5982
J. Phys. Chem. C 2007, 111, 5982-5989
Molecular Dynamics of Pyridine Adsorbed on the Silica Surface Joseph A. DiVerdi, Takeshi Kobayashi, and Gary E. Maciel* The Department of Chemistry, Colorado State UniVersity, Fort Collins, Colorado 80523 ReceiVed: NoVember 7, 2006; In Final Form: February 21, 2007
The molecular dynamics of pyridine adsorbed onto dry high-surface-area silica gel was studied using solidstate deuterium NMR spectroscopy. Selectively and totally deuterated pyridine samples were used to identify the spectral signatures associated with each ring location and to identify the dynamical modes present in the surface adsorbed species. Loading levels corresponding to 0.8 and 0.2 monolayer coverage were studied. At 174 K and 0.8 monolayer, the adsorbed pyridine molecules are found in three motional modes: a fraction is found to be static, a larger fraction is found executing fast discontinuous rotation (180° ring flips) about the pyridine Cγ-N axis, and a very small fraction is found in fast continuous rotation (diffusion) about the pyridine Cγ-N axis, all referred to a 5 × 10-6 s time scale. No evidence of O-H-N rotation about the Si-O bond (“swinging arm” motion) is observed. The pyridine flips and rotations permit measurement of the angle between the Cγ-N axis and each of the CR-D and Cβ-D axes are found to be 55.9 ( 0.3° and 60.4 ( 0.5°, respectively. As the temperature is lowered, the fraction of static pyridine rings increases, while the fractions of flipping and freely rotating pyridine rings decrease. At 78 K and 0.8 monolayer, pyridine ring flip motion is still observed, implying a very low potential barrier to discontinuous rotation for some of the surface population. At 221 K, the flipping rings dominate, rotating rings are a minority, and no static rings remain. Above 221 K, the chemical exchange rate among pyridine molecules becomes significant and further motional averaging is observed. At 221 K and below, the spectra show no contributions corresponding to intermediate-rate motions; the notable absence of intermediate-rate patterns is explained in terms of a previously proposed model based on a broad distribution of motional correlation times. The surface structures and dynamics with 0.2 monolayer are found to be substantially similar to those found at 0.8 monolayer. These dynamical data are interpreted in terms of the structure of the silica surface as probed by pyridine molecules.
Introduction Knowledge of the structure of the silica surface and of its interactions with adsorbed molecules is key to a fundamental understanding of the important chemistry that occurs on it. Silica structure is well known to be a network of siloxane (Si-OSi) linkages that extend throughout the bulk of the solid and to the surface, which is terminated by hydroxyl groups in silanol moieties, (-O)3SiOH and (-O)2Si(OH)2.1,2 These surface features dominate the surface interactions and chemistry. The formation of covalent bonds between these surface structures and a wide variety of chemical functionalities gives rise to modified surfaces with an even greater range of interesting and useful surface chemistry and properties.3-5 The many ways that the surface structural motifs can be juxtaposed creates a rich variety of microenvironments in which the characteristics of binding to adsorbates can vary substantially.6 Because of this wide range of surface properties and functionality and as a prime example of complex amorphous, heterogeneous surface structures, the nature of the silica surface is of great interest and importance. Over the years a great deal has been learned regarding the silica surface from the study of silica itself and of surfacederivatized silicas.6-8 Additional information on the silica surface has been gleaned by the study of weakly adsorbed (i.e., physisorbed) molecules to probe the surface. As a dominant surface feature of silica is the silanol, it is not surprising that * To whom correspondence should be addressed. E-mail: gary.maciel@ colostate.edu.
some of the more successful probe molecules contain functional groups that interact strongly with it.9-12 Pyridine is well known to form hydrogen bonds between its ring nitrogen as a proton acceptor and a proton donor, such as a surface silanol.13 Deuterium NMR spectroscopy is a powerful and very well established method for determining the dynamical properties of solids14-16 and is often able to differentiate among various motional types or modes and provide dynamical rates for those modes. Deuterium NMR spectra are dominated by the interaction of the nuclear electric quadrupole moment with the electric field gradients at the spin-1 nucleus.17 In the work reported here, a line shape analysis of variable-temperature solid-state deuterium NMR spectra is used to characterize the molecular dynamics of several isotopic forms of deuterated pyridine adsorbed on silica gel. Often in deuterium NMR spectroscopy, the spectra display unique and identifiable line shapes corresponding to slow, intermediate, and fast-motional states. Much less frequently (as will be seen in the present case) the system being examined contains a broad distribution of motional dynamics that results in the superposition of spectra corresponding to the slow-motional and fast-motional limits, while conspicuously lacking observable spectral contributions corresponding to the intermediate-motional state. Experimental Section Materials. Silica gel (S679, Fisher Scientific, Lot 000232) with a particle size range of 100-200 mesh and a surface area of 456 m2 g-1 was dried by evacuation at 5 × 10-3 Torr and
10.1021/jp067353q CCC: $37.00 © 2007 American Chemical Society Published on Web 03/30/2007
Molecular Dynamics of Pyridine on Silica Surface 150 oC for 15 h.18,19 Pentane (Fisher), 4-bromopyridine hydrochloride (Aldrich), D2O (99.9 atom % as 2H, Cambridge Isotope Labs), 98% D2SO4 (99.5 atom % as 2H, Aldrich), pyridine-d5 (99.5 atom % as 2H, Cambridge Isotope Labs), and pyridine (spectroscopic grade, Acros) were used as received. The remaining materials were reagent grade. Deuterium Labeled Pyridine. Details of deuterium labeling were established by high-resolution liquid-state 1H NMR. Pyridine-R,R′-d2 (with ∼90% isotopic labeling in the R and R′ positions) was prepared from unlabeled pyridine by deuterium exchange in neutral aqueous solution (neutralized by added D2SO4) at 190 °C.20,21 Pyridine-γ-d1 (with >90% isotopic labeling in the γ-position) was prepared from 4-bromopyridine hydrochloride according to the method of Hildebrand et al.22 Each labeled pyridine was separated from the aqueous reaction liquor by alkalization with aqueous sodium hydroxide, distillation of the pyridine-water azeotrope, addition of carbon tetrachloride, dehydration by distillation of the carbon tetrachloride-water azeotrope,23 scavenging residual moisture by refluxing over solid calcium hydride, and distillation from the drying agent at ∼650 mm Hg. In some cases, the azeotropic dehydration step was replaced by extraction with dodecane, and simple distillation over solid calcium hydride was used to separate pyridine from the solvent. Sample Preparation. Pyridine was deposited on the dry silica gel surface using liquid-phase absorption of a prescribed mass of labeled pyridine in a pentane solution at 20 °C for several hours with subsequent removal of the solvent under flowing nitrogen gas at 20 oC.24 Pyridine was deposited in the proportion 2.45 and 0.635 mMol pyridine g-1 silica gel, corresponding to 80 and 20% of one monolayer (based on an estimated pyridine surface area of 0.25 nm2 per molecule24), respectively. Samples for deuterium spectroscopy were contained in thin-wall, 5 mm OD glass tubes and were sealed with a fitted Teflon plug topped with quick-set epoxy adhesive. All sample manipulations were performed under a dry, N2 atmosphere. NMR Spectroscopy. Solid-state deuterium NMR spectra were obtained using a CMX-Infinity spectrometer (Otsuka Electronics, USA, Fort Collins, CO) operating at 14.1 T (92.1 MHz for 2H). A single resonance, purpose-built probe with solenoidal sample coil (5 mm ID and 10 mm long) was used. The circuit Q was maintained at a value of roughly 100 by the addition of a damping resistor. The quadrupolar echo method was used throughout.17 Spectra were obtained by complex Fourier transformation of complex data after shifting the data to the echo top and subsequent apodization with 400 Hz of Lorenzian line broadening. Only zero-order phase correction was applied in the frequency domain. The half-echo time used was 15 µs, unless otherwise noted. The π/2 pulse time used was 2.6 µs. The recovery time varied between 20 ms and 30 s, and the number of acquisitions varied between 100 and 80 000, depending on sample and temperature. The sample temperature was regulated using a commercial microprocessor-based controller and laboratory-built cryostat that interfaced to the probe. The cryostat used N2 gas cooled by a heat exchanger in a liquid nitrogen bath. Temperature calibration was performed against a copper-constantan thermocouple made with fine wires (#30 AWG) and placed in a dummy sample of paraffin wax within a glass sample tube. The estimated accuracy of the temperature measurement is (2 K. Calculations of Theoretical Deuterium Spectra. Theoretical NMR spectra were calculated in the frequency domain on the basis of static powder patterns or motionally averaged powder
J. Phys. Chem. C, Vol. 111, No. 16, 2007 5983 patterns in the fast-motional (exchange between sites) regime by application of analytic relations based on specific motional models. No evidence was found for spectral contributions corresponding to the intermediate-motional regime. For cases in which multiple components are present in one spectrum, linear combinations of the independently determined component powder patterns were convolved with suitable Lorenzian and/ or Gaussian line shape functions. The best-fit weights of the components were determined by visual comparison of the experimental and calculated spectra. By varying each fitted powder pattern parameter from its optimum value until the agreement between the experimental and calculated spectra degraded, an estimate of that parameter’s uncertainty was made; these estimated standard deviations are 0.2 kHz, 0.001, and 0.2 kHz, respectively, for δ, η, and the Gaussian line width (full width at half-maximum (fwhm)). Results and Discussion Deuterium NMR Spectroscopy. Deuterium NMR has a rich and well-developed history of successful applications to the characterization of molecular motion, based on this nuclide’s relatively large and dominant electric quadrupole moment, modest gyromagnetic ratio, and relatively small chemical shift range. The quadrupole effect arises from the electrostatic interaction of the nuclear quadrupole moment with the electric field gradient at the nucleus.25 The electric field gradient is characterized by a symmetric second rank tensor V with principal elements Viso, Vδ, and Vη (with the latter two also denoted δ and η, respectively) in an irreducible spherical form.26 With a nuclear spin quantum number I ) 1, there are two allowed transitions between three adjacent Mz spin states, -1 T 0 and 0 T 1, resulting in two resonance frequencies symmetrically disposed about the isotropic resonance frequency. The separation frequency, ∆ν, of these two resonances is given by
∆ν ) 2δ(3 cos2 θ - 1 - η sin2 θ cos 2φ)
(1)
where θ and φ are polar angles that specify the orientation of the electric field gradient tensor in the laboratory frame, and η describes the asymmetry of the interaction (0 e η e 1). θ is the angle between the static magnetic field and the direction of the largest Cartesian tensor element of V and φ specifies the azimuthal orientation of the other two tensor elements. In powder samples, all orientations θ and φ are sampled, with scaling reflecting the orientational probability, resulting in characteristic powder patterns.14 The commonly quoted quadrupole coupling constant, νQ, for which its inverse sets the fundamental time scale for motional averaging, is equal to e2qQ/h,25 where eQ is the nuclear quadrupole moment and eq is the electric field gradient.27 δ equals 3νQ/8. In the presence of molecular motion, a time-averaged interaction that depends on the nature and time scale of the motion results in motionally altered powder patterns. The observed NMR powder patterns are characterized by the three tensorial parameters noted above, the isotropic value (Visoobs), the anisotropy (δobs), and the asymmetry (ηobs). To first order, the isotropic value is zero and is neglected.17 Together, the anisotropy and asymmetry define a family of line shapes, as shown for several hypothetical examples in Figure 1. The relatively large quadrupolar coupling moment of deuterium nuclei results in line shapes with large frequency breadth and consequently much of the spectral information in the time domain is found at very short times after the excitation pulse,
5984 J. Phys. Chem. C, Vol. 111, No. 16, 2007
DiVerdi et al.
Figure 2. Experimental deuterium spectra of labeled pyridines adsorbed on silica at 0.8 monolayer coverage as a function of temperature. All spectra are normalized to constant height.
Figure 1. Theoretical powder patterns representative of deuterium NMR spectra governed by a time-independent nuclear quadrupolar Hamiltonian. The abscissa displays normalized frequency in units of δ, the anisotropy of the interaction. Each of the five traces shows a value of η, the asymmetry parameter of the tensor. The isotropic component of the interaction is zero in all traces. The individual traces are normalized to constant integral. Convolution with a Gaussian function (0.05δ, fwhm) has been performed on each trace.
during which the spectrometer’s receiver suffers from a transient desensitization or “dead-time”. Dead-time problems were circumvented by use of a “solid-echo” technique that employs two π/2 pulses separated by a time T and shifted in phase by π/2.17,28 The solid-echo decay at times t > 2T is recorded; this decay is identical to the free induction decay for solid systems governed by a time-independent Hamiltonian, which is obtained in the limit of slow or no motion or in the fast-motional limit, in which rapid motions give rise to a time-averaged Hamiltonian.17,29 When motion exists with a correlation time on the order of the interaction strength, the governing Hamiltonian becomes time-dependent and if that time dependence, again dependent on the motional correlation time, is on the same scale as T, then the echo decay can be substantially different from the free induction decay.14,30 Solid-state deuterium NMR spectroscopy was applied to elucidate the motion experienced by pyridine adsorbed onto the silica gel surface. As the only deuterium present in the samples occurs in one or more locations of the pyridine ring, the observed signals directly probe the dynamics (and environment) experienced by the pyridine molecules as they interact with the silica surface. The strategy used in this work is first to analyze the experimental line shapes in terms of powder patterns (and, hence, tensors) that represent time-independent Hamiltonians (i.e., with a characteristic motional time scale far removed (either much faster or much slower) from the reciprocal of the interaction strength). Next, the measured tensors are related to specific position(s) on the pyridine ring, and then the motional modes responsible for observed averaging of the measured tensors are elaborated.
Temperature Dependence for Deuterium-Labeled Pyridines. Figure 2 shows experimental deuterium spectra of three isotopically labeled forms of pyridine, adsorbed on silica gel (nominally 0.8 monolayer) over a range of temperatures. All of these spectra were obtained with sufficiently long recovery time to ensure that they are fully relaxed in terms of spinlattice relaxation. The spectra include those of (1) a single deuteron at the γ-position, (2) two deuterons at the R and R′ positions, and (3) five deuterons at the R, R′, β, β′, and γ-positions. All of the spectra in Figure 2 are scaled to the same vertical dimension for visual clarity. Taken together, these patterns are suitable for elucidating the separate contributions to the spectra that presumably correspond to different modes of motion of the pyridine ring on the supporting silica structure. At high temperature (i.e., 243 K and above) all structure in the spectra of Figure 2 is washed out by the preponderance of liquidlike motional modes that collapse all powder patterns to featureless signals. At the lowest temperature, 78 K, almost all molecular motion is frozen out; only a small amount of motionally averaged structure is observed in the pyridine-R,R′d2 case. At 174 K, several motionally averaged powder patterns emerge; these patterns display sharp features and are indicative of motionally averaged powder patterns in the fast-exchange limit. Theoretical Deuterium Powder Patterns. The experimental spectra of Figure 2 contain a number of contributing powder patterns corresponding to specific deuterium ring positions and presumably different motional environments of pyridine molecules. We adopt a strategy here of describing the analysis and theoretical simulation of the experimental spectra by first using constituent powder patterns as abstract, mathematical, secondorder tensor entities and subsequently ascribing specific motional models to each pattern based on its specific characteristics and the surface structure. Figure 3 shows the collection of theoretical constituent powder patterns used to simulate the experimental spectra of Figure 2. On the right side of Figure 3, the theoretical patterns are presented after convolution with a Gaussian function (2.0 kHz, fwhm). Line shapes with a 2.0 kHz fwhm are often found in solid-state deuterium NMR spectroscopy, arising from residual homouclear and heteronuclear (with protons) dipolar interactions and were chosen to prevent obscuring the detailed
Molecular Dynamics of Pyridine on Silica Surface
J. Phys. Chem. C, Vol. 111, No. 16, 2007 5985
Figure 4. Experimental and theoretical deuterium NMR spectra of 0.8 monolayer of pyridine-d5 adsorbed on silica at 174 K and their difference spectra. Theoretical spectra were calculated from linear combinations of theoretical powder pattern components (I, IIA, IIB, IIIA, and IIIB), each convolved with independently determined Gaussian functions. Details of the theoretical spectra are shown in Table 2.
Figure 3. Theoretical deuterium NMR powder patterns, labeled I, IIA, IIB, IIIA, and IIIB, used for simulating experimental spectra. Each of the five patterns is shown on the left and after convolution with a Gaussian function (2.0 kHz fwhm) on the right. Values for δcalc and ηcalc are shown in Table 1.
TABLE 1: Summary of Principal Values for Each Constituent Powder Pattern and Corresponding Convolved Gaussian Line Width Used at 174 and 221 K
constituent powder pattern I IIA IIB IIIA IIIB
anisotropy and asymmetry values
convolved Gaussian line width (kHz, fwhm) Temperature
δ calc, kHz
ηcalc
174 K
221 K
135.2 71.0 86.0 3.9 18.1
0.045 0.85 0.55 0.00 0.00
2.0 2.0 2.0 16.0 16.0
4.0 16.0 16.0 16.0 16.0
Figure 5. Experimental and theoretical deuterium NMR spectra of 0.8 monolayer of pyridine-d5 adsorbed on silica at 221 K and their difference spectra. Theoretical spectra were calculated from linear combinations of theoretical powder pattern components (I, IIA, IIB, IIIA and IIIB), each convolved with independently determined Gaussian functions. Details of the theoretical spectra are shown in Table 2.
TABLE 2: Summary of Weighting Factors Used to Calculate Theoretical Spectra for Simulating Experimental Spectra of Labeled Pyridines on Silica at 174 and 221 K weighting factors 174 K
features of the powder patterns that would occur if wider Gaussian functions were used in this figure. The patterns in Figure 3 can be seen to be members of the family of powder patterns of the types found in Figure 1. The values of δcalc and ηcalc used to calculate each of the patterns are summarized in Table 1, including the widths of the Gaussian functions actually used in the calculating the theoretical spectra. Simulation of Pyridine-on-Silica Spectra. The experimental deuterium NMR spectra of the labeled pyridines adsorbed on silica, shown in Figure 2, were each fit to a theoretical spectrum by forming weighted linear combinations of the powder pattern components shown in Figure 3, each convolved with an independently selected Gaussian function. The results of this simulation process performed on the experimental spectra obtained at 174 and 221 K are presented in Figures 4 and 5, respectively, in which the experimental and theoretical spectra are shown together with the corresponding differences. The quality of the fits can be seen in the small amplitudes of the difference spectra (bottom). Weighting factors of the constituent powder patterns (I, IIA, IIB, IIIA, and IIIB) used in the fitting process are shown in Table 2. The five constituent powder patterns that were used to create theoretical spectra matching the experimental spectra are now analyzed in terms of the type, rate, and nature of the motion(s) required to account for each component. Motional Modes Attributed to Component I. The following three key points can be made regarding Component I: (1) The
weighting factors 221 K
component
γ-d1
R,R′-d2
d5
γ-d1
R,R′-d2
d5
I IIA IIB IIIA IIIB
1.00 0.00 0.00 0.00 0.00
0.06 0.92 0.00 0.02 0.00
0.25 0.37 0.37 0.01 0.01
1.00 0.00 0.00 0.00 0.00
0.00 0.77 0.00 0.23 0.00
0.20 0.32 0.32 0.08 0.08
experimentally consistent values for calculated Component I’s tensor (δobs ) 135.2 kHz and ηobs ) 0.045) (Figure 3 and Table 1) are in close agreement with the corresponding values found by Barnes and Bloom for neat pyridine-d5 at 77 K.31 These values correspond to those of a deuterium tensor that is static (on a τQ ) 1/νQ time scale of 5 × 10-6 s). In that work at 77 K and in the present work at 78 K, all ring positions are labeled in pyridine-d5 and all modes of motion are frozen out; so, assuming all the νQ values are the same for all of the deuterium positions, only a single powder pattern is observed. (2) A clear association is found between the γ-deuteron in pyridine adsorbed on silica and Component I (e.g., in samples in which only the γ-position of pyridine is deuterium-labeled (Figure 2, left), Component I is found to be the only contribution at low temperature, e 221 K). (3) Component I can also be found in the spectra of samples in which the γ-deuteron is not deuteriumlabeled (e.g., pyridine-R,R′-d2 at 78 K (Figure 2, bottom middle)). Taken together, these points provide strong evidence that (on the time scale of τQ) (a) at temperatures e221 K, pyridine adsorbed on the silica surface experiences no motion
5986 J. Phys. Chem. C, Vol. 111, No. 16, 2007 that would cause reorientation of the Cγ-D bond and motional narrowing of the γ-deuteron powder pattern; (b) at temperatures >221 K, pyridine adsorbed on the silica surface experiences some motion that does cause reorientation of the Cγ-D bond and motional narrowing of the γ-deuteron powder pattern; and (c) some of the pyridine-R,R′-d2 molecules adsorbed on the silica surface experience no motion that would cause reorientation of the CR D bond and motional narrowing of the R-deuteron powder pattern; this portion of the adsorbed pyridine increases with decreasing temperature and approaches zero at 221 K and above. The Cγ-D bond axis in pyridine-γ-d1 is collinear with the C2 axis of the pyridine ring, as is the unique component of the (almost) axially symmetric quadrupolar tensor. Hence, the corresponding deuterium tensor and powder pattern are insensitive to motions about this axis. However, this tensor is sensitive to other types of motional modes that cause reorientation of the Cγ-D bond (e.g., swinging rotations about the Si-O bond of the silanol to which the pyridine is presumably hydrogenbonded). Such rotations about the Si-O bond would be manifested at the γ-deuteron in such a manner to cause its quadrupole tensor and corresponding powder pattern to experience some mode of averaging. A Pake-doublet powder pattern (δobs ) 135.2 kHz, ηobs ) 0.045) corresponding to a static Cγ-D bond is observed at 221 K and below in the spectra of pyridine-γ-d1 (Figure 2, left), indicating that there is no motion about the Si-O bond (as fast or faster than νQ) at these temperatures (STATIC). At temperatures of 243 K and above, the pattern is highly averaged and a featureless signal of intermediate line width (Lorenzian, e 12 kHz, fwhm) is observed. This indicates that, for temperatures of 243 K and above, there is substantial motion, as fast or faster than the same time scale, about an axis that is not collinear with the axial symmetry axis of the Cγ-D bond. These motional averaging effects are indicative of the relatively sharp onset of one or more modes of motion. Rotation about the Si-O bond alone cannot explain this averaging, as it would result in a motionally averaged powder pattern with reduced but nonzero value of δave.32 This possibility is excluded by the experimental data, which are consistent only with δobs ∼ 0 kHz. Under such motion, the value of ηave would be somewhere between zero and one, depending on the Si-O-Cγ angle. Another possible motional mode that could account for this kind of averaging is chemical exchange of pyridine molecules among the surface silanol sites. The manifold of orientational possibilities corresponding to surface heterogeneity would provide the opportunity for sufficient reorientation of the Cγ-D bond direction to affect the observed averaging. The exchange rate for such a process is difficult to estimate. Figure 6 depicts the schematic structure of pyridine adsorbed on silica together with the identification of flipping and rotating pyridine ring motions and the definition of various angles as detailed in the following sections. Motional Modes Attributed to Components IIA and IIB. Component IIA is found only in the spectra of samples in which the R and R′ positions of pyridine have been labeled with deuterium. The unique labeling at this site in a sample (Figure 2, center) requires the unequivocal attribution of a Component IIA contribution to the R-position. Reorientation of the Cγ-D bond axis has been excluded at temperatures below 174 K (from the data for pyridine-γ-d1). Therefore, motional modes that average the R-deuterium tensor, while leaving the γ-tensor unaffected, are required to account for the experimental spectra in the analysis of Components IIA and IIB. Such modes are
DiVerdi et al.
Figure 6. Schematic representation of the structure of pyridine adsorbed on silica with the definition of angles used in the text and identifying flipping and rotating pyridine ring motions.
limited to discontinuous rotations (jumps or flips) with two or more equally populated sites (up to the limiting case of continuous rotation) about the Cγ-D axis. Fast (relative to νQ) jumps among three or more sites would average the static tensor to one corresponding to a Pake doublet (ηrot ) 0) with a reduced anisotropy (δrot) dependent on the angle (χR) made by the CR-D bond axis with the C2 symmetry axis of the pyridine molecule; this dependence is given by eq 2:33 static δrot (1/2)(3 cos2 χR - 1) R ) δR
(2)
However, such jump motional modes with three or more sites are excluded on the basis of Component IIA’s nonzero asymmetry (Table 1). Fast, discontinuous rotation between two sites (i.e., a pyridine ring flip (FLIP)), will cause the indicated averaging of the static tensor. Values of the elements of the flip-averaged tensor are dependent on the angle (χR) between the CR-D bond axis and the flipping axis (i.e., the C2 symmetry axis of the pyridine molecule). The calculation of the flipaveraged tensor is carried out most expediently in its Cartesian form. Conversion from spherical to Cartesian form is performed by eqs 3a-c26 (i) (i) V(i) XX ) -(1/2) δ (1 + η )
(3a)
(i) (i) V(i) YY ) -(1/2) δ (1 - η )
(3b)
(i) V(i) ZZ ) δ
(3c)
where the superscript refers to the type of tensor (e.g., static or average) being converted. The flip-averaged Cartesian tensor elements are the given by eqs 4a-c34 static static 2 2 Vflip XX ) VXX cos χR + VZZ sin χR
(4a)
static Vflip YY ) VYY
(4b)
2 2 static static Vflip ZZ ) VZZ cos χR + VXX sin χR
(4c)
Evaluation of these equations for χR ) 55.9° yields δflip ) 70.5 kHz and ηflip ) 0.83, which compare favorably with the experimentally determined values for Component IIA (δobs ) 71.0 kHz and ηobs ) 0.85). Component IIB is found only in the spectra of samples in which the β and β′ positions of pyridine have been labeled with deuterium. The unique labeling at this site (Figure 2, right, and
Molecular Dynamics of Pyridine on Silica Surface
J. Phys. Chem. C, Vol. 111, No. 16, 2007 5987
Figure 8. Experimental deuterium NMR spectra of 0.8 monolayer of pyridine-d5 adsorbed on silica as a function of temperature and halfecho time. All spectra are shown without amplitude scaling and at true amplitude.
Figure 7. Experimental deuterium NMR spectra of 0.8 monolayer of pyridine-R,R′-d2 adsorbed on silica as a function of temperature. The same spectra as shown in Figure 2 except that spectra are shown here at true amplitude, scaled only for number of acquisitions. The integrated intensity for each spectrum is shown on its right.
Supporting Information) requires the unequivocal attribution of a Component IIB contribution to the β deuteron. The motional averaging analysis for the β and β′ deuterons follows closely the corresponding analysis above for the R- and R′-deuterons. The difference lies in the involvement of the angle (χβ) made by the Cβ-D bond axis with the C2 symmetry axis of the pyridine molecule. Evaluation of eqs 3 and 4 for χβ ) 60.4° yields δflip ) 85.0 kHz and ηflip ) 0.52, which compare favorably with the experimentally determined values for Component IIB (δobs ) 85.0 kHz and ηobs ) 0.55). Motional Modes Attributed to Components IIIA and IIIB. Components IIIA and IIIB are relatively narrow and motionally averaged spectral components (δAflip ) 3.9 kHz, δBflip ) 18 kHz, ηAflip ) ηBflip ) 0) found in samples labeled in the R and β positions, respectively (Table 2). Neither of these components is found in spectra of the pyridine-γ-d1 samples. In consideration of the value of δcalc for Components IIIA and IIIB in comparison to that of the static deuterium tensor in labeled pyridine,31 Components IIIA and IIIB are substantially motionally averaged. This motional averaging must take place in a mode or modes in which the γ-deuteron tensor and powder pattern are not motionally averaged, because reorientation of the Cγ-D bond axis has been excluded at temperatures below 174 K (from the data for pyridine-γ-d1). Candidates for a suitable motion fulfilling these requirements include fast, discontinuous rotation among three or more sites about the C2 symmetry axis of the pyridine molecule with continuous rotation as the limiting case (ROTOR). The members of this ensemble of motional modes are equally effective in producing the requisite averaging, and it is not possible to distinguish among them on the basis of the observed line shape. Using eq 2 and the values obtained earlier for χR and χβ, the values for δARot and δBRot identified above were obtained. Pyridine Dynamics on Silica at 221 K. The deuterium NMR spectra of pyridine adsorbed on silica (Figure 7) obtained at 221 K display several characteristics not observed in the spectra obtained at other temperatures (e.g., 174 K). First, the Gaussian broadening of each of the component powder patterns observed at 221 K is larger, substantially in some patterns, than at 174 K (Figure 2 and Table 1). In moving from 174 to 221 K, broadening for the STATIC component (Component I) increases
from 2.0 to 4.0 kHz, the FLIP components (IIA and IIB) increase from 2.0 to 16 kHz, and the ROTOR components (IIIA and IIIB) remain at the already large 16 kHz. Notably, the characteristic parameters of the constituent powder patterns, δobs and ηobs, are unchanged over this temperature range. Second, the total integrated intensity of the pyridine-R,R′-d2 spectrum at 221 K is markedly smaller than that obtained at lower temperatures. The integrated intensity is roughly constant from 78 to 174 K (although there is considerable uncertainty in this measurement), then begins dropping at 198 K, experiences a minimum at about 221 K, and increases at 243 and 300 K without achieving its low-temperature value. Third, in some of the constituent powder patterns, transverse relaxation is enhanced at 221 K, relative to 174 K (i.e., greater attenuation of the signal as the half-echo time is increased) (Figure 8). At 174 K (Figure 8, left), the STATIC component (Component I) decreases by roughly 20% as the half-echo time increases from 15 to 100 µs, while the FLIP components (IIA and IIB) and the ROTOR components (IIIA and IIIB) decrease by roughly 40%. In sharp contrast, at 221 K (Figure 8, right), the STATIC component (Component I) decreases by greater than 90% as the half-echo time increases from 15 to 100 µs, while the FLIP components (IIA and IIB) and the ROTOR components (IIIA and IIIB) have essentially disappeared. Pyridine Dynamics on Silica above 221 K. Figure 2 (top) depicts deuterium spectra of pyridine adsorbed on silica, obtained at 243 and 300 K. The spectra for all three labeling patterns display similar line shapes that are dominated by a single Lorenzian peak of varying width. At 243 K, the values of the line width for each of the three labeling patterns (pyridineγ-d1, pyridine-R,R′-d2, and pyridine-d5) are 12.0, 9.3, and 12.0 kHz (fwhm), respectively. The corresponding values at 300 K are 3.4, 2.9, and 2.9 kHz. The extreme line narrowing displayed by these peaks arises from fast (relative to νQ) reorientation of the pyridine rings about multiple axes. This reorientation results in complete averaging of the quadrupolar interaction that gives rise to the powder pattern line shape. It should be noted that despite this complete averaging, the effect of the quadrupolar interaction is still present in the relaxation behavior of the deuterons (see Supporting Information). For this type of reorientation to occur it is necessary for the hydrogen bond between a pyridine and surface silanol to be broken, as there are insufficient (rotational) modes of motion available to reorient all the R, β, and γ-C D bonds over multiple axes with the hydrogen bond intact. Once a pyridine molecule is released from its surface anchor, it is free to reorient isotropically and also to translate across the surface. A previous investigation of molecular liquids adsorbed on silica glasses has shown that pyridine’s behavior in the temperature range 260 to 310 K follows a two-state, fast-exchange model with two distinct
5988 J. Phys. Chem. C, Vol. 111, No. 16, 2007
DiVerdi et al. TABLE 4: Changes in Enthalpy (∆H0) and Entropy (∆S0) of Pyridine Adsorbed on Silica at 0.2 Monolayer Coverage among the Observed Motional Modes
Figure 9. Variation of motional mode population fractions with temperature in pyridine-d5 adsorbed on silica with 0.8 monolayer coverage. Left: population fractions vs temperature (T). Right: equilibrium constant vs inverse temperature (T-1) for the equilibria among the motional modes.
TABLE 3: Changes in Enthalpy (∆H0) and Entropy (∆S0) of Pyridine Adsorbed on Silica at 0.8 Monolayer Coverage among the Observed Motional Modes process
∆H0 (kJ mol-1)
∆S0 (J mol-1 K-1)
STATIC f FLIP FLIP f ROTOR STATIC f ROTOR
6.0 ( 1.0 4.7 ( 1.0 12.0 ( 0.8
56 ( 5 -5 ( 5 57 ( 5
phases: a bulk phase with deuterium relaxation properties similar to those of bulk liquid and a surface-interacting phase with greatly enhanced relaxation.35 Temperature Dependence of the Distribution of Motional Components. As noted above, the dynamics of pyridine molecules adsorbed on the silica gel surface is explainable in terms of three motional modes (STATIC, FLIP and ROTOR) below 221 K and the fractions of each motional mode vary with temperature. The γ-deuterons of pyridine rings that are flipping or rotating about the Cγ D axis give rise to contributions to the static powder pattern Component (I); those contributions are distinguished by taking into account the number of each type of deuteron on the ring (see Supporting Information). Because the integrated intensity of the total spectrum is roughly constant from 78 to 198 K, a quantitative analysis of changes of the integration-derived fractions with temperature is worthwhile in this range. The fractions of each contribution to the total spectral intensity (given for two temperatures in Table 2) were determined by varying the weighting factor of each powder pattern so that the experimental spectra were fit to the spectra by reproducing weighted linear combinations of those components. Figure 9 (left) shows changes of the fraction of each mode for pyridine-d5. Assuming that the pyridine molecules adsorbed on any site have the potential to be in any of the three types of motional modes depending on temperature or that all states of pyridine molecules are interchangeable within a reasonable time, apparent equilibrium constants can be derived and changes of enthalpies and entropies can be estimated by fitting the data to the van’t Hoff equation, ln K ) -∆H0/RT + ∆S0/R. Figure 9 (right) shows ln K plotted against 1/T for the apparent equilibria between pairs of the three motional modes. The changes of enthalpies and entropies calculated from these plots are summarized in Table 3. At 198 K, no static pyridine rings are observed, the flipping rings dominate, and rotating rings are a minority. As the
process
∆H0 (kJ mol-1)
∆S0 (J mol-1 K-1)
STATIC f FLIP FLIP f ROTOR STATIC f ROTOR
15.1 ( 1.6 6.6 ( 1.0 23.3 ( 0.1
116 ( 9 11 ( 5 138 ( 1
temperature is lowered, the fraction of the static pyridine rings increases, while the fractions of the rotating and the flipping pyridine rings decrease. Although the thermodynamic parameters given in Table 3 were obtained independently from corresponding plots, there is a good agreement with respect to the relationships, ∆H0STATICfROTOR ) ∆H0STATICfFLIP + ∆H0FLIPfROTOR and ∆S0STATICfROTOR ) ∆S0STATICfFLIP + ∆S0FLIPfROTOR. Motions of the molecules in the static mode are totally restricted by the interactions with either neighboring molecules or structural features of the silica surface, and the enthalpy change for the STATIC f ROTOR process corresponds to the energy of the interactions. The fact that the enthalpy change for the STATIC f FLIP process is smaller than that for the STATIC f ROTOR process suggests that the molecules in the flipping state partially break the interaction but are still somehow restricted in their motion. The change of the Gibbs free energy, ∆G ) ∆H T∆S for constant temperature, is relatively entropy dominated for the case of the STATIC fFLIP transformation and retains a negative value down to 83 K. The result is that the pyridine ring-flip motion is observed even at 78 K. Changes of the enthalpy and entropy were also estimated for the 0.2 monolayer surface and are shown in Table 4. It is interesting to note that changes in these thermodynamic parameters for the 0.2 monolayer surface between the STATIC and the other motional modes are remarkably larger than those for the 0.8 monolayer surface, even though the corresponding series of spectra look similar. On the other hand, the parameter changes for the FLIP f ROTOR transformation of the 0.2 monolayer surface are close to those of the 0.8 monolayer surface. These differences evoke an intuitive explanation that the static mode in the 0.2 monolayer case is energetically more stable than in the 0.8 monolayer case. Our earlier work has indicated that single silanols are fairly predominant over geminal silanols and that approximately 60% of the single silanols are non-hydrogen-bonded after the evacuation at 150 °C.18,36 Pyridine molecules presumably adsorb preferentially onto the hydrogen-bonded silanols because the adsorption heat of pyridine onto them is larger than onto nonhydrogen-bonded silanols.37 The hydroxyl density of the silica surface used in this work11 is 6.2 OH nm-2 and the number of pyridine molecules, even on the 0.8 monolayer surface (3.2 molecules nm-2), is less than the number of the hydrogenbonded silanols. The population of the pyridine molecules adsorbed onto hydrogen-bonded silanols is dominant on both the 0.8 and 0.2 monolayer surfaces; therefore, both samples are similar in terms of the silanol groups. Silica gel surfaces feature porous structures and provide a variety of pore diameters. Molecules that favorably adsorb to the pore wall are confined predominantly in micropores and experience strong dispersion interactions (van der Waals interactions) with any neighboring molecules in close proximity on the surface in addition to hydrogen bonds between surface silanols and nitrogen sites of pyridine. The molecules confined in the smaller pores are strongly restricted in their motions35,38 and their surface structures are more ordered, resulting in lower entropy and increased free energy.39 The lower surface coverage
Molecular Dynamics of Pyridine on Silica Surface (i.e., 0.2 monolayer) results in a larger fraction of adsorbed molecules in confined environments as compared to the 0.8 monolayer case. The larger changes of the enthalpies and entropies for the 0.2 monolayer surface arise from the strong interaction between the pyridine molecules and neighboring molecules or structural features of the surface and more ordered structure in the static-state, respectively. Thus, the dependences of the thermodynamic parameters on surface coverage can be rationalized by invoking preferential adsorption of pyridine molecules at the lowest-G adsorption sites within the heterogeneous structure of the silica surface. It is noteworthy that the deuterium NMR spectra of deuterated pyridine adsorbed on silica obtained at various temperatures are well described by the superposition of components that correspond to static or rapid-motion patterns and do not display powder patterns corresponding to intermediate-motion line shapes (Figures 2-4). This is strikingly different than the case of deuterated pyridine adsorbed on Ca-montmorillonite,40 or most cases of variable-temperature deuterium NMR experiments in which temperature-dependent deuterium NMR spectra display a wide variety of powder patterns corresponding to an entire range of intermediate-motion line shapes.40 The lack of observable intermediate-motion line shapes has been reported previously, most often in disordered, glassy solids in some heterogeneous systems (as in the present case) but overall infrequently.41-44 This behavior has been interpreted as due to an underlying broad temperature-dependent distribution of rotational correlation times for the system studied, which in turn is caused by a broad temperature-independent distribution of activation energies for the various modes of motion. The existence of the broad distribution of rotational correlation times leads at any given temperature to a situation in which only a small fraction of the observed systems will be in the intermediate-motional regime, while most of them will be either in the very-fast regime or the slow-motional regime. Further, the NMR signals due to those systems in the intermediate-motional regime display reduced spectral amplitudes due to the effects of that motion and, hence, are rendered even less visible in the measured spectra. The existence of a broad distribution of activation energies affecting the motion of a probe molecule on the surface of amorphous silica is not unexpected, given the wide variety of surface environments present. Efforts have been made by other investigators to quantify the distribution of activation energies through the analysis of the temperature dependence of the population fractions (as referred to in the work).41-44 The results of such an analysis are highly desirable in the quest for chemical interpretation, but the method requires assumptions that may or may not be justified in the present case. Acknowledgment. The authors gratefully acknowledge support of this project by the Department of Energy grant DEFG-03-95ER14558 and National Science Foundation grant CHE-9021003. Supporting Information Available: Synthesis of pyridineβ, β′,γ-d3, experimental T1 method, experimental spectra of pyridine-d5 versus temperature, T1 measurements of pyridineR,R′-d2 on silica gel at 174 K, T1 measurements of pyridine-d5 on silica gel at 174 K, changes of the motional mode with temperature of the 0.2 monolayer coverage of pyridine-d5 adsorbed on silica gel, enthalpy, and entropy estimates for 0.2 monolayer coverage of pyridine-d5 adsorbed on silica gel, detailed motional mode populations for 0.8 and 0.2 monolayer coverage of pyridine-d5 adsorbed on silica gel and additional references.
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