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

Abstract

We studied the compression and interpenetration properties of two opposing monodisperse polymer brushes under external load by analytical theory and by a numerical self-consistent field (SCF) approach. Analytical expressions are proposed for the brush density profiles in the interpenetration zone and verified by numerical SCF calculations. We quantify the interpenetration of two opposing brushes by the characteristic penetration length and by two integral parameters: the overlap integral, Γ, representing the number of interbush contacts, and the number of brush monomer units in the foreign half-space, Σ. The interpenetration parameters are studied in two conjugate ensembles as functions of the brush separation and of the external pressure. We propose a theoretical description of the solvent-mediated friction force in the low shearing rate regime on the basis of the Brinkman equation for two compressed brushes sliding against each other. We demonstrate that the total friction force which also includes direct brush–brush friction is expressed in terms of Γ and Σ. The SCF data for the interpenetration parameters Γ and Σ and hence for the total sliding friction force in the pressure ensemble collapse onto universal master curves when rescaled by the factor (N/σ)1/3 as suggested by the theory, where N is the chain length and σ is the surface grafting density. Finally, we define the kinetic friction coefficient as a function of the external pressure and analyze its universal rescaled behavior in the two limits of nondraining and free-draining brushes.