The search for the hydrophobic force law

Abstract

After nearly 30 years of research on the hydrophobic interaction, the search for the hydrophobic force law is still continuing. Indeed, there are more questions than answers, and the experimental data are often quite different for nominally similar conditions, as well as, apparently, for nano-, micro-, and macroscopic surfaces. This has led to the conclusion that the experimentally observed force–distance relationships are either a combination of different ‘fundamental’ interactions, or that the hydrophobic force-law, if there is one, is complex – depending on numerous parameters. The only unexpectedly strong attractive force measured in all experiments so far has a range of D ≈ 100–200 Å, increasing roughly exponentially down to ~ 10–20 Å and then more steeply down to adhesive contact at D = 0 or, for power-law potentials, effectively at D ≈ 2 Å. The measured forces in this regime (100–200 Å) and especially the adhesive forces are much stronger, and have a different distance-dependence from the continuum VDW force (Lifshitz theory) for non-conducting dielectric media. We suggest a three-regime force-law for the forces observed between hydrophobic surfaces: In the first, from 100–200 Å to thousands of ångstroms, the dominating force is created by complementary electrostatic domains or patches on the apposing surfaces and/or bridging vapour cavities; a ‘pure’ but still not well-understood ‘long-range hydrophobic force’ dominates the second regime from ~ 150 to ~ 15 Å, possibly due to an enhanced Hamaker constant associated with the ‘proton-hopping’ polarizability of water; while below ~ 10–15 Å to contact there is another ‘pure short-range hydrophobic force’ related to water structuring effects associated with surface-induced changes in the orientation and/or density of water molecules and H-bonds at the water–hydrophobic interface. We present recent SFA and other experimental results, as well as a simplified model for water based on a spherically-symmetric potential that is able to capture some basic features of hydrophobic association. Such a model may be useful for theoretical studies of the HI over the broad range of scales observed in SFA experiments.

Anti-Icing Superhydrophobic Surfaces: Controlling Entropic Molecular Interactions to Design Novel Icephobic Concrete

“…These forces, however, are similar to the capillary force and they may have complex molecular origin. Israelachvili et al reports the range of hydrophobic forces as 10-20 nm with exponential decay [34]. The hydrophobic force also leads to the preferential attraction of hydrophobic particles towards each other (Figure 2c), as well as a hydrophobic surface in water [31].…”

Hydrophobic interactions with coarse-grained model for water

“…[18,23,24] Of particular relevance to the present study is the recent work of Shell and co-workers, [23,24] who have shown that several thermodynamic and dynamic anomalies of pure water, as well as various features of hydrophobic interactions can be reasonably well reproduced with a coarse-grained water model based on an isotropic pairwise additive "Lennard-Jones plus Gaussian" (LJG) interaction potential. While the work of Shell and co-workers employed simulation-based techniques, their microscopic model based on an isotropic pair potential is ideally suited for approaches such as integral equation theory and mode-coupling theory (MCT), which would reduce computational expenses even further.…”

“…As a coarse-grained model for water, we consider a system comprised of spherical particles interacting via an isotropic LJG pair potential of the following form: [23,24] φ s (r) = 4ǫ σ r…”

Electrostatic attraction between overall neutral surfaces

“…Several experimental studies have examined the interaction between two such overall neutral surfaces, made of positive and negative domains ("patches") that are much larger than the molecular size [7][8][9][10][11][12][13][14]. For example, negative mica surfaces can be coated with neutralizing cationic surfactants that later dissociate and form positively charged bilayer patches.…”

“…This is a mean field (MF) theory, within which ions are treated as point-like particles obeying a Boltzmann distribution, the aqueous solution is taken as a continuous and homogeneous dielectric medium, and in most treated cases , the bounding surfaces are assumed to be homogeneously charged [1][2][3][4][5][6]. However, as many charged surfaces in soft and biological matter are heterogeneous over mesoscopic length scales, several experimental [7][8][9][10][11][12][13][14][15][16] and theoretical studies have investigated the effects of surfacecharge heterogeneity on the inter-surface electrostatic interactions.…”