Surface forces in the tapping mode: Solvent permeability and hydrodynamic thickness of adsorbed polymer brushes

A surface forces apparatus modified to apply small-amplitude oscillatory displacements in the normal direction was used to measure the drainage of tetradecane (a good solvent) past polybutadiene (PB) brushes end-attached to two opposed mica surfaces. The PB was attached by selective adsorption of the poly(vinylpyridine) (PVP) block of a PB-PVP diblock copolymer. In-phase motion in the normal direction reflected elastic forces; these were found to be equivalent to the static force-distance profile measured directly. Out-of-phase motions reflected viscous flow of solvent since the PB chains did not contribute to dissipation over the oscillation frequencies studied. No frequency dependence was observed from 1 to 100 Hz. The hydrodynamic forces at a given plate separation (D) implied an effective plate separation less than D by a constant hydrodynamic thickness (R(H)) but otherwise the flow of a Newtonian liquid with viscosity same as in the bulk. The value of the hydrodynamic thickness was less than the value (L(0)) measured in the equilibrium force-distance profile, implying significant penetration of the velocity field into the brush layer. The value of R(H) diminished monotonically as the plate separation was reduced from 4L(0) to 0.2L(0). In other language, the ''slip plane'' changed monotonically with decreasing film thickness. The magnitude of hydrodynamic forces grew in proportion to D--1.2. This would be expected from scaling arguments for a Theta solvent but deviates decidedly from the prediced D--0.5 from scaling arguments for semidilute good solvent conditions. This could reflect inapplicability of the Brinkman equation or could reflect different scaling behavior of the static and hydrodynamic screening lengths.