Diffusivities in Binary and Ternary Mixtures Containing Poly(ethylene) Glycol, Acetonitrile, and Water by Dynamic Light Scattering

In the present study, one of the
eigenvalues D̂1 of the Fick diffusion
matrix for ternary
mixtures consisting
of polydisperse poly(ethylene) glycol (PEG), acetonitrile, and water
as well as the mutual diffusivity D11 in
two binary subsystems were determined by dynamic light scattering.
PEGs with molecular weights Mn ranging from (400 to 4000) g·mol–1,
a solvent mixture containing acetonitrile, and an experimental temperature
of 323 K were selected because of their relevance to the application
of reversed-phase liquid chromatography. In general, the accessed D̂1 decreases with increasing Mn and presents different concentration
dependences. It was demonstrated that the accessed D̂1 is associated with the diffusion of PEGs in the solvent
mixture and can be considered as the self-diffusivity of the sphere-like
PEG molecules in the vicinity of infinite dilution regime. Using the
self-diffusivity and the dynamic viscosity of the solvent mixture,
the hydrodynamic diameter of the PEG molecules was determined via
the Stokes–Einstein relation. While the values match that determined
in water for smaller Mn, they tend to be smaller than that in water for larger Mn. This indicates a minor influence of
the solvent or temperature on the hydrodynamic diameter of the PEG
molecules. The determined diffusivities and hydrodynamic diameters
of PEGs under process-relevant conditions are of relevance for the
development of chromatographic separations.