Simulations on the reinforcement of poly(dimethylsiloxane) elastomers by randomly distributed filler particles (original) (raw)
Related papers
2000
Reinforcement of elastomers is modeled using Monte Carlo simulations on rotational isomeric state chains, to characterize their spatial configurations in the vicinity of filler particles. The resulting filler-perturbed distributions of the chain end-to-end distances are in agreement with experimental results gotten by neutron scattering. The use of these distributions in a standard molecular theory of rubberlike elasticity produces stress-strain isotherms for elongation that are consistent with available experimental results.
Polymer
Although the ®ller particles typically used to reinforce elastomers are at least approximately spherical, prolate (needle-shaped) or oblate (disc-shaped) particles have been used in some cases. The fact that anisotropic structures and properties can be obtained in these cases has encouraged a number of experimental and theoretical investigations. The present study extends some earlier Monte Carlo simulations on prolate particles in an amorphous polyethylene matrix, but now focuses on oblate particles. The particles were placed on a cubic lattice, and were oriented in a way consistent with their orientation in composites that were the subject of an experimental investigation by one of the authors. Rotational isomeric state representations of the chains were then generated to model the elastomeric network in the presence of the ®ller particles. The chain end-to-end distributions were found to be non-Gaussian, and to depend signi®cantly on the excluded volumes of the particles. The particle-induced deformations of the network chains were consistent with results of some other relevant simulations and with recent neutron scattering results. Speci®cally, the chain dimensions were found to decrease with increase in the axial ratios characterizing the oblate shapes. As anticipated, the chain dimensions became anisotropic, with signi®cant differences parallel and perpendicular to the direction of the particle axes. In general, the network chains tended to adopt more compressed con®gurations relative to those of prolate particles having equivalent sizes and aspect ratios. Use of these distributions in a standard molecular model for rubberlike elasticity gave values of the elongation moduli, and these were found to depend on the sizes, number, and axial ratios of the particles, as expected. In particular, the reinforcement from the oblate particles was found to be greatest in the plane of the particles, and the changes were in at least qualitative agreement with the corresponding experimental results.
Some Simulations on Filler Reinforcement in Elastomers
Molecular Crystals and Liquid Crystals, 2002
This review illustrates how elastomer reinforcement can be modeled using Monte Carlo simulations on rotational isomeric state chains to characterize their spatial configurations in the vicinity of filler particles. The results are distributions of the chain end-to-end distances as perturbed by this excluded-volume effect, and the results obtained are in agreement with experimental results gotten by neutron scattering. The use of these distributions in standard molecular theories of rubberlike elasticity then produces stress-strain isotherms suitable for comparison with those in elongation experiments. Such simulations have now been carried out for elastomeric matrices reinforced by spherical filler particles (either on a cubic lattice or randomly dispersed), or by prolate or oblate particles on cubic lattices (either with their axes oriented or randomized). The simulated mechanical properties are consistent with experimental results available at the present time, and should provide encouragement and guidance for additional simulations and experiments.
Polymer, 2004
Reinforcing effects in an amorphous polyethylene matrix were estimated for spherical filler particles arranged either on a cubic lattice or randomly in space. Attention was first focused on the effects of the type of arrangement of the particles on the microscopic properties of the polymer chains. Specifically, Monte Carlo rotational isomeric state (MC-RIS) simulations were carried out to predict the effects of the volumes excluded by the filler particles on the configurational distribution functions of the chains, and from these distributions the elastomeric properties of the composites. The calculations were carried out for a range of particle sizes and particle volume fractions. As expected, filler inclusions are found to increase the non-Gaussian behavior of the chains. The results were compared with those from smallangle neutron scattering (SANS) experiments. In the case of arrangement on a cubic lattice, chains dimensions were always found to decrease. In the randomly-dispersed filler arrangements, there were significant increases in chain dimensions relative to the unfilled system in some instances, and the changes were in excellent agreement with the SANS results. The present simulations thus give further encouragement to interpretations of chain deformations in filled systems in terms of volume exclusion effects from the nanoparticle inclusions, including their dispersions and arrangements within polymer matrices.
European Polymer Journal, 2006
Monte Carlo simulations based on rotational isomeric state models were carried out to determine how amorphous polyethylene chains are deformed by the presence of spherical filler particles. The resulting distributions of the chain end-to-end distances were then employed to calculate mechanical properties of the cross-linked chains. The basic goals were (i) to refine previous simulations of this type carried out on this system to remove possible sampling biases, and (ii) to document the circumstances under which the particles stretch the chains to larger end-to-end distances, rather than compress them to smaller distances, and (iii) to study in more detail the flattening of the chains near particle surfaces. Comparisons with experiments include filler-induced changes in chain dimensions measured by neutron scattering, and general features of the stress-strain isotherms widely observed for reinforced elastomers in simple elongation.
The stress–strain response and ultimate strength of filled elastomers
Computational Materials Science, 2001
A constitutive model is derived for the mechanical behavior of reinforced elastomers at ®nite strains. A polymer is treated as a rigid-rod network, whose rupture is tantamount to breakage of chains treated as bond scission. Adjustable parameters in the stress±strain relations are found by ®tting observations in tensile tests for ®lled and un®lled ethylene± octene copolymers. It is demonstrated that the model correctly describes stress±strain curves up to the break points. We analyze the eects of temperature, the degree of crystallinity and the ®ller content on Young's modulus and the ultimate strain per bond. It is shown that the dependences of material constants on the volume fraction of carbon black are substantially altered at the critical ®ller contents which correspond to the percolation thresholds found by dc conductivity measurements.
Modeling the response of filled elastomers at finite strains by rigid-rod networks
Archive of Applied Mechanics (Ingenieur Archiv), 2002
A constitutive model is developed for the isothermal response of particle-reinforced elastomers at ®nite strains. An amorphous rubbery polymer is treated as a network of long chains bridged to permanent junctions. A strand between two neighboring junctions is thought of as a sequence of rigid segments connected by bonds. In the stress-free state, a bond may be in one of two stable conformations:¯exed and extended. The mechanical energy of a bond in the¯exed conformation is treated as a quadratic function of the local strain, whereas that of a bond in the extended conformation is neglected. An explicit expression is developed for the free energy of a network. Stress±strain relations and kinetic equations for the concentrations of bonds in various conformations are derived using the laws of thermodynamics. In the case of small strains, these relations are reduced to the constitutive equation for the standard viscoelastic solid. At ®nite strains, the governing equations are determined by four adjustable parameters which are found by ®tting experimental data in uniaxial tensile, compressive and cyclic tests. Fair agreement is demonstrated between the observations for several ®lled and un®lled rubbery polymers and the results of numerical simulation. We discuss the effects of the straining state, ®ller content, crosslink density and temperature on the adjustable constants.