Hydrodynamic Scaling of Viscosity and Viscoelasticity of Polymer Solutions, Including Chain Architecture and Solvent Quality Effects

Abstract

This paper examines the dependence of polymer solution viscosity and higher viscoelastic parameters (e.g., y" Je°) on polymer concentration, molecular weight, chain architecture, and solvent quality. For solutions of linear chains, a transition from a solutionlike (stretched-exponential) to meltlike (power-law) dependence of on c or M occurs at [ ] » 1, and sometimes [ ] > 100. The hydrodynamic scaling description of polymer transport coefficients remains applicable to concentrations far above the overlap concentration c[?;j «= 1. Star polymers remain in the solutionlike regime at c and M far above the c and M at which linear chains show a transition to meltlike behavior. Other viscoelastic parameters, notably yr and Je°, have the same c and M dependences (stretched exponential at lower (c, M), power law at larger (c, M)) that does, with the same solutionlike-meltlike transition concentration for all three parameters. If for a single polymer in a series of solvents is fit to exp(acv), the several-fold variation in a at fixed M is almost entirely accounted for by the dependence of a on solvent quality, as expressed by the chain expansion parameter a,. Experiment is consistent with the a ~a,3 here shown to be predicted by the hydrodynamic scaling model (Phillies, G.

Viscosity of Hard Sphere Suspensions

“…Lin et al (14) found the same bifunctional behavior in high-molecular-weight poly-acrylic acid solutions. Similar transitions are found (15)(16)(17) in literature on solutions of some (not all) large-M polymers. In various systems, 4 ≤ φ + [η] ≤ 150, the intrinsic viscosity being [η].…”

“…The form was conjectured because (i) it is accurate (13)(14)(15)(16)(17) for another class of complex fluids whose dynamics are dominated by the forces (hydrodynamics, excluded volume) important here, and (ii) a known (18) ansatz leads to the form.…”

Newtonian Viscosity of Dilute, Semidilute, and Concentrated Polymer Solutions

“…Phillies notes that Eq. (1.106) is in agreement with experimental data for many polymer-solvent systems [Phillies, 1995;Phillies and Quinlan, 1995] and finds that the parameter α p varies with solvent quality as α p ∼ α 3 η = [η]/[η] θ , predicted by the hydrodynamic scaling model. Phillies further suggests [Phillies, 1995;Phillies and Quinlan, 1995] that the limit of applicability of Eq.…”

“…Efforts have been made to model the viscometric behavior of polymer solutions through this entanglement transition. First, Phillies [Phillies, 1995[Phillies, , 2002aPhillies and Quinlan, 1995] has derived a pseudovirial expansion of the form Eq. (1.97), describing the concentration dependence of polymer solution viscosity by evaluating interchain hydrodynamic interactions to third order via an extension of the Kirkwood-Riseman model.…”

Rheology of polymeric solutions I. Zero shear conditions

“…Table IV contains data of eight researchers who studied rheological properties of four polar 36 that contain five adjustable constants). According to this equation, viscosity is a continuous function of polymer concentration and molecular weight.…”