Multicomponent solutions: Combining rules for multisolute osmotic virial coefficients

Predictive Thermodynamics for Isochoric (Constant-Volume) Cryopreservation Systems

Cryopreservation is the preservation and storage of biomaterials using low temperatures. There are several approaches to cryopreservation, and these often include the use of cryoprotectants, which are solutes used to lower the freezing point of water. Isochoric (constant-volume) cryopreservation is a form of cryopreservation that has been gaining interest over the past 18 years. This method utilizes the anomalous nature of water in that it expands as it freezes. The expansion of ice on freezing is used to induce a pressure in the system that limits ice growth. In this work, we use Gibbsian thermodynamics, the Elliott et al. multisolute osmotic virial equation, the Feistel and Wagner correlation for ice Ih, and the Grenke and Elliott correlation for the thermodynamic properties of liquid water at low temperatures and high pressures to predict how the pressure, volume fraction of ice, and solute concentration in the unfrozen fraction change as the solution is cooled isochorically. We then verified our model by predicting experimental results for saline solutions and ternary aqueous solutions containing NaCl and organic compounds commonly used as cryoprotectants: glycerol, ethylene glycol, propylene glycol, and dimethyl sulfoxide. We found that our model accurately predicts experimental data that were collected for cryoprotectant concentrations as high as 5 M, and temperatures as low as -25 °C. Since we have shown that our liquid water correlation, on which this work was based, makes accurate predictions to -70 °C, as long as the pressure is not higher than 400 MPa, we anticipate that the prediction methods presented in this work will be accurate down to -70 °C. In this work we also modeled how sealing the isochoric chamber at room temperature versus at the nucleation temperature impacts isochoric freezing. The prediction methods developed in this work can be used in the future design of isochoric cryopreservation experiments and protocols.

Predicting freezing points of ternary salt solutions with the multisolute osmotic virial equation

Previously, the multisolute osmotic virial equation with the combining rules of Elliott et al. has been shown to make accurate predictions for multisolute solutions with only single-solute osmotic virial coefficients as inputs. The original combining rules take the form of an arithmetic average for the second-order mixed coefficients and a geometric average for the third-order mixed coefficients. Recently, we derived generalized combining rules from a first principles solution theory, where all mixed coefficients could be expressed as arithmetic averages of suitable binary coefficients. In this work, we empirically extended the new model to account for electrolyte effects, including solute dissociation, and demonstrated its usefulness for calculating the properties of multielectrolyte solutions. First, the osmotic virial coefficients of 31 common salts in water were tabulated based on the available freezing point depression (FPD) data. This was achieved by polynomial fitting, where the degree of the polynomial was determined using a special criterion that accounts for the confidence intervals of the coefficients. Then, the multisolute model was used to predict the FPD of 11 ternary electrolyte solutions. Furthermore, models with the new combining rules and the original combining rules of Elliott et al. were compared using both mole fraction and molality as concentration units. We find that the mole-fraction-based model with the new combining rules performs the best and that the results agree well with independent experimental measurements with an all-system root-mean-square error of 0.24 osmoles/kg (0.45 °C) and close to zero mean bias for the entire dataset (371 data points).