Towards statistical mechanics of a 2D random cellular structure

Abstract

Using the methods of statistical mechanics the authors construct the partition function of a system of a large number of 2D cells that covers without pores or overlaps a flat surface. Each cell is defined by its position, area, perimeter and number of sides. Besides topological and space-filling constraints, they impose new ones regarding the energy and maximum area of the cells. The entropy and free energy of the system are calculated and the mean values of the macroscopic parameters are determined in the equilibrium configuration. The results are compared with experimental ones for soap froths and metallurgical aggregates.