1746
J. Phys. Chem. 1996, 100, 1746-1752
Chain End Dynamical and Conformational Properties of n-Nonadecane Molecules in Urea Inclusion Compounds: A Study by Deuterium NMR Spectroscopy A. El Baghdadi,† E. J. Dufourc,‡ and F. Guillaume*,† Laboratoire de Spectroscopie Mole´ culaire et Cristalline, URA 124 CNRS, UniVersite´ de Bordeaux I, 351 cours de la Libe´ ration, 33405 Talence Cedex, France, and Centre de Recherche Paul-Pascal, CNRS, AVenue A. Schweitzer, 33600 Pessac, France ReceiVed: June 20, 1995; In Final Form: October 23, 1995X
The 2H NMR spectra of selectively deuterated n-nonadecane guest molecules CD3CD2(CH2)15CD2CD3 included within the channels of urea, CO(NH2)2, have been measured between 120 K and room temperature for two orientations of the applied magnetic field with respect to the single-crystal main axis (channel axis). The spectra reveal clearly the existence of a slow reorientational process (on the 2H NMR time scale) of the whole chain in the low-temperature phase of the sample, while the chain ends perform fast torsional vibrations. On crossing the phase transition, the slow reorientational process transforms into fast uniaxial reorientations of the whole chains while a new fast dynamical process involving transitions between the tt, gt, and tg conformations is evidenced. Assuming that the amplitude of the fast torsional vibrations do not change abruptly on crossing the transition, we find an amount of gt conformers on the order of 5%, in excellent agreement with that obtained from other techniques. We also discuss and summarize the dynamical behavior of the guest n-nonadecane molecules in both the low-temperature and high-temperature phases of the urea inclusion compound, on the basis of the time windows probed by different spectroscopic techniques.
1. Introduction Long-chain hydrocarbon molecules such as n-alkanes, aliphatic carboxylic acids, R,ω-dihalogenoalkanes, and others are known to form inclusion adducts with urea.1,2 In these inclusion compounds, the hydrogen-bonded network of urea molecules (hereafter called the host) contains essentially “infinite”, parallel channels of 5.2 Å approximate diameter (at room temperature) in which the long-chain guest molecules are densely packed in a one-dimensional arrangement. Because the interchannel distance is ca. 8.2 Å, lateral guest-guest interactions are weak as compared to the corresponding ones in the “pure” crystalline phases of n-alkanes. The n-alkane/urea inclusion compounds are known to undergo a phase transition from a low-temperature (LT) orthorhombic structure to a high-temperature (HT) hexagonal structure of the urea host at a temperature that depends in a nonlinear way on the length of the guest molecules. In general, the phase transition temperature Tt increases as the length of the guest molecule increases (i.e. with increasing number of carbon atoms of the guest). This transition is also associated with an abrupt change in the dynamical properties of the n-alkane molecules, and it has been shown that these molecules undergo considerable motions in the high-temperature phase.3 At sufficiently high temperature, the inclusion compound decomposes to produce the pure crystalline phase of urea (which is tetragonal and does not contain empty channels). Whatever the structural phase, the guest periodic repeat distance cg is incommensurate with the ch host lattice periodic repeat distance along the b c axis so that urea inclusion compounds belong to the class of incommensurate composite structures.4 Because of this one-dimensional constraining environment, urea inclusion compounds have been extensively studied as prototype materials for the analysis of the dynamical and spectroscopic properties of alkyl chains forced to adopt their fully extended “all-trans” conformation.5 Among the large variety of guest †
Universite´ de Bordeaux. Centre de Recherche Paul-Pascal. X Abstract published in AdVance ACS Abstracts, January 1, 1996. ‡
0022-3654/96/20100-1746$12.00/0
species that can form urea inclusion compounds, the n-alkane ones are particularly good model systems and have been consequently independently investigated from the viewpoint of their structural, dynamical, and conformational properties using various spectroscopic techniques.6 The dynamic properties of the guest molecules in nnonadecane/urea inclusion compounds in the HT phase have been studied in detail by means of 2H NMR,7-11,14 incoherent quasi-elastic neutron scattering,12,13 and computer simulations.14-16 From the results obtained by means of 2H NMR on the perdeuterated n-nonadecane C19D40 molecules in the urea inclusion compound (noted hereafter C19D40/urea-h4), the motion of the guest was assigned to an unrestricted rotational diffusion of the chain about its long axis. Moreover, incoherent quasielastic neutron scattering (IQNS) experiments performed on the inclusion compound of n-nonadecane C19H40 in deuterated urea (C19H40/urea-d4) have provided direct evidence of the existence, in the HT phase of the sample, of large amplitude restricted translational diffusion of the n-nonadecane guests within the urea channels. In addition, reorientations of the chains were also evidenced, and both motions were shown to be effective on a ca. 50 ps time scale. From computer simulations of the molecular dynamics (MD) of n-nonadecane chains in urea, the interpretations of the MD trajectories for the reorientations15,16 and translations16 were in good agreement with the IQNS results. Some controversy arose in the literature regarding the conformational properties of the included n-alkane guest molecules. The results obtained by vibrational spectroscopy17-19 were found to be in marked disagreement with those obtained by NMR spectroscopy11,20 and MM2 molecular mechanics calculations.20 Indeed, Imashiro et al.20 measured CH dipolar splitting in switched angle spinning 13C spectra of n-alkane CnH2n+2 urea inclusion compounds with n ) 7-10. They concluded that about 25-35% of conformers with gauche defects near the end of the chains were existing in urea inclusion compounds. From 2H NMR spectra of CnD2n+2/urea-h4 samples with n ) 8, 10, 12, 16, 19, and 20, and recorded at room © 1996 American Chemical Society
n-Nonadecane Molecules in Urea Inclusion Compounds
J. Phys. Chem., Vol. 100, No. 5, 1996 1747
temperature, Cannarozzi et al.11 claimed that the amount of end-gauche conformations was in the range 16-32%. From Raman scattering measurements,19 gauche defects involving the terminal CH3CH2CH2CH2-groups were evidenced both in the low-temperature (LT) orthorhombic and in the high-temperature (HT) hexagonal phases of n-CnH2n+2/urea inclusion compounds with n ) 8-19. Furthermore, we were able to identify the vibrational modes of the tt, gt, and tg conformers, defined as follows. tt stands for an n-alkane chain with both terminal CH3CH2CH2CH2-groups in the “trans” conformation: t
t
CH3-CH2-CH2-CH2gt stands for an n-alkane chain with one gauche bond at the position of the first -CH2CH2- group starting from the methyl group and which is otherwise “all trans”: g
t
CH3-CH2-CH2-CH2tg stands for an n-alkane chain with one gauche bond at the position of the second -CH2CH2- group starting from the methyl group and which is otherwise “all trans”: t
g
CH3-CH2-CH2-CH2From the Raman intensities of the rocking modes of the methyl group, we have measured an amount of about 5% gt conformers and a few tg (5% at the maximum) defects,19 whatever the temperature or the length of the included chains. Undoubtedly, n-alkane guest molecules are distorted at their ends and this property is quite general, the extent of distortion depending only upon both the size of the terminal substituents and the hydrostatic pressure.19,21 It must be concluded that end gauche conformations originate in the strong longitudinal interactions between neighboring molecules and are therefore related to the particular driving forces which have to be taken into account in these 1D prototype materials of incommensurate composite structure. Because it is essential to assess the conformational properties of the n-alkane guest molecules to get a better understanding in the unusual physicochemical properties of urea inclusion compounds, it is particularly important to reach a unified interpretation of the results obtained by using the various techniques mentioned above. If we were able to detect conformational defects by Raman spectroscopy, we were however unable to analyze further their dynamical properties because of the characteristic time scale of this technique (t < 1 ps). We have therefore undertaken a complementary study of the chain end dynamics in n-alkane/urea inclusion compounds by deuterium NMR, this technique allowing us to detect motions effective on a much longer time scale (t < 1 µs). The aim of this study is to present a detailed investigation by means of deuterium NMR spectroscopy of the chain end dynamics of n-nonadecane molecules when incarcerated within the channels of urea inclusion compounds. From previous measurements,8 the phase transition temperature, Tt, was estimated to be in the 160-170 K range for n-nonadecane/urea. We have therefore performed these experiments as a function of the temperature between 120 and 300 K, i.e. in both the LT and HT phases of the sample. To avoid the undesirable spectral contributions due to the inner -CD2- methylene groups, we have used a selectively deuterated CD3CD2(CH2)15CD2CD3/ urea-h4 sample. Finally, to get a precise description of the conformational dynamics of the chain ends, single crystals of the sample were oriented with their long axis (the channel axis) either parallel or perpendicular to the applied magnetic field.
Figure 1. Angles defining the orientation of a C-D bond with respect to the external magnetic field B B0. The Z axis of the fixed laboratory frame is collinear to the channel axis.
In the following, we will describe the experimental procedure and introduce some elementary theoretical aspects to make clear the analysis and discussion of the experiments. We will then, on the basis of simple dynamical models, analyze the new NMR data and discuss their validity in view of the complementary observations obtained by other techniques, in particular by means of Raman19 and quasi-elastic neutron scattering.12,13 2. Experimental Procedure The selectively deuterated n-nonadecane sample CD3CD2(CH2)15CD2CD3 was prepared by courtesy of M. F. Lautie (CNRS, LASIR, Thiais, France), following the method described in ref 22. Crystals of the urea inclusion compounds were grown from a methanolic solution following standard methods.19 The needle-like single crystals (typical dimensions 0.5 × 0.5 × 5 mm3) were placed in cylindrical NMR glass tubes such that the urea channel axes (crystallographic b c axis of the host structure) of all crystals were parallel to each other and aligned with the tube axis. However, the orientations of the crystals were random with respect to rotation about this axis. We could therefore record spectra with the applied magnetic field B B0 either parallel (this geometry will be noted hereafter B B|0) or perpendicular (this geometry will be noted B B⊥0 ) to the channel axis. Deuterium NMR was carried out on a Bruker MSL 200 operating at 30.7 MHz. A phase-cycled quadrupolar echo composite sequence23 was used to record NMR signals. Solenoid-type and horse-saddle-type coils were respectively used B⊥0 geometries. Typical acquisition parameters for the B B|0 and B were spectral window of 500 kHz; 90° pulse widths of 7.25 µs B⊥0 ); delay τ between the two pulses to form the (B B|0) and 5 µs (B echo of 40 µs in both geometries; recycle delays ranging from 0.1 to 1 s depending on temperature (a quick T1z estimate was performed prior to each experiment); 10 000 scans. Quadrature detection was used in all cases, and samples were allowed to equilibrate at least 30 min at a given temperature before the NMR signal was acquired; the temperature was regulated to (1 °C. Line-shape simulations were performed on a VAX/VMS 8600 computer, using homemade software.24 3. Theoretical Background Let us define the system as sketched in Figure 1. The angle R defines the orientation of the b c channel axis with respect to the magnetic field direction B B0. The orientation of a given C-D bond is defined in the (x, y, z) axes system through the angles ψ and φ. Considering that the electric quadrupolar interaction dominates all internal magnetic interactions, the spectrum of a C-D bond in such a system will be defined by the so-called quadrupolar splitting,25,26 ∆νQ:
1748 J. Phys. Chem., Vol. 100, No. 5, 1996
(
∆νQ ) AQ
El Baghdadi et al.
)
3 cos2 β - 1 2
(1)
where
AQ )
3 e2Qq 2 p
and e2Qq/p is the static quadrupolar coupling constant (167 kHz for methyl and methylene CD2 groups27). In eq 1, it is considered that the electric field gradient tensor is axially symmetric, with its Z axis collinear with the C-D bond direction.27 The angle β then defines the orientation of a C-D bond with respect to B B0 and can therefore be defined according to the axis system in Figure 2 as
cos β ) cos φ sin ψ sin R + cos ψ cos R
(
)
3 cos2 ψ - 1 2
TABLE 1: Quadrupolar Splittings, ∆νQ, Observed for -CD2a and -CD3b Groups of a Hydrocarbon Chain Embedded within a Linear Channel Oriented Parallel and Perpendicular to the Magnetic Field B B0
(2)
We will now derive the expressions of the quadrupolar splittings when the channel axes are oriented parallel and perpendicular to the magnetic field B B0, both for the static case (encountered in the LT phase) and for the case of a fast axial rotation of the hydrocarbon chain around the b c axis (HT phase). The Static Case (LT Phase). When B B0 is oriented parallel to the channel axis b c, then R ) 0 and eq 1 becomes (using eq 2)
∆νQ| ) AQ
Figure 2. Angles defining the orientation of a C-D bond for the methyl group with respect to the external magnetic field B B0. The Z′ axis is the C3 axis of the -CD3 groups.
(3)
fast axial rotation
static CD2
CD3
CD2
CD3
b c|B B0 -AQ/2 -AQ/6 -AQ/2 -AQ/6 b c⊥B B0 AQ/(3 cos2 φ - 1)/2 -(AQ/3)(3 cos2 φ - 1)/2 AQ/4 AQ/12 maximumc at maximumc at AQ and -AQ/2 0 and AQ/6 a It is considered that both deuterons are equivalent and oriented at ψ ) 90° with respect to the channel axis. b Fast rotation about the C3 axis of the -CD3 group is assumed, then the orientation of the CnCn-1 bond with respect to b c is ψ ) 32.25°. c In the cylindrical distribution of orientations, there are two maxima for φ ) 0° and 90°, respectively.
and when R ) π/2 (c b perpendicular to B B0) it becomes
∆νQ⊥ ) AQ
(
)
3 cos2 φ sin2 ψ - 1 2
(4)
Fast Rotations around the b c Axis (HT Phase). Considering that the correlation time τc for axial rotation is much smaller than the reciprocal of the quadrupolar interaction (τc < ∆νQ-1), then 〈cos2 φ〉 ) 1/2, and eq 4 becomes
(
∆νQ⊥ ) AQ
)
3/2 sin2 ψ - 1 2
(5)
Equation 3 is unchanged upon fast rotation. It clearly appears that only the orientation of our system perpendicular to the field will give a hint about the onset of fast axial rotations of the aliphatic chain (compare eqs 4 and 5). It is now interesting to predict the patterns that will be observed for the -CD2 and -CD3 groups both in the static and fast motional regimes and with the b c axis orientations parallel and perpendicular to B B 0. Table 1 summarizes such calculations, and we have also reported in Figure 3 the theoretical profiles expected for the tt form of the selectively deuterated n-nonadecane CD3CD2(C15H30)CD2CD3 molecule. The time-dependent NMR signals (FIDs) were calculated according to eqs 3, 4, and 5, for both the -CD3 and -CD2 groups. A weighting factor of 3/2 was applied to the -CD3 FID prior to summing the -CD2- signal. A Gaussian decay with an arbitrary broadening of 5 kHz was taken for both labeled groups. A subsequent Fourier transformation was applied to obtain the spectra reported in Figure 3. Examination of Table 1 and Figure 3 clearly indicates that the static case (LT phase) may be straightforwadly detected (bottom spectra in Figure 3) by performing experiments in the B⊥0 geometries. A fast axial rotation around the b c axis B B|0 and B can also be clearly evidenced, but only in the B B⊥0 geometry. We can note, by examination of Table 1, that the quadrupolar splittings expected in the B B|0 geometry are half of those
Figure 3. Theoretical B B⊥0 and B B|0 profiles expected for an “all-trans” n-alkane chain in the static limit (a) and reorienting rapidly about the b c channel axis (b).
expected in the B B⊥0 geometry, in the fast modulation regime. Any deviation between the measured quadrupolar splittings, G (g), and those predicted in Table 1 or Figure 3, ∆νQ,exp. G (g), will therefore be an indication of the presence of ∆νQ,the. other fast dynamical processes. These additional components may be characterized by a so-called order parameter S (0 e S e 1) such that G G ∆νQ,exp. (g) ) ∆νQ,the. (g)S
(6)
n-Nonadecane Molecules in Urea Inclusion Compounds
J. Phys. Chem., Vol. 100, No. 5, 1996 1749 TABLE 2: Values of the Order Parameter S Obtained by Fitting the Theoretical Line Shapes (See Text) to the Experimental Profiles
a
T/K
B B⊥0
B B0
120 140 155 165 290
0.86 0.80 0.70 0.80 0.80
n.i.a 0.90 0.90 0.80 0.80
|
n.i. ) not investigated.
Figure 5. Temperature variation of the quadrupolar splittings ∆νQ⊥,φ)0(CD3), ∆νQ⊥,φ)π/2(CD3), and ∆νQ⊥ (CD3).
Figure 4. B B⊥0 (left) and B B|0 (right) 2H NMR spectra of the C19H30D10/ urea-h4 inclusion compound for selected temperatures between 120 and 290 K.
where the label g stands for the chemical group and G for the experimental geometry. It is noteworthy that eq 6 is general and must be valid whatever the experimental geometry (B B|0 or ⊥ B B0 ), the structural phase (LT or HT), or the considered group (-CD2- or -CD3). 4. Results 4.1. Analysis of Spectra. We have reported in Figure 4 the temperature dependence of the experimental 2H NMR spectra of the CD3CD2(CH2)15CD2CD3/urea-h4 sample in both B⊥0 geometries. The spectral line shapes reported in the B B|0 and B Figure 4 were fitted by means of eq 3-6 using the single parameter S, and the results are reported in Table 2 for both orientations and at all the temperatures investigated. We note that in the HT phase a single value of S (0.8) has been obtained for all temperatures and both orientations. In the LT phase,
the value of S is constant (0.90) for the B B|0 geometry and decreases (from 0.86 to 0.70) on increasing the temperature in B⊥0 , S increases the B B⊥0 geometry. In addition, we note that in B from 0.70 to 0.80 on crossing the phase transition. In B B|0, S decreases from 0.90 to 0.80. The temperature dependence of S in the B B|0 geometry is consistent with the onset of fast reorientations occurring at the phase transition, whereas the behavior of S in the B B⊥0 geometry cannot be described by such processes. The apparent discrepancy between results obtained in the LT phase for parallel and perpendicular orientations clearly indicates that the B B⊥0 geometry is sensitive to dynamical processes that do not affect the B B|0 geometry. From the examination of the ⊥ B B0 spectra reported in Figure 4, we note a drastic modification in spectral line shapes between 155 and 165 K. This shows that the phase transition involves the guest molecule reorientations which are effective within this temperature range and leads to the theoretical line shapes expected in the HT phase for a molecule undergoing fast axial rotation (Figure 3b, B B⊥0 case). However, the central line expected for an ”all-trans” static chain (see Figure 3a, B B|0 case) is split into two components, even at the lowest temperature investigated (120 K). The only way to account for such a situation is to introduce a nonzero S value in the simulation, which as we already mentioned, unexpectedly decreases from 120 K (S ) 0.85) to 155 K (S ) 0.7). It is worthwhile mentioning that we have also considered the case of a distorted geometry of the chain ends at low temperature. In fact, by assuming that the ∠CCD angles are modified, we failed to obtain theoretical line shapes fitting well the experiB|0 geometries. Help can mental ones, for both the B B⊥0 and the B be obtained from Figure 5, where we plotted the -CD3 quadrupolar splittings as a function of temperature, for the B B⊥0 geometry. The collapse of the φ ) 0° and φ ) 90° components of the cylindrical pattern, at the transition temperature, suggests that there is a motion in the intermediate regime on the NMR time scale (t ≈ 1 µs), in the LT phase, which
1750 J. Phys. Chem., Vol. 100, No. 5, 1996
El Baghdadi et al.
TABLE 3: Definitions of the Probabilities Pi of Finding a n-Nonadecane Molecule in the Conformational State i conformers i
Pi
tt gt tg gg
pp′ (1 - p)p′ (1 - p′)p (1 - p)(1 - p′)
reaches the fast modulation limit above 155 K. The fact that the B B|0 line shapes are not affected by such a process indicates that this motion must be the long axis rotation of the guest molecule. As a consequence of the intermediate regime, S values reported for the B B⊥0 geometry are meaningless in the LT phase: an assumption of fast processes is indeed made in writing eq 6. In fact, the S value obtained at very low temperatures for B B⊥0 (S ) 0.85) is the only one comparable to that obtained in the B B|0 geometry. This indicates that at 120 K the long axis rotation begins to freeze, in the NMR time scale. To summarize, an S value of 0.9 is therefore the only value to be considered within the temperature range investigated in the LT phase. In the HT phase (above 160 K), we observe four peaks, as expected for the n-nonadecane chain reorienting rapidly about its main molecular axis. The B B⊥0 experimental quadrupolar splittings for the -CD2- and -CD3 groups were measured respectively at 50.0 and 16.4 kHz, and they do not change with temperature variations within the HT phase. Here again, we note that these splittings are smaller than those expected for the fully extended all-trans chain reorienting rapidly about its molecular axis (62.6 and 20.9 kHz, respectively). From eqs 10, 11, and 14, we found S ) 0.8 ( 0.01 for the -CD2- and -CD3 groups. As expected from the above theoretical analysis, we note that the observed quadrupolar splittings are half the values obtained in the B B|0 geometry in the HT phase (100.0 and 33.0 kHz), demonstrating that our sample is well oriented with respect to the applied magnetic field. From this analysis, we may already conclude that in the lowtemperature phase of the n-nonadecane CD3CD2(CH2)15CD2CD3/urea-h4 compound, a slow reorientational motion of the whole chain is effective on the 2H NMR time scale (t ≈ 1 µs) and only affects the B B⊥0 spectral line shapes. In addition, we may suggest that additional fast motions of the chain ends -CD2CD3 are also effective, and they are characterized by an order parameter S ) 0.9. We will discuss this point in the following section. On crossing the phase transition temperature, the slow reorientational dynamical regime transforms into fast reorientations of the whole chains about the channel axis. The time scale of this fast process has already been determined by other techniques11,12,15 and ranges in the 1-50 ps time scale. While the order parameter is constant at low temperature (as determined from the B B|0 spectra), its value changes suddenly on crossing the phase transition, demonstrating that another motion (fast compared to the 2H NMR time scale) becomes effective in the high-temperature phase only. We will now propose a model for this additional dynamical process. 4.2. Simplified Models for the Additional Dynamics of the -CD2CD3 Groups. Several authors have already proposed models for the particular dynamics of the chain ends in the HT phases of n-alkane/urea inclusion compounds.8,10,28 In short, two point of views may be emphasized. In a first approach (model I), it is considered that the new motional process is described by fast and large amplitude torsional oscillations about the penultimate C-C bonds. Using this model, Harris and Jonsen28 found an average angle of 21° for this motion in the n-hexadecane/urea inclusion compound. However, in this model, the existence of gauche defects at the chain ends was not considered.
TABLE 4: Probabilities ((2 × 10-3) Pi for the Various Conformations of n-Nonadecane (i ) tt, gt, tg, gg) in the Urea Inclusion Compound i a
HT phase HT phaseb HT phasec LT phasec
tt
gt
tg
gg
0.805 0.900 g0.92 g0.92
0.095 0.050 0.04 0.04
0.089 0.050 e0.04 e0.04
0.011 0.000
a Model II using eqs 11 and 12. b Model II considering that there are additional fast vibrational processes in the LT and HT phases (see text). c Estimated by Raman spectroscopy.18
In a second approach (model II), a fast conformational exchange of the chain ends between the gt, tt, and tg conformations may be considered.11 To derive the probabilities Pi for each conformer (given in Table 3), we define by p the probability of having a gt defect and by p′ the probability of having a tg defect. Assuming, in addition to the fast uniaxial reorientational process, fast exchanges between the tt, gt, and tg conformations, the S order parameter becomes 9
S ) ∑PiSi
(7)
i)1
with
Si )
(
)
3 cos2 βi - 1 2
(8)
where, for a particular deuteron of conformer i and probability B0 for a -CD2 Pi, βi is the angle between the C-D bond and B group or between the Cn-Cn-1 bond and B B0 for the -CD3 groups. Let us now examine for simplicity the case B B|0. Given the above equations and referring also to section 3, it is easy to derive the expressions for the quadrupolar splittings and therefore the following equations for the order parameters of -CD2- and -CD3 groups:
S(CD2) ) 1/2(pp′ + p + p′ - 1)
(9)
S(CD3) ) pp′ + p - p′
(10)
From the experimental spectra recorded in the HT phase of C19H30D10/urea-h4, we have found S(-CD2-) ) S(-CD3) ) S ) 0.8. By equating eqs 9 and 10, we get
p)
3S + 1 S+3
(11)
and
1 p′ ) (S + 1) 2
(12)
Finally, we can now estimate the relative amount of endgauche conformations assuming a fast conformational exchange between the gt, tg, and tt conformers. We find about 19% of distorted molecules in the HT phase. The details of the results are reported in Table 4. 5. Discussion On the basis of the NMR results only, it is difficult to definitively conclude about the different models described above. However, the results of the literature on neat n-alkanes and n-alkane/urea will help consistently in the following discussion: First, it is essential to recall that gt and tg conformers are undoubtedly detected by means of Raman spectroscopy in both
n-Nonadecane Molecules in Urea Inclusion Compounds
J. Phys. Chem., Vol. 100, No. 5, 1996 1751
the LT and HT phases of the n-nonadecane/urea-h4 sample19 and other n-alkane/urea inclusion compounds.18,19 Unfortunately, this technique cannot tell us more about the characteristic time scale of the conformational dynamics at the chain ends. Second, the rotational barrier for torsional jumps between gt, tg, and tt conformers is ≈3 kcal.mol-1 in n-alkanes.29 The height of the barrier is such that a conformational dynamics is expected to be effective at the chain ends, at least in the HT phase where both large amplitude reorientational and translational motions of the chains take place. Such a conformational dynamics has been found to be effective in the HT phase of n-nonadecane/urea using molecular dynamics simulations15,16 on a time scale (≈100 ps) that is short compared to the characteristic time scale of 2H NMR. Clearly model I (no conformational defects) cannot explain such a behavior. However, the amount of gt and tg defects was found from Raman measurements19 to remain approximately constant at all temperatures and in both structural phases. This result is not consistent with the present observation of an order parameter S ) 0.9 in the LT phase which suddenly drops to S ) 0.8 in the HT phase. This behavior cannot be accounted for by a model taking into account only conformational exchange in both phases. There must be another additional dynamical process to describe the chain end dynamics of n-nonadecane in the urea inclusion compound. Additional information could be gained from the analysis of the 2H NMR spectra performed by Taylor et al.30 on a pure n-nonadecane powder sample. Indeed, these authors have recorded these spectra in the crystalline and rotator phases of n-nonadecane. In the crystalline phase of the compound, the quadrupolar splittings (measured on the 90° orientation of the powder sample) associated to the terminal -CD2- and -CD3 deuterons were observed at 110 and 36 kHz, respectively, and 120 kHz for the inner methylene groups. Furthermore, it is well established that the n-nonadecane chains are in their “all trans” conformation in the crystal phase (a very wide range of techniques, including among others X-ray diffraction,31 Raman scattering, and infrared absorption,32 have been used to assess the all-trans conformation of the n-nonadecane molecules in the ordered crystalline phase). It must therefore be concluded that the terminal -CD2CD3 groups of n-nonadecane molecules in their crystalline phase perform fast torsion fluctuations about the penultimate C-C bond without involving conformational defects (the amplitude of vibrations near the chain ends in crystalline n-alkanes has indeed been reported, by means of vibrational spectroscopy, to increase near the chain ends33). By analogy to pure n-nonadecane in its crystalline phase, we may define an order parameter associated with these vibrational motions as Svib and write the quadrupolar splitting expected in such conditions as
(∆νQ)vib ) (∆νQ)rigidSvib
(13)
where (∆νQ)rigid refers to the quadrupolar splitting of the static -CD2- deuterons. For a powder sample of perdeuterated n-nonadecane, the quadrupolar splitting (∆νQ)rigid has been measured at 120 kHz. Following the work performed by Taylor et al.30 we find Svib ) 0.9 for the terminal -CD2CD3 deuterons, in very good agreement with the value of the order parameter S ) 0.9 found in the LT phase of C19H30D10/urea-h4. Since in the crystal of pure n-nonadecane there are no conformational defects, one may therefore assume that in the LT phase of the inclusion compound there is no fast exchange between the tt, tg, and gt conformers and that these fast conformational transitions are effective in the HT phase only. The only fast dynamical process observed in the LT phase therefore originates
in the vibrations of the chain ends, whose amplitude remains approximately constant in the LT phase. It comes out that the major assumptions made throughout the following consider first a fast conformational exchange between gt, tg, and tt conformers effective only in the HT phase of the n-nonadecane/urea inclusion compound and second that the vibrational amplitude of the chain ends remains constant in both the LT and HT phases. Under these conditions, we find with Svib ) 0.9 in the LT phase (see Table 4)
Pgt ) 0.05 and Ptg ) 0.05 in the HT phase in excellent agreement with the values estimated from the Raman spectra:19 this result confirms nicely our previous findings and strengthens the above assumptions. Let us now discuss these results in comparison with previous NMR investigations on the dynamics of n-nonadecane guest molecules in urea inclusion compounds. Cannarozzi et al.11 report 13.2% and 2.8% of gt and tg conformers, respectively, from quadrupolar splitting measurements on powder samples of n-nonadecane/urea using e2Qq/p ) 164 kHz. Our results at room temperature are in fair agreement with theirs as far as the total amount of gt and tg conformational defects is concerned (16% Vs 18.4% in our case when we do not consider the vibrational contribution; see Table 4). However, we disagree with individual values of gt and tg. This is related first to the experimental methods used; the above authors measure ∆νQ on powder samples, whereas we obtain our data on macroscopically oriented single crystals, which clearly leads to more accurate measurements. Second, Cannarozzi et al.11 interpret their data in terms of conformational disorder only, whereas we model the chain end dynamics with both conformational and vibrational motions. In summary, the present analysis of 2H NMR measurements made on single crystals of the urea inclusion compounds and over a very wide range of temperatures has shown that vibrational motions at the chain ends of the n-nonadecane molecules must be considered so that the amount of gt and tg defects drops to 5%. Our results agree only qualitatively with the 13C NMR data of Imashiro et al.20 in which the reductions of the splittings were interpreted in terms of vibrational motions and conformational exchange of the chain ends in n-CnH2n+2/urea with 7 e n e 10. However, our findings are in marked disagreement with their MM2 molecular mechanics calculations.20 Our spectra clearly show that the n-nonadecane molecules are able to perform whole chain reorientations on a microsecond time scale in the LT phase of the inclusion compound. In agreement with this result, the IQNS spectra12,13 did not display any quasi-elastic broadening due to the existence of chain reorientations in the LT phase, because the time window probed by this technique is much shorter (at most 300 ps). In addition, we have shown34 that in the LT phase of the urea inclusion compound, the n-nonadecane molecules were not able to perform translational diffusive motions, but only low-energy excitations assigned to the sliding of the guest subsystem with respect to the urea host lattice have been evidenced. On the basis of the present 2H NMR spectra, we suggest that the tt, gt, and tg n-nonadecane conformers do not perform fast conformational exchanges (on the microsecond time scale) in the LT phase of the inclusion compound. The few conformers containing end-gauche defects are therefore “static” in the LT phase, and their amount remains constant. In the HT phase, the dynamics of the guest molecules becomes more complex. Obviously, fast reorientations of the guest molecules are effective, and a description of this motion in terms of unrestricted reorientational diffusion is probably adequate within the
1752 J. Phys. Chem., Vol. 100, No. 5, 1996 time window probed by 2H NMR. On the time window probed by IQNS12,13 and computer simulations,15,16 these reorientations are interpreted in terms of restricted uniaxial reorientations. In addition, the chains perform large amplitude diffusive translations along the channels, and the present 2H NMR results show that fast conformational transitions also become effective, the amount of distorted molecules remaining constant in the HT phase. There may be a little variation in probabilities Pi with increasing temperature, but it is too small to be detected (e0.1%), as can be seen from the thermal invariance of quadrupolar splittings Vs temperature (Figure 5). In agreement with this model, the Raman spectra did show that the amount of distorted n-nonadecane molecules was approximately constant and independent of the phase and the temperature. 6. Concluding Remarks It is important to recall that the results obtained by means of deuterium NMR spectroscopy cannot be interpreted unambiguously. Several models can be used to describe the fast dynamics of the chain ends of the n-nonadecane molecules trapped within the channels of the urea inclusion compound. Additional information is gained, however, by a careful analysis of the Raman spectra, and a good agreement between the two techniques is reached by assuming several points. In particular, our results strongly suggest that the fast torsional vibrations at the chain ends will contribute to the quadrupolar splitting and that this fast dynamical process is effective in both the LT and HT phases of the sample. In addition, tt, gt, and tg conformers of the included molecules are able to perform fast conformational exchanges (on the NMR timescale) in the HT phase only. Confirming this interpretation, the amount of end-gauche defects as obtained from NMR is in very good agreement with that obtained by means of the Raman technique. We now claim that the amount of end-gauche conformers of n-alkane molecules is low in urea inclusion compounds and reaches ≈5% gt and 5% tg. An important question which arises now is to understand why the n-alkane chains do adopt such distorted structures. Obviously the answer has to be found in the mode of longitudinal packing of the guest molecules and also in the particular interactions, due to the incommensurability between the host and guest substructures, which exists in such composite molecular system. References and Notes (1) Parsonage, N. G.; Pemberton, R. C. Trans. Faraday Soc. 1967, 63, 311.
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