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Distribution functions in elasticity
Author(s) -
Eichinger B. E.,
Shy L. Y.,
Wei Gaoyuan
Publication year - 1989
Publication title -
makromolekulare chemie. macromolecular symposia
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.257
H-Index - 76
eISSN - 1521-3900
pISSN - 0258-0322
DOI - 10.1002/masy.19890300120
Subject(s) - statistical physics , eigenvalues and eigenvectors , elasticity (physics) , matrix (chemical analysis) , tensor (intrinsic definition) , elastomer , computation , random matrix , constant (computer programming) , classical mechanics , physics , computer science , mathematics , materials science , quantum mechanics , geometry , algorithm , composite material , thermodynamics , programming language
The formation of a gel or elastomer entails the linking together of molecules to form a contiguous random network that has macroscopic dimensions. Forces are propagated in networks along polymer chains and through junctions to other chains. It is important to understand the structure of the force constant matrix that describes a system as complicated as this, even in the case where the potential energy is approximated by a simple harmonic function. This force constant matrix was first formulated by James, but because it is a large random matrix, very little progress can be made in the analysis of its properties. We have opted to approach this problem with the use of large scale computations that are based upon simulations of the formation of networks. Subsequent evaluation of the eigenvalue spectrum of the matrix lends considerable insight into the equilibrium and dynamic properties of elastomers. For present purposes this analysis is couched in terms of the calculation of the probability distribution of the gyration tensor for a phantom network in which non‐bonded interactions are not considered.