Lithuanian Journal of Physics article / Lietuvos fizikos žurnalo straipsnis

SECULAR AND SEMI-NONSECULAR MODELS OF CROSS-POLARIZATION KINETICS FOR REMOTE SPINS: AN APPLICATION FOR NANO-STRUCTURED CALCIUM HYDROXYAPATITE
Vytautas Klimavičius^a,b, Feliksas Kuliešius^a, Edvinas Orentas^b, and Vytautas Balevičius^a
^aInstitute of Chemical Physics, Vilnius University, Saulėtekio 3, 10257 Vilnius, Lithuania
^bDepartment of Organic Chemistry, Vilnius University, Naugarduko 24, 03225 Vilnius, Lithuania
Email: vytautas.balevicius@ff.vu.lt

Received 15 January 2021; revised 18 February 2021; accepted 19 February 2021

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.

Keywords: solid-state NMR, cross-polarization, spin diffusion, magic-angle spinning, calcium hydroxyapatite

SEKULIARUSIS IR PUSIAU NESEKULIARUSIS SUKINIŲ KINETIKOS MODELIAI NUTOLUSIEMS SUKINIAMS: TAIKYMAS NANOSTRUKTŪRIZUOTAM KALCIO HIDROKSIAPATITUI
Vytautas Klimavičius^a,b, Feliksas Kuliešius^a, Edvinas Orentas^b, Vytautas Balevičius^a

^aVilniaus universiteto Cheminės fizikos institutas, Vilnius, Lietuva
^bVilniaus universiteto Organinės chemijos katedra, Vilnius, Lietuva

Ištirta ¹H → ³¹P kryžminės poliarizacijos (CP) taikant magiškojo kampo sukimą (MAS) kinetika, vykstanti nanostruktūrizuotame kalcio hidroksiapatite (nano-CaHA). Matavimai atlikti kambario temperatūroje (T = 298 K) sukant bandinį 5 kHz dažniu. Šiai medžiagai yra būdingas didelis protonų mobilumas išilgai OH^–...OH^–... grandinių. Dėl šios savybės CaHA priskiriamas medžiagų klasei, vadinamajai protonų laidininkei. Eksperimentiniai CP MAS duomenys buvo apdoroti taikant sekuliarųjį ir pusiau nesekuliarųjį sukinių kinetikos modelius. Sekuliarusis apibendrintos kvantinės mechaninės Liouville’o – von Neumann’o lygties sprendinys yra išvedamas išpildant dvi asimptotines sąlygas: 1) pridėtųjų radiolaukų dažniai ω₁ yra daug didesni už dominuojantį dipolinį I–S (šiame darbe I = ¹H ir S = ³¹P) sukinių sąveikos suskilimą, t. y. ω_1I, ω_1S ≫ |b|; 2) I–S sąveikos suskilimas yra daug didesnis už sukinių difuzijos spartas (|b| ≫ R^I_df, R^I_dp). Pastaroji sąlyga yra sunkiai išpildoma tokiai nutolusių sukinių sistemai, kokia yra nano-CaHa. Kyla abejonių dėl sekuliariojo modelio taikymo. Gautieji kokybiškai identiški rezultatai byloja, kad CP MAS kinetikos gali būti aprašytos taikant tiek sekuliarųjį, tiek pusiau nesekuliarųjį sukinių kinetikos modelius, netgi tais atvejais, kai |b| ir R^I_dp yra tos pačios eilės dydžiai. Aptikta anomaliai didelė sukinių difuzijos anizotropija, kuri nepriklauso nuo taikyto modelio. Tai gali būti siejama su žemos dimensijos ¹H sukinių dinamika nano-CaHA protonų rezervuare.

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