Role of deliquescence lowering in enhancing chemical reactivity in physical mixtures

Mixtures of deliquescent solids are susceptible to deliquescence lowering, where water vapor condensation occurs in mixtures at a lower critical relative humidity (RH(0mix)) than individual component critical relative humidities (RH(0)s). The purpose of this study was to evaluate the effect of deliquescence lowering on chemical reactivity. Sucrose, citric acid and their physical mixtures were characterized using vapor sorption analysis to determine RH(0) and RH(0mix). Acid-catalyzed sucrose hydrolysis kinetics was determined using polarimetric analysis. Physical mixtures of sucrose and citric acid crystals were prepared and stored at various relative humidities at 22 degrees C. For these physical mixtures, sucrose hydrolysis was found to occur only when the environmental RH exceeded RH(0mix). Degradation kinetics correlated with the storage RH, being fastest at higher RH. In addition, a lag period was initially observed, which was most prominent for samples stored close to RH(0mix). With exposure to RHs below RH(0mix), no sucrose degradation was detected over the experimental time period. In conclusion, mixtures of deliquescent solids showed increased water sorption at lower RHs, which caused solid dissolution and subsequently led to an increase in the chemical reactivity.     

Restricting Hecke-Siegel operators to Jacobi modular forms

We compute the action of Hecke operators on Jacobi forms of “Siegel degree” n and m×m index M, provided 1?j?n−m. We find they are restrictions of Hecke operators on Siegel modular forms, and we compute their action on Fourier coefficients. Then we restrict the Hecke-Siegel operators T(p), Tj(p²) (n−m<j?n) to Jacobi forms of Siegel degree n, compute their action on Fourier coefficients and on indices, and produce lifts from Jacobi forms of index M to Jacobi forms of index M^′ where detM|detM^′. Finally, we present an explicit choice of matrices for the action of the Hecke operators on Siegel modular forms, and for their restrictions to Jacobi modular forms.