A Simple Model for Rubber
Teunis C. Dorlas · Statistical mechanics · 2021
Rubber consists of very long flexible molecules. We shall model them as little sticks linked in a chain. The chains are cross-linked at random but relatively sparse positions. We model here a single chain segment. For simplicity, we assume that each stick can have only six positions: forward and backward in each of the coordinate directions. We also assume that each stick has length l. If each stick is completely free to bend in any of these six directions, the energy of the chain is independent of the configuration of the chain but highly degenerate. The square of the end-to-end length of the chain L is then the sum of the squares of random variables X, Y, and Z. The important observable of rubber as regards its elasticity is the tensionF.