A phenomenological theory of long-range hydrophobic attraction forces based on a square-gradient variational approach

Abstract

Through recent surface force measurements it has been convincingly demonstrated that strong and amazingly long-range, attractive interaction forces act between hydrophobic surfaces immersed in water. Upon separating two such surfaces from molecular contact a vapour/gas cavity normally forms. This is not the case, however, when gradually diminishing the surface separation. The hydrophobic attraction forces have been recorded in this latter, metastable regime.A mean-field theory based on a square-gradient assumption is presented in this paper which is shown to account reasonably well for the surface forces found experimentally for two cylindrically shaped, hydrophobic surfaces interacting in water. The order parameter/ variational approach taken is closely related conceptually to earlier theories of repulsive hydration forces by Marcelja et al. and Cevc et al. The present theory implies that rather minor, hydrogen-bond-propagated molecular ordering effects, in the contact layers of water molecules next to the hydrophobic surfaces and in the core of the thin water film, give rise to the attraction observed. However, it does not fully address the intriguing question as to how it comes about that the hydrophobic attraction forces extend over such a wide range as 70–90 nm. It merely points in the direction that surface-induced structural changes in the core of the this water film (so far not captured by molecular dynamics simulations) which demand minimal free-energy expense may generate an interaction of a long-range nature.