Excluded Volume Demo
This is a super-easy app to make a super-important point. We have the same setup as in the Hydrotrope Demo app, but you can only change one parameter, the size of the hydrotrope, 2. All other relative attractions are fixed. Simply making the hydrotrope larger gives a big "excluded volume" reduction in its ability to solubilise the solute. Many formulators focus simply on attractions (e.g. some hydrogen bonds). If you are not aware of the excluded volume effects then you might be disappointed if your large, "smart", hydrotrope is less effective than a small, dumb, hydrotrope such as urea.
When it comes to proteins, large amounts of handwaving in the classical literature about the effects of small and large "co-solvents" such as urea or sucrose, can be best analysed via excluded volume effects. This is scientific elegant simplicity.
Excluded Volume Demo
There is a lot of confusion about "Excluded Volume" effects, where various solubility effects are put down to the large size of the added molecule ("co-solvent"). Although the excluded volume effects can be seen in the Hydrotrope Demo there is so much else going on that it is easy to miss the point. And the point is that the excluded volume mechanism is totally trivial even though the result is often significant and, in many biological systems such as protein folding, is the dominant effect.
All that excluded volume is doing is starting off the RDF more and more badly the larger the molecule. Because Gu2 depends on the integral of the RDF, the bigger the radius before the contribution to the integral becomes positive, the smaller the resulting value.
At its heart, this app is the same as the Hydrotrope Demo. But to focus on excluded volume, all variables other than the size of the hydrotrope or co-solvent have been fixed to reasonable values (though you can still perform trade-offs between visual detail and processing speed via the other two sliders). The system is strictly neutral in that all the molecular interactions (Attractions) are identical and set to 1.
When Size2 is small, Gu2 is large, allowing the co-solvent to help to stabilise the solute. When Size2 is large, Gu2 is small (negative!) meaning that the co-solvent is making things worse.
Another way to look at it is via the chemical potential calculated by Widom insertion. Widom is incredibly simple yet powerful. All it's doing is seeing what the chances are of inserting a solute and finding an empty spot. The bigger the co-solvent, the less likely the solute is to find an empty spot, so the chemical potential is less favourable.
To play with the demo requires some patience. Start with Size2=1. Let the simulation run till you think it's stabilized and note, especially, μu and Gu2. Now set Size2=2, run again and note how much less favourable those values are. Finally set Size2=0.5 and see how the solute is much happier. The reason you need patience is that it takes some time till things have stabilized, and even so there are quite large variations between runs. Hitting the Re-Average button is an alternative way to sample a set of variations as it can remove some tendencies of averages to get "stuck" owing to some chance configurations near the start of the averaging.