Lubrication by Polyelectrolyte Brushes

Abstract

We develop a scaling model relating the friction forces between two polyelectrolyte brushes sliding over each other to the separation between grafted surfaces, number of monomers and charges per chain, grafting density of chains, and solvent quality. We demonstrate that the lateral force between brushes increases upon compression, but to a lesser extent than the normal force. The shear stress at larger separations is due to solvent slip layer friction. The thickness of this slip layer sharply decreases at distances on the order of undeformed brush thickness. The corresponding effective viscosity of the layer sharply increases from the solvent viscosity to a much higher value, but this increase is smaller than the jump of the normal force resulting in the drop of the friction coefficient. At stronger compression we predict the second sharp increase of the shear stress corresponding to interpenetration of the chains from the opposite brushes. In this regime the velocity-dependent friction coefficient between two partially interpenetrating polyelectrolyte brushes does not depend on the distance between substrates because both normal and shear forces are reciprocally proportional to the plate separation. Although lateral forces between polyelectrolyte brushes are larger than between bare surfaces, the enhancement of normal forces between opposing polyelectrolyte brushes with respect to normal forces between bare charged surfaces is much stronger resulting in lower friction coefficient. The model quantitatively demonstrates how polyelectrolyte brushes provide more effective lubrication than bare charged surfaces or neutral brushes.

Figure 1

Schematic dependence of PE brush thickness H on chain grafting density ρ in logarithmic coordinates.

Figure 2

Normal force per unit area in compressed osmotic PE brushes as a function of distance D between surfaces in logarithmic coordinates. c₀ = fNρ/H₀. The interval of D with a sharp increase in force is shadowed pink.

Figure 3

Reduced effective viscosity η_eff/η_s (equal to enhancement of shear stress σ_brush/σ_bare) as a function of distance D between surfaces in logarithmic coordinates. Charges on polyions and mobile ions are not shown, brush interpenetration regions are shadowed gray, the gap of laminar solvent flow with width ΔD + 2ξ_h is shadowed blue. Regions with sharp increase in reduced effective viscosity η_eff/η_s are shadowed pink.

Figure 4

Ratio of normal forces per unit area P_brush/P_bare for PE brush-decorated and bare surfaces with the same surface charge density as a function of distance D in logarithmic coordinates. Region of sharp increase in P_brush/P_bare is shadowed pink.

Figure 5

(a) Friction coefficient μ between planar surfaces decorated by PE brushes (solid lines) and neutral brushes with the same degree of chain polymerization N and grafting density ρ (dotted lines) as a function of distance D between surfaces in logarithmic coordinates. (b) Ratio of friction coefficients μ_brush/μ_bare for PE brush-decorated and bare surfaces with the same surface charge density in logarithmic coordinates. The region of enhanced lubrication by PE brushes is shadowed pink.