Scaling form of viscosity at all length-scales in poly(ethylene glycol) solutions studied by fluorescence correlation spectroscopy and capillary electrophoresis

Abstract

We measured the viscosity of poly(ethylene glycol) (PEG 6000, 12,000, 20,000) in water using capillary electrophoresis and fluorescence correlation spectroscopy with nanoscopic probes of different diameters (from 1.7 to 114 nm). For a probe of diameter smaller than the radius of gyration of PEG (e.g. rhodamine B or lyzozyme) the measured nanoviscosity was orders of magnitude smaller than the macroviscosity. For sizes equal to (or larger than) the polymer radius of gyration, macroscopic value of viscosity was measured. A mathematical relation for macro and nanoviscosity was found as a function of PEG radius of gyration, R(g), correlation length in semi-dilute solution, xi, and probe size, R. For R < R(g), the nanoviscosity (normalized by water viscosity) is given by exp(b(R/xi)a), and for R > R(g), both nano and macroviscosity follow the same curve, exp(b(R/xi)a), where a and b are two constants close to unity. This mathematical relation was shown to equally well describe rhodamine (of size 1.7 nm) in PEG 20,000 and the macroviscosity of PEG 8,000,000, whose radius of gyration exceeds 200 nm. Additionally, for the smallest probes (rhodamine B and lysozyme) we have verified, using capillary electrophoresis and fluorescence correlation spectroscopy, that the Stokes-Einstein (SE) relation holds, providing that we use a size-dependent viscosity in the formula. The SE relation is correct even in PEG solutions of very high viscosity (three orders of magnitude larger than that of water).

The effect of macromolecular crowding on mobility of biomolecules, association kinetics, and gene expression in living cells

“…We show that the cytoplasm has transport property described by the length scale-dependent viscosity. It means that the effective viscosity experienced by moving probes depends on their size [14,25].…”

“…We have proposed [14] the phenomenological description of the diffusion in the complex fluid, either synthetic or biological, as well as the viscosity of those complex systems. The model is primarily applied to polymers [14,25], to micellar systems [14] and recently to colloidal systems [26]. In this model the viscosity is defined via the fluctuation dissipation theorem:…”

In situ microfluidic dialysis for biological small-angle X-ray scattering

“…For PEG 20 000 at 10% w/w, = 0.01 Pa s, an order of magnitude larger than water (Holyst et al, 2009). Conveniently, the density of PEG 20 000 is quite close to unity.…”

Microstructure and Dynamics of Magnetic Iron Nanoparticles Aggregates in Protein Gels

“…In the studied case σ v of the isolated particles is in the range of 1 mm/s, thus the viscosity must be treated locally. The problem of scaling form of viscosity and the diffusion has been studied intensively [23][24][25][26][27]. The iron nanoparticles in the gelatine gel exhibit the bounded diffusion within the water voids, about 1 µm in diameter, kept by the three-dimensional network of the amine chains.…”