Paper accepted in JCP

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:

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

Fig1: Schematic representation of hydrogen bonds between water modules. Credit to

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.

Screen Shot 2019-02-22 at 06.16.20
Fig2: Response amplitude of a system to a very localised excitation. A local response signifies that the medium only responds at the point of stimulation but not elsewhere.

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.

Screen Shot 2019-02-22 at 06.23.31
Fig3: Response amplitude of a system to a very localised excitation. A nonlocal response signifies that the system responds in principle at all points in the system.

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.

Screen Shot 2019-02-22 at 01.04.42
Fig4: Figure extracted from the accepted manuscript. Electric polarisation (roughly the water molecule mean orientation) in water in the vicinity of a positively charged point-like ion at the origin. The red dots are extracted from “All-atom” molecular dynamics (MD) simulations, the dashed line shows the expected response from a local theory and the blue line shows the predicted curve from the new theory. Although quantitative agreement is not perfect, the important features of the MD data points are well captured beyond 3 Angstroms.

For intersted readers, an early version of the accepted manuscript is available on the arXiv.

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