Two-fluid model for the interpretation of quartz crystal microbalance response: Tuning properties of polymer brushes with solvent mixtures

A new approach, involving a two-fluid model, has been developed to interpret the quartz crystal microbalance response of adsorbed viscoelastic polymers. The model utilizes the Navier-Stokes-Brinkmann equation to describe the motion of a porous, semirigid, viscoelastic polymer-brush film with a viscous solvent flowing through it. The two phases, solid (polymer brush) and liquid (solvent mixture), hydrodynamically interact with each other, as represented by means of a Darcy term with a characteristic correlation factor. The two-fluid model is used to estimate structural changes in polymer brushes consisting of the copolymers poly(l-lysine)-graft-poly(ethylene glycol) (PLL-g-PEG) or poly(l-lysine)-graft-dextran (PLL-g-dextran) adsorbed on an amorphous SiO₂-coated quartz surface in aqueous solutions of glycerol, ethylene glycol (EG), and dimethyl sulfoxide (DMSO). Layer thickness, polymer volume fraction, and shear modulus of the polymer films with varying co-solvent concentration are determined with this approach. It was found that preferential hydrogen-bonding interactions of solvent mixtures with the polymers leads to variation in the structural properties of the polymer brushes upon changing the co-solvent composition. Furthermore, the conformation of polymer brushes in solvent mixtures is influenced by the solvent-solvent interactions, which can be explained in terms of the free energy of solvent mixing.