Swelling and large deformation of polymer brushes

A polymer brush consists of polymer chains with one end anchored on a solid substrate and the other end being free. This paper formulates a thermodynamic model to quantitatively characterize the swelling and deformation of polymer brushes. The model integrates the freely jointed chain model to describe the elasticity of polymers and the Flory-Huggins model to describe the swelling of polymers. The swelling and deformation are unidirectional, confined in a cell defined by the graft area and the height of a polymer. Depending on the three conformations: a dilute brush, a contact brush, and a high-density brush, the swelling and deformation behaviors are strongly influenced. The model links the physical parameters of polymers and solvents, e.g., graft area, polymer length, and solvent quality, to the polymer brush conformations, swelling, and deformation. The predicted brush heights at dry and swollen states agree with both the established scaling laws and the experimental data collected from the literature. The model is further applied to characterize the force-stroke relationship in polymer brush actuation when the swelling is constrained. The blocking force, maximum free stroke, and the conditions under which they are obtained are determined. This model may be useful to guide the polymer brush design to achieve desired functions in a broad range of practical applications.