The structural characterization of bitumen system by Prony-like method applied to NMR and Rheological relaxation data

In order to characterize colloidal structures the T2-Nuclear Magnetic Resonance (NMR) and rheological relaxation times are used. NMR Car-Purcell sequence and mechanical stress relaxation experiments have been performed on a bitumen system at different temperatures. The rheological relaxation times spectra are finger prints of the structures present in the system. These typical relaxation times have been obtained from an exponential fitting of the experimental data, based on a Prony-like method. The unknown parameters are estimated on the base of a linear regression equation which uses altered signals obtained directly from the NMR and rheological measurements. The approach uses the derivative method in the frequency domain yielding exact formula in terms of multiple integrals of the signal, when placed in the time domain. These integrals are explicitly solved by projecting signal on some set of orthogonal basis functions or, more in general, by using a polynomial that its data in the least-squares sense. The method is able to deal with the case of non-uniform sampled signal.