12 research outputs found
Simulation studies of permeation through two-dimensional ideal polymer networks
We study the diffusion process through an ideal polymer network, using
numerical methods. Polymers are modeled by random walks on the bonds of a
two-dimensional square lattice. Molecules occupy the lattice cells and may jump
to the nearest-neighbor cells, with probability determined by the occupation of
the bond separating the two cells. Subjected to a concentration gradient across
the system, a constant average current flows in the steady state. Its behavior
appears to be a non-trivial function of polymer length, mass density and
temperature, for which we offer qualitative explanations.Comment: 8 pages, 4 figure
Scaling for the Percolation Backbone
We study the backbone connecting two given sites of a two-dimensional lattice
separated by an arbitrary distance in a system of size . We find a
scaling form for the average backbone mass: , where
can be well approximated by a power law for : with . This result implies that for the entire range . We also propose a scaling
form for the probability distribution of backbone mass for a given
. For is peaked around , whereas for decreases as a power law, , with . The exponents and satisfy the relation
, and is the codimension of the backbone,
.Comment: 3 pages, 5 postscript figures, Latex/Revtex/multicols/eps