08 October 2015 Me and thermodynamics.

I've met very few people who like thermodynamics. Most of us have been scarred for life when we've had to pass some thermodynamics exams at university and having scraped through have forgotten the nightmare.

It's not so much that it's hard. Most of it is basic arithmetic. It just comes across as pointless. It's full of ideal states and reference states and subtle distinctions and when it comes down to "can I use it in real life?" the answer generally seems to be "No!".

Sure, most of us can get by with activity coefficients. If the activity coeffient of one chemical in another is high we know that the chemicals don't like each other; if it's low then they positively are drawn to each other. And that's about it.

For the past 7 years I've been part of the HSPiP team writing, selling and supporting Hansen Solubility Parameters software. Although I know that HSP are based on thermodynamics and "regular solution theory" and although, at a pinch, I can understand the theory, there simply has been no advantage to understanding the thermodynamics in depths - it doesn't help solve any of the issues that I encounter with HSP. Similarly, when I got to know the wonderful COSMOtherm software, I could "get" the necessary thermodynamics without having to worry about it. The magic was in the brain of Prof Andreas Klamt who created it and all I had to do was to use the magic.

But along came hydrotropes. These (in the definition that is of interest here, see Practical Hydrotropes for the other definitions) are small molecules which, when added in modest amounts to a solution, increase the solubility of a hard-to-dissolve solute, typically in water but also in supercritical CO2. The solubility effect of hydrotropes is very different from the well-known and much-used approach of adding a co-solvent.

They first came up when I was challenged about "solubilizers" in pharma applications. I assumed that I could bluff my way through hydrotropes and find some good-enough approach via HSP or COSMOtherm. But I was wrong. Neither approach stands a chance of explaining hydrotropy. Like most solubility theories they are "mean field" theories that assume an absence of "special" ordering in solution - and clearly there is some special ordering behind hydrotropy.

Being desperate, I contacted the only statistical thermodynamicist I happened to know, Dr Seishi Shimizu at U. York who is featured in my Sugar in Coffee blog. He'd not come across hydrotropes before, but quickly spotted that a "well-known" technique he was using for the problem of protein denaturation in the presence of additives like urea or sugars would be ideal for solving hydrotropy.

So he asked me to help in the project of getting the data to prove or disprove his hypothesis. With the help of a brilliant final-year student, Jonathan Booth, we got the data, crunched the numbers, solved the problem of hydrotropy and wrote a paper. Unfortunately, given my ignorance and fear of thermodynamics I didn't fully understand what we had written. As it turns out, and as is typical of thermodynamics, we had used one set of equations which, though correct, were confusing to all of us. As we got to understand the system better and gathered more data and examples, we were able to rewrite the equations in a way that made it much easier to understand what was going on. The three papers1, 2, 3 have more or less solved the problem of classical hydrotropy that has been a confused mess for many decades.

But as is typical of me, although I could perfectly follow the equations (they are mostly simple arithmetic) I still didn't "get" the theory behind them, Kirkwood-Buff. But one Sunday night after a glass or two of wine, thinking about what was going to be my next big, long-term project, to my surprise I realised that I wanted to write a book on solubility science based on Kirkwood-Buff (KB) theory. Because the best way to learn is to teach, if I am to convince ordinary researchers like myself that KB is a great approach, then I've got to convince myself. As I am useless just looking at equations I've done what I always do which is to write a set of apps. It's amazing how much I've learned in the past few weeks, just writing 3 apps. One of them required a molecular dynamics simulation using the Verlet algorithm. There's no way I could write one from scratch, but as is so often the case a kind expert, Dr Dan Schroeder at Weber State University, allowed me to repurpose his elegant code and the user can now calculate some key KB parameters from first principles. Seishi had a quick look at it and said "Why not add the Widom Insertion Algorithm for chemical potential?". Why not? Because I've never heard of it and surely it's too hard. But a painful hour or two later and the app was doing the Widom calculations and I've learned another fundamental and powerful bit of statistical thermodynamics.

I've got a very long road ahead and I might fail completely. But already I'm much more comfortable with the theory and it's making it much easier to read interesting papers that previously would have been incomprehensible. I'm not, yet, trying to convince you to become a KB afficionado, but if the ideas slightly intrigue you, why not have a peek at the current prototype KB apps and see what you think. If you happen to already be an expert on statistical thermodynamics then let me know where I'm wrong and/or what I can do better.

1JJ Booth, S Abbott, S Shimizu, Mechanism of Hydrophobic Drug Solubilization by Small Molecule Hydrotropes, The Journal of Physical Chemistry B 116 (51), 14915-14921, 2012;
2S Shimizu, JJ Booth, S Abbott, Hydrotropy: binding models vs. statistical thermodynamics, Physical Chemistry Chemical Physics 15 (47), 20625-20632, 2013
3JJ Booth, M Omar, S Abbott, S Shimizu, Hydrotrope accumulation around the drug: the driving force for solubilization and minimum hydrotrope concentration for nicotinamide and urea, Physical Chemistry Chemical Physics 17 (12), 8028-8037, 2015