Polymers in disordered environments

Abstract

A brief review of our recent studies aiming at a better understanding of the scaling behaviour of polymers in disordered environments is given. The main emphasis is on a simple generic model where the polymers are represented by (interacting) self-avoiding walks and the disordered environment by critical percolation clusters. The scaling behaviour of the number of conformations and their average spatial extent as a function of the number of monomers and the associated critical exponents γ and ν are examined with two complementary approaches: numerical chain-growth computer simulations using the PERM algorithm and complete enumerations of all possible polymer conformations employing a recently developed very efficient exact counting method.

Percolation characteristics of filled polyurethane auxetics

“…Peculiarities of structure formation in polymer auxetics indicate thermodynamic nonequilibrium of these processes and their nonlinearity. This makes it possible to use, as for other polymers, fractal and percolation approaches [11][12][13][14].…”

Scaling laws for random walks in long-range correlated disordered media

“…Right at the percolation point, even diffusion and polymer statistics show a modified, anomalous behavior, which has been extensively studied using field-theoretic renormalization group methods [15,16] and computer simulations [17]. For recent examples see [18][19][20][21][22][23][24][25] and further references therein.…”

Analysis of critical percolation clusters of mixtures of conducting and dielectric polymers

“…Note that this distance varies from the Euclidean distance. Several studies on chemical distance in lattice-based percolation [14] and continuum percolation [15] have been reported. The presented definition of chemical distance distribution is the natural extension of the classical definition of chemical distance in a continuum percolation medium described in [15], which was inspired by similar formulation used in polymer chain-growth algorithm described in [14].…”

“…Several studies on chemical distance in lattice-based percolation [14] and continuum percolation [15] have been reported. The presented definition of chemical distance distribution is the natural extension of the classical definition of chemical distance in a continuum percolation medium described in [15], which was inspired by similar formulation used in polymer chain-growth algorithm described in [14]. The chemical distance distribution is based on the shortest paths between domain boundaries (particles that belong to these paths equal 0), the values assigned to other particles outside the shortest paths determine the chemical distance from the shortest paths, and thus determine the possible paths of electric current in the percolation cluster.…”