A disruption index for quantifying the solid state disorder induced by additives or impurities. I. Definition and evaluation from heat of fusion

Abstract

A dimensionless disruption index (d.i.) is proposed for quantifying the solid state disorder induced by 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 is defined as the rate of change of the difference between the entropy of the solid and that of the liquid, with respect to the ideal entropy of mixing of the components of the solid, ΔS m ideal. From fundamental thermodynamic considerations d.i. is closely approximated by the slope of the plot of the entropy of fusion of the solid, ΔS f, against ΔS m ideal for x 2 < 0.05. ΔS f is given by the heat of fusion divided by the absolute melting point, while ΔS m ideal = − RΣx j ln x j is calculated from the analytical data of the crystals, where x j is the mole fraction of a given component. The linear relationship was tested using the limited literature data available for 7 systems and was found to be obeyed for x 2 < 0.05. Values of d.i. range from zero for ideal solutions through about 10 −1 for doping of the intermetallic compound InCd 3 with either of its components, (somewhat higher, 0.423, for cadmium doped with InCd 3), to about 10 for the doping of a stable, ordered organic crystal with an organic additive. The d.i. values for phenacetin doped with benzamide, griseofulvin + lecithin, acetaminophen + water + p-acetoxyacetanilide, and pp-DDT + op-DDT, are 7.94, 5.09, 6.53 and 15.1, respectively. The d.i. values are discussed in relation to the properties of the host and guest. The method of determining d.i. from ΔS f is critically assessed. The d.i. values may be useful in predicting the sensitivity of the crystal lattice of a drug or excipient to the presence of traces of a given impurity in solid solution. If the presence of impurities gives rise to batch-to-batch variations, d.i. values may also be useful for quantifying the observed differences in properties between batches of materials.