Calculation of the wetting parameter from a cluster model in the framework of nanothermodynamics

The critical wetting parameter omega(c) determines the strength of interfacial fluctuations in critical wetting transitions. In this Brief Report, we calculate omega(c) from considerations on critical liquid clusters inside a vapor phase. The starting point is a cluster model developed by Hill and Chamberlin in the framework of nanothermodynamics [Proc. Natl. Acad. Sci. USA 95, 12779 (1998)]. Our calculations yield results for omega(c) between 0.52 and 1.00, depending on the degrees of freedom considered. The findings are in agreement with previous experimental results and give an idea of the universal dynamical behavior of the clusters when approaching criticality. We suggest that this behavior is a combination of translation and vortex rotational motion (omega(c)=0.84).