Monte Carlo simulations on the effects of nanoparticles on chain deformations and reinforcement in amorphous polyethylene networks

Sharaf, M. A.; Mark, J. E.

doi:10.1016/j.polymer.2004.02.073

Cited by 60 publications

(42 citation statements)

References 40 publications

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“…The statistical behavior of long polymer chains on lattices is often studied using the Monte Carlo sampling method introduced in [34]. This method has been used extensively in the literature [39]. The existence of polymer science traces back to the 1930s [27].…”

Section: Literature Reviewmentioning

confidence: 99%

Position and Orientation Distributions for Non-Reversal Random Walks using Space-Group Fourier Transforms

2010

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This paper presents an efficient group-theoretic approach for computing the statistics of non-reversal random walks (NRRW) on lattices. These framed walks evolve on proper crystallographic space groups. In a previous paper we introduced a convolution method for computing the statistics of NRRWs in which the convolution product is defined relative to the space-group operation. Here we use the corresponding concept of the fast Fourier transform for functions on crystallographic space groups together with a non-Abelian version of the convolution theorem. We develop the theory behind this technique and present numerical results for two-dimensional and three-dimensional lattices (square, cubic and diamond). In order to verify our results, the statistics of the end-to-end distance and the probability of ring closure are calculated and compared with results obtained in the literature for the random walks for which closed-form expressions exist.

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Section: Literature Reviewmentioning

confidence: 99%

Position and Orientation Distributions for Non-Reversal Random Walks using Space-Group Fourier Transforms

2010

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“…This convolution of functions on the group can be calculated by direct sequential products of Fourier transform of each function as (12) Note that unlike the case of the classical convolution theorem the order of multiplication matters.…”

Section: Matrix Elements Of the Irreducible Unitary Representations Omentioning

confidence: 99%

“…(12). Let us denote the Fourier transform of an N-link polymer as F. This can be obtained simply by multiplying each Fourier transform in reversed order as (20) when we apply the above arguments to obtain the end-to-end distance distribution.…”

Section: The Freely-rotating Modelmentioning

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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“…The existence of NPs can change the dynamics of polymers and therefore shifts the glass transition temperature [14] and slows down the diffusion of polymer chains [15]. Recently, the dynamics of polymer melts and concentrated polymer solutions have been studied intensively by experiments [16,17], theory and computer simulations [18][19][20][21]. It was found that the properties of polymers would be influenced by many parameters, such as size, shape, and concentration of NPs and interaction strength between polymer and NP [10].…”

Section: Introductionmentioning

confidence: 99%

Statistical Properties of a Polymer Chain in the Environment with Low Concentration of Nanoparticles

Tsehay

Luo

2018

Acta Phys. Pol. A

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We have investigated the statistical properties of polymer in the environment with low concentration of nanoparticles by using large-scale molecular dynamics simulations. The scaling law for the mean square radius of gyration was examined and simulation results for the polymer lengths 64 ≤ N ≤ 144 yielding a reasonably accurate value of the Flory exponent ν = 0.58 at weak polymer-nanoparticle interaction εPN. Within the same range of N , the mean asphericity of the chain is independent of N . We found that the polymer behaves like a self-avoiding walk chain at small εPN and a compact sphere at large εPN. The results are attributed to the increase in the contact between polymer and nanoparticles with increasing εPN. Normal diffusions of polymer are always observed at whatever εPN and size and concentration of nanoparticles. Our result shows that the normal diffusion behavior of polymer is independent of polymer's state even though there is a phase transition from a desorbed polymer phase at small εPN to an adsorbed polymer phase at large εPN.

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Monte Carlo simulations on the effects of nanoparticles on chain deformations and reinforcement in amorphous polyethylene networks

Cited by 60 publications

References 40 publications

Position and Orientation Distributions for Non-Reversal Random Walks using Space-Group Fourier Transforms

Position and Orientation Distributions for Non-Reversal Random Walks using Space-Group Fourier Transforms

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

Statistical Properties of a Polymer Chain in the Environment with Low Concentration of Nanoparticles

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