Photocatalytic degradation processes of different materials are fitted with Mittag-Leffler function and incomplete gamma function,which are response functions for Cole–Cole relaxation and Davidson–Cole relaxation.Th...Photocatalytic degradation processes of different materials are fitted with Mittag-Leffler function and incomplete gamma function,which are response functions for Cole–Cole relaxation and Davidson–Cole relaxation.The fitting results show that both functions can fit experimental data fairly well.The order of derivative in the kinetic differential equations can be either less,or greater than one.In the case of the order of derivative is greater than one,only incomplete gamma function is reasonable for describing the photocatalytic degradation.This work further confirms the existence of the universality in photocatalytic degradation kinetics.展开更多
Two parameters are proposed as Jonscher indices,named after A.K.Jonscher for his pioneering contribution to the universal dielectric relaxation law.Time domain universal dielectric relaxation law is then obtained from...Two parameters are proposed as Jonscher indices,named after A.K.Jonscher for his pioneering contribution to the universal dielectric relaxation law.Time domain universal dielectric relaxation law is then obtained from the asymptotic behavior of dielectric response function and relaxation function by replacing parameters in Mittag–Leffler functions with Jonscher indices.Relaxation types can be easily determined from experimental data of discharge current in barium stannate titanate after their Jonscher indices are determined.展开更多
基金This work is financially supported by the National Natural Science Foundation of China(51672159,51501105 and 51611540342).
文摘Photocatalytic degradation processes of different materials are fitted with Mittag-Leffler function and incomplete gamma function,which are response functions for Cole–Cole relaxation and Davidson–Cole relaxation.The fitting results show that both functions can fit experimental data fairly well.The order of derivative in the kinetic differential equations can be either less,or greater than one.In the case of the order of derivative is greater than one,only incomplete gamma function is reasonable for describing the photocatalytic degradation.This work further confirms the existence of the universality in photocatalytic degradation kinetics.
基金the National Natural Science Foundation of China(51672159,51501105,51611540342).
文摘Two parameters are proposed as Jonscher indices,named after A.K.Jonscher for his pioneering contribution to the universal dielectric relaxation law.Time domain universal dielectric relaxation law is then obtained from the asymptotic behavior of dielectric response function and relaxation function by replacing parameters in Mittag–Leffler functions with Jonscher indices.Relaxation types can be easily determined from experimental data of discharge current in barium stannate titanate after their Jonscher indices are determined.
