Some comments on correlation‐function formulas for polymer intrinsic viscosity

Effects of bead-bead interactions on the static and dynamical properties of model polymer solutions

The effects of segment-segment interactions on the static and dynamical properties of model polymer solutions are examined by Brownian dynamics simulations in the free-draining limit over a wide concentration range. A bead-and-spring model is used to describe the polymer chains at a coarse-grained level, in which segment-segment interactions are represented by a bead-bead pair potential with a Gaussian analytic form, beta u(ev)(r)=A exp(-r(2)/2 sigma(2)), where beta=1/k(B)T and A and sigma are characteristic energy and distance scales, respectively. The chain dimensions, self-diffusion coefficient, and viscosity of the systems are studied as functions of number density of beads of the system, rho, at given excluded-volume potential parameters, A and sigma. Our results show that in the limit of infinite dilution even for short chains (N approximately 10) there is statistically significant scaling behavior in the static and dynamical properties. For a system with given values of A and sigma the change in polymer coil size shows a realistic trend as the concentration of the system increases. In the dilute and concentrated regions the coil size decreases as a result of increasing interchain repulsions, while in the highly concentrated region the coil size increases again, showing a return to Rouse-like behavior because the intrapolymer and interpolymer segment-segment interactions become effectively indistinguishable for an arbitrary bead and to a large extent are "balanced out." In the limit of infinite dilution, the self-diffusion coefficient of the center of mass, D(cm), depends on N only and not on the potential parameter A, while in contrast the specific viscosity eta(sp) depends on both N and A. As the concentration increases D(cm) decreases and eta(sp) increases consistent with the behavior of real polymers. When the system becomes highly concentrated, however, both D(cm) and eta(sp) unrealistically return to the Rouse limit. This suggests that from the concentrated region upward in concentration, the entanglement or the topological constraints caused by the physical connectivity of the chains significantly influence their dynamical behavior. The mean-field segment-segment interactions or excluded-volume effects incorporated in the current coarse-grained bead-spring approach cannot capture this entanglement effect, and therefore give rise to unrealistic dynamical behavior in the concentrated regime.