2ND VIRIAL-COEFFICIENT CALCULATIONS FOR SQUARE-WELL CHAIN MOLECULES

The second virial coefficient, B2, 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 B2 = 0 , is independent of chain length around lambda = 0.5, increases with c hain length for lambda > 0.5, and decreases with chain length for lamb da < 0.5. A scaling relation, T(theta)(n)-T(theta)*(infinity) is-prop ortional-to n(-phi), accurately describes the departure of the theta t emperature from the infinite chain length value for lambda greater-tha n-or-equal-to 0.6. A closed-form expression for the second virial coef ficient of square-well chains is presented which accurately fits the M onte 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 th e generalized Flory-dimer theory for square-well chains is found to be increasingly inaccurate as chain length increases. If we correct the generalized Flory-dimer equation of state by forcing it to have the co rrect second virial coefficient, the compressibility factor is accurat ely predicted at densities below eta = 0.04.