More on the hydrophobic gap

Alongside Steve Granick’s paper below on the hydrophobic gap, I should have mentioned a study by Harald Reichert of the MPI in Stuttgart and colleagues, published in PNAS in December, which comes to much the same conclusions: X-ray reflectivity shows a definite depletion layer for water against an alkylsilane monolayer. They’re not able to pin down the width of the gap beyond limiting it to 1-6 Å, but the integrated density deficit (density x width) is 1.1 Å g/cm3 – and like Granick et al., they rule out the possibly influence of dissolved gases forming nanobubbles.

Even more gratifyingly, this is now accompanied by a study in Langmuir
by Marco Maccarini at McGill and colleagues, which uses neutron reflectivity to probe density depletions at solid-liquid interfaces for both water and non-polar liquids, the latter in contact with hydrophilic surfaces. This is precisely the sort of comparison that has been previously neglected: rather than focusing on water as something unusual, we need to establish to what extent it behaves just as other liquids do. And indeed Maccarini et al. find that a solvophobic gap is a quite general phenomenon: they say “The results show that the density deficit of a fluid in the boundary layer is not unique to aqueous solid-liquid interfaces but is more general and correlated with the affinity of the liquid to the solid surface.”

This all seems to add up to a rather consistent and satisfying story. But I remain troubled by one thing. Work in this area generally seems to posit the problem as one motivated by previous contradictions and discrepancies in the experimental data but about which we can say nothing that is not empirical. Being led by experiment seems like a good principle; but there is a well established literature on the theory of inhomogeneous fluids and their behaviour at surfaces, with which these discussions rarely connect. This theoretical work provides a general framework for thinking about the problem which does not immediately plunge into considerations of hydrophobicity, dangling hydrogen bonds and so on but starts, as it should, from consideration of wetting and contact angles, and the structure of simple liquids. (Maccarini et al. do touch on this.) The prediction for hard spheres against hard walls – that is, purely repulsive (contact) forces – is clear: the density profile is oscillatory, with a sharp peak at 1r (r = molecular radius) and decaying oscillations with a period of around 2r after that. In other words, there is molecular layering due solely to packing effects, even before one starts to take attractive forces into account. The question is how this picture is modified for more realistic fluids. A Lennard-Jones potential gives something similar – the short-ranged repulsion dominates the structure. Density functional theories show similar density profiles, with the layering getting flattened out as the reduced temperature T/Tc starts to approach 1. Getting appreciable depletion – partial drying – near the surface requires rather large contact angles, as I recall (this was 20 years ago).

Now, the directionality of the hydrogen bond in water may well change this picture in significant ways, but it seems logical to me to start with the expectations for a simple liquid and to go gradually from there to the complexities of water, so that we can see what is generic and what is not. So I’m keen to see these illuminating new results cast in the context of the theory of inhomogeneous fluids, so that we can start to develop a unified view and not treat water as a unique case, nor indeed enshrine the concept of a ‘depletion layer’ without relating it to our understanding of wetting and drying phenomena. The study by Maccarini et al. is a step in that direction.