Patterns of hydrogen bonding in water and ice

The six-vertex lattice model is augmented with ionic vertices and bonding effects. These represent sources and sinks for hydrogen atoms, and the extra vertices account for the pH of water. This 14-vertex lattice model with Bjerrum bond defects represents a not unrealistic model of ice, and possibly also of structured water next to a surface. Such surfaces polarise the adjacent molecules, which greatly restricts the possible patterns of hydrogen bonds. The polarisation is screened by the defective vertices and bonds, which leads to a strong exponentially decaying repulsion between two similar surfaces. The model is solved in mean field approximation, and the relevance to the experimentally measured hydration forces is discussed.