Casimir force in dense confined electrolytes

ABSTRACT

Understanding the force between charged surfaces immersed in an electrolyte solution is a classic problem in soft matter and liquid-state theory. Recent experiments showed that the force decays exponentially but the characteristic decay length in a concentrated electrolyte is significantly larger than what liquid-state theories predict based on analysing correlation functions in the bulk electrolyte. Inspired by the classical Casimir effect, we consider an additional mechanism for force generation, namely the confinement of density fluctuations in the electrolyte by the walls. We show analytically within the random phase approximation, which assumes the ions to be point charges, that this fluctuation-induced force is attractive and also decays exponentially, albeit with a decay length that is half of the bulk correlation length. These predictions change dramatically when excluded volume effects are accounted for within the mean spherical approximation. At high ion concentrations the Casimir force is found to be exponentially damped oscillatory as a function of the distance between the confining surfaces. Our analysis does not resolve the riddle of the anomalously long screening length observed in experiments, but suggests that the Casimir force due to mode restriction in density fluctuations could be an hitherto under-appreciated source of surface–surface interaction.

GRAPHICAL ABSTRACT

KEYWORDS:

• Casimir force
• density fluctuations
• concentrated electrolytes
• correlation length

Acknowledgements

This work is dedicated to Daan Frenkel on the occasion of his 70th birthday, as a token of appreciation of the authors' wonderful interactions with him – over a range of time-scales. In particular, J.-P.H. wishes to express his sincere gratitude for an inspirational friendship and constant support over more than 40 years.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

B. R. acknowledges financial support from the French Agence Nationale de la Recherche (ANR) [grant number ANR-15-CE09-0013-01]. A. A. L. acknowledges support from the Winton Program for the Physics of Sustainability at the University of Cambridge.