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.