Open Access

ARTICLE

Statistical Analysis of Macromolecular Chains in the Space Filled by Nanoparticles

J. Zidek^1,2, J. Kucera¹, J. Jancar^1,2

1 Brno University of Technology, Brno, Czech Republic.
2 Central European Institute of Technology, Brno, Czech Republic.

Computers, Materials & Continua 2012, 28(3), 213-230. https://doi.org/10.3970/cmc.2012.028.213

Abstract

The paper presents a combination of worm-like chain numerical models and one with a finite set of nano-particles. The primary objective of the models was to analyze the distribution of space in a system filled by particles. Information on the distribution of space was compared to properties of chains inside the set of particles. The set of nanoparticles was constructed with a tool generating a finite set of particles that is randomly distributed in a given space. The particles have a prescribed volume fraction and uniform size. First, the proportions of chains and particles were compared. The length of chain was expressed in terms of end-to-end length. It was then compared to the size of gaps between two particles. The volume of chain was compared to the volume of space delimited by the particles. Next, a set of 10,000 random chains was generated and these were introduced into the particle set. The contact of a chain with the surface of a particle resulted in the special structural elements of the chain: a chain connecting two different particles, a loop which begins and ends at the same particle, a part of a chain which is completely adhered to the particle surface, a chain attached to a particle with one free end, as well as completely free chains. The chains were classified under three classes: chains which were not in contact with particles, chains which were in contact with one particle, and chains which were in contact with two or more particles. A statistical representation of each class is presented. The contact between chain and particle can influence macroscopic properties such as those that are elastic.

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Keywords

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