A non‐Gaussian theory of rubberlike elasticity based on rotational isomeric state simulations of network chain configurations. II. Bimodal poly(dimethylsiloxane) networks

Sliding Dynamics of Ring Chains on Two Asymmetric/Symmetric Chains in a Simple Slide-Ring Gel

The sliding dynamics along two asymmetric/symmetric axial chains of ring chains linked by a linear chainis investigated using molecular dynamics (MD) simulations. A novel sub-diffusion behavior is observed for ring chains sliding along eithera fixed rod-like chain or fluctuating axial chain on asymmetric/symmetric axial chainsat the intermediate time range due to their strongly interplay between two ring chains. However, two ring chains slide in the normal diffusion at along time range because their sliding dynamics can be regarded as an overall motion of two ring chains. For ring chains sliding on two symmetric/asymmetricaxial chains, the diffusion coefficient D of ring chains relies on the bending energy of axial chains (Kb) as well as the distance of two axial chains (d). There exists a maximum diffusion coefficient Dmax at d = d* in which ring chains slide at the fastest velocity due to the maximum conformational entropy for the linking chain between two ring chainsat d = d*. Ring chain slide on fixed rod-like axial chainsfaster in the symmetric axial chain case than that in the asymmetric axial chain case. However, ring chains slide on fluctuatingaxial chainsslower in the symmetric axial chain case than that in the asymmetric axial chain case. This investigation can provide insights into the effects of the linked chain conformation on the sliding dynamics of ring chains in a slide-ring gel.

Elasticity and photoelasticity relationships for polyethylene terephthalate fiber networks by molecular simulation

We present a framework for the development of elasticity and photoelasticity relationships for polyethylene terephthalate fiber networks, incorporating aspects of the primary molecular structure. Semicrystalline polymeric fiber networks are modeled as sequentially arranged crystalline and amorphous regions. Rotational isomeric states-Monte Carlo simulations of amorphous chains of up to 360 bonds (degree of polymerization, DP=60), confined between and bridging infinite impenetrable crystalline walls, have been characterized by Omega, the probability density of the intercrystal separation h, and Deltabeta, the polarizability anisotropy. ln Omega and Deltabeta have been modeled as functions of h, yielding the chain deformation relationships. The development has been extended to the fiber network to yield the photoelasticity relationships. We execute our framework by fitting to experimental stress-elongation data and employing the single fitted parameter to directly predict the birefringence-elongation behavior, without any further fitting. Incorporating the effect of strain-induced crystallization into the framework makes it physically more meaningful and yields accurate predictions of the birefringence-elongation behavior.

Translocation of a proteinlike chain through a finite channel

We use the pruned-enriched-Rosenbluth method and the modified orientation-dependent monomer-monomer interaction model to study the translocation of a proteinlike chain through a finite channel. The mean-square radius of gyration per bond <S2>/N and shape factor <delta*> of proteinlike chains with different secondary structures transporting through a finite channel with different channel radii R=1, 2, 3, 4, and 20 are investigated in the translocation. The average Helmholtz free energy per bond A/N and the mechanical force f are also presented. A/N remains unchanged when X(0)<0 and X(0)>1, and decreases monotonously when 0.5<X(0)<0.1. Here X(0)=X/N identical with 2X/L,X is the position of the first monomer, N is chain length, and L is channel length. No free energy barrier is found in our calculation. f is negative and has a plateaulike behavior. The plateau becomes narrow and the value of f increases as R increases. The total energy per bond <U>/N is also calculated in the process of translocation. An energy barrier is shown. The proteinlike chains must cross this energy barrier when they escape from the channel. The position of the maximum of <U>/N depends on the secondary structures and the channel radius. We also discuss the average contact energy per bond <U>c/N, the average alpha-helical energy per bond <U>h/N, and the average beta-sheet energy per bond <U>b/N.

A Unified Approach to Conformational Statistics of Classical Polymer and Polypeptide Models

We present a unified method to generate conformational statistics which can be applied to any of the classical discrete-chain polymer models. The proposed method employs the concepts of Fourier transform and generalized convolution for the group of rigid-body motions in order to obtain probability density functions of chain end-to-end distance. In this paper, we demonstrate the proposed method with three different cases: the freely-rotating model, independent energy model, and interdependent pairwise energy model (the last two are also well-known as the Rotational Isomeric State model). As for numerical examples, for simplicity, we assume homogeneous polymer chains. For the freely-rotating model, we verify the proposed method by comparing with well-known closed-form results for mean-squared end-to-end distance. In the interdependent pairwise energy case, we take polypeptide chains such as polyalanine and polyvaline as examples.

Some interesting things about polysiloxanes

Poly(dimethylsiloxane) [-Si(CH3)(2)O-] is by far the most studied of the polysiloxanes and is known to exhibit some intriguing physical properties, in particular very high permeability to gases. Simulations are underway in an attempt to understand some of these peculiarities. In addition, other symmetrically substituted polysiloxanes exhibit mesophases that are not understood at all. In the case of cross-linked polysiloxanes, there have been many important developments, including (i) elastomers undergoing strain-induced crystallization through control of chain stiffness or stereochemical structure, (ii) model elastomers (including dangling-chain networks), (iii) possible thermoplastic elastomers, (iv) bimodal network chain-length distributions, and (v) cross linking in solution. Interesting elastomeric composites include those with (i) in-situ-generated ceramiclike particles, (ii) ellipsoidal fillers, (iii) claylike-layered fillers, (iv) polyhedral oligomeric silsesquioxane (POSS) particles, (v) porous fillers, (vi) controlled particle-elastomer interfaces, and (vii) elastomeric domains generated within ceramic phases. Also of interest are some new techniques that have been used to characterize polysiloxane networks.

Elastic behavior of short compact polymers

In this paper, we investigate the elastic behaviors of short compact polymers using the enumeration calculation method and the HP model on a two-dimensional square lattice. Both the mean-square end-to-end distance R(2) and the ratio of R(2)/S(2) increase with lambda. However, when the elongation ratio becomes larger, the curves of R(2)/S(2) become smooth and they are close to the limit of 10.50 for different compact polymers. We also investigate the changes of interior conformations in the process of tensile elongation through calculating the probabilities of three bond angles (i.e., 90 degrees, 180 degrees, and 270 degrees). The average energy and Helmholtz free energy per bond are both negative and increase with elongation ratio lambda. In the meantime, the elastic force per bond (f ) also increases with elongation ratio lambda, and the energy contribution to the elastic force (f(U)) increases first and then drops, and there exists the maximum of f(U) in the region of lambda=1.40-1.80 for different sequences. The entropy contribution to force (f(S)) is close to zero at a small elongation ratio lambda and then increases with lambda. Some comparisons with different sequences (including nonfolding and folding sequences) are also made.