A disruption index for quantifying the solid state disorder induced by additives or impurities. II. Evaluation from heat of solution

Abstract

In a previous report a dimensionless disruption index (d.i.) was proposed for quantifying the disruptive influence of an additive or impurity (the guest substance) when present in solid solution in the crystal lattice of a host substance at mole fractions, x 2, less than 0.05. The d.i. value was defined as the rate of change of the difference between the entropy of the solid, S solid, and that of the liquid, S liquid, with respect to the ideal entropy of mixing of the components of the solid, ΔS ideal m , i. e. d. i. = − δ ( S liquid − S solid )/ δ( ΔS ideal m ). The determination of (S liquid − S solid) from the heat of fusion and the melting point using differential scanning calorimetry (DSC) or differential thermal analysis (DTA) could itself change the entropy and the concentration of point defects and dislocations by an annealing process. To overcome these problems δ(S solulion − S solid) = δ (ΔS s), which is shown to approximate closely to δ(S liquid − S solid), is determined isothermally (e.g. at 25 or 37° C) using solution calorimetry and measurements of J, the dissolution rate per unit surface area. ΔS s is derived from the heat of solution, ΔH s, and from the Gibbs free energy of solution which is changed by RT · δ(In J) on doping, where R is the gas constant and T is the absolute temperature. The possibilities that ΔS s can be calculated from ΔH s directly assuming enthalpy-entropy compensation, or simply by ignoring the term containing δ(In J), are also considered. The above possibilities are examined using the limited data available for adipic acid doped with hexanoic, octanoic, undecanoic or oleic acid. The d.i. values from solution calorimetry are of the order 10 3, indicating an enormous potential for lattice disruption, while d.i. values from DSC are generally smaller and decrease with decreasing chain-length of the guest molecule. This suggests that heating in DSC promotes rearrangement of the guest molecules and annihilation of crystal defects. Ignoring δ(In J) changes d.i. by up to 15%. Much larger influences of δ(In J) are given by oleic acid as the guest which tends to concentrate on the surface. In general, the pseudo-disruption index p.d.i., calculated as −δ(ΔH s/T)/δ(ΔS ideal m), may approximate sufficiently closely to d.i. to be useful. Thus, the p.d.i. value for cephaloridine monohydrate doped with cephaloridine anhydrate, corresponding to slight moisture loss from the lattice of the former, is of the order 1, which suggests very little lattice disruption.