# Scaling of activation energy for macroscopic flow in poly(ethylene glycol) solutions: Entangled – Non-entangled crossover

## A. Wiśniewska, K. Sozański, T. Kalwarczyk, K. Królika, C. P. Stefan, A. Wieczorek, S. Jakieła, J. Enderlein and R. Hołyst

## Polymer, Volume 55, Issue 18, 2014, Pages 4651-4657

We postulate an empirical scaling equation, which accurately describes flow of polymer solutions, complimenting the paradigm of length-scale-dependent viscosity. We investigated poly(ethylene glycol) aqueous solutions and observed an exponential dependence of viscosity on the hydrodynamic radius of a single coil *R*_{h} divided by the correlation length *ξ*. Properties of the system changed abruptly with the onset of chain entanglement at concentration corresponding to *ξ* = *R*_{h}. We propose a single equation valid for all the investigated systems, analyze the physical meaning of parameters appearing therein and discuss the impact of chain entanglement. Viscous flow is treated as an activated process, following the Eyring rate theory. We show that the difference of activation energy for flow between pure solvent and polymer solution, Δ*E*_{a}, is a function of concentration, whose derivative has a discontinuity at the crossover concentration. For dilute PEG solutions Δ*E*_{a} takes values of up to several kJ/mol and is proportional to the intrinsic viscosity. We successfully apply the scaling approach to the diffusive motion of a protein (aldolase) in solutions of 25 kg/mol PEO (concentrations of 2–20%), investigated by fluorescence correlation spectroscopy (FCS). A significant difference in the influence of crowding on translational and rotational motion of the protein is revealed.