Redox Flow Batteries (RFBs) rely on fluid electrolytes as charge carriers. Water – the most abundant liquid on our planet – is naturally the main solvent for vanadium-based RFBs. As would be expected, it is also the most researched compound ever, especially at electron and atomistic scales. However, there has always been a mismatch between models in terms of carrying properties, features and functions across scales. Ideally, methodologies across the scales should be “on the same page” – i.e. predict the same properties to within a numerically small error in very different ways based on different theoretical approaches and different numerical methodologies.
In our case, we have been aiming to propagate atomistic water properties and features up the scales so that they can be trustworthily used at the mesoscopic level. Getting a mesoscopic scale model for water means we can accurately predict how it behaves at even larger scales, including looking at engineering-scale situations. Obviously, we must rely on the “relative truth” being represented accurately by the atomistic interactions when we build our models. So far, many coarse-grained (CG) water models (WM) have been predominantly apolar, where the functional particle or “bead” representing multiple water molecules bears no charge. Our team has already worked successfully to build an important knowledge-base in the area of generating trustworthy CG WMs to represent experimental properties correctly – we have done this for a 4DPD-5:1 (5 water molecules per bead) apolar WM (cite nDPD enhanced). However, water is a polarisable medium and, most importantly in the case of RFBs, it bears a high concentration of charged species from salts and acids present in the electrolytes. Therefore, we have set ourselves to enhance our model to represent the polar nature of water on a meso-scopic level as truthfully as possible. Although very few researchers have spent the effort to obtain or enhance their CGWMs, none so far, to our knowledge, has done this in a systematic manner so that models can correctly reproduce the electric relative permittivities of water-based media.
The figures above exemplify the change of dipole and quadrupole moments probability distributions for different CG levels (3:1 to 13:1) using both stoichiometric and topological representations (DOI: 10.1021/acs.jpclett.0c03300) as well as 50:50 mixtures of both.
As part of this project, we have systematically addressed the build-up of a dipole on top of our CGWM beads, relying on the atomistic TIP3P water model as a trustworthy “ground truth” representation. Like others (DOI: 10.1021/jp1019763), including our own previous research (DOI: 10.1063/5.0226871), we first considered adding two oppositely charged satellite sites to the centre of each bead by connecting them with springs to emulate water polarity. Fixing the spring constants and optionally the angle between the springs enables us to achieve the correct electric permittivity for the fluid. This enhancement is the most popular one in the literature (DOI: 10.1080/08927022.2017.1405159), but it does not provide for good model stability due to the large charge-charge attraction within the furnished bead, and often leads to overly low average dipole moments.
Such models additionally do not provide general quadrupole moments; hence water interactions and behaviours near interfaces such as bio-membranes and inorganic surfaces would be inaccurately represented. To promote stability and enhance our CGWM with such important aspects and features, we have adopted a three-charge CGWM, which somewhat mimics actual water molecules as well as several other atomistic water models do (DOI: 10.1039/d0cp04782a, 10.1021/jp1019763). Although we are not the first to have pioneered this approach for a CGWM, we are the first to have built it in a particularly systematic manner, finding out its limitations and the important parameters required to produce the relevant properties of CG water beads. In particular, we have determined dipole moments, quadrupole moments and polarisations for clusters of water molecules from our ground truth atomistic model: this information has informed the parameterisation of our CGWM, meaning we can obtain good and representative emulations of these atomistically-determined properties at larger scales.
The figures above compare the dipole moment probability distributions for different types of CG – stoichiometric (blue), topological (orange) and mixed (green) – based TIP3P “ground truth” with respect to the ones obtained from the two most promising CG models (blue). The left panel compares these to a model with a fully flexible pseudo bond (with a force constant, k) between the bead centre (charge -2) and its two satellite sites (charge +1 each) whereas the right to a model also enforcing an equilibrium bond-length (ro). It is important to note that charge penetration plays a role in matching the mesoscopic scale model’s dipole distribution to that coming from atomistic scale “ground truth”.
We have done this in a significantly different, non-ad hoc manner than those of other researchers, and have generated a polar CGWM, p4DPD-5:1, that preserves the correct thermodynamical and rheological properties of our previous apolar CGWM.
Benjamin Speake, Michael Seaton and Ilian Todorov,
UKRI-STFC