Viscosities of concentrated polymer solutions

A general relationship between the viscosity and the concentration of polymer solutions has been derived for relatively low concentration regions by means of the method which was proposed by Brinkman. The relationship was extended so as to be applicable for extremely concentrated solutions by allowing for the volume shrinkage of polymers. With increasing concentration, the apparent volume which a polymer in solution occupies above some critical volume fraction ϕc, is assumed to be given by Ω = sv0ϕ−β, where s is the swelling factor at ϕ = 1 and β is a constant which measures a reluctance against the intermolecular permeation; v0 and ϕ are the net volume of the polymer molecule and the volume fraction of the polymer, respectively. The dependence of η on ϕ is given by the equation d log η/dϕ = C/ϕγ (1 − ϕ), where C and γ are constants to be determined empirically. In order to test the validity of the equation, our experimental and some other available data were used. Although neither temperature nor molecular weight factor is involved in this equation, it accounts well for the dependence of the viscosity on the concentration of polymers over a wide range of concentration, and fairly satisfactory agreement was found between theory and experiment.