Simulations on the reinforcement of poly(dimethylsiloxane) elastomers by randomly distributed filler particles

Yuan, Qiaolong; Kloczkowski, Andrzej; Mark, J. E.; Sharaf, M. A.

doi:10.1002/(sici)1099-0488(19960715)34:9<1647::aid-polb14>3.0.co;2-7

Cited by 92 publications

(103 citation statements)

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“…Different simulations and theories have previously predicted expansion, contraction, or little to no effect on polymer radii of gyration [38,[41][42][43][44][45]. For the systems we studied, however, we find the chains are universally compressed.…”

Section: Than 1 K B T Along the Opposite Branch (Open Symbols)mentioning

confidence: 99%

Structure of phase-separated athermal colloid-polymer systems in the protein limit

2013

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Structural features of phase separated athermal colloid-polymer mixtures in the so-called "protein limit," where polymer chain dimensions exceed those of the colloid, are investigated using grand canonical Monte Carlo simulations on a fine lattice. Previous work [N. A. Mahynski, et al. Phys. Rev. E 85, 051402 (2012)] has shown that this model accurately captures the phase behavior of experimental systems, and that colloids with sufficiently small diameters, σc, relative to that of the monomeric segments, σs, phase separate more readily than their large-diameter counterparts. In the present study, we directly connect colloid and polymer structure with their phase behavior by investigating these solutions along their binodal curves; we also explore the role of colloid surface curvature in destabilizing such solutions. Our findings suggest that simple consideration of an additional depletion radius, on the order of the σs, leads to a quantitatively accurate prediction of the division between stable and unstable ranges of d = σs/σc. We compare these results to continuum models with different bonding potentials between monomer segments in order to elucidate the significance of the lattice model's bond fluctuations and inherently coarse colloid surface. In a number of cases, the continuum models deviate both qualitatively and quantitatively from the lattice results, but the binodals of the continuum models are presently not known, making a strong conclusion about these differences impossible.

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Section: Than 1 K B T Along the Opposite Branch (Open Symbols)mentioning

confidence: 99%

Structure of phase-separated athermal colloid-polymer systems in the protein limit

2013

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“…The Mark-Curro approach has also been applied to investigations on the effect of particle reinforcement [26][27][28]. In these particle reinforcement investigations, various volume fractions, inclusion sizes, and inclusion shapes and orientations are considered, where the chain conformation is excluded from occupying any volume dedicated to an inclusion.…”

Section: Introductionmentioning

confidence: 99%

“…In this work RIS theory is applied in a manner analogous to the particle inclusion works [26][27][28] in order to capture each of these contributions, where inclusion volumes are now taken to be clusters. Cluster morphology is assumed a priori, based on available experimental measurements for the various cases; the subsequent backbone conformation in response to this morphology is applied to obtain stiffness predictions.…”

Section: Introductionmentioning

confidence: 99%

Application of Rotational Isomeric State Theory to Ionic Polymer Stiffness Predictions

et al. 2005

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Presently, Rotational Isomeric State (RIS) theory directly addresses polymer chain conformation as it relates to mechanical response trends. The primary goal of this work is to explore the adaptation of this methodology to the prediction of material stiffness. This multi-scale modeling approach relies on ionomer chain conformation and polymer morphology and thus has potential as both a predictive modeling tool and a synthesis guide. The Mark-Curro Monte Carlo methodology is applied to generate a statistically valid number of end-to-end chain lengths via RIS theory for four solvated Nafion cases. For each case, a probability density function for chain length is estimated using various statistical techniques, including the classically applied cubic spline approach. It is found that the stiffness prediction is sensitive to the fitting strategy. The significance of various fitting strategies, as they relate to the physical structure of the polymer, are explored so that a method suitable for stiffness prediction may be identified.

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“…The inverse Fourier transform is defined as (9) or in component form as (10) The convolution of two functions on rigid-body motion group F 1 (g), F 2 (g) is defined as (11) where h, g ∈ SE (3). The geometric meaning of this convolution is that the second function is swept and weighted by the first.…”

Section: Matrix Elements Of the Irreducible Unitary Representations Omentioning

confidence: 99%

“…(9) or (10). To obtain the probability density function of end-to-end distance, let us first consider the integral over SO (3) of F(g) (13) If we separate and write for the last integral, then it becomes where .…”

Section: Pdf Of End-to-end Distancementioning

confidence: 99%

A unified approach to conformational statistics of classical polymer and polypeptide models

Kim

Chirikjian

2005

Polymer

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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 closedform 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.

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Simulations on the reinforcement of poly(dimethylsiloxane) elastomers by randomly distributed filler particles

Cited by 92 publications

References 0 publications

Structure of phase-separated athermal colloid-polymer systems in the protein limit

Structure of phase-separated athermal colloid-polymer systems in the protein limit

Application of Rotational Isomeric State Theory to Ionic Polymer Stiffness Predictions

A unified approach to conformational statistics of classical polymer and polypeptide models

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