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# The Local Compressibility of Liquids near Non-Adsorbing Substrates: A Useful Measure of Solvophobicity and Hydrophobicity?

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### Abstract

We investigate the suitability of the local compressibility chi(z) as a measure of the solvophobicity or hydrophobicity of a substrate. Defining the local compressibility as the derivative of the local one-body density w.r.t. the chemical potential at fixed temperature, we use density functional theory (DFT) to calculate chi(z) for a model fluid, close to bulk liquid-gas coexistence, at various planar substrates. These range from a neutral' substrate with a contact angle of approximately 90 degrees, which favours neither the liquid nor the gas phase, to a very solvophobic, purely repulsive substrate which exhibits complete drying (i.e. contact angle 180 degrees). We find that the maximum in the local compressibility, which occurs within one-two molecular diameters of the substrate, and the integrated quantity chi_ex (the surface excess compressibility, defined below) both increase rapidly as the contact angle increases and the substrate becomes more solvophobic. The local compressibility provides a more pronounced indicator of solvophobicity than the density depletion in the vicinity of the surface which increases only weakly with increasing contact angle. When the fluid is confined in a parallel slit with two identical solvophobic walls, or with competing solvophobic and solvophilic walls, chi(z) close to the solvophobic wall is altered little from that at the single substrate. We connect our results with simulation studies of water near to hydrophobic surfaces exploring the relationship between chi(z) and fluctuations in the local density and between chi_ex and the mean-square fluctuation in the number of adsorbed molecules.

### Most cited references3

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### Long-range correlations in adsorbed layers

(1982)
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### Wetting and drying at a curved substrate: Long-ranged forces

(2005)
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### The phase behaviour and structure of a fluid confined between competing (solvophobic and solvophilic) walls

(2012)
We consider a model fluid with long-ranged, dispersion interparticle potentials confined between competing parallel walls. One wall is solvophilic and would be completely wet at bulk liquid-gas coexistence while the other is solvophobic and would be completely dry at bulk coexistence. When the wall separation L is large and the system is below the bulk critical temperature and close to bulk liquid-gas coexistence, a delocalized interface' or soft mode' phase forms with a liquid-gas interface near to the centre of the slit; this interacts with the walls via the power-law tails of the interparticle potentials. We use a coarse-grained effective Hamiltonian approach to derive explicit scaling expressions for the Gibbs adsorption, the surface tension, the solvation force and the total susceptibility. Using a non-local density functional theory (DFT) we calculate density profiles for the asymmetrically confined fluid at different chemical potentials and, for sufficiently large L, confirm the scaling predictions for the four thermodynamic quantities. Since the upper critical dimension for complete wetting with power-law potentials is <3 we argue that our (mean-field) scaling predictions should remain valid in treatments that incorporate the effects of interfacial fluctuations. As the wall separation L is decreased at bulk liquid-gas coexistence we predict a capillary evaporation transition from the delocalized interface' phase to a dilute gas state with just a thin adsorbed film of liquid-like density next to the solvophilic wall. This transition is connected closely to the first order pre-wetting transition which occurs at the solvophilic wall in the semi-infinite system. We compare the phase diagram for the competing walls system with the phase diagrams for the fluid confined between identical solvophilic and identical solvophobic walls.
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### Author and article information

###### Journal
09 September 2014
1409.2729 10.1088/0953-8984/27/19/194111

23 pages, 9 figures, submitted to Journal of Physics: Condensed Matter as a Special Issue Article
cond-mat.soft

Condensed matter