Second Virial Coefficient Calculations for Square-Well Chain Molecules

Abstract

The second virial coefficient, B[sub 2], has been calculated for square-well chain molecules of lengths n = 2--50 and well widths of [lambda] = 0.25--1.0 by Monte Carlo integration. The theta temperature, at which B[sub 2] = 0, is independent of chain length around [lambda] = 0.5, increases with chain length for [lambda] > 0.5, and decreases with chain length for [lambda] < 0.5. A scaling relation, T[sub [theta]]*(n) [minus] T[sub [theta]]*([infinity]) [alpha] n[sup [minus][phi]], accurately describes the departure of the theta temperature from the infinite chain length value for [lambda] [ge] 0.6. A closed-form expression for the second virial coefficient of square-well chains is presented which accurately fits the Monte Carlo data for n = 2--50 and [lambda] = 0.25--0.75. When compared to the Monte Carlo results, the second virial coefficient predicted by the generalized Flory-dimer theory for square-well chains is found to be increasingly inaccurate as chain length increases. If one corrects the generalized Flory-dimer equation of state by forcing it to have the correct second virial coefficient, the compressibility factor is accurately predicted at densities below [eta] = 0.04.