lower-order derivatives than the bulk equations. The functional obtained in this way has the form where boldface capital letters denote matrices. The transpose of the columnar vectors v and v ′ are v $^{T}$( z ) = ( ϑ ( z ) , η ( z )) and v ′ $^{T}$( z ) = ( dϑ ( z ) /dz, dη ( z ) /dz ) respectively. The elements of the matrix C 0 = ( C 0 $_{ij}$)$_{i,j}$$_{=1}$$_{,}$$_{2}$ , where indices 1 and 2 correspond to s and ρ , respectively, are given by The second matrix in (26) is J := ( J$_{ij}$ )$_{i,j}$$_{=1}$$_{,}$$_{2}$, again with indices 1 and 2 corresponding to s and ρ , respectively. The electrostatic energy-density e$_{e}$ in the case of a fluctuating dielectric constant has the form (9). The linear surface fields h = ( ¯ h$_{s}$, ¯ h$_{ρ}$ ) are and P is obtained from the expansion of W about s = ¯ s and ρ$_{c}$ = ¯ ρ$_{c}$ with the linear and quadratic parts in the fields ϑ and η subtracted. The length unit is the lattice constant v 1 / 3 0 , comparable with the molecular diameter. The last term describes the electrostatic interaction with the uniformly charged surface possessing the surface charge density eσ . In order to find the bulk correlation functions in the Gaussian approximation as well as the spinodal surface and the critical line of this model in MF, let us consider the Gaussian part of the LG functional in the bulk. In the Fourier representation we have, 11 C. Spinodal surface and bulk correlation functions L$_{G}$ = ∫ d k (2 π ) 3 1 2 ˜ v $^{∗}$( k ) ˜ C ( k )˜ v ( k ) (31) C 0 ss = k$_{B}$T 1 − ¯ ρ$_{c}$ (1 − ¯ ρ$_{c}$ ) 2 − ¯ s 2 − 6 J$_{ss}$ (27) C 0 ρρ = k$_{B}$T ( 1 − ¯ ρ$_{c}$ (1 − ¯ ρ$_{c}$ ) 2 − ¯ s 2 + 1 ¯ ρ$_{c}$ ) − 6 J$_{ρρ}$ (28) C 0 sρ = C 0 ρs = k$_{B}$T ¯ s (1 − ¯ ρ$_{c}$ ) 2 − ¯ s 2 − 6 J$_{ρs}$. (29) L = ∫ ∞ 0 dz { 1 2 v $^{T}$( z ) C $^{0}$v ( z ) + 1 2 v ′ $^{T}$( z ) Jv $^{′}$( z ) + e$_{e}$ + k$_{B}$T P } (26) + v $^{T}$(0) Jv (0) 2 − hv (0) + eσψ (0) , ¯ h$_{s}$ = h$_{s}$ − J$_{ss}$ ¯ s − J$_{sρ}$ ¯ ρ$_{c}$, ¯ h$_{ρ}$ = h$_{ρ}$ − J$_{ρρ}$ ¯ ρ$_{c}$ − J$_{ρs}$ ¯ s, (30)