Critical wetting : the domain of validity of mean field theory

E. Brézin , B.I. Halperin , S. Leibler

Below the consolute point of a binary mixture, the presence of a wall which adsorbs preferentially one of the two liquids may induce a new transition, the wetting transition. Above the wetting temperature Tw the phase adsorbed by the wall forms a macroscopic film. This transition has recently been analysed in the framework of mean field theory, and for a range of values of the parameters one observes a second order transition. In this work we construct a Ginzburg criterion for this transition in order to determine the upper critical dimension dc (above which mean field theory remains quantitatively correct). For that purpose we study the correlations near Tw (T ≲ Tw); long range correlations parallel to the wall appear with an associated length which diverges near Tw as 1/(Tw - T). The determination of the effective interactions of the modes responsible for long range correlations gives rise to delicate problems. The analysis reveals that dc = 3 (i.e. three-dimension bulk, with two-dimensional surface).

Mots clés: adsorption; critical points; mixtures; wetting

Domaines: Articles anciens

E. Brézin, B.I. Halperin, S. Leibler. Critical wetting : the domain of validity of mean field theory. Journal de Physique, 1983, 44 (7), pp.775-783. ⟨10.1051/jphys:01983004407077500⟩. ⟨jpa-00209658⟩