Two-dimensional analysis of the nuclear relaxation function in the time domain: the program CracSpin

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Abstract
The analysis of the NMR relaxation function for microheterogenous systems usually starts with the decomposition of the relaxation function to discrete components, or finding a continuous distribution of the components. Several approaches can be applied to do this: linear least-squares fitting, non-linear least-squares fitting or inversion of the data, based on the Laplace transformation. The spin-grouping technique - a correlated analysis of the spin-lattice relaxation function (recovery or decay) and spin-spin relaxation decay (free induction decay or Carr-Purcell decay) - usually enables a decomposition of relaxation data into a proper set of discrete components. In our paper, we present CracSpin, a program for one and/or two-dimensional analysis of the relaxation function in the time domain. It uses Marquardt's algorithm for non-linear least-squares fitting. The results of analyses of simulated data containing discrete as well as continuous distributions of the components are shown. CracSpin resolves the components of FID even if the ratio of their relaxation times is as small as 2, for comparable component magnitudes (at least about 10% of total signal) and for signal-to-noise ratio (S/N) >100. If the ratio of component relaxation times is higher than ~3, the decomposition is satisfactory for S/N >10, even for a component magnitude of about 1%. The noise level is defined here as equal to the three standard deviations of the normal distribution. The two-dimensional analysis significantly improves the quality of the multicomponent decomposition, for composed decays or in the case of close values of the relaxation time of the components. The representative examples of the analysis, starting from spin-lattice relaxation curves, as well as from spin-spin relaxation curves, are presented and discussed.

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