Fractional kinetics on thermal analysis: application to lumefantrine thermal decomposition.

The fractional derivative concept to treat non-isothermal solid state thermal decomposition was employed in this work. Simulated data were compared with the exact solutions for the method validation. Calculated fractional kinetics data for four heating rates were initially considered and the Kissinger-Akahira-Sunose (KAS) method demonstrate that, although the activation energy is not retrieved, it can be useful to determine a single or multistep process. Experimental thermal decomposition data of lumefantrine heated at 5, 10 ,15, and 20 oC min- 1 were fitted for a single-step process. The kinetic parameters were retrieved for integer and fractional kinetics, considering some ideal and general models. Application of the KAS method to these data demonstrated an activation energy dependent on the conversion rate, indicating a multistep process. Five data subintervals were fitted separately using the general model with variable derivative order. It was found a process that occours with integer order derivative until α = 0.3 and fractional order for α > 0.3 with combination of simultaneous reactions, since the parameters do not correspond to any ideal model. The determined activation energies showed the same increasing behavior observed in the KAS approach. The results for multistep process presented an error 102 times smaller if compared with the best result, considering a single-step process. Therefore, the fractional kinetic model presents a powerful extension to the usual thermal data analysis.

Retrieval of transverse relaxation time distribution from spin-echo data by recurrent neural network.

Inversion of transverse relaxation time decay curve from spin-echo experiments was carried out using Hopfield neural network, to obtain the transverse relaxation time distribution. The performance of this approach was tested against simulated and experimental data. The initial guess, necessary for the integration procedure, was established as the analytical Laplace inversion. Together with errors in the simulated data, inversion was also carried out with errors in this initial guess. The probability density function, calculated by the neural network, is used in multiple sclerosis diagnostics.