Nonuniversality of the dynamic exponent in twodimensional random media 

: 248 : 2019.04.15 00:00 
SCIENTIFIC REPORTS 
Cho, HW (Cho, Hyun Woo); Sung, BJ (Sung, Bong June) 2019.01.22 
Nonuniversality of the dynamic exponent in twodimensional random media
Cho, HW (Cho, Hyun Woo)^{[ 1,2,3,4 ] }; Yethiraj, A (Yethiraj, Arun)^{[ 3,4 ] }; Sung, BJ (Sung, Bong June)^{[ 1,2 ]}
[ 1 ] Sogang Univ, Dept Chem, Seoul 04107, South Korea
[ 2 ] Sogang Univ, Res Inst Basic Sci, Seoul 04107, South Korea
[ 3 ] Univ Wisconsin, Theoret Chem Inst, Madison, WI 53706 USA
[ 4 ] Univ Wisconsin, Dept Chem, 1101 Univ Ave, Madison, WI 53706 USA The diffusion of solutes in twodimensional random media is important in diverse physical situations including the dynamics of proteins in crowded cell membranes and the adsorption on nanostructured substrates. It has generally been thought that the diffusion constant, D, should display universal behavior near the percolation threshold, i.e., D  (phi  phi(c))(mu), where phi is the area fraction of the matrix, phi(c) is the value of phi at the percolation threshold, and mu is the dynamic exponent. The universality of mu is important because it implies that very different processes, such as protein diffusion in membranes and the electrical conductivity in twodimensional networks, obey similar underlying physical principles. In this work we demonstrate, using computer simulations on a model system, that the exponent mu is not universal, but depends on the microscopic nature of the dynamics. We consider a hard disc that moves via random walk in a matrix of fixed hard discs and show that mu depends on the maximum possible displacement Delta of the mobile hard disc, ranging from 1.31 at Delta <= 0.1 to 2.06 for relatively large values of Delta We also show that this behavior arises from a powerlaw singularity in the distribution of transition rates due to a failure of the local equilibrium approximation. The nonuniversal value of mu obeys the prediction of the renormalization group theory. Our simulations do not, however, exclude the possibility that the nonuniversal values of mu might be a crossover between two different limiting values at very large and small values of Delta The results allow one to rationalize experiments on diffusion in twodimensional systems.
