Percolation Thresholds and Excluded Area for Penetrable Rectangles in Two Dimensions.

The percolation threshold for penetrable rectangles in two dimensions is examined by way of an analogy to a lattice model that employs the averaged pairwise excluded area between particles as a key ingredient. Percolation thresholds are calculated as functions of: (i) the aspect ratio of the rectangles for the case of a random, isotropic, orientational distribution, and: (ii) the orientational order parameter for situations in which the particles exhibit varying degrees of alignment. The threshold volume fraction is found to rise with increases in the degree of particle alignment, and our results for isotropically distributed systems are in close agreement with findings from recent Monte Carlo (MC) simulations. [ABSTRACT FROM AUTHOR]