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

The analysis of the NMR relaxation function for microheterogenous systems u sually starts with the decomposition of the relaxation function to discrete components, or finding a continuous distribution of the components. Severa l approaches can be applied to do this: linear least-squares fitting, non-l inear least-squares fitting or inversion of the data, based on the Laplace transformation The spin-grouping technique-a correlated analysis of the spi n-lattice relaxation function (recovery or decay) and spin-spin relaxation decay (free induction decay or Carr-Purcell decay)-usually enables a decomp osition of relaxation data into a proper set of discrete components. In our paper, we present CracSpin, a program for one and/or two-dimensional analy sis of the relaxation function in the time domain. It uses Marquardt's algo rithm for non-linear least-squares fitting. The results of analyses of simu lated data containing discrete as well as continuous distributions of the c omponents are shown. CracSpin resolves the components of FID even if the ra tio of their relaxation times is as small as 2, for comparable component ma gnitudes (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 sim ilar to 3, the decomposition is satisfactory for S/N > 10, even for a compo nent 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 decomposi tion, for composed decays or in the case of close values of the relaxation time of the components. The representative examples of the analysis, starti ng from spin-lattice relaxation curves, as well as from spin-spin relaxatio n curves, are presented and discussed.