SCALING PROPERTIES OF THE CAPILLARY-WAVE MODEL WITH INTERFACIAL BENDING RIGIDITY

The scaling properties of interfacial correlations in the extended cap illary-wave model (Romero-Rochin, V., Varea, C., and Robledo, A., 1992 , Physica A, 184, 367) are analysed and the procedure developed previo usly by Weeks and collaborators for studying interfacial correlations is confirmed to apply to the extended case and to reproduce most of th e earlier features. In addition to this it is found that: (i) the exte nded model is consistent with the expression for the bending rigidity kappa given by the fourth moment of the direct correlation function; ( ii) the scaling properties of the extended model differ from those of the ordinary model and we find that for d = 3 dimensions the correlati ons obey scaling on length scales less than the capillary length L(c). The consequences for kappa and the interfacial width W when scaling o ccurs at all length scales are examined, and it is suggested that thei r limiting values as L(c-->infinity) depend on the range of the molecu lar interactions. When these are sufficiently long ranged, kappa diver ges but W remains finite for d = 3. It is pointed out that multicompon ent systems with long-range interactions allow for a finite kappa. Fin ally, the case is studied of small or vanishing interfacial tension ga mma, in which case W scales with gravity a as W similar to g(-1/4).