Random elastic networks. I. Computer simulation of linked stars

Abstract

Results of computer simulations of random networks with spatial constraints are reported. An algorithm has been devised to produce networks from δ‐branched stars with Gaussian arms, the nodes of the stars being sited at lattice points. Structural statistics in the form of the percentage of loops, unreacted ends, single and multiple chains, and average junction functionality are given. The eigenvalue spectra of the Kirchhoff matrices of the nets are analyzed in terms of the density function and moments. The spectra for small λ are different from those for random regular nets formed without constraints, in that small eigenvalues are much more numerous when constraints are imposed. Network collapse remains a problem. Viscoelasticrelaxation time spectra are also considered, and in one case the spectrum exhibits the beginnings of a rubbery plateau.