Effect of a confining surface on a mixture with spontaneous inhomogeneities

Abstract

A binary self-assembling mixture near a planar wall is studied by theory and Monte Carlo simulations. The grand potential functional of the local concentration and the local volume fraction of all particles is developed in the framework of the density functional and field-theoretic methods. We obtain ordinary differential Euler–Lagrange equations for the concentration and the volume fraction, and solve them analytically in the perturbation expansion. The obtained exponentially damped oscillations of the concentration, with the characteristic lengths the same as in the concentration-concentration correlation function, agree very well with simulations. For the excess volume fraction we obtain a monotonic decay superimposed on the exponentially damped oscillations with a fair agreement with simulations. The period of the density oscillations is equal to half the period of the concentration oscillations in both the theory and simulations. Simulations show local ordering in the layers parallel to the wall that are rich in one of the two components. Bubbles, stripes and clusters appear in the subsequent layers for increasing distance from the wall. Between these almost one-component layers the density takes minima, and a bulk-like structure with clusters of different particles being nearest neighbors appears.