Subnanoscale Order and Spin Diffusion in Complex Solids through

Jan 18, 2016 - blurring phenomenon, and to determine the spin distribution at the short- and moderate internuclear distances. The contribution of the...
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Subnanoscale Order and Spin Diffusion in Complex Solids through the Processing of Cross-Polarization Kinetics Vytautas Klimavicius,† Laurynas Dagys,† and Vytautas Balevicius*,† †

Department of General Physics and Spectroscopy, Vilnius University, Sauletekio 9-3, LT-10222 Vilnius, Lithuania ABSTRACT: The advanced strategy of processing of NMR crosspolarization (CP) data has been developed separating the short-range order- and the bulk effects in the manifold of spin interactions. The effectiveness of such treatment have been demonstrated on 1H−31P CP kinetics in the nanostructured calcium hydroxyapatite (nano-CaHA) and that containing amorphous phosphate phase (amorph-CaHA). This allowed to describe the oscillatory manner of CP kinetics, oscillation blurring phenomenon, and to determine the spin distribution at the short- and moderate internuclear distances. The contribution of the dipolar coupling with remote spins has been removed modeling their spatial distribution using a set of radial profiles. The short 31P−1H contact peak at 0.24−0.27 nm has been well resolved in the spatial distribution profile of the nano-CaHA sample and it is hardly noticeable in the case of amorph-CaHA. It reflects the differences in surface organization in nanostructured and amorphous materials. The spin diffusion processes in both systems are practically unaffected upon MAS. The MAS decimates 31P interactions with the protons on the surface layers and with the remote protons (>0.5 nm) that are plausibly involved in the H-bond network.

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INTRODUCTION Calcium phosphate compounds, especially hydroxyapatite (Ca10(PO4)6(OH)2, further CaHA), play an important role in many areas of innovative medical science.1−3 They have found numerous applications in implantology, orthopedic, and periodontal surgery. Some of these compounds show close similarity to the mineral of hard tissues (bone, enamel, dentin, and so forth) and therefore have high biocompatibility with them.3 It is necessary to note that these and other related synthetic materials are in the high scientific interest for a long time not only because of their importance in biological and medical applications but also because mimicking their properties could provide advanced functional materials having excellent strength, flexibility, resistivity, and other desirable macroscopic features.4 Among a broad variety of physical characterization techniques, solid-state NMR spectroscopy can be considered as the method that provides probably the most insightful view of the structure and dynamics on the molecular and nanoscopic length scales. Therefore, NMR magic-angle spinning (MAS), cross-polarization (CP) kinetics, heteronuclear correlation (HETCOR), and so forth experiments have been widely exploited in the studies of calcium phosphates and related systems.5−10 In addition, some recent works on 1H and 31P spin−lattice and spin−spin relaxation times measurements and the effect of variable MAS rate on the 31P signal shape,11 phosphate-ion distribution by employing 31P multiple-quantum coherence,12 ultrahigh speed MAS13,14 and NMR crystallography15 have to be noted as very advanced and promising. The growing interest in the area called as “NMR crystallography” © XXXX American Chemical Society

was noted in ref 15. This term is given to the combined application of solid-state NMR and, X-ray diffraction techniques as well as high level calculations to obtain the structural information that would be difficult or even impossible to get using any of these methods in isolation.15,16 However, characterizing the distribution of various chemical species in complex materials, like amorphous, highly heterogeneous, or soft and partially disordered solids over a nanometer scale is an extremely challenging task, where the most traditionally used diffraction or microscopy methods do not provide detailed or enough rigorous information. A variable contact time crosspolarization technique can be very effective complementary tool solving this problem. Cross-polarization (CP) is a solid-state NMR technique originally developed for enhancing the peak intensities of rare nuclei by the polarization transfer from abundant nuclei, typically from protons.17−19 CP is also feasible between abundant nuclei. The signal enhancement in such case is ineffective. Sometimes the signals can be even weaker than those obtained from a conventional single pulse-acquire Blochdecay (BD) experiments. However, the CP technique between abundant nuclei is very useful extracting the unique information on the structure and dynamics of complex materials through the analysis of the time (contact time) evolution of communication between the subsystems of interacting spins. The processing of such CP kinetic data provides the rates of Received: December 1, 2015 Revised: January 18, 2016

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Figure 1. SEM micrographs of nano-CaHA (commercial, from Aldrich) at various zooming.

(amorph-CaHA) has been derived using the sol−gel synthesis route. The steps and conditions are detailed in ref 22. The materials were characterized by scanning electron microscopy (SEM) and energy-dispersive X-ray analysis (EDX) using a Helios NanoLab 650 scanning electron microscope coupled with energy-dispersive X-ray spectrometry system. SEM micrographs of nano-CaHA are given in Figure 1; for amorph-CaHA, see ref 22.

spin-diffusion and spin−lattice relaxation in rotating frame, the dipolar coupling constants, as well as some other parameters accounting for the effective compositions of spin clusters and the information on the spatial distribution of interacting spins (orientations and internuclear distances).18−21 All these can elucidate very fine aspects of structural organization and dynamics therein. However, the complexity of the system complicates the extraction of desired information. In the existing literature, plenty of incorrectly performed variable contact time CP experiments are present, like insufficient number of points, especially for very short contact times, and exploitation of classical CP transfer models, which look in many cases to be nonadequate. In order to reveal the differences between nanostructured and amorphous materials in various length scales, two calcium hydroxyapatites of corresponding structure have been chosen and studied applying CP and CP MAS techniques. The purposes of the present work were (i) the high data point density measurements of 1H−31P cross-polarization kinetics that would make a rigorous approval of the theoretical models and more fitting parameters could be used and determined unambiguously; (ii) to create the advanced processing of CP kinetic data to explain various degrees of oscillation blurring separating dynamic (spin diffusion, relaxation) and spatial effects in the subnanoscale and in the bulk; and (iii) to obtain novel information concerning the physical origin of the effect of MAS on CP transfer and spin coupling in nanostructured systems.

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RESULTS AND DISCUSSION Thanks to the proper instrumental setting, high data point density measurements of 1H →31P CP kinetics have been carried out for amorph-CaHA and nano-CaHA. Each experimental curve contains up to 500 equidistance points over the whole contact time range of 50 μs to 10 ms (see Figures 2−4). Such high data point density reduces the excess

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EXPERIMENTAL SECTION NMR Measurements. NMR measurements were carried out on Bruker AVANCE III HD spectrometer operating at resonance frequencies of 400 and 162 MHz for 1H and 31P, respectively, at 298 K. MAS measurements for 1H−31P CP were performed at 5/9 kHz. A rectangular variable contact time pulse shape was used in CP MAS experiments in order to fulfill one of Hartmann−Hahn matching conditions. Supplementary static NMR experiments were performed. NMR spectra were processed using Topsin 3.2 software. The signal shapes and CP kinetic curves were processed using Microcal Origin 9 and Mathcad 15 packages. Materials. Two CaHA having different morphological features were selected for the present study. The nanostructured CaHA (further - nano-CaHA) was used from Aldrich, synthetic, 99.999%, from metal basis. Calcium hydroxyapatite containing amorphous phosphate phase

Figure 2. 1H →31P CP kinetics (integrated signal intensity versus variable contact time) in the static nano-CaHA sample. The fitting was carried out using eq 4 taking P(b/2) to be Gauss, Lorentz, and Radial functions and using T2-averaging (eq 6). The fit parameters are given in Table 1. More comments in the text.

degrees of freedom in the nonlinear curve fitting procedure targeting its flow toward the “true” (i.e., “deepest”) minimum on the multiparameter surface χ2, that is, the sum of weighted squares of deviations of the chosen theoretical model curve from the experimental points. It makes possible more rigorous decision concerning the validity of the hypothetic models and more fitting parameters can be used and determined unambiguously. B

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mimicking the energy exchange between a pair of coupled pendelums.19 The oscillations are damped by the subsequent spin-diffusion. Going from isolated spin pairs in single crystals to the soft and disordered solids another factor that contributes the oscillation blurring and acts beside the spin-diffusion has to be taken into account. Namely, in order to apply eq 1 to the CP kinetic data for complex solids it has to be averaged over the whole distribution of dipolar splitting b that depends on the spatial parameters (internuclear distance (r) and orientation in the magnetic field (θ)): b=

2 μ0 γγ ℏ (1 − 3 cos2 θ) I S (1 − 3 cos θ ) = DIS 3 4π r 2 2

(2)

where DIS is the dipolar coupling constant. The averaging of cos(2πbt/2) is performed summing its values weighted by the fraction of spin pairs with a set of spatial parameters that corresponds to the oscillation frequency bi/2

Figure 3. 1H →31P CP kinetics in static amorph-CaHA. The fitting was carried out using various spin coupling distribution profiles. The fit parameters are presented in Table 1.

⎛ 2πbt ⎞ ⎟ = cos⎜ ⎝ 2 ⎠

⎛ bi ⎞ ⎛ 2πbit ⎞ ⎟ ⎟cos⎜ 2⎠ ⎝ 2 ⎠

∑ P⎜⎝ i

(3)

where the normalized spin coupling distribution profile P(b/2) is introduced. Its shape for disordered solids is complex. P(b/2) can be considered as the envelope of the superposition of Pake singularities from the pairs of spins having different internuclear distances. Symbolically it is pictured in Figure 5.

Figure 4. 1H →31P CP MAS (9 kHz) kinetics in nano-CaHA. The fitting was carried out using various spin coupling distribution profiles. The fit parameters are presented in Table 1.

The CP kinetics observed in the nano-CaHA exhibit the blurred oscillation of intensity in the short contact time range (Figure 2), whereas it is completely lost in amorph-CaHA (Figure 3). In order to describe this phenomenon, let us start with 1H →13C CP experiments in stationary single crystals,23,24 where the oscillations of CP intensity have been observed for the first time. There it was deduced that the frequency of oscillation depends on the orientation of the crystal in the external magnetic field and it is equal to one-half of the dipolar splitting. The CP kinetics for an isolated pair of spins 1/2 can described by the equation23 ⎡ ⎛ b ⎞⎤ 1 1 I(t ) = I0e−t / T1ρ⎢1 − e−t / Tdif − e−3t /2Tdif cos⎜2π t ⎟⎥ ⎝ 2 ⎠⎦ ⎣ 2 2

Figure 5. Dipolar splitting and spin coupling distribution profile P(b/2) for disordered solids. The “fine” structure of P(b/2), if such is resolved, corresponds to the “edges” of Pake-like doublets.

The shape of P(b/2) is in generally unknown. Moreover, it is different at various length scales. However, the blurring of CP signal oscillations due to the increase of structural disorder and spin-diffusion rate can be demonstrated roughly taking P(b/2) to be Gauss function G ∼ exp(−(b − b0)2/2w2). This choice can be supported by the fact that the 31P NMR signals were found being in many cases Gauss- or Voigt-shaped with dominant Gauss contribution.11,22 The width parameter (w) reflects the extent of the overall spin coupling distribution and the relaxation rates. The results of simulation are shown in Figure 6. The observed evolution of I(t) upon changing Tdif and w means that the information about the dynamic features (spin diffusion and relaxation) as well as about the structural organization can be obtained by the proper processing of the experimental CP kinetic curves. Before starting to process the experimental data some modifications of eq 1 are necessary. It is rewritten carrying on the averaging over spin coupling distribution

(1)

where T1ρ is the spin−lattice relaxation time in the rotating frame, Tdif is the spin-diffusion time constant, and b is the dipolar splitting (in Hz). Later on, eq1 was modified introducing a more general thermodynamic model that includes a set of relaxation and spin diffusion rates.25 However, those complex formulas return to eq1 in the case of slowly relaxing rare spins S and fast isotropic diffusion of spins I (protons). Some more details on it are given in ref 19. Hence, eq 1 is a basic one to describe the oscillating magnetization in the frame of so-called nonclassical I−I*−S model, where the asterisk denotes protons in close neighborhood to S spins (31P in the present case). According to this model the I*−S spin pairs or clusters exchange polarization in an oscillatory manner C

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relation fwhm·T2= 0.355.22 This is very close to the exact value 0.375 for the “true” Gauss function. The experimental kinetic curves (Figures 2−4) were processed applying eqs 4 and 6. The spin coupling distribution profile P(b/2) that is necessary to eq 4 was modeled by various simple functions. The radial distribution function approach has been developed for this purpose. It is based on some ideas of atomic distribution functions developed to describe disordered (polycrystalline and amorphous) systems.28 Namely, the atomic radial distribution function g(r) contains several sharp peaks close to r = 0 that correspond to the first- and the second coordination shells (Figure 7). The number of atoms in the

Figure 6. Oscillation blurring in CP kinetics upon increase of structural disorder and spin-diffusion rate. The averaged intensity I(t) (eq 1) is shown by bold line in each graphs. The spin coupling distribution profile P(b/2) was modeled using Gauss function centered at b0 = 1800 Hz and T1ρ → ∞ in all cases. ⎡ I(t ) = I0e−t / T1ρ⎢1 − λe−t / Tdif − (1 − λ)e−3t /2Tdif ⎢⎣

⎛ bi ⎞ ⎛ 2πbit ⎞⎤ ⎟cos⎜ ⎟⎥ 2 ⎠ ⎝ 2 ⎠⎥⎦

∑ P⎜⎝ i

(4)

where the parameter λ is introduced. It describes the distribution of polarization in the 31P−(1H)n spin cluster during the initial stage of CP and depends on the cluster composition (λ = 1/(n + 1) for a rigid lattice) as well as molecular motion.9,18,19 Thus, λ values must be refined for each system during the fitting of the model curve to the experimental data set. Equation 4 can be essentially simplified replacing the averaging part by Gauss decay ⎛ t2 ⎞ ⎛ bi ⎞ ⎛ 2πbit ⎞ ⎟ ≅ exp⎜ − 2 ⎟ ⎟cos⎜ 2⎠ ⎝ 2 ⎠ ⎝ 2T2 ⎠

∑ P⎜⎝ i

Figure 7. Radial distribution function approach. The optimal step for discrete treatment h and the spin coupling extent (from bSC to bmax) were determined in each cases adjusting them during the curve fitting routine (see Table 1).

(5)

Originally, this formula was derived in ref 26 using the series expansion of cosines and, according to the assumptions made there, it should be valid for very short contact times. Later on it has been shown22 that in the case where P(b/2) is Gaussshaped function or close to it, then eq 5 must be valid without any limitation in time. Hence, eq 4 can be simplified as I(t ) = I0e−t / T1ρ[1 − λe−t / Tdif − (1 − λ)e−3t /2Tdif e−t

2

/2T22

]

spherical shell having the radius r and the thickness dr is proportional to 4πg(r)r2dr. In order to apply it to constructing the spin coupling distribution profile, the number of atoms have to be considered as the number of spins I concentrated in the sphere shell surround the spin S, that is, NI(r) ∼ 4πg(r)r2dr. The profile P(b) is then proportional to NI, expressed as the function of the dipolar splitting b. It is well-known (eq 3) that b ∼ 1/r3. On the other hand, g(r) → 1 if r → ∞. Hence, asymptotically NI(r) ∼ r2. Then the shape of spin coupling distribution can be approximated by the radial distribution R(b) ∼ b− 2/3 that should work well in the far range, that is, at low b values (Figure 7). Beside this, more “traditional” Gauss (G(b) ̂ ̂ ∼ exp(− (b/w)2)) and Lorentz (L(b) ∼ 1/(1 + (b/w)2)) profiles as well as T2 averaging (eq 6) were probed processing CP kinetic curves in addition. The perfect global fit (the fit over the all experimental points) was achieved in all cases (R2 ∼ 0.993−0.999 and (χ2̅)1/2/Imax ∼ 0.3−1.6%, see Table 1), independently on the spin coupling distribution profile was used. However, the problem is in the details; no one of the used profiles can reproduce the run of CP in the range of short contact time 0−2 ms (see Figure 2, the same was also revealed in the next

(6)

where T2 is the time constant of Gauss decay (eq 5). This equation is perhaps the most often used for the processing of experimental CP kinetic data in the cases where it was deduced that the nonclassical I−I*−S model19,25 was to be more appropriate, compared to the classical one (I−S model),19,27 see, for example, refs 9, 14, 18, and 22. The time constant T2 characterizes the dipolar 31P−1H coupling. T2 value should be approximately equal to the 31P spin−spin relaxation time at very long contact time. And indeed, for the static samples the full widths at half-maximum (fwhm) obtained by the fitting of 31 P signal shape after CSA contribution is removed, that is, the case in which the signal shape is determined mainly by the dipole−dipole interactions, and T2 values, which follow from the processing of CP kinetic curves, obey the “uncertainty” D

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The Journal of Physical Chemistry C Table 1. Fit Parameters of CP Kinetic Curves Presented in Figures 2−4 Nano-CaHA static sample P(b) ⇒ I0, au λ ± 0.01 Tdif, ms ±0.2 T1ρ, s b0, Hz w, Hz T2, ms bmax, Hz bSC, Hz R2 χ2̅/Imax, %

R 0.39 2.2

G

MAS, 9 kHz L

T2averag

1.000 ± 0.003 0.30 0.39 2.6 2.2 ∞ 0 320 1920 1290

0.33 2.5

R 0.61 2.1

G

I0, au λ ± 0.01 Tdif, ms ±0.2 T1ρ, s ± 0.001 b0, Hz w, Hz T2, ms bmax, Hz bSC, Hz R2 χ2̅/Imax, %

T2averag

0.24 3500 330 0.998 0.7

0.998 1.4

R

G

0.994 0.7

0.998 0.8 Amorph-CaHA

0.994 1.6

0.995 1.5

T2averag

(8.47 ± 0.03) × 10 0.64 0.65 1.4 1.4 0.015 0 0 4600 2500

R

G

L

0.999 0.5

T2averag

(2.07 ± 0.02) × 10 0.73 0.75 0.9 0.9 0.011 0 0 2500 1400

11

0.69 1.4

0.8 0.9

0.12 7600 470 0.999 0.7

0.992 2.0

MAS, 5 kHz L 11

0.69 1.3

0.47 3.2

0.28 2200 740 0.993 1.8

static sample P(b) ⇒

L

(1.08 ± 0.02) × 1010 0.60 0.60 2.2 2.2 ∞ 800 885 850 590

0.999 0.6

0.999 0.7

0.70 1.0

0.34 2400 540 1 0.4

1 0.3

1 0.3

1 0.3

Figure 8. Spin coupling distribution profiles P(b/2), spatial distributions of protons surround 31P nuclei in nano- and amorph-CaHA, and the MAS effect. In the cases of CP MAS, DIS were rescaled (see comment in text).

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The Journal of Physical Chemistry C figures). It means that the information concerning the shortrange order structure (first and second coordination shells, Figure 7) is lost if any of R, G, and L profiles or the overall T2 averaging (eq 6) are applied. This becomes particularly obvious in the case of the radial distribution function R(b) ∼ b− 2/3 that was derived taking g(r) → 1, r → ∞. The steepness of R, G, and L are similar at b → 0, that is, moving to the far range. Therefore, it was not surprising that for each studied system the values of “bulk” parameters (I0, λ, Tdif, and T1ρ) that were determined by the global fitting are practically the same (Table 1). The challenge to recover the lost information pushes the idea to reconstruct the strategy of the processing of CP kinetic curves in the opposite direction to determine the true P(b/2) that should allow to reproduce the distribution of interacting spins at the short- and moderate internuclear distances. The precise information about the spatial distribution of interacting spins (protons surround 31P for the present systems) can be extracted from this true dipole coupling distribution profile P(b/2) by the reverse recalculation from b-variable to the distances (r). If “edges” of Pake-like doublets (Figure 5) are valid |(1−3 cos2 θ)/2| → 1, then b is equal to the dipolar coupling constant DIS (eq 2). In the cases where CP MAS was applied, the dipolar coupling constants DIS were rescaled depending on which of the Hartmann−Hahn sideband matching conditions (ωII − ωIS = nωMAS) were fulfilled, that is, by a factor of √2 for n = ±1 and by 2 for n = ±2.29−31 One of the possibilities to reproduce the CP oscillations and at the same to describe the kinetic curves over a wide range of contact time was given in ref 22. This was succeeded in a rather artificial way by using a truncated (cutoff) Gauss profile. The nice fit with the experiment was achieved because of higher flexibility of the model, that is, more adjustable parameters were used. However, this function does not reflect the true profile P(b/2). In the present work, for this purpose the far range order effects were removed or at least sufficiently reduced. This strategy was realized in the following way. The summing of the weighted cosine values (eq 3) can be considered as the discrete cos-Fourier transform of function P(b/2) from b- to t-domain22 ∞

∑i

⎧ ⎛ b ⎞⎫ ⎛ b ⎞ ⎛ 2πb t ⎞ P ⎜ i ⎟cos⎜ i ⎟ = Re FT ⎨̂ P ⎜ ⎟⎬ ⎝2⎠ ⎝ 2 ⎠ ⎩ ⎝ 2 ⎠⎭

protons surround 31P nuclei in the studied nano- and amorph-CaHAs are seen in the short-range. The spatial distribution profiles consist of three maxima at 0.24−0.27, 0.30−0.34, and at ca. 0.5 nm. The differences are seen in their relative heights and in the resolution of the peaks. Particularly interesting is the clear presence of the peak at 0.24−0.27 nm in nano-CaHA (Figure 8). The distances of 0.21−0.25 nm are typical for P−O−H structures that are found in some related systems, as calcium phosphate gelatin nanocomposites,6 sol−gel derived SnO2 nanoparticles capped by phosphonic acids,31 and potassium- and ammonium dihydrogen phosphates (KDP and ADP).32 In CaHA, the protons are not part of the phosphate group and thus such short P···H contacts should not be met. In pure crystalline CaHA, each P atom has two protons distanced at 0.385 nm, further two at 0.42 nm, while others are 0.6 nm or more away.18 Nevertheless, the observations using FTIR and NMR techniques suggest or even confirm the presence of hydrogen phosphate units in the nanostructured samples. It is a hard task because the spectral manifestation of hydrogen phosphate groups are often hidden under other features. For example, the FTIR band of HPO42− at ca. 540 cm−1 is strongly overlapped by the intensive modes of PO43− in the regular apatitic environment.33 The signals of HPO42− in NMR spectra, that is, 1 H at ∼11 ppm10 and 31P at ca. 0.45−1.3 ppm,8,33 look like the shoulders of the strong central dominant peaks from the bulk. Hence, in all these cases HPO42− signal/band to be resolved it requires rather precise band separation procedures with a priori knowing that this is present indeed. More clearly, the presence of HPO42− can be extracted from 2D HETCOR experiments.10 Also, note the possible presence 31P−1H spin pairs with the closest distance 0.22−0.25 nm in calcium phosphate gelatin nanocomposites, which has been deduced from the simulation of CP kinetics.6 The P−O−H structural motifs with P···H distances of 0.2− 0.25 nm are present mainly on the surface layer that is not seen in XRD because of its disordered nature.10 Therefore, the fact that the peak at 0.24−0.27 nm is clearly resolved in the spatial distribution profile of the nano-CaHA sample and hardly noticeable in the case of amorph-CaHA (Figure 8) is easily understood by taking into account the differences in surface organization in nanostructured and amorphous materials. These two differently structured systems are interesting to compare talking also about the remote P···H contacts. It is clearly noticeable that the relative amount of the remote P···H contacts (r(31P−1H) > 0.5 nm) in amorph-CaHA is much higher than in nano-CaHA (Figure 8). Both materials were already compared respect to the presence of structural manifolds of hydroxyl groups by means of 1H NMR and FTIR spectroscopy.11,22 It was deduced that the amount of structural −OH groups in nano-CaHA is significantly higher than that from adsorbed water and vice versa in amorph-CaHA. The 1H and 31P spin−lattice and spin−spin relaxation time (T1 and T2) measurements push toward the presence of significant amount of the adsorbed water in amorph-CaHA.11 These experiments have revealed the fast spin motion with the correlation time τ = 6.9 × 10−6 s at ∼300 K takes place in amorph-CaHA. The effect of MAS rate on the 31P signal shape supports that the correlation time of this motion gets into the time scale of microseconds or even nanoseconds. Such fast dynamics can be attributed to the rotational diffusion of water molecules. The spin dynamics in nano-CaHA is one order slower (τ ∼ 3.3 × 10−5 s).11 Hence, correlating the 1H NMR

(7)

Hence, the shape P(b/2) can be determined from eq 4 taking experimentally measured CP intensities I(t) and performing an inverse Fourier transform from t- to b-domain I(t )

1 − λf1 − I f ⎛b⎞ −1 02 P ⎜ ⎟ ∼ FT ̂ ⎝2⎠ (1 − λ)f 3/2 1

(8)

where, however, two dynamic factors of spin-diffusion f1 = exp(−t/Tdif) and spin−lattice relaxation in the rotating frame f 2 = exp(−t/T1ρ) as well as the parameter λ that characterizes the cluster structure have to be known. Those overall quantities describe the CP kinetics over the long contact time. The values of I0, λ, Tdif, and T1ρ were taken as the averages over the set of profiles (R, G, L) for each curves (Table 1) and used in the actions of eq 8. The profile P(b/2) obtained in this way can be considered as a goal. The final results of this processing of experimental data including the recalculation of P(b/2) from bvariable to internuclear distances (r) are presented in Figure 8. The essential differences between spatial distributions of F

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The Journal of Physical Chemistry C and FTIR data for both materials11,22 with the corresponding profiles presented in Figure 8, we can state that the remote protons are certainly involved in the H-bond network. However, we do not get into polemic for these protons from the adsorbed water34 or due to the deviation of the H atom of the −OH ions with sequent displacements of corresponding oxygen atoms that lead to the appearance of distances typical for H-bonds.35 More comments concerning the MAS effect on the obtained spin distribution profiles are necessary. If the spin diffusion processes are slow enough, the assumption of isolated 31P−1H spin pairs becomes more realistic.36 The CP kinetics should exhibit more pronounced oscillations of intensity (Figure 6). The dominant dipolar coupling can be then revealed and the P···H distance values can be extracted either performing Fourier transform of the magnetization curves,29,36,37 or from CP kinetic curves by a single cosine treatment (eq 1).31,33 It means no reducing of the far range order effects through the developed treatment, that is, applying eq 8 is necessary. However, for the studied nano-CaHA the value of Tdif is practically not changing getting from the static regime to MAS, whereas for amorph-CaHA it even slightly decreases (Table 1). On the other hand, it is known that MAS technique fails to suppress anisotropic spin interactions fully, if intensive reorientational dynamics is present.38 The line width upon MAS becomes dependent on the spin interaction strength, the time scale of the motion, and the spinning rate.11,38 Hence we can speak about a certain decimation of dipolar interactions that is reflected in the changes of NMR signal widths and in the spatial distribution of interacting spins (Figure 8). It follows that 31P interactions with the protons on the surface layers (the peak at 0.24−0.27 nm) or with remote protons (r(31P−1H) > 0.5 nm) are affected by MAS most dramatically. Note the decimation of spin interactions upon MAS is pronounced also on the structural parameter λ. Its change from λ ≈ 0.35 (static sample) to 0.6 (MAS, see Table 1) means that the effective number of interacting spins in the 31P− (1H)n spin cluster in nano-CaHA reduces from n ≈ 1.9 to ∼0.7. The weak point of the above treatment has to be recognized. Namely, it starts from the expression (eq 1) that is valid for one particular orientation of the dipolar tensor with respect to the external magnetic field (eq 2). The averaging in eq 4 using P(b/2) covers the b-distribution over the distances as well as over the orientations. This can mask or distort the true distribution of the internuclear distances alone. On the other hand, the peaks in the fine structure of P(b/2), if it is succeeded to resolve experimentally (see Figure 8), correspond to the edges of Pake-like doublets, that is, they are valid for one particular orientation (θi, as it is shown in Figure 5). Note the purely distance-depending distribution P(D) can be determined by removing the angular effects. Such treatment can be carried out starting from the expressions for CP kinetics derived for a powdered sample.20,21 However, a rather complicated mathematical problem appears in this case; instead of routine Fourier transform determining P(b/2) (eq 8), the distribution P(D) is extracted processing CP kinetic data either by applying nontrivial Hankel transform or solving the equation of convolution that gets into the class of so-called ill-posed problems. The work in these directions is in progress.

distribution of interacting spins and allows to determine the coupling- and time parameters that characterize the structure, diffusion, and composition of the spin clusters in the subnanoscale. This can be considered as a certain step toward NMR crystallography for complex solids, however, going not via the traditional tensor analysis of chemical shifts and spin interactions but in a complementary way through the kinetics of CP transfer. The short 31P−1H contact peak at 0.24−0.27 nm was resolved in the spatial distribution profile of the nano-CaHA sample and being hardly noticeable in the case of amorphCaHA reflects the differences in surface organization in nanostructured and amorphous materials. The spin diffusion processes in both systems are practically unaffected by MAS. The MAS decimates 31P interactions with the protons on the surface layers and with the remote protons (>0.5 nm) that are plausibly involved in the H-bond network and thus are highly mobile. In the future, this method can be useful for the searching and monitoring of technological processes to create a series of novel nanomaterials via control of their uniformity in the subnano scale as well as correlating the short-range order effects with macroscopic properties, for example, strength, flexibility, and so forth, and maybe even with the feature that is extremely important for medical applications, that is, with biocompatibility.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: vytautas.balevicius@ff.vu.lt. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge Center of Spectroscopic Characterization of Materials and Electronic/Molecular Processes (Scientific infrastructure “SPECTROVERSUM”) at Lithuanian National Center for Physical Sciences and Technology for the use of spectroscopic equipment. We thank Dr. Torsten Gutmann for fruitful discussions and Professor Aivaras Kareiva for the help during microscopy experiments.

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REFERENCES

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CONCLUDING REMARKS The refined treatment of CP kinetics has been developed. It is based on the reducing the far range order effects via radial G

DOI: 10.1021/acs.jpcc.5b11739 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.jpcc.5b11739 J. Phys. Chem. C XXXX, XXX, XXX−XXX