Quantifying Site-Specific Proton Dynamics in Phosphate Solid Acids

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Article

Quantifying Site-Specific Proton Dynamics in Phosphate Solid Acids by H Double Quantum NMR Spectroscopy 1

Gabrielle Y Foran, Darren H Brouwer, and Gillian R. Goward J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b06034 • Publication Date (Web): 26 Oct 2017 Downloaded from http://pubs.acs.org on October 30, 2017

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The Journal of Physical Chemistry

Quantifying Site-Specific Proton Dynamics in Phosphate Solid Acids by 1H Double Quantum NMR Spectroscopy Gabrielle Y. Forana, Darren H. Brouwerb and Gillian R. Goward*a a

Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario, Canada L8S 4L1

b

Department of Chemistry, Redeemer University College, Ancaster, Ontario, Canada L9K 1J4

* Corresponding Author Prof. Gillian R. Goward Email: [email protected] Phone: (905)-525-9140 x 24176 Fax: (905)-522-2509 1

ACS Paragon Plus Environment


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Abstract Solid state MAS NMR was used to investigate changes in proton dynamics in phosphate solid acids which exhibited increased proton conductivity between room temperature and 110 °C. Double quantum dipolar recoupling methods were used to quantify site-specific changes in proton-proton dipolar coupling as a function of temperature. The static dipolar coupling and motionally-induced changes to it were compared. This was accomplished by calculating (from crystal structures) and measuring (from the initial parts of the DQ recoupling curves) the rootsum-square of the dipolar coupling, a geometry-independent measure of dipolar coupling strength referred to as the “apparent dipolar coupling”, Dapp. The analysis of KH2PO4 and RbH2PO4 showed that the experimentally determined apparent dipolar couplings were reduced from the calculated values at increased temperatures in dynamic systems.

Higher proton

conductivity was associated with greater reduction of the apparent dipolar coupling as measured by dipolar recoupling NMR methods. Most interestingly, in its monoclinic phase, RbH2PO4 has two chemically distinct proton environments; one disordered and one ordered, which are resolved by 1H MAS NMR. These sites exhibit different dipolar coupling responses as a function of temperature, revealing that proton conduction in this temperature range arises from motions involving only one of the sites. This site specific dynamics is measured directly for the first time, using a combination of magic-angle spinning to resolve the 1H sites and dipolar recoupling experiments to probe the temperature dependence of the 1H-1H dipolar interactions.

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Introduction Nafion is a commonly used material in the manufacture of proton-conducting membrane electrolyte assemblies (MEA) found in proton exchange membrane fuel cells (PEMFCs).1 The sulfonated ionomer owes its prominence to its high proton conductivity. The proton conductivity of fully hydrated Nafion has been shown to be on the order of 1 S/cm.1 Membrane hydration is an important factor in proton conductivity in Nafion because water is a necessary vehicle for the transport of protons between sulfonate groups in the polymer side chains.1 The necessity of membrane hydration imposes non-ideal operating conditions on the PEMFC because the platinum catalysts, found in the anode and the cathode, are less efficient and more prone to deactivation via the adsorption of carbon monoxide when the fuel cell is used below the boiling point of water.1,2 Improved catalyst performance can be obtained through fuel cell operation above 120 °C.1,2 Higher temperature operation is dependent on the development of a MEA material that is capable of anhydrous proton conduction. The use of a solid electrolyte is preferable as this eliminates issues such as flooding and drying.1,2 Phosphate solid acids have been proposed as an alternative to Nafion. Phosphate solid acids are materials comprised of an alkali cation and a phosphate oxyanion.1 Phosphate solid acids can conduct protons anhydrously and have been identified as potential MEA materials for use in PEMFCs.1-4 A working laboratory-scale fuel cell was created by Haile et al. which took advantage of the monoclinic to cubic phase transition in CsH2PO4 (CDP) which occurs at 238 °C.4 This phase change has been described as being superprotonic, meaning that proton conductivity in the material increases by several orders of magnitude following the transition to the cubic phase.2,4 The basis of the superprotonic phase change is that the level of disorder in the hydrogen bonded system surrounding the phosphorous tetrahedra increases such that the phosphorous tetrahedra becomes more mobile. This facilitates the 3



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formation and deformation of hydrogen bonds needed for proton conduction to occur via the Grotthuss mechanism.1,2,4 Controversy surrounding the stability of superprotonic phases has been extensively documented in the literature.4,5 It is often argued that superprotonic phases of solid acids are not reliable proton conductors because humidity and pressure must be tightly controlled in order to prevent the decomposition or melting of the material.4,5 This work will focus on changes in proton dynamics in materials without documented superprotonic transitions5 to take advantage of stable phases to gain a better understanding of the mechanics of proton conduction in phosphate solid acids. To this end, proton conductivity and accompanying changes in proton dynamics as a function of temperature will be quantified in the following solid acid proton conductors: KH2PO4 (KDP) and RbH2PO4 (RDP) as well as in calcium hydroxyapatite, a nonconductive material. Molecular-level dynamics in phosphate solid acids have been previously studied via NMR. These studies have focused primarily on the determination of molecular structure and the characterization of local dynamics involved in proton transport. Kim et al.2,6 have characterized two unique processes contributing to proton transport via the Grotthuss mechanism in CDP: proton exchange via hydrogen exchange and phosphate oxyanion rotation. Activation energies for these processes have been determined via variable temperature (VT) proton and phosphorus NMR.2 Structural models of these processes have been constructed using a combination of

17

O

NMR and computational methods.6 One of the goals of their work was to determine whether proton motion in phosphate solid acids can be attributed to proton hopping, phosphate rotation or a combination of these processes. Monoclinic RDP has been previously investigated by Vijayakumar et al.7 at 900 MHz at a spinning speed of 25 kHz. Under these conditions, three distinct proton sites were resolved.7 Two of these resonances, labelled A where assigned to the

4


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protons occupying sites along the disordered hydrogen bonded network.7 The remaining resonance, labelled B, was assigned to the proton occupying the ordered hydrogen bonded network.7 Proton dynamics were determined from Arhenius plots of T1 data and were attributed to phosphate tetrahedra rotation.7 Anion dynamics have also been investigated in RDP by Traer et al. [8] via 31P CODEX NMR where phosphate tetrahedra rotation was found to occur on the millisecond timescale. Proton hopping was not discussed in either of these works but we believe that it may make significant contributions to proton dynamics in solid acids, particularly at temperatures well below the superprotonic transition. Previous double quantum (DQ) NMR studies probing both proton and rubidium environments in RDP and rubidium methane phosphonate were performed by Vijayakumar et al. [3], in this work, dipolar recoupling methods were used to determine the relative strength of proton-proton dipolar coupling interactions.3 Although proton-proton interactions were the focus of these prior studies, site-specific protonproton dipolar coupling has yet to be quantified in these materials. Site-specific proton dipolar coupling is expected to provide new insight in the assignment of motional processes to unique proton sites in multi-site systems. NMR Methodology The quantification of proton dipolar coupling interactions in solid acid proton conductors can be performed using solid state NMR as dipolar coupling between NMR-active nuclei is a through-space interaction that depends on the internuclear distance as well as the orientation of the coupled nuclei with respect to the external magnetic field.9 The Hamiltonian operator for the homonuclear dipolar coupling (in a strong external magnetic field) between two spins j and k of the same type of nucleus (e.g. 1H) is given by the following equation: 𝐻! = 𝐷!" 3 cos ! 𝜃 − 1

3𝐼!" 𝐼!" − 𝐼! 𝐼! 2

(1) 5



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where Djk is the dipolar coupling constant (in Hz) 𝐷!" =

1 𝜇! 𝛾! 𝛾! ℏ ! 2𝜋 4𝜋 𝑟!"

(2)

rjk is the internuclear distance between the two spins, θ is the angle between the internuclear vector and the external magnetic field, 𝐼!" and 𝐼!" are spin operators between spins j and k and the external magnetic field, 𝐼! and 𝐼! are the spin operators, and µ0 is the magnetic constant. As nuclei undergo motions such as the transport of protons via the Grotthuss mechanism both the distances between the nuclei, as well as the orientations of the spins with respect to each other and the magnetic field, can change.10,11 These atomic and molecular-scale motions typically lead to a reduction of the observed dipolar coupling between spins.10,11 The reduction of dipolar coupling interactions has a complicated dependence on the rate of proton motion and on the orientation dependence of that motion. For example, a sufficiently rapid and fully isotropic motion will reduce the dipolar interaction to zero. However, in many materials (such as the solid acids studied in this paper), the nuclei do not occur as isolated spin pairs related by dipolar coupling, but rather exist as multi-spin networks of coupled spins.2-6 Quantification of dipolar couplings in multi-spin networks is much more complicated than the relatively straightforward situation of isolated spin pairs. This situation is usually the case in solid state 1H NMR due to the ubiquity of H atoms, the high natural abundance of 1H, and the large gyromagnetic ratio of 1H nuclei. This paper explores how multispin 1H dipolar interactions in solid acid proton-conducting materials can be quantified through advanced solid state MAS NMR experiments as a function of temperature and be related to the motions that give rise to proton conduction in these materials. In order to obtain chemical-shift resolved spectra in solid-state NMR, it is necessary to carry out magic angle spinning (MAS). However, in doing so, the dipolar couplings are averaged 6


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to zero. Dipolar recoupling pulse sequences are designed to interrupt the spatial averaging of the dipolar interaction with sequences of rotor synchronized rf pulses, so that dipolar couplings are re-introduced and can be quantified under high resolution MAS conditions.10,12 For the recoupling between nuclei of the same type (e.g. 1H-1H), there are a variety of homonuclear dipolar recoupling pulse sequences available, including the BaBa sequence13 and a variety of symmetry-based recoupling pulse sequences (e.g. C7, R14, etc).10-13 Here, we have employed the R26411 pulse sequence for homonuclear 1H dipolar recoupling.12 The strength of the dipolar coupling is typically quantified by observing the intensities of the DQ coherences that develop under the recoupling pulse sequence as a function of the recoupling time.11 This is typically referred to as a DQ curve. For an isolated pair of dipolar-coupled spins, the DQ curve increases according to the strength of the dipolar interaction and then the intensity oscillates at a frequency related to the dipolar coupling constant. By fitting such a DQ curve (through simulations14 or suitable analytical solutions,10,15 the dipolar coupling constant can be obtained, and then converted into an internuclear distance. In the case of multi-spin networks (common for protons in the solid state), the DQ curves are much more complicated. The form of the DQ curve is strongly geometry-dependent in the sense that the DQ curve is quite sensitive to the spatial arrangement of the nuclei relative to each other.11 Extracting dipolar coupling constants from multi-spin situations is possible in only the simplest cases involving clusters of spins in which much is already known about the geometry of the spins, rather than extended networks of coupled spins. For most materials of interest, simulating and fitting the DQ curves in order to extract quantitative information is a usually a futile endeavour due to the complexity of the problem. However, a number of authors have pointed out that the initial rise of the DQ curve is largely insensitive to the geometry of the multi7



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spin system.10-12 By carrying out a normalization of the homonuclear DQ signals, the initial part of the normalized DQ curve can be approximated as if it were an isolated spin pair, but with an apparent dipolar coupling constant that is the root-sum-square of the dipolar coupling constants between a central spin j and all of its neighbours k (within a defined radius) as demonstrated in equation 3.

𝐷!" !

𝐷!"",! =

(3)

!

To obtain and construct normalized DQ curves, two spectra are collected at each value of the dipolar recoupling time τDQ: a “reference” (REF) spectrum and a “double quantum” (DQ) spectrum, the difference being found in the phase cycling used to collect each spectrum which selects different coherence pathways.11 The normalized DQ curves (nDQ) are constructed by calculating the ratio nDQ = DQ/MQ where MQ = DQ+REF at each recoupling time. An example of this is shown in Figure 1a.

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150

Absolute Signal Intensity (Arb. Units)

a)

100

Double Quantum Reference Multi Quantum

50

0

0

50

100

150

Recoupling Time ( s) 0.4

b) Normalized Intensity

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Fresnel fit normalized DQ

0.3

0.2

0.1

0.0

0

50

100

150

Recoupling Time ( s)

Figure 1: Normalization of DQ intensity acquired by the analysis of calcium hydroxyapatite with the R26411 pulse sequence: a) shows the signal intensities of the DQ and reference spectra along with the sum of the DQ and reference intensities to which the DQ signal was normalized, b) shows the Fresnel function fit to the first three points of the normalized DQ curve.

A number of functions have been proposed to fit the initial rise of a normalized DQ curve, including a quadratic function16 and a Gaussian-type function.11 Here, we employ the Fresnel function analytical solution to the powder averaged DQ signal of an isolated spin pair under gamma-encoded homonuclear dipolar recoupling, as shown in equation 4:

𝑛𝐷𝑄 𝜏!" =

1 1 − 𝐹 𝑥 2 cos 2𝜃 + 𝐹! 𝑥 2 sin 2𝜃 2 𝑥 8 !

(4)

9



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where Fc and Fs are the cosine and sin Fresnel integrals respectively, 𝑥 =

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2𝜃/𝜋, 𝜃 = !! 𝜅 𝐷!"" ,

and κ is the scaling factor for the dipolar recoupling sequence (κ = 0.1708 for the R26411 sequence).The dipolar coupling constant has been replaced with the multi-spin apparent dipolar coupling constant, Dapp as defined in equation 3, above. Like the quadratic and Gaussian-type functions referred to above, this Fresnel function for the normalized DQ curves is very rapid to calculate and depends only on the single parameter Dapp. It is important to point out that since the nDQ curves are being fit as if they were behaving as an isolated spin pair but with an apparent dipolar coupling constant Dapp, the fit is only valid for the initial rise of the nDQ curve (no more than about half way to maximum intensity) before geometry-dependent multi-spin effects become pronounced. An example of a fit with the Fresnel function to the initial part of an nDQ curve is shown in Figure 1b. In the absence of dynamics, the expected apparent dipolar coupling constant can be calculated from the crystal structure of a material of interest. Here, we designate this calculated value as D!!"" . For the KDP and RDP materials studied in this work, it was necessary to slightly modify the equation for the apparent dipolar coupling (equation 3) to take into account the fact that the hydrogen atoms are disordered over symmetry related sites in the crystal structures having partial occupancy at each crystallographic site, for example protons in KDP have an occupancy of pj = 0.5:

𝑝! 𝐷!" !

! 𝐷!"",! =

(5)

!

Figure 2 displays the value of the apparent dipolar couplings calculated from the crystal structures of KDP and RDP as a function of the coordination sphere distance. The apparent 10


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dipolar couplings are calculated based on the tetragonal phase for both materials. A lower apparent dipolar coupling was found for RDP, despite it being isostructural to KDP, because the larger cation size resulted in larger internuclear distances causing decreased internuclear interaction. These data show that a cut off distance of 15 Å in calculating the D!!"" values is sufficient to ensure convergence.

7.5

Apparent Dipolar Coupling (kHz)

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7.0

6.5

KH2PO4 RbH2PO4

6.0

0

5

10

15

20

25

Coordination Sphere Size (A)

Figure 2: Calculated apparent dipolar coupling in KDP and RDP as a function of coordination sphere size calculated from the tetragonal crystal structures of both materials using coordination spheres ranging in size from 5 to 20 Å. The calculated apparent dipolar couplings were found to converge when a 15 Å coordination sphere was used. Similar results were achieved when apparent dipolar coupling was calculated in calcium hydroxyapatite. In order to probe the dynamics of the protons as a function of temperature (and the subsequent reduction of the dipolar interactions), the initial parts of normalized DQ curves obtained over a range of temperatures were fit with equation 4. These experimentally determined apparent dipolar coupling constants are referred to here as D!!"" . In the absence of motions these experimentally determined values should agree well with the D!!"" values calculated from the crystal structure, while the presence of dynamics should give rise to D!!"" values that are less

11



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than D!!"" in some manner that is related to the nature of and rates of motion. DTapp is expected to trend toward zero when the superprotonic temperature, characterized by rapid proton motion caused by increased disorder around the phosphate tetrahedra,4 is reached. The superprotonic transition is expected to occur at 273°C in RDP when the monoclinic to cubic phase change takes place.5 The cubic phase is expected to correspond to the “isotropic proton lattice gas” condition.5 KDP is not expected to undergo a superprotonic transition as decomposition occurs at 233 °C prior to any phase change.5 The NMR experiments performed here focus primarily on the temperature range spanning -7 to 107 °C. Therefore, DTapp is expected to decrease as local motions increase, but will not drop to zero, as the isotropic proton lattice gas conditions will not be met. Instead, for each phase, we report the percent change of DTapp relative to D0app which was calculated based on the crystal structure.

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Experimental Sample Preparation KDP and RDP were prepared by dissolving 1.00 g of the corresponding carbonate in a stoichiometric amount of phosphoric acid. A minimal amount of deionised water was added to completely dissolve any remaining solid. The solid acid samples were precipitated out of solution via the addition of methanol. The resultant crystals where filtered and then dried in a vacuum oven at 80 °C for several hours. The calcium hydroxyapatite sample was purchased from Sigma Aldrich and dried in a furnace at 600 °C for several hours prior to use to ensure that sufficient dehydration had taken place. Impedance Spectroscopy Powdered KDP and RDP samples were pressed for 15 minutes at 5000 psi to yield pellets with a diameter of 14 mm and a width of 1.5-3 mm. Pellets were sintered at 130 °C overnight and then gold coated for one minute on each side. Calcium hydroxyapatite pellets were prepared similarly but were pressed at 12000 psi and were sintered at 300 °C. Impedance measurements were taken using a Gamry Interface 1000 potentiostatat with constant voltage and frequencies ranging from 100000 to 10 Hz. Pellets were contained within a glass and Teflon two electrode cell where they were pressed between two metal disks allowing current to flow through them widthwise. Measurements were taken in ten degree increments between 50 and 170 °C with the sample being allowed to equilibrate at temperature inside the oven for one hour between measurements. X-ray Diffraction Powdered samples were mounted on disks using a mixture of Vaseline and toluene. These samples were analyzed at room temperature between 15 and 60 ° (2θ) in steps of 0.017 ° over a period of two hours. These measurements were performed using a 0.134 nm Cu source. 13



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NMR Measurements The experiments were performed on a 300 MHz wide bore Ascend spectrometer using a 4 mm VT MAS probe. The samples were packed in a 4 mm thick-walled rotor and spun at 13.7 kHz. Spectra were referenced to adamantane (1.63 ppm) for a 2.5 µs π/2 pulse at a power level of 100 W. Pseudo two dimensional and one dimensional experiments were performed at -7 °C, 6 °C and in eight degree increments from 67 to 107 °C. This was the highest stable temperature which could be reproducibly obtained. NMR Sample temperature was calibrated using a calibration curve that was constructed based on the response of a mixture of Sm2Sn2O7 and SnO2 to probe heating under MAS conditions.17 Experimental error in the calibration curve was determined to be ±5 °C based on the beginning of the formation of the monoclinic phase at 75 °C when it has been reported to occur in literature at 80°C.18 Pseudo two dimensional spectra were acquired using the R26411 pulse sequence and one dimensional spectra were acquired via a single pulse. The recycle delay time varied between samples depending on the rate of relaxation of hydrogen bonded protons in the corresponding crystal lattice.

14


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Results and Discussion The conductivity trends for the three samples of interest are given in Figure 3. As expected, calcium hydroxyapatite is a very poor conductor, and its conductivity does not increase with temperature. In contrast, both KDP and RDP show substantial conductivity, which increases with temperature. There is no break or step-function in the conductivity trend, which would be indicative of a superprotonic phase transition. This is consistent with other studies of these phases.5 -3

KDP RDP CaHA

-4

Log(Proton Conductivity)

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-5 -6 -7 -8 -9 -10 -11 0

50

100

150

200

o

Temperature ( C)

Figure 3: Proton conductivity of KDP, RDP and calcium hydroxyapatite (CaHA) as measured via impedance spectroscopy over a temperature range spanning 50-170 °C. Impedance measurements were performed at constant voltage in a two-electrode cell where frequency was varied from 100000 to 10 Hz. Calcium hydroxyapatite was found to be significantly less conductive than the solid acids and did not undergo significant increases in conductivity over this temperature range Figure 4 shows the 1H MAS spectra of all samples considered in the following DQ dipolar coupling studies. For each sample, we apply the DQ NMR build-up curve method, and assess the measured apparent dipolar coupling constant (DTapp) as compared to that calculated for the pristine phase (D0app).

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RDP Tetragonal RDP Monoclinic

KDP Tetragonal

CaHA

20

δ/ppm

0

Figure 4: 1D proton NMR for calcium hydroxyapatite (CaHA), KDP and RDP acquired at room temperature at 300 MHz with 13.7 kHz spinning. The calcium hydroxyapatite sample (0 ppm) was dried at 600 °C for ten hours prior to analysis. The tetragonal KDP (15 ppm) and RDP (14.2 ppm) samples were analyzed as prepared. The monoclinic RDP sample (11.9 ppm and 14.2 ppm) was heated to 130 °C overnight prior to analysis. In this series of materials, the range of dipolar coupling constants (D0app) for the static phases is from 3-8 kHz. Within this range of dipolar coupling the build up of DQ intensity occurs within 0.1 to 0.3 ms. This sets the timescale over which we expect to observe proton dynamics. Thus, when we interpret the attenuation of the dipolar coupling curves, we are in effect assessing the lower limit on the rate of ion hopping. At correlation times faster than 100us the build-up curve will show attenuation.10,11 Much slower than this, we would not expect attenuation, and right in this range we would expect intermediate motional behaviour, similar to the coalescence point of a standard variable temperature 1D NMR experiment.9-11 It is important to note we are not extracting specific rates of motion in the studies here, but rather trends in the dipolar coupling constants as a function of temperature. Calcium Hydroxyapatite: A non-conductive reference 16


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Calcium hydroxyapatite, a common bio-composite material, is the main component of bones and teeth.19 The material is used as a reference to test the suitability of using DQ NMR to quantify apparent proton dipolar coupling in phosphate solid acids. This non-conductive material is chosen as it contains hydrogen-bonded protons and phosphate tetrahedra making it an ideal structural analogue for the materials of interest. At room temperature, calcium hydroxyapatite is expected to be in the monoclinic phase which possesses a single proton environment located around 0 ppm.19 Preliminary single pulse 1H MAS NMR experiments revealed that the hydroxyapatite sample, as received from Sigma Aldrich, contained many additional proton sites as evidenced by the large amorphous feature spanning 0-16 ppm (Figure S1). These proton sites were attributed to sample hydration. Sample hydration was not desired in the reference material as a single well-understood phase is required to simplify DTapp calculations as well as comparison with the crystal structure. The water-associated peaks were completely removed following sample dehydration at 600 °C for 10 hours (Figure 4a – blue spectrum). The DQ NMR build-up experiment was performed at room temperature on the dehydrated sample yielding a DTapp of 2.97 kHz. This differed by 4 % from D0app, calculated using a 15 Å coordination sphere via equation 5, 3.08 kHz. The difference between DTapp and D0app was determined to be within the error of the DQ method. The good agreement between DTapp and D0app in calcium hydroxyapatite reveals that the technique is suitable for the quantification of proton dipolar coupling in multispin systems. KH2PO4: Single Proton Site with Dynamics Tetragonal KDP has a single proton environment which was represented as a peak at 15 ppm in the one dimensional proton NMR spectrum (Figure 4b – green spectrum). This site was used to fit the DQ spectra to obtain DQ intensity as a function of recoupling time. The rate of 17



build up of double quantum intensity decreases with increasing temperature indicating weaker proton-proton interactions as protons become more mobile in the heated sample (Figure 5). This process is illustrated via decreasing slope in plots of normalized DQ intensity as a function of recoupling time (Figure 5). DTapp was determined to be 7.07 kHz at -7 °C, the lowest temperature measured by DQ NMR. The DTapp at low temperature is only 1.5 % less than D0app, 7.18 kHz, again within error of the static case and signifying that proton mobility was limited at low temperature. DTapp decreases substantially at higher temperatures (Figure 5) as is evidenced by a slower rate of build up of DQ intensity at 39, 75 and 98 °C. Weakening DTapp is indicative of increased proton dynamics as was expected based on the observation of increased proton conductivity at elevated temperatures (Figure 3). 1.0 o

Normalized DQ Intensity

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-7 C o 39 C o 75 C o 98 C

0.8 0.6 0.4 0.2 0.0 0

100

200

300

RecouplingTime ( s)

Figure 5: The rate of build up of DQ intensity as a function of recoupling time for a KDP sample analyzed at -7, 39, 75 and 98 °C. DQ intensity is built up more quickly at lower temperatures where proton-proton interactions in the material are expected to be stronger due to reduced dynamics. The experimental DQ intensity curves were fit with the Fresnel function (equation 4) for the extraction of apparent dipolar coupling. This is evidenced by a 15 % decrease in DTapp between -7 and 107 °C (Figure 6). It is important 18


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to note that other factors, in addition to proton dynamics might impact the observed DTapp. The most significant was thought to be unit cell expansion. To account for this, we consider the change in the value of D0app by utilizing the expansion of the unit cell as a function of temperature based on the coefficients for thermal expansion in tetragonal KDP as provided by Cook.20 The calculations were performed according to equation 6 where dl was the calculated change in size, Lo was the length of the crystallographic dimension as provided by Nelmes et al.21 at -146 °C, α was the coefficient of thermal expansion and ΔT was the change in temperature relative to -146 °C. 𝑑𝑙 = 𝐿! 𝛼∆𝑇

(6)

Based on this analysis, D0app decreases by only 1.25 % over the same temperature range. This indicates that thermally induced lattice expansion does not contribute significantly to the experimentally observed changes in dipolar coupling. A similar treatment is applied below for the two RDP phases, based on their known unit cell parameters at the temperatures of interest. As a further cross-check into the causes of change in the build-up curves, the sum MQ data sets (sum of the DQ and ref intensities) for KDP were analysed. Figure S2 shows the sum of the DQ and reference curves for KDP. All curves were normalized to the corresponding backextrapolated zero recoupling time intensity. True T2 relaxation can be analyzed only when the full pulse sequence has been completed, which for R26411 corresponds to four rotor periods of recoupling time.12,22 A recoupling time of 286 µs corresponded to the four rotor period condition. Comparing the signal intensity from the initial data point and the four rotor period data point shows only the overall decrease in intensity, and the oscillations at shorter recoupling times are not significant as they are the result of higher-order effects caused by an incomplete pulse sequence. Normalized intensities collected at temperatures between -7 and 75 °C were the same

19



within error but at higher temperatures, 91 to 107 °C, normalized intensity decreases with increasing temperature. The Curie effect was thought not to be a significant cause of T2 signal decay as Nelmes et al.21 have reported that tetragonal KDP is paraelectric. These changes were instead interpreted to indicate that a T2 minimum is being approached in the slow motion regime22 where system dynamics are slower than both the MAS rate and 1/DTapp. T1 effects were considered to be minimal as KDP signal intensity did not change significantly as the sample was heated. Further heating (in the absence of sample decomposition) is expected to result in a T2 minimum beyond which fast limit averaging will be observed.22 Having considered both the influence of T2 relaxation and unit cell expansion on the recoupling build-up curves, we can conclude that changes in the build-up curves as a function of temperature can be robustly interpreted as changes in local proton dynamics. In particular, the KDP experiment showed that the R26411 pulse sequence can be used to quantify changes in proton motion in a dynamic, multi spin sample with a single hydrogen-bonded proton site. 8


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7

6

D D

5

4

0

0 app T app

50

100 o

Temperature ( C) T

0

Figure 6: D app in KDP at -7 °C was found to be within 1.5 % of D app which was calculated based on the tetragonal crystal structure using a 15 Å coordination sphere. DTapp was found to decrease by 15 % between -7 and 107 °C indicating increased proton mobility in this system. D0app (dotted line) was found to decrease by only 1.25 % over the same temperature range 20


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indicating that thermal lattice expansion does not have a significant impact on proton dipolar coupling in this temperature regime.

RbH2PO4: Two Proton Sites with Dynamics RDP exists in the tetragonal phase at room temperature.18 The tetragonal phase contains a single proton environment, observed at 14.2 ppm (Figure 4c – orange spectrum). As the temperature is increased, a phase transition from the tetragonal to the monoclinic phase begins. This is evident in the 1H MAS spectra in the appearance of a second proton environment, at 11.9 ppm, which was first observed to occur at 75 °C (Figure 7) consistent with the onset of the phase transition.5,18 In the monoclinic phase, the two proton environments have been described in previous studies by our group in reference [7]; a high frequency resonance (A), which is weakly split at 900 MHz, (14.2 ppm & 13.8 ppm) and a lower frequency site (B) at 11.9 ppm, which are correlated with specific sites in the crystal lattice. Our chemical shift assignments are based on the previous assignment by Vijayakumar et al. [7] which state that increasing oxygen-oxygen (2.5 Å for O-HB...O and 2.49 Å for O-HA...O)23 distance results in lower chemical shift. In the present study, the combination of a phase change and a new multi-site phase presented a challenge. The presence of two distinct proton chemical shifts above 75oC is either indicative of the tetragonal and monoclinic phases being present simultaneously as part of a solid-solid phase transition or the monoclinic phase only, with its two chemically distinct protons. It is also clear in Figure 7 that individual proton sites are not well resolved at this field strength, which introduces error in the fitting required to calculate DTapp while the sample is undergoing the phase change. For this reason, two distinct samples were created; one in the tetragonal phase, and a second thermally treated sample in the meta-stable monoclinic phase.

21



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The latter sample was fully converted to the monoclinic phase at 130 °C, as evidenced by PXRD (Supporting Information Figure S3). The presence of two resolved proton sites in the monoclinic phase presents an opportunity to resolve individual apparent dipolar couplings using DQ NMR. Site-specific resolution is provided by the 1H MAS spectrum resulting in separate DQ build-up curves (Figure 8) which allows DTapp to be evaluated at each chemically distinct 1H site. This is an interesting and potentially useful advantage of the DQ methodology described herein.

130 °C 107 °C 98 °C 91 °C 75 °C 67 °C 33 °C -7 °C

20

δ/ppm

10

Figure 7: 1D single pulse 1H MAS NMR spectra of RDP acquired between -7 and 130 °C showing the transition from the tetragonal to the monoclinic phase.

In order to investigate whether differences in the DTapp for each proton site could be resolved, the two proton sites at 14.2 (A) and 11.9 (B) ppm were fitted (Figure 8a), and DQ build up curves were constructed for each site (Figure 8b). Clearly, the build-up curves are 22


Page 23 of 35

distinct, and thus the measured DTapp can be used to give a quantitative evaluation of the differences in proton dynamics between these two sites. B

A

*

20

15

10

δ/ppm 0.6

Normalized DQ Intensity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.4

0.2

0.0

14.2 ppm (A) 11.9 ppm (B)

0

100

200

300

Recoupling Time ( s)

Figure 8: The proton spectrum of the monoclinic RDP sample, pretreated at 130 °C prior to measurement at room temperature at 300 MHz with 13.7 kHz spinning, contains two distinct resonances: A at 14.2 ppm and B at 11.9 ppm. Both proton sites were fit allowing individual T curves of DQ intensity as a function of recoupling time to be determined. Individual D app values were obtained. Larger proton dipolar coupling, as evidenced by faster build up of the DQ curve, was found for the A protons. Figure 9 shows the calculated D0app values for the tetragonal phase and the two sites within the monoclinic phase, in black data points. The values of D0app for the A and B sites were calculated as 7.9 kHz and 5.9 kHz respectively. D0app of the tetragonal phase, 6.7 kHz is quite close to the average of the two sites in the monoclinic phase, 6.9 kHz.

This difference is consistent with

closer proton-proton distances of the proton network following the phase change. In the tetragonal phase, protons are separated by 3.34 Å.24 Proton-proton distances in the tetragonal 23



phase were compared to those in the monoclinic phase II structure as described by Magome et al. [23] and Hagiwara et al. [25]. A protons were separated by 3.16 Å and B protons were separated by 4.78 Å.23,25 9


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Figure 9: D

T app

8

7

D

T

D

0

D

T

D

0

app

Tetragonal

A

Tetragonal app app

Monoclinic

Monoclinic app

B 6

5

4

Tetragonal

Monoclinic

14.2 ppm

11.9 ppm 14.2 ppm

was measured at room temperature in tetragonal and monoclinic RDP. These 11

measurements were performed using the R264 pulse sequence at 300 MHz with 13.7 kHz spinning. The tetragonal phase contains a single site at 14.2 ppm and the monoclinic phase T 0 contains two proton sites at 11.9 (B) and 14.2 (A) ppm. In all cases, D app is less than D app indicating mobile proton species. Next, we compare these proton dipolar couplings as a function of temperature at each site to the local environments in the crystal structure. Figure 10 shows the calculated D0app and measured DTapp over a temperature range -7 to +67oC for the tetragonal phase, and then for +83 to +107oC for the monoclinic phase. The value of D0app for the tetragonal phase is 6.71 kHz which represents the immobile lattice. The phase exhibits a range of DTapp starting at 6.79 kHz at the lowest temperature measured, -7oC.

This is consistent with low proton dynamics,

approximately slower than the inverse of the value of D0app, or a correlation time for ion hopping of slower than 150µs. The trend of DTapp with increasing temperature for the tetragonal site is similar to what was observed for KDP; namely at the lowest temperature, DTapp is equal to D0app 24


Page 25 of 35

within error, and thereafter, DTapp decreases with increasing temperature, consistent with increasing conductivity. This coupling is attenuated with temperature to 6.3 kHz, prior to the onset of the phase change to the monoclinic phase. This modest change of 8% is nevertheless larger than would be expected from the thermal expansion alone. 9

D


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


D 8

D D

7

0

T

app T

T

app 0

MA

app T

MA

app

D

0

D

T

MB app MB

app

6

5

0

50

100 o

Temperature ( C) 11

Figure 10: DTapp for tetragonal (T) and monoclinic (M) RDP as measured using the R264 was compared to D0app. For the tetragonal phase, DTapp matched D0app at low temperatures but decreases by 8 % by 67 °C after which the transition to the monoclinic phase occurs. The monoclinic phase, prepared by heating RDP to 130 °C prior to analysis by NMR, contains two proton sites. Proton dipolar coupling decreases relative to D0app were 16 % at the A (blue) site and by 5 % at the B ppm (red) site . Intriguingly, DTapp of the two sites in the monoclinic phase respond independently. The DTapp values are attenuated to differing degrees, relative to the corresponding D0app for each site. As mentioned above, the average of the D0app values of the monoclinic phase is quite close to that of the original tetragonal phase. The degrees of attenuation at the two sites are clearly distinct, with 18% attenuation at the 14.2ppm site, in contrast with almost negligible attenuation of 3% for the 11.9ppm site at the highest temperature measured in this study. The D0app values can be used to set the upper limit on the associated proton correlation times in monoclinic RDP: of τc ≤ 25



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200us. It must be noted, that although apparent proton dipolar coupling is attenuated with increasing temperature, the surprising lack of coalescence excludes the possibility that these sites are in exchange with one another. The monoclinic RDP proton sites are separated by 700 Hz. Due to the lack of coalescence, the peak separation, corresponding to a correlation time of τc ≥ 1400us, can be taken as the lower limit for the correlation time for proton hopping between the two types of proton environments in this system. As chemical exchange between protons in the 11.9 and 14.2 ppm sites is not detected, the difference in response at the two proton sites, must be interpreted in another way. Site specific apparent proton dipolar couplings were calculated based on the monoclinic RDP crystal structure. This allows us to compare interactions between like and distinct-sites with the purpose of determining whether the observed proton dynamics are site-dependent. Likesite and distinct-site apparent dipolar coupling could not be determined directly via NMR without performing multi-dimensional experiments. Nevertheless, values calculated based on the position of individual proton sites in the monoclinic crystal structure23,25 were used to better understand the motional relationships between protons in monoclinic RDP. These quantities are summarized in Table 1. The phase II variant of the monoclinic structure exists between 44 and 104 °C and is characterized by a doubling along the c-axis (relative to phase I) and disordered hydrogen bonded protons along the b-axis.23 The phosphate tetrahedra are connected through a two-dimensional network of hydrogen bonds along the b-c plane.22 Based on both our own, and previous studies of the RDP phases, we anticipate that the relative proton-proton internuclear distances, which dictate the values of D0app at the A and B proton sites, also play an important role in determining the influence of site-specific dynamics on DTapp. Table 1: Apparent Proton Dipolar Coupling Calculated Based on the Crystal Structure of

26


Page 27 of 35

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Monoclinic RDP (note the 14.2ppm and 13.8ppm sites are not resolved at 300MHz, but are resolved in previous work at 900MHz,21 and thus are assigned to their unique crystallographic positions to calculate the relevant dipolar couplings.

HB (11.9 ppm) HA1 (13.8 ppm) HA2 (14.2 ppm)

Total (kHz)

HB (11.9 ppm) (kHz)

HA1 (13.8 ppm) (kHz)

HA2 (14.2 ppm) (kHz)

5.9

3.33

3.34

3.41

7.9

4.79

1.59

6.08

7.9

4.83

6.08

1.59

Table 1 shows that the A-type protons with resonances of 13.8 and 14.2 ppm at 25 kHz and 900 MHz (which are both found at 14.2 ppm in this work) are more strongly coupled to one another (6.08 kHz) than they are to the 11.9 ppm B proton (4.8 kHz). The A protons are disordered within the hydrogen bonds along the b-axis23 and exhibit partial site occupancy. The 11.9 ppm site corresponds to the type B protons7 which are located along the c-axis in phase II and exist in ordered hydrogen bonds.23 As the D0app values in Table 1 describe the static structure only, DTapp in Figure 10 were used to interpret the impact of dynamics on the two proton sublattices. The substantial attenuation of DTapp at the 14.2 ppm site suggests that the disordered A protons undergo significantly more motion than the well-ordered B protons as temperature increases. Mechanisms of transport have been investigated by both Kim[6] & Vijiaykumar[7], using solid-state NMR strategies.

Proton motion via the Grotthuss mechanism can occur

through two main pathways in phosphate solid acids: rotation of the phosphate tetrahedra or inter-site proton hopping.6 In the work of Vijayakumar et al. [7] the interbond proton migration model was used to suggest that type B protons reorient along the c-axis via a two-fold rotation 27



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Page 28 of 35

and that in contrast, type A protons reorient along the b-axis via a three-fold rotation.7 The threefold rotation of the type A protons was thought to be more favorable as the oxygen atoms are required to travel a lesser distance. Rotation of the phosphate tetrahedra was observed by Traer et al. [8] in CDP, RDP and KDP but this process was found to occur on the order milliseconds which is much slower than the dynamics observed here. Meanwhile, structural data from Magome et al. [23] suggests that the type A protons are optimally positioned to migrate along the b-axis by hopping between disordered hydrogen-bonded sites. Hopping between the disordered A sites is thought to be more favourable than hopping between the B sites as proton-proton distances are shorter: 3.16 Å relative to 4.78 Å.23 O17 NMR performed by Kim et al. [6] showed that proton hopping can occur at temperatures as low as room temperature. We note that while proton hopping was described, no site-specific 1H transport data was reported. Kim et al. found that the rotation of the phosphate tetrahedra was not observed until 147 °C. As this temperature was outside of the scope of our work, the attenuation of DTapp that was observed here at the A site was attributed to proton hopping between the disordered A sites themselves (Figure 11). Proton hopping was found to be significant enough to cause a 18 % reduction in apparent dipolar coupling at the A site. A reduction of only 3 % was observed at the B site. The lesser influence of proton dynamics on the overall apparent dipolar coupling of the B site was attributed to larger proton-proton distances and greater order of hydrogen bonds along the c-axis23 which were thought to make proton hoping less favourable. Differences in the favourability of proton hopping are believed to account for the experimentally observed differences in the extent of attenuation of DTapp at the ordered B proton sites (11.9 ppm) and the disordered A proton sites (14.2 ppm) which was quantified here for the first time. It is assumed that further increases in sample temperature, resulting in the “proton lattice gas” condition, are required for significant

28


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reduction of apparent dipolar coupling to be observed at the B site.

a b

Rb

P O

c

H (A) H (B)

Figure 11: Several RDP phase II unit cells are stacked to show the hopping of A protons along the b-axis via the Grotthuss mechanism. Type A protons (blue and white) are located along the b-axis. The atoms partially occupy two sites and form disordered hydrogen bonds. The adjacent phosphorous tetrahedra exist in two possible orientations23 creating a disordered network of oxygen (red and white) which the protons are hydrogen bonded to. Proton hopping occurs at the A site and follows the pathway indicated by the blue arrows. This process is facilitated by the disorder of the hydrogen bonded network and the proton-proton internuclear distance. It is noted that the B protons (white) are bonded to oxygen which exist in one possible orientation resulting in ordered hydrogen bonds along the c-axis. Proton dynamics were not observed at the ordered B site. The use of symmetry-based dipolar recoupling techniques was overall advantageous in the study of a multi-site dynamic system such as RDP. The site specific apparent dipolar couplings reveal distinct behaviour at each proton site. Notably, DTapp decreases by 18 % at the 14.2 ppm site and 3 % at the 11.9 ppm site. Connections made to previously published neutron diffraction data22 allowed the greater decrease in DTapp at the 14.2 ppm site to be attributed to proton hopping along the b-axis in phase II monoclinic RDP between the disordered A sites for the first time. The distinction of mobility amongst the A and B sublattices would not have been possible without site-specific resolution of proton dipolar coupling that was afforded by the use

29



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Page 30 of 35

of the R26411 pulse sequence and the ability to extract apparent proton dipolar couplings directly from the experimental build up curves.

Conclusion The suitability of the low spinning speed, symmetry-based dipolar recoupling pulse sequence R26411 for the quantification of apparent proton-proton dipolar coupling in multi spin systems was verified via the analysis of a non-conductive, hydrogen-bonded sample, calcium hydroxyapatite. It was found that DTapp matched D0app calculated using a 15 Å coordination sphere within 4 %. Standard coordination sphere size was chosen to be 15 Å as it was found that D0app did not increase significantly when larger coordination spheres were used. Site-specific DTapp was also quantified in the dynamic systems: KDP and RDP which are solid state proton conductors. The magnitude of DTapp in these systems was shown to decrease with increasing temperature. This behavior was expected based on increases in proton conductivity that were measured via impedance spectroscopy. Monoclinic RDP contained two distinct proton sites, labelled A and B with resonances: 14.2 and 11.9 ppm. These sites exhibited distinct changes in DTapp with A being attenuated 18 % relative to D0app while B was attenuated by 3 %. The proton dynamics observed at the A site where attributed, for the first time, to structural factors including shorter proton-proton distances and disorder along the b-axis. It is anticipated that this technique could be applied in the quantification of DTapp in an expanded series of solid proton conducting materials, including those with multiple proton sites, for the purpose of elucidating site-specific proton transport

30


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Acknowledgements G.R.G. would like to acknowledge funding through Canada’s Natural Science and Engineering Research Council’s (NSERC) Discovery Grant program as well as the Catalysis Research for Polymer Electrolyte Fuel Cells (CaRPE-FC) network. The authors would also like to acknowledge Reviewer 1 for their insightful comments.

31



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References 1. Goni-Urtiaga, A.; Presvytes, D.; Scott, K. Solid Acids as Electrolyte Materials for Proton Exchange Membrane (PEM) Electrolysis: Review, Int. J. Hydrogen Energy, 2012, 37, 3358-3372. 2. Kim, G.; Blanc, F.; Hu, Y.-Y; Grey, C.P. Understanding the Conduction Mechanism of the Protonic Conductor CsH2PO4 by Solid State NMR Spectroscopy, J. Phys. Chem. C, 2013, 117, 6504-6515. 3. Vijayakumar, M.; Traer, J.W.; Britten, J.F.; Goward, G.R. Investigations of the Phase Transition and Proton Dynamics in Rubidium Methane Phosphonate Studied by Solid State NMR, J. Phys. Chem. C, 2008, 112, 5221-5231. 4. Haile, S.M.; Chisholm, C.R.I.; Sasaki, K.; Boysen, D.A.; Uda, T. Solid Acid Proton Conductors: From Laboratory Curiosities to Fuel Cell Electrolytes, Faraday Disc., 2007, 134, 17-39. 5. Li, Z.; Tang, T. High-temperature Thermal Behavior of XH2PO4 (X= Cs, Rb, K, Na) and LiH2PO3, Thermochim. Acta., 2010, 501, 59-64. 6. Kim, G.; Griffin, J.M.; Blanc, F.; Haile, S.M.; Grey, C.P. Characterization of the Dynamics in the Protonic Conductor CsH2PO4 by 17O Solid-State NMR Spectroscopy and FirstPrincipals Calculations: Correlating Phosphate and Protonic Motion, J. Am. Chem. Soc., 2015, 137, 3867-3876. 7. Vijayakumar, M., Bain, A.D., Goward, G.R. Investigations of Proton Conduction in the Monoclinic Phase of RbH2PO4 Using Multiniclear Solid-State NMR, J. Phys. Chem. C, 2009, 113, 17950-17957 8. Traer, J.W., Soo, K.J., Vijayakumar, M., Goward, G.R., Elucidating the Time Scale and Geometry of Phosphonate Rotation in Solid Electrolytes Using Multinuclear NMR, J. Phys. Chem. C., 2011, 115, 6064-6072

9. Reichert, D. and Saalwäcther, K. Dipolar Coupling: Molecular-Level Mobility. Encyclopedia of Nuclear Magnetic Resonance, Volume 9, Wiley, 2002. 10. Pileio, G.; Consistre, M.; McLean, N.; Gansmuller, A.; Brown, R.C.; Levitt, M.H. Analytical Theory of γ-Encoded Double-quantum Recoupling Sequences in Solid State Nuclear 32


Page 33 of 35

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Magnetic Resonance, J. Magn. Reson., 2007, 186, 65-74. 11. Saalwächter, K. 1H Multiple-quantum Nuclear Magnetic Resonance Investigations of Molecular Order in Polymer Networks, II. Intensity Decay and Restricted Slow Dynamics, J. Chem. Phys., 2004, 120, 454-464. 12. Kristiansen, P.E.; Carravetta, M.; Lai, W.C.; Levitt, M.H. A Robust Pulse Sequence for the Determination of Small Homonuclear Dipolar Couplings in Magic Angle Spinning NMR, Chem. Phys. Lett., 2004, 390, 1-7. 13. Feike, M., Demco, D.E., Graf, R., Gottwald, J., Hafner, S., Spiess, H.W. Broadband Multiple-Quantum NMR Spectroscopy, J. Magn. Reson. Series A, 1996, 122, 214-221. 14. Bak, M., Rasmussen, J.T., Nielsen, N.C. SIMPSON: A General Simulation Program for Solid State NMR Spectroscopy, J. Magn. Reson., 2000, 147, 296-330. 15. Rienstra, C.M., Hohwy, M., Mueller, L.J., Jaroniec, C.P., Reif, B., Griffin, R.G. Determination of Multiple Torsion-Angle Constraints in U-13C, 15N-Labeled Peptides: 3D 1 H-15N-13C-1H Dipolar Chemical Shift NMR Spectroscopy in Rotating Solids, J. Am. Chem. Soc., 2002, 124, 11908-11922. 16. Strojek, W., Kalwei, M., Eckert, H. Dipolar NMR Systems Involving Quadrupolar Nuclei: 31 P {23Na} Rotational Echo Double Resonance (REDOR) of Crystalline Sodium Phosphates and Phosphate Glasses, J. Phys. Chem. B., 2004, 108, 7061-7073. 17. van Moorsel, G.-J.M.P.; van Eck, E.R.H.; Grey, C.P. Pr2Sn2O and Sm2Sn2O7 as HighTemperature Shift Thermometers in Variable-Temperature 119Sn MAS NMR, J. Magn. Reson. Series A, 1995, 113, 159-163. 18. Botez, C.E.; Martinez, H.; Tackett, R.J.; Chianelli, R.R.; Zhang, J.; Zhao. Y. Hightemperature Crystal Structures and Chemical Modifications in RbH2PO4, J. Phys.: Condens. Matter, 2009, 21, 325401-325407. 19. Pourpoint, F.; Gervais, C.; Bonhomme-Coury, L.; Azais, T.; Coelho, L.; Mauri, F.; Alonso, B.; Babonneau, F.; Bonhomme. C. Calcium Phosphates and Hydroxyapatite Solid State NMR Experiments and First Principals Calculations, Appl. Magn. Reson., 2007, 32, 435457. 20. Cook, W.R. Thermal Expansion of Crystals with KH2PO4 Structure, J. Appl. Phys., 1967, 38, 1637-1642 33



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21. Nelmes, R.J., Meyer, G.M., Tibballs, J.E. The Crystal Structure of Tetragonal KH2PO4 a as Function of Temperature, J. Phys. C., 1982, 15, 59-75 22. Saalwächter, K. Proton Multiple-Quantum NMR for the Study of Chain Dynamics and Structural Constraints in Polymeric Soft Materials, Prog. Nucl. Magn. Reson. Spectrosc., 2007, 51, 1-35 23. Magome, E., Komukae, M., Machida, M. Neutron Diffraction Study of Ferrielectric Phase Transistion in Monoclinic RbD2PO4, J. Phys. Soc. Jpn., 2007, 76, 044606 24. Kennedy, N.S.J., Nelmes, R.J. Structural Studies of RbH2PO4 in its Paraelectric and Ferroelectric Phases, J. Phys. C., 1980, 13, 4841-4853 25. Hagiwara, T., Itoh, K., Nakamura, E. Structure of Monoclinic Rubidium Dideuterium Phosphate, RbD2PO4, in the Intermediate Phase, Acta. Cryst., 1984, 40, 718-720

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Table of Contents Figure:

Normalized Intensity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Recoupling Time (µs)

35


Quantifying Site-Specific Proton Dynamics in Phosphate Solid Acids

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