Chains between Two Parallel Walls:  Distribution Functions and Force−Deformation Relations

Force−deformation relations for finite chains between two parallel walls are studied. First, the force−deformation relation for a single finite chain between two walls is derived from a second-order tensorial Chebychev distribution function of the end-to-end vector. Second, the case of several chains between two parallel walls is studied. The chains bridging the gap between the two walls are assumed to exert forces only at their ends at the walls. The model is constructed by assuming a very long chain to bridge the gap between two parallel walls. At contact points, the chain is assumed to adsorb to the walls by an adsorption energy of ΔH c per contact point. Thus the chain is divided into N s strands, each extending from one wall to the other and N s + 1 contact points. The contact points at the walls are assumed as “hinges” over which the chain passes. The most probable distribution of strand lengths is obtained, from which mechanical variables such as the force−extension relations, maximum extensibility, ductility, and toughness of the chain−wall system are calculated.