Hydrotrope Demo

This app assumes familiarity with the RDF Demo. It adds a 3rd molecule, a solute, and explores what happens to the RDF with different values of the different "attractive" forces. In particular, it is looking to see how to increase the solubility of the solute, u, via addition of a "hydrotrope" molecule, 2, to a solvent, 1, which doesn't especially like the solute so gives a low unaided solubility.

Like the RDF Demo, this app is based on the excellent code from Dr Daniel V. Schroeder's Interactive Molecular Dynamics app and I warmly thank Dr Schroeder for his generosity in allowing me to use the code from that app plus extracts from some of his other MD code.

Assuming that you know from the RDF Demo basically what is going on, you can focus on the way that a hydrotrope (molecule 2) can increase the solubility of a solute, u. But first we need to do a few runs with the default settings to see some apparently odd behaviour. The run starts and the RDFs look a mess. This is because the statistics on the low level of solute are too noisy. Suddenly there is a change and then the plot starts to settle down. The longer you run it, the smoother it gets. The code simply takes the long-term average of the RDF to smooth out the noise, but it has to reject the start-up highly ordered values which are clearly not relevant. Clicking the Re-Average button re-sets the long term average if you think it might be "stuck" in some statistical anomaly.

Although the app cannot calculate the solubility, it can calculate the chemical potential of the solute via the Widom insertion method described in the RDF Demo. The more negative this is for the solute, μ_u, the happier the solute. Because the solute is generally difficult to dissolve, it is present only in small amounts, limited in the app to x_u=0.1 (which is a bit on the high side). And because the hydrotrope, 2, is not intended to be a major feature, it is limited to x₂=0.4. The simulation allows realistic u-u dynamics, but because u-u pairs are relatively rare, the RDF g_uu is not calculated.

When everything attracts each other equally, there is no reason that the solute should be especially happy, so the hydrotrope 2 has no significant effect. So you can take whatever is μ_u with all attractions=1 as the baseline value.

Conventional wisdom says that a hydrotrope has to self-associate to solubilise the solute. Well, try it. Set Attr₂₂ to 2. This does nothing for the solute, for the obvious reason that any 2's that are attracted to other 2's are less likely to be attracted to the solute.

So now try setting Attr_u2 to 2. You see, once the calculation settles down, a large g_u2 peak in the RDF but you also see that μ_u decreases, indicating that the solute is "happier" and therefore will have a higher solubility.

When you analyse real hydrotrope systems you find that the G_u2 value (i.e. the KB integral) is greatly enhanced with good hydrotropes and G₂₂ is not much changed (or if it has increased then that reduces the overall effect). So the G_ij values are calculated in the app from the RDF, but requiring the g_ij long-term average to be 1 to give meaningful values. Hence the trick discussed above.

When people hear that the hydrotrope increases solubility via increased association with the solute, they tend to hear "increases solubility by forming a complex with the solute", especially if they are told that the excess number (the number of hydroropes in the vicinity of the solute compared to a random state) is, say, 2. But when you look at the simulation rather than the RDF you see that 2's and u's are indeed a bit more likely to be together than when Attr_u2 = 1, but there is no trace of "complex" formation. This is statistical thermodynamics and the hydrotope effect is a statistical effect.