Dear Thomas Nicol!
If I understood correctly, then you describe a nonequilibrium system undergoing a phase transition with supercooling. The choice of approach to the theoretical description depends on what processes you are considering - at the micro level or statistically at the macro level. In the second case, you can write the nonequilibrium thermodynamic potential with Gibbs free energy through the Ginzburg – Landau functional by introducing an order parameter. Statistically, such a description was previously successfully developed in the theory of alloys.
With best regards,
Dr. Olga Mazur
Olga Mazur Thank you very much for your response.
The main focus of what I'm investigating is equilibrium thermodynamics, I'm attempting to understand solubility and dissolution. Each state, before (solid) and after (solution) the dissolution transition would be in thermodynamic equilibrium if I'm not mistaken.
The aspect of a supercooled liquid form in this case is a theoretical simplification used historically in chemical thermodynamics which I am trying to avoid as it does not represent the reality of the system.
Dear Thomas Nicol!
Your question reminded me of the statistical theory of ordering in solid solutions, especially when you mentioned supercooling. But when you explained that in chemistry this is a slightly different concept, I realized that a developed statistical approach is hardly suitable for describing your problem. Nevertheless, I am attaching a link to the article, it may be useful to you.
Article Order Parameter Oscillations in a Bounded Solid Solution and...
With best regards,
Dr. Olga Mazur
The following paper considers the calculation of the MP of a pure substance (is the problem you're asking about?)
Eike, D. M. and Brennecke, J. F. and Maginn, E. J., Toward a robust and general molecular simulation method for computing solid-liquid coexistence, J. Chem. Phys., 122, 14115 (2005)
Dear Dr Nicol
As you know free energy is expressed only as a relative value with respect to a reference state (e.g. as G of formation). In the case of mixtures with components in different aggregation states, usually an unsymmetrical reference is used, i.e. a hypothetical ideal dilute solution of unit concentration. A symmetrical reference system is used for mixtures of totally miscible components. In this case the standard chemical potential is the Gibbs free energy of the pure component, for all the components. In order to use this system for the dissolution of a solid in a solvent, as you have mentioned, you have to know the G (of formation) of the hypothetical (eventually super-cooled liquid solute). This is possible in some extent by means of estimation - extrapolation methods. Prof. Chickos and his collaborators have elaborated and used such algorithms mainly (but not only) for the enthalpy of fusion. I give you a few references :
Chickos, J. S.; Acree, Jr. W. Liebman, J. F. “Estimating Phase Change Entropies and Enthalpies,” (Frurip, D.; Irikura, K., Editors) ACS Symposium Series 677, Computational Thermochemistry, Prediction and Estimation of Molecular Thermodynamics, ACS: Washington DC, 1998, pp 63-93.
Chickos, J. S. Thermochim. Acta 1998, 313, 19-26.
Chickos, J. S.; Hesse, D. G.; Liebman, J. F. Struct. Chem. 1993, 4, 261-269.
St. Perisanu, I. Contineanu, A. Neacsu, N.P. Rath, J.S. Chickos, R. Notario, J.F. Liebman, “Thermochemical and structural study of a dibenzocycloheptane cyanoenamine”, Struct. Chem., 24, Issue 6 (2013), 1975-1980.
To estimate/calculate the solubility of a crystalline solid in a solvent at a given (T,P), one needs to solve the equation
musol(T,P;m)= mu*(T,P) (1)
where m is the molality (or any other concentration variable).
Eq. (1) can be solved for m if one has an equation for musol(T,P;m) and the value of mu*(T.P). This requires:
(1) The expression of musol(T,P;m) in analytical form, which is usually expressed by means a semiempirical model or it can be calculated using a molecular model. The equation for musol must extend to super-saturation values
(2) The same standard state for the solute in each phase must be incorporated in both mu*(T,P) and musol(T,P;m). The standard state chemical potential of the solute in solution is usually the Henry-Law quantity mu#, the calculation of which requires its ideal-gas formation free energy at the given T and its solvation free energy in the solvent at (T,P).
(3) A problem arises in determining musol*(T,P) from experimental data. The only information usually available is the solute's melting, sublimation and vaporization curve data, at all points of which the chemical potentials of the coexisting phases are equal. One then needs to ascribe a value to the chemical potential of one of the phases relative to its ideal-gas free energy of formation. Then, one must extrapolate the solid chemical potential from a point on the curve to the (T,P) of interest. The references provided by Dr. Parisanu may provide a methodology to do this part. If one wants to do this by molecular simulation, then the paper of the Maginn group mentioned earlier are relevant.
Hopefully this helps?
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