The role of nanoparticle structure and morphology in the dissolution kinetics and nutrient release of nitrate-doped calcium phosphate nanofertilizers

Bio-inspired synthetic calcium phosphate (CaP) nanoparticles (NPs), mimicking the mineral component of bone and teeth, are emergent materials for sustainable applications in agriculture. These sparingly soluble salts show self-inhibiting dissolution processes in undersaturated aqueous media, the control at the molecular and nanoscale levels of which is not fully elucidated. Understanding the mechanisms of particle dissolution is highly relevant to the efficient delivery of macronutrients to the plants and crucial for developing a valuable synthesis-by-design approach. It has also implications in bone (de)mineralization processes. Herein, we shed light on the role of size, morphology and crystallinity in the dissolution behaviour of CaP NPs and on their nitrate doping for potential use as (P,N)-nanofertilizers. Spherical fully amorphous NPs and apatite-amorphous nanoplatelets (NPLs) in a core-crown arrangement are studied by combining forefront Small-Angle and Wide-Angle X-ray Total Scattering (SAXS and WAXTS) analyses. Ca2+ ion release rates differ for spherical NPs and NPLs demonstrating that morphology plays an active role in directing the dissolution kinetics. Amorphous NPs manifest a rapid loss of nitrates governed by surface-chemistry. NPLs show much slower release, paralleling that of Ca2+ ions, that supports both detectable nitrate incorporation in the apatite structure and dissolution from the core basal faces.


SAXS data analysis
The scattered intensity is given as a function of the modulus of the scattering vector: where λ is the wavelength of the incident radiation and 2 is the scattering angle. Conventional SAXS analysis was done as a first step. The intensity is expressed as where the form factor 〈 ( )〉 is related to the average size and the shape of the particles, and the structure factor S(q) is related to concentration and/or aggregation effects. 1 The form factor was taken as that of circular thin discs with a radius R and a thickness T, which for monodisperse and particles with large anisotropy can be written as: ( ) = 2 ( ) 3 (1 − 8 (2 )) 9 sin( /2) /2 9 3 where 8 (x) is the Bessel function of first kind and first order. Polydispersity of the thickness T was included using a Zimm-Schulz distribution, which allows an analytical result to be obtained: 2 〈 ( )〉 = 2 ( ) 3 =1 − 8 (2 )> ? 2 3 3 (1 + )(2 + ) C ?1 − cos((1 + ) Atan( / ))) (1 + 3 / 3 ) (8IJ)/3 C with = 1/ 3 − 1, where is the relative standard deviation of the distribution and = ( + 1)/ and T is now the number average thickness. In order to get good fits at the low Q values, concentration effects had to be considered and this was done using a random-phase approximation structure factor: 3 ( ) = 1 1 + n 〈 ( )〉 where n is an increasing function of the concentration. The model could describe the SAXS data for the nAp and N0.2-nAp samples satisfactory, however, the N0.3-nAp sample could not be described by this model and it was necessary to include an additional population of thinner platelets jointly to a thicker one, resulting in a bimodal distribution of platelets. The ACP and N0.3-ACP samples have a SAXS intensity with a Q dependence, which is quite different from that of the nAp, N0.2-nAp, and N0.3-nAp, with a much steeper Q dependence, and a different model had to be used. A model for polydisperse spheres was able to fit the data at high Q, however, due to aggregation and clustering, an additional empirical cluster structure factor was used: 3 Here TU = , TU , h TU > is the hard-sphere structure factor 4 that depends on an effective hard-sphere interaction radius TU and an effective hard-sphere volume fraction h TU , and describes correlations of the particles within the cluster. The last term describes the overall cluster and is taken as the Debye-Bueche expression 5 with a scale factor A in front. The parameter x is related to the overall size of the clusters.
Optimization of the scales, a background, and the structural parameters in the models was done using leastsquares methods and the error bars on the parameters were obtained as in ref. 1. Average sizes and size dispersions and other parameters or quantities derived by these models are given in Table S3.

SAXS and WAXTS data analysis by the Debye scattering equation (DSE) method
The DSE modelling of CaP nanomaterials here investigated was carried out using the DebUsSy Suite through subsequent steps, following a bottom-up approach. At first, for each sample, the hydroxyapatite cell parameters (a = b and c) were determined through the Rietveld refinement method implemented in the MAUD software, 6 using a spherical harmonics model 7 to phenomenologically describe the finite-size broadening of diffraction peaks. The hydroxyapatite unit cell, with adjusted cell parameters, was then used as a building block to generate populations of atomistic models of nanocrystals of increasing size. Nanocrystals were modelled according to a prismatic shape considering two perpendicular (independent) growth directions, one along the c axis and one in the ab plane. By varying the b/a ratio from 1 to 8, the nanocrystals shape can be modelled as an elongated prism (when a = b), resembling the hexagonal morphology proper of the hydroxyapatite structure, or as a platelet, progressively wider by increasing the b/a ratio, breaking the hexagonal crystal symmetry as observed in bone or biomimetic apatite samples. For each nanocrystal, sampled interatomic distances were computed and stored in a database used to simulate the diffraction pattern through the Debye equation. A sampling algorithm of the true distances is adopted, thus reducing by order of magnitude the number of terms in the Debye equation without losing accuracy in the calculated pattern; this makes the analysis through the Debye equation affordable in terms of computational time. The simulated scattering patterns were calculated (within a non-interfering particle model approximation) in the SAXS and WAXTS regions using the same (morphological) databases, then compared to the experimental ones. The difference between measured and calculated patterns were minimized by refining a number of adjustable structural and microstructural parameters in the model using the Simplex algorithm. In particular, platelets with optimized b/a ratio equal to 7 were used to model SAXS data of nAp, N0.2-nAp and N0.3-nAp. The lowest Q region (more influenced by aggregation effects) was removed from the DSE fitting (Fig.  S4). The nanoplates size distribution was described by a bivariate lognormal function, for which the average size and associated standard deviation for the two independent growth directions (Dab, equivalent diameter of the area in the ab plane, and length along the c axis) were refined. The thickness of the platelets is retrieved from the Dab values, at known b/a ratio. Due to the limited content of information of SAXS data, the model of platelets with adjustable width, length and their dispersions is beyond the capability of SAXS modelling. However, extensive tests (presented elsewhere jointly to many additional technical details, which are out of the scope of this work 8 ) suggested that the thickness remains a reliable estimate (as also demonstrated by the matching with the conventional analysis) and that SAXS analysis may benefit from reasonable restrains taken from WAXTS analysis. For the WAXTS model, platelets with optimized b/a ratio equal to 6 (nAp) or 5 (N0.2-nAp, N0.3-nAp) were used. The nanocrystals size distribution was described by a bivariate lognormal function, for which the average size and standard deviation in the ab plane and the pairs associated to the nanocrystal length along the c axis were relaxed. Average sizes and size dispersions and other parameters or quantities derived by the WAXTS-DSE modelling are given in Table 1 of the main text (number-based values) and Table S4 (mass-based values). The site occupancy factors of the two Ca atoms and the isotropic Debye-Waller factor of all atoms were also refined (Table S4). For the WAXTS analysis, the atomistic models of platelets were suitably managed to obtain additional peak broadening due to anisotropic lattice strain, as detailed in the next paragraph. 8

Lattice strain model
An isotropic lattice strain was modelled through a phenomenological approach, 9 by convoluting the DSE sample pattern with a Gaussian function of width 4e tanq, where e = Δr/r is the adimensional (adjustable) parameter measuring the radial expansion/contraction of r around its average value. This model did not provide satisfactory matching with the experimental data. An anisotropic strain model was introduced at the atomistic level, as much as described in ref. 10 Two different (elastic) strain tensors were considered: (1) a strain tensor accounting for two independent components, εa=Δa/a (ε11 in matrix notation) and εc=Δc/c (ε33), along the a and c lattice parameters, in line with the hexagonal crystal symmetry of apatite, for which εb = εa and all the off-diagonal terms of the strain tensor vanishing; 11 (2) a strain tensor accounting for three independent components, εa=Δa/a (ε11), εb=Δb/b (ε22) and εc=Δc/c (ε33), along a, b and c lattice parameters, in line with the morphological symmetry of platelets (breaking the structural one). Accordingly, an additional (not vanishing) off-diagonal term of the strain tensor (ε13 = ε31) would have been considered but it was neglected being typically smaller than the diagonal terms. The lattice parameters were assumed (in both models) to be distributed about their average values according to a Gaussian function of width Δx, properly binned in order to avoid undesired effects on the DSE simulation, due to a coarse binning; limiting the computational time was also an important issue, leading to the choice of 30 bins as the best compromise. Accordingly, for each Dab, Lc nanocrystal size combination of the bivariate population, 30 atomistic models were managed and combined into a single set of pseudo-multiplicities vs equi-spaced pair distances, according to the algorithm implemented in the Debussy Suite for speeding up calculation by applying a Gaussian sampling of interatomic distances. A grid search algorithm exploring the GOF statistical value (matching the agreement between simulated and experimental patterns) while varying the strain parameters (with a 0.05% sampling step) was applied to find the best strain model. The model 2, accounting for doping-induced effects driven by both structural and morphological influences, provided the best agreement; the εa, εb and εc values are reported in Table S4 for all nanocomposites.

Saturation index
Whether, during our dissolution experiments, saturation conditions are approached, or reached, it was calculated by comparing the actual (measured) [Ca2+] concentration, with the maximum solubility calculated at equilibrium. Taking the apatite formulation as Ca5(PO4)3(OH), and the thermodynamic constants defined below, it is possible to demonstrate that in the 5 < pH < 8 range, the maximum concentration of calcium obtained by apatite dissolution in saturated conditions is:  Fig. S1. Lab X-ray powder diffractograms of biomimetic CaP nanoparticles. The patterns of ACP and N0.3-ACP (yellow and orange curves, respectively) confirm the amorphous nature of the materials. On the other hand, XRPD data of nAp and Nx-nAp materials show the typical diffraction pattern of nanosized hydroxyapatite. The absence of reflections due to other crystalline phases confirms the purity of all materials.  16 suggest the presence of carbonate ions admixed with the ACP material. On the other hand, the analysis of nanocomposite materials (green, purple, turquoise and pink curves) shows several PO4 3bands typical of apatite: strong absorption bands in the 1100 to 1000 cm -1 region, associated to the antisymmetric ν3(PO4) stretching (blue diamonds), and in the 650 to 550 cm -1 one, for antisymmetric ν4(PO4) bending (blue stars). 15 Additional bands, associated to CO3 2vibrational modes, 17 can be identified at ~ 1485 cm -1 and ~ 1425 cm -1 [ν3(CO3)] and at ~ 871 cm -1 [ν2(CO3)] (blue squares), indicating the partial substitution of PO4 3by carbonate ions in the apatite crystal lattice, with very minor OHgroups replacement. 18 These results are well in agreement with the experimental observations showing that carbonate is the major substituent in biological apatite and confirm that biomimetic CaP are obtained. 19 Additionally, the presence of nitrate ions in the isolated nitrate-doped nanomaterials, namely N0.3-ACP and Nx-nAp, is confirmed by the presence of the sharp (though weak) IR band associated to the ν3NO3 asymmetric stretching falling at 1384 cm -1 (grey triangles). 20   Table 1 of the main text and Table S4.   Table S3. Number-based average thickness (T) and diameter (D) of Nx-nAp and ACP samples provided by classical SAXS analysis using a finite disk-shape and a spherical model, respectively. The relative thickness dispersion (σT/T) of disc was modeled using a Zimm-Schultz distribution function, whereas the disc diameters were assumed to be monodisperse by fixing σD/D = 0.