Effects of excluded volume on the conformation of adsorbed polymers

We consider adsorption of a polymer from solution onto a planar interface. The self-consistent mean field method due to Edwards is used to handle excluded volume effects, and segment adsorption is treated by introducing a short range attractive potential between each segment and the adsorbing surface. In the limit where the adsorbed segment density is uniform, so that the self-consistent method is valid, an analytic solution is obtained. To first order in the excluded volume parameter, v, we find that the critical segment free energy of adsorption necessary for an adsorbed layer is ϕc=ϕ°c(1 +6nvz0//l2+…) where ϕ°c is the critical segment free energy of adsorption at the θ point, n is the total number of adsorbed segments per unit area, l is the polymer bond length and z0(∼l) is the range of the adsorption potential. The mean adsorbed layer thickness t(z0) is t=t0(1 +6nvt0)//l2 where t0 is the mean adsorbed thickness at the θ point. The number of polymers adsorbed per unit area, C=C(1–kN2vC°) where N is the number of segments per polymer chain (n=NC) and C° is the value at the θ point. Both C° and k depend on the free energy of adsorption [cf. eqn (6) and (48)].