Quantification of solid-phase chemical reactions using the temperature-dependent terahertz pulsed spectroscopy, sum rule, and Arrhenius theory: thermal decomposition of α-lactose monohydrate.

Transformations of the low-energy vibrational spectra are associated with structural changes in an analyte and closely related to the instability of weak chemical bounds. Terahertz (THz)/far-infrared optical spectroscopy is commonly used to probe such transformation, aimed at characterization of the underlying solid-phase chemical reactions in organic compounds. However, such studies usually provide quite qualitative information about the temperature- and time-dependent parameters of absorption peaks in dielectric spectra of an analyte. In this paper, an approach for quantitative analyses of the solid-phased chemical reactions based on the THz pulsed spectroscopy was developed. It involves studying an evolution of the sample optical properties, as a function of the analyte temperature and reaction time, and relies on the classical oscillator model, the sum rule, and the Arrhenius theory. The method allows one to determine the temperature-dependent reaction rate V(T) and activation energy E. To demonstrate the practical utility of this method, it was applied to study α-lactose monohydrate during its temperature-induced molecular decomposition. Analysis of the measured THz spectra revealed the increase of the reaction rate in the range of V ≃ ~9 × 10-10 min, when the analyte temperature rises from 313 to 393 K, while the Arrhenius activation energy is E ≃ ~45.4 kJ/mol. Thanks to a large number of obtained physical and chemical parameters, the developed approach expands capabilities of THz spectroscopy in chemical physics, analytical chemistry, and pharmaceutical industry.