ARTICLE pubs.acs.org/JPCA
Dynamics by Solid-State NMR: Detailed Study of Ibuprofen Na Salt and Comparison with Ibuprofen Elisa Carignani, Silvia Borsacchi, and Marco Geppi* Dipartimento di Chimica e Chimica Industriale, Universita di Pisa, v. Risorgimento 35, 56126 Pisa, Italy ABSTRACT: The various internal rotations and interconformational jumps of the Na-salt form of ibuprofen in the solid state were characterized in detail by means of the simultaneous analysis of a variety of low- and high-resolution NMR experiments aimed at measuring several 13C and 1H spectral and relaxation properties at different temperatures and frequencies. The results were first qualitatively analyzed to identify the motions of the different molecular fragments and to assign them to specific frequency regimes (slow, 106 Hz). Subsequently, a simultaneous fit of the experimental data sets most sensitive to each frequency range was performed by using suitable motional models, thus obtaining, for each motion, correlation times and activation energies. The motions so characterized were: the rotations of the three methyl groups and of the isobutyl group, occurring in the fast regime, and the π-flip of the phenyl ring, belonging to the intermediate motional regime. The results obtained for the Na-salt form were compared with those of the acidic form of ibuprofen, previously obtained from a similar solid-state NMR approach: despite the very similar chemical structure of the two compounds, their dynamic properties in the solid state are noticeably different.
1. INTRODUCTION Molecular motions occurring in solid phases can be intimately connected to fundamental properties for many different systems. The study of these dynamic processes, typically internal motions, has an intrinsic value because it provides an accurate knowledge of the solid system from a physicochemical point of view and, moreover, results in being very important for a deep understanding of properties like stability of solid phases, solidsolid phase transitions, intra- and intermolecular interactions, and chemical reactivity. For instance, in pharmaceutics, a very interesting field of application for these studies, the drug bioavailability is related not only to its structural properties but also to its dynamics in formulations.1 Moreover, it is known that solid-state reactions and degradations of pharmaceuticals are often linked to molecular mobility.2 Solid-state NMR spectroscopy (SSNMR) is certainly one of the most powerful techniques for the study of molecular motions in solids, both giving very detailed information and being able to explore a very wide range of characteristic frequencies (from hertz to gigahertz). This is due to the possibility of exploiting a large variety of nuclei and of different nuclear properties. In the literature, molecular mobility has been investigated through SSNMR for different kinds of solid systems, such as synthetic polymers,3,4 biomacromolecules,57 small organic molecules,810 organicinorganic composite materials,11 and organometallics.12 In a recent paper,13 we showed that it is possible to obtain a very detailed characterization of the dynamics of small organic molecules by combining and simultaneously analyzing a variety of SSNMR experimental data, including various types of relaxation times (T1 and T1F) of different nuclei (13C and 1H), measured at different temperatures r 2011 American Chemical Society
and frequencies, and spectral properties, such as lineshapes. This approach was applied to crystalline racemic ibuprofen [2-(4isobutylphenyl) propionic acid] (IBU-A), and the motions of all of its molecular fragments (π-flip of the phenyl ring, rotation of the methyl groups about their ternary symmetry axes, interconformational jumps of isobutyl and propionic groups, π-flip of the (COOH)2 dimeric structure) were characterized in detail.13 In this work, we have applied a similar SSNMR approach to the Na-salt solid form of ibuprofen to investigate in detail its dynamic behavior and, moreover, to compare it with the results previously found for IBU-A. Indeed, we previously had indications that IBU-A and IBU-S, despite their very similar chemical nature, could show a very different dynamic behavior.14 The results here obtained are interesting not only from a mere physicochemical point of view but also because IBU-A and IBU-S are active pharmaceutical ingredients widely used in the pharmaceutical industry. The first stage of this study consisted of the identification of the molecular motions occurring in IBU-S and the assignment of their characteristic frequency to a given regime (slow, 106 Hz), whereas in a second stage, we made use of suitable models to describe the trends of the most sensitive nuclear parameters to obtain a quantitative characterization of the motions, determining parameters like correlation times and activation energies. The results obtained for IBU-S are eventually compared with those previously reported by us for IBU-A, and the differences observed are highlighted and discussed. Received: March 21, 2011 Revised: July 4, 2011 Published: July 11, 2011 8783
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2. EXPERIMENTAL METHODS 2.1. Samples. Sodium salt of ibuprofen (2-(4-isobutylphenyl) sodium propionate) (IBU-S, racemic mixture) was purchased from Sigma-Aldrich Chimica Srl (Milan, Italy) and used as received. 2.2. NMR Measurements. The NMR experiments were carried out on two different NMR spectrometers: a Varian InfinityPlus 400 (“Varian”) equipped with a 7.5mm CP-MAS probe working at a Larmor frequency of 399.89 and 100.56 MHz for 1H and 13C, respectively, and a Varian XL-100 interfaced with a Stelar DS-NMR acquisition system (“Stelar”) equipped with a 5 mm static probe used for low-resolution measurements at a Larmor frequency of 25.00 MHz for proton. The 1H 90° pulse lengths were 4.0 and 2.6 μs on the Varian and Stelar spectrometers, respectively, whereas the 13C 90° pulse length was 4.5 μs on the Varian spectrometer. Relaxation delays of 5 s were used in all of the experiments. All cross-polarization (CP) spectra were acquired using a contact time of 1 ms, which was found to give the maximum signal intensity. 13C chemical shifts were referred to hexamethylbenzene and TMS as secondary and primary references, respectively. 1H spinlattice relaxation times in the laboratory frame (T1) were measured at low resolution by direct proton observation using either saturationrecovery or inversionrecovery pulse sequences, followed by a solid echo, with variable delays ranging from 100 μs to 5 s. 1 H spinlattice relaxation times in the rotating frame (T1F) were measured at low resolution by direct proton observation using a variable spin-lock field pulse sequence, followed by a solid echo:15 variable spin-lock times ranging from 100 μs to 35 ms were used. 13C spinlattice relaxation times in the laboratory frame (T1) were measured at high resolution using Torchia pulse sequence16 with high-power proton decoupling (HPD) during 13 C signal acquisition, spinning the sample at the magic angle with a frequency of 6 kHz; the variable delay ranged from 100 μs to 180 s. 13C spinlattice relaxation times in the rotating frame (T1F) were measured at high resolution using a variable spin-lock field sequence17 with HPD during 13C signal acquisition, spinning the sample at the magic angle with a frequency of 6 kHz; the spin-lock time ranged from 20 μs to 20 ms. 432 and 80 transients were accumulated for proton and carbon relaxation measurements, respectively. 13 C relaxation times were obtained by reproducing the spectra as sums of peaks through a nonlinear least-squares minimization procedure, thus allowing the integrals of each peak to be determined without the biasing effect due to peak superposition; then, the integrals versus the variable time of the pulse sequence were fitted by means of suitable analytical functions to obtain the relaxation times.18 All measurements were performed in the temperature range from 50 to 85 °C; the temperature was controlled with an accuracy of 0.1 °C, except for temperatures below 7 °C, where the accuracy was 0.4 °C. At least 15 min was allowed for sample temperature stabilization. The temperature scale was calibrated by measuring the 207Pb chemical shift of Pb(NO3)2 under the same experimental conditions as those used for IBU-S.19
3. THEORETICAL BASIS SSNMR spectroscopy is a very powerful technique for the characterization of dynamic processes because NMR observables, sensitive to different ranges of frequency, allow the
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investigation of different motional processes over a very wide range of frequencies. Moreover, different NMR observables, sensitive to the same range of frequencies, provide independent information and hence a robust characterization of the motion investigated. By the measurement of the single NMR observable, it is possible to discriminate if the characteristic frequencies (νC = 1/τC with τC the correlation time of the motion) of the motions affecting such property are higher, lower, or of the same order of magnitude of the reference frequency, and in the latter case, it is often possible to determine the value of νC. The reference frequency is peculiar for each NMR observable and can be either an instrumental frequency or a frequency related to a specific nuclear property investigated. The different analysis methods for the obtainment of qualitative and quantitative dynamic information from spectral and relaxation properties, exploited in the present work, are briefly described in the following, referring to the fundamental literature for a complete theoretical treatment. 3.1. Spectral Properties. The shape of a spectrum can be remarkably influenced by motional processes: these can affect the linewidth of the peaks or, more generally, the shape of two or more peaks when exchange phenomena are present. These effects are of primary importance in dynamic studies because they often provide the first evidence to infer the occurrence of molecular motions. Exchange. Motions that exchange nuclei in different spatial positions have been largely investigated in dedicated 1D and 2D SSNMR experiments.20,21 In 1D magic-angle spinning (MAS) spectra, as those exploited in this work, jumps among sites with different chemical shifts have peculiar effects on linewidths and positions of the peaks. In this case, the reference frequency is given by the difference between the isotropic resonance frequencies of the exchanging nuclei (typically hundreds of hertz for 13C nuclei). Two separate signals or a single averaged signal are present when the exchange frequency is much lower or higher than the reference frequency, respectively. When the two frequencies are of the same order of magnitude, a coalescence of the two signals takes place. Linewidth. In SSNMR experiments, motions can affect the linewidth of the signals of the nuclei involved; in particular, in high-resolution spectra of rare nuclei when the motional frequency matches either MAS or HPD frequency (typically 130 and 30100 kHz, respectively), the interference results in a significant linebroadening.22,23 The linebroadening effect depends on the spectral density of the motion at the frequency of the external modulation; assuming that the interference is the main cause of linebroadening and applying the BloembergenPurcellPound (BPP) model,24 the following expression for the linewidth (LW) is obtained22 LW µ
τC 1 þ ω2int τ2C
ð1Þ
where ωint is the frequency of the interference source (MAS or HPD). It must be noticed that the maximum linebroadening is obtained when τC = 1/ωint. 3.2. Relaxation Times. Spinlattice relaxation times values (T1 and T1F) are directly related to molecular motion frequencies because the corresponding relaxation processes are determined by oscillating magnetic fields, locally generated in the sample through the modulation of the nuclear interactions operated by molecular motions. 8784
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The efficiency of a relaxation mechanism is related to the values of the spectral densities J(ω), which are functions of the correlation time of the molecular motion, τC, and of the reference frequency of the kind of relaxation (i.e., the Larmor frequency (typically 101000 MHz) for T1 and the frequency of the spinlock field (30100 kHz) for T1F). The dependence of J(ω) on correlation times is described differently in different models, but in all the cases, the closer the frequency of the motion is to the reference frequency, the higher the value of the spectral density and so the efficiency of the relaxation. Following Redfield theory,25 relaxation rates are expressed as linear combinations of the spectral densities J(ω). The form of the linear combinations depends on the kind of nucleus (1H or 13 C) and relaxation mechanism (T1 or T1F). Different theoretical treatments are required for 1H and 13C relaxation times, taking into account the different interactions experienced by rare and abundant nuclei. Carbon-13. The relaxation of 13C nuclei in natural abundance, and particularly those having directly bonded protons, is dominated by the dipolar interaction with 1H nuclei. Every chemically distinct 13C has its own relaxation time, influenced only by the motion of the molecular fragment to which the nucleus belongs. When the relaxation is determined by the sole dipolar interaction with directly bonded protons, the value of 13C T1 is given by the expression R1C ¼
1 n CC ¼ 6 ½ Jðω1H ω13C Þ þ 3Jðω13C Þ T1C 15 rCH
ð2Þ
þ 6Jðω1H þ ω13C Þ where n is the number of protons directly bonded to the specific carbon-13 nucleus, rCH is the CH bond distance, ω13C and ω1H are the Larmor frequencies of 13C and 1H, respectively, and CC is 3 μ0 2 2 2 2 CC ¼ γH γC p ð3Þ 4 4π where μ0 is the magnetic vacuum permeability and γH and γC are the gyromagnetic ratios for 1H and 13C, respectively. The trends of 13C T1 with temperature present a minimum when the frequency of the motion is of the order of the reference frequency, which in this case corresponds to the 13C Larmor frequency, whereas T1 increases or decreases with increasing T when the motion frequency is higher or lower than the reference frequency, respectively. Hydrogen-1. Relaxation of 1H nuclei is dominated by the homonuclear dipolar interaction. Moreover, a very important role is played by the spin diffusion phenomenon, which, on the contrary, is largely negligible for 13C nuclei. Spin diffusion tends to average the intrinsic T1 and T1F of the different protons to a single value. When the average is complete, a single average relaxation rate ( or ) is measured, which can be directly interpreted in terms of molecular motions; otherwise, a partial averaging takes place, and for different protons, different relaxation times are measured, which, however, are not the intrinsic ones and therefore do not have a direct dynamic meaning. Even in the latter case, however, dynamic information can be obtained by calculating the population weighted rate average (PWRA) quantity, defined in eq 4, which is independent of spin diffusion.26,27 wi PWRA ¼ ð4Þ i T i x
∑
where x = 1 or 1F, Txi is the ith measured relaxation time, and wi is its corresponding fractional weight, and the sum runs over all the different measured relaxation times. Because of their averaged nature, and/or PWRA are, in principle, determined by all motions occurring throughout the sample, but in practice only the motions with a characteristic frequency of the order of the reference frequency will give a nonnegligible contribution. The relationship linking , PWRA, or both to the spectral densities is the following 1 ð5Þ or PWRA ¼ C al ½Jl ðω0 Þ þ 4Jl ð2ω0 Þ T1 l
∑
and the relationship linking , PWRA, or both to the spectral densities is
1 T1F
or PWRA ¼ C
∑l al
3 1 1 Jl ð2ω1 Þ þ Jl ðω0 Þ þ Jl ð2ω0 Þ 10 2 5
ð6Þ where ω0 is the proton Larmor frequency, ω1 is the spin-lock field frequency, and the sums run over the number of motional processes, each contributing to the relaxation with the relative weight al. Different expressions of the spectral density J(ω) in terms of the correlation time of the motion τC have been derived by theoretical or semiempirical models28 for different cases of applications. In the present work, the simplest BPP24 model was used. Within this model, the analytical expression for the spectral densities is the following J BPP ðωÞ ¼
2τC 1 þ ω2 τ2C
ð7Þ
For describing the dependence of τC on temperature, the Arrhenius law was found to be suitable for our purposes Ea τC ¼ τ∞ exp ð8Þ kT where τ∞ is the correlation time in the limit of infinite temperature and Ea is the activation energy of the motion.
4. RESULTS 4.1. Identification of Molecular Motions and Assignment to Frequency Regimes. In Figure 1 the 13C CP-MAS spectrum
of IBU-S recorded at room temperature is shown, together with the signals assignment, previously reported in ref 14. As already discussed in refs 13 and 14, the presence of a single signal for the two methyl carbons of the isobutyl group (m, n) and of only two partially superimposed signals for the tertiary aromatic carbons (dg) clearly indicates that at room temperature the interconformational motions of both of these groups, that is, the rotation of the isobutyl group and the π-flip of the aromatic ring, are fast with respect to the reference frequencies of the exchange processes (hundreds of hertz). It is worth noticing that contrary to IBU-S in the acidic form of ibuprofen (IBU-A)13,14 two and four distinct signals were observed for methyl and tertiary aromatic carbons, respectively, indicating that both of these motions are frozen at room temperature, whereas a behavior similar to IBU-S was detected for IBU-A encapsulated in MCM-41.29 Variable temperature 13C spectra of IBU-S do not 8785
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Table 1. 13C SpinLattice Relaxation Times in the Laboratory Frame (T1) of ag and i Nuclei of IBU-S Measured at Different Temperaturesa T/°C
13
C T1/s
a
wi
Figure 1. C CP-MAS spectrum of IBU-S (T = 25 °C, νMAS = 5 kHz). Spinning sidebands are marked with asterisks. The chemical structure of IBU-S and the labels for 13C nuclei are reported. Signals assignment is taken from ref 14. 13
b 0.3
c 0.4
0.6
i
0.2
0.8
25.0
46
9
39
5.4
19
1.3
16.4
10.9
34.0
54
10
43
6.1
23
1.7
15.9
11.6
43.8
59
9
46
7.4
23
1.8
14.0
12.6
53.9 64.3
57 55
13 9
41 51
6.4 7.7
23 23
2.0 1.9
11.6 9.1
13.3 14.6
74.6
58
2
43
6.9
23
1.5
6.4
15.1
85.2
51
19
58
9.1
30
1.3
4.6
17.6
(2 (1
(3
err
0.7
dg
(0.6 (1
(0.1 (0.2 (0.2
a
For nuclei a and i, the decay was monoexponential. For nuclei bg, a biexponential decay was found: the two components and their fractional weights (wi) are reported. In the last line, the estimated experimental error is reported.
Table 2. 13C SpinLattice Relaxation Times in the Laboratory Frame (T1) of h and lo Nuclei of IBU-S Measured at Different Temperaturesa T/°C
Figure 2. Aromatic region of the 13C CP-MAS spectra of IBU-S acquired at different temperatures (reported on the right of the spectra in degrees Celsius). Spectra below room temperature were recorded with νMAS = 5 kHz, whereas those above room temperature were recorded with νMAS = 6 kHz. The peaks at 135 and 125 ppm are spinning sidebands of the carboxylic carbon signal in the two cases, respectively.
show any significant change in the line shape of m and n signals, indicating that the frequency of the interconformational motion of the isobutyl group is always higher than 200300 Hz over the whole range of temperatures investigated (50 to +85 °C). On the contrary, the signals of aromatic carbons dg present a significant linebroadening within the temperature range 50 to +30 °C (Figure 2), which is maximum for the spectrum recorded at 13.3 °C. However, the evolution of the line shape with temperature suggests that this linebroadening should be ascribed to an interference of the motion with MAS or decoupling field rather than to an exchange phenomenon, thus indicating the occurrence of a motion of the aromatic ring with a characteristic frequency on the order of kilohertz or tens of kilohertz (intermediate regime) rather than of hundreds of hertz. This point will be discussed in more detail later on. 13 C T1 measurements were performed in the temperature range 50 to +85 °C; all experimental values are reported in
13
C T1/s
h
l
49.2
0.46
0.86
0.13
0.102
41.9 23.8
0.41 0.37
0.76 0.71
0.13 0.18
0.094 0.090
o
13.3
0.31
0.67
0.21
0.081
0.8
0.33
0.64
0.25
0.088
10.2
0.30
0.65
0.29
0.122
25.0
0.44
0.86
0.40
0.146
34.0
0.50
0.90
0.43
0.148
43.8
0.52
1.02
0.49
0.181
53.9 64.3
0.57 0.68
1.08 1.28
0.55 0.63
0.185 0.236
74.6
0.78
1.43
0.70
0.256
85.2
0.89
1.59
0.86
0.294
(0.03
(0.02
(0.01
(0.005
err a
mn
In the last line, the estimated experimental error is reported.
Tables 1 and 2. Values of T1 close of the minimum values predictable on the basis of eqs 2, 3, and 8 (ca. 0.05, 0.075, and 0.15 s for methyl, methylene, and methyne carbons, respectively) were found for methyl carbons m/n (0.13 to 0.80 s) and o (0.10 to 0.29 s) and for isobutyl carbons h (0.3 to 0.9 s) and l (0.6 to 1.6 s), indicating that these carbons are involved in motions with characteristic frequencies on the order of the 13C Larmor frequency (100 MHz). For methyl groups, the rotation about their ternary symmetry axis is expected to be fast (as also found for IBU-A13). Indeed, both m/n and o T1 values show increasing trends with increasing temperature (Figure 3), indicating that the rotations of methyl groups are in the fast motion side of T1 curve. As far as h and l carbons are concerned, their T1 values present a minimum between 0 and 10 °C (Figure 3). The ratio between h and l T1 values is about two at all temperatures, indicating that, on the basis of eq 2, the corresponding carbons undergo the same dynamic process, which can be identified as the rotation of the isobutyl group, also in agreement with the previous observation of a single peak for m and n methyl carbons. 8786
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Figure 3. 13C spinlattice relaxation times in the laboratory frame versus temperature curves at a Larmor frequency of 100.56 MHz for IBU-S: (a) carbon o, (b) carbon l, (c) carbon h, and (d) carbons m/n (signal at 23 ppm). 1H spinlattice relaxation times in the laboratory frame versus temperature curves at Larmor frequencies of (e) 399.89 and (f) 25.00 MHz. Symbols and black lines indicate experimental and calculated relaxation times, respectively. Dashed and dotted-dashed lines in parts e and f and in the inset of part d indicate the global contribution of methyl rotations and that of isobutyl reorientations, respectively.
All of the other carbons exhibit much larger T1 values, indicating that the motions in which they are involved have characteristic frequencies very far from 13C Larmor frequency. Carbon i T1 varies from 11 to 18 s in the investigated range. Such high values and the increasing trend with increasing temperature indicate that the motion responsible for the relaxation of i is much faster with respect to the Larmor frequency. It is hence possible to exclude that this motion is a rotation because its frequency should be much higher than that of methyl groups, which is not physically meaningful; it might be therefore ascribed to either fluctuations or vibrational motions. Tertiary aromatic 13C T1 values give direct information about the motion of the aromatic ring. Because of the exchange phenomenon, only two signals are observed, which, moreover, at some temperatures are not distinguishable because of the above-discussed linebroadening, thus preventing individual relaxation time values for the four different tertiary aromatic carbons to be measured. The analysis of the decay of the integral of the whole signal revealed the presence of two different components, assuming values between 5 and 16 s (weight 80%) and between 1 and 2 s. The shortest component does not show a trend with temperature, whereas the longest is decreasing, and even though a detailed assignment of the two components is not straightforward, this suggests that the frequency of the motion of the ring is lower than the 13 C Larmor frequency. Quaternary aromatic b, c, and carboxylic carbon T1 values cannot be straightforwardly commented on in terms of dynamic information: the lack of directly bonded protons strongly decreases the dipolar interactions, and a contribution to relaxation from chemical shift anisotropy cannot be ruled out. It is, however,
interesting to observe that the carboxylic carbon T1 is significantly smaller than that in IBU-A, which is possibly ascribable to a larger mobility due to the absence of the dimeric structure present in the acid. 13 C relaxation times in the rotating frame (T1F) were also measured, but, as also previously found for IBU-A, they could not be exploited for obtaining dynamic information because of the presence of a non-negligible spinspin contribution.13 Spinlattice relaxation times in the laboratory frame (T1) for 1 H nuclei were measured at two different Larmor frequencies, 25 and 400 MHz. In both cases, a single T1 value was measured for all 1H nuclei, as a consequence of the complete average operated by spin-diffusion. T1 values at both frequencies are quite small and show clear trends with temperature (Figure 3). On the basis of 13C T1 data, we can hypothesize that 1H T1 trends are mainly determined by methyls and isobutyl rotations. Spinlattice relaxation times in the rotating frame (T1F) of 1H nuclei were measured at three different spin-lock field frequencies. In all cases the relaxation was found to be biexponential, indicating that spin-diffusion average was not complete. To obtain dynamic information, we calculated PWRA values. At all three spin-lock field frequencies, clear trends of 1/PWRA with temperature were obtained with minima at 020 °C (Figure 4), indicating the occurrence of a motion with characteristic frequency in the intermediate regime, which, on the basis of the previous observations, can be identified with the π-flip of the aromatic ring. 4.2. Quantitative Characterization of Specific Dynamic Processes through Theoretical Motional Models. A quantitative analysis was performed for the most suitable sets of data 8787
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Figure 4. PWRA1 of IBU-S 1H spinlattice relaxation times in the rotating frame versus temperature curves at spin-lock field frequencies of (a) 90, (b) 50, and (c) 35 kHz. Symbols and lines indicate experimental and calculated relaxation times, respectively.
sensitive to the dynamic processes identified in the previous section, whose characteristic frequencies in the temperature range investigated are in the intermediate or fast regimes, that is, the aromatic ring π-flip and the methyl and isobutyl rotations, respectively. The analysis was conducted by means of a global fitting procedure, consisting of the simultaneous fitting of all of the different data curves versus temperature belonging to the same dynamic regime, through the equations described in the Theoretical Basis section. In particular, relaxation data curves of different nuclei, measured at different instrumental frequencies, were fitted simultaneously to determine motional parameters such as activation energies and correlation times. This method results in being more robust and reliable than the separate fittings of single curves, which may bring biased results.30 Intermediate Motion Regime. 1H T1F versus temperature curves measured at three different spin-lock frequencies were analyzed for characterizing the phenyl ring π-flip. Because the BPP model well describes a jump motion between two equally probable conformations,31 1H T1F data were fitted by eqs 68. A good correspondence was obtained between calculated and experimental curves, as shown in Figure 4, and the best-fitting parameters are reported in Table 3. We previously observed that this motion also affects the 13C linewidth because of interference with either the decoupling field or the MAS frequency. From the dynamic parameters obtained by fitting the 1H T1F data, it is possible to demonstrate that this motion interferes with the decoupling field rather than with the MAS frequency. Moreover, from eqs 1 and 8, it was possible to predict the temperature at which the maximum interference (i.e., the maximum 13C linebroadening) should occur using the Arrhenius parameters found from the 1H T1 fitting and the value of the decoupling field used for recording 13C spectra (42 kHz); this temperature resulted in being 16.3 °C, in very good agreement with the observed maximum linebroadening at about 13 °C (Figure 2). Fast Motion Regime. A quantitative analysis of the motions in the fast regime was performed by fitting the proton and carbon T1 versus temperature curves. The motions previously recognized to belong to this regime were the rotations of the three methyl groups about their ternary symmetry axes and the reorientation of the isobutyl fragment. A global fitting procedure was applied to the 13C T1 curves of h, l, m/n, and o carbons and the 1H T1 curves obtained at two different Larmor frequencies using eqs 2, 5, and 8. We tried to reproduce the experimental curves considering: isobutyl motion only, o methyl motion only, and m/n methyl and isobutyl motions for describing the curves
Table 3. Motional Parameters Obtained from the Fit of Experimental Data As Described in the Text and Corresponding Errors motion
Ea (kJ/mol)
Log(τ∞ (s))
methyl m/n rotation
12.1 ( 0.9
12.5 ( 0.1
methyl o rotation
12.0 ( 1.0
12.0 ( 0.2
isobutyl reorientation
16.1 ( 0.4
12.2 ( 0.1
aromatic ring π-flip
22.4 ( 0.8
10.0 ( 0.2
of h/l, o, and m/n carbons, respectively. The motions of isobutyl and methyl groups were assumed to be independent; consequently, their contributions to the relaxation rate of carbons m/n were considered to be additive.30 However, the agreement between calculated and experimental curves was found to be good only when CC for the sole isobutyl motion was taken as a fitting parameter rather than calculated from eq 4. (See Figure 3.) The best-fitting value found for CC was ∼25% of the theoretical value. A similar behavior has been explained with the contribution to 13C T1 relaxation of CH bond librations.32,33,30 Indeed, if librations are considered to be independent from and much faster than the main motion (the isobutyl rotation, in our case), then their contribution to the relaxation results in a simple reduction of the theoretical constant CC exp
CC ¼ χCtheor C with the scaling factor χ < 1. In our case, a scaling factor of 0.25 indicates a significant contribution of librations to relaxation. The contribution of the isobutyl motion to the relaxation rate of carbons m/n was found to be very small (∼9%). As far as the rotation of the three methyl groups about their ternary symmetry axes is concerned, the activation energies for m/n and o were found to be very similar (∼12 kJ/mol). Moreover, an activation energy for the reorientational motion of the isobutyl group of ∼16 kJ/mol was obtained, higher than that of the methyl rotations, as expected.
5. DISCUSSION The measurement and analysis of several spectral properties and relaxation times of IBU-S over an extended range of temperatures (50 to +85 °C) has allowed all possible interconformational motions to be investigated and characterized. In particular, whereas the methyl and isobutyl groups rotations 8788
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Table 4. Comparison of the Dynamic Processes in the Two Forms of Ibuprofen: Motional Regimes and Correlation Times at 25 °Ca motion methyl m/n rotation
IBU-A
IBU-S
fast regime
fast regime
τC = 3.5 1011 s
τC = 2.1 1011 s
τC = 3.1 1011 s methyl o rotation
fast regime
fast regime
isobutyl reorientation
τC = 1.6 1011 s frozen
τC = 3.5 1011 s fast regime τC = 3.9 1010 s
aromatic ring π-flip a
slow regime
intermediate regime
τC = 1.2 102 s
τC = 9.1 107 s
Data of IBU-A are derived from the results reported in ref 13.
result in being fast in this temperature range, that is, with frequencies on the order of 100 MHz, the π-flip of the aromatic ring is significantly slower, having a frequency on the order of tens of kilohertz. It is particularly interesting to look at these results in comparison with those obtained for ibuprofen in its acidic solid form in the same temperature range.13 The chemical modification from acid to sodium salt is associated with relevant dynamic differences, with an average mobility much higher in IBU-S than in IBU-A. In particular, the isobutyl rotation resulted frozen for IBU-A, whereas the π-flip of the aromatic ring was observed to be in the slow motion regime. The rotation of the methyl groups about their ternary symmetry axes was found to be fast for both IBU-A and IBU-S, but, whereas for IBU-A slightly different activation energies were found for m, n, and o, in IBU-S, the same value was found for all three groups. As far as the isopropionic group is concerned, whereas its rotation was found to be frozen in both IBU-A and IBU-S, in the latter, the occurrence of rapid fluctuations could be inferred, reasonably related to the absence of the carboxylic acid dimeric structure present in IBU-A. For a more immediate comparison of the dynamic processes quantitatively characterized in IBU-A and IBU-S, correlation times at room temperature, calculated on the basis of the experimental results obtained, have been reported in Table 4. It is possible to notice that the correlation times of all methyl motions in both ibuprofen forms result in being quite similar and fall within the range of 1535 ps. The very different correlation times found for the isobutyl reorientation and the aromatic ring π-flip between IBU-A and IBU-S could be ascribed to noticeably different crystalline packings, which at the moment cannot be confirmed by X-ray data because the crystallographic structure of IBU-S has not been reported yet.
6. CONCLUSIONS This Article reports the application to the Na-salt form of ibuprofen of a SSNMR method, previously reported by us and applied to the acidic form of ibuprofen, aimed at obtaining a complete characterization of the rotational and interconformational motions of molecular fragments occurring in the solid state for organic molecules. To identify and reliably characterize each motion with a characteristic frequency in the range accessible by SSNMR, from 100 to 1010 Hz, we have exploited a variety of nuclear observables, ranging from 13C linewidth to 1H and 13C T1 and T1F, which have been measured at different temperatures and, in some cases, frequencies, employing both high- and
low-resolution techniques. The results were analyzed at first identifying the motions involving the different molecular fragments and assigning them to a given frequency range (slow, intermediate, or fast); afterward, for each motion, parameters such as correlation times and activation energies were determined by simultaneously fitting, through suitable motional models, the experimental data sets most sensitive to each frequency range. In particular, a detailed description was obtained of the rotations of the three methyl groups and the isobutyl group (fast regime) and of the π-flip of the phenyl ring (intermediate regime). A noticeable difference of the dynamic properties was found between the acidic and the Na-salt form of ibuprofen. This concerned, in particular, the motions of the phenyl ring (much faster in the Na-salt form) and the isobutyl group (experiencing fast rotation in the Na salt while being frozen in the acidic form). The SSNMR method used is confirmed to be suitable for getting a very detailed characterization of the dynamics of small organic molecules in the solid state.
’ AUTHOR INFORMATION Corresponding Author
*Tel: +39-0502219289. Fax: +39-0502219260. E-mail: mg@ dcci.unipi.it.
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