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Feb 26, 2008 - Silica Gel Surface: Molecular Dynamics of Surface Silanols ... Deuterated silica gel samples were prepared by replacement of the exchan...
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J. Phys. Chem. C 2008, 112, 4315-4326

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Silica Gel Surface: Molecular Dynamics of Surface Silanols Takeshi Kobayashi, Joseph A. DiVerdi, and Gary E. Maciel* The Department of Chemistry, Colorado State UniVersity, Fort Collins, Colorado 80523 ReceiVed: October 5, 2007; In Final Form: December 21, 2007

The molecular dynamics of the silanols of high surface-area silica gel was studied using solid-state deuterium NMR spectroscopy. Deuterated silica gel samples were prepared by replacement of the exchangable silanol protons upon exposure to liquid 2H2O and subsequent dehydration under vacuum at various temperatures that were selected to provide samples with varying populations of specific surface features, including (a) “isolated” silanols, that is, those that are not hydrogen-bonded (as demonstrated by the 1H NMR chemical shift), (b) hydrogen-bonded silanols with a wide range of hydrogen-bonding strengths (as shown by the broad 1H NMR peak), and (c) a hydrogen-bonded network of physisorbed water. On a highly dehydrated surface obtained by dehydration at 500 °C and containing only isolated silanols, analysis of the deuterium line shapes indicates that the “isolated” silanols exhibit a broad, inhomogeneous distribution of librational amplitudes of O-H entities about the internuclear Si-O vector, all in the fast-exchange limit (with reference to a 5 × 10-6 s time scale defined by deuterium quadrupole interactions). The librational amplitudes depend on the observation temperature: increasing amplitudes with increasing temperature and vice versa. At the lowest observation temperature of 78 K, a small part of the silanols is essentially immobilized, but a sizable fraction remains mobile. At dehydration temperatures of 150 and 300 °C, the silica surface contains silanols with a distribution of hydrogen-bond strengths. At each observation temperature, the heterogeneous population of hydrogenbonded silanols exhibits a broader distribution of librational amplitudes than those exhibited by the “isolated” silanols at the same observation temperature. Less-aggressive dehydration conditions, for example, dehydration temperatures of 25 and 75 °C, creates samples in which, in addition to the silanols, a significant amount of physisorbed (deuterated) water is present. At lower observation temperatures, the effect of this physisorbed water is to narrow the librational amplitude for all of the silanols and water molecules. At the lowest observation temperature of 78 K, most of the surface silanols and water molecules of silica gel dehydrated at 25 and 75 °C are essentially immobilized. For silica gel dehydrated at 25 and 75 °C, at observation temperatures of 200 K and above, chemical exchange among a fraction of the surface silanols becomes significant, resulting in highly narrowed line shapes, while a substantial fraction of the surface silanols continue to execute the librational motions characteristic of more dehydrated surfaces. Line-shape analysis of the librational motion of the silanols permits the estimation of 121 ( 1° as the Si-O-2H bond angle. The deuterium quadrupole coupling constant of the silanol hydrogens is found to vary with the dehydration conditions and is interpreted as reflecting variations of the ensemble-averaged O-O distance between silanol oxygens and their various hydrogenbonded partners. These data are interpreted in terms of a distribution of hydrogen-bonding arrangements on the heterogeneous silica surface, as witnessed by the silanols. This work provides an indirect indication that the popular view of a hydrogen bond (e.g., one with an O-O distance of 0.33 nm or less and with a nearly linear O-H-O arrangement) can be extended to admit a class of “weak” hydrogen bonds, for which the distance and geometry of the O-H-O triples are outside the typical view; but at such O-H-O configurations there are still significant interaction energies and molecular dynamics is affected.

Introduction Silica surfaces play important roles in a wide variety of applications, such as catalysis, separations, and advanced materials. It is well known that the many relevant properties of silicas are based on the concentration, distribution, and nature of surface silanols.1,2 Much of the work performed on surface silanols has been carried out using NMR,3-11 infrared,5,7,11-16 and theoretical calculations.17-21 In terms of the terminal structure of silica, there are principally two types of silanols, (-O)3SiOH (Q3) and (-O)2Si(OH)2 (Q2). Some surface silanols form hydrogen bonds with neighbors, depending on their proximity, while some portion of the surface silanols is not * Corresponding author. E-mail: [email protected].

involved in hydrogen bonding; the non-hydrogen-bonded silanol population increases with increasing extent of dehydration.4,6 Structural information on surface silanols is important in understanding their interactions with adsorbates.5,22 There have been numerous investigations of the framework of silica,23-26 but details on the silanol moiety, for example, the Si-O-H bond angle and motion of the hydroxyl group, have not previously been definitively determined experimentally. The dynamics of the surface silanols of silica gel is of interest in the context of the structural environment around the silanols. Because the motional modes of the silanols reflect their local environments through interactions with their neighbors, the dynamics of the silanols can be used as a probe for hydrogen bonding and the topological surface structure associated with

10.1021/jp709759e CCC: $40.75 © 2008 American Chemical Society Published on Web 02/26/2008

4316 J. Phys. Chem. C, Vol. 112, No. 11, 2008 those hydrogen bonds. IR spectroscopy has been an informative tool and has provided dynamical information such as the identities of vibrational modes and their frequencies as well as static characteristics of the silanols.13,15 Nevertheless, knowledge of surface silanol dynamics remains limited and the details of the dynamics of the surface silanols, such as motional modes and their rates and the relationships between the dynamics and the static characteristics, are still incompletely understood. The deuterium nucleus has a spin quantum number of 1, and its quadrupolar interaction is very sensitive to dynamical properties. Line-shape analysis can be used to interrogate dynamical properties, such as the types of motional modes and their rates.27-33 In the work described in this paper, deuterated silica gel samples were prepared by exposure to 2H2O, followed by dehydration at various temperatures, and the resulting deuterated surface silanols were studied by solid-state deuterium NMR over a wide range of observation temperatures. The experimentally obtained deuterium NMR spectra are matched to theoretically generated line shapes to characterize the molecular dynamics of the silanols. The analysis of the deuterium NMR spectra also permits estimation of the Si-O2H bond angle. The relationships between the surface silanol dynamics and corresponding local environments, for example, strength of the hydrogen bonds and configuration of the silanols and their hydrogen-bonded partners, are discussed. Experimental Section Sample Preparation. Silica gel (S679, Fisher Scientific, Lot 000232), with a particle diameter range of 100-200 mesh, was suspended in 2H2O (99.9 atom %, Cambridge Isotope Labs, MA) at a ratio of 5 mL 2H2O per gram of silica gel with stirring at room temperature for 12 h, after which the supernatant liquid was decanted. After repeating the process three times, each time with fresh 2H2O, the silica gel was filtered to remove excess 2H O. The resultant 2H O-exchanged silica gel was dehydrated 2 2 by evacuation at 5 × 10-3 Torr for 15 h at various temperatures.6,10,33 Samples for deuterium NMR spectroscopy (ca. 100 mg) were contained in thin-wall glass tubes (5 mm OD) and were flame-sealed under vacuum. Samples for 1H NMR experiments were prepared in the same manner as those for deuterium NMR, except for the omission of 2H2O exchange; samples (ca. 15 mg) were contained in zirconia MAS rotors (4.0 mm OD) with tight-fitting Teflon closures and caps equipped to minimize exposure to atmospheric moisture. All reagents were used as received. NMR Spectroscopy. Solid-state deuterium NMR spectra were obtained using a CMX-Infinity spectrometer (Otsuka Electronics, Fort Collins, CO) operating at 14.1 T (92.1 MHz for 2H). A single-resonance, purpose-built probe with a solenoidal sample coil (5 mm ID and 10 mm long) was used. Spectra were obtained by the quadrupolar echo method27 and complex Fourier transformation of the sampled complex data, after shifting the data to the echo top and subsequent apodization with 2.0 kHz of Gaussian line broadening. Only zero-order phase correction was applied in the frequency domain. The π/2 pulse time used was 2.4 µs, and the half-echo time used was typically 15 µs, but 50 and 100 µs were used in some experiments. The recovery time used varied between 0.2 and 30 s, and the number of acquisitions varied between 400 and 4000, depending on the sample and observation temperature. The sample temperature was regulated using liquid N2, employing a commercial microprocessor-based controller and purpose-built cryostat that interfaced to the probe. The estimated accuracy of the experimental temperature measurement is (2 K.33 Solid-state 1H NMR

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Figure 1. (a) Shorthand representation of librational motion of O-H moiety of silanol. (b) Distribution of angular positions.

spectra were obtained with magic-angle spinning (MAS), with a MAS speed of 14.2 kHz, using a CMX-II spectrometer (Otsuka Electronics, Fort Collins, CO) operating at 8.46 T (360.0 MHz for 1H); the π/2 pulse time and the recovery time were 3 µs and 5 s, respectively. A Gaussian line broadening of 20 Hz was applied prior to Fourier transformation. All of the 1H MAS spectra were obtained with sufficiently long recovery time to ensure full magnetization recovery. 1H chemical shifts are reported in parts per million, referenced to liquid TMS (0.0 ppm), based on substitution of the secondary reference of polydimethylsilane (PDMS, 0.0 ppm). Surface silanol density was estimated by 1H spin counting, referenced to 1,3,5trimethoxybenzene.34 Calculation of Deuterated-Silanol Theoretical Spectra. The examination of the motional modes of the silanols on a silica gel surface is approached in this work, as is customary with deuterium NMR,28,29 by matching the experimentally obtained spectrum to a computed theoretical spectrum; the theoretical spectrum was calculated for a model in which the silanol executes fast (vide infra), limited-extent rotational (librational) diffusion about the Si-O axis described by a torsional angle, φ, and with a fixed Si-O-H bond angle, θ.35-37 The torsional angle of the silanol is defined as the orientation of the internuclear O-H axis about the relevant internuclear Si-O axis. This model is represented in Figure 1. The silanol rotor dynamics is described by a classical mechanical treatment and the silanol rotor trajectory is approximated by a time-independent Gaussian distribution of angular positions (librational motion) with a standard deviation, σφ. According to this model, the size of the σφ varies with both the shape of the potential energy curve and the temperature at which it is observed. The deuterium NMR spectrum of such a librating silanol consists of a spectral line shape, that is, the static-type line shape, characteristic of the site, but averaged over the librational motions in the fast-motion regime. Examples of motionally averaged spectra corresponding to the silanol rotor system under fast, librational motion are provided in the Supporting Information. The silica gel surface manifests a high level of structural inhomogeneity, and the surface silanols thus experience a wide range of potential energy features. This inhomogeneity is described by a distribution of the shapes of potential energy curves and in turn by a distribution of angular positions (each with a characteristic width, σφ) with weights, P(σφ). The complete theoretical deuterium NMR spectrum is a linear combination of individual, librationally averaged spectra with weights, P(σφ). In practice, a basis set of individual deuterium NMR spectra was calculated (vide infra) with suitable values of quadrupolar coupling constant (QCC) and asymmetry parameter (η) for a range of σφ, using the line-shape simulation program, EXPRESS.38 The complete theoretical deuterium

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Figure 2. 1H MAS NMR spectra of silica gel obtained at room temperature and dehydrated at various temperatures. Experimental conditions are given in the text. All spectra are normalized to constant height.

TABLE 1: Estimation of Surface Silanol Concentrations of Silica Gel Dehydrated at a Variety of Temperatures (Concentrations Obtained by Spin Counting 1H MAS NMR) dehydration temperature (°C)

silanol concentration (nm-2)

25 75 150 300 500

8.7a 6.5a 6.2 4.0 1.2

a Includes contribution from physisorbed water. For the sample dehydrated at 75 °C, the contribution of physisorbed water was determined by deuterium NMR.

NMR spectrum is created by forming a linear combination of the members of this basis set with weighting factors, P(σφ). Further explanatory details of the computational model are provided in the Supporting Information. Geometry of Silanols and Their Hydrogen-Bonded Partners. Possible configurations of surface silanols on a silica gel surface were explored by calculating potential energy curves for the librational motions of the silanols. For the energy calculations, model surfaces were “carved out” of a β-cristobalite structure26 and silanol-silanol or silanol-siloxane pairs were created by adding hydrogen atoms to the corresponding Si-O moieties at the surface. Silicon atoms at the boundary of a computational cluster were terminated by hydrogen atoms. Energy calculations were performed using the semiempirical PM3 method,39 which is adequate to describe variations of hydrogen bonding as the torsional angle, φ, of the silanols about the Si-O bond is varied.40,41 Results 1H MAS NMR. Figure 2 shows the 1H MAS NMR spectra of silica gel samples dehydrated at 25, 75, 150, 300, and 500 °C. The number of silanols per unit surface area was estimated by 1H spin counting for each sample and is summarized in Table 1. All spectra are characterized by features that have been assigned previously;6,42 the spectra show three identifiable regions attributed as follows: a relatively narrow peak due to “isolated” silanols at 1.7 ppm, an extensive signal due to hydrogen-bonded hydroxyls ranging from 1.7 to 8.0 ppm, and

a peak of intermediate width centered at about 3.5 ppm and assigned to physisorbed water (obvious only in the sample dehydrated at 25 °C). The breadth of the signal spanning 1.7 to 8.0 ppm can be ascribed to inhomogeneous broadening associated with a wide distribution of chemical shifts provided by a wide variety of hydrogen-bonding strengths. Dehydration above 75 °C results in a substantial loss of the physisorbed water. As the dehydration temperature is increased further, the contribution of the hydrogen-bonded silanols decreases, while the peak at 1.7 ppm attributed to an isolated silanol persists. It is known that hydrogen bonding produces a proton chemical shift to lower shielding and that the magnitude of this effect increases with stronger hydrogen bonding.43,44 The increase in shielding for the hydrogen-bonded silanols with increasing dehydration temperature (25-500 °C) indicates that silanols with stronger hydrogen bonds are preferentially removed by higher-temperature treatment. The single narrow peak remaining at 1.7 ppm for the sample dehydrated at 500 °C suggests that the remaining surface silanols do not have neighboring silanols within a distance that would permit perturbation of their chemical shift. Deuterium NMR. Figure 3 shows experimental deuterium NMR spectra obtained over a range of observation temperatures of 2H2O-exchanged silica gels dehydrated at 25, 75, 150, 300, and 500 °C. The spectra obtained from samples dehydrated at or above 75 °C are well characterized by a combination of a broad, relatively featureless signal and a broadened powder pattern. Those spectra are almost identical, except for the sharp center peak in the spectrum of the sample dehydrated at 75 °C. At an observation temperature of 295 K, the Gaussian-shape signal accounts for most of the spectral area for the samples dehydrated at 75 °C or above. For all of the samples, as the observation temperature is lowered, the contribution of the Gaussian-shape signal decreases, while a broad Pake-type powder pattern emerges and accounts for a larger portion of the spectral area. For the sample dehydrated at 500 °C, the Gaussian-shape signal accounts for a large spectral area over the entire observation temperature range. At an observation temperature of 78 K, the motions of the silanols are almost frozen out and the broad static powder pattern accounts for most of the spectral area, except for the sample dehydrated at 500 °C. A large portion of the silanols on the sample dehydrated at 500 °C is still mobile even at 78 K. For the sample dehydrated at 25 °C, a sharp center peak with a broad base is observed at 295 K, indicating the presence of components executing a liquid-like, near-isotropic motion. Physisorbed water present in this sample and executing isotropic motion gives rise to the sharp central peak. A vertical expansion of the spectrum of the sample dehydrated at 25 °C and recorded at 295 K is shown in Figure 4. The broad component of this spectrum has a shape similar to that of the spectra of samples dehydrated above 75 °C; this shape corresponds to a specific motional mode of the silanols. Separate experiments were performed in which the half-echo time was varied to reveal any T2 distortion present in the experimental line shapes. None was found with half-echo times in the range of 15-100 µs (see the Supporting Information). The absence of T2 distortion implies that the experimental line shapes do not arise from intermediate-exchange time scale averaging processes and that transverse relaxation is likely dominated by a nonspecific set of static dipolar and/or quadrupolar interactions. For a single motional mode, this situation can arise only if any motion is either very slow or very fast, or if there is a sufficiently large distribution of correlation times that the intermediate-exchange line shapes are not observed

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Figure 3. Experimental deuterium NMR spectra of 2H2O-exchanged silica gels dehydrated at various temperatures. Other experimental details are given in the text. All spectra are normalized to constant height.

Figure 4. Vertically expanded 295 K deuterium NMR spectrum of the sample dehydrated at 25 °C.

because of a combination of fast transverse relaxation and minimal population of the intermediate-exchange systems.27,36,45 These three possibilities will result in, respectively, a slowexchange-limit line shape, a fast-exchange-limit line shape, or a weighted sum of the two of these limiting line shapes. However, in all cases singularities are expected in the line shapes. In the experimental spectra shown in this paper singularities are notably absent, with the principal exceptions being those cases associated with the contributions from Pakelike static powder patterns. Because singularities are absent in the motionally averaged line shapes, a single motional mode cannot account for the motional averaging and an inhomogeneous distribution of motional amplitudes must be considered in the analysis. Further evidence of the lack of intermediateexchange time scale averaging processes comes from another series of experiments in which frequency-selective, shaped pulses46 were used successfully to “burn holes” in the experimental line shapes and demonstrate their inhomogeneous and nonintermediate exchange nature (see the Supporting Information). On the basis of the 1H MAS NMR results, the sample dehydrated at 500 °C contains only isolated silanols (a), that is, those that are not involved in hydrogen bonds (as typically understood). The samples dehydrated at 150 and 300 °C contain (a) + hydrogen-bonded silanols (b) with a wide range of

hydrogen-bonding strengths. The samples dehydrated at 25 and 75 °C contain (a) + (b) + hydrogen-bonded physisorbed water (c). Less-aggressive dehydration allows more hydrogen-bonding networks to be retained, which results in less mobility of the silanols at lower observation temperatures. A quadrupolar coupling constant (QCC) and an asymmetry parameter (η) were calculated for the sample prepared at each dehydration temperature by matching the spectrum experimentally obtained at an observation temperature of 78 K to the theoretical spectrum. These quantities are required to compute the motionally averaged line shapes. A Pake-type static powder pattern (A) was calculated in the frequency domain with Gaussian line broadening and combined linearly with a Gaussian-shape signal (B), which reflects the sum of a family of motionally averaged powder patterns (vide infra). QCC, η, and the weights of those two components were estimated by visual comparison of each experimental spectrum with the corresponding theoretical one. The results of the matching process carried out on the experimental spectra collected at 78 K are shown in Figure 5, together with the corresponding difference spectra. The calculated QCC and η values are tabulated in Table 2. The parameters summarized in Table 2 are found to be markedly dependent on the dehydration temperature; QCC increases and η decreases with increasing dehydration temperature. It is known that strong hydrogen-bond formation results in a decrease in QCC and an increase in η.43,47-52 Dehydration removes water from hydrogen-bonded silanol pairs and decreases the relative number of strongly hydrogenbonded silanols, while increasing the proportion of the weakly hydrogen-bonded and isolated silanols, as shown in the 1H MAS spectra of Figure 2. A decrease in the population of strongly hydrogen-bonded silanols should result in a longer average O-O distance of a hydrogen bond pair (RO-O) and a shorter average silanol OH bond.43 The electric field gradient at the deuterium nucleus is increased as a consequence of a shorter OH bond.47 Thus, a higher dehydration temperature results in larger QCC and smaller η values. Calculation of Theoretical Deuterium NMR Spectra. The silanols of silica and related materials have been observed previously by solid-state deuterium NMR techniques.53-55 Those spectra were deconvolved into a broad Gaussian-shape signal, a static powder pattern, and a motionally averaged powder

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Figure 5. Experimental and theoretical deuterium NMR spectra of silica gel at an observation temperature of 78 K. Theoretical spectra were calculated from linear combinations of theoretical powder pattern components (A and B; see text).

TABLE 2: Principle Values for Each Powder Pattern at 78 K Observation Temperature dehydration temperature (°C)

QCC (kHz)

η

25 75 150 300 500

244.1 247.1 250.7 258.9 260.0

0.080 0.075 0.053 0.036 0.001

pattern. The Gaussian-shape peak was attributed to hydrogenbonded silanol clusters; however, neither the motional modes of the silanols nor the origins of the line shapes were interpreted. The experimental deuterium NMR spectra of the 2H2Oexchanged silica gels shown in Figure 3 were fitted to a theoretical spectrum by forming weighted linear combinations of various motionally averaged powder patterns and applying 11 kHz Gaussian broadening to the resultant line shapes. Because a deuterium NMR powder pattern depends on the angle θ made between the internuclear O-H axis and the internuclear Si-O axis,56 a basis set of line shapes was generated for various values of θ and the fitting processes were performed for each of those values. Figure 6 shows the experimental spectra and corresponding theoretical spectra (and their differences) for the sample dehydrated at 500 °C and observed at several temperatures. The theoretical spectra are in excellent agreement with the spectra shown in Figure 3. (Experimental and theoretical spectra of all of the silica samples and 2H NMR measurements of this study are shown in the Supporting Information.) The 1H MAS NMR results (Figure 1) indicate that lessaggressive dehydration conditions, 25 and 75 °C, create samples in which, in addition to the silanols, physisorbed water was present. For those samples, a Lorentzian component representing liquid-like isotropic motions of the physisorbed water is added for matching the deuterium NMR spectra obtained at observation temperatures of 200 and 295 K. Analysis of the deuterium NMR spectra also permits estimation of the Si-O-2H bond angle, the first experimental measurement of this important structural parameter. As stated above, the fitting processes were performed for various values of θ over the range of observation temperatures. In this manner, the value of θ is determined to be 59° ( 1° and the Si-O-2H bond angle is found to be 121° ( 1°. This angle is quite close to the values, in the 114-120° range, predicted theoretically for the Si-O-2H bond angle.17-20,57 It should be noted that this bond angle, like all measurements of geometric parameters, is an aVerage over the time span characteristic of the specific type of measurement.

Figure 6. Experimental (top of each triplet) and theoretical (middle) deuterium NMR spectra and their differences (bottom) for the sample dehydrated at 500 °C and observed over a range of indicated temperatures. All groups of experimental and theoretical spectra are normalized to constant height.

Figure 7 shows the experimentally estimated widths of distributions of librational motions (values of σφ from Figure

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Figure 7. Distribution of standard deviations of the librational amplitudes used in the line-shape simulations.

Silica Gel Surface 1) required for the successful simulation of the experimental spectra shown in Figure 3, within the simulation model described above. This analysis of the deuterium NMR spectra indicates that the silanol OH moieties execute librational motions about the internuclear Si-O axis, all in the fast exchange limit (relative to a 5 × 10-6 s time scale). The broad distributions of librational-amplitude breadths (σφs) indicate that silanols execute librational motions with various librational amplitudes, reflecting an inhomogeneous environment on the silica gel surface, presumably related to the detailed nature of the hydrogen bonds. The librational amplitudes depend on the observation temperature; the librational amplitudes increase with increasing temperature and vice versa. In the sample dehydrated at 500 °C, for which the silanols are all isolated, the deuterium line shapes indicate that some of the silanols are essentially immobilized, but a sizable fraction remain mobile and are not frozen out, even at the lowest observation temperature of 78 K. On the basis of the 1H NMR results of Figure 2, it can be seen that, for dehydration temperatures of 150 and 300 °C, some of the silanols exist in a distribution of various hydrogen bond strengths, while some are isolated silanols. At each observation temperature, the hydrogen-bonded silanols exhibit smaller librational amplitudes than those exhibited by the isolated silanols. Less-aggressive dehydration conditions, that is, dehydration temperatures of 25 and 75 °C, yield samples in which, in addition to the silanols, a significant amount of physisorbed water is present. At the lower observation temperatures, the effect of physisorbed water is to narrow the librational amplitude for all of the silanols and water molecules. At the lowest observation temperature of 78 K, most of the surface silanols and water molecules are essentially immobilized. The trend in which the librational amplitudes increase with increasing dehydration temperature reflects the fact that the motions of the silanols are restricted by hydrogen bonds. It is interesting to note that, even for the sample dehydrated at 500 °C, in which only isolated silanols are observed by 1H MAS NMR, motional modes of the silanols are still affected by hydrogen bonds. This observation is consistent with earlier work based on infrared spectroscopy15,16 in which two kinds of isolated silanols were invoked for the silica surface; one kind is truly isolated silanols without observable interactions, and another type is composed of silanols that weakly interact with other silanols, as evidenced in the IR by effects on the vibrational frequencies of the torsional motion. Discussion QCC and η Parameters. As seen above, values of QCC and η depend on dehydration temperature. Relations among QCC, η, and hydrogen-bond length (RO-O) have previously been derived empirically from observations on crystalline solids in which the O-H-O angle of the hydrogen bonds are found to be around 180°.49,52 These empirical relationships among RO-O, QCC, and η do not extend to nonlinear hydrogen bonds.49 In the present case, nonlinear hydrogen bonds cannot be excluded; only qualitative trends are ascribed here to the relationships among RO-O, QCC, η and the dehydration temperature. Interpretation Strategy. In the material presented below, we do not claim to determine accurate surface structures, but present plausible models that are qualitatively, or semiquantitatively, consistent with the experimental deuterium NMR observations and patterns presented above. There are almost certainly other surface models that would also be consistent with the deuterium NMR results.

J. Phys. Chem. C, Vol. 112, No. 11, 2008 4321 The final product derived from the experimental results presented above is a distribution, P(σφ), a function of the standard deviations, σφ, that define the probability functions G(φ) (with the standard deviations, σφ), that is, the weighting factors for the Gaussian distributions G(φ) that represent the contributing librational motions (with angular displacement, φ) of silanol hydroxyl moieties about the corresponding internuclear Si-O axes. Such experimentally grounded distributions, as summarized in Figure 7, are presented for samples dehydrated at 25, 75, 150, 300, or 500 °C and observed in deuterium NMR experiments at temperatures ranging from 78 to 295 K. In order to interpret, or at least rationalize, the experimentally derived P(σφ) patterns in terms of physicochemical concepts that are useful for visualizing the silica surface, we tend to think about the problem along the lines outlined in cartoon form in Figure 8. Part a of Figure 8 corresponds with the basic assumptions of Figure 1 and conventional views of the potential energy curve for the torsional angle, φ, describing constrained (restricted) rotation (libration). The combination of 1H and 2H NMR spectra indicates that the motional modes of surface silanols on silica gel are constrained by hydrogen-bonding interactions. Because the strength of a hydrogen bond depends on the configuration of the O-H-O triplet, estimating the hydrogen-bonding behavior from the distribution of librational amplitudes of the silanol permits interrogation of the local structure of the silica gel surface in terms of its silanols. A site population distribution function of the torsional angle, G(φ), is dependent on both the details of the potential energy curve for libration and the temperature. For our purposes, it is convenient and reasonable to approximate the potential energy curve by a function of the form, V(φ) ) V/2(1 - cos φ), where V is a constant and is the only parameter that varies from one such function to another, that is, from one system to another (Figure 8a). The thermal energy of the silanols executing uniaxial librational motion is determined according to a function resembling the MaxwellBoltzmann distribution. From knowledge of the potential energy curve, V(φ), one can in principle calculate the corresponding probability distribution function, G(φ), and derive a standard deviation, σφ, of the probability distribution function, G(φ), for given V values (bringing one from stage a to stage b in Figure 8). Thus, one can obtain the relationship between a potential energy barrier, V, and a standard deviation, σφ, of the probability distribution function, G(φ) at a given observation temperature (Figure 8c). Such a G(φ) curve exists for each distinct structural environment of silanols on the silica surface at a particular observation temperature; then, from the experimental deuterium NMR results, one knows the distributions (weighting factors) of such sites on the surface, P(σφ), from which one could readily construct the distribution of sites (Figure 8e). Analysis of the deuterium NMR spectra provides a key element (distribution of stage d in Figure 8) in this progression. Thus, the experimentally grounded determination of the distribution function, P(σφ), allows one to relate the σφ to the potential energy barrier, so one can approach a probability distribution of potential energy barriers, P(V) (Figure 8e). Analyses of the deuterium NMR spectra (Figure 7) provide a type of site distribution function, P(σφ), for the motions of the silanol hydroxyls in terms of the librational-amplitude breadths, σφ. The librational-amplitude breadth (σφ) for a given temperature is calculated from the potential energy curve and the librational thermal energy of the silanols. A probability that

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Figure 8. Diagram of the interpretation strategy. (a) Potential energy curve for silanol hydroxyl moiety. (b) Probability distribution of librational angle φ corresponding to the potential energy diagram of a. (c) Relationship between the potential energy barrier to librational motion and the librational-amplitude breadth. (d) Relationship between the distribution function, P(σφ), and the librational-amplitude breadth, σφ. (e) Probability distribution of potential energy barriers, P(V), on the silica gel surface.

Figure 9. (a) Maxwell-Boltzmann distribution at a given temperature. The area within  < ′ accounts for 95% probability of the thermal energy distribution. (b) Potential energy curve and distribution of angular positions of the silanols executing fast librational motions. 95% of the silanols are found within a V(φ) range of V(0) e V(φ) e V(0) + ′. 95.44% of the total probability described by a Gaussian distribution with a standard deviation, σφ, corresponds to the range of -2 σφ to 2 σφ.

silanols with thermal energy between  and  + d, F(), for a given system can be estimated from the Maxwell-Boltzmann distribution (Figure 9a). For a given temperature, an energy value, ′, for which 95% of the systems (i.e., librating silanols) are found between 0 and ′, is obtained from the MaxwellBoltzmann distribution (eq 1); ′ is estimated to be 9.5 kJ/mol at 295 K.

∫0′ F()d ) 0.95

(1)

In the model used for the deuterium line-shape analysis, silanols execute librational motions in a single-well potential energy curve, as represented in Figure 1. The distribution of angular positions of the silanols are approximated by a Gaussian distribution centered at φ ) 0. For a given potential energy curve, which is approximated here by V(φ) ) V/2(1 - cos φ), 95% of the silanols are found within the V(φ) range between V(0) and V(0) + ′ and eq 1 can be rewritten as follows (see Figure 9b): V(0)+′ F(V(φ)) dV(φ) ∫0′ F()d ) ∫V(0)

(2)

The librational-amplitude breadths can be obtained by comparing these energy values and the potential energy curve. From the discussion above 2σ φ′ V(0)+′ F(V(φ)) dV(φ) ) ∫-φ′ F(V(φ)) dφ ) ∫-2σ ∫V(0)

φ

G(φ)dφ

φ

(3) Thus, one can visualize a relationship between the potential energy curves, V(φ), and the probability function, G(φ), for a given temperature. This relationship relates the librationalamplitude breadth, σφ, of the probability function G(φ) to the size of the potential energy barrier, V, of the cosine function, V(φ) ) V/2(1 - cos φ), at a given temperature. Figure 10a shows the relationship between the librationalamplitude breadth and the potential energy barrier, V, for an observation temperature of 295 K. By knowing (or assuming a trial value of a specific) V in the potential-energy function, one can estimate from a plot of the type shown in Figure 9 a corresponding σφ. Thus, the relationship between the potential energy barrier, V, and the librational-amplitude breadth, σφ, can be obtained (Figure 10a). The net result is that distributions of librational-amplitude breadths, P(σφ), which are derived from the deuterium NMR line-shape analysis (Figure 7), permit

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Figure 11. Interactions between a silanol and its hydrogen-bond partner on silica gel surfaces. (a) Side view of (111)-type plane (dashed line representing an edge of such a plane; dotted line representing a weak hydrogen bond between the distant silanols pair). (b) Closer silanolsilanol pair (dotted line representing strong hydrogen bonds). (c) Silanol-siloxane pair (dotted line representing a weak hydrogen bond between the distant silanol-siloxane pair). Figure 10. (a) Relationship between the librational-amplitude breadth and potential energy barrier for an observation temperature of 295 K. (b) Distribution function, P(V), as a function of the potential energy barrier for samples dehydrated at various temperatures.

one to depict a distribution of the potential energy barrier, V, on the silica gel samples, by relating a librational-amplitude breadth, σφ, with a potential energy barrier, V. Consequently, we obtain site distributions in terms of potential energy barriers as represented in Figure 10b, which corresponds to Figure 8e. The broad distributions shown in Figure 10b clearly indicate that the silica gel surface has a high level of structural inhomogeneity. The sites for which the potential energy barrier, V, is in the range between 5 and 30 kJ/mol have high populations on the silica gel surface dehydrated at 150 °C and above; the most probable V values are around 10 kJ/mol. The distributions of the site populations (in terms of potential energy barrier) depend on the dehydration temperature, decreasing population of sites with higher potential energy barrier as the dehydration temperature is increased. This trend suggests that more aggressive dehydration conditions preferentially retain weakly hydrogenbonding silanols, in which lower potential-energy barriers permit silanol hydroxyl moieties to execute larger librational-amplitude motions. There are silanols whose motions are quite restricted on the silica surface as well. According to Figure 10b, a potential energy barrier of about 300 kJ/mol is estimated for a site with a probability distribution, G(φ), with σφ ) 10°. In such highly restricted surface sites, the silanol motions are presumably restricted by strong repulsive interactions (“steric effects”) that probably overwhelm hydrogen-bonding interactions.

Geometry of Silanols and Their Hydrogen-Bonded Partners. As a starting point for this discussion (Figure 8a), we recognize that the surface of the silica gel sample dehydrated at a temperature of 150 °C or higher consists of mostly siloxane group (Q4 sites) and a small number of silanols as presented in Table 1. The population of silanols is dominated by (SiO)3SiOH (Q3) sites.58,59 These sites are often represented by a hydroxylterminated (111) facet of β-cristobalite, as represented in Figure 11a; in this arrangement, adjacent silanol oxygens are about 0.4-0.5 nm apart. On the surface of the silica sample dehydrated at 500 °C, silanol-silanol distances are expected to be much larger, if one assumes that silanols are distributed uniformly on the surface. In both cases, strong hydrogen bonds cannot form between nearest-neighbor silanols.58 However, the preponderance of an uneven surface, with steps and kinks, will allow for a closer approach of Q3 silanols, permitting strong hydrogen bonding, even on a silica surface dominated by (111) facets.58,59 A short-hand representation of this possibility is depicted in Figure 11b. Weak hydrogen bonds can also form between silanol-siloxane pairs, as depicted in Figure 11c. The calculation of hydrogen-bonding energies of silanolsilanol and silanol-siloxane pairs has been reported previously;21 according to those calculations, the hydrogen-bonding energy of a silanol-siloxane pair is smaller than that of a silanol-silanol pair for the same internuclear O‚‚‚O distance (RO-O). However, these calculations also predict that the hydrogen-bonding energy of a relatively close silanol-siloxane pair, such as that shown in Figure 11c (RO-O ) ca. 0.37 nm), is comparable to that of a distant silanol-silanol pair (Figure 11a; RO-O ) ca. 0.50 nm) for which the distance and geometry of the O-H-O triples are outside the prevailing hydrogenbond model (i.e., a H-bonded silanol is one with an O-O

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Figure 12. Surface cluster used for potential energy calculations. Silicon atoms are light gray, oxygen atoms are dark gray, and hydrogen atoms are black. Silanol hydrogens are the only hydrogens shown. Silicon atoms at the boundary of the cluster are terminated by hydrogen in the calculation. Additional details are given in the text.

distance of 0.33 nm or less and with a nearly linear O-H-O arrangement). In order to visualize more clearly the possibilities depicted in Figure 11 and addressing the task depicted in Figure 8, a model surface (“cluster”) containing steps was generated from the crystal structure of β-cristobalite; the model contains four different possible hydrogen-bonding pairs. In the computational cluster, hydrogen atoms were added to “dangling” oxygen atoms to form silanols and the silicon atoms that do not carry the full complement of hydroxyl or siloxane linkages were terminated by hydrogen atoms. The resulting model is shown in Figure 12. Energy calculations were performed for one silanol-siloxane pair and for three silanol-silanol pairs, using the semiempirical PM3 method,39 varying the O-Si-O-H torsional angle, φ, of the silanol O-H internuclear axis about the Si-O internuclear axis. In the calculations, only silanols for which the potential energy dependence on φ is examined were included in the model; the others were replaced by hydrogens. The configuration with minimum calculated potential energy defines the zero value of φ. For a silanol-siloxane pair model, the potential energies were calculated as a function of the O-Si-O-H torsional angle φ of silanol-1 shown in Figure 12. The results are summarized in Figure 13a. For a silanol-silanol pair model (e.g., a silanolsilanol pair with RO-O ) 0.40 nm in Figure 12), the torsional angle of silanol-2 was varied for the case in which the orientation of the partner silanol, silanol-3, was adjusted to that of a minimum in the total potential energy (Figure 13b). The potential energy was also calculated with respect to variation of the torsional angle of silanol-3; these calculations were carried out with the orientations of the silanol-2 for which the potential energy is at a minimum (Figure 13c). One can see that the barrier height and the width of the potential energy well are dependent on RO-O; the potential energy barrier decreases and the width increases with increasing the RO-O. The potential energy curves shown in Figure 13 are all of roughly the same shape, albeit with different widths and heights, for the region of primary

Kobayashi et al. interest (most probable values of φ). For our purposes, it is convenient and reasonable to approximate this region by a function of the form V(φ) ) V/2(1 - cos φ) (where V represents the potential energy barrier and is the only parameter that varies from one such function to another). The cosine-form approximations to the calculated potential energy curves are also shown in Figure 13 (dashed lines). In full rigor, the potential energy dependence on torsional angles for a silanol-silanol pair is a coupled system, whereas we have considered the two angular dependencies (e.g., φ2 and φ3 in Figure 12) as independent. This defect is unlikely to dominate the interpretation but should be taken into account for a more definitive treatment. Silanol-Siloxane Interactions. For librational motions of silanols that are restricted by silanol-siloxane interactions with RO-O ) 0.37 nm, the estimated potential energy curve is given by Figure 13a. Within the cosine-form approximation, the potential energy barrier, V, can be estimated by fitting the cosine function to the calculated potential curve and is found to be ca. 8.6 kJ/mol. For the samples dehydrated at 150, 300, and 500 °C, the most probable (center) values of the broad distributions of the potential energy barrier (V) are estimated from Figure 10b and to be 11.7, 10.9, and 10.4 kJ/mol, respectively. The potential energy barrier, V ) 8.6 kJ/mol, derived above from the cosineform approximation for the silanol-siloxane pair model with RO-O ) 0.37 nm is relatively close to these most probable values; this suggests that the silanol-siloxane pair with RO-O ) 0.37 nm modeled in Figure 12 is a “reasonable” configuration for visualizing those silica samples in the sense of being consistent with a substantial segment of the experimental data. A hydrogen bond between a silanol hydrogen and a siloxane oxygen can form within a 12-membered ring containing six silicon atoms that is a major structure that can be derived from a silica (111) facet, because the Si-O bond vector is not perpendicular to the (111) facet and atoms belonging to the ring are not in the same plane due to the Si-O-Si bond angle of 147°.26 This situation is represented in Figure 14b. Dehydration removes water from hydrogen-bonded silanol pairs (e.g., silanol-6 and silanol-7 of Figure 12) and forms SiO-Si linkages, with deformation of the ring.60-62 The resulting inhomogeneous surface structure generates a wide range of potential energy features for silanol libration, which results in a broad distribution of librational-amplitude breadths, as found in the deuterium NMR line-shape analysis. Silanol-Silanol Interactions. For librational motions of silanols restricted by silanol-silanol interactions with RO-O ) 0.40, 0.36, and 0.26 nm, the potential energy barriers (V) of those six silanols of the three pairs of silanols (silanol-2/silanol3, silanol-4/silanol-5, and silanol-6/silanol-7 pairs) are estimated by fitting cosine functions to the potential energy curves derived from energy calculations as follows: silanol-2 (RO-O ) 0.40 nm), 7.8 kJ/mol; silanol-3 (RO-O ) 0.40 nm), 3.8 kJ/mol; silanol-4 (RO-O ) 0.37 nm), 58.6 kJ/mol; silanol-5 (RO-O ) 0.37 nm), 25.6 kJ/mol; silanol-6 (RO-O ) 0.26 nm), 326.1 kJ/ mol; silanol-7 (RO-O ) 0.26 nm), 74.0 kJ/mol. According to Figure 10b, the most probable V values (potential energy barriers) are in the range between 5 and 30 kJ/mol; this suggests that silanol-4, silanol-6, and silanol-7 are improbable structures on silica gel samples dehydrated at 150 °C and above. Because dehydration removes water from hydrogen-bonded silanol pairs and decreases the relative number of strongly hydrogen-bonded silanols, mainly weakly hydrogen-bonded silanols, in which the

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Figure 13. Potential energy curves as a function of silanol orientations, for silanols in the framework shown in Figure 12. Torsional angles of the silanol are defined, in accordance with Figure 1, as the orientation of the internuclear O-H axis about the relevant internuclear Si-O axis. (a) Potential energy curves for the torsional angle of silanol-1 of a silanol-siloxane pair. (b) Potential energy curves for the torsional angle of silanol-2 of a silanol-2/silanol-3 pair model with RO-O ) 0.40 nm. (c) Potential energy curves for the torsional angle of silanol-3 of a silanol-2/silanol-3 pair model with RO-O ) 0.40 nm. (d) Potential energy curves for the torsional angle of silanol-4 of a silanol-4/silanol-5 pair model with RO-O ) 0.37 nm. (e) Potential energy curves for the torsional angle of silanol-5 of a silanol-4/silanol-5 pair model with RO-O ) 0.37 nm. (f) Potential energy curves for the torsional angle of silanol-6 of a silanol-6/silanol-7 pair model with RO-O ) 0.26 nm. (g) Potential energy curves for the torsional angle of silanol-7 of a silanol-6/silanol-7 pair model with RO-O ) 0.26 nm. Solid lines and dashed lines represent calculated potential energy curves and their approximation by a cosine function, respectively.

Figure 14. (a) Side view of (111)-type facet (hydrogens are not shown; dotted line represents (111)-type facet). (b) Top view of (111)-type facet and a possible intra-ring interaction (dotted line). Silicon atoms are represented in light gray, oxygen atoms in dark gray, and hydrogen atoms in black.

potential energy barrier is shallow, remain on the silica gel surface dehydrated at 150 °C and above. These results are consistent with the view that strongly interacting (hydrogen-bonded) silanol pairs can be removed readily by dehydration at 150 °C and above, while weakly interacting silanols or isolated silanols may remain on the surface. “Weak” hydrogen bonds can form between pairs of silanols on silica (111)-type surfaces, if RO-O g 0.33 nm or the O-H-O angle of the hydrogen bond is far from linear geometry

even if RO-O e 0.33 nm. Weak hydrogen bonds also can form between a silanol and a siloxane oxygen at a silica(111)-type surface with an internuclear O‚‚‚O distance (RO-O) of 0.37 nm (e.g., silanol-1 of Figure 12). The deuterium NMR data indicate that strongly hydrogen-bonded silanols that form at step or defect sites are unlikely on the samples dehydrated at 150 °C and above. Hydrogen-bonded silanols are observed in 1H MAS NMR experiments on the samples dehydrated at 150 and 300 °C, but those are not the “strong” hydrogen bonds (with RO-O e 0.33 nm or less) that can form at step or defect sites; that is, sites for which the potential energy barrier, V, is in the range between 5 and 30 kJ/mol have high populations on the silica gel surface dehydrated at 150 °C and above and those potential energy barriers are expected for a pair of silanols with RO-O ) 0.37 or 0.40 nm, or for a silanol-siloxane pair with RO-O ) 0.37, on the basis of the above discussions. This implies that dehydration removes silanols at step or defect sites and preferentially retains silanols on the relatively flat parts of the surface. The model hydrogen-bonding configurations with RO-O g 0.33 nm are outside the prevailing concept of a hydrogen bond (e.g., one with an O-O distance of 0.33 nm or less and with a nearly linear O-H-O arrangement). Nevertheless, our analysis indicates that with such O-H-O configurations there are still significant interaction energies and molecular dynamics is affected. Conclusions Analysis of the deuterium NMR line shapes for silanols on 2O-exchanged high-surface-area silica gel indicates that the silanols’ O-H moieties execute librational motions about the internuclear Si-O axes with a broad distribution of librational amplitudes, all in the fast exchange limit (relative to a 5 × 10-6 s time scale); the breadths of the librational amplitude distributions depend on both the dehydration temperature and observa2H

4326 J. Phys. Chem. C, Vol. 112, No. 11, 2008 tion temperature, increasing breadth with increasing dehydration temperature and observation temperature and vice versa. The librational amplitude is also dependent on the dehydration temperature; at each observation temperature, the librational amplitudes increase with the dehydration temperature due to a net decrease in hydrogen bond strengths after dehydration at higher temperatures. The line-shape analysis of the deuterium NMR spectra permits the estimation of the time-averaged Si-O-2H bond angle, which is found to be 121° ( 1°. Analysis of the librational motions in terms of the potential energy determined by interactions of silanol pairs suggests that most of the silanol pairs are separated by more than 0.37 nm. On a “real” silica gel surface, because the interactions experienced by each O-H-O triplet are slightly different from those of other such triplets as a result of the substantial inhomogeneity of the silica gel surface, there is a wide distribution in the shapes of “individual” potential energy curves for surface hydroxyls, even for a given RO-O value. The prevailing concept of a hydrogen bond, that is, with an O-O distance of 0.33 nm or less, can be extended to include a class of weak hydrogen bonds in which the distance and geometry of the O-H-O triples are outside the classical definition; but significant interaction energies are manifested, and molecular dynamics is significantly affected. To describe more definitively the surface silanols of silica gel would require further studies, including explicit consideration of the effects of repulsive interactions and of cooperativity in silanol-silanol interactions. Acknowledgment. We gratefully acknowledge support of this project by Department of Energy grant DE-FG-0395ER14558 and National Science Foundation grant CHE9021003. Supporting Information Available: Details of the model used for the deuterium NMR line-shape computations, the entire collection of experimental and theoretical spectra, together with distributions of the librational amplitudes used in the fitting, and details of the theoretical estimation of the librationalamplitude breadths of silanols. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Bergna, H. E. Colloid Chemistry of Silica - An Overview. In Colloid Chemistry of Silica AdVances in Chemistry Series; American Chemical Society: Washington D.C., 1994; Vol. 234, p 1. (2) Iler, R. K. The Chemistry of Silica; Wiley: New York, 1979. (3) Maciel, G. E.; Sindorf, D. W. J. Am. Chem. Soc. 1980, 102, 7606. (4) Sindorf, D. W.; Maciel, G. E. J. Am. Chem. Soc. 1983, 105, 1487. (5) Kohler, J.; Chase, D. B.; Farlee, R. D.; Vega, A. J.; Kirkland, J. J. J. Chromatogr. 1986, 352, 275. (6) Bronnimann, C. E.; Zeigler, R. C.; Maciel, G. E. J. Am. Chem. Soc. 1988, 110, 2023. (7) Legrand, A. P.; Hommel, H.; Tuel, A.; Vidal, A.; Balard, H.; Papirer, E.; Levitz, P.; Czernichowski, M.; Erre, R.; Vandamme, H.; Gallas, J. P.; Hemidy, J. F.; Lavalley, J. C.; Barres, O.; Burneau, A.; Grillet, Y. AdV. Colloid Interface Sci. 1990, 33, 91. (8) Tuel, A.; Hommel, H.; Legrand, A. P.; Chevallier, Y.; Morawski, J. C. Colloids Surf. 1990, 45, 413. (9) Chuang, I. S.; Kinney, D. R.; Maciel, G. E. J. Am. Chem. Soc. 1993, 115, 8695. (10) Kinney, D. R.; Chuang, I. S.; Maciel, G. E. J. Am. Chem. Soc. 1993, 115, 6786. (11) Haukka, S.; Root, A. J. Phys. Chem. 1994, 98, 1695.

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