STATISTICS OF CONFINED SELF-AVOIDING WALKS .2. ENTROPY AND PRESSURE OF CONFINEMENT

Self-avoiding walks (SAWs) up to 198 steps and random-flight walks (RFWs) up to 598 steps were computer generated. The entropy change upon confinement of the walks, as well as the pressure exercised by corresponding chains obeying Hamiltonian mechanics on the surface of the confining spheres, was derived from the Monte Carlo data for the 'compactness' parameter W of the walks. If appropriate reduced radii rho(0) = R/[r] are introduced, where [r] is the mean end-to-end distance, it is found, in accord with theory, that a plot of the entropy change Delta S versus rho(0)(-2) for RFWs is linear. The same is also found to be true for SAWs, though in a somewhat more limited rho(0) range. The quantity PV/KT, where P is the pressure, V the volume of the confining boundary, T the absolute temperature, and K is Boltzmann's constant, is also found to vary linearly with rho(0)(-2), for both kinds of walks, in accord with the Edwards-Freed theory. The general conclusion to be drawn from the present paper and also a previous one, is that if proper reduction lengths are introduced for SAWs and RFWs (respectively, N-0.592 and 0.922 N-0.5), then the general properties of confined SAWs and RFWs are quite comparable. These properties include chain dimensions, concentration profiles, entropy change upon confinement, and finally pressure.