FIGURE 9.

Free energy per unit length as a function of distance for (A) cylindrical and (B) planar surfaces with n = 50, pK_a = 3.5, c = 0.1 M, and a grafting density of σ_a = 0.032 nm⁻². The radius of the cylinder is R = 0.5 nm; hence the number of polymers per unit length or line density is σ_l = 0.1 nm⁻¹. For the cylinder, the left-hand scale is the free energy per unit length and the right-hand axis gives the free energy per unit area which is needed for the comparison with that of the planar surface.