ARTICLE pubs.acs.org/JPCA
Mobility of Solid tert-Butyl Alcohol Studied by Deuterium NMR Alena M. Nishchenko,† Daniil I. Kolokolov,‡ and Alexander G. Stepanov*,‡ †
Faculty of Physics, Department of Chemical and Biological Physics, Novosibirsk State University, Pirogova Street 2, Novosibirsk 630090, Russia ‡ Boreskov Institute of Catalysis, Siberian Branch of Russian Academy of Sciences, Prospekt Akademika Lavrentieva 5, Novosibirsk 630090, Russia
bS Supporting Information ABSTRACT: The molecular mobility of solid deuterated tert-butyl alcohol (TBA) has been studied over a broad temperature range (103283 K) by means of solid-state 2H NMR spectroscopy, including both line shape and anisotropy of spinlattice relaxation analyses. It has been found that, while the hydroxyl group of the TBA molecule is immobile on the 2H NMR time scale (τC > 105 s), its butyl group is highly mobile. The mobility is represented by the rotation of the methyl [CD3] groups about their 3-fold axes (C3 rotational axis) and the rotation of the entire butyl [(CD3)3-C] fragment about its 3-fold axis (C30 rotational axis). Numerical simulations of spectra line shapes reveal that the methyl groups and the butyl fragment exhibit three-site jump rotations about their symmetry axes C3 and C30 in the temperature range of 103133 K, with the activation energies and preexponential factors E1 = 21 ( 2 kJ/mol, k01 = (2.6 ( 0.5) 1012 s1 and E2 = 16 ( 2 kJ/mol, k02 = (1 ( 0.2) 1012 s1, respectively. Analysis of the anisotropy of spinlattice relaxation has demonstrated that the reorientation mechanism of the butyl fragment changes to a free diffusion rotational mechanism above 173 K, while the rotational mechanism of the methyl groups remains the same. The values of the activation barriers for both rotations at T > 173 K have the values, which are similar to those at 103133 K. This indicates that the interaction potential defining these motions remains unchanged. The obtained data demonstrate that the detailed analysis of both line shape and anisotropy of spinlattice relaxation represents a powerful tool to follow the evolution of the molecular reorientation mechanisms in organic solids.
1. INTRODUCTION tert-Butyl alcohol (TBA) represents a monohydric alcohol widely used in chemistry as a solvent,1 a denaturant for ethanol, ingredient in paint removers, octane booster for gasoline, oxygenate gasoline additive,2 and as an intermediate in the synthesis of other chemical commodities such as methyl tert-butyl ether, ethyl tert-butyl ether, tert-butyl hydroperoxide, other flavors, and perfumes. Most physical properties of butyl alcohols either increase or decrease monotonically across the series of four isomers, n-, iso-, sec-, and tert-, with one very distinct exception: the freezing points (in K) are 183.85, 165, 158.45, and 298.8, respectively. Astonishingly, the tert-butyl isomer freezes at temperatures more than 100 K higher than the other alcohols in this series. Its effectively spherical form apparently makes it much easier to pack and H-bond in its crystal form than the three other isomers with their more flexible alkyl groups. The characterization of a molecular arrangement of TBA in the solid state is a challenging task as it can exist in five distinct solid phases. TBA represents a crystal with noncubic structure (phase I)3 right below the melting point at 298.77 K. At a temperature as low as 282 K the triclinic P3 phase II is a stable one.36 The structure of phase II was derived only recently by a combination of X-ray diffraction and ab initio density functional r 2011 American Chemical Society
calculations.6 In this phase, the tert-butyl alcohol molecules are bonded together in hexamers, packed in a chairlike conformation.6 Phase II transforms to phases I or III if kept at 286.14 or 281.54 K, respectively.3,79 Phase III can exist between 282 and 295 K and is noncubic. If the sample is pure enough and is given the time to recrystallize between 286 K and the melting point TBA, it transforms to phase IV.5,6 If the cooling rate is fast enough, a glassy state is achieved.10 Phase IV was the first TBA crystalline phase structure that was possible to determine by single crystal X-ray diffraction.5 It represents a triclinic structure composed by hydrogen-bonded TBA molecules ordered in helical chains along the a-axis,5 a pattern strongly different from hexamer ordering seen in phase II. Apparently, the formation of hydrogen-bonded chain polymers is typical for all TBA solid phases, except phase II; the only difference is in a degree of disorder of the chains.5,11 Because the hydrogen-bonded TBA molecules in a chain polymer or in a hexamer are not completely free to rotate, and they do not form a plastic crystal, in contrast to an assumption made by Timmermans in 1961.12 Such an assumption was made Received: April 11, 2011 Revised: May 27, 2011 Published: May 31, 2011 7428
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The Journal of Physical Chemistry A by considering a relatively low melting entropy (2.7 R) of TBA and dielectric investigations that had clearly pointed to the presence of intramolecular rotations in solid TBA.12 Thus it becomes evident, that molecular reorientations in solid tert-butyl alcohol could strongly influence its physical properties and thermodynamic quantities. Various experimental techniques such as neutron scattering,7,8 far-IR,13 low-field 2H,14 1H,15,16 13C, and 17O NMR17 were used in an attempt to characterize the molecular reorientations in solid TBA. Unfortunately, the results obtained by different techniques for the solid alcohol are controversial. Neutron scattering and farIR techniques give the estimation of the value of the internal methyl rotation barrier about 1617 kJ/mol in solid state, whereas the values for the same barrier determined by NMR methods vary from 1117 to 22 kJ/mol.15 At the same time, the height of the tert-butyl group rotation barrier varies even more from 13.415 to 37 kJ/mol.17 Even the models for TBA intramolecular dynamics vary, so there are authors that did not consider the rotation of the tert-butyl group at all.14 As far as previous investigations could not provide the full picture about dynamic characteristics of TBA in the solid state, we have applied 2H NMR spectroscopy to elucidate this question. Solid state 2H NMR spectroscopy has been demonstrated to be one of the most powerful tools to probe molecular dynamics in molecular solids,1823 inclusion compounds,2428 and heterogeneous systems with molecular species confined in nanosized pores.2936 The spectrum line shape and spin relaxation of 2H nuclei are mainly governed by electric intramolecular quadrupolar interaction,18,37 which gives the possibility to characterize the molecular dynamics over a broad time scale from 104 to 106 s and 108 to 1010 s, respectively. In the present paper, we report on the results of 2H NMR studies of the dynamic behavior of TBA in the solid state in a temperature range of 113283 K. We have described 2H NMR line shapes for tert-butyl alcohol selectively deuterated either in the methyl groups (TBA-d9) or in the hydroxyl group (TBA-d1). Also, for TBA-d9 interpretation of the line shape of the 2H NMR spectra and the temperature dependence of the spinlattice relaxation time T1 are made in terms of mobility, exhibited by the CD3- and tert-butyl groups.
2. EXPERIMENTAL SECTION 2.1. Materials and Sample Preparation. tert-Butyl alcohol (TBA), selectively deuterated either in the methyl groups, TBA-d9, or the hydroxyl group, TBA-d1, was used in this work. TBA-d9 (CD3)3OH (99.6% 2H enrichment) had 0.12 mol % of water content. TBA-d1, (CH3)3OD was prepared from TBA by hydrogendeuterium exchange with deuterium oxide (99.96% 2 H enrichment) at room temperature and subsequent distillation over CaO. The extent of deuteration was 86% and the residue content of D2O was 1.75 mol %. The melting and boiling points for both deuterated TBA samples were 25.5 and 81 °C, respectively. The samples of TBA-d9 and TBA-d1 were sublimated under vacuum into the 5 mm (o.d) glass tubes, degassed by four freezepumpthaw cycles, and sealed under vacuum. 2.2. NMR Measurements. 2H NMR experiments were performed at 61.424 MHz on a Bruker Avance-400 spectrometer using a high power probe with a 5 mm horizontal solenoid coil. All 2H NMR spectra were obtained by Fourier transformation of the quadrature-detected phase-cycled quadrupole echo arising in
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the pulse sequence:38,39 π π τ1 τ2 acquisition t 2 (X 2 Y
ðiÞ
where τ1 = 20 μs, τ2 = 21.5 μs, and t is a repetition time of the sequence (i) during the accumulation of the NMR signal. The duration of the π/2 pulse was 3.53.7 μs. The 2H NMR quadrupolar constant in methyl groups is usually ∼160 kHz. For such spectrum, a π/2 pulse of 3.5 μs duration is in general too long for an ideal (τ2 = τ1) solid echo refocusing. However, when a shorter pulse is not technically achievable, it is possible to significantly decrease the line shape distortions, arising from the finite pulse width. It was shown by Davis et al.39 a less distorted spectrum line shape can be achieved by adding a certain delay to the refocusing time τ2 = τ1 þ dt. Typically, dt is about a half of the value of the π/2 pulse width; dt = 1.5 μs gave the best result in present work. Spectra were typically obtained with 5005000 scans and repetition time was 2 s. Inversionrecovery experiments to derive spinlattice relaxation times (T1) were carried out using the pulse sequence:40 π π ðπÞX tν τ1 τ2 acquisition t 2 (X 2 Y ðiiÞ where tν was a variable delay between the 180° (π)X inverting pulse (as in standard inversion recovery pulse sequence40) and the quadrupole echo sequence (i). As far as the different phase interconversions of the solid TBA are sensitive to the cooling procedure, a special temperature variation protocol was used: at each measurement the sample was rapidly cooled down to 100 K and then heated slow up to a target temperature. The temperature of the samples was controlled with a variabletemperature unit BVT-3000 with a precision of (1 K. The samples were allowed to equilibrate at least 15 min at a given temperature before the NMR signal was acquired. 2.3. Data Treatment. The NMR data acquisition and treatment was performed using BRUKER TopSpin commercial software. All simulations and fitting procedures were performed using homemade FORTRAN routines according to the formalism described in refs 41 and 42.
3. RESULTS The tert-butyl alcohol (see Figure 1) can exhibit three types of intermolecular rotational motions in a solid state. These are the rotation of the methyl [CH3] groups about their 3-fold axes (C3 rotational axes), the rotation of the entire butyl [(CH3)3-C] group about its 3-fold axis (C30 rotational axis), and the reorientation of the OH group about the same C30 axis. The reorientations of the hydrophobic ((CH3)3-C group) and hydrophilic (OH group) parts in the solid TBA are expected to be independent as these motions are governed by the distinctly different molecular interaction forces. The hydroxyl group is involved in hydrogen bonding with the oxygen of the neighbor TBA molecule.5,6 Its reorientational motion can be associated with crossing the barrier on breaking the hydrogen bonds. In case of reorientation of the C30 axis itself, it should make impact on 2H NMR signals of both methyl and hydroxyl groups, because the whole molecule is involved in the reorientation in such a case. 7429
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Figure 1. TBA molecule consists of hydrophobic (CH3)3-C group with two 3-fold rotational axes (C3 and C30 ) and a hydrophilic OH group.
Figure 3. Temperature dependence of 2H NMR line shape for the CD3 group of TBA-d9: (A) experimental spectra; (B) spectra simulated within a frame of the JJ model with k1 and k2, presented also in Figure 5.
3.2. 2H NMR Spectra of TBA-d9. Figure 3 shows the tem-
Figure 2. 2H NMR spectra line shape for hydroxyl group of TBA-d1 at 223 and 273 K.
Thus, in order to elucidate the possible dynamics of different fragments of TBA molecule in a solid state, the dynamics of either methyl or hydroxyl groups should be considered separately. 3.1. 2H NMR Spectra of TBA-d1. Figure 2 shows 2H NMR spectra of solid tert-butyl alcohol with deuterated hydroxyl group (TBA-d1). The line shape remains almost unchanged and represents a broad Pake powder pattern over the temperature range of 103283 K. The fitting by means of basic equations for the static case18,37 yields a quadrupolar constant QOD = 208 kHz with an asymmetry parameter ηOD = 0.12. These values are typical for hydrogen-bonded OD groups,43,44 which are static on the deuterium NMR time scale. Above 223 K, a liquid-like signal appears at the central part of the spectrum. This indicates the presence of mobile deuterated molecules involved into some fast isotropic reorientation. The intensity of the central peak increases with the temperature increase. However, the fraction of the mobile molecules is estimated to be below 1% of the total intensity even at 10 degrees below the melting point. Thus, the presence of the mobile component is most probably due to the residues of the deuterated water after the purification and due to the premelting phenomenon in the solid TBA. Therefore, we conclude that almost all TBA molecules are rigidly fixed by their hydrogen bonded hydroxyl groups below the melting point, which is in accordance to the molecules arrangement in a crystalline alcohol.5,6
perature dependence of 2H NMR spectrum of the TBA-d9. The spectrum represents a Pake powder pattern with Qmet = 178 kHz and ηmet = 0 below 100 K. These are the characteristic values of electric field gradient tensor (EFGT) main axis components for deuterons in static CDx groups (x = 13) of hydrocarbons.45,46 Between 103 and 173 K the line shape exhibits a remarkable change due to the intramolecular mobility of TBA. Above 173 K internal molecular reorientations reach the fast exchange limit (τC e Qmet1 ∼ 106 s), where the line shape is characterized ~ met = 18 kHz by a Pake powder pattern with the constant Q and ~nmet = 0. The observed decrease of the value of the effective quadrupole constant is in full agreement with the model of the intramolecular dynamics of TBA (Figure 1). For the CD3 group involved in two consecutive uniaxial rotations about the molecule symmetry axes C3 and C30 , the effective quadrupolar constant in the fast exchange limit can be estimated as ! ! 2 2 3 cos R 1 3 cos β 1 ~ met ¼ Qmet ð1Þ Q 2 2 where R is the rotation angle between the CD and CC bonds and β is the rotational angle between the CC and CO bonds. For the ideal tetrahedral geometry of the butyl fragment (R = β =109.5°), eq 1 yields an effective quadrupolar constant decreased ~ met = 18 kHz indicates that the by a factor 9. The resulting value Q angles R and β deviate from ideal tetrahedral geometry not larger than (1.5°. To understand the detailed mechanism of these internal rotations and their kinetic parameters (the activations barriers and rate constants), a detailed fitting analysis of the 2H NMR spectra line shape at the temperature range of 103173 K was performed. The fitted spectra were obtained by Fourier transform of the powder-average over the polar angles θ and j of the correlation function G(t,θ,j), which governs the time evolution of the transverse 2H spin magnetization after the solid echo pulse sequence. The correlation function can be computed using the 7430
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following equation:41 Gðt, θ, jÞ ¼ l expðAtÞ expðAτÞ expðA τÞP
ð2Þ
where A is a complex matrix composed as follows: A ¼ ΩþK
ð3Þ
The diagonal matrix Ω is composed by elements ωi describing the frequencies of the exchanging sites and K corresponds to a kinetic matrix that defines the jump rates: 8 8 > > < Ω ¼ iω 1=T 0 < K ii ¼ kij ii i 2 j6¼ i ð4Þ and > > : Ωij ¼ 0 : K ij ¼ kij
∑
The 1/T20 term stands for the residual line width which reflects the contributions from homo- and heteronuclear dipolar interactions of the spin Hamiltonian. l is a vector (1, 1, ..., 1) with N elements, where N is the number of exchange sites; P is a vector of equilibrium population of each site peq(i); and kij is the exchange rate between sites i and j. The 2H NMR frequency at the i-th site ωi(θ,j) is defined as rffiffiffi 31 2 ωi ðθ, jÞ ¼ q D ðΩi ÞDa0 ðj, θ, 0Þ 2 2 a, b ¼ 2 2b ba ! rffiffiffi ηmet 3 ηmet , 0, , 0, Qmet ð5Þ q2 ¼ 2 2 2
∑
Here Dba(Ω) are the Wigner rotation matrices18 defining the CD bond orientation for each site and q2 is static interaction tensor. To apply such a jump-model concept to the particular case of the TBA internal dynamics, a certain mechanism for these rotations is to be specified. In fact, for each rotational degree of freedom, there are only two possibilities. In one case the rotation is performed by a 3-site jump exchange (the J model) induced by the internal symmetry of the TBA molecule. In the other case it is represented by a continuous uniaxial diffusion (or at least a jump rotation around an axis with the number of evenly distributed sites N g 6,27 the D model). Once the mechanisms of individual rotations are specified, the remaining degrees of freedom are the elementary acts of cross transitions, which reflect the way of the two internal rotations coupling. For TBA at 103128 K, the correct fitting of the experimental line shape is possible (see Figure 3B) only if both rotations are described by a 3-site jump exchange, so that the kinetic matrix K of such JJ model is formed as 0 1 Δd Δoff Δoff B C C K ¼B @ Δoff Δd Δoff A , Δoff Δoff Δd 0
Λ B B Δd ¼ @ k1 k1
k1 Λ k1
1 k1 C k1 C A, Δoff ¼ Λ
0
k2 B Bk @ 3 k3
k3 k2 k3
1 k3 C k3 C A k2
ð6Þ
Here Λ = (2k1 þ 2k2 þ 4k3), k1 is the rate constant for one elementary transition in the methyl group (i.e., for a jumps around CC bond) and k2 is the rate of a single jump of the
Figure 4. A schematic representation of the jump-exchange mechanism of tert-butyl alcohol internal rotations. The rate constant k1 governs the jump rotation inside the methyl groups (e.g., deuteron at the position B1 moves to the position B2), while k2 is responsible for the jump rotation of the whole butyl fragment (e.g., deuteron at A1 moves to B1). k3 is the rate for cross transitions which require concerted jumps around CC and CO bonds (e.g., deuteron at B3 moves to C2).
entire butyl fragment around the CO bond. The elementary rate constant for the transition that normally require concerted jumps around CC and CO bonds is defined as k3 = k1k2/ (k1 þ k2), that is, the cross transitions are assumed to be completely governed by the individual elementary rate constants. Such a choice will be discussed in more details in the next section dedicated to the spin relaxation analysis. A comprehensive picture of the mechanism of the TBA internal motion is given in the Figure 4. The rate constants are assumed to obey the Arrhenius law k = k0exp( E/kBT), where E is the activation barrier, k0 is the preexponential factor and kB is the Boltzmann constant. The orientations for each site relative to the crystalline frame of the TBA molecule are given by a set of Euler angles (in the manner presented by H. Spiess,18 who adopted the Euler conventions of A.R. Edmonds): Dba ðΩi Þ ¼
2
∑ Dbc ðΩk ÞDca ðΩl Þ c¼ 2
Ωk ¼ ð0, R, ðk 1Þ2π=3Þ, Ωl ¼ ð0, β, ðl 1Þ2π=3Þ, i ¼ 3ðk 1Þ þ l
k ¼ f1, 2, 3g k ¼ f1, 2, 3g
ð7Þ
ð8Þ
All deuterons positions in the case of intramolecular motions are equal, thus, peq(i) = 1/N (N = 9 for the JJ model). The Arrhenius plots for the jump process rate constants k1 and k2 used to fit the temperature dependence of the 2H NMR spectra line shape for TBA-d9 are given in the Figure 5. The kinetic parameters derived from these plots are summarized in Table 1. Line shape analysis presented in Figure 3 gives the information on how the 2H NMR spectra line shape is affected by the intramolecular motion. At lowest temperatures the methyl groups rotation is almost completely suppressed and only the rotation about the CO bond is present. In such a case, the 2H NMR spectrum from the internal deuterons (marked as 1 in Figure 4) 7431
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Table 1. Values of the Simulation Parameters Used To Fit 2H NMR Line Shape, Arised from the Intramolecular Rotations of Both Methyl and Butyl Groups in TBA-d9 within the Temperature Range of 103173 Ka methyl groups E1, kJ/mol
21
k01, s1
2.6 1012
tert-butyl group
E2, kJ/mol
16
k02, s1
1 1012
Qmet, kHz
178
ηmet
0.01
R β
70.5° 69°
Errors in estimating the parameters: Qmet (3 kHz; ηmet ( 0.005; for activation barriers E1,2 ( 2 kJ/mol ; for the preexponential factors ∼20%; for R and β ( 0.5°. a
remains unaffected by the motion42 since the C-D bond direction for such deuterons is parallel to the rotation axis C30 .47 The moving deuterons (marked as 2 and 3 in Figure 4) give rise to an additional signal with reduced effective quadrupolar constant. The characteristic feature of this signal is the presence of two symmetric peaks at (63 kHz from the center of the powder pattern (e.g., see Figure 3, T = 113 K). Their position is sensitive to geometry of the TBA molecule (i.e., to the angles R and β). As the temperature increases, the rotation of the methyl groups starts to reveal itself by the growth of the central peak and simultaneous decay of the original static signal. The latter is a direct consequence of the fact, that the deuterons marked as 1 in Figure 4 are not anymore fixed and thus start to be affected by the C30 axis rotation. In such a way, the 2H NMR spectroscopy shows a powerful capability to distinguish the C30 and C3 rotations , so that it is possible to visually follow the gap between the rates of the two motions.47 At 173 K, the system reaches its fast exchange limit. The line shape is again characterized by Pake powder pattern, whose effective quadrupolar constant specifies the geometry of methyl group rotation about C3 and C30 axes. Because the line shape does not change further, the information about dynamics of TBA at 173283 K can not be derived from the line shape analysis. However, this information can be accessed by analyzing the anisotropic spinlattice relaxation (T1). 3.3. Analysis of 2H NMR T1 Relaxation for TBA-d9. To expand the temperature range of the experimental kinetic parameters for intramolecular motions and verify the validity of the chosen dynamic model above the 173 K, we have performed the analysis of the temperature dependence of the anisotropy of spinlattice relaxation (T1) for Pake-powder pattern with ~ met = 18 kHz. A series of partially relaxed spectra (different Q by tν) for (CD3)3COH were recorded at 173283 K with a step of 10 degrees (see, e.g., Figures 6 and 8). The simulation of the partially relaxed spectra line shapes provides information on the mechanism of the molecular motion and gives the values of the rates. These line shapes can be accessed by the Fourier transform of the partially relaxed correlation function G(t,tν,τ) given by the eq 9: Gðt, tν , τÞ ¼ ½1 2 expð tν =T1 ÞGðt, τÞ
ð9Þ
Here, tν is the delay time in the inversionrecovery pulse sequence and τ is the time delay between pulses in the solid echo
Figure 5. Arrhenius plots for the rate constants of the jump exchange process (JJ model) for intramolecular motion of TBA-d9 at 103168 K: (blue squares) methyl group rotation (k1), (red circles) butyl group rotation (k2).
sequence. Both fully relaxed G(t,τ) and spinlattice relaxation time T1 are anisotropic and depend on the observation angles θ and j in the powder pattern. T1 is given by the usual formula:41 1 3 ¼ π2 Q02 ðJ1 ðω0 Þ þ 4J2 ð2ω0 ÞÞ T1 4
ð10Þ
where the spectral density function Jm(ω) for the chosen model of the molecule motion is defined by the expression Jm ðωÞ ¼ 2
5
∑ Dm, aðΩL Þ Dm, bðΩLÞ a, b ¼ 1
N
∑
l, k, n ¼ 1
Dl3, a ðΩl Þ Dk3, a ðΩk Þpeq ðlÞVl, n
λn V 1 λn 2 þ ω2 n, k
ð11Þ Here ΩL are the observation angles θ and j, which connect the molecular frame with the laboratory frame; Ωk are the Euler angles which connect the molecular frame with the k-th distinct position of the CD bond within the assumed geometry of the jump model; Vl,n is a matrix composed by Eigen vectors of kinetic matrix K and λn is its Eigen values; N is the number of distinct jump-sites. The angular dependence of the spectral density function is determined by the chosen motional model and is reflected in the anisotropy of T1. Because anisotropy of T1 depends on the motional model, the line shapes of the partially relaxed spectra are strongly influenced by the motional model. So, it is possible to discriminate among possible motional models by analyzing the partially relaxed spectra with different tν delays. The first glance on the spectra simulated within the jumpjump (JJ) model at 173 K (see Figure 6B), clearly shows that, despite the model works perfectly for the fully relaxed spectra, this model does not give a satisfactory agreement with the experimental line shapes for the partially relaxed spectra. Such observation points out, that at least one of the rotations changes its mechanism: the JJ model changes to DJ or JD or DD models. (The first position in the abbreviation of DJ model stands for the methyl group reorientation, the second position in DJ model abbreviation stands for butyl fragment reorientation.) The simulations performed for each case have shown that, 7432
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Figure 6. Partially relaxed 2H NMR spectra of TBA-d9 at 173 K: (A) experimental data; (BE) simulated spectra: (B) JJ model, (C) JJ model with k3 = 0, (D) JD model, (E) JD model with k3 = 0. 2
Figure 7. Simulation 2H NMR spectra line shape of the TBA-d9 at 103173 K within the frames of different models: (A) JD model below 133 K; (B) JJ model below 133 K; (C) both JJ and JD models above 133 K.
among possible models, only the 3-site jump-free diffusion (JD) model fits the experimental data (see Figure 6D). The free diffusion of the butyl fragment was simulated as a six-site jump exchange process. The modifications of the overall kinetic matrix for such case are trivial; they are given in Supporting Information. The partially relaxed spectra for other temperatures were also successfully fitted within the JD model. The kinetic parameters for both rotations are the following: E1 = 22 ( 2 kJ/mol, k01 = 1.6 1012 s1 (3-site jump exchange for the methyl group); E2 = 18 ( 2 kJ/mol, k02 = 0.6 1012 s1 (free diffusional rotation for the butyl group). The parameters are very close to those obtained from 2H NMR spectra line shape simulations at 103173 K (Table 1). The sensitivity of the T1 anisotropy to the reorientation mechanism allows also to justify the presence of the cross transitions with the rate constant k3. In principle, experimental
H NMR spectra of the TBA-d9 presented in the Figure 3 can be simulated using a kinetic model with k3 = 0, rather than with 6 0. The simulations with k3 = 0 will be reflected only in a relatively k3 ¼ small decrease of the preexponential factors k10 and k20. Weak dependence of the JJ model on k3 would be preserved also in the fast limit regime if it were realized (see Figure 6C). For the JD model, the presence of the cross transitions is crucial: variation of the k3 strongly affects the partially relaxed spectra line shape. The change of the constant from k3 = 0 (Figure 6E) up to k3 = k1k2/ (k1 þ k2) (Figure 6D) results to the best fit of the experimental line shape. The physical reason behind such dependence is straightforward: in any jump-exchange model, the rate of the exchange is in fact the inverse residence time on a certain position between two jumps. The jump itself is assumed to be very fast taking thus a negligibly small amount of time. In such a case the slowest possible scheme for a double jump will be for the case when the molecule first waits for τ1 = 1/k1, then jumps over the first axis and then waits for τ2 = 1/k2 to jump over the second axis, so that τ3 = τ1 þ τ2. The definition τ3 = 1/k3 brings straightforwardly to the formula presented above. Note that we have tried a different proportion for k3 and have found that already in the case of k3 = 0.5 k1k2/(k1 þ k2) the fitted partially relaxed spectra are notably inconsistent with the experiment.
4. DISCUSSION The experimental results show a picture of the intramolecular dynamics of TBA in the solid state over a broad temperature range, with a detailed description of the reorientational mechanism. The molecules as a whole are rigidly fixed at 103283 K by a strong hydrogen bonding with their hydroxyl groups as follow from the line shape analysis of the hydroxyl OD groups. This is in a good agreement with the molecules disposition in the alcohol crystal.5,6 At the same time, the alkyl fragment of the molecule is highly mobile: both methyl groups and the butyl fragment rotate about their symmetry axes, C3 and C30 , respectively. The observed experimental values for the activation energies (∼21 kJ/mol for the C3 rotation and ∼16 kJ/mol for the C0 3 rotation) show that the potential barriers are created by van der 7433
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Figure 8. Partially relaxed spectra of the TBA-d9 at 243 K: (A) experimental; (BD) simulated within the frame of (B) JJ model, (C) JD model, (D) JJ and JD model with k3 = 0.
Waals forces for both motions.6,48 Both rotational motions start above ∼100 K as the 3-site jump rotations. The methyl groups preserve their reorientation mechanism up to the temperatures closed to the melting point, which is not the case for the rotation about C0 3 axis. Analysis of anisotropy of spinlattice relaxation shows that, as soon as the fast exchange limit (τC e Qmet1 ∼ 106 s) for both methyl and butyl groups is reached (∼173 K), the reorientation mechanism of the butyl fragment changes from 3-site jump rotation to a free diffusional rotation. Such peculiar motional behavior can not be associated with any of phase transitions in solid alcohol, because TBA does not exhibit any structural change below ∼283 K.48 This can be possibly related to a peculiarity of the rotational potential of the butyl fragment, which is mostly of intermolecular origin. Such conclusion results from the value of the activation barrier of this motion. In fact, in gas phase the rotation about the C30 axis is represented by 3-site jump rotation of the OH group. The activation barrier for such purely intramolecular process is ∼4 kJ/mol,48 while the activation barrier for the butyl fragment found in present work is ∼4 times larger (see Table 1). Ab initio calculations also support such conclusion stating that the butyl fragment rotation potential is mainly created by intermolecular methylmethyl interactions.6 Apparently, this is not exactly the case for the methyl groups rotational potential as the gas phase barrier for the rotation is ∼16 kJ/mol,48 which is only ∼1.4 times smaller that in the solid state, indicating, thus, that the intramolecular forces are still important for the C3 axis rotation. Lastly, we would like to discuss the limits and the accuracy of the 2H NMR as a tool for the motional mechanism determination. Below 173 K, in slow exchange regime (τC > 106 s), the motion can be characterized by line shape analysis. The simulation of the line shape within the frames of JJ and JD models (Figure 7) shows that the difference in the line shape evolution of the two models is evident up to 123 K. Above 133 K, both models give exactly the same patterns. Such a finding points out that the rotational mechanism can be changed within a range of ∼40°, without making any particular impact on the experimental line shapes. This marks the limits of the 2H NMR line shape analysis
Figure 9. Temperature dependence of 2H NMR spin-lattice relaxation time at perpendicular (green squares) and parallel (blue triangles) edges of TBA-d9 spectra, together with simulated curves for JD model, solid lines.
in discriminating the mechanisms of intramolecular rotations in the particular case of a double rotation. The second thing concerns T1 anisotropy analysis used to probe the TBA dynamics at T g 173 K. At 173 K, the simulation of the partially relaxed line shapes within the frames of two rotational models show a rather striking difference, so that a correct model can be easily established (JD model, Figure 6D). Further, the question is how the models display themselves at higher temperatures. In fact, following the JD and JJ models, predictions at higher temperatures we have found that above ∼243 K both models offer similar predictions for the T1 anisotropy (see Figures 8B,C and S1). Also, note that both models still clearly require the presence of the elementary cross transitions (see Figure 8D). 7434
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Figure 10. The angular dependence of the spin-lattice relaxation time for (A) JJ model, 173 K, slow exchange regime (ω0τC > 1); (B) JD model, 173 K, slow exchange regime (ω0τC > 1); (C) JJ model, 243 K, extreme narrowing limit (ω0τC , 1); (D) JD model, 243 K, extreme narrowing limit (ω0τC , 1).
To understand the reasons for such behavior it is necessary to analyze the rate of the motion in the system between 173 and 243 K with respect to Zeeman frequency ω0. We have analyzed temperature dependence of the T1 at two characteristic positions of the spectra, that is, at the perpendicular and parallel edges (see Figure 9). The minimum in the T1 temperature dependence around 203213 K indicates on the motional modes with the correlation times τC ∼ ω01 ∼ 109 s at this temperature. Above the temperature of the minimum, the motion is considered to be in the extreme narrowing limit (ω0τC , 1). This underlines the actual differences in the conditions: at 243 K, the exchange rates are fast enough to be considered being in the extreme narrowing limit, while at 173 K the motions are still too slow (slow exchange regime with regard to Zeeman frequency ω0). Simulation of T1 anisotropy at slow exchange regime (ω0τC > 1) and extreme narrowing limit (ω0τC , 1) clearly show that while the dependences of T1 on the angles θ,j in the powder pattern are clearly different for JJ and JD models at slow exchange limit (T = 173 K), the difference in these dependences disappear at extreme narrowing limit at 243 K (Figure 10). Thus, we can conclude that, in the case of the double rotation, the analysis of T1 anisotropy can be used to differentiate between the JJ and JD reorientation mechanisms only up to the point when motions reach the extreme narrowing limit, that is, τC < ω01 ∼ 109 s.
’ CONCLUSIONS Analysis of the line shape and anisotropy of spin-lattice relaxation time of 2H NMR spectra of solid deuterated tert-butyl alcohol (TBA) allowed us to make the following conclusions on its dynamic properties over a temperature range 103283 K: TBA molecules as a whole are immobile on the 2H NMR time scale (τC > 106 s) presumably due to involvement of their hydroxyl groups in hydrogen bonding with neighbor alcohol molecules. In contrast, the butyl group is highly mobile at T g 103 K both the methyl groups and the butyl fragment exhibit a 3-site
jump rotation about their symmetry axes C3 (k1) and C30 (k2), with E1 = 21 kJ/mol and E2 = 16 kJ/mol, respectively. Rotation rate of butyl fragment is 1 order of magnitude faster than that of the methyl groups at 103173 K. The values of the activation barriers indicate that butyl fragment rotation is mainly governed by the intermolecular van der Waals forces, and the methyl group rotation mainly by the intramolecular van der Waals potential. 2 H NMR line shape and anisotropy of spin-lattice relaxation time allows us to follow the evolution of the mechanisms of the methyl and butyl groups rotations. At 103123 K line shape analysis unequivocally show that reorientation of both the methyl groups and the butyl group occurs by 3-site jump (JJ) mechanism. Reorientation mechanism changes within a temperature range 123173 K. At 173243 K analysis of anisotropy of T1 of the observed powder pattern show that reorientation of the methyl groups occurs by 3-site jump mechanism, while the butyl fragment rotates by free diffusion mechanism (JD mechanism). Simulation of anisotropy of T1 relaxation within the frames of JJ and JD mechanism show that analysis of T1 anisotropy does not allow to distinguish between two mechanisms at T > 243 K. Experimentally observed T1 anisotropy fits both mechanisms at T > 243 K. The values of the activation barriers for both rotations derived from line shape analysis at 103123 K and those derived from T1 temperature dependence at 173283 K have similar values, which indicates that the interaction potential remains unchanged. The presented 2H NMR data allow us to characterize the motional behavior of TBA in the solid state: it was possible to discriminate both C3 and C30 rotations, to derive their kinetic parameters, and follow the evolution of the reorientation mechanisms over a wide temperature range.
’ ASSOCIATED CONTENT
bS
Supporting Information. Additional figure demonstrating similar predictions for the T1 anisotropy for JJ and JD models at T > 243 K and the modifications of the overall kinetic matrix
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The Journal of Physical Chemistry A for modeling free diffusion of the butyl fragment as a 6-site jump exchange process are available. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*Tel.: þ7 383 326 9437. Fax: þ7 383 330 8056. E-mail:
[email protected].
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