Diffusivities in\nBinary and Ternary Mixtures Containing\nPoly(ethylene) Glycol, Acetonitrile, and Water by Dynamic Light Scattering

In the present study, one of the\neigenvalues <i>D̂</i><sub>1</sub> of the Fick diffusion\nmatrix for ternary\nmixtures consisting\nof polydisperse poly(ethylene) glycol (PEG), acetonitrile, and water\nas well as the mutual diffusivity <i>D</i><sub>11</sub> in\ntwo binary subsystems were determined by dynamic light scattering.\nPEGs with molecular weights <i>M</i><sub><i>n</i></sub> ranging from (400 to 4000) g·mol<sup>–1</sup>,\na solvent mixture containing acetonitrile, and an experimental temperature\nof 323 K were selected because of their relevance to the application\nof reversed-phase liquid chromatography. In general, the accessed <i>D̂</i><sub>1</sub> decreases with increasing <i>M</i><sub><i>n</i></sub> and presents different concentration\ndependences. It was demonstrated that the accessed <i>D̂</i><sub>1</sub> is associated with the diffusion of PEGs in the solvent\nmixture and can be considered as the self-diffusivity of the sphere-like\nPEG molecules in the vicinity of infinite dilution regime. Using the\nself-diffusivity and the dynamic viscosity of the solvent mixture,\nthe hydrodynamic diameter of the PEG molecules was determined via\nthe Stokes–Einstein relation. While the values match that determined\nin water for smaller <i>M</i><sub><i>n</i></sub>, they tend to be smaller than that in water for larger <i>M</i><sub><i>n</i></sub>. This indicates a minor influence of\nthe solvent or temperature on the hydrodynamic diameter of the PEG\nmolecules. The determined diffusivities and hydrodynamic diameters\nof PEGs under process-relevant conditions are of relevance for the\ndevelopment of chromatographic separations.