Polymer-like Behavior of Inorganic Nanoparticle Chain Aggregates

Studies of the behavior of nanoparticle chain aggregates (NCA) have shown properties similar to those of molecular polymers. Like polymer chains, NCA tend to gather up and become more compact when heated. Under tensile stress, folded chain segments pull out and the NCA elongates. When the tension is relaxed, the chains contract. The stretching of NCA may contribute to the ductility of compacts made from nanoparticles, a subject of current research interest. In a well established technological application, carbon black and pyrogenic silica NCA produce remarkable increases in elastic modulus and tensile strength when added to commercial rubber. This may be due to the mechanical interaction between the polymer chains and NCA. However, basic mechanisms of NCA elasticity differ from those of molecular polymers. The alignment of chain segments when the NCA are subjected to tension probably results from rotation and translation at grain boundaries between neighboring nanocrystals. The elastic properties depend on the van der Waals forces between segments of the chain that fold to minimize surface free energy. Under tension, these segments pull out, but tend to reform when the tension is relaxed. The processes that lead to NCA formation and control the strength of interparticle bonds are briefly reviewed.     

Piezoelectricity of chiral nematic elastomers

A molecular model of freely jointed chains of chiral monomers is developed to describe the piezoelectric effect in chiral nematic elastomers. The model, an extension of the neo-classical theory of nematic polymer networks, takes into account a chiral biasing of molecular alignment under shear which leads to induced polarisation if the monomers contain a transverse dipole moment. The resulting theory is fully non-linear in elastic deformations, in the spirit of ordinary rubber elasticity. The expansion to the highest order in small strains gives the three linear piezoelectric coefficients predicted by phenomenological models. Received 7 September 1998 and Received in final form 19 October 1998     

Elastic Behavior of Polymer Chains

在三维非格子模型中研究了高分子链的弹性行为. 使用蒙特卡罗方法在构相空间中对高分子链抽样,每种链都得到了超过109个样本,然后使用类橡胶弹力的非高斯理论对这些样本进行数值分析并进行统计分析. 通过观测链柔性以及伸长量对高分子链的均方末端距、平均能量、平均赫尔姆霍兹自由能、弹力、能量对弹力的贡献和熵对弹力的贡献等性质的影响,发现刚性链比柔性链更加容易被拉伸. 而由于熵的作用,当拉伸长度大到一定程度时,刚性链的拉伸难度会大大增加.     

Buckling instability in liquid crystalline physical gels

In a nematic gel we observe a low-energy buckling deformation arising from soft and semisoft elastic modes. We prepare the self-assembled gel by dissolving a coil-side-group liquid-crystalline polymer-coil copolymer in a nematic liquid crystal. The gel has long network strands and a precisely tailored structure, making it ideal for studying nematic rubber elasticity. Under polarized optical microscopy we observe a striped texture that forms when gels uniformly aligned at 35 degrees C are cooled to room temperature. We model the instability using the molecular theory of nematic rubber elasticity, and the theory correctly captures the change in pitch length with sample thickness and polymer concentration. This buckling instability is a clear example of a low-energy deformation that arises in materials where polymer network strains are coupled to the director orientation.     

Elasticity of polymer solutions in Couette flow measured by fluorescence resonance energy transfer (FRET)

Polymer solutions are complex fluids that show elasticity and deformation in response to shear flows. A fluorescence resonance energy transfer (FRET) technique has been applied to measure the end-to-end distances of individual polymer molecules in Couette flow, using end-tagged reversible-addition fragmentation chain transfer (RAFT) polymerised poly(methyl methacrylate) (PMMA). Real-time rheofluorescence measurements on these polymers in solution above the critical overlap concentration are reported at several shear rates. The PMMA in Couette flow shows a systematic decrease in fluorescence, corresponding to a reduction in end-to-end distance of the polymer molecules with shear exposure. Full reversibility of the fluorescence signal is observed after the cessation of shear. These results show that polymer solution elasticity arises from compressive deformation of the polymer molecules in Couette flow. At polymer concentrations above the critical overlap, the polymer molecules are restricted by their neighbours and the net hydrodynamic forces are compressive rather than extensive.     

Force distributions and force chains in random stiff fiber networks

We study the elasticity of random stiff fiber networks. The elastic response of the fibers is characterized by a central force stretching stiffness as well as a bending stiffness that acts transverse to the fiber contour. Previous studies have shown that this model displays an anomalous elastic regime where the stretching mode is fully frozen out and the elastic energy is completely dominated by the bending mode. We demonstrate by simulations and scaling arguments that, in contrast to the bending dominated elastic energy, the equally important elastic forces are to a large extent stretching dominated. By characterizing these forces on microscopic, mesoscopic and macroscopic scales we find two mechanisms of how forces are transmitted in the network. While forces smaller than a threshold F_c are effectively balanced by a homogeneous background medium, forces larger than F_c are found to be heterogeneously distributed throughout the sample, giving rise to highly localized force chains known from granular media.     

Tensile properties of styrene-butadiene rubber/silica composites with mercapto functional silane coupling agents: influences of loading method and alkoxy group number

The influences of alkoxy group number and loading method of silane coupling agents on the mechanical properties of a styrene-butadiene rubber/silica composite were investigated. Mercapto functional silane coupling agents with dialkoxy and trialkoxy structures were used. The pre-treatment method and the integral blend method were compared. Both the fracture stress and modulus at 200% strain were higher in the pre-treatment than in the integral blend for dialkoxy type composites. However, they were higher in the integral blend than in the pre-treatment for trialkoxy-type composites. The interaction between the silane chains on the silica surface and the rubber molecular chains at the interfacial region was estimated by ¹H pulse nuclear magnetic resonance spectroscopy using an unvulcanized silica/rubber mixture. It was found that the binding of rubber molecular chains by the silane chains was higher in the pre-treatment system for dialkoxy-type composites, whereas it was higher in the integral blend for trialkoxy-type composites. The reason is proposed as follows: in the pre-treatment for dialkoxy type, a linear silane chain formed in the case of multi-layer coverage. The silane chain entangled with the rubber chain in the interfacial region and improved the reinforcement effect. For the trialkoxy type, a network structure formed using the pre-treatment method, lowering the amount of entanglement. However, in the integral blend for trialkoxy type, the formation of the silane network and the entanglement progressed simultaneously during the preparation process. A well-entangled interfacial region was formed.     

Extensive stretch of polysiloxane network chains with random- and super-coiled conformations

The stress-elongation relations at large deformations for the polymer network chains with randomcoiled and supercoiled conformations are investigated using the polysiloxane networks with high elongations at break far over 10. Supercoil is the conformation of network chains in deswollen polymer networks which are made by removing solvent from the networks crosslinked in solutions at low polymer concentrations. The validity of the scaling concept of Pincus blob for the mechanical response of a polymer chain is experimentally confirmed for the network composed of randomcoiled chains. The analysis of the stress- relations for the deswollen networks comprised of supercoiled chains on the basis of the Pincus blob concept suggests that supercoil is a much more contracted conformation relative to randomcoil. Received: 25 August 1997 / Received in final form: 13 October 1997 / Accepted: 22 January 1998     

Nonlinear elasticity of composite networks of stiff biopolymers with flexible linkers

Motivated by recent experiments showing nonlinear elasticity of in vitro networks of the biopolymer actin cross-linked with filamin, we present an effective medium theory of flexibly cross-linked stiff polymer networks. We model such networks by randomly oriented elastic rods connected by flexible connectors to a surrounding elastic continuum, which self-consistently represents the behavior of the rest of the network. This model yields a crossover from a linear elastic regime to a highly nonlinear elastic regime that stiffens in a way quantitatively consistent with experiment.     

Stepwise elastic behavior in a model elastomer

Monte Carlo simulations of an entanglement-free cross-linked polymer network of semiflexible chains reveal a peculiar stepwise elastic response. For increasing stress, step jumps in strain are observed that do not correlate with changes in the number of aligned chains. We show that this unusual behavior stems from the ability of the system to form multiple ordered chain domains that exclude the cross-linking species. This novel elastomer shows a toughening behavior similar to that observed in biological structural materials, such as muscle proteins and abalone shell adhesive.     

Constrained fluctuation theories of rubber elasticity: General results and an exactly solvable model

We present a new model of rubber elasticity where linear forces act to constrain the fluctuations of the eigenmodes of the phantom model. The model allows us to treat the constrained junction and the tube model within the same, transparent formalism, does not require any further approximations, and is particularly suited for the analysis of simulation data for (strained) model polymer networks. As an interesting side result we show that in order for the model to be consistent, the constraints (but not the mean polymer conformations!) have to deform affinely, a severe restriction that might also apply to other models. Complementary, we prove in analogy to the derivation of the virial theorem that introducing constraints into the phantom network Hamiltonian leads to extra terms in addition to the usual Doi-Edwards formulas for the polymer contribution to the stress tensor which vanish only for affinely deforming constraints. Received: 28 November 1997 / Received in final form and accepted: 31 March 1998     

Stretching of polymer chains by fluctuating flow fields

We investigate polymer stretching by fluctuating flow fields via numerical solutions of the Brownian dynamics of multibead polymer chains taking into account nonlinear elasticity, hydrodynamic interactions and good solvent, excluded volume interaction effects. By varying the scaling exponent of the energy spectrum whilst keeping the same Reynolds and Deborah numbers, as well as microscale length and turnover times, we show that steeper spectra are associated with stronger stretching. We compute the probability density functions of chain length, and explain their main features by examining explicit molecular histories. We quantify the interaction between strain rate tensor structure and chain geometry as a means of understanding better the different stretching mechanisms in mild, moderate and strong polymer stretching regimes.     

An effective bead–spring model for polymer simulation

An effective bead–spring model combining the advantages of large time steps of traditional bead–rod models and computational rigor of traditional bead–spring models is proposed to simulate the dynamic behaviors of flexible polymer chains with arbitrary longitudinal stiffness. The proposed model can be used to simulate many types of polymer chains or networks with different chain elasticity via a unified integration scheme with reasonably large time steps.     

Non―Gaussian-Type Tube-Based Entropy Model for Elastomeric Networks with Polymer Phase Influenced by Filler Loading: Data Analysis for Lightly to Highly Carbon-Black Filled Styrene-Butadiene Rubber Networks

Recently the author proposed a new, non-Gaussian, tube-based entropy model for filled elastic networks, characterized by a filler-environmental parameter that was proposed to represent the extent of filler-agglomeration; it was specifically introduced for the polymer phase entropically affected by the presence of very irregularly structured fillers. In this report, the stress-strain relations derived from the above model were used together with the traditional and latest mechanisms of amplification of the strain due to the presence of a filler: namely, literature tensile data for styrene-butadiene rubber networks with a series of carbon-black loadings were systematically analyzed to understand the filler-loading dependence of the above parameter. As a consequence, it is proposed that this parameter is linked, from the static-mechanical standpoint, to a critical filler-loading coupled to the filler-networking. In addition, prior to commencing the examinations of the high-loading networks' tensile data, the data-fitting performance of the underlying elastic molecular model for non-filled networks was also examined using the unfilled and low-loading networks' tensile curves.     

Molecular origin of shear thickening in transient polymer networks: A molecular dynamics study

This paper proposes a simple model of transient networks of telechelic associating polymers for molecular simulations and reports the main results obtained by molecular dynamics on the rheological properties of the transient networks. The steady shear viscosity obtained by the non-equilibrium molecular dynamics simulation exhibits shear thickening at moderate shear rates and shear thinning at larger shear rates. The behavior is similar to that observed in experiments of telechelic associating polymers. By analyzing the distribution function of the end-to-end vector of bridge chains as a function of the shear rate, we find that shear thickening is mainly caused by the stress from the bridge chains highly stretched by shear flow. We also find that fracture of the transient network occurs in the shear-thinning regime at high shear rates.     

Four Non-Gaussian-Type Tube Models of Rubber-Like Elasticity: Analysis of Tensile Data for Lightly and Highly Carbon-Black Filled Styrene-Butadiene Elastomers

Recently, using a new, non-Gaussian, tube-based entropy model for active-filler filled elastic networks with the polymer phase influenced by the filler loading, proposed by the author, a data analysis of literature tensile data for carbon-black filled styrene-butadiene rubber (SBR) networks of different loadings was carried out; the data-fittability and the particular influence of the filler loading were examined in detail. In this report, the data-fitting performances of three other non-filled network models, all tube-based and finite chain extensible, along with a common strain-amplification factor that is necessary to extend them to the analysis of the filled networks, as well as the model which was employed in the above study were compared. As tensile data for this analysis, those observed for the same unfilled SBR, the same lightly loaded SBR and one of the same highly loaded SBR networks, as in our previous study, were chosen.     

Fluorescence quenching kinetics in short polymer chains: Dependence on chain length

Monte Carlo simulations of chain conformations and the diffusion equation were used to analyze the fluorescence kinetics of short polymer chains labeled with a probe and a quencher at opposite ends. In simulations, three chain models were considered: an ideal chain (without volume interactions); a self-avoiding chain taking into account the exclusive volume effect; and a self-avoiding chain with limited flexibility between nearest segments. For each model, end-to-end distance distribution functions were obtained, which were different from Gaussian ones. The distribution functions were used in a diffusion equation to simulate the fluorescence kinetics of the probe affected by intramolecular end-to-end collisions of short chains. The kinetics has been numerically calculated for a representative experimental system in a nonviscous solution. The simulated time-resolved fluorescence decays were monoexponential except at very short times (<2 ns). Diffusion coefficients were calculated for different chain models and different chain lengths. The experimental data could be reproduced by assuming systematically smaller end-to-end diffusion coefficients for the shorter chains.