0 50 100 150 200 250 z -0.006 -0.004 -0.002 0 FIG. 1: (Color online) Charge density profiles in the semi-infinite system. The dashed line is the solution of the linearized equation (55), φ $^{(1)}$( z ), the dash-dotted line is the correction term (74), φ $^{(2)}$( z ), and the solid line is the sum of the two functions, φ $^{(1)}$( z ) + φ $^{(2)}$( z ), for κ = 0 . 01, σ = 0 . 5, ξ$_{b}$ = 100, and n$_{1}$ = 0 . 5. The charge density is in e/v$_{0}$ units, where e is the elementary charge, and z is in v 1 / 3 0 units, where v$_{0}$ is the volume per molecule in the close-packed system and we assume that all molecules are of similar size. For T → T$_{c}$ we have ξ − 1 b → 0, and using ξ − 1 b ≪ κ we obtain the approximation For z ≪ ξ$_{b}$ the above takes the simple form The correction term changes sign for z$_{0}$ ≈ 1 /κ . Equations for the first corrections to the nonelectrostatic part read where v (2) = ( ϑ $^{(2)}$, η$^{(2)}$), and the components of the vector D T = ( D$_{s}$, D$_{ρ}$ ) are 20 D$_{ρ}$ = D b $_{ϑϑ}$ϑ 2 + D b $_{ηϑ}$ϑη + D b $_{ηη}$η 2 + D b $_{φφ}$φ 2 J (82) D$_{s}$ = D a $_{ϑϑ}$ϑ 2 + D a $_{ϑη}$ϑη + D a $_{ηη}$η 2 + D a $_{φφ}$φ 2 J (81) ( v $^{(2)}$) ′′ = Mv (2) + D , (80) φ $^{(2)}$( z ) /φ $^{(1)}$( z ) ≃ n$_{1}$ 2 [ 1 − κz ] (79) φ $^{(2)}$( z ) /φ $^{(1)}$( z ) ≃ n$_{1}$ 2 [ 1 − κ (1 − e − z/ξ b ) ξ − 1 b ] κ ≫ ξ − 1 b (78)