Water molecules alignments on a hydrophobic surface – I

By
Peter Fedichev, Quantum CTO
– April 11, 2010Posted in: polar liquid, water

Water molecules interact strongly “using” both the long range dipole-dipole and short-range “hydrogen bonds” to form sophisticated networks. As described in our previous post, water molecules align along a hydrophobic surface and form an strongly-interacting 2d system of molecular dipoles. Normally there is no true long range order at zero temperature in 2d, though there may still be a BKT-type order-disorder transition associated with dissociation of topological defects associated with the order parameter.

To clarify the nature of the water molecules configurations on a hydrophobic surface we chose the following simple field-theoretic model Free Energy functional of a water layer:


F=\int d^2X(C\sum_{\alpha,\beta}\frac{ds_\alpha ds_\alpha}{dX_\alpha dX_\beta}+V(s)+K\rho(X)\int d^2X^\prime \frac{\rho(X^\prime)}{|X-X^\prime|}),

where s(X) is the averaged dipole moment of the layer area element X, the indices \alpha, \beta = x, y enumerate the Cartesian coordinates. The first of terms describes the energy of the hydrogen bonding and the second one describes Coulomb interaction of the polarization charge densities \rho(X)=-{\rm div}s(X). The “potential energy” term V(s) = As^2+ Bs^4, where A<0 ensures spontaneous polarization of the water layer. The specific values of the constants A, B, C and K depend on the density of the liquid and the properties of the surface.

The phase transition in the model without Coulomb interaction (K=0) is described by the standard BKT theory. The power-law correlations of the polarization (quasi-long range order) change into exponentially decaying correlations at a finite temperature due to dissociation of the virtual vortex-antivortex pairs. Below we post an example (numerical) solution representing a pair of the hydrogen bonds network defects in a water-like liquid without long range interactions:




The red arrows represent the water molecules orientations (vector S). The vortices show logarithmic attractions and are topologically stable. In a few following posts we will show how the long range interactions change the picture and define a few novel features on top of the standard BKT description.

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About Peter Fedichev, Quantum CTO

Peter Fedichev, Ph.D., Chief Scientific Officer, co-founder