A collaboration between Dr Fabien Paillusson from the School of Mathematics and Physics Lincoln UK and Dr Helene Berthoumieux from the Laboratory for the Theoretical Physics of Condensed Matter at Sorbonne University, Paris France just got a research paper accepted in the Journal of Chemical Physics.
The theme of the paper revolves around the modelling of liquid water. Now, to give a bit of perspective, water is one of the least understood pure substances out there in spite of being ubiquitous and obviously crucial for most living organisms. Among many of its unusual properties one may mention:
- That there are 17 different kinds of ice that have been listed so far,
- If the diversity of the solid states was not enough, there is also increasing evidence that liquid water could have 2 different states as well,
- Even when all minerals are removed, the amphoteric character of water gives rise to the generation of relatively free ions in the solution (albeit in low concentrations); thus making liquid water an inherent electrolyte,
- The physico-chemical properties of liquid water appear to be affected by imposed external magnetic and electric fields (more research needs to be done on this),
- Water has also been reported to display a negative dielectric constant.
It is commonly thought that these specific traits of water are in most part due to water modules being prone to form hydrogen bonds as illustrated in the figure below
When these bonds are formed, they force the water molecules to be oriented in a very specific way (on average) with respect to their neighbours. This leads to water responding more “collectively” to external local stimulations than more common liquids.
In general, the spatial response of a system to a spatially distributed excitation is often split in two categories: local responses and nonlocal responses.
Local responses see the system “respond” an excitation (by changing one of its state variables say) with an amplitude at a given point in space that is only depending on the excitation amplitude at that very point. This is illustrated in the Figure 2 below.
Nonlocal responses on the other hand see the response amplitude of a system depend on the amplitude of the excitation at all points in the system which captures this collaborative response from a medium to a localised external solicitation. This is illustrated in the Figure 3 below.
In addition to having a nonlocal character, water also reacts nonlinearly to an external electric field i.e. the amplitude of the response is not just simply proportional to the amplitude of the excitation. Sometimes the response can be enhanced by nonlinearity and some other times the response is almost null because of (nonlinear) saturation effects near highly charged solutes for example.
While simulations allow in principle to capture most features of water (provided the appropriate model is being used), they tend to be relatively time and resource consuming. An alternative route consists in developing theoretical, pen-and-paper theories of water by trading of quantitative accuracy for versatility and physical understanding. The nonlocal and nonlinear features of the electric response of water to an electric field are usually captured separately in theoretical models. In the work of Berthoumieux and Paillusson, they proposed a field-theoretic approach that combines the two ingredients in a single theory. This gives rise to promising more realistic outputs of the model as illustrated in Figure 4 below.
For intersted readers, an early version of the accepted manuscript is available on the arXiv.