Comparison of non-ideal solution theories for multi-solute solutions in cryobiology and tabulation of required coefficients

Abstract

Thermodynamic solution theories allow the prediction of chemical potentials in solutions of known composition. In cryobiology, such models are a critical component of many mathematical models that are used to simulate the biophysical processes occurring in cells and tissues during cryopreservation. A number of solution theories, both thermodynamically ideal and non-ideal, have been proposed for use with cryobiological solutions. In this work, we have evaluated two non-ideal solution theories for predicting water chemical potential (i.e. osmolality) in multi-solute solutions relevant to cryobiology: the Elliott et al. form of the multi-solute osmotic virial equation, and the Kleinhans and Mazur freezing point summation model. These two solution theories require fitting to only single-solute data, although they can make predictions in multi-solute solutions. The predictions of these non-ideal solution theories were compared to predictions made using ideal dilute assumptions and to available literature multi-solute experimental osmometric data. A single, consistent set of literature single-solute solution data was used to fit for the required solute-specific coefficients for each of the non-ideal models. Our results indicate that the two non-ideal solution theories have similar overall performance, and both give more accurate predictions than ideal models. These results can be used to select between the non-ideal models for a specific multi-solute solution, and the updated coefficients provided in this work can be used to make the desired predictions.

Comment on “Determination of the quaternary phase diagram of the water–ethylene glycol–sucrose–NaCl system and a comparison between two theoretical methods for synthetic phase diagrams” Cryobiology 61 (2010) 52–57

“…However, this analysis suffered from a number of issues, notably including the use of inconsistent solute-specific coefficients for the multi-solute osmotic virial equation. Herein, we reanalyse the data using a recently-updated and consistent set of solute-specific coefficients (Zielinski et al, 2014). Our results indicate that the two models have very similar performance, and, in fact, the multi-solute osmotic virial equation can provide more accurate predictions than the freezing point summation model depending on the concentration units used.…”

“…Experimental multi-solute phase diagrams provide a means of evaluating the accuracy of theoretical multi-solute solution theories, as the model predictions can be compared to the experimental data [1,4,7,14,18]. Recently, Han et al [7] published an extensive set of freezing point depression data for the quaternary system water-ethylene glycol-sucrose-NaCl.…”

“…In addition, although the Elliott et al multi-solute osmotic virial equation was proposed in two forms expressed in terms of either molality or mole fraction, only the molality-based form was considered in Han et al's analysis. We have recently shown [18] that although these two forms of the multi-solute osmotic virial equation appear very similar, their performance can vary considerably for a given solution system. Finally, it should be noted that while Han et al compared the predictions of the two non-ideal models to their experimental measurements, no comparison was made to predictions made using an ideal dilute model.…”

“…However, most solutions in cryobiology tend to be highly concentrated and thus thermodynamically non-ideal. As such, use of the ideal model can negatively impact prediction accuracy [4,14,18]. Alternatively, non-ideal solution theories can be used, although these models introduce additional complexity as they rely on solute-specific thermodynamic coefficients to account for solute-solute interactions.…”

“…Such coefficients are typically obtained empirically, i.e. by curve-fitting to experimental solution data [3,4,9,14,18]. Cryobiological solutions are predominantly multi-solute in nature.…”