Structural characterization of bitumen system by Prony-like method applied to NMR and rheological relaxation data

In order to characterize colloidal structures, T2-nuclear magnetic resonance (NMR) and rheological relaxation times are used. NMR CarPurcell sequence and mechanical stress relaxation experiments have been performed on a bitumen system at different temperatures. The rheological relaxation times spectra are fingerprints of the aggregates that constitute 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 basis of a linear regression equation that uses altered signals obtained directly from the NMR and rheological measurements. This 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 fits data in the least-squares sense. The method is able to deal with the case of nonuniform sampled signal.