Though hydroxyapatite (HAp, Ca10(PO4)6(OH)2) is the most essential inorganic component of bones, teeth and enamel, the structural caracterization related to substituted HAp (by carbonates, silicates, Na+, ...) remains a formidable challenge. Whereas hundreds of contributions have been published in the fields of vibrational spectroscopies, X ray diffraction and solid state NMR applied to the study of substituted HAp, no clear concensus has been proposed regarding the local ionic associations in the apatitic architecture. 13C-13C/31P correlation DNP experiments allowed for the description of the carbonate associations in HAp, involving local order and obvious anionic clustering. Such clustering has been hypothesized in the past years (mainly on energetic considerations) but never demonstrated experimentally. All correlations in 13C-13C/31P experiments could be assigned safely leading to an entirely new structural model related to zig-zag chains of adjacent carbonates in the structure. For the first time, the DNP CP MAS approach was successfully extended to 43Ca in natural abundance (0.14%). 2D 1H-43Ca HETCOR experiments were obtained in 2 hours whereas months would have been necessary by using standard NMR. Most importantly, Ca surface species were clearly distinguished from the bulk as they are chelated by glycerol. In other words, the DNP juice acted here as spectroscopic spy. Moreover, successful 43Ca MAS experiment were implemented as well at ultra high magnetic field (35T) demonstrating first a net increase in sensitivity (especially for natural abundance experiments). In terms of resolution, it was demonstrated that second-order quadrupolar broadening was almost suppressed for all involved 43Ca sites at 35T. Finally, substituted HAp act as amazing model compounds for DNP calculations: the DNP effect is efficiently mediated by quasi one-dimensional proton spin diffusion (SD) through the OH- columns present in the structure. Usually, the associated spin dynamics is solved numerically using heavy time slicing methods and hindering any analytical insight in the calculations. In the second part of this contribution, an entirely novel mathematical approach will be presented, called Path-Sum. Path-Sum relies on algebraic and combinatorial properties of walks on graphs which lead to analytical solutions for spin diffusion processes, even under time-dependent forces . The whole DNP process will be revisited in the context of Path-Sum.

Hydroxyapatite revisited by DNP and spin diffusion: Natural abundance 43Ca DNP MAS and ultra high magnetic field (35T) 43Ca experiments, modeling and new mathematical treatment of dynamic nuclear polarization process

ACS Spring Meeting 2021

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