Quantitative analysis of solid-state processes studied with isothermal microcalorimetry.

Quantitative analysis of solid-state processes from isothermal microcalorimetric data is straightforward if data for the total process have been recorded and problematic (in the more likely case) when they have not. Data are usually plotted as a function of fraction reacted (α); for calorimetric data, this requires knowledge of the total heat change (Q) upon completion of the process. Determination of Q is difficult in cases where the process is fast (initial data missing) or slow (final data missing). Here we introduce several mathematical methods that allow the direct calculation of Q by selection of data points when only partial data are present, based on analysis with the Pérez-Maqueda model. All methods in addition allow direct determination of the reaction mechanism descriptors m and n and from this the rate constant, k. The validity of the methods is tested with the use of simulated calorimetric data, and we introduce a graphical method for generating solid-state power-time data. The methods are then applied to the crystallization of indomethacin from a glass. All methods correctly recovered the total reaction enthalpy (16.6 J) and suggested that the crystallization followed an Avrami model. The rate constants for crystallization were determined to be 3.98 × 10(-6), 4.13 × 10(-6), and 3.98 × 10(-6) s(-1) with methods 1, 2, and 3, respectively.

Quantifying the rates of relaxation of binary mixtures of amorphous pharmaceuticals with isothermal calorimetry.

While the use of isothermal calorimetry to quantify the rate of relaxation of one-phase amorphous pharmaceuticals, through application of models, is well documented, the resolution of the models to detect and quantify relaxation in systems containing two independent amorphous phases is not known. Addressing this knowledge gap is the focus of this work. Two fitting models were tested; the Kohlrausch-Williams-Watts model (KWW) and the modified-stretch exponential (MSE). The ability of each model to resolve relaxation processes in binary systems was determined with simulated calorimetric data. It was found that as long as the relaxation time constants of the relaxation processes were with 10(3) of each other, the models could determine that two events were occurring and could quantify the correct reaction parameters of each. With greater differences in the time constants, the faster process always dominates the data and the resolving power of the models is lost. Real calorimetric data were then obtained for two binary amorphous systems (sucrose-lactose and sucrose-indomethacin mixtures). The relaxation behaviour of all the single components was characterised as they relaxed individually to provide reference data. The ability of the KWW model to recover the expected relaxation parameters for two component data was impaired because of their inherently noisy nature. The MSE model reasonably recovered the expected parameters for each component for the sucrose-indomethacin system but not for the sucrose-lactose system, which may indicate a possible interaction in that case.