Relaxation times of spin states of all ranks and orders of quadrupolar nuclei estimated from NMR z-spectra: Markov chain Monte Carlo analysis applied to 7Li+ and 23Na+ in stretched hydrogels

► NMR z-spectra of 7Li+ and 23Na+ in stretched hydrogels show five critical values. ► The mathematical representation of z-spectra from spin-3/2 nuclei contains nine distinct relaxation rate constants. ► Relaxation times of the various spherical tensors differ markedly. ► The Markov chain Monte Carlo (MCMC) method yielded statistically robust estimates of the parameter values. ► The approach can estimate all relaxation times under many experimental circumstances.