On determining the relaxation time of glass and amorphous pharmaceuticals’ stability from thermodynamic data

Spontaneous relaxation of an amorphous solid changes its properties with time, as does its slow crystallization, both resulting from slow molecular diffusion that decreases its free energy. When the solid is a pharmaceutical, this occurrence decreases its solubility and hence bioavailability, thus decreasing its effectiveness during storage. Its stability against crystallization or “shelf-life” is currently modeled by calculating the relaxation time, τglass, by using the specific heat Cp and the enthalpy of melting data in the viscosity-configurational entropy relation. We consider merits of such calculations, and find that use of, (i) the excess Cp and its hyperbolic dependence on temperature, (ii) the enthalpy of melting, and (iii) the fictive temperature, is inconsistent with the glass relaxation phenomenology, and their use leads to overestimate of τglass, and thus to a longer than real shelf-life of an amorphous pharmaceutical. We also argue that τglass is not the same as the characteristic time of spontaneous structural relaxation of a glass, and would not determine the nucleation or crystal growth rate in it.