VISCOSITY OF POLYMER SOLUTIONS REVISITED

Abstract

A rubbery sphere as a hydrodynamic model for the polymer molecule is useful in predicting many aspects of the solution behavior, but it has some inconsistencies in its physics. Instead of this model of hydrodynamic volume, we propose the Gaussian cloud with its average density as the characterization parameter. The Stokes-Einstein equation is applied, not to the molecules as solid spheres, but to the individual mass points that makes up the cloud. The cloud has no definitive boundary, but has an average internal density, ci in g/cm3, which is equal to c* or 2.5/[η] at c→0. With increased concentration, the internal density of clouds increases, starting at 0 concentration. The increased density adds another term to the increase of viscosity. The Huggins equation is derived from this increased density affecting the internal viscosity in the cloud. Further increase in the concentration will cause the overlap among more than two neighbors, resulting in higher order terms. The resulting equation for the specific viscosity: 1ηsp = c[η]{1+kHc[η]+(kHc[η])2/2!+(kHc[η])3/3!}, is a four term polynomial of the parameter, c[η], which might be called the generalized Huggins equation. Each term is related to the number of the interacting neighbors. This equation seems to be applicable to all kinds of polymers, from rigid polyphenylenes to semi-rigid hexyl isocyanates to flexible vinyl polymers, provided the equation is fitted directly to raw data, rather than by first obtaining kH and [η] from an approximate straight line at small concentrations. The universal equation holds from the dilute to the concentrated solutions including the so-called entanglement regime, i.e., where η~M3 to M4, and to a polyelectrolyte such as hyaluronan with added salt ions to shield intramolecular coulombic repulsion.