Generalized correlations for molecular weight and concentration dependence of zero-shear viscosity of high polymer solutions

Viscosity of Polymer Solutions and Molecular Weight Characterization

Since the pioneering research by Staudinger on dilute solution viscosity and its relation to the polymer molecular weight, viscosity analysis has become a valuable technique for polymer characterization. The conventional approach is based on the Huggins approximation of the solution-specific viscosity by a quadratic function of concentration, c. We show how to reformulate this approach in a universal form by representing a solution-specific viscosity, η_sp, as a generalized universal function η_sp(c) = α(c/c*) + (1 - α)(c/c*)² of chain overlap concentration, c*, determined at η_sp = 1, with numerical coefficients α = 0.745 ± 0.005 for good and 0.625 ± 0.008 for a θ solvent. This viscosity representation can be viewed as a calibration curve for molecular weight determination from a measurement of the solution viscosity at a given solution concentration. Furthermore, the molecular weight dependence of the overlap concentration provides a means for quantifying the polymer/solvent affinity and the solvent effect on chain flexibility. The extension of the approach to semidilute solutions opens a path for obtaining molecular weight in a broad concentration range without requiring a dilution and monitoring its change during the polymerization reaction from solution viscosity.

Quantifying Properties of Polysaccharide Solutions

We apply a scaling theory of semidilute polymer solutions to quantify solution properties of polysaccharides such as galactomannan, chitosan, sodium carboxymethyl cellulose, hydroxypropyl methyl cellulose, methyl cellulose, xanthan, apple pectin, cellulose tris(phenyl carbamate), hydroxyethyl cellulose, hydroxypropyl cellulose, sodium hyaluronate, sodium alginate, and sodium κ-carrageenan. In particular, we obtain the molar mass of the chain segment inside a correlation blob M _g = B̂ ^3/(3ν-1) c ^1/(1-3ν) as a function of concentration c, interaction parameter B̂, and exponent ν. Parameter B̂ assumes values B̂ _g, B̂ _th and M ₀/N _A ^1/3 l for exponents v = 0.588, 0.5 and 1, respectively, where M ₀ is the molar mass of a repeat unit, l is the projection length of a repeat unit, and N _A is the Avogadro number. In the different solution regimes, the values of the B̂-parameters are extracted from the plateaus of the normalized specific viscosity η_sp (c)/M _w c ^1/(3ν-1), where M _w is the weight-average molecular weight of the polymer chain. The values of the B̂-parameters are used in calculations of the excluded volume v, Kuhn length b, and crossover concentrations c*, c _th, and c** into a semidilute polymer solution, a solution of overlapping thermal blobs and a concentrated polymer solution, respectively. This information is summarized as a diagram of states of different polysaccharide solution regimes by implementing a v/bl ² and c/c** representation. The scaling approach is extended to the entangled solution regime, allowing us to obtain the chain packing number, P̃ _e. This completes the set of parameters {B̂ _g, B̂ _th, P̃ _e} which uniquely describes the static and dynamic properties of a polysaccharide solution.