Entropy, pressure, and chemical potential of multiple chain systems from computer simulation. I. Application of the scanning method

Using the scanning simulation method we study a system of many chains with excluded volume contained in a ‘‘box’’ on a square lattice. With this method an initially empty box is filled with the chains monomers step by step with the help of transition probabilities. The probability of construction, P of the whole system is the product of the transition probabilities used and hence the entropy S is known, (S∼ln P). Thus the pressure and the chemical potential can be calculated with high accuracy directly from the entropy using standard thermodynamic relations. In principle, all these quantities can be obtained from a single sample without the need to carry out any thermodynamic integration. Various alternatives for performing the scanning construction are discussed and their efficiency is examined. This is important due to the fact that for lattice polymer models the scanning method is ergodic (unlike some dynamical Monte Carlo techniques). The computer simulation results are compared to the approximate theories of Flory, Huggins, Miller, and Guggenheim and to the recent improved theories of Freed and co-workers.