Viscosity of Polymer Solutions over the Full Range of Composition: A Thermodynamically Inspired Two-Parameter Approach

The approach yields the following relation for the relative viscosity η rel as a function of polymer concentration c (mass/volume): ln η rel = c̃ /(1 + pc̃ + qc̃ 2 ). Reduced concentrations c̃ (defined as c̃ = c [η], where [η] is the intrinsic viscosity) are used instead of c to incorporate thermodynamic information. The parameters p and q account for changes in the free volume of the solvent caused by the polymer. The analysis of literature data for seven very dissimilar systems discloses the following common feature: p > 0 and q < 0. This means that the curves in the plots of ln η rel as a function of c̃ are normally located below the tangent at low c̃ and above it at high c̃ . The values of p and q correlate strongly with the temperature distance to the glass-transition temperature of the polymer ( T g ). Beyond the mere modeling of viscosity data, the approach allows the determination of [η] from data at high polymer concentrations and provides information on the generalized intrinsic viscosity, {η}. Measurements for T < T g give access to glass curves, i.e., to T g ( c ). Moreover, the modeling helps to recognize systems with special behavior, such as solutions of poly(dimethyl siloxane) in its oligomers.