Scaling Equation for Viscosity of Polymer Mixtures in Solutions with Application to Diffusion of Molecular Probes

Abstract

We measured macroscopic viscosity as well as nanoviscosity experienced by molecular probes diffusing in solutions containing two polymer species vastly differing in the molecular weight. On this basis we postulated a scaling equation for viscosity of complex liquids characterized by two distinct length-scales. As an experimental model, we used aqueous solutions of low-polydispersity poly(ethylene glycol) and poly(ethylene oxide) with molecular weight ranging from 6 to 1000 kg/mol, polymer concentrations from 0.25% up to 50%, and viscosity up to 500 mPa•s. The proposed model distinguishes between the contributions to the total viscosity stemming from the mesoscopic structure of the complex liquid and from the magnitude of interactions dictated by the chemical nature of its constituents. It allows to predict diffusion rates of nanoscaled probes in polymer solution mixtures and can be adapted to various multilength-scale complex systems.

A Unified Description of Intrinsically Disordered Protein Dynamics under Physiological Conditions Using NMR Spectroscopy

“…[53][54][55][56][57] As noted above, the friction coefficients ( ) would be expected to decrease for smaller probes, as described in recent studies that have parameterized analytical relationships between microscopic viscosity and probe dimensions in complex mixtures and across a range of length scales. 58,59 Assuming that the dynamic modes associated with timescales t2 and t3 originate from motions of groups of atoms, or segments having different dimensions (a single peptide plane or multiple planes respectively), these contributions may be expected to be characterized by distinct length scales and therefore distinct friction coefficients.…”

Molecular Morphology and Viscoelasticity of ASP Solution under the Action of a Different Medium Injection Tool

“…When the solution flows through the contraction section of the tool, its speed change is the most intense due to the reduced cross-sectional area forming high-strength shearing action, and the damage to the intermolecular network structure is the most serious [30], causing defects, breakage of molecular chains, rarer meshes, and reduced intermolecular force, reducing the molecular weight and viscosity [67]. Moreover, due to the effect of molecular chains and molecular structure grids, the higher the molecular weight of ASP solution, the longer the molecular chain, and the stronger the ability of molecular weights to entangle with each other, the higher the viscosity [68,69] and the stronger the shear resistance. The higher the concentration of ASP solution, the more the number of molecular chains in the solution.…”

“…The higher the concentration of ASP solution, the more the number of molecular chains in the solution. The molecular chains are intertwined due to insufficient extension, resulting in increased viscosity [69,70,71] and stronger shear resistance.…”

Diffusion and flow in complex liquids

“…42 Another effect which modifies nanoparticle diffusion is related to its interactions (e.g., electrostatics) with surrounding macromolecules. 47,48 This effect can be included in the governing equations used in this article but was neglected in our phenomenological assumptions. It thus remains an open question to include the interactions within the presented formalism.…”