Molecular thermodynamics of precipitation
Using a simple theory for fluids and a simple theory for a solid, it is possible to construct a semi-quantitative corresponding-states phase diagram where a reduced temperature is plotted as a function of a reduced density. The reducing parameters are molecular size (sigma3) and molecular potential energy (&unknown;/kB); the phase diagram includes both low-density and high-density fluid regions and the solid region. These calculations apply to a pure substance or, of more interest, to a solute dissolved in a continuous solvent. The qualitative nature of the phase diagram depends strongly on the range of attractive intermolecular forces as indicated by an exponential parameter n; when coordination number z=8 and n is about 6, we obtain the usual phase diagram where the fluid-solid region lies to the right of the fluid-fluid coexistence curve. But when n is about 7 or 8, the fluid-solid region lies above the fluid-fluid coexistence curve. Applications are discussed for aqueous solutions of a colloid or a globular protein that may also contain a salt or a polymer to induce precipitation.