Secular and semi-nonsecular models of cross-polarization kinetics for remote spins: an application for nano-structured calcium hydroxyapatite

Abstract

The 1H → 31P cross-polarization (CP) kinetics in the nanostructured calcium hydroxyapatite (nano-CaHA) was measured under moderate (5 kHz) magic-angle spinning (MAS) rate. This material was chosen as it contains the distanced 1H–31P spin pairs and the interactions between them are characterized by a relatively low dipolar coupling (b) that could be comparable with the spin-diffusion rates (R). Therefore, the physical legitimacy to use the secular solution of the quantum Liouville–von Neumann equation is doubtful. The semi-nonsecular model of spin dynamics was applied, and the results were compared with those obtained by the secular approach. The comparable results obtained by both models show that the secular model is applicable, with certain reservation, also in the case of |b| ≈ R. The extremely high anisotropy of spin diffusion in the nano-CaHA was deduced. This can be a matter of the applied approach, as the interactions of the 31P spins with the proton bath were neglected in both models. The high anisotropy could also be caused by the physical reasons that stem from the structural and proton diffusion features of CaHA. This material belongs to low-dimensional proton conductors possessing a large motional freedom for protons along OH– chains.

Solid-State NMR and Impedance Spectroscopy Study of Spin Dynamics in Proton-Conducting Polymers: An Application of Anisotropic Relaxing Model

“…To avoid the effects of spin–lattice relaxation in the rotating frame, the 1 H → 31 P CP MAS kinetics has been measured for the nanostructured calcium hydroxyapatite and the seminonsecular model 27 has been applied. 38 The results have been compared with those obtained by the secular approach ( eq 1 ). It was concluded that the secular model can be used with certain reservations also in the case | b | ≈ R I dp .…”

“…However, it was derived for nonrelaxing spin systems ( T I 1ρ , T S 1ρ → ∞). To avoid the effects of spin–lattice relaxation in the rotating frame, the 1 H → 31 P CP MAS kinetics has been measured for the nanostructured calcium hydroxyapatite and the seminonsecular model has been applied . The results have been compared with those obtained by the secular approach (eq ).…”

Step-by-step from amorphous phosphate to nano-structured calcium hydroxyapatite: monitoring by solid-state 1H and 31P NMR and spin dynamics

“…As distinct from AMP, the CP MAS kinetics in nano-CaHA measured at the 5 kHz MAS rate pointed towards an extremely high anisotropy of spin-diffusion process in this system. 41 It even looks like the Ising-type interaction ( R I df = R S df = 0) should be dominant. However, from the practice, the CP MAS experiments with HH sideband matching are rather sensitive to radiofrequency (RF) field inhomogeneity.…”

Solid-state NMR study of spin dynamics and local disorder in smart polymers: PDMAEMA

“…In the present work, the angular averaging (Eq. ( 3)) was carried out analytically using the series of Bessel J n functions [29,30].…”