MONTE-CARLO SIMULATION OF OFF-LATTICE POLYMER-CHAINS - EFFECTIVE PAIR POTENTIALS IN DILUTE-SOLUTION

Monte Carlo methods are used to calculate the mean squared radius of gyration, [R(g)2], potential of mean force, U(r), and second osmotic virial coefficient, B2, of polymer chains. Two models of polymers as off-lattice chains of tangent hard spheres are used. In the first, the beads of the chains are simply hard spheres (the athermal case). In the second, the beads of the chains are allowed to interact with nonadjacent beads on the same chain and with beads on a different chain via a square-well potential. In both models, conformations of chains with 50, 100, 200, and 500 segments were generated. In the square-well model, square-well potentials epsilon = -0.15kT, -0.3kT, and -0.45kT were used. Examination of the radius of gyration of single chains shows a theta-point (defined to be the temperature at which [R(g)2] depends linearly on the chain length) at epsilon(theta) congruent-to -0.32kT. The radius of gyration of two interacting chains shows that as the chains are brought close together, they become compressed along the axis between their centers of mass and expanded perpendicular to this axis. The potential of mean force, U(r), between two polymer chains is calculated as a function of the separation between the chains' centers of mass and is found to decrease as chain length increases. This is in contrast to the Flory-Krigbaum theory but is in agreement with previous findings of Grosberg et al. For chains of different lengths, U(r) decreases as the difference between the lengths of the chains increases. Near the THETA-point, the U(r) curves tend to be indistinguishable for all chain lengths. The second osmotic virial coefficient is calculated from the potential of mean force. Scaling analysis on the second osmotic virial coefficient for athermal chains gives a scaling exponent of gamma = 0.272 +/- 0.005, in agreement with the findings of Yethiraj et al. The THETA-point (defined here as the point where B2 = 0) is found to be at a square-well potential of epsilon(theta) congruent-to -0.32kT. This is the same as the THETA-point defined in terms of the radius of gyration and is in agreement with the results of Wichert and Hall. A correlation for U(r) that fits the simulation data reasonably well is also presented.