Interpenetration and Friction of Brush-Coated Surfaces under External Load: Analytical Theory and SCF Calculations

We studied the compression and interpenetration propertiesof twoopposing monodisperse polymer brushes under external load by analyticaltheory and by a numerical self-consistent field (SCF) approach. Analyticalexpressions are proposed for the brush density profiles in the interpenetrationzone and verified by numerical SCF calculations. We quantify the interpenetrationof two opposing brushes by the characteristic penetration length andby two integral parameters: the overlap integral, Gamma, representingthe number of interbush contacts, and the number of brush monomerunits in the foreign half-space, sigma. The interpenetration parametersare studied in two conjugate ensembles as functions of the brush separationand of the external pressure. We propose a theoretical descriptionof the solvent-mediated friction force in the low shearing rate regimeon the basis of the Brinkman equation for two compressed brushes slidingagainst each other. We demonstrate that the total friction force whichalso includes direct brush-brush friction is expressed in termsof Gamma and sigma. The SCF data for the interpenetration parameters Gamma and sigma and hence for the total sliding friction forcein the pressure ensemble collapse onto universal master curves whenrescaled by the factor (N/sigma)(1/3) assuggested by the theory, where N is the chain lengthand sigma is the surface grafting density. Finally, we define thekinetic friction coefficient as a function of the external pressureand analyze its universal rescaled behavior in the two limits of nondrainingand free-draining brushes.