Van der Waals theory of wetting with exponential interactions

The wetting transition in a model with exponential attractions is investigated within the framework of modern Van der Waals theory. The transition is first studied by a numerical procedure due to Tarazona and Evans. The basis for this procedure is scrutinized and found to be sound in principle. Semi-quantitative estimates for the convergence rate are given. However, in practice, this numerical procedure is not able to locate precisely the tricritical line in the parameter space separating regions with a first-order transition from those with a continuous wetting transition. For this purpose an analytic approach is developed, asymptotically exact as the wall-fluid and fluid-fluid forces become equal. The tricritical line is located and found to have qualitatively different properties from those found in previous work on this model. Wetting exponents, including a new exponent describing the energy barrier in a weakly first-order transition, are determined. In large parts of the parameter space they are found to be non-universal, changing with the model parameters in a continuous manner.