Effect of Ligand Binding on Polymer Diffusiophoresis

Diffusiophoresis is the migration of a macromolecule in response to a concentration gradient of a cosolute in liquids. Diffusiophoresis of polyethylene glycol (PEG) in water occurs from high to low concentration of trimethylamine-N-oxide (TMAO). This is consistent with the preferential hydration of PEG observed in the presence of TMAO. In other words, PEG migrates in the direction in which it lowers its chemical potential. On the other hand, although PEG is found to preferentially bind urea in water, PEG diffusiophoresis still occurs from high to low urea concentration. Thus, PEG migrates in the direction that increases its chemical potential in the urea case. Here, a ligand-binding model for polymer diffusiophoresis in the presence of a cosolute that preferentially binds to polymer is developed. It includes both actual polymer–ligand binding and the effect of the polymer on cosolute thermodynamic activity. This model shows that polymer–cosolute binding has a marginal effect on polymer diffusiophoresis and indicates that weak repulsive interactions, such as hard-core exclusion forces, are the main factor responsible for the observed PEG diffusiophoresis from high to low urea concentration. This work contributes to a better understanding of diffusiophoresis of macromolecules in response to gradients of nonelectrolytes.