The Shear-Rate Dependence of Viscosity in Concentrated Solutions of Narrow-Distribution Polystyrene

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Abstract
Viscosity was measured as a function of shear rate for a series of concentrated solutions of polystyrene in n‐butyl benzene, using a plate‐cone viscometer. The polymers had narrow distributions of molecular weight (M w /M n =1.01–1.20) with M w ranging from 19,800 to 2,400,000. Polymer concentrations ranged from 0.20 to 0.55 g/cc and temperatures from 30 to 60°C. A master curve of reduced viscosity versus reduced shear rate was prepared and found to be similar to one recently predicted for monodisperse entangling polymers. An experimental relaxation time τ 0 was deduced for each solution by superposition with the theoretical master curve. The values ranged from 0.0024 to 9.1 sec and were always of the order of the Rouse relaxation time, τ r =(6/π 2 )(η 0 M/cRT), calculated for the solution. Residual variations in the ratio τ 0 /τ r with both concentration and molecular weight were noted however, although a single curve was formed when τ 0 /τ r was plotted as a function of the product cM. This suggested that the number of chain entanglements per molecule influences the course of the relaxation process. A very simple equation correlated all the data, yielding τ 0 =( const. ) η 0 M/cT at low values of the entanglement density and τ 0 =( const. ) η 0 /c 2 T at high values.
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