Critical exponent for 3-D percolation conductivity, revisited

Abstract

When we apply finite-size-scaling analysis to Monte-Carlo calculations of the electrical conductivity of simple-cubic, bond- and site-percolation lattices, we obtain a correlation-length critical exponent in good agreement with current values but, for the conductivity exponent, we find t = 2.06 ± 0.16, significantly higher than the value currently cited. This new value appears, however, in essential agreement with a recently proposed theoretical conjecture

Physicochemical Studies on Microemulsions

“…The results are given in Table 1 with errors. The expected value of n is again 1.9 where u is the temperature corresponding to the specific conductance s, u t is the transition temperature, and n is an (24,26) like m. The derived values fall in the range 1.9-3.8 in the presence of the additives NaC, TEAI, SDS, exponent.…”

Physicochemical studies on microemulsions

“…At high dispersion concentration, t becomes unity converting (2) with Φ c = 0.333. This is the expectation for static percolation of mixtures of conductors and insulators [35][36][37]. The dynamic percolation of microemulsion may not comply with this requirement [3,[37][38][39].…”

Concentration Dependence of Mechanical Properties of Polyacrylamide near the Sol-Gel Transition Point

“…Both values of t are similar to that calculated from the percolation theory. [9][10][11][12]17) In this study, the critical exponent twas about 2, suggesting that the dependence of the shear modulus of the copolymer on the concentration was also described approximately by the percolation theory. Tokita and Hikichp6,19,20) stated that the bond formation probability P b corresponded to such parameters as time and temperature, and that the site occupation probability P s corresponded to the monomer concentration.…”