Source: https://pubs.rsc.org/en/content/articlehtml/2017/gc/c6gc03002e?page=search
Timestamp: 2019-04-19 20:57:08+00:00

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Steven Abbott has a chemistry PhD from Oxford and Harvard and has worked for many years in the chemicals and coating industry. He is now an independent scientist and consultant. He is Visiting Professor at the School of Mechanical Engineering, University of Leeds. His Practical Adhesion, Practical Solubility and Practical Surfactants websites represent his attempt to “appify” as much science as possible in these areas, allowing the science to become alive and usable by non-experts. His most recent apps are designed for Virtual Reality.
Jonathan Booth studied Chemistry at the University of York where, under the supervision of Dr Seishi Shimizu, he carried out an MChem research project of solubility enhancement. This led to the first rational theory of how hydrotropes work, and the development of a thermodynamic toolkit for explaining many areas of solubility and formulation science. After graduating Jonathan completed a PhD in computer modelling and algorithm development at the University of Leeds under the supervision of Prof. Dmitry Shalashilin. Jonathan now works for Croda as a formulation scientist.
Seishi Shimizu is a Senior Lecturer in the York Structural Biology Laboratory, Department of Chemistry, University of York. He has received a BSc in Physics, MSc in Physics and PhD in Biotechnology from the University of Tokyo, prior to his postdoctoral training in the Faculty of Medicine, University of Toronto. As a theorist specializing in statistical thermodynamics, he has worked in wide-ranging fields and applications including solvation, protein folding and stability, protein–ligand interaction, food science, formulation science and hydrotropy.
When water is chosen as a principal solvent for green chemistry,1–5 the challenge is to find green “solubilizers” (using a deliberately vague word) to help bring hydrophobic solutes into solution.6–11 If we are lucky we can use conventional “cosolvents” such as ethanol and we need little new theory to guide us in the right choice. Similarly, it is relatively straightforward to find surfactant systems (such as Tweens) that increase solubility when present at concentrations above their critical micelle concentration (CMC) by bringing the solute somewhere within the micelle structure (tail, head or intermediate region, depending on the solute).6–11 Although the theory of such systems is complex,12,13 in many situations a formulator can find adequate formulations via simple design of experiment approaches.
Our concern here is with solubilizers that fall between these two extremes. Here there is a confusing mix of terminologies such as “hydrotrope”, “solvosurfactant”, “solubilizer”, “cosolvent” and even “pre-ouzo” formulations.6–11 Although such systems offer much promise, it is hard to formulate rationally because of the confusing terminology and the obscurity of the mechanisms by which solubility is increased.14–17 The confusion leads directly to a waste of intellectual and developmental resources, as well as sub-optimal formulations. The aim of this paper is to provide a set of practical tools to counter this wastefulness.
For decades the debate about the general mechanism of hydrotropes could not be resolved because there was no objective way to look at the thermodynamics of this complex ternary system.14–17 Classical thermodynamic values such as enthalpy and entropy are useful, yet are not the most straightforward entry into a molecular understanding, as will be shown below.
3. The vapour pressure (VP) or (equivalently) osmotic pressure of the hydrotrope solutions.
No complex experimental equipment is required (though it is possible to derive some of the data via SAXS/SANS after much effort and cost) and modern high throughput machines make it trivial to obtain the necessary data.
This means that the green formulator merely has to add a few rather routine measurements (density & VP) to their solubility measurements to get an assumption-free, fundamental thermodynamic analysis of all the relevant effects within their solubilization experiments. The community gains a universal tool for comparing/contrasting the effects of different hydrotropes on different solutes and once a sufficient body of data exists, the technique will allow prediction and optimization. As a community we can transition from rather vague (and often confusing) terms such as “hydrotrope” to a few fundamental thermodynamic numbers which describe what is really going on.
Fig. 1 A simple simulation of an RDF (gij(r)) and 4πr2[gij(r) − 1] as a function of intermolecular separation, r.
The RDF between species i and j is designated gij(r), which is a function of the intermolecular separation, r. By integrating the gij(r) − 1 over the whole solution space (via the function 4πr2[gij(r) − 1] shown in the bottom part of Fig. 1) one obtains a number which would be 0 if the distribution were entirely average (no special interactions), positive for typical small molecules if the molecules have fairly strong interactions and negative for systems with unfavourable interactions.14–17,28–36 The values for systems of interest are readily found from the hydrotrope app discussed below. These numbers are called the Kirkwood–Buff Integrals (KBI) and the free energy of the system can be calculated on a rigorous, assumption-free basis from the KBI.14–17,28–36 For two components i and j the KBI is written as Gij. It is important to note that a positive (negative) KBI implies an increase (decrease) in the measured density of the solution, i.e. microscopic phenomena are reflected in macroscopic effects, as discussed below.
A simple 2D pseudo-molecular dynamics app (based upon an interactive molecular dynamics programme by Schroeder38) allows the rapid development of an intuitive feel for RDFs and the resulting Gij values. The app is http://www.stevenabbott.co.uk/practical-solubility/rdf-demo.php and the screen shot (Fig. 2) gives some idea of the capabilities of the app.
Fig. 2 A 2D simulation of simple Lennard-Jones fluid mixtures from which an RDF is calculated. In this example, the 1-2 “attraction” is 50% greater than that of 1-1 and 2-2 so the G12 values are higher.
Another advantage of KBIs is in their ability to rationalize the formulators’ general preference for smaller solvents to larger ones for dissolution. The KBI is the integral of the radius r from 0 to infinity of the RDF.28–36 As shown in Fig. 1, the RDF is exactly 0 in the early part of the integral because other molecules are excluded from the volume of whichever molecule we are taking to be the reference for our distribution. This means that larger molecules have a 0 value of an RDF for a longer distance than smaller ones.30–33 So, other things being equal, KBIs for larger molecules will always be smaller (more negative) than those for smaller molecules. And because KBIs are a measure of the strengths of interactions, larger molecules always start with a disadvantage. There are many ways to talk of this “excluded volume” effect and it is common to describe it in terms of entropy. But by thinking of it in terms of the KBI, an idea that can be slippery and confusing becomes concrete and intuitive.30–33 An app (http://www.stevenabbott.co.uk/practical-solubility/ev-demo.php, not shown) allows exploration of this effect by omitting all other confusing variables.
So two simple concepts, density and excluded volume are key to understanding many formulation issues, yet are used surprisingly little.
KBIs are directly related to activity coefficients, provided that density changes are also taken into account.14–17,28–37 Because this paper is deliberately app-based, the reader is urged to explore the relationship between activity coefficients, densities and molecular weights (which affect molar volumes and excluded volumes) by using http://www.stevenabbott.co.uk/practical-solubility/kbgs.php.
The default settings, shown in Fig. 3, use constant densities, identical molecular weights and (via pseudo Wilson parameters) a system with modestly large activity coefficients. The three KBI (G11, G12 and G22) are plotted across the mole fraction range of 0 to 1 and will quickly make intuitive sense as the relative activity coefficients are changed. By changing molecular weight, simple excluded volume effects become apparent, then by adding a polynomial density plot of any shape that seems of interest, i.e. adding the effects of internal interactions, the full system can be explored.
Fig. 3 KBIs derived directly from MWt, density and activity coefficient data. Extra parameters such as “excess numbers” are also calculated.
All that remains for the formulator to have a deep understanding of any given system is to see how the various Gij values change over the concentration range of interest and then, to find optimum systems, compare and contrast how changes to the system change the key terms in the equation.
The equations for obtaining the various Gij data from the experimental data are not particularly complex and the procedure is not especially difficult. They are fully described in our previous papers.14–17 Nevertheless, most formulators, including the present authors, would struggle to get every detail correct and to avoid classic pitfalls in a plethora of unit conversions. The (open-source) KB-hydrotrope app, http://www.stevenabbott.co.uk/practical-solubility/kb-hydrotropes.php, does all the hard work (see ESI† for instructions on how to use it).
3. Osmolality versus molality for a series of hydrotrope concentrations (the same samples can be used for density measurements, but this is not a necessary requirement).
Again, the expectation is that from such analyses of many datasets the reasons for the success or failure of various solute/hydrotrope pairs will become apparent.
The current app is limited to situations where the solute is at relatively low concentrations.14–17 At higher concentrations the KB theory still remains assumption-free but the methodology for extracting the Gij values becomes more complex and is not included in the current version. An alternative app based upon a more general theory36 for handling a full ternary phase diagram shows that KB theory has no intrinsic limitation. However, the ternary app deals only with fully miscible liquids and is currently not so useful for the green formulator.
Another limitation is that the KB equations are not good at critical points of phase separation.28–38 So a ternary system that has regions of immiscibility can only give Gij numbers surrounding the phase boundaries. KB can probably handle the fascinating “pre-ouzo” region (which has attractive green solubilization potential) but certainly cannot handle the phase separation domain.8,11 Nevertheless, a good delineation of phase boundaries still provides a lot of key information that maps to a formulator's intuition.
Fig. 4 The KB-hydrotrope app does all the hard work of fitting the raw data to the fundamental theory, outputting graphs and data for further processing. In addition to 16 datasets from the literature, the user can load their own datasets for analysis.
One of the many beautiful aspects of thermodynamics is that the same problem can be viewed from several different perspectives. Those who prefer to work with enthalpies and entropies (and the issue of entropy/enthalpy compensation) could, in principle, take the same experimental data and derive thermodynamic values that are equally valid. The problem is that there is no direct, rigorous and tractable link between solubility and solution structure from an entropy/enthalpy point of view,42–44 nor is there an appified version of such an approach that allows the formulator to easily gain a deep, intuitive understanding of what is going on. It would be very useful if such alternatives existed because the different ways of looking at the same problem can provide insights that neither approach on its own can give. For those who are interested in such aspects, it is indeed possible to go from KBIs to entropy/enthalpy values but the present authors have not provided this functionality in the apps.
What about prediction? As mentioned above, even with advanced molecular dynamics simulations it happens to be extremely difficult to go from computed RDFs to reliable KBIs.38 Even if this were possible, molecular dynamics will show the same complicated picture of multiple, statistical interactions that are somewhat stronger or weaker depending on the system. So prediction, as opposed to understanding, is currently not possible via the KB approach.
This is, to say the least, unfortunate. But the present authors believe that with a sufficient corpus of datasets, formulators will be able to generate rules of thumb or more sophisticated algorithms to provide the necessary prediction. Already it is possible to see why urea may or may not be a better hydrotrope than nicotinamide.17 For solutes where, by intuition, nicotinamide is not going to be strongly attracted to the solute, urea would tend to win because the rather large G22 value of nicotinamide gives it a significant disadvantage. With a proper KB analysis of the cases where SCS (or the similar sodium xylene sulfonate, SXS) are used on an industrial scale it should be possible to intuit why they are so successful in these specific applications, and to suggest alternatives for cases where they do not work.
The KB molecular thermodynamics approach described here links the macroscopic world of solubilities, densities and vapour pressures to the molecular realm in a fundamental manner.14–17 For issues of solubilization in the area between the comparatively well-understood zones of cosolvency and micellar solvency, it offers a fundamental, assumption-free way for the green formulator to grasp what is going on in a complex aqueous system.14–17 Because KB uses radial distribution functions,28–38 the formulator can gain an intuitive insight, via KB integrals, into what is going on at the molecular level. Because the key values can be obtained from a set of rather simple measurements (solubility, density, vapour pressure) which, in turn, can be obtained by modern high-throughput techniques,14–17,28–38 the green community has the opportunity to build up a wide dataset of KB values for different solutes and solubilizers. From a wider dataset, a more general understanding of what works and what does not should emerge.
For those who are comfortable with the algebra of statistical thermodynamics, the approach adopted here is described in rigorous detail in our previous papers.14–17 For those who are less comfortable, the KB theory itself can be explained via a series of apps that allow the formulator to build up an understanding of what the theory really means.
While the extraction of the KB parameters from experimental data requires a series of tedious calculations, a set of general-purpose, open source apps allows the green community to obtain the key KB values easily and reliably from their own experimental data. By being open source, the apps can be challenged, modified and developed collaboratively by the hydrotrope community.
Alternative app-based approaches via different, complementary thermodynamic methods would be welcomed. The present authors have chosen KB because it seems to handle these complex systems with a welcome clarity and precision and provides numbers (KBIs) that map onto chemists’ understanding of radial distribution functions. But clearly, other approaches have their own merits.
We thank Joshua Reid and Shuntaro Chiba for insightful discussions. S. S. acknowledges the support from the Gen Foundation.
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‡ Present address: Croda Europe, Cowick Hall, Snaith, Goole, East Yorkshire, DN14 9AA, UK.

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