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2H and 17O NMR studies of hydrogen-bond exchange and molecular motion in diluted pivalic acid
161
Journal of lWoEeculurStructure, 270 (1992) 161-171 Elsevier Science Publishers B.V., Amsterdam
2H and l70 NMR studies of hydrogen-baud exchange and molecular motion in diluted pivalic acid* L. Kimty@, V. BaleviEius” and D.W. Aksnesb ‘Fruity of Physics. Vilnius University, 2734 Vilnius (Lithuania) bDepartment of Chemistry, University of Bergen, 5007 Bergen (Norway) (Received 10 December 1991)
Abstract 2H and 170NMR spin-lattice relaxation times, linewidt~ and chemical shifts have been measured over a wide temperature region for pivalic acid dissolved in inert solvents. The observed singularities in temperature dependences of the NMR parameters at 259-269 K have been interpreted as the second-order phase transition in an ensemble of the cyclic dimer, i.e. as the change of their average symmetry due to a decrease in the rate of hydrogen-bond exchange. The theoretical approach has been developed on the basis of a stochastic model of an overdamped oscillator in a double-well potential whose harmonic part is noise-modulated. The activation energies for proton exchange have been evaluated and their relationship with other parameters of the association processes examined.
INTRODUCTION
The proton exchange and intramolecular rearrangement in carboxylic acid dimers are the subjects of numerous papers published in recent years. In one of the first works in this field [l], which is still being investigated today, the microwave rotation spectra have been obtained for hydrogenbonded carboxylic acid heterodimers. The tunneling barrier has been found to be about 60 kJmol_‘, which is comparable with the results of IR spectroscopy (75-85 kJmol_‘) [Z]. The F’T-IR hydrogen-bond stretching fundamentals for formic acid (HCOOH and HC002H) in the gas phase have been studied, with the conclusion that proton tunneling should have an inversion rate of less than lo-l2 s-’ [3]. Recently solid-state NMR [4-‘71 and dynamical NMR studies for liquids using solvents with very low freezing points [8] have been carried out. The Correspondence to: Professor L. Kimtys, Faculty of Physics, Vilnius University, 2734 Vilnius, Lithuania. *Dedicated to Professor N.D. Sokolov on the occasion of his 66th birthday.
0022-2880/92/$05.00
@ 1992 Elsevier Science Publishers
B.V. All rights reserved.
162
L. Kimtys et d/J.
Mol. Struct,, 270 (1992) 161471
obtained barrier heights of 0.8-20 kJ mol-1 and activation energies of 0.‘715 kJ mol-’ are not compatible with the IR and microwave spectroscopic data, nor ab initio calculations. The results of ab initio quantum chemical calculations are conflicting because of large differences in the calculated barrier heights (within 50200 kJ mol-l). It is obvious that some discrepancies arise from the different calculation schemes and basis sets [9] but there could be some more important causes [lo]. Namely, a significant lowering of the potential barrier can be achieved by total optimization of the molecular geometry, assuming that the proton motion is coupled to a deformation of the frame of heavy nuclei. Later it was shown that additional optimization in the crystal field can reduce the barrier height for benzoic acid by 3-10 kJmol_’ 111,121in comparison with the value for the isolated dimer. A very interesting model has been proposed in ref. 13. It has been assumed that the proton tunneling is modulated by coupling to the acoustic phonons in the solid. This causes a negligible energy of reorganization of the transfer. It indicates that hydrogen-bond exchange in carboxylic acid dimers is most probably a cooperative process of nuclear motion, which involves not only the nuclei in the dimer but those from its nearest surroundings also. Some other possibilities, e.g. breakdown of the BornOppenheimer approximation [14], cannot be rejected either. The mechanism of this process itself is not completely clear. The data are contradictory [G-19] with respect to two models: (i) concerted jumps of two protons along the hydrogen bonds; (ii) 180’ flips around the long axis. The coexistence of both (i) and (ii) is most likely; however, their relative contributions can be different for various systems [20,21]. Continuing our earlier studies on the hydrogen bond and association processes in liquid carboxylic acids [22-241, the new results of ‘H and I70 NMR over a wide temperature range of pivalic acid solutions in inert solvents are presented in this paper. Some theoretical aspects of the possible description of proton transfer in the liquid state are discussed in terms of a noise-modulated potential barrier. EXPERIMENTAL
Pivalic acid was obtained from Fluka ( > 99.5%) and deuterated acid was prepared from pivalyl chloride and deuterium oxide slightly enriched in I70 (approximately 1.5%). The extent of deuteration was measured to be approximately 98*/oby 1H NMR. After careful purification using azeotropic distillation and sublimation a melting point of 309.9K was reached (the highest reported value). All solvents were additionally purified and dried using molecular sieves. The samples for measurements were prepared in
L. Kbntys et al-/J. Mol. Stmet., 270 (1992) 161471
163
1Omm NMR tubes, degassed by four freeze-pump-thaw cycles and sealed under vacuum. The 2H and 170 NMR spectra were measured at 61.43 and 5424MHz, respectively, on a Bruker 460 AM WB spectrometer. The sample temperature was regulated and stabilized to within + 1 K by means of a Bruker B-VT 1000 temperature control unit. The spin-lattice relaxation TX times were masured by standard inversion-recovery (1800-z-9Oo-T),, typically using 16-18 values of z, a recycle delay of T 2 5 Tl and a 90’ pulse length of 14-18,~s (dependent on the temperature of the sample). A non-linear three-parameter fitting of peak heights (including the ~uilibri~ value) was used for calculating the TX values. The reproducibility of Tl was within 3%.
RESULTS AND DISCUSSION
The main temperature region focused on in the experimental measurements was 250-280 K, for which the singularities in the temperature dependences of the chemical shift (6) of the -COOH proton have been found for several aliphatic carboxylic acids [23]. Namely, an abrupt change of temperature coefficient As/AT has been observed for this region. Every singularity of the spectral or thermodyn~ical parameters can be considered as a manifestation of the phase transition or chemical reaction in the system. The last process can be excluded at once, since no new NMR signals have been detected for the studied samples. The following phase transitions are possible in binary liquids: (i) the phase separation of a homogeneous mixture of two phases, one rich in component A and one rich in component B, i.e. the second-order transition; (ii) freezing out of one of the components or impurities, i.e. the first-order transition. As it has been shown for an aqueous solution of isobutyric acid 1251,the phase separation manifests itself as a jump of As/AT whereas the freezing out of H,O gave a jump of 6(T). Thus the observed singularities [23] cannot be due to the freezing out of one component or to the freezing out of impurities. The possibility of phase separation has been checked by the measurement of the integrated intensities of the ‘H NMR signal of the -COOH group (Icoon) relative to the signal of the external reference of CHCl, in a capillary (&>. No change in lcooH/l,f within rt 2% has been detected within the investigated temperature range. It seems that the most reasonable explanation of the above-mentioned singularities can be based on an idea about the occurrence of the phase transition within cyclic dimers, which is caused by the change of the average (in the NMR time scale) symmetry of the dimer. A proper microscopic model of the cyclic dimer has been examined in ref. 26.
L. Kitntys et al./J. Mol. Struct., 270 (1992) 161-171
a
0
a
X
Fig. 1. Shape of the potential V(x) described by eqn. (l), and temperature evolution of the proton distribution along reaction coordinate x.
Microscopic
model
Let us consider proton (or deuteron) motion in the symmetric double-well potential (Fig. 1). V(x) = (&+X*)(X2 - .2)2
(1)
where x is the reaction coordinate, which is generally rather sophisticated [9], a is the model parameter, and V, is the barrier height. In such a classical treatment the barrier height and activation energy (&) are identical. It is known that crystal-lattice effects can distort symmetry and remove the energetic degeneracy of the tautomers. In some cases the difference in depth of the two wells (AE) reaches 0.4-6 kJ mol-’ [P-7]. Nevertheless this approach can be considered good enough for the liquid state because of fast relaxational motion there. In other words the rearrangements of nuclei in the dimer and its surroundings keep up with the rate of proton motion. Equation (1) can be rewritten as V(x) = - w2x2/2 + hx4/4
(2)
where h = 4 VJu4. Let us assume that the frequency, i.e. harmonic part of V(x), fluctuates upon molecular motion o”(t) = 0; + y(t)
(3)
where CR&$ = 4Vo/a2 and y(t) is a stochastic white noise. In this case the proton motion can be described by a non-linear Langevine equation: rn2 + @ + hx3 - c&x + y(t)z = 0
(4)
165
L. Kimtys et al./J. Mol. Struct., 270 (1992) 161-171
where m is the mass of a proton (or deuteron) and [ is the damping constant. A very ~po~ant ~s~ption can be drawn here: the motion of the proton along the hydrogen bond is overdamped, i.e. inf~&iJ
(5)
Taking into account this approach (a validity will be discussed below) eqn. (4) can be simplified: k = dx - bx3 + S(t)
(6)
where d = og/l, b = h/c and F(t) = y(t)/c. F(t) represents the S-correlated gaussian process. The intensity of fluctuation is given by V’(O)W))
=
QW
(7)
In this case the steady-state solution f0 (i.e. when At < zNMR)transforms it to a Fokker-Planck equation:
K
- & Kdx - bx3 + :Q4fl+
at
After straightforward
(Q/2) $
aflat = 0
within
Wf)
integration this gives
f. = 2(b/Q)d’Q/r(d/Q)x-1+2d’* exp
(- bx2/Q)
(9)
The most probable expression for proton distribution along x is
W - QlWW’”
x, =
0
Q
< 2d
Qa2d
(10)
This behaviour is analogous to the second-order phase transition when x0 is interpreted as an order parameter and Q is of the same order of magnitude as the temperature. At small Q values the solution equilib~um f. is basically a gaussian distribution centred at x fi: a; having reached the threshold Q = 2d, i.e. T = IT,, the solution peaks at around x = 0 (Fig. 1). Note the population diverges at x = 0, which is a consequence of model s~pl~cation, where no additive stochastic forces are presented [26]. Thus at T < T, the cyclic dimers exist as an ordered structure of symmetry C2, U...H 0
/7
R\
OH...
jR
Off
and at high temperatures (T > T,) as a disordered one
166
L. Kimtya et al&J. Mol. Struct., 270 (1992) 161-171
12.0
I ’ 200
I
I
250
300
T,K
Fig. 2. The temperature dependences of ‘H and ‘H NMR cheqical shifts of tlie -COOH(l) and -CO@H (2) group of pivalic acid in n-hexane at 0.03mol. fraction. O...H...O /
\
“i
O...H...O
;”
NMR parameters Before analysing the NMR results it is important to note that the existence of the extremely broad IR bands of hydrogen-bond stretching vibrations [3] can be considered to support the assumption of overdamped motion of the proton in a hydrogen bond (eqn. (5)). However, this assumption appears from the critical condition in the dependence on the oscillator mass. So, the value of Z’, should be the same in the case of the OH *I- 0 bridge as the 02H *. *0 bridge. Indeed, all singularities in the temperature dependences of the NMR parameters {Figs. 2-4) have been found to be at the same value of T, ( z 230 K) for solutions of pivalic acid (CH,),CCOOH as well as for its deuteroanalogue (CH,),CCOO’H. Thus the assumption (eqn. (5)) can be considered as tolerable, although there is a more pronounced shift of T, (x 20 K) in the dependences of 6(T) for ‘H (see Fig. 2).
L. Kimtys et al.lJ. Mol. Struct., 270 (1992) 161-171
167
Fig. 3. I70 NMR linewidths (Hz) as a function of temperature at different concentrations of (CH,),CCOOZH in CCC: (1) 0.386, (2) 0.255mol. fraction, and (3) 0.04mol. fraction in n-pentane.
The noticeable broadening of the 170 NMR signal at T,(Fig, 3) can be interpreted as a manifestation of the beginning of the change in symmetry of the dimer, i.e. in the low-temperature dimer (C,,) the two 0 nuclei are no longer equivalent. Hence, the magnetic screening is expected to be nonidentical for the 0 nuclei; however, their NMR signals are not separated because of persisting fast hydrogen-bond exchange. The temperature dependence of the ‘Ii spin-lattice relaxation time of the -C002H group at different concentrations of acid (Fig. 4) presents many questions. The 2H NMR relaxation of neat pivalic acid has been studied at a high spectrometer frequency [27]; it was assumed that the principal electric field gradient at the carboxylic deuterons is almost parallel to the long axis of the dimer, and thus their relaxation is not affected by the rotation about this axis. Therefore it is believed that the relaxation is modulated by the overall tumbling of the dimer unit only. The analysis of the temperature dependences of the relaxation times for dissolved pivalic acid indicates that the mechanism of relaxation has a more complicated character if the temperature changes occur over a wide range. The calculated
168
L. Kimtys et al&I. Mol. Struct., 270 (1992)
\
I
161-171
‘4
’
I
I
3.0
3.5
4.0
1000/T,K-' Fig. 4. 2H !fI relaxation times of (CH,),CCOO*H versus reciprocal temperature at different concentrations in Ccl,: (1) 0.094, (2) 0.491; (3) 0.707; (4) l.Omol. fraction.
activation energy for overall tumbling in neat pivalic acid of approximately 20 kJ mol-’ [27] is significantly larger than for other tert-butyl compounds (approximately 8-10 kJmol_‘). As can be seen in Fig. 4, for pivalic acid solutions in inert solvents the calculated activation energy decreases drastically with dilution and reaches approximately 8 kJ mol-l at a concentration of about 0.09mol. fraction in Ccl,. Such a large effect can scarcely be attributed to a decrease in viscosity and steric hindrance. Hence it can be assumed that the overall tumbling of a monomer unit involving the making and breaking of two hydrogen bonds affects the carboxylic 2H relaxation. Another cont~bution can arise from the internal motion within a cyclic dimer, e.g. due to the dependence of the quadrupolar coupling constant (e’~~~) for the 02H - 1.0 bridge 2H on temperature. The dependences of e’Qq/h on the geometrical parameters of the hydrogen bond have been established for many systems [28]. Thus at a higher temperature T > T, (N 280K) the most probable value of 2H distribution along coordinate x is temperature-independent (x,, = 0, eqn. (lo)), and e2Qq/h can be assumed to be constant over this temperature range, which is valid for the plastic crystalline and liquid phases of neat pivalic acid [27]. The variation of the distribution at T < T, (eqn. (lo), Fig. 1) causes the temperature dependence of the value of e2Qq/h. Furthermore, the increase in a slope of In TI vs. l/T at T < T, (Fig. 4) can be interpreted as due to this effect, in addition to the “regular” temperature dependence of the rotational diffusion correlation time. The peculiar changes in the temperature dependences of the NMR parameters can be attribute to a spontaneous increase in the concentration of acid (on a local microscopic scale) at
L. Kimtys et al./J. Mol. Strut.,
l-
270 (1992) 161-l 71
169
(al
_TIg
0.5
-&”
0.6
50
55
60
AH,CJ mol” Fig. 5. The correlations between (a) activation energies (EJ and molecular mass (M) and (h) hydrogen bond energy (A&) for several carboxylic acids: (1) formic; (2) acetic; (3) propionic; (4) butyric; (5) isobutyric; (6) pivalic; (7) adamantane (all in inert solvents 1241);(8) benzoic; (9) benzoic-d, (10) p-nitrobenzoic; (11) decanoic (all in the solid state [5]).
T < T,. In other words, the process of the formation of complicated structures, e.g. large Ritter-type aggregates [29], can be taken into account. In this case the value of T, can be interpreted as a critical point, above which the breaking of these structures occurs. If the above-mentioned microscopic model is accepted as real, the activation energies (E,) for hydrogen-bond exchange can be roughly evaluated [24] as E, z kT,/4
01)
The values of E, calculated in this way are presented in Fig. 5. Both correlations of E, with molecular mass and hy~ogen-bond energies (AH,)
170
L. K~~~~get al@
Mol. Struct., 270 (1992) 161-I 71
seem to be logical. The first relationship can be understood as the consequence of proton motion coupled with deformation of the frame on the heavy nuclei, as follows from quantum chemical treatment [9, lo]. However, the increase in strength of the hydrogen bond leads to the lowering of the potential barrier, and thus to a lower E,. Note that the calculated values of E, for Iiquid solutions are less (0.3-0.8 kJ mallI) than those found for solid carboxylic acids (0.8-1.3 kJmol_‘) [5]. This is most probably due to the steric hindrance acting on replacements of nuclei, due to denser packing and thus stronger interactions in the crystalline state. Moreover, there is a strong correlation between V, and OH out-of-plane bending vibrations (y(OH)): for systems with low barriers (V, x 4 kJ mol-“) all y(OH)) are of about 950 cm-‘, while those of systems with V, x 50 kJ mol-’ are about 920 cm-’ [5]. Indeed, for all studied carboxylic acids in solutions (see Fig. 5) y(OH) h as a narrow range of values 945-955 cm-‘, corresponding to a lower potential barrier, whereas these values disperse on crystallization: 920 cm-’ for acetic, 936 cm-’ for propionic and 902 cm-’ for pivalic acid [24]. Note that the crystalline structure as well as hydrogen bonding is very different for all those acids.
The hydrogen-bond exchange in liquid carboxylic acid seems to be an extremely easily activated process, and it persists even at low temperatures. At a certain temperature in an ensemble of cyclic dimers a lowering of their average symmetry occurs (second-order phase transition) due to the reduced rate of the proton motion. An alternative possibility of the aggregation process which could cause analogous behaviour of NMR parameters with decreasing temperature should be investigated in the near next future. ACKNOWLEDGEMENT
We are grateful to Professor Dr. Al. Weiss and Dr. N. Weiden for valuable discussions. REFERENCES 1 2 3 4 5 6 7
CC. Costain and G.P. Srivastava, J. Chem. Phys., 41 (1964) 1620. H. Morita and S. Nagakura, J. Mol. Spectrosc., 42 (1972) 536. W.G. Rothschild, J. Chem. Phys., 61 (1974) 3422. B.H. Meier, F. Graf and R.R. Ernst, J. Chem. Phys., 76 (1982) 767. S. Nagaoka, T. Terao, F. Imashiro, A. Saika and N. Hirota, J. Chem. Phys., 79 (1983) 4694. B.H. Meier and R.R. Ernst, J. Solid State Chem., 61 (1966) 126. T. Agaki, F, Imashiro, T. Terao, N. Hirota and S. Hayashi, Chem. Phys. Lett., 139 (1987) 331.
L. Kimtys et al.lJ. Mol. Struct.. 270 (1992) 161-171 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
171
G.S. Denisov, S.F. Bureiko, N.S. Golubev and K.G. Tokhadxe, Molecular Interactions, Vol. 2, Wiley, New York, 1980. N. Shida, P.F. Barbara and J, Ah&f, J. Chem. Phys., 94 (1991) 3633. F. Graf, R. Meyer, T.K. Ha and R.R. Ernst, J. Chem. Phys., 75 (1981) 2914. R. Nakaniura and S. Hayashi, J. Mol. Struct., 145 (1986) 331. R. Nakamura, K. Machida and S. Hayashi, J. Mol. Struct., 146 (1986) 101. R.I. Cukier and M. Morillo, J. Chem. Phys., 93 (1990) 2364. Y. Marechal, J. Mol. Struct., 189 (1988) 55. K.Furic’, Chem. Phys. Lett., 108 (1984) 518. B.H. Meier, R. Meyer, R.R. Ernst, A. Stiickli, A. Furrer, W. Hiilg and I. Anderson, Chem. Phys. Lett., 108 (1984) 522. S. Nagaoka, T. Terao, F. Imashiro, N. Hirota and S. Hayashi, Chem. Phys. Lett., 108 (1984) 524. M. Bee, W. Longueville, J.P. Amoureux and R. Fouret, J. Phys. (Paris), 47 (1986) 305. A. Cough, M.M.I. Haq and J.A.S. Smith, Chem. Phys. Lett., 11 (1985) 389. W. Scheubel, H. Zimmermann and U. Haeberlen, J. Magn. Reson., 80 (1988) 401. S. Idxiak, Mol. Phys., 68 (1989) 1335. L. Kimtys and V. BaleviEius, Adv. Mol. Relaxation Processes, 15 (1979) 151. L. Kimtys, Spectrosc. Lett., 10 (1977) 43. V. BaleviEius, M. KreneviEiene and L. Kimtys, Chem. Phys. (USSR), 8 (1989) 1624. V. BaleviEius, M. Strumskis, P. Misiunas and L. Kimtys, Liet. Fiz. Rinkinys, 29 (1989) 459. W. Coffey, M. Evans and P. Grigolini, Molecular Diffusion and Spectra, Wiley, New York, 1984. D.W. Aksnes and L.L. Kimtys, Magn. Reson. Chem., 28 (1990) 520. A. Weiss and N. Weiden, in J.A.S. Smith (Ed.), Adv. Nuclear Quadrupole Resonance, Vol. 4, Heyden, London, 1980. H.L. Ritter and J.H. Simons, J. Am. Chem. Sot., 67 (1945) 757.
Journal of lWoEeculurStructure, 270 (1992) 161-171 Elsevier Science Publishers B.V., Amsterdam
2H and l70 NMR studies of hydrogen-baud exchange and molecular motion in diluted pivalic acid* L. Kimty@, V. BaleviEius” and D.W. Aksnesb ‘Fruity of Physics. Vilnius University, 2734 Vilnius (Lithuania) bDepartment of Chemistry, University of Bergen, 5007 Bergen (Norway) (Received 10 December 1991)
Abstract 2H and 170NMR spin-lattice relaxation times, linewidt~ and chemical shifts have been measured over a wide temperature region for pivalic acid dissolved in inert solvents. The observed singularities in temperature dependences of the NMR parameters at 259-269 K have been interpreted as the second-order phase transition in an ensemble of the cyclic dimer, i.e. as the change of their average symmetry due to a decrease in the rate of hydrogen-bond exchange. The theoretical approach has been developed on the basis of a stochastic model of an overdamped oscillator in a double-well potential whose harmonic part is noise-modulated. The activation energies for proton exchange have been evaluated and their relationship with other parameters of the association processes examined.
INTRODUCTION
The proton exchange and intramolecular rearrangement in carboxylic acid dimers are the subjects of numerous papers published in recent years. In one of the first works in this field [l], which is still being investigated today, the microwave rotation spectra have been obtained for hydrogenbonded carboxylic acid heterodimers. The tunneling barrier has been found to be about 60 kJmol_‘, which is comparable with the results of IR spectroscopy (75-85 kJmol_‘) [Z]. The F’T-IR hydrogen-bond stretching fundamentals for formic acid (HCOOH and HC002H) in the gas phase have been studied, with the conclusion that proton tunneling should have an inversion rate of less than lo-l2 s-’ [3]. Recently solid-state NMR [4-‘71 and dynamical NMR studies for liquids using solvents with very low freezing points [8] have been carried out. The Correspondence to: Professor L. Kimtys, Faculty of Physics, Vilnius University, 2734 Vilnius, Lithuania. *Dedicated to Professor N.D. Sokolov on the occasion of his 66th birthday.
0022-2880/92/$05.00
@ 1992 Elsevier Science Publishers
B.V. All rights reserved.
162
L. Kimtys et d/J.
Mol. Struct,, 270 (1992) 161471
obtained barrier heights of 0.8-20 kJ mol-1 and activation energies of 0.‘715 kJ mol-’ are not compatible with the IR and microwave spectroscopic data, nor ab initio calculations. The results of ab initio quantum chemical calculations are conflicting because of large differences in the calculated barrier heights (within 50200 kJ mol-l). It is obvious that some discrepancies arise from the different calculation schemes and basis sets [9] but there could be some more important causes [lo]. Namely, a significant lowering of the potential barrier can be achieved by total optimization of the molecular geometry, assuming that the proton motion is coupled to a deformation of the frame of heavy nuclei. Later it was shown that additional optimization in the crystal field can reduce the barrier height for benzoic acid by 3-10 kJmol_’ 111,121in comparison with the value for the isolated dimer. A very interesting model has been proposed in ref. 13. It has been assumed that the proton tunneling is modulated by coupling to the acoustic phonons in the solid. This causes a negligible energy of reorganization of the transfer. It indicates that hydrogen-bond exchange in carboxylic acid dimers is most probably a cooperative process of nuclear motion, which involves not only the nuclei in the dimer but those from its nearest surroundings also. Some other possibilities, e.g. breakdown of the BornOppenheimer approximation [14], cannot be rejected either. The mechanism of this process itself is not completely clear. The data are contradictory [G-19] with respect to two models: (i) concerted jumps of two protons along the hydrogen bonds; (ii) 180’ flips around the long axis. The coexistence of both (i) and (ii) is most likely; however, their relative contributions can be different for various systems [20,21]. Continuing our earlier studies on the hydrogen bond and association processes in liquid carboxylic acids [22-241, the new results of ‘H and I70 NMR over a wide temperature range of pivalic acid solutions in inert solvents are presented in this paper. Some theoretical aspects of the possible description of proton transfer in the liquid state are discussed in terms of a noise-modulated potential barrier. EXPERIMENTAL
Pivalic acid was obtained from Fluka ( > 99.5%) and deuterated acid was prepared from pivalyl chloride and deuterium oxide slightly enriched in I70 (approximately 1.5%). The extent of deuteration was measured to be approximately 98*/oby 1H NMR. After careful purification using azeotropic distillation and sublimation a melting point of 309.9K was reached (the highest reported value). All solvents were additionally purified and dried using molecular sieves. The samples for measurements were prepared in
L. Kbntys et al-/J. Mol. Stmet., 270 (1992) 161471
163
1Omm NMR tubes, degassed by four freeze-pump-thaw cycles and sealed under vacuum. The 2H and 170 NMR spectra were measured at 61.43 and 5424MHz, respectively, on a Bruker 460 AM WB spectrometer. The sample temperature was regulated and stabilized to within + 1 K by means of a Bruker B-VT 1000 temperature control unit. The spin-lattice relaxation TX times were masured by standard inversion-recovery (1800-z-9Oo-T),, typically using 16-18 values of z, a recycle delay of T 2 5 Tl and a 90’ pulse length of 14-18,~s (dependent on the temperature of the sample). A non-linear three-parameter fitting of peak heights (including the ~uilibri~ value) was used for calculating the TX values. The reproducibility of Tl was within 3%.
RESULTS AND DISCUSSION
The main temperature region focused on in the experimental measurements was 250-280 K, for which the singularities in the temperature dependences of the chemical shift (6) of the -COOH proton have been found for several aliphatic carboxylic acids [23]. Namely, an abrupt change of temperature coefficient As/AT has been observed for this region. Every singularity of the spectral or thermodyn~ical parameters can be considered as a manifestation of the phase transition or chemical reaction in the system. The last process can be excluded at once, since no new NMR signals have been detected for the studied samples. The following phase transitions are possible in binary liquids: (i) the phase separation of a homogeneous mixture of two phases, one rich in component A and one rich in component B, i.e. the second-order transition; (ii) freezing out of one of the components or impurities, i.e. the first-order transition. As it has been shown for an aqueous solution of isobutyric acid 1251,the phase separation manifests itself as a jump of As/AT whereas the freezing out of H,O gave a jump of 6(T). Thus the observed singularities [23] cannot be due to the freezing out of one component or to the freezing out of impurities. The possibility of phase separation has been checked by the measurement of the integrated intensities of the ‘H NMR signal of the -COOH group (Icoon) relative to the signal of the external reference of CHCl, in a capillary (&>. No change in lcooH/l,f within rt 2% has been detected within the investigated temperature range. It seems that the most reasonable explanation of the above-mentioned singularities can be based on an idea about the occurrence of the phase transition within cyclic dimers, which is caused by the change of the average (in the NMR time scale) symmetry of the dimer. A proper microscopic model of the cyclic dimer has been examined in ref. 26.
L. Kitntys et al./J. Mol. Struct., 270 (1992) 161-171
a
0
a
X
Fig. 1. Shape of the potential V(x) described by eqn. (l), and temperature evolution of the proton distribution along reaction coordinate x.
Microscopic
model
Let us consider proton (or deuteron) motion in the symmetric double-well potential (Fig. 1). V(x) = (&+X*)(X2 - .2)2
(1)
where x is the reaction coordinate, which is generally rather sophisticated [9], a is the model parameter, and V, is the barrier height. In such a classical treatment the barrier height and activation energy (&) are identical. It is known that crystal-lattice effects can distort symmetry and remove the energetic degeneracy of the tautomers. In some cases the difference in depth of the two wells (AE) reaches 0.4-6 kJ mol-’ [P-7]. Nevertheless this approach can be considered good enough for the liquid state because of fast relaxational motion there. In other words the rearrangements of nuclei in the dimer and its surroundings keep up with the rate of proton motion. Equation (1) can be rewritten as V(x) = - w2x2/2 + hx4/4
(2)
where h = 4 VJu4. Let us assume that the frequency, i.e. harmonic part of V(x), fluctuates upon molecular motion o”(t) = 0; + y(t)
(3)
where CR&$ = 4Vo/a2 and y(t) is a stochastic white noise. In this case the proton motion can be described by a non-linear Langevine equation: rn2 + @ + hx3 - c&x + y(t)z = 0
(4)
165
L. Kimtys et al./J. Mol. Struct., 270 (1992) 161-171
where m is the mass of a proton (or deuteron) and [ is the damping constant. A very ~po~ant ~s~ption can be drawn here: the motion of the proton along the hydrogen bond is overdamped, i.e. inf~&iJ
(5)
Taking into account this approach (a validity will be discussed below) eqn. (4) can be simplified: k = dx - bx3 + S(t)
(6)
where d = og/l, b = h/c and F(t) = y(t)/c. F(t) represents the S-correlated gaussian process. The intensity of fluctuation is given by V’(O)W))
=
QW
(7)
In this case the steady-state solution f0 (i.e. when At < zNMR)transforms it to a Fokker-Planck equation:
K
- & Kdx - bx3 + :Q4fl+
at
After straightforward
(Q/2) $
aflat = 0
within
Wf)
integration this gives
f. = 2(b/Q)d’Q/r(d/Q)x-1+2d’* exp
(- bx2/Q)
(9)
The most probable expression for proton distribution along x is
W - QlWW’”
x, =
0
Q
< 2d
Qa2d
(10)
This behaviour is analogous to the second-order phase transition when x0 is interpreted as an order parameter and Q is of the same order of magnitude as the temperature. At small Q values the solution equilib~um f. is basically a gaussian distribution centred at x fi: a; having reached the threshold Q = 2d, i.e. T = IT,, the solution peaks at around x = 0 (Fig. 1). Note the population diverges at x = 0, which is a consequence of model s~pl~cation, where no additive stochastic forces are presented [26]. Thus at T < T, the cyclic dimers exist as an ordered structure of symmetry C2, U...H 0
/7
R\
OH...
jR
Off
and at high temperatures (T > T,) as a disordered one
166
L. Kimtya et al&J. Mol. Struct., 270 (1992) 161-171
12.0
I ’ 200
I
I
250
300
T,K
Fig. 2. The temperature dependences of ‘H and ‘H NMR cheqical shifts of tlie -COOH(l) and -CO@H (2) group of pivalic acid in n-hexane at 0.03mol. fraction. O...H...O /
\
“i
O...H...O
;”
NMR parameters Before analysing the NMR results it is important to note that the existence of the extremely broad IR bands of hydrogen-bond stretching vibrations [3] can be considered to support the assumption of overdamped motion of the proton in a hydrogen bond (eqn. (5)). However, this assumption appears from the critical condition in the dependence on the oscillator mass. So, the value of Z’, should be the same in the case of the OH *I- 0 bridge as the 02H *. *0 bridge. Indeed, all singularities in the temperature dependences of the NMR parameters {Figs. 2-4) have been found to be at the same value of T, ( z 230 K) for solutions of pivalic acid (CH,),CCOOH as well as for its deuteroanalogue (CH,),CCOO’H. Thus the assumption (eqn. (5)) can be considered as tolerable, although there is a more pronounced shift of T, (x 20 K) in the dependences of 6(T) for ‘H (see Fig. 2).
L. Kimtys et al.lJ. Mol. Struct., 270 (1992) 161-171
167
Fig. 3. I70 NMR linewidths (Hz) as a function of temperature at different concentrations of (CH,),CCOOZH in CCC: (1) 0.386, (2) 0.255mol. fraction, and (3) 0.04mol. fraction in n-pentane.
The noticeable broadening of the 170 NMR signal at T,(Fig, 3) can be interpreted as a manifestation of the beginning of the change in symmetry of the dimer, i.e. in the low-temperature dimer (C,,) the two 0 nuclei are no longer equivalent. Hence, the magnetic screening is expected to be nonidentical for the 0 nuclei; however, their NMR signals are not separated because of persisting fast hydrogen-bond exchange. The temperature dependence of the ‘Ii spin-lattice relaxation time of the -C002H group at different concentrations of acid (Fig. 4) presents many questions. The 2H NMR relaxation of neat pivalic acid has been studied at a high spectrometer frequency [27]; it was assumed that the principal electric field gradient at the carboxylic deuterons is almost parallel to the long axis of the dimer, and thus their relaxation is not affected by the rotation about this axis. Therefore it is believed that the relaxation is modulated by the overall tumbling of the dimer unit only. The analysis of the temperature dependences of the relaxation times for dissolved pivalic acid indicates that the mechanism of relaxation has a more complicated character if the temperature changes occur over a wide range. The calculated
168
L. Kimtys et al&I. Mol. Struct., 270 (1992)
\
I
161-171
‘4
’
I
I
3.0
3.5
4.0
1000/T,K-' Fig. 4. 2H !fI relaxation times of (CH,),CCOO*H versus reciprocal temperature at different concentrations in Ccl,: (1) 0.094, (2) 0.491; (3) 0.707; (4) l.Omol. fraction.
activation energy for overall tumbling in neat pivalic acid of approximately 20 kJ mol-’ [27] is significantly larger than for other tert-butyl compounds (approximately 8-10 kJmol_‘). As can be seen in Fig. 4, for pivalic acid solutions in inert solvents the calculated activation energy decreases drastically with dilution and reaches approximately 8 kJ mol-l at a concentration of about 0.09mol. fraction in Ccl,. Such a large effect can scarcely be attributed to a decrease in viscosity and steric hindrance. Hence it can be assumed that the overall tumbling of a monomer unit involving the making and breaking of two hydrogen bonds affects the carboxylic 2H relaxation. Another cont~bution can arise from the internal motion within a cyclic dimer, e.g. due to the dependence of the quadrupolar coupling constant (e’~~~) for the 02H - 1.0 bridge 2H on temperature. The dependences of e’Qq/h on the geometrical parameters of the hydrogen bond have been established for many systems [28]. Thus at a higher temperature T > T, (N 280K) the most probable value of 2H distribution along coordinate x is temperature-independent (x,, = 0, eqn. (lo)), and e2Qq/h can be assumed to be constant over this temperature range, which is valid for the plastic crystalline and liquid phases of neat pivalic acid [27]. The variation of the distribution at T < T, (eqn. (lo), Fig. 1) causes the temperature dependence of the value of e2Qq/h. Furthermore, the increase in a slope of In TI vs. l/T at T < T, (Fig. 4) can be interpreted as due to this effect, in addition to the “regular” temperature dependence of the rotational diffusion correlation time. The peculiar changes in the temperature dependences of the NMR parameters can be attribute to a spontaneous increase in the concentration of acid (on a local microscopic scale) at
L. Kimtys et al./J. Mol. Strut.,
l-
270 (1992) 161-l 71
169
(al
_TIg
0.5
-&”
0.6
50
55
60
AH,CJ mol” Fig. 5. The correlations between (a) activation energies (EJ and molecular mass (M) and (h) hydrogen bond energy (A&) for several carboxylic acids: (1) formic; (2) acetic; (3) propionic; (4) butyric; (5) isobutyric; (6) pivalic; (7) adamantane (all in inert solvents 1241);(8) benzoic; (9) benzoic-d, (10) p-nitrobenzoic; (11) decanoic (all in the solid state [5]).
T < T,. In other words, the process of the formation of complicated structures, e.g. large Ritter-type aggregates [29], can be taken into account. In this case the value of T, can be interpreted as a critical point, above which the breaking of these structures occurs. If the above-mentioned microscopic model is accepted as real, the activation energies (E,) for hydrogen-bond exchange can be roughly evaluated [24] as E, z kT,/4
01)
The values of E, calculated in this way are presented in Fig. 5. Both correlations of E, with molecular mass and hy~ogen-bond energies (AH,)
170
L. K~~~~get al@
Mol. Struct., 270 (1992) 161-I 71
seem to be logical. The first relationship can be understood as the consequence of proton motion coupled with deformation of the frame on the heavy nuclei, as follows from quantum chemical treatment [9, lo]. However, the increase in strength of the hydrogen bond leads to the lowering of the potential barrier, and thus to a lower E,. Note that the calculated values of E, for Iiquid solutions are less (0.3-0.8 kJ mallI) than those found for solid carboxylic acids (0.8-1.3 kJmol_‘) [5]. This is most probably due to the steric hindrance acting on replacements of nuclei, due to denser packing and thus stronger interactions in the crystalline state. Moreover, there is a strong correlation between V, and OH out-of-plane bending vibrations (y(OH)): for systems with low barriers (V, x 4 kJ mol-“) all y(OH)) are of about 950 cm-‘, while those of systems with V, x 50 kJ mol-’ are about 920 cm-’ [5]. Indeed, for all studied carboxylic acids in solutions (see Fig. 5) y(OH) h as a narrow range of values 945-955 cm-‘, corresponding to a lower potential barrier, whereas these values disperse on crystallization: 920 cm-’ for acetic, 936 cm-’ for propionic and 902 cm-’ for pivalic acid [24]. Note that the crystalline structure as well as hydrogen bonding is very different for all those acids.
The hydrogen-bond exchange in liquid carboxylic acid seems to be an extremely easily activated process, and it persists even at low temperatures. At a certain temperature in an ensemble of cyclic dimers a lowering of their average symmetry occurs (second-order phase transition) due to the reduced rate of the proton motion. An alternative possibility of the aggregation process which could cause analogous behaviour of NMR parameters with decreasing temperature should be investigated in the near next future. ACKNOWLEDGEMENT
We are grateful to Professor Dr. Al. Weiss and Dr. N. Weiden for valuable discussions. REFERENCES 1 2 3 4 5 6 7
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