Yukawa fluid at a hard wall: field theory description

Abstract

We adopt a field-theoretical approach to study the structure and thermodynamics of a spatially confined fluid interacting with the Yukawa potential. We derive analytic expressions for the pressure, the Helmholtz free energy, the correlation function, the density profile, and the adsorption. Different simple analytic expressions of the density profile are compared with the numerical estimation of the mean field results. Beyond the mean field approximation, we show that fluctuations can contribute significantly to the properties of the system. Notably they lead to a desorption phenomenon regardless of the sign of the interaction. As a consequence, a non-monotonous density profile at the wall and adsorption curves as a function of the density are found for some systems. This behaviour rationalizes the ionic depletion phenomenon responsible for the anomalous behaviour of the electric capacitance as a function of temperature. Particular attention is given to the contact theorem condition.

Keywords:

• inhomogeneous systems
• Yukawa potential
• classical field theory
• contact theorem

Acknowledgments

M. Holovko and D. di Caprio are grateful for the support of the National Academy of Sciences of Ukraine (NASU) and the Centre National de la Recherche Scientifique (CNRS) (project no. 23999), J. Stafiej and D. di Caprio are grateful for the support of the Polish Academy of Science and of the CNRS (project no. 22557).