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:

where is the averaged dipole moment of the layer area element , the indices 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 . The “potential energy” term , where 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 () 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 ). 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.

Related posts:

1. Water polarization and density profiles at a gas-liquid interface
2. Molecular polarization on a polar liquid interface: the structure of a water surface
3. Three great ways to calculate Born radii beyond the Coulomb Field Approximation
4. The nature of percolation phase transition in films of hydration water around immersed bodies.
5. Non-polar contribution to solvation energy from Born models: