Cross-polarization kinetics and fractal nature of thermal equilibration in spin systems: From low-dimensional proton conductors to tripeptides

Abstract

Cross-polarization with magic-angle spinning (CP MAS) kinetics (1H–13C and 1H–31P) between remote spins were studied in a series of selected materials: from poly-(vinyl phosphonic acid) (pVPA) to calcium hydroxyapatite (CaHA), poly(2-hydroxyethyl methacrylate) (pHEMA), glycine and ultimately to tripeptides (Gly-Pro-Gly, Gly-Phe-Gly and Gly-Gly-Gly). The selection was based on the working concept that the pathways of thermal equilibration in the proton bath should be linked to the structural features of materials. Therefore we attempted to cover the maximal range of dimensionality of conceivable fractal structures as depicted in numerous literature sources. The ‘stretched exponential’ decay was involved in a purely phenomenological way to describe the thermal equilibration during the polarization transfer between remote spins. Its ‘stretching’ index allowed determining the fractal dimensions (Dp) of equilibration pathways. The spin-diffusion model improved by the thermal equilibration in the proton bath was the most appropriate to describe the experimental CP kinetics in the studied series.The fractal dimensions obtained for studied compounds are very reasonable: CaHA and pVPA behave as one-dimensional systems, whereas pHEMA and glycine are close to 2D-systems, and tripeptides can be considered as ‘almost’ 3D-systems. This rational sequence allows us to state that the developed treatment of CP kinetics with included thermal equilibration can reproduce the fractal images of complex compounds. The thermal equilibration is mainly mediated through the strongest interatomic/intramolecular vibrations. In addition to elasticity, a peculiar role of high mobility of protons along H-bonds has to be stressed.