Temperature dependent structure and dynamics in smectite interlayers: 23Na MAS NMR spectroscopy of Na-hectorite

23Na MAS NMR spectroscopy of the smectite mineral hectorite acquired at temperatures from −120 °C to 40 °C in combination with the results from computational molecular dynamics (MD) simulations show the presence of complex dynamical processes in the interlayer galleries that depend significantly on their hydration state. The results indicate that site exchange occurs within individual interlayers that contain coexisting 1 and 2 water layer hydrates in different places. We suggest that the observed dynamical averaging may be due to motion of water volumes comparable to the dripplons recently proposed to occur in hydrated graphene interlayers (Yoshida et al. Nat. Commun., 2018, 9, 1496). Such motion would cause rippling of the T-O-T structure of the clay layers at frequencies greater than ∼25 kHz. For samples exposed to 0% relative humidity (R.H.), the 23Na spectra show the presence of two Na+ sites (probably 6 and 9 coordinated by basal oxygen atoms) that do not undergo dynamical averaging at any temperature from −120 °C to 40 °C. For samples exposed to R.H.s from 29% to 100% the spectra show the presence of three hydrated Na+ sites that undergo dynamical averaging beginning at −60 °C. These sites have different numbers of H2O molecules coordinating the Na+, and diffusion calculations indicate that they probably occur within the same individual interlayer. The average hydration state of Na+ increases with increasing R.H. and water content of the clay.


Introduction
The interactions among ions, water, and a substrate are fundamental processes in elds as diverse as biology, medicine, chemistry, materials science, geology, and space science. In many of these elds, and especially materials science and the geosciences, the substrate for the interactions is oen a solid oxide or hydroxide material which can have wide ranging structural and chemical properties. Thus, there has been substantial effort devoted to understanding the structural, dynamical, and energetic aspects of the interaction of ions and water with geochemically important minerals 1-28 and materials of technological importance. [29][30][31][32] The temperature and pressure dependence of these interactions is complex and has been a long standing topic of discussion. [33][34][35][36][37][38] The smectite group of clay minerals has been of particular interest in geoscience, chemistry and materials science, because of their abundance and ability to intercalate a wide variety of organic and inorganic cations, along with water and other uid species. Because of their remarkable swelling capacity, they have been of longstanding interest in nuclear waste management, in composites with polymers and in 2D-nanomaterials. 37,[39][40][41][42] Because the ions and molecules in the interlayer galleries of smectite clays are structurally and dynamically disordered, their molecular scale behavior is difficult to study with diffraction methods, and in recent years experimental spectroscopic methods and computational molecular modeling have been widely employed. 1,2,5,[7][8][9][10][11][12]43 This paper reports the results of an experimental, variable temperature 23 Na nuclear magnetic resonance (NMR) and computational molecular dynamics (MD) modeling study of the structural and dynamical behavior of Na + in the widely investigated smectite clay, hectorite. The 23 Na NMR behavior of hectorite has been studied previously, 1 but the results here provide more comprehensive understanding, because the spectra were obtained at a higher H 0 eld strength (850 MHz 1 H frequency) and over a wider range of temperatures and water contents. The MD modeling results provide important insight into the molecular scale behavior of the interlayers and support the structural and dynamical interpretations of the NMR results. Hectorite is commonly used in NMR studies of smectites, because its low Fe content greatly reduces paramagnetic line broadening compared to other natural smectites such as montmorillonite. 44 Hectorite containing a wide variety of exchangeable species has been studied by NMR methods, 1,8,9,22,23,44 X-ray diffraction (XRD), 1,45-48 thermogravimetric analysis (TGA), 1,44,46 and quasi-elastic neutron scattering (QENS). [24][25][26][49][50][51] In parallel, there have also been several computational molecular modeling studies of it using principally MD methods. 10,14,16,21,25,43,49,52 The results here show complex, temperature dependent dynamical behavior that depends greatly on the water content of the sample. We interpret this complex behavior to be due to diffusional motion in individual interlayer galleries with varying local hydration states and, thus, varying interlayer thicknesses (basal spacings) along their length. Such behavior requires the tetrahedral-octahedral-tetrahedral (T-O-T) layers of the clay to be exible and dynamic. The basal XRD reections of smectites are commonly quite broad, which is usually interpreted to be due to coexisting interlayers with different basal spacings, rather than variable spacings within individual interlayers. However, as discussed in detail below there is growing evidence that smectite T-O-T layers are exible and dynamic, and thus that their interlayer galleries could be comparably dynamic. 11,12,[33][34][35][36][37][38] Materials and methods

Materials
The hectorite sample used in this study was the standard San Bernardino hectorite (SHCa-1), which is available from the Source Clays Repository of the Clay Minerals Society. This hectorite develops its permanent structural charge from Li + for Mg 2+ substitution in the octahedral sheet of the T-O-T layers and contains only a trace amount of paramagnetic iron, making it useful for the NMR studies. 1,9,44 The charge balancing cation in the as-received sample is predominantly Na + , with lesser amounts of K + , Mg 2+ , and Sr 2+ . It's permanent structural layer charge is À0. 35

Na MAS NMR methods
The temperature dependent 23 Na Bloch-decay NMR experiments were performed at a resonance frequency of 224.77 MHz under magic angle spinning (MAS) conditions at a spinning frequency of 10 kHz using an 850 MHz Agilent DDR2 solid state NMR spectrometer located at the Environmental and Molecular Science Laboratory of the Pacic Northwest National Laboratory. The spectra were collected with 500 transients using a spectral width of 100 kHz, and the spectra contain 2048 data points.
A pulse delay of 1.5 to 5 s was used depending on the temperature. The chemical shis of all the spectra were referenced to a 1 M NaCl(aq) solution that was also used for the pulse width calibration. Power was adjusted to produce a liquid-state p pulse of 10 ms. A quantitative and central-transition-selective pulse width of 0.45 ms was used to obtain the spectra of the clay samples, since 23 Na is a spin 3/2 quadrupolar nucleus. All spectra were processed using MestreNova soware and received one zero ll. An exponential apodization of 100 Hz was used for the 40 C, 20 C, 0 C, À20 C and À40 C spectra, and 1000 Hz was used for the À60 C, À80 C, À100 C, and À120 C samples. Samples were equilibrated for 30 min at each temperature prior to NMR data acquisition. The temperature was controlled using a standard Varian VT stack temperature controller with a liquid nitrogen cooled VT gas. Samples were packed in 4 mm, thick wall zirconia NMR rotors sealed at both ends with a rubber cap in order to prevent water loss during data acquisition. All the samples were weighed before and aer the experiment to evaluate water loss during the NMR data acquisition and showed negligible water loss (AE0.2%). All the spectra were analyzed using the iterative tting program DMt with an estimated tting uncertainty of AE1%. 55

Computational methods
The simulated hectorite model has a structural formula of Na 0.4 (Mg 2.6 Li 0.4 )Si 4 O 10 (OH) 0.94 F 1.06 , in close agreement with the composition of the natural sample. 1,18 The F À atoms are located in two different nearest neighbor environments: (i) coordinated to three Mg and (ii) coordinated to two Mg and one Li. The ratio of these two sites is 3/2, in accordance with site intensities from 19 F NMR spectra of the natural sample. 56 There is no tetrahedral Al 3+ for Si 4+ substitution in this model, since the natural sample contains a negligible fraction of such sites.
The simulation supercell contains 2 interlayer regions and consists of 32 unit cells of hectorite (4 Â 4 Â 2) with lateral dimensions of approximately L x ¼ 21.0Å and L y ¼ 36Å. The size of the model allows for a quasi-disordered distribution of the Li + /Mg 2+ substitution sites following generalization of Lowenstein's rule. 57 The Li + /Mg 2+ and F À /OH À distributions were assigned only aer building the supercell to avoid the possibility of repetitive patterns in different T-O-T layers. For each simulation, all the Na + ions were initially placed at the midplane of the interlayers. Twenty six different models were investigated with water contents ranging from 0 to 24H 2 O molecules/Na + ion. The water contents used in our simulation model will permit us to probe a range of hydration states, starting with collapsed interlayers and up to 4-layer hydrates. As a result, these simulated models will be able to predict different hydration states observed experimentally at different R.H. conditions. We performed classical MD simulations in the NPT and NVT ensembles at ambient conditions (T ¼ 300 K and P ¼ 1 bar) using the LAMMPS simulation package. 58 A Nose-Hoover thermostat and barostat were used to control the temperature and pressure independently in all 3 directions. 59,60 Threedimensional periodic boundary conditions were employed. A cutoff distance of 10Å was applied for the short-range nonelectrostatic interactions, and Ewald summation technique was used to compute long-range electrostatic interactions. A time step of 1 fs was employed in our simulations. Each system was equilibrated for 5 ns followed by a production run for another 2 ns in NPT ensemble. The MD trajectories were recorded every 10 fs during production run for the analysis of thermodynamic properties. The potential stable hydration states were determined based on the thermodynamic analysis from NPT simulations. The interlayer structural and dynamic properties were then obtained subsequently by running simulation in the NVT ensemble for these hydration states. These simulations were run for 5 ns for equilibration and an additional 2 ns for data production where the trajectories are recorded every 10 fs for structural interpretation. Our previous papers provide further details about this hectorite model and the simulation and analysis methods. 11,12,61,62

Experimental results
The 23 Na MAS NMR spectra of Na-hectorite show great variation with R.H. and temperature ( Fig. 1, 2, Table S1, and Fig. S1 †). At 0% R.H. there are two resonances centered at $À29 ppm and $À19 ppm at all temperatures from À120 C to 20 C. The peak maxima and relative intensities of these two resonances do not vary signicantly with temperature, and the relative intensity and FWHH of the resonance at $À29 ppm are less than those of the À19 ppm at all temperatures. The spectra of the samples exposed to 29% and 43% R.H. vary greatly with temperature. At À120 C, À100 C, and À80 C they contain ve resonances, which coalesce to three at higher temperatures ( Fig. 1b and c). At 29% R.H. the two most shielded resonances at $À21 and À27 ppm resemble the $À19 and À29 ppm resonances observed at 0% R.H. and are observable above the baseline at all temperatures. At 43% R.H. the most shielded resonance at $À27 ppm is not resolvable above the baseline except at À120 C, where it occurs at À27.4 ppm, and the resonance at $À19 ppm does not change signicantly with temperature. For both the 29% and 43% R.H. samples at À120 C, À100 C, and À80 C there are three other, more deshielded resonances with peak maxima of $À11 ppm, $À6 ppm and $0 to 1 ppm. For the 29% R.H. sample, from À120 C to À80 C these resonances become generally narrower (especially the one at $0 to 1 ppm), and at À60 C they merge into a single, symmetrical resonance centered at $6 ppm. With increasing temperature this resonance narrows and becomes more symmetric, and its peak maximum becomes more shielded (more negative). The behavior of the 43% R.H. sample with increasing temperature is generally similar, except that from À60 C to 0 C tting of the merged peak requires two resonances. For the 70% and 100% R.H. samples at À120 C there are three resolvable resonances centered at $1.2 to À2.7 ppm, $À6 ppm, and $À20 ppm. The resonance at $À29 ppm observed at low temperatures and lower R.H.s is not resolvable above baseline for these samples, and the position, FWHH and relative intensity of the $À20 ppm resonance does not change signicantly with temperature. At 70% R.H. the width of the most deshielded resonance at $0 ppm decreases from À120 C to À80 C, and at À60 C it merges with the $À6 ppm resonance into an asymmetrical peak. At higher temperatures, this peak becomes narrower and more symmetrical, and its peak maximum becomes more shielded (more negative). At 100% R.H. the two most deshielded resonances centered at $À1 and À5 ppm at À120 C merge into a single asymmetrical resonance at À100 C which becomes more symmetrical, narrower (except at À60 C), and more shielded (more negative) with increasing temperature. Fig. 2 highlights the greatly different effects of varying temperature and R.H. on the 23 Na NMR spectra. For instance, at low temperature (À100 C) there is progressive loss of signal intensity for the $À6 and À12 ppm resonances with increasing R.H. (Fig. 2a), and at high temperature (40 C) the merged peak in the $ À4 to 2 ppm range becomes progressively more shielded (Fig. 2b).

Computational results
The computed interlayer spacings of the model Na-hectorite increase with increasing water content and show well-dened monolayer (1L) and bilayer (2L) hydrates, along with continuous expansion at higher hydration states (Fig. 3a). The basal spacing of 9.5Å for the collapsed (0H 2 O) model is in good agreement with the experimental value of 9.7Å. 1 The 1L and 2L hydrates are characterized by distinct plateau regions at basal spacings of $12.0Å and 15.0Å, respectively and is consistent with the experimental values. 1 For both the 1L and 2L states, however, the computed basal spacings increase slightly with increasing water content. The computed basal spacings for the dry and 1L and 2L hydrates here are very close to those calculated for Na-hectorite with no F À for OH À substitution, 10 suggesting that the macroscopic expansion behavior of hectorite is not greatly affected by the F À /OH À ratio.
The computed interlayer hydration energies for Na-hectorite show three minima at H 2 O/Na + ratios of 3.0, 6.7 and 10.8 with values of À56, À52 and À48 kJ mol À1 , respectively (Fig. 3b). The minima at H 2 O/Na + ¼ 3.0 and 6.7 coincide with the beginning and complete formation of a 1L hydrate structure with basal spacings that increase from 12.0Å to 12.6Å. The broader and  shallower minimum centered at H 2 O/Na + ¼ 10.8 corresponds to the 2L hydrate with varying water contents and shows that the hydration energy does not vary much with H 2 O/Na + ratio in this range as the basal spacing increases from about 14.8Å to 15.6Å. Although the computed energies are similar to those for Na-hectorite with no F À for OH À substitution, 10 the H 2 O/Na + ratios are somewhat higher here, because the smaller layer charge of our model (À0.8 |e| vs. À1.0 |e| in the earlier study) requires fewer Na + /formula unit, leaving more interlayer space for H 2 O adsorption. The computed atomic density proles (ADPs) for the interlayer species in the simulations with H 2 O/ Na + ¼ 0, 3, 6.7, and 10.8 (Fig. 4) are generally similar to the comparable proles for Na-hectorite with no F À for OH À substitution, 10 except at H 2 O/Na + ¼ 3, which has the global minimum energy (Fig. 3). The ADP of Na + for this composition is characterized by a broad distribution near the center of the interlayer (Fig. 3b) These results support the interpretation of experimental XRD results for uorohectorite that indicate that the Na + ions are located on two different positions closer to one or the other basal surface and that H 2 O molecules are at the midplane of the interlayer gallery. 46 The absence of two well resolved ADP peaks for Na + in our studies is probably due to the presence of $50% OH À as opposed to the 100% F À composition studied by Kalo et al. 46 In this case, the Na + is located at the center of a ditrigonal cavity of one basal surface and above a Si tetrahedron of the other (Fig. 6c). The details of the RDFs and RCNs at higher hydration states are similar to those for Na-hectorite with no F À for OH À substitution. 10 This result indicates that F À for OH À substitution has progressively less effect on the interlayer cations with increasing distance from the basal surface.
The Na + ADP for Na-hectorite with no F À for OH À substitution, 10 shows a single, narrow peak near the center for the interlayer O b , that H 2 O molecules partially hydrate them, and that they also coordinate the O b atoms. The computed radial   distribution functions (RDFs) and associated running coordination numbers (RCNs) of Na + show substantially different coordination environments at different hydration states (Fig. 5a-d). For the collapsed (0H 2 O) structure the mean nearest neighbor interatomic distance between Na + and O b is $2.4Å with a shoulder at $3.0Å (Fig. 5a). This distribution is signicantly different from that for Na-hectorite with no F À for OH À substitution, which has a well resolved peak at 2.5Å and does not have the shoulder at 3.0Å. 10 These differences are due to differences in the coordination environments of Na + ions near an F À on both sides of the interlayer and those near an F À on one side and an OH À on the other (Fig. 6a and b). There is a negligible number of Na + near OH À on both sides. The nearest neighbor O b -Na + RCN for Na + near two F À sites is 6, 3 from each basal surface. That for Na + near one F À and one OH À is 9, 6 from one side and 3 from the other.

Structural interpretations
The two temperature-independent 23 Na NMR resonances at $À29 and $À19 ppm for the 0% R.H. Na-hectorite sample that are also present with decreasing abundances at higher R.H.s ( Fig. 1) represent rigidly held interlayer Na + . Since the molar H 2 O/Na + ratio of the 0% R.H. sample is 0.40 ( Table 1) and some of this water is probably on external particle surfaces, we interpret these resonances to be due to Na + coordinated by only O b atoms of the basal surfaces with little coordination by the oxygen atoms of water molecules (O w ). Similar behavior has been observed for 133 Cs in Cs-hectorite. 44 The NMR chemical shis of such nuclides as 23 Na, 133 Cs, 27 Al, and 29 Si in oxide systems are well known to become more shielded (more negative) with increasing nearest neighbor (NN) coordination number. 44 For these two resonances, the $10 ppm difference in the peak maxima indicates signicantly different NN coordination numbers. The MD simulations for fully dry Na-hectorite here show Na + with either 6 and 9 NN O b . Thus, we interpret the $À19 ppm resonance to be due to Na + in dominantly 6-fold coordination by O b and $À29 ppm resonance to Na + in dominantly 9-fold coordination by O b , with the specic structural environments discussed above (Fig. 6a-c). These coordinations are very different than the 9-and 12-fold coordinations proposed for Cs + in Cs-hectorite 44 due to the smaller size of Na + .
The presence of the $À19 ppm resonance at all R.H.s and temperatures shows that our Na-hectorite contains interlayers in which the Na + is not signicantly coordinated by H 2 O molecules under any of the experimental conditions. The spectral tting results (Table S1 †) indicate that at 29% and 43% R.H. approximately 35 to 40% of the Na + is in such environments and that at 100% R.H. this amount is in the 10-16% range. The loss of the $À29 ppm resonance at R.H.s of 43% and greater suggests that some water is entering these interlayers and causes the Na + ions to preferentially occupy 6-coordinate sites. Similarly, the decreased relative intensity of the $À19 ppm resonance with increasing R.H. indicates that progressively more of these interlayers become hydrated as the H 2 O activity (R.H.) increases.
The appearance of the resonances in the low temperature spectra near 0, À6 and À12 ppm at R.H.s greater than 0% clearly demonstrates that they are due to Na + coordinated to at least some O w . The resonance at $0 ppm is readily assigned to Na + coordinated by 6 O w . Na + in 6-coordination in aqueous solutions occurs near 0 ppm, 54,[63][64][65] and NaCl in 1 M solution is the chemical shi standard for 0 ppm. This interpretation is supported by the known deshielding of Na + with increasing coordination by water, 1,66 and the observations that this resonance is the most deshielded one observed and dominates at 100% R.H. Steric considerations require that 6-fold coordination of Na + by H 2 O in smectites must occur in interlayers that are at least 2L hydrates, and our MD simulations show that all the Na + in 2L layers in Na-hectorite have this coordination by O w (Fig. 5d). The presence of both the $À19 and 0 ppm resonances at R.H.s of 29% and more, thus, clearly demonstrates the coexistence of interlayer environments with greatly different hydration states with signicant amounts of H 2 O present.
The presence of the resonances near À6 and À11 ppm observed at low temperatures at R.H.s of 29% and greater and their progressive decrease in relative intensity at larger R.H. demonstrates that they must be due to interlayer Na + coordinated to fewer than 6 O w along with some number of O b . Given the observation of coexistence of 0L and 2L states in our samples and the previously reported coexistence of at least 1L and 2L states in Na-hectorite at 43% R.H. 1 at least one of these resonances must be due to Na + in 1L hydration. Our MD simulations for 1L interlayers shows that the average NN coordination of Na + is 3.0 O w and 2.0 O b at H 2 O/Na + ¼ 3.0 and 4 O w and 1 O b at H 2 O/Na + ¼ 6.7 and that the interlayers are disordered. Since coordination to O w causes deshielding relative to coordination to O b (e.g., the NN coordinations of the $0 ppm and $À19 ppm resonances), we assign the $À11 ppm resonance to Na + with 3.0 O w and 2.0 O b nearest neighbors and the $À6 ppm resonance to Na + with 4 O w and 1 O b nearest neighbors. These assignments are in agreement with the progressive decrease in the relative intensity of the $À11 ppm peak compared to that of the $À6 ppm peak with increasing R.H. The interlayers are, of course, highly disordered, and other coordinations are also like to be present at lower abundances. Collectively then, the 23 Na NMR spectra of our samples in combination with the MD modeling results demonstrate that in the presence of water Na-hectorite contains multiple coexisting hydration states at a given R.H. and that the average hydration of the Na + ions increases with increasing R.H. The relatively small energy differences between the different hydration states (Fig. 3b) supports the argument that they can be expected to coexist, especially given the potential for different local compositions of the T-O-T layers themselves.

Dynamical interpretations
The temperature dependence of the 23 Na NMR spectra demonstrates that the rate of dynamical exchange of Na + among the structural environments represented by the resonances centered near $0, $À6, and $À11 ppm increases with increasing temperature and provides some constraint on this rate. In NMR spectra, dynamical site averaging causes observable merging of peaks if the frequency of exchange is greater than approximately 0.1Â the difference in peak positions in frequency units, with full merging occurring at frequencies $10Â this difference. 44 Dynamical effects can also cause narrowing of a single peak due to averaging of chemical shi anisotropy (CSA), second order quadrupolar broadening or static structural disorder. Both effects occur in our samples. The presence of the $0, À6 and À11 ppm peaks at À80 C and below demonstrates that there is no exchange of Na + between these environments at frequencies >$0.25 kHz (0.1 Â 11 ppm Â 224 Hz ppm À1 ). With increasing temperature, these peaks merge into one that becomes progressively narrower with increasing temperature. In a three-site exchange model the chemical shi of the averaged peak (d avg ) is given by where d i and I i (i ¼ 1, 2, 3) represent the observed chemical shis and average fractional intensities of the respective resonances. Comparison of the observed chemical shis of the resonance in the 0 to À6 ppm range for the 40 C spectra with that calculated values assuming complete dynamical averaging of the three low temperature peaks $0, À6 and À11 ppm shows very good agreement (Table 2), clearly demonstrating that this resonance is the average of the three low temperature ones. The appearance of multiple resonances in the 133 Cs NMR spectra of Cs-hectorite at low temperature and their peak averaging at higher temperature supports this argument. 44 With increasing R.H. the sum of the relative intensities of the $0, À6 and À11 ppm peaks at low temperatures and the averaged peak at 40 C increase and the sum of intensities of the $ À19 and À27 ppm decrease (Table S1 †) indicating that progressively more of the interlayers are being hydrated and that all the Na + in the hydrated interlayers is participating in the dynamical averaging. The progressively more deshielded (less negative) position of the dynamically averaged peak at 40 C with increasing R.H. is due to averaging among sites with progressively more NN O w . It is not possible to uniquely model the frequencies of this site exchange at each temperature due to uncertainty related to potential quadrupolar and CSA effects. However, the widths of the averaged peaks at À60 C are approximately half the full range of the chemical shis at low temperature, indicating that the frequency of the site exchange process is of the order of 2.5 kHz at this temperature. The decreasing width of the averaged peak with increasing temperature shows that this exchange frequency progressively increases, but it is not possible to uniquely calculate the values. The decreasing width of the averaged peak at 40 C with increasing R.H. suggests that this frequency increases with increasing water content and average hydration state of the Na + .
The narrowing of the individual resonances with increasing temperature in the À120 C to À80 C range demonstrates an increasing frequency of dynamical averaging within the NN environments of Na + (e.g., cage rattling) without rapid exchange among the different environments. This is clearest for the $0 ppm resonance for Na + coordinated by 6 water molecules (Fig. 1). Such line narrowing is expected, because the activation energy for motion of the Na + ions relative to their NN H 2 O molecules is expected to be much less than that for Na + or H 2 O site exchange. The interplay of this nearest neighbor motion and site exchange is clearly illustrated for the $0 ppm peak at 70% and 100% R.H. From À120 C to À80 C this resonance narrows, but intensity for the less hydrated sites remains resolvable. At À60 C, however, the resonance in this region broadens due to the exchange among these sites, and at higher temperatures it narrows again due to more rapid site exchange.
The molecular scale mechanism of the observed site exchange is likely to involve both motion of the H 2 O molecules and the Na + ions. MD simulations of Na-hectorite with no F À for OH À substitution show that the diffusion coefficients of H 2 O molecules are somewhat larger than those of Na + ions in both 1WL and 2WL interlayers, but that they are of the same order of magnitude (10 À7 cm 2 s À1 for 1L and 10 À6 cm 2 s À1 for 2L hydrates near room temperature). 10 For these values, characteristic diffusion distances ($[Dt] 1/2 ) on the ms NMR time scale are of the order of 0.1 mm for 1L and 0.3 mm for 2L hydrates. 10 These distances are much more than enough to cause local averaging within a homogeneous interlayer at room temperature. The diffusion coefficients at À60 C, the lowest temperatures at which site exchanges are observed, are not known but are certainly much less than at room temperature. The characteristic diffusion lengths are, thus, expected to be much less than at room temperature. The lateral dimensions of the individual particles of the hectorite we use are of the order of 1 to a few mm, larger than the characteristic diffusion lengths at room temperature and certainly larger than at À60 C. This result suggests that site exchange between separate 1L and 2L interlayers would not occur rapidly enough to cause the observed changes in the NMR spectra. We conclude, then, that the NN coordination environments of Na + giving rise to the $0, À6 and À11 ppm resonances at low temperature all occur within individual interlayers, and thus that the hydration state at a specic position in an individual interlayers varies with time.
For the observed site averaging to occur within in individual interlayer, the basal spacing of that interlayer must dynamically expand and contract as the Na + and H 2 O diffuse relative to the T-O-T layers and each other. This requires that the T-O-T layer bend and ripple with an out-of-phase component to the power spectrum. The ability of the T-O-T layers of clays and micas to bend has been reported in many experimental and computational studies. For instance, MD simulations of the smectite mineral beidellite show reversible (elastic) bending due to an external stress of about <0.7 GPa. 33 Similar elastic behavior has been reported for muscovite mica at external stresses as high as 2 GPa. 33 A combination of MD modeling and AFM and TEM observations for clays and mica show that this bending occurs by bond stretching and bending and causes rearrangement of the alkali metal ions on the surfaces of the layers. 38 Large-scale MD simulations of smectite clays show dynamical undulatory behavior. 35,36 There are also other reports showing bending of clay layers in polymer composites. 37 Cryo-TEM images of montmorillonite in water show bent T-O-T layers and variable interlayer thickness in the osmotic swelling regime, demonstrating exibility of the T-O-T layers under these conditions. 67 To our knowledge there have been no large-scale computational studies of smectites with partially hydrated interlayers that might be expected to show dynamic uctuations in local interlayer hydration state in addition to undulatory behavior. MD studies of water in graphene, however, do show dynamical rippling of the C-sheets and the coexistence of 1L and 2L water domains within individual interlayers. 68 In these simulations, the 2L domains (called dripplons by the authors) move rapidly within the interlayer gallery during the 1 ns simulation time and cause bending of the graphene sheets. The dripplons are stable to the addition of solute and show rapid lateral motion at rates comparable to that of the diffusion of individual water molecules. Large scale MD studies of layered double hydroxides also show rippling of the metal hydroxide layers and small uctuations of the thickness of individual interlayers. 69 For such behavior to cause complete averaging of the $0, À6 and À11 ppm resonances in our 23 Na NMR spectra, this frequency must be greater than approximately 25 kHz, the range of chemical shis of the averaged peaks. This frequency is orders of magnitude slower than the calculated rate of motion of Table 2 Calculated average peak maxima (d avg ) assuming 3-site averaging of the three most shielded Na + resonances at À120, À100, and À80 C compared to the observed value of the dynamically average resonance at 40 C for Na-hectorite exposed to he indicated R.H.s

R.H. (%)
T dripplons in graphene. MD simulations of very large smectitewater systems at a range of temperatures and experimental approaches such as uid cell TEM 67 will be needed to explore this issue further.

Conclusions
Variable temperature 23 Na NMR spectra of variably hydrated Nahectorite in combination with computational MD modeling shows the coexistence of several local hydration states of Na + in an individual sample and that the average hydration state increases with increasing R.H. NMR resonances for these different hydration states are observable at temperature of <À80 C. At higher temperatures they merge due to dynamical site exchange, and the results show that this must occur within individual interlayers. This dynamics must result in rippling of the T-O-T layers as the interlayers expand and contract, as recently proposed for hydrated graphene. 68

Conflicts of interest
There are no conicts to declare.