Small Molecule Hydrotropy

The reason why classical small-molecule hydrotropes such as urea or nicotinamide enhance the solubility of molecules in water has been debated for decades, with a number of theories such as hydrotrope clustering or "complex formation" being put forward with no solid evidence. The work of Booth et al¹, with later refinements of terminology and calculation methodology^2,3, resolved the issue via Kirkwood-Buff and showed that it was solute/hydrotrope assocation that drove the solubilisation and that hydrotrope self-association reduced the effect of the hydrotrope for the obvious reason that self-association hydrotropes were not doing anything to help the solute.

A later paper by Shimizu and Matsubayasi⁴ is able to describe the hydrotropy curve in terms of cooperative binding. Their approach is included here because although it is cannot provide all the molecular detail of KB, it provides key insights about cooperativity using a profound molecular thermodynamic approach related to KB.

The app, written by Booth and Abbott, with algorithms refined by Shimizu, takes in three key sets of experimental data and calculates the most important KB parameters. The original paper used the old terminology of 1 for water, 2 for solute and 3 for hydrotrope. To be consistent across all the KB apps, this app uses the now standard terminology that 1 is water, 2 is hydrotrope and u is solute.

Inputs & Outputs

For simplicity the calculations are all performed at a nominal 298 K. Tests show that the effect of changes from a typical lab range of 293 - 303 K are not significant, with density calculations automatically scaled to the extrapolated zero value from the specific dataset. The inputs are:

1. Density against molarity for hydrotrope water solution
2. Osmolality against molality of hydrotrope water solution
3. Solubility of solute in water against hydrotrope concentration

The outputs are:

1. Fitted density against molarity for hydrotrope water solution
2. Fitted osmolality against molality of hydrotrope water solution
3. Solubility of solute in water against hydrotrope concentration, with a fitting curve based on Shimizu and Matubayasi
4. Calculated and fitted -RTln(c_u)
5. All the key parameters (concentrations, mole fractions, partial molar volumes, G_ij values) across the concentration range
6. The formula for fitting -RTln(c_u)
7. The data and linear fitting curve for cooperative binding, plus the fitting parameters.

You can get detailed data from the graphs by moving your mouse to points of interest. The output data are in text boxes. You must Ctrl-A to select all and Ctrl-C to copy the data which can then be pasted into, say, Excel for further processing. The reason the data are provided in this manner is that Javascript apps are safe/secure by design and are not allowed to save data or put data onto the Clipboard.

The default data are for butyl acetate solubilised by urea. For simplicity, all data are assumed to be at 298 K. Errors from this assumption are small. You can choose other datasets from the combo box or load your own data from a text file in a format described below. The codes are:

Solutes: AB - p-AminoBenzoic Acid, BA - Butyl Acetate, BS - Butyl Stearate, BuAc - Butyl Acetate, BzBz - Benzyl Benzoate, EB - Ethyl Benzene, LA - Lauric Acid, MB - Methyl Benzoate, oHAP - o-Hydroxyacetophenone.
Hydrotropes: NA - Nicotinamide, SB - Sodium Benzoate, SS - Sodium Salicylate, SCS - Sodium Cumene Sulfonate, Urea

Density data

Density of water-hydrotrope solution against hydrotrope molarity
Data is fit as follows:ρ=a+b⋅c₂+c⋅c₂²

Osmotic data

Osmolality of water-hydrotrope solution agains hydrotrope molality
Data is fit as follows:Osmolality=iF⋅m₂+c⋅m₂²+d⋅m₂³. iF is the "ionic factor" which is 1 for neutral molecules and 2 for ionic salts.

Solubility data

Solubility of solute in three component water-solute-hydrotrope solution against hydrotrope molarity
Data is fit to -RTln(c_u) versus RTln(a₁) via a generic sigmoidal.

The Kirkwood-Buff parameters

Finally we get to see what is driving the solubility. In all cases so far examined, G_2u dominates and G₂₂ has only a small effect, typically reducting solubility. The fact that G₁₁ hardly changes is a reminder that "water structure" is totally irrelevant to hydrotropy.

Bad fits

Fitting to density and osmolality data is generally good. Small errors in these can be amplified in creation of the G₂₂ value but the effects are not too drastic. However, the -RTln(c_u) plot is based on a derivative of the solubility data and the general sigmoidal formula used can be difficult to fit to "bad" data. The fits are reasonable for all the samples provided but there is no guarantee that your own data will fit well. Smoothing your data might help - you will see that some of the raw solubility data in our examples show some "surprising" points, but it was not our job to smooth the published data.

Your own data files

These are simple tab-separated files. You can download the current datasets as a Hydrotrope Data zip file to give you some templates.
The first line should contain the molar volume of the solute (V_u) and the MWt of the hydrotrope (MWt₂) as Vu 116 M2 60. If the hydrotrope is ionic, this is shown with an extra field saying Ionic (not case sensitive).
The second line is an optional header file for the columns: c2 ρ g/cc m2 Osmol c2 cu
Each following line contains data in the order suggested by the column header: Hydrotrope molarity, Density of the aqueous solution, Hydrotrope molality, Osmolality of the solution, Hydrotrope molarity, Molar solubility of the solute.
This 3-in-1 format allows you to have tables of different lengths for the 3 different properties - just as you see in the table in the app. The easiest way to create such a text file is within Excel and to save it in tab-separated text format.

The Javascript code is Copyright © 2016 Prof Steven Abbott and is distributed under the Creative Commons BY Attribution license. Users are encouraged to examine the code themselves. All key aspects of the calculation are flagged up with comments.