffusion process ( 3

0η φ∝ , 2rD φ−∝ )

by Brownian motion according to the Doi-Edwards theory providing that these nanofillers are well dispersed and stabilized in the suspending liquid. However in the case of carbon nanotubes2,3, the Brownian motion combined with low shear deformations induces an aggregation mechanism. However, these aggregates broke down at high shear, forming small aggregates with less “entanglements”, leading to non linearity effects. Actually, the aggregation of nanoparticles can be controlled in suspensions. If we can expect to control the particles aggregations in suspension, the situation is obviously different in nanocomposites where the viscous forces are the dominant ones. Actually, the anisotropic particles or aggregates are submitted do strong orientations under flow leading to some specific particle rearrangements and finally to anisotropic properties. The non linearity effect (Payne effect for example) can be then explained from the breakdown of aggregates. Qualitatively, there is a strong analogy in Payne effect observed in molten nanocomposites and the transition between Newtonian and shear-thinning behavior of suspensions. Actually, the rheological behavior of suspensions and the non-linearity of nanocomposites are correlated to the spatial organization of primary particles and aggregates deriving from the balance of the different forces involved in such complex media. [1] Cassagnau P, Zhang W, Charleux B, Rheol Acta, 2013, 52:815-822 [2] Moreira L, Fulchiron R, Seytre G, Dubois P, Macromolecules, 2010, 43(3), 1467-1472 [3] Ma AWK, Mackley MR, Rahatekar SS, Rheol.Acta, 2007, 46: 979–987

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RHEOLOGICAL MODELING OF ROD SUSPENSIONS WITH INTERACTIONS: FROM PARTICLES TO MACROSCOPIC BEHAVIOR J. Férec Univ. Bretagne-Sud, Laboratoire d’Ingénierie des Matériaux de Bretagne (LIMATB), EA 4250, LIMATB, F-56100 Lorient, France julien.ferec@univ-ubs.fr Nanofibers, carbon nanotubes (CNTs) and nanocrystalline celluloses (NCCs) are now widely investigated in order to modulate polymer functionalities at nanoscale. As for short fibers at microscale, these nanoparticles present a rod-like shape and form nanosuspension systems, which exhibit different nanostructures depending on their concentrations. The first part of this talk deals with the mathematical development of a rheological model for fiber suspensions with a more precise modeling of fiber-fiber interactions. This constitutive equation consists in an extension of the Dinh and Armstrong (1984) model. In addition to the hydrodynamic contribution of the fibers, the total stress results from an additional component due to fiber-fiber interactions. Accordingly, novel second and fourth order interaction tensors are defined. Moreover, a new time evolution equation is proposed, where the diffusion term is proportional to the average number of contacts between fibers. The model is validated using experimental data in transient and steady shear flows for concentrated fiber suspensions in a polybutene. Measured reduced viscosity and primary normal stress differences exhibit quadratic functions, as predicted by the model. The transient behavior is also fairly well estimated, considering that the model only requires three parameters to fit the behaviour of suspensions over a wide range of fiber concentrations. The second part of this talk focus on CNTs. Carbon nanotubes have been recognized as one of the most attractive material with a wide range of possible applications. As a polymer filler, CNTs have shown improvements of mechanical properties, but a complete understanding of the rheological behavior of CNT suspensions is an objective yet unfulfilled. In order to explain the shear thinning of untreated CNT suspensions, a new set of rheological equations is developed. The CNTs are modelled as rigid cylinders dispersed in a Newtonian matrix and the evolution of the system is controlled by hydrodynamic and rod-rod interactions. The force due to the interactions is modelled as a non-linear lubrication force which is a function of the relative velocity at the contact point, and it is weighted according to the contact probability. The total stress tensor is evaluated calculating the well known fourth order orientation tensor and a new fourth order interaction tensor. The Fokker-Planck equation is numerically solved for steady state simple shear flows using a finite volume method avoiding the need of closure approximations. The model predictions show a good agreement with the simple steady shear data of CNTs dispersed in a Newtonian Epoxy matrix. Finally, the last part proposes a first attempt to define a two-scales kinetic theory description of suspensions involving short fibers, nano-fibers or nanotubes. When the concentration becomes high enough, complex microstructures can be observed. They involve a diversity of fiber clusters or aggregates with complex kinematics, and different sizes and shapes. These clusters can interact to create larger clusters and also break because the flow induced hydrodynamic forces. It is proposed a double-scale kinetic theory model that at the first scale considers the kinematics of the clusters, whose structure itself is described at the finest scale, the one related to the rods constituting the clusters. The procedure is then extended to more general particle shapes such as platelets.

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RELAXATION SPECTRUM OF A POLYMER NETWORK WITH INCLUDED PARTICLES: A REGULAR CUBIC NETWORK MODEL V. Toshchevikov1,2,*, Yu. Gotlib2 1) Leibniz-Institut für Polymerforschung Dresden e. V., Hohe Straße 6, 01069 Dresden, Germany 2) Institute of Macromolecular Compounds, Bolshoi pr. 31, Saint-Petersburg, 199004, Russia Polymeric composites based on cross-linked polymer networks with included rigid particles remain a subject of extensive investigations due to wide use of these materials in engineering and in everyday life [1]. Understanding of an interrelation between the structures of polymeric composites and their physical properties is one of the determining factors for the further development of these materials. In the present work, a theory of the viscoelastic properties of crosslinked polymer networks with included particles is developed. A regular cubic network model is used, which was proposed previously to study the mechanical properties of polymer networks of different structures [2-5]. In the present study the regular cubic network model is modified for polymer networks with included particles and takes into account the viscoelastic interaction of the included particles with the network fragments [6]. The particles are assumed to be close to isotropic (spherical), and their mobility is described by introduction of the friction coefficient that is directly proportional to the size of particles. The relaxation-time-density function is calculated depending on the viscoelastic parameters of the proposed dynamic model. In the framework of this model, the relaxation spectrum consists of two branches: One corresponds to the local displacements of the particles relative to the crosslink sites; the other describes the long-scale collective motions of the particles together with the network fragments. Increase in the friction coefficient of the included particles (e.g., due to increase in their size), as well as an increase in the coefficients of mutual friction between the chain fragments and between the particles and crosslink sites (due to an increase in kinetic rigidity of macromolecules), leads to the increase in the relaxation times of both branches of the relaxation spectrum for the network with included particles. An increase in the coefficient of the elastic interaction between the particles and network junctions leads to a decrease in the relaxation times of both branches of the spectrum due to an appearance of rapid motions of the particles and crosslink sites relative to each other. At all values of the viscoelastic parameters of the model, the relative width of the relaxation spectrum for the network with included particles is higher than this quantity for the initial network without included particles. This theoretical result are in agreement with experimental data on the mechanical and dielectric relaxations of crosslinked composites [1], which demonstrated the broadening of the frequency and temperature dependences of the storage modulus, loss modulus, and dielectric loss factor for the filled crosslinked polymers relative to these dependences for the initial (unfilled) polymer networks. [1] T. A. Vilgis, G. Heinrich, and M. Klüppel: Reinforcement of Polymer Nanocomposites. Cambridge Univ.

Press, Cambridge, 2009. [2] A. Gurtovenko, Yu. Gotlib: Macromolecules 33 (2000), p. 6578. [3] Yu. Gotlib, V. Toshchevikov: Polymer Science, Ser. A 48 (2006), p. 649. [4] V. Toshchevikov, Yu. Gotlib: Macromolecules 42 (2009), p. 3417. [5] V. Toshchevikov, G. Heinrich, Yu. Gotlib: Macromol. Theory Simul. 19 (2010), p. 195. [6] V. Toshchevikov, Yu. Gotlib: Polymer Science, Ser. A 55 (2013), p. 556.

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DISCRIMINATING ENTROPIC AND NON-ENTROPIC CONTRIBUTIONS TO ELASTOMER REINFORCEMENT P. Sotta Laboratoire Polymères et Matériaux Avancés, CNRS / Solvay UMR 5268 R&I Centre – Lyon, 85 rue des frères Perret, 69192 Saint-Fons Cedex, France paul.sotta-exterieur@solvay.com Understanding reinforcement mechanisms, which are responsible for the remarkable mechanical properties of elastomers filled with nanometric particles, implies combining complementary techniques. Here, we propose an approach based on the combination of different experiments in order to discriminate various reinforcement effects in elastomers filled with carbon black or silica: mechanical reposne, independent measurements of the crosslink density by multiple quantum proton NMR and of the chain segment orientation undre stretching by X-ray scattering, in unfilled and filled vulcanized natural rubbers with various crosslink densities. In unfilled materials, all measurements correlate nicely, in agreement with rubber elasticity theory. In filled materials, analyzing the deviations with respect to the behavior of the pure unfilled elastomer allows discriminating various physical mechanisms. We demonstrate that the mechanical response at medium/large strains is essentially driven b ystrain amplification effects, while in the linear regime, there is a strong additional reinforcement, which corresponds to a breakdown of entropic elasticity theory and thus is not related to the properties of the elastomer matrix.

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FLOCCULATION IN ELASTOMERIC POLYMERS CONTAINING NANOPARTICLES: JAMMING AND THE NEW CONCEPT OF FICTIVE DYNAMIC STRAIN Ch. G. Robertson Eastman Chemical Company, 260 Springside Dr., Akron, OH 44333-2433, USA crobertson@eastman.com The recent literature has revealed some fascinating parallels between the effect of temperature on traditional glassy materials and the role of deformation on the behavior of granular solids, foams, and particle-filled polymers and pastes. A new concept of fictive dynamic strain is developed in the present work for nanoparticle-reinforced rubbery polymers by drawing an analogy to the use of fictive temperature in the phenomenological treatment of structural relaxation (physical aging) in the non-equilibrium glassy state. The progressive structural arrest (jamming) that occurs during the filler flocculation process in uncrosslinked elastomers is modeled as a function of both the actual dynamic strain and the fictive strain. The fictive strain converges toward the actual strain as the system approaches steady state. The utility of the modeling approach is demonstrated using literature data for the flocculation of silica nanoparticles in an ethylene-propylene-diene rubber (EPDM) melt.

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RUBBER REINFORCEMENT AT SMALL STRAINS J. J. C. Busfield, L. B. Tunnicliffe and A. G. Thomas Queen Mary University of London, Materials Research Institute, Mile End, London, E1 4NS, UK j.busfield@qmul.ac.uk Reinforcement of rubber with fillers such as carbon black and silica produces an increase in both the elastic and viscoelastic behaviour. While the increase in elastic modulus with particulate volume fraction is well understood in terms of hydrodynamics, dynamic filler networking and occlusion of rubber matrix by the filler agglomerates, the temperature-dependent changes in viscoelastic behaviour are less well understood. This is partially due to the complexity of studying filled rubber systems. For example, the fillers do not homogeneously disperse throughout the rubber matrix with the extent of particulate aggregation depending upon the filler type and the detailed processing conditions. Understanding the behaviour is also complicated by chemical crosslinking varying between filled samples despite the use of equivalent curing systems as the crosslinking chemistry is affected by the presence of highly active, high surface area filler particles. This also makes a direct comparison between samples with differing volume concentrations difficult. Under conditions of small dynamic strains (typically < 0.1 %) many of the issues associated with the Payne Effect non-linearity, such as filler structure breakdown, are not encountered; which permits a simplified study of the reinforcement. Working at small strains, in the linear viscoelastic region allows viscoelastic parameters (tanδ, G’, G’’) of filled rubbers to be understood in terms of three effects: 1. How active-surface particles alter the chemical crosslinking processes and how this might alter

the dynamic properties (G’, G’’) of the rubber matrix in filled systems. 2. How the dispersion of the filler phase (as well as the filler volume fraction) might determine both

the extent of hydrodynamic amplification of the modulus (G’) and any non-linear filler structure breakdown.

3. How an interphase polymer region at the filler interface where the labile attachment of the

polymer to the filler surface affects both the magnitude of the hydrodynamic reinforcement (G’) and viscous dissipation losses in the bulk material (G’’).

Model filled rubbers prepared using a variety of filler particles of various surface areas, morphologies and surface activities are characterised to help understand the effects of each of these on the viscoelastic properties.

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RUBBER REINFORCEMENT BY NANOPARTICLES: PREPARATION AND PROPERTIES A. Das1, 2, K. W. Stöckelhuber1 and G. Heinrich1,3 1) Leibniz-Institut für Polymerforschung Dresden e. V., Hohe Straße 6, 01069 Dresden, Germany 2) Tampere University of Technology, Fi-33101, Tampere, Finland 3) Technische Universität Dresden, Institut für Werkstoffwissenschaft, 01069 Dresden, Germany Reinforcement of rubber is generally realized by the incorporation of fine solid particles into the elastomer matrix. This is absolutely necessary to achieve desired wearing properties, strength and durability of the final elastomer products. For this purpose, usually carbon black and silica have been used by the industries since some decades. As is known, when silica is used as fillers in tire tread formulation the benefit from reinforcement is also connected with a lowering of the tire rolling resisitance. On the other hand in the last decade, exploitation of nano-dimensional fillers in rubber composites has evoked a lot of interest due to the reinforcement effect of nano-fillers relatively at lower loading as compared with carbon black and silica. Although the primary particle size of both amorphous silica and carbon black remains in the range of nano-scale, practically these particles exist in the micrometer size range due to aggregation and agglomeration. This aggregates and agglomerates are difficult or nearly impossible to dissociate into individual particles. However, if a proper technique is followed the nano-dimentional fillers, for example, carbon nanotubes, layered silicate etc. can be efficiently dispersed into individual particles in the rubber matrix. The present talk reviews our recent work on the preparation and characterisation of reinforced elastomeric materials with carbon nanotubes and some layered materials. As far as carbon nanotubes are concerned the dispersion of the tubes are facilitated by the use of imidazolium based ionic liquid. A significant increase of the mechanical and electrical properties is observed when the method is applied in the chloroprene rubber matrix. Extremely fine dispersion and a strong tube-tube networking of the tubes are understood by several experimental techniques. In another work, the layered silicate minerals are considered as nano-size filler in natural rubber compounds. Gradual intercalation of fatty acids inside the layered space expands the gallery gap between two crystalline layers of the minerals. The use of such expanded form of the clay develops a highly exfoliated morphology of the clay particles in natural rubber matrix. The established filler clusters and the filler networks show interesting scaling laws of the modulus-loading relationship above a percolation threshold which differ significantly from the corresponding laws in the carbon black or silica case. The reinforcement effect of these silicate minerals is not only understood by the observation of enhanced stress-strain properties but also is reflected in tear-fatigue properties. A significant reduction in crack growth rate was noticed when the natural rubber is comprised with fatty acid modified clay. [1] Subramaniam, K.; Das, A.; Stöckelhuber, K.W.; Heinrich, G. Rubber Chemistry and Technology 86 (2013)

367-400 [2] Rooj, S.; Das, A.; Stöckelhuber, K.W.; Wang, De-Yi; Galiatsatos, V.; Heinrich, G., Soft Matter 9 (2013) 3798-

3808

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THE INFLUENCE OF NON-RUBBER CONSTITUENTS ON THE REINFORCEMENT OF NATURAL RUBBER BY A SILICA/SILANE FILLER SYSTEM J.W.M.Noordermeer1, W.K.Dierkes1, S.S.Sarkawi1,2, K. Sahakaro1,3 1) University of Twente, Department of Elastomer Technology and Engineering, 7500 AE Enschede,

The Netherlands 2) Malaysian Rubber Board, RRIM Research Station Sg. Buloh, 47000 Selangor, Malaysia 3) Centre of Excellence in Natural Rubber Technology (CoE-NR), Department of Rubber Technology

and Polymer Science, Faculty of Science and Technology, Prince of Songkla University, Pattani 94000, Thailand

Silica/silane filler systems are more and more replacing the traditionally used carbon black as reinforcing filler in elastomers. The key element of the high-dispersion silica technology is the chemical reaction of the silanol groups on the surface of silica with the coupling agent. The latter eventually creates a chemical link between the silica particles and the elastomer molecules during vulcanization, the basis of the outstanding reinforcing strength of this filler system as well as the specific dynamic properties of silica-filled elastomers. However, when applied to natural rubber (NR), this technology poses several problems, and the most crucial but unavoidable one is the fact that NR is a natural product. Natural rubber contains non-rubber constituents such as proteins and phospholipids up to a concentration of 6%, and these organic components contribute to the outstanding strength properties of NR. In silica-filled NR, however, proteins and coupling agents have an antagonistic effect; they compete with each other during the silanization reaction. The presence of proteins makes the silane less efficient in improving dispersion and filler-polymer coupling, and thus negatively influences the reinforcement strength of silica and the final properties of the rubber: stress strain properties vary with protein content, as do dynamic properties. Furthermore, the protein content influences the rheological properties as well as filler-filler interactions: the dispersion of silica is improved when a high amount of protein is present; the interactions between proteins and silica are able to disrupt the silica-silica network. Another characteristic of NR is the intrinsically low thermal stability compared to most synthetic polymers. For the silica-silane reaction, the rather high temperatures and long reaction times put a considerable thermal burden on the polymer, which can lead to a partial degradation of NR during the mixing and silanization process. High amounts of proteins reduce the thermal sensitivity, and this effect is most pronounced when no silane is used. However, proteins are not able to replace a coupling agent.

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TEMPERATURE DEPENDENCE OF THE LINEAR AND NON-LINEAR MECHANICAL RESPONSE OF ELASTOMER NANOCOMPOSITES C. Fayolle1, R. Pérez-Aparicio1, O. Sanséau1, D. Long1, P. Sotta1 and L. Vanel2 1) Laboratoire Polymères et Matériaux Avancés, CNRS/Rhodia-Solvay, UMR5268, 85 avenue des

Frères Perret, 69192 Saint Fons Cedex, France 2) Institut Lumière Matière, CNRS/Université Lyon 1, UMR5306, 69622 Villeurbanne Cedex, France caroline.fayolle@solvay.com Reinforced elastomers are used in tread tires because of their interesting mechanical properties. Indeed, the addition of nanofillers in the matrix, such as Carbon Black or Silica, modifies the mechanical response, in particular the dissipation [1]. Understanding the mechanisms involved in the non-linear mechanical reinforcement of elastomer is thus a key point to control this property. Reinforcement is complex and may involve different mechanisms related to the morphology of the compounds [2],[3], the molecular dynamics [4] and the filler-matrix interface. Although the temperature dependence of reinforcement is well-known [1], the physical mechanisms controlling it both in the linear and non-linear regime are still debated [5]. In order to get a better understanding, reinforcement of filled cross-linked elastomer networks have been investigated for a wide variety of materials, through viscoelastic characterizations in both linear and non-linear regimes and at different temperatures. The following materials have been processed: (1) elastomer matrix (Natural Rubber or Styrene Butadiene Rubber), (2) type of filler (Carbon Black or Silica), (3) volume ratio, (4) Silica-matrix interface (covering agent and coupling agent) and (5) cross-linking densities have been changed. [1] Wang M.J.: Rubber Chemistry and Technology 71 (1998), p. 520-589 [2] Kraus G.: Rubber Chemistry and Technology 51 (1978), 297-321 [3] Huber G., Vilgis T.A. and Heinrich G.: Journal of Physics Condensed Matter 8 (1996), p. 409-412 [4] Berriot J., Montes H., Lequeux F., Long D. and Sotta P.: Macromolecules 35 (2002), p. 9756-9762 [5] Meera A.P., Said S., Grohens Y. and Thomas S.: The Journal of Physical Chemistry C 113 (2009), p. 17997-

18002

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CARBON BLACK FLOCCULATION EFFECTS IN NATURAL RUBBER L. B. Tunnicliffe, A. G. Thomas, J. J. C. Busfield Soft Matter Group, Queen Mary University of London, UK The tendency of particulate fillers such as carbon blacks and precipitated silicas to flocculate in rubber melts during processing is a key issue defining the strain-dependent viscoelastic properties of vulcanised, filled rubbers; for example the Payne Effect. We examine the effects of varying the surface free energies of various carbon black fillers through thermal treatment (graphitisation) on flocculation processes in natural rubber melts. Various experiential techniques are used to characterise these effects: flocculation measurements taken on a Rubber Process Analyser (RPA) and determination of the electrical and mechanical percolation thresholds of vulcanisates via D/C conductivity testing and dynamic mechanical analysis. The results show that the surface free energies of the carbon blacks play a key role, along with particle size and loading, in defining the magnitude of the flocculation process. This is interpreted in terms of the varying interactions of polymer chains with high energy sites on the filler surfaces such as graphitic plane edges. The nature of the boundary condition defined by the polymer-filler interaction influences the diffusion coefficient of the particulates. This is explored further using Brownian Dynamic simulations implemented in the LAMMPs software.

21

FINITE ELEMENT MICRO-FIELD SIMULATION ILLUSTRATING THE EFFECT OF MICRO-STRUCTURE MORPHOLOGY ON STRESS SOFTENING IN FILLED ELASTOMER NETWORKS St. Reese and D. Sodhani RWTH Aachen University, Institute of Applied Mechanics, Mies-van-der-Rohe Str 1, 52074 Aachen, Germany stefanie.reese@rwth-aachen.de, deepanshu.sodhani@rwth-aachen.de Characteristic properties of elastomers including their fatigue behaviour and wear resistance can be tailored by embedding them with filler particles. Along with enhancing the overall properties of the system, filler particles also induce some inelastic stress softening effects like the Mullins effect. Modelling concepts like debonding of elastomer chains from filler surface [1] or breakage and formation of filler networks [2], under the given loading condition have been used to explain the stress softening effects. But so far there does not exist a unanimously agreed upon theory to describe the Mullins effect. In this work, computational modelling using full-field finite element simulations has been employed to study the mechanical behaviour of such systems. Non-linear models are applied to predict the macroscopic large deformation behaviour, with morphology evolution and deformation occurring at the microscopic level, using the representative volume element (RVE) approach. The approach is based on a micro mechanically motivated constitutive model, describing the behaviour of elastomeric matrix within the RVE [3]. The elastomeric matrix is divided into two phases; stiff bound elastomer close to the surface of the filler particles which transforms into a soft bulk elastomer away from the surface of the filler particle. Theory of the shift in the glass transition temperature of the elastomer in the vicinity of filler particles is used to model the changing stiffness of the bound rubber [4]. The overlapping of bound elastomer around filler particles lead to the formation of glassy bridges between different filler particles resulting in a filler network, which along with the macro-molecular chain network forms the microstructure of the system. Microstructure morphology can be explained by breakdown (yielding) and formation (healing) of glassy bridges under loading. To incorporate this effect a micro- mechanically motivated finite plasticity model for elastomers is used to model the bound elastomer [5]. To reduce the computation time filler particles are modelled using repetitive mesh units which is referred to as filler element. The nano-composite micro-structure is reconstructed at the RVE level using a random particle generation algorithm, with the assumption of periodicity. Computational experiments using this methodology enable prediction of the strain- softening behaviour of filled elastomers, observed experimentally, and to understand the behaviour of the inter-phase interaction between two filler particles and its effect on the characteristics of filled elastomers. The benefit of this approach is the predictability of the model relating one or more micro-structural effects to a macroscopic phenomenon. [1] S. Govindjee and J. Simo, Journal of the Mechanics and Physics of Solids, 39, pp. 87-112, 1991. [2] M. Klüppel, Chemistry and Materials Science, 164, pp. 1-86, 2003. [3] S. Reese, International Journal of Plasticity, 19, pp. 909-940, 2003. [4] S. Merabia, P. Sotta and D. Long, Macromolecules, 41, pp. 8252-8266, 2008. [5] W. Dettmer and S. Reese, Computer Methods in Applied Mechanics and Engineering, 193, Nr. 1-2, pp. 87-

116, 2004.

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THE ROLE OF POLYMER CONFINEMENT BETWEEN FILLER PARTICLES IN RUBBER REINFORCEMENT M. Klüppel

Deutsches Institut für Kautschuktechnologie e. V., Eupener Straße 33, 30519 Hannover, Germany The structure and dynamics of confined polymer between adjacent filler particles play a key role in understanding the mechanical properties of filler-reinforced elastomers. It has been demonstrated that several aspects of linear and non-linear viscoelasticity of filled rubbers can be traced back to the specific rate and temperature dependent properties of the confined polymer, forming glassy-like polymer bridges which transmits the stress between adjacent filler particles [1-6]. The pronounced non-linear behavior was shown to be related to the rupture of this kind of filler-filler bonds, which deform under strain and break if a critical strain is exceeded. This mechanism has been described analytically in the frame of a microstructure-based model of rubber reinforcement, denoted Dynamic Flocculation Model, where the cyclic breakdown and re-aggregation of tender filler clusters connected by glassy-like polymer bridges is formulated [6-9]. It allows for a microscopic understanding of the complex stress-strain response during repeated, quasi-static deformations up to large strains, i.e. the well known filler induced stress softening and hysteresis effects. Recently, the mechanical and fracture properties of glassy polymer bridges under tension have been explored by a series of non-equilibrium molecular dynamics simulations of polymer films confined between two attractive solid walls [10,11]. Depending on the degree of confinement, different rupture mechanisms are found which can be related to the interplay of polymer-polymer and polymer-wall interactions. The yield stress and the Young modulus of the polymer films are calculated from the stress-strain response of the confined polymer film at various temperatures, strain rates, polymer-wall interaction strengths and film thickness. These investigations provide a useful molecular tool for understanding the strongly non-linear mechanical response of filled elastomers. For sufficient small gap size, the temperature dependence of the modulus indicates glassy behavior of the confined polymer, also above the glass transition temperature of the bulk. The estimated temperature behavior of the yield stress is found to be in fair agreement with experimental estimates of the tensile strength of filler-filler bonds (glassy-like polymer bridges), as obtained from adaptations of the quasi-static stress-strain response of carbon black filled SBR-rubber with the Dynamic Flocculation Model. [1] Klüppel M., Adv. Polym. Sci. 164, 1 (2003) [2] Klüppel, M., J. Phys.: Cond. Matter. 21, 035104 (2009) [3] Fritzsche, J., Klüppel, M., J. Phys.: Cond. Matter. 23, 035104 (2011) [4] Montes, H., Chaussee, T., Papon, A., Lequeux, F., Guy, L., Eur. Phys. J. E31, 263 (2010) [5] Papon, A., Montes, H., Lequeux, F., Oberdisse, J., Saalwächter, K., Guy, L., Soft Matter 8 , 4090 (2012) [6] Lorenz, H.; Freund, M.; Juhre, D.; Ihlemann, J.; Klüppel, M., Macromol. Theory Simul. 19, 110 (2010) [7] Freund, M., Lorenz, H., Juhre, D., Ihlemann, J., Klüppel, M., Int. J. Plasticity 27, 902 (2011) [8] Lorenz, H., Klüppel, M., J. Mech. Phys. Solids 60, 1842 (2012) [9] Lorenz, H., Klüppel, M., Heinrich, G., ZAMM, Z. Angew. Math. Mech. 92, 608 (2012) [10] Froltsov, V., Klüppel, M., Raos, G., Phys. Rev. E 86, 041801 (2012)Klüppel, M., Froltsov, V. and Juhre, D., P.

287 in N. Gil-Negrete and A. Alonso (Eds.), "Constitutive Models for Rubber VIII", Taylor and Francis Group, London (2013)

23

MECHANICAL NON LINEARITY OF ELASTOMERS IN THE GLASS TRANSITION DOMAIN P. Shi1, H. Montes1, F. Lequeux 1, E. Munch 2, R. Schach2

1) Soft Matter Science and Engineering, ESPCI ParisTech - CNRS, UMR 7615, 10 rue Vauquelin, 75005 Paris, France

2) Manufacture Française des Pneumatiques Michelin, Centre de Technologies, 63040 Clermont Ferrand Cedex 9, France

francois.lequeux@espci.fr If cross-linked elastomers are able to undergo elastic deformation of large amplitude– up to a few unities - glassy polymer exhibit a plastic behaviour a few per cent deformation. We have recently performed non-linear mechanical measurments in the crossover between the glassy and the rubber behaviour. We have indeed used perfectly miscible blends (PB/SBR) to enlarge the glass transition domain, and we have take a lot of care in quantifying the eventual self-heating. We have shown quantitatively that the linear visco-elastic properties of these blends behave like a tiling of domains with different glass transition temperatures that can be easily measured by calorimetry [1]. We show from a non-linear mechanical study in the glass transition domain that: 1) if the entanglement slipping model [2]

described well the mechanical response above the glass transition, when approaching the glass transition, the entanglement sliding is slow down, and as the results the mechanical response tends to be exactly the one predict by the Gaussian affine model.

2) Slightly below the glass transition, a plastic behaviour appears, extremely similar to the Payne effect. We show that this phenomenon appears at the percolation threshold of the slow domains – i.e. the polymeric domains with a relaxation time slower than the inverse of the frequency.

Indeed, we have also observed also these properties in the single component polymers. Dynamics heterogeneities have been the object of many studies and are now well accepted. Here we show indeed that, the mechanical properties of a polymer glass have to be modelled by an array of elementary domains that exhibit each one a very different mechanical properties, with a hugely distributed relaxation time We observe for the first time Payne effect on non filled elastomers. We will also explain why the Payne effect in the glass transition domain, of unfilled polymer, should be of importance in the understanding of the mechanical properties of filled elastomers. [1] Peiluo Shi, Régis Schach, Etienne Munch, Hélène Montes, and François Lequeux Macromolecules, 2013, 46

(9), 3611–3620 [2] Michael Rubinstein, Sergei Panuykov Macromolecules 2002, 35, 6670-6686

The red curve described the non-linearity amplitude as compared to the deviation to the Gaussian Affine model. The black curve describes simply the elastic modulus. The horizontal axis is the reduced frequency. The left part of the curve (domain II) reveals the disappearance of entanglement slipping. The right part (domain III and IV) exhibits the plasticity appearance. The boundary between domain II and II is the onset of percolation of the slow domain.

24

STRESS RELAXATION IN STRAINED FILLED ELASTOMERS

F. Ehrburger-DolleLaboratoire Interdisciplinaire de Physique (LIPhy), UMR 5588 CNRS-UJF, 38402 Saint-Martin d'Hères, France

The aim of our work was to relate, at a given strain , the dynamics of the filler particles observed at the mesoscopic scale to the macroscopic relaxation of the tensile modulus E(t). To this end, X-ray photon correlation spectroscopy (XPCS) and tensile relaxation modulus measurements were performed simultaneously on samples maintained at a constant elongation during about 4000 s. In order to investigate sequences effects (Mullins effect in filled elastomers), different strain levels (0.20, 0.40, 0.60) reached by first positive (UP1), negative (DOWN) and second positive (UP2) jumps have been considered. It is well known that the filler-filler and the filler-matrix interactions play an essential role in the properties and the dynamics of filled rubbers. Therefore, different nanoparticles as hydrophilic (Si-OH) or hydrophobic (Si-OR) silica and carbon black (CB) were used as fillers. The matrix consisted in an Ethylene Propylene Diene Monomer (EPDM) rubber cross-linked with dicumyl peroxide. Filler loading was equal to 40 phr. XPCS was performed mainly in the heterodyne mode [1] that yields the true velocity of the filler particles and its evolution with time in the strained sample. It appears that the velocity always

decreases with time as a power law tn . The value of the exponent n, however, depends on the sample. As an example, for the Si-OH sample (strong filler-filler interaction), n is close to 1 or slightly larger (1.2). On the opposite, for the CB sample (strong filler-matrix interaction), n is close to 2 or slightly smaller (1.8). Furthermore, for the former, the velocity remains significantly larger than for the latter sample. For a strain , the tensile relaxation modulus measured after an UP jump decreases as log(t) for the CB sample. For the DOWN jumps and for the Si-OH sample (UP and DOWN), the experimental data can be fitted by the following power law equation (similar to the Chasset-Thirion one): ( ) [ ( ⁄ ) ] where for UP jumps and for DOWN jumps. The exponent m ranges between 0.04 and 0.28, depending on the value of the strain and on the type of jump. These features imply a power law dependence of the rate of change of the tensile modulus: | ( ) ⁄ | . In this equation ( ) varies between 1 (logarithmic decrease of E(t)) and 1.28. It will be shown that the combined XPCS and mechanical experiments bring clues for soft glassy

rheology (SGR) in filled elastomers strained above 0.20. Particularly, the exponent could be assimilated to the noise temperature introduced by Sollich [3], corresponding to a glass transition and corresponding to a liquid state. For strains , all UP curves are better fitted by a stretched exponential equation:

( ) ( ) [ ( ⁄ ) ] in which is close to 0.5 whilst the DOWN curves follow the

power law equation. All these features which bring new information about stress relaxation in strained filled elastomers will be thoughtfully discussed in the presentation.

[1] F. Livet et al. J. Synchrotron Rad. 13 (2006) p. 453–458.

[2] F. Ehrburger-Dolle et al. Macromolecules 45 (2012) p. 8691-8701. [3] P. Sollich Phys. Rev. E 58 (1998) p. 738-759.

____________________

This work was achieved in collaboration with Isabelle Morfin (LIPhy), Françoise Bley and Frédéric Livet (SiMap, Saint-Martin d'Hères, France), Gert Heinrich (IPF Dresden, Germany), Luc Piché and Mark Sutton (McGill University, Montreal, Canada). Use of the APS was supported by the DOE, Office of Basis Energy Sciences, under Contract No. W-31-109-Eng-38.

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FILLER EFFECTS ON SEGEMENTAL DYNAMICS AND LOCAL CHAIN DEFORMATION IN ELASTOMERS: INSIGHTS FROM NMR K. Saalwaechter Martin-Luther-University Halle-Wittenberg, Faculty of Natural Sciences II, Institute of Physics - NMR Group, Betty-Heimann-Str. 7, 06120 Halle, Germany The mechanical properties of filled elastomers crucially rely on the arrangement, structure and in particular connectivity of the hard (undeformable) filler components. In addressing connectivity, constrained polymer chains and dynamic interphases represent a certain fraction of the overall matrix material and are thought to contribute significantly to the overall reinforcement effect. NMR is a well-suited technique to study the structure and the dynamics of such constrained phases with molecular resolution, possibly using simple low-field equipment [1]. In this presentation, I will discuss recent results on immobilized interphases arising from adsorption or binding of chains to filler particles in both, idealized model systems as well as real-life silica-filled elastomers. Our work on model materials shows that the structure factor of silica nanospheres in non-crosslinked poly(ethylene oxide) melts as detected by scattering techniques depends on the amount and length of grafted chains that emanate from an immobilized surface layer [2]. Concerning the latter, recent strong evidence has been gathered on the existence of a glass transition temperature gradient, being responsible for the complex thermomechanical behavior of filled rubbers [3,4]. Our new work on model materials reveals that such interphases do not form a contiguous layer around rigid filler particles or crystallites, but reside in island-like regions such as concave structures of a rough filler/crystallite surface. The phenomenon may be related to the requirement of stronger higher-dimensional constraints rather than a flat interface, or to the general nanoscale dynamic heterogeneity of polymers close to Tg. The phenomenon appears of general nature, and was also confirmed for interphases in semicrystalle polymers or SBS block copolymers. We could further show that there is a unique, strongly non-linear correlation between the rather low (a few percent) amount of immobilized material and the viscoelastic reinforcement in silica-filled SBR. We have further conducted NMR experiments on strained samples [5], where we detect the degree of local chain deformation on the level of the elastically active chains between crosslinks or entanglements. Our data on unfilled elastomers supports recent tube theories of rubber elasticity, and experiments on filled elastomers directly reveal the expected overstrain of the rubber matrix and a more inhomogeneous distribution of local strain as compared to the unfilled counterparts. [1] K. Saalwächter. Microstructure and molecular dynamics of elastomers as studied by advanced low-

resolution nuclear magnetic resonance methods. Rubber Chem. Technol. 85 (2012) 350-386. [2] S. Y. Kim, H. W. Meyer, K. Saalwächter, C. F. Zukoski, Polymer Dynamics in PEG-Silica Nanocomposites:

Effects of Polymer Molecular Weight, Temperature and Solvent Dilution. Macromolecules 45 (2012) 4225-4237.

[3] A. Papon, H. Montes, M. Hanafi, F. Lequeux, L. Guy, K. Saalwächter. Glass-Transition Temperature Gradient in Nanocomposites: Evidence from Nuclear Magnetic Resonance and Differential Scanning Calorimetry. Phys. Rev. Lett. 108 (2012) 065702

[4] A. Papon, K. Saalwächter, K. Schäler, L. Guy, F. Lequeux, and H. Montes. Low-Field NMR Investigations of Nanocomposites: Polymer Dynamics and Network Effects. Macromolecules 4 (2011) 913.

[5] R. Pérez Aparicio, M. Schiewek, J. L. Valentín, H. Schneider, D. R. Long, M. Saphiannikova, P. Sotta, K. Saalwächter, Maria Ott. Local Chain Deformation and Overstrain in Reinforced Elastomers: An NMR Study. Macromolecules 46, 5549 (2013).

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NEUTRON SCATTERING OF SUPRAMOLECULAR INTERACTIONS IN POLYMER NETWORKS W. Pyckhout-Hintzen, B. Gold, A.R. Bras, C. Weiss, C. Hövelmann, A. Wischnewski, D. Richter Forschungszentrum Jülich, Jülich Centre for Neutron Science (JCNS1) and Institute for Complex Systems (ICS-1), D-52425 Jülich, Germany Telechelic or comblike interactions of hydrogen-bonding groups may lead to chain extension, more complicated clustering or even network-like behaviour. Using systems that are of the double-network type with both covalent and transient linkages new enhanced properties for novel applications like self-healing could be achieved. We present a first neutron scattering approach that addresses both structural and dynamic aspects of such linear assembly and networks, combined with dynamical and mechanical analysis. Supramolecular bonding effects will be discussed from the sight of neutron scattering.

27

DYNAMICS OF NANOPARTICLES IN POLYMER MELTS AND NETWORKS AND THEIR EFFECT ON RHEOLOGY M. Rubinstein1, L.-H. Cai2, S. Panyukov3

1) University of North Carolina, Department of Chemistry, Chapel Hill, North Carolina 27599-3290, USA

2) Harvard University, School of Engineering and Applied Sciences, Cambridge, Massachusetts 02138, USA

3) Russian Academy of Sciences, P. N. Lebedev Physics Institute, Moscow 117924, Russia We use scaling theory to derive the time dependence of the mean-square displacement <r2(t)> of a nanoparticle in polymer melts and networks. We distinguish several qualitatively different regimes depending on the size d of the particle in comparison to tube diameter a of entangled polymers. In addition, we propose a hopping mechanism for diffusion of large nanoparticles subjected to topological constraints in polymer networks and entangled polymer melts. The combination of non-activated and hopping diffusion describes the motion of nanoparticles in polymeric nanocomposites and the transport of drug carriers in biological gels, such as mucus. The effect of nanoparticles on dynamics of host melts and networks is calculated based on the idea that nanoparticles primarily couple to modes with wavelength smaller than the size d of the particles. This theory predicts that smaller nanoparticles act as plasticizers by reducing melt viscosity, while larger nanoparticles act as hardeners.

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MODELLING REVERSIBLE AND IRREVERSIBLE POLYMER NETWORKS WITH VARIABLE FUNCTIONALITY FOR REINFORCEMENT K. K. Müller-Nedebock Stellenbosch University, Department of Physics, Institute of Theoretical Physics, Matieland 7602, South Africa We present a theoretical study of the properties of polymer networks where polymer strands are not only cross-linked but also linked to and by other objects embedded within the medium of the gel. The aims are to understand both how these different modes of linking as well as how the physics of the possibly complex reinforcing particles influence the predicted elastic and structural behaviour of the medium. Our model includes multiple functionalities for linking polymer chains. It also allows for species of links that are permanent and reversible – a mixture of quenched and annealed network formation conditions. For these purposes we draw on a field theoretical formalism developed by Edwards [1]. These methods enhance the scope for describing different mechanisms of linking, network and cluster formation [2,3]. The resulting highly nonlinear theory can be shown to have sensible, readily interpretable physical results. We demonstrate how the formalism enables the embedding of complex reinforcing structures into a network under both quenched and annealed conditions of linking. Interestingly, we show how the field theory also provides perspectives on dynamics of such networks. [1] S.F. Edwards: Journal de Physique France 49 (1988) pp. 1673-1682 [2] S. Kuchanov, S.V. Korolev, S.V. Panyukov: Advances in Chemical Physics 72 (1988) pp. 115-325 [3] R. Fantoni, K.K. Müller-Nedebock: Physical Review E 84 (2011) art. no. 011808

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EFFECTIVE INTERACTIONS OF NANOPARTICLES IN POLYMER MATRICES J.-U. Sommer1,2, X.-Z. Cao1,3, H. Merlitz1,3

1) Leibniz-Institut für Polymerforschung Dresden, Hohe Straße 6, 01069 Dresden, Germany 2) Technische Universität Dresden, Institut für Theoretische Physik, 01062 Dresden, Germany 3) Xiamen University, Department of Physics and ITPA, China It is well known that particles in polymer matrices attract each other due to entropic depletion forces which are caused by the gain of free volume if the depletion-zones of the particles with respect to the polymers overlap. We have used Molecular Dynamics simulation techniques to calculate two- and three-body forces between nano-particles immersed in semi-dilute and concentrated polymer solutions with different interactions between monomers and particles and in the presence of solid walls. For purely repulsive interactions the entropic depletion attraction is in excellent agreement with the scaling predictions by Joanny and de Gennes, and is independent of the chain length for concentrations well above the overlap threshold [1]. Since the depletion attractions are proportional to the osmotic pressure of the polymer solution they can become strong in the case concentrated solutions and melts and can lead to cluster-formation and segregation of nanoparticles there. The latter effect is further enhance by three-particle interactions [2]. Attractive forces between particles and monomers can compensate for this effect as long as the direct attraction is small. For large parti-cle-monomer interactions each particle can be considered as being “coated” with a dense polymer layer which in turn interacts with other “coated” particles via an effective depletion attraction [3]. Thus, only in a small window of interaction (or temperature) depletion-attraction can be compen-sated and particles can be perfectly dispersed in a polymer matrix. These results are in good agree-ment with calculations using density-functional methods [3]. The presence of a hard wall has a simi-lar effect as an infinitely large particle and thus attract nanoparticles from the bulk entropically. Three-body interaction effects even lead to crystallization of particles at the walls [2]. This effect can be avoided by introducing an attractive interaction between polymers and the walls. Our studies show that only balanced enthalpic interactions between the particles, polymers and confining sur-faces can avoid strong segregation and clustering of nanoparticles in polymer matrices. [1] X.-Z. Cao, H. Merlitz, C.-X. Wu and J.-U. Sommer, Phys. Rev. E 84, 041802 (2011) [2] X.-Z. Cao, H. Merlitz, C.-X. Wu and J.-U. Sommer, ACS Nano 7, 9920 (2013) [3] X.-Z. Cao, H. Merlitz, C.-X. Wu, S. A. Egorov and J.-U. Sommer,

Soft Matter 9, 5916 (2013)

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A MICRO-MECHANICALLY BASED CONTINUUM MODEL FOR STRAIN-INDUCED CRYSTALLIZATION IN NATURAL RUBBER S. Govindjee University of California, Structural Engineering, Mechanics, and Materials Department of Civil and Environmental Engineering, Berkeley s_g@berkeley.edu Recent experimental results show that strain-induced crystallization can substantially improve the crack growth resistance of natural rubber. While this might suggest superior designs of tires or other industrial applications where elastomers are used, a more thorough understanding of the underlying physics of strain-induced crystallization in natural rubber has to be developed before any design process can be started. The objective of this talk will be the presentation of the development of a computationally-accessible micro-mechanically based continuum model, which is able to predict the macroscopic behavior of strain crystallizing natural rubber. While several researchers have developed micro-mechanical models of partially crystallized polymer chains, their results mainly give qualitative agreement with experimental data due to a lack of good micromacro transition theories or the lack of computational power. However, recent developments in multiscale modeling in polymers give us new tools to continue this early work. To begin with, a micromechanical model of a constrained partially crystallized polymer chain with an extend-chain crystal is presented and connected to the macroscopic level. Several option for doing this are discussed and nal we concretely use the non-ane micro-sphere model. Subsequently, a description of the crystallization kinetics is introduced using an evolution law based on the gradient of the macroscopic free energy function (chemical potential) and a simple threshold function. Finally numerical predictions of the performance are examined against published data.

31

KINETICS OF SELF-REINFORCEMENT OF NATURAL RUBBER BY STRAIN-INDUCED CRYSTALLIZATION: AN X-RAY DIFFRACTION APPROACH K. Brüning1, K. Schneider1, G. Heinrich1,2

1) Leibniz-Institut für Polymerforschung Dresden e. V., Hohe Straße 6, 01069 Dresden, Germany 2) Technische Universität Dresden, Institut für Werkstoffwissenschaft, 01062 Dresden, Germany The outstanding resistance of natural rubber (NR) against tearing and tear fatigue is ascribed to strain-induced crystallization, which occurs to this extent exclusively in NR and thus sets its apart from competing elastomers [1]. Even though numerous rubber products take advantage of the mechanical strength of NR, the precise mechanism of self-reinforcement by strain-induced crystallization is not well understood. This is also owed to the time-dependency of the crystallization process, adding complexity to the reinforcement mechanism. The formation of highly oriented crystallites not only requires a certain temperature-dependent strain level, it also requires time. Since most rubber products undergo dynamic mechanical loads at short time scales compared to the crystallization time scales, the study of the crystallization kinetics is essential for the understanding of the self-reinforcement. Synchrotron X-ray diffraction with unprecedented resolution in time and space gave insight into the very early stages of strain-induced crystallization, employing a strain-jump technique (fig. 1) [2]. We found that the crystallization proceeds initially very fast, such that first signs of crystallinity are evident after less than 10 ms; but it takes around 10 s to approach the steady state degree of crystallinity, which is classicaly measured in quasistatic tensile tests. In a second experimental setup, natural rubber was exposed to cyclic dynamic load, similar to those found in tear fatigue experiments. It was found that the maximum degree of crystallinity under cyclic loading at a frequency of 1 Hz is significantly lower than under static load. This is reflected in the different crack growth mechanisms under static and dynamic load, which is well known for NR. Finally, the crystallinity around a crack tip under cyclic load was directly measured in-situ, confirming the conclusions made from the previous bulk experiments [3].

Fig. 1: Crystallinity vs. time for a natural rubber gum vulcanizate (containing 2 phr dicumyl peroxide) after a strain-jump experiment, stretching the sample from 0 % to 410 % uniaxial optical strain at st 0= . The crystallinity follows a stretched exponential function [2]. [1] B. Huneau. Strain-induced crystallization of natural rubber: A review of x-ray diffraction investigations.

Rubber Chemistry and Technology, 84(3):425–452, 2011. [2] K. Brüning, K. Schneider, S.V. Roth, G. Heinrich. Kinetics of strain-induced crystallization in natural rubber

studied by WAXD: Dynamic and impact tensile experiments. Macromolecules, 45(19):7914–7919, 2012 [3] K. Brüning, K. Schneider, S.V. Roth, G. Heinrich. Strain-induced crystallization around a crack tip in natural

rubber under dynamic load. Polymer, 54(22): 6200–6205, 2013

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STRESS RELAXATION BEHAVIOR OF CARBON BLACK FILLED RUBBER UNDER UNI- AND BIAXIAL STRETCHING T. Tada1, T. Kawamura1, K. Urayama2, and T. Takigawa3 1) Sumitomo Rubber Industries, Ltd. 2) Kyoto Institute of Technology, Department of Macromolecular Science & Technology, Japan 3) Kyoto University, Department of Material Chemistry, Japan T-tada.cx@srigroup.co.jp Carbon black filled rubber exhibits viscoelastic behavior. For FEM analysis, an adequate constitutive model to describe the nonlinear viscoelastic behavior is required. The separability of time and strain effects on stress should be verified to establish the constitutive model. The separability has been studied on rubber vulcanizates by many researchers. However, the conclusion is still unsettled. In the present study, the separability for carbon black filled and unfilled styrene butadiene rubber (SBR) is examined on the basis of the nonlinear stress relaxation under uniaxial stretching, pure shear, and equibiaxial stretching. We demonstrated that the separability is valid on the relaxation component∆σ(t)= σ(λx,λy,tint)− σ∞(λx,λy), both of filled and unfilled SBR (∆σ(t)=∆σtotal(λx,λy)⋅ψ(t); ∆σtotal(λx,λy) = σ(λx,λy,tint)− σ∞(λx,λy) tint tint represents shortest time scale for analysis). Here ψ(t) is defined as ∆σ(t)/ ∆σtotal(λx,λy) and time dependent term. We revealed that ψ(t) can be approximated by sum of exponential function with 5 terms and ψ(t) for carbon black filled SBR is common to that for unfilled SBR. We also found that ∆σtotal(λx,λy) can be described by c⋅ σ∞(λx,λy) independent of type and degree of deformation [1]. Here c is a constant intrinsic for filled and unfilled SBR, and c for filled SBR is larger than that for unfilled SBR, reflecting the higher degree of relaxation strength on filled SBR. On the basis of these results, we propose a constitutive model (W(λx,λy)=((c⋅ψ(t)+1) W∞ (λx,λy), where W ∞ (λx,λy) represents equilibrium state. W ∞ (λx,λy) can be obtained by fitting a experimental stress-strain relation at a loading speed sufficiently longer than that corresponding to relaxation time. We will compare the stress-strain relations predicted by the constitutive model with the experimental ones obtained at various loading speeds.

[1] T. Tada, K. Urayama, T. Mabuchi, K. Muraoka, T. Takigawa, J. Polym. Sci. Part B Polym. Phys. 2010, 48,

1380.

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DENSITY FLUCTUATION OF REVERSIBLE CROSS-LINKS IN PERMANENT NETWORK St. Mebwe Pachong, K. K. Müller-Nedebock and L. Boonzaaier Stellenbosch University, Department of Physics, Institute of Theoretical Physics, Matieland 7602, South Africa We develop a model of a polymer network made of both permanent and reversible cross-links (such as myosin II clusters). The formalism of Edwards [1, 2] for a permanent network is used and, was adapted by Fantoni et al to describe clustering [3]. The combination of these two ideas comprises the model of network resembling a natural network. The interesting point here is that the cross-linkages are random and this constraint is ensured by the field theory. As is well known, the randomness causes severe mathematical challenges. Fortunately, many tools have been developed in order to circumvent this. The network is made by mixing many chains of identical lengths, and two different types of cross-linkers with fixed functionality each. The field theory used for polymer network developed by Edwards provides various approaches to dealing with this kind of cross-linkage problem. Edwards used the well known properties of Gaussian integration over the fields defined for each specific type of cross-linker and solved the field-theory using the saddle point approximation method. We expand the field theoretic model and compute the average density of reversible cross-links along the polymeric chain. The behaviour of the network formed has also been investigated including the activity of the linkers (i.e. when the reversible linker can move and when the permanent linker exerts a force [4]). The result of the calculations lead to derivation of the bulk elastic properties for such systems. [1] Edwards S. F. ”A field theory formulation of polymer networks”, Journal de Physique France, 1988, 49,

1673-1682 [2] Deam and Edwards.”The theory of rubber elasticity”, Philosophical Transactions of the Royal Society of

London A: Math. Phys. Sciences, 1976, 280, 317 [3] Fantoni et al, ”Field-theoretical approach to a dense polymer with an ideal binary mixture of clustering

centers”, Phys. Rev. E,2011, 84, 011808 [4] T. B. Liverpool, M. C. Marchetti, J.-F. Joanny and J. Prost, ”Mechanical response of active gels”,EPL, 85

(2009) 18007

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MATRIX CHAIN DEFORMATION IN REINFORCED NETWORKS: A SANS APPROACH St. Westermann1, W. Pyckhout-Hintzen2, J. Domurath3, M. Meyer1, M. Saphiannikova3, G. Heinrich3 and D. Richter2 1) Goodyear Innovation Center Luxembourg, Avenue Gordon Smith, L-7750 Colmar-Berg 2) Jülich Centre for Neutron Science (JCNS1) and Institute for Complex Systems (ICS1),

Forschungszentrum Jülich, D-52428 Jülich, Germany 3) Leibniz-Institut für Polymerforschung Dresden e. V., Hohe Straße 6, 01069 Dresden, Germany In our contribution we revisit a study conducted and published earlier on matrix chain deformation in an especially designed model system for a filled rubber-elastic network using small-angle neutron scattering (SANS) (1). The data published in ref (1) are newly interpreted in the light of a recently published, new theory on the modelling of stress and strain amplification effects in filled polymer melts (2). SANS experiments on the structure of polyisoprene homopolymer chains introduced into a well-microphaseseparated triblock polyisoprene-polystyrene-polyisoprene (PI-PS-PI) system of the ABA type will be presented. Use was made of the phase- and composition-matching techniques. The data were described in terms of the scattering behavior of the corresponding pure polyisoprene network at larger microscopic than macroscopic strains. Complementarily, the structure of the model filler and its detailed behavior under strain was studied using small-angle X-ray scattering (SAXS). This work provided the first direct experimental determination of the overstrain factor (1). All available information will be discussed in the light of the new model of stress and strain amplification. It will be shown that the strain amplification predicted by Domurath et al (2) is in excellent agreement with the matrix chain overstrain measured by SANS (1). [1] S. Westermann, K. Kreitschmann, W. Pyckhout-Hintzen, D. Richter, E. Straube, B.Farago, G. Goerigk;

Macromolecules 1999, 32, 5793 - 5802. [2] J. Domurath, M. Saphiannikova, G. Ausias, G. Heinrich; Journal of Non-Newtonian Fluid Mechanics, 2012,

171-172, 8-16.

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EVALUATION OF STRUCTURE OF RUBBER (NANO)COMPOSITES BY TIME-DOMAIN NMR J. L. Valentin, M. A. Malmierca, P. Posadas, A. González-Jiménez Instituto de Ciencia y Tecnología de Polímeros (CSIC). C/ Juan de la Cierva, 3. 28006 Madrid, Spain jlvalentin@ictp.csic.es It is clear that reinforcement of elastomers by addition of (nano)particles is a complex phenomenon that depends on several factors in different time- and length-scales. The final properties of rubber composites are primarily dictated by the addition of inherent properties of the different components that constitute the material: the rubber network structure and the so-called hydrodynamic effect. In addition, the actual reinforcement is strongly affected by the arrangement of the particles dispersed in the rubber matrix (filler networking), whereas the last central factor that determines the variation of the bulk properties in filled polymers is related to the particle-polymer interface. In the last years, time-domain NMR experiments performed on low-field spectrometers have shown their potential applicability on this field. This feasible, versatile and novel experimental approach allow us to obtain a complete and quantitative characterization of rubber network structure1 in filled rubber compounds (evaluating the effect of filler particles in the vulcanization process), and true molecular-level information on structure and dynamics in polymer-filler interface2. Recently, it was also applied to evaluate the local characteristics of filled compounds in deformed state3. By means of this innovative experimental approach, which involves low-cost technology with reliable possibilities to scale it into the industrial level, different elastomer nano-composites were evaluated2. In all cases, filled elastomers do not show any variation in the actual number of elastically active junctions (cross-links and rubber-filler bonds) neither their spatial distribution that could explain the dramatic changes in the macroscopic properties of these (nano)compounds. In rubber-clay nano-composites, even in the case of exfoliated structures, no effect of filler-rubber interface was observed. It means that substantial reinforcement effects in rubber-clay nano-composites (i) can be achieved without chemical or physical bonds between polymer and filler and (ii) are mainly due to geometric effect of stiff and well-dispersed filler platelets. A complete different scenario was observed in graphene-rubber nano-composites. The addition of just a few percent of these carbon-based nanoparticles leads to an impressive reduction in the swelling capacity without any change in the actual cross-link density as it was measured by NMR. These results suggest that enhanced mechanical properties of these materials are completely dominated by the interface behaviour. Although the existence of filler-rubber interactions has been demonstrated by using low-field NMR measurements, the expected modification of rubber chain dynamics until create a glassy layer of rubber around active fillers has still being investigated. It is a central point to understand the rein- forcement mechanism in rubber compounds4. For that reason, different time-domain NMR approaches has been applied to characterize elastomeric ionommers that shows a hierachical structure of ionic nano-aggregates that act as cross-links and reinforcing points. It was demonstrated that the applied methodology is sensitive to the rubber segments closer to the ionic groups which are firmly attached by the strong electrostatic interactions. This fact reduces the chain mobility in comparison with the bulk polymer promoting the formation of trapped rubber layer around the ionic aggregates. The complex network structure and aggregates morphology, the co-existence of rubber chains with quite different dynamics and the dynamic nature of ionic contacts (they act as temporary cross-links) leads to these materials unique physical properties. [1] Valentín, J. L.; Posadas, P.; Fernández-Torres, A.; Malmierca, M. A.; González, L.; Chassé, W.; Saalwächter, K.,

Macromolecules 2010, 43 (9), 4210-4222 [2] Valentin, J. L.; Mora-Barrantes, I.; Carretero-Gonzalez, J.; Lopez-Manchado, M.A.; Sotta, P.; Long, D.R.; Saalwachter,

K., Macromolecules, 2010, 43, 334-346. [3] Pérez-Aparicio, R.; Schiewek, M.; Valentín, J.L.; Schneider, H.; Long, D.R.; Saphiannikova, M.; Sotta, P.; Saalwächter,

K.; Ott, M., Macromolecules, 2013, 46, 5549-5560. [4] Papon, A.; Saalwächter, K.; Schäler, K.; Guy, L.; Lequeux, F.; Montes, H., Macromolecules 2011, 44 (4), 913-922.

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APPROACHES TO HYDRODYNAMIC REINFORCEMENT IN POLYMER MELTS AND NETWORKS J. Domurath, M. Grenzer-Saphiannikova Leibniz-Institut für Polymerforschung Dresden e. V., Hohe Straße 6, 01069 Dresden, Germany The theoretical description of the properties of filled polymeric materials is an extremely challenging topic. The main reason is that the polymer matrices, such as polymer melts and networks, are usually filled with particles that actively interact not only with each other, by building fractal agglomerates, but also with the surrounding polymer chains, by changing their equilibrium and dynamic properties in a nanosized layer around the particles. Because of those interactions the prediction of the final mechanical properties of reinforced polymeric materials stays, in many cases, an unsolved problem due to the interplay of too many parameters. Even when the particle-particle and particle-matrix interactions can be neglected and there exist only so-called hydrodynamic interactions, arising as a result of perturbations of the deformation field due to the presence of particles, the task of predicting the properties from those of the matrix and the filler becomes immediately more complicated when one enters the non-linear regime of deformation. Recently we proposed a stress and strain amplification approach (SSAA) in which both the stress and strain tensors have been modified to describe the behavior of filled polymer melts in the non-linear regime [1]. SSAA results have been compared with predictions of two other approaches existing in literature – stress only and strain only amplification approaches – as well as with experimental data for a thermoplastic polymer filled with non-interacting glass spheres. This comparison showed the SSAA is the only one of the three approaches that predicts and reproduces a number of intricate effects observed in the non-linear regime. To be able to modify a non-linear constitutive equation “exactly” one should consider different powers of the rate-of-strain tensor and their averages over the deformable volume. This however cannot be done analytically and thus one should reserve to computational fluid dynamics simulations. Performing the latter for a representative volume element (RVE) containing a hard sphere, we studied the influence of different thinning exponents in the Bird-Carreau model on the shift of the thinning behavior. Analysis of the simulation results allowed us to propose a modification of the Bird-Carreau model for dilute suspensions with a non-Newtonian matrix fluid. The modified model reproduces the numerical data very well. To describe the behavior of filled polymer networks different kinds of the strain amplification approaches are used. One approach is based on the old recommendation of Mullins and Tobin [2], who proposed that the engineering strain in a hyperelastic constitutive equation should be amplified with the same reinforcing factor X as the linear modulus. Another approach has been proposed by Govindjee and Simo [3] who amplify the macroscopic deformation gradient F in the constitutive equation with the geometrical reinforcement factor )1/(1 φ− , where φ is the volume fraction of particles. It is claimed by Castañeda that better results can be achieved if F is multiplied with

)1/( φ−X [4, 5]. Presently, it is clear that neither the first nor the second approach describes the influence of strain amplification on macroscopic properties correctly. The reason is that it is not possible to modify a hyperelastic constitutive equation properly even if particular analytical averages are known. However, similar to the filled polymer melts, such a modification can hopefully be done after performing finite element simulations of an RVE filled with hard spheres. [1] J. Domurath et al.: J. Non-Newton. Fluid Mech. 171-172 (2012) p. 8-16 [2] L. Mullins, N.R. Tobin. J. Appl. Polym. Sci. 9 (1965) p. 2993-3009 [3] S. Govindjee and J.C. Simo, J. Mech. Phys. Solids 39 (1991) p. 87-112 [4] P.P. Castañeda. J. Mech. Phys. Solids 39 (1991) p. 45-71 [5] M. Schikowsky. Doktorarbeit, Technische Hochschule Merseburg (1988).

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Abstracts of the posters

MESOSCOPIC SIMULATIONS OF COLLOIDS IN POLYMERIC SYSTEMS BY RESPONSIVE PARTICLE DYNAMICS W.K. den Otter1,2,*, I.S. Santos de Oliveira2, B. Fitzgerald1,2, S. Luding1 and W.J. Briels2 1) University of Twente, MultiScale Mechanics, P.O. Box 217, 7500 AE, Enschede, NL 2) University of Twente, Computational BioPhysics, P.O. Box 217, 7500 AE, Enschede, NL We have developed Responsive Particle Dynamics (RaPiD) to efficiently simulate the non-Newtonian flow behaviour of polymeric systems at the mesoscopic level. In RaPiD, each polymer is simulated as a single particle performing an extended Brownian motion. The conservative interactions between the particles are modeled by a free-energy functional based on the local polymeric density, e.g. the well-known Flory-Huggins theory. While this soft potential provides an adequate description of the thermodynamics behaviour of the system, it misses out on a key feature of polymer dynamics, namely the entanglements of the polymers. The formation and release of entanglements creates a memory effect on the mesoscopic level that is responsible for the visco-elastic flow behaviour on the macroscopic level. Hence, the slow relaxation dynamics of the (dis-)entanglements is modeled in RaPiD by introducing non-conservative interactions between particle pairs, by means of internal coordinates that qualitatively represent the degree of entanglement of two neighbouring polymers. The slow Brownian dynamics of these internal coordinates endows the simulated system with a transient memory of its past, and thereby creates a model with visco-elastic flow characteristics. The thermodynamic properties of the system are not affected by this altered dynamics. In this contribution, we will show how the coarse-grained RaPiD approach can be used to describe the flow behaviour of various shear-thinning fluids. As an example, we present the behaviour of colloidal particles dissolved in two distinct visco-elastic fluids, representing a solution of worm-like micelles and a polymer solution. The simulation parameters of the two model fluids were chosen to match the experimental flow behaviour of these solutions, i.e. the storage and loss moduli and the shear thinning viscosity. Under shear flow, the colloids are observed to align along the flow direction in the worm-like micellar solution, see figures, while the colloids remain randomly distributed in the sheared polymeric fluid and in the quiescent fluids, in excellent agreement with experiments [1]. By analysing the simulation results at the particle level, we obtain a physical explanation of this non-equilibrium ordering effect. The simulations also explain the shear-induced segregation by size of bidisperse colloids in a worm-like micellar solution [2]. In a polymer solution confined between two moving walls, the suspended colloids are observed to drift to the nearest wall. Simulations of colloidal particles in a polymer melt are under way.

Figure: The alignment of colloids (blue) in a worm-like micellar solution (grey) under shear flow. The flow is in the horizontal direction, the flow gradient in the vertical direction. [1] I.S. Santos de Oliveira W.K. den Otter and W.J. Briels, J. Chem. Phys. 137 (2012) 204908 [2] I.S. Santos de Oliveira, W.K. den Otter and W.J. Briels, EPL 101 (2013) 28002

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STRAIN AMPLIFICATION EFFECTS IN FILLED ELASTOMERS J. Domurath1,*, M. Saphiannikova1, T. Horst2, G. Heinrich1,2

1) Leibniz-Institut für Polymerforschung Dresden e. V., Hohe Straße 6, 01069 Dresden, Germany 2) Technische Universität Dresden, Institut für Werkstoffwissenschaft, 01062 Dresden, Germany When hard filler particles are added to an elastomer, it is usually assumed that the mean local strain field is equal to the externally applied strain multiplied by a hydrodynamic amplification factor given by Einstein’s or a similar formula. This assumption is based on the old recommendation of Mullins and Tobin [1]. Govindjee and Simo derived a considerably lower value of the strain amplification factor in the case of affine deformation [2]. In this contribution the amplification of different kinematic measures is studied with the help of 3D finite element analysis in the dilute regime. In particular, we consider a representative volume element containing a spherical particle. The applied deformation is uniaxial extension. The matrix is described using the Neo-Hooke model. The particle is represented either as an infinitely hard spherical inclusion or as a second phase, also using the Neo-Hooke model. The amplification of the kinematic measures has been studied by means of direct averaging over the matrix volume. The obtained numerical results for the deformation gradient tensor confirm the Govindjee und Simo prediction. Contrary, the Mullins and Tobin approach is shown to considerably overpredict the value of mean local strain field, even at small deformations. Further, we have shown that the amplification of the Green-Lagrange-strain tensor does not only depend on the volume fraction of particles but also on the applied external deformation. [1] L. Mullins and N.R. Tobin, J. Appl. Polym. Sci. 9, 2993 (1965). [2] S. Govindjee and J.C. Simo, J. Mech. Phys. Solids 39, 87 (1991).

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ANALYSIS OF CRACK GROWTH IN ELASTOMERS UNDER MULTI-AXIAL LOAD STATE S. Gorelova1, K. Schneider1, G. Heinrich1,2 1) Leibniz-Institut für Polymerforschung Dresden e. V., Hohe Straße 6, 01069 Dresden, Germany 2) Technische Universität Dresden, Institute of Material Science, 01069 Dresden, Germany Elastomers are a large group of polymer materials with specific properties. These properties allow the using it in a variety of fields of technical application, for example tires, V-belts, gaskets, damper and other. For the proper use of elastomer materials the investigation of behaviour under the near realistic load conditions, especially the behaviour of damaged material, is hugely important. The known methods for fracture analysis of elastomers are based mainly on the uni-axial tests. Therefore the different specimen geometry will be used. The SENT- („single edge notched tension“) or DENT-Geometry („double edge notched tension“) or „Pure Shear“– geometry are the best known. Using the SENT- or DENT specimen the crack growth will be investigated in the complex loading conditions. It has to be evaluated for the correct analysis of the results. The so-called “Pure-Shear” geometry realises nearly pure shear stress conditions [1][2]. The aim of the present work is it to analyze the fracture mechanics of elastomer materials under multi-axial load state. The experiments were carried out on the novel Biaxial-Tester, which was planned and built of Fa. Coesfeld GmbH together with Leibniz-Institut für Polymerforschung Dresden e. V. [3][4]. Pre-notched sample were used for the experiments. Well-defined loading conditions, namely uni-axial, pure-shear, equibiaxial, and its effect on the stress conditions on the stretched zone ant crack tip were investigated. The analysis was carried out with the J-Integral method. This method was used due to its possibility to determine the tearing energy in the case of crack deflection, which is common in the multi-axial load state. The crack growth propagation and tearing energy was analysed in the dependence of load state and will be discussed in the present work. [1] R. Stoček: Dynamische Rissausbreitung in Elastomerwerkstoffen. Dissertation, TU Chemnitz, 2012 [2] R. Stoček, G. Heinrich, M. Gehde, R. Kipscholl: Analysis of dynamic crack propagation in elastomers by

simultaneous tensile- and pure-shear-mode testing. Fracture mechanics and statistical mechanics of reinforced elastomeric blends. Springer (2013) 269-301

[3] http://products.coesfeld.com/WebRoot/WAZ/Shops/44402782/5238/4E9A/BB18/5A3B/993E/D472/521A/76A8/61-490_Biaxtester_engl.pdf Stand: 19.02.2014

[4] K. Schneider, R. Calabrò, R. Lombardi, C. Kipscholl, T. Horst, A. Schulze, G. Heinrich: Charakterisierung und Versagensverhalten von Elastomeren bei dynamischer biaxialer Belastung, KGK 2014 (accepted)

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PHYSICALLY BASED MULTI-SCALE APPROACH TO DYNAMIC-MECHANICAL BEHAVIOR OF REINFORCED RUBBERS I. Ivaneiko1, V. Toshchevikov1, K.W. Stöckelhuber1, M. Saphiannikova, G. Heinrich1,2 1) Leibniz-Institut für Polymerforschung Dresden e. V., Hohe Straße 6, 01069 Dresden, Germany 2) Technische Universität Dresden, Institut für Werkstoffwissenschaft, 01069 Dresden, Germany The main goal of present work is to develop a physically based multi-scale approach for description of the viscoelastic properties of reinforced elastomers, in particular those based on a solution-polymerized styrene butadiene rubber [1]. Influence of different fillers such as fumed silica with three different surface modifications, precipitated silica in three different grades and carbon black is investigated. For all samples we observe four distinct frequency regimes on the master curves constructed for the small strain storage E’(ω) and loss E’’(ω) moduli at a chosen reference temperature (0°C): 1) At very high frequencies, non-polymer relaxation modes due to rotational and vibrational motions inside the monomer can be identified. 2) For frequencies in the rubber-glass transition region, a semiflexible chain behaviour is observed with a typical scaling exponent of 3/4 for E’(ω) for unfilled rubber and it decreases upon the filler addition. 3) For lower frequencies, the Rouse-like 1/2 exponent is seen for unfilled rubber. For filled rubbers we assume that the free and the localised polymer chains contribute with exponents 1/2 and 3/8, respectively. 4) For even lower frequencies, the power-law behaviour with a smaller value of the exponent due to entangled dangling chain concept, valid for randomly cross-linked rubbers, for unfilled rubbers. For filled rubbers the exponent decreases due to appearance of filler aggregates. To fit the master curves for unfilled and filled rubbers in the whole range of frequencies over 20 decades, we propose a multiscale approach based on the continuity of the logarithmic spectral density function H(τ) [2]. This approach is implemented in a fully automatic software and helps to identify the structural parameters, such as the fraction of localized chains and the apparent tube diameter, which show quantitative differences between the elastomers reinforced with different fillers. [1] K.W. Stöckelhuber, A.S. Svistkov, A.G. Pelevin, G. Heinrich: Macromolecules (2011) 44, p. 4366-4381 [2] V. Toshchevikov, Yu.Ya. Gotlib. Polymer Science A (2013) 55, p. 556

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TUNING MECHANICAL PROPERTIES IN MAGNETO-SENSITIVE ESLASTOMERS D. Ivaneyko1,2,*, V. Toshchevikov1, M. Saphiannikova1, G. Heinrich1,2

1) Leibniz-Institut für Polymerforschung Dresden e. V., Hohe Straße 6, 01069 Dresden, Germany 2) Technische Universität Dresden, Institut für Werkstoffwissenschaft, 01062 Dresden, Germany ivaneiko@ipfdd.de Magneto-sensitive elastomers (MSEs) represent composite magnetic materials based on soft non-magnetic polymers filled with magnetics inclusions. These materials are able to change their shape (magneto-induced deformation) and mechanical behaviour under external magnetic field. Nowadays, MSEs have found a wide range of industrial applications in controllable membranes, rapid-response interfaces designed to optimize mechanical systems and in automobile applications such as adaptive tuned vibration absorbers, stiffness tunable mounts and automobile suspensions (Khoo and Liu, 2001; Lanotte et al., 2003). Usually MSEs consist of micron-sized ferromagnetic particles dispersed within an elastomeric matrix. The particles are separated by the polymer matrix and are fixed in their position due to perfect adhesion between particles and polymer matrix. The spatial distribution of particles in MSEs can be either isotropic or anisotropic, depending on whether they have been aligned by an applied magnetic field before the cross-linking of the polymer. Depending on the inner structure of the particles, the MSEs exhibits different mechanical behaviour (Borbáth et al., 2012). The magnetorheological (MR) effect, e.g., the relative change of the shear modulus, 𝐺, and the Young’s modulus, 𝐸, in MSEs has been subject of many experimental studies. In the most of experimental studies usually the measurements of 𝐺 have been done and shown that 𝐺 increases with increasing strength of the magnetic field. Also, it has been mentioned that 𝐺 strongly depends on the microstructure of these materials, e.g., on the volume fraction and spatial distribution of magnetic particles. That fact that inner structure of MSEs is anisotropic and external magnetic field also has pre-defined anisotropy, the classical relation between the Poisson’s coefficient, 𝐺 and 𝐸 is not valid. Thus, for getting full picture about mechanical behaviour of MSEs in an external magnetic field one needs additional studies. On today there have been done a few theoretical investigations, which can be roughly classified as phenomenological, continuum-mechanics and microscopic approaches. The continuum-mechanics approach considers the deformation-dependent demagnetizing shape factor and homogeneous particle distribution. In the frame of this approach only estimation for 𝐸 is possible, that increases with increase of the strength of the magnetic field. However, this approach is not able to consider the effect of particle distribution on the MR effect. The microscopic approach has a clear advantage, while a discrete particle distribution and pair-wise interaction between induced magnetic dipoles can be considered explicitly. In the last decade a number of microscopic models have been proposed for study of the MR effect, in particular, one-chain discrete model (Shiga et al., 19956; Jolly et al., 1996), multi-chain discrete model (Zhu et al., 2006) for calculation of MR effect for 𝐺. In present study we extend former microscopic models that allows to calculate 𝐺 and 𝐸 independently, considering different types of deformation (none and affine deformations) and initial shape of the sample (sphere or elongated ellipsoid) [1]. The analytical results for 𝐺, obtained in the frame of microscopic approach (affine deformation, tetragonal lattice model) are in good agreement with the experimental data, where the increase of 𝐺 with increase of the external magnetic field has been found (Varga et al., 2006). This means that the MR effect is positive for shear deformation. Additionally, the tensile experiments have shown the increase of 𝐸 with increase of the external magnetic field. The microscopic approach predicts however results for 𝐸, which are very sensitive to the particle distribution and, as a consequence, the MR effect for can 𝐸 be positive or negative. [1] D. Ivaneyko, V. Toshchevikov, M. Saphiannikova, G. Heinrich: Macromol. Theory Sim. 20 (2011) p. 411-424;

Cond. Matter Physics 15 (2012) p. 33601; Soft Matter 10 (2014) p. 2213.

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ORDER AND PHASE BEHAVIOR OF COPOLYMER/NANOPARTICLE MIXTURES: A MOLECULAR DYNAMICS SIMULATIONS STUDY L. S. Shagolsem1,2, J.-U. Sommer1,2 1) Leibniz-Institut für Polymerforschung Dresden e. V., Hohe Straße 6, 01069 Dresden, Germany 2) Technische Universität Dresden, Institut für Theoretische Physik, 01062 Dresden, Germany By means of molecular dynamics simulations, we study AB diblock copolymer and nanoparticle mixtures confined between two identical walls in slit geometry. The nanoparticles are selective to the minority A-block, while the walls are neutral to both copolymer and nanoparticle. We obtained the various structures of the copolymer nanocomposites and are summarized in a phase diagram constructed in diblock composition and nanoparticle concentration space. In comparison to the phase diagram in bulk, we observe a much wider lamellar region with a broad class of lamellar structures, and the phase boundaries are shifted with increasing nanoparticle concentration. We find that both vertically and horizontally oriented lamellar structures are realized. The vertically oriented lamellae are formed by slightly asymmetric and symmetric diblock copolymers at low nanoparticle concentrations and have a very limited region of stability in the phase space, whereas the horizontally oriented lamellae are formed by asymmetric copolymer at large nanoparticle concentrations. In the vertically oriented lamellae, the segregated nanoparticles at the polymer-wall interfaces form nanoparticle monolayer above the A-domains and exclude A-monomers from this region. Consequently, the copolymer interface lines near walls are perturbed; also, the chains close to the walls are overstretched as compared to the bulk. For horizontally oriented lamellae there is no overstretching of chains near the walls. The test of stability of the lamellar structures against the different thermodynamic pathways is also performed. For the case of horizontal lamellae, we study the effect of nanoparticle concentration on the lamellar layer thickness. [1] Lenin S. Shagolsem, Jens-Uwe Sommer: Macromolecules (2014). DOI: 10.1021/ma402184w

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EFFECT OF MELT MIXING CONDITIONS ON THE FILLER DISPERSION AND RHEOLOGICAL PROPERTIES OF PC/SAN POLYMER BLENDS FILLED WITH GRAPHENE NANOPLATELETS M. Liebscher1,2, P. Pötschke1, G. Heinrich1,2

1) Leibniz-Institut für Polymerforschung Dresden e.V., Hohe Straße 6, 01069 Dresden, Germany 2) Technische Universität Dresden, 01062 Dresden, Germany Graphene Nanoplatelets (GnPs) tend to localize within the polycarbonate component (PC) in PC / poly(styrene-acrylonitrile) (SAN) binary polymer blends [1]. In this study different GnP loadings were premixed with PC via melt mixing in a microcompounder. Afterwards the premixtures were blended with the SAN in a second mixing step for 5 min at 100 rpm. For the premixing step two different parameter sets were applied. For the first set, it was chosen 5 min mixing time at 100 rpm. For the second premixing set, a higher specific mixing energy was applied by using 15 min mixing time at 250 rpm. As proven with the optical- and transmission electron microscopy, the filler dispersion was improved significantly for the samples, which were exposed to a higher specific mixing energy. The rheological characterization of the samples was based on frequency sweeps measured at processing temperature of 260°C. A more pronounced shear thinning effect with increasing frequency was observed for the samples with improved filler dispersion. The relative changes of the storage modulus were also higher for the samples with improved filler dispersion (figure 1). This indicates presumably increased polymer-filler interactions. The van-Gurp-Palmen-Plots confirm this interpretation by showing smaller phase angles at higher complex modulus for the samples with improved filler dispersion.

Figure 1: Relative changes of storage modulus G´of the polymer blends with different filler loadings compared to the unfilled polymer blend, calculated at 0,063 rad/s [1] Liebscher M, Blais M-O, Pötschke P, and Heinrich G. Polymer 2013;54(21):5875-5882.

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HOMOGENIZATION OF SLENDER STRUCTURES IN SMALL-STRAIN REGIMES St. Neukamm Weierstraß-Institut für Angewandte Analysis und Stochastik, Berlin, Germany The effective macroscopic behavior of hyperelastic composites can be derived with help of variational homogenization methods. These analytical methods lead to homogenization formulæ that require to solve auxilliary problems that take an infinite number of representative cells into account – which is in contrast to linear elasticity, where a single cell suffices. In a series of papers [1,2,3,4] we proved that in the small-strain limit the infinite-cell formulæ reduce to single-cell formulæ and thus become tractable to numerical and analytical investigations. The method is naturally applicable to slender structures, such as rods and plates. In [3] we derived by simultaneous homogenization and 3d-2d dimensional reduction an effective von-Karman plate theory. The new homogenization formula, which is obtained without assuming a kinematic Ansatz, is sensitive to the relative ratio between the thickness of the plate and the size of the microstructure. Although the derived model is nonlinear, the effective elastic properties are described by relaxation on a single cell. [1] S. Müller, S. Neukamm: Archive for Rational Mechanics and Analysis 201/2 (2011) p.465-500 [2] S. Neukamm: Archive for Rational Mechanics and Analysis 206/2 (2012) p.645-706 [3] S. Neukamm, I. Velcic: Mathematical Models and Methods in Applied Sciences, 23/14 (2013) p.2701-2748 [4] P. Hornung, I. Velcic: Calculus of Variations and Partial Differential Equations (to appear)

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REINFORCEMENT MECHANISMS IN NATURAL RUBBER MATERIALS: LOW-FIELD NMR AND X-RAY DIFFRACTION STUDY A. Vieyres1, K. Schneider1, G. Heinrich1,2

1) Leibniz Institut für Polymerforschung, Hohe Straße 6, 01069 Dresden, Germany

2) Technische Universität Dresden, Institut für Werkstoffwissenschaft, 01069 Dresden, Germany

Reinforced elastomers refer to materials consisting of an elastomer matrix in which particles or aggregates of sub-micrometric size (denoted as fillers) are finely dispersed. In a wide range of industrial applications, fillers such as carbon blacks are used since they impart significantly improved properties in terms of modulus, ultimate properties and wear resistance as respect to unfilled elastomers. The reinforcement effects have been the object of numerous studies but some issues are still under debate [1]. In this study we shall focus on the large strain regime where the main reinforcement mechanism is strain amplification [2]. Among the important materials parameters that affect the mechanical properties of filled composites, we focus in this work on the filler amount and the structure of carbon black aggregates (as given by DBP absorption measurements). Natural Rubber (NR) samples with different filler amounts and different filler structure have been prepared. For each of these systems, several samples with different amount of curatives have been processed following standard procedures. Unfilled natural rubber materials have also been prepared and used as references. Double-Quantum NMR measurements have been performed on a low-field Spectrometer in order to accurately access the crosslink density of unfilled and reinforced NR samples. Incorporation of fillers was found to slightly decrease the crosslink density whereas filler morphology seems to have virtually no effect on the network crosslink density. NR samples were also studied by means of in-situ stretching Wide-Angle X-ray Scattering (WAXS) carried out at the DESY Synchrotron. Using a well-suited X-ray diffraction pattern analysis, the strain-induced crystallization and the segmental chain orientation (in the amorphous phase) have been obtained adding to simultaneous measurements of stress and strain. SIC strain onset is shifted towards lower values and segmental orientation is increased in reinforced NR as compared to unfilled NR suggesting a strain amplification effect in the rubber matrix. The modification of properties in terms of modulus, crystallization and chain orientation can be separated into a contribution of the rubber matrix taking advantage of crosslink density measurements and a contribution due to the fillers. The influence of the filler fraction and morphology on the matrix overstrain is discussed on the basis of this combination of techniques [3,4]. [1] G. Heinrich, M. Klüppel, T. A. Vilgis: Current Opinion in Solid State and Materials Science 6 (2002) p. 195–

203 [2] R. Pérez-Aparicio, A. Vieyres, P. Albouy, O. Sanseau, L. Vanel, D. R. Long, P. Sotta: Macromolecules 46

(2013) p. 8964–8972 [3] A. Vieyres, R. Pérez-Aparicio, P. Albouy, O. Sanseau, K. Saalwächter, D. R. Long, P. Sotta: Macromolecules

46 (2013) p. 889–899 [4] S. Dupres, D. R. Long, P.-A. Albouy, P. Sotta: Macromolecules 42 (2009) p. 2634–2644

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POLYMER DYNAMICS AND CROSSLINK DENSITY OF SBR NANOCOMPOSITES CONTAINING FILLERS WITH DIFFERENT SURFACE AREA

A. Mujtaba1,2, M. Keller3, S. Ilisch3, H-J. Radusch3,T. Thurn-Albrecht2, K. Saalwächter2, M. Beiner* 1)Fraunhofer Institut für Werkstoffmechanik IWM, Walter-Hülse-St. 1, 06120 Halle (Saale), Germany2)Naturwissenschaftliche Fakultät II, Martin-Luther-University Halle-Wittenberg, 06099 Halle (Saale),Germany 3)Zentrum für Ingenieurwissenschaften, Martin-Luther-University Halle-Wittenberg, 06099 Halle(Saale), Germany

Mechanical properties and crosslink density of model composites of Styrene butadiene rubber (SBR) samples filled with different amounts of silica nanoparticles or mixtures of high-surface area silica (Si) and low-surface area borosilicate particles (BK3) are investigated by dynamic shear measurements and solid state NMR. The crosslink density of the rubber matrix is estimated in absolute units based on a combination of double-quantum NMR measurements [1] and shear measurements on unfilled rubber samples with different crosslink densities. Shear data show that the mechanical properties like plateau modulus related to reinforcement and dissipation in the rubber plateau range depend systematically on the surface area of the filler system. The silica content is most important for these properties while additional large BK3 particles do not lead to significant changes. Different contributions to reinforcement are quantified based on a comparison of linear response measurements with strain sweeps performed at different temperatures. The results indicate that a solid 'filler network' incorporating filler particles as well as shielded occluded rubber from filler clusters contributes strongly to reinforcement above the percolation threshold at silica contents of about Φ ~ 0.155 [2]. The strength of the 'filler network' decreases significantly with temperature. This may indicate the existence of a immobilized polymer located within the filler network which softens several ten degrees above the bulk Tg of SBR. In accordance with this picture two regimes are found in the dissipation above Tg which both depend systematically on the surface area of the filler system: (i) A strongly frequency-dependent dissipation showing power-law behavior at temperatures up to 70K above the bulk Tg and (ii) nearly constant, frequency-independent G'’ values dominating at higher temperatures are observed. The nature of the underlying molecular processes and the importance of these observations for the optimization of filled elastomers for tire applications are discussed.

[1] Saalwächter, K., Progress in NMR spectroscopy, 51 (2007) 1-35 [2] A. Mujtaba, T.Thurn‐Albrecht, K. Saalwaechter & M. Beiner., Macromolecules 45

(2012),6504‐6515

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