Entropy of processing: a new quantity for comparing the solid state disorder of pharmaceutical materials

Abstract

During the pharmaceutical processing of a solid (e.g. crystallization, drying, gain or loss of impurities or additives, milling. compression, heating or irradiation), defects and other imperfections develop, wander or disappear in the crystal lattice. Crystal imperfections contribute to the disorder of the crystal lattice, and entropy is here proposed as a practical and fundamental measure of this effect. The difference between the entropy of a given sample and that of the same amount of the reference material is designated the “entropy of processing (or imperfection)”, ΔS p, of the sample. Thermodynamic cycles are described for evaluating ΔS pof a sample from differential scanning calorimetry or from solution calorimetry with solubility studies. ΔS p may be evaluated for polymorphs, solvates (e.g. hydrates), amorphous forms, glasses, impure, or variously processed samples of a given substance. ΔS p calculated from literature data for processed pharmaceutical solids is found to be positive with respect to a highly pure. stable. crystalline reference material and to range from 0 to 200 J. K −1 · mol −1. Small values of ΔS p (0–10 J · K −1 · mol −1) are given by crystals which have been “doped” with additives or impurities in solid solution. Literature data for milled calcium gluceptate suggest that enthalpy-entropy compensation occurs and may be exploitable. ΔS pof ground samples of chloramphenicol palmitate A or B parallels their dissolution rate and bioavailability. Data for β-lactam antibiotics and calcium gluceptate indicate that ΔS p increases with decreasing X-ray crystallinity, purity and stability and with increasing processing stress. ΔS p may decrease during annealing and/or storage and appears to be useful for quantifying, understanding and predicting batch-to-batch differences in pharmaceutical solids.