Phys.,ca 136B (1986) 161-164 North-Holland, Amsterdam
DYNAMICS OF HYDROGEN BONDS IN CARBOXYLIC ACIDS A. S T O E C K L I , A. F U R R E R Laboratory for Neutron Scattering, ETH Ziirich, CH-5303 Wiirenlingen. Switzerland
CH. S C H O E N E N B E R G E R , B.H. M E I E R , R.R. E R N S T Laboratory for Physical Chemistry, ETH Ziirich, CH-8092 Ziirich, Switzerland
I. A N D E R S O N Institut Laue -Langevin, F-38042 Grenoble, France
The double-proton exchange in carboxylic acids has been studied for a polycrystalline sample of ring-deuterated terephthalic acid (TA), H O O C - C 6 D a - C O O H , and for both single-crystal and polycrystalline samples of acetylene dicarboxylic acid (ADA), HOOC-C2-COOH, by incoherent neutron scattering. For temperatures above 100K the observed energy spectra reveal quasielastic contributions which indicate that the disorder of the hydrogen-bonded dimeric units is of dynamic nature involvinga translational jump across the hydrogen bonds. The data have been analysed in terms of a two-site jump model. Jump vectors, relaxation rates and population factors within the asymmetric double-minimum potential have been derived.
ls(Q, t) = ~ ~
Many carboxylic acids are known to form dimeric hydrogen-bonded systems in the gas phase as well as in the liquid and solid phases. The hydrogen-bonded dimers possess a doubleminimum potential which is symmetric in the gas and in the liquid phase, but normally asymmetric in the solid phase because of crystal-lattice effects, X-ray diffraction [l] revealed an orientational disorder of the hydrogen-bonded dimers in the solid state. N M R measurements  gave evidence that the observed disorder is due to a dynamic process between the two tautomeric forms as shown in fig. 1. In order to obtain further experimental insight into the dynamic nature of the hydrogen bond, we performed quasielastic neutron scattering experiments on T A and ADA.
(e -'Q'5(°) e'QgU)) ,
o~ c ~ o I
2. Theoretical aspects I
The motion of an individual particle may be directly probed by incoherent neutron scattering. The central role is played by the scattering autocorrelation function
Fig. 1. Schematic sketch of the double-proton exchange in carboxylic acids. V(r) is the asymmetric double-minimum potential, E a the activation energy, AG the free enthalpy difference, and R the jump vector.
0378-4363/86/$03.50 (~) Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
A. Stoeckli et al. / Dynamics o f hydrogen bonds in carboxylic acids
from which the incoherent scattering law is obtained by Fourier transformation in the time variable t: Sinc(Q, o9) = ~
if Is( Q, t) e i~, dt.
In eqs. (1) and (2), N is the number of protons in the sample, rj(t) is the position operator of the scatterer, Q is the scattering vector, and hw is the energy transfer in the neutron scattering process. The hydrogen bond protons are assumed to be located either at the sites A or B of the doubleminimum potential. The hopping process between the sites A and B may be described by the kinetic equations
ture-dependent line width of the Lorentzian. For k T > ZIG the temperature dependence may be described by an Arrhenius law :
1 _ 1 exp - ~ - ~ r ro
pA(t) -t- pB(t) = 1,
Sp = 1 _ 2/~AfiU(1
1 + (wr)
(5) So= 1 - 4fiAfiB s i n 2 ( - ~ - ~ ) ,
where e -2w(O) is the Debye-Waller factor, R is the proton jump vector between the sites A and B, fix is the equilibrium occupation probability of the site X, and r is the relaxation time which may be expressed in terms of the hopping rates kx: 1 -
k A +
sin(QR) ] Q-R / "
where k x is the hopping rate indicated in fig. 1, and px(t) is the occupation probability of the site X. A semiclassical treatment of the two-site jump model yields  S, n c ( O , t.o) =
where E a can be interpreted as the apparent activation energy indicated in fig. 1. When polycrystalline samples are used, the amplitudes So and S 1 defined by eqs. (6) and (7) have to be replaced by the powder averaged values (R = IRI):
Sp = 2fiafiB( 1
/gA(t) = --/gB(/) = --kAPA(t ) +
The neutron scattering spectrum thus corresponds to a superposition of an incoherent elastic peak and a quasielastic Lorentzian line centered at o) = 0. The hopping rates k x are temperature dependent, which manifests itself in a tempera-
3. E x p e r i m e n t s and results
In order to be able to resolve the quasielastic line from the incoherent elastic peak, a neutron spectrometer with high energy resolution is required. Therefore the experiments were performed on the backscattering spectrometer IN13 at the high-flux reactor of the Institute LaueLangevin at Grenoble. The energy resolution was about 10/xeV, and the maximum modulus of the scattering vector Q was limited to 5.5 A-1 because of kinematical constraints. The first experiments have been performed on polycrystalline samples. Here the data analysis is impeded by the presence of Bragg scattering contributions. As a consequence the intensity of the incoherent elastic peak cannot be reliably determined, and the data interpretation is generally restricted to the analysis of the quasielastic Lorentzian. The observed energy spectra have to be corrected for transmission and Debye-Waller factor. Experiments were carried out for polycrystalline samples of TA and ADA, and the following model parameters were obtained: TA:
z o ~ = 2 . 3 x 1 0 n s -1,
T(71 = 1.5 x 101~ s -~,
A. Stoeckli et al. / Dynamics of hydrogen bonds in carboxylic acids
For both compounds the jump distance R turned out to be less then 1 ~ . The mentioned difficulties do not exist for single-crystal measurements. The amplitudes SO and S 1 given by eqs. (6) and (7) can be directly determined from the observed intensities Ic~ and Iqc of the incoherent elastic and quasi-elastic lines, respectively, e.g.
S1 - lei + Iqe "
Both SOand S 1 a r e determined by intensity ratios, therefore neither transmission corrections nor Debye-Waller factor corrections have to be applied to the experimental data. A second series of experiments has been per-
Fig. 2. Quasielastic energy spectrum of neutrons scattered from ADA single-crystals at 250K for Q = 4 . 7 A - L The scattering vector Q was approximately parallel to the jump vector R.
Sl .8 .6 .4 .2
formed on a sample composed of 23 ADA single crystals (2 × 2 × 1.5 mm B) which were individually oriented by x-ray scattering. A typical example of an observed energy spectrum is shown in fig. 2. The absence of contributions from Bragg scattering was checked by the Q-dependence of let which followed the expected Debye-Waller factor behavior predicted by eq. (5). The experimental data were analyzed according to eq. (12). The Q-dependence was found to be in excellent agreement with the predictions of the two-site jump model (eqs. (5)-(7)) as shown in fig. 3. At present experiments have only been performed at 250 K; the resulting model parameters are R
10 -11 s,
PB = 0.80.
4. Concluding remarks
Fig. 3. Q-dependence of the quasielastic amplitude S 1 . The experimental values (full circles) have been determined from eq. (12) for ADA single-crystals at 250 K. The theoretical curve results from eq. (7) with the parameter values given at the end of section 3.
Quasielastic neutron scattering has been applied to study the dynamics of hydrogen bonds in carboxylic acids. No other experimental technique is known able to provide an equally detailed picture of the double-proton exchange process. We particularly wish to emphasize the advantage of using single-crystal specimens, since the relevant model parameters result directly from a straight forward analysis of the raw data. Moreover, single-crystal data exhibit a considerably more pronounced variation of the intensities as a function of the scattering vector Q than data obtained for polycrystalline samples, see eqs. (6), (7), (10), (11). Recently there has been some discussion concerning the mechanism of proton dynamics in carboxylic acids. An alternative mechanism to the proton jump across the hydrogen bonds involving a 180° rotation of the carboxylic group has been suggested . A clear-cut distinction of the two mechanisms by NMR turns out to be difficult [6, 7, 8]. On the basis of our quasielastic neutron results, however, the 180° rotational model (with a jump vector of more than 2.2 A) can be clearly rejected in favor of the translational motion (jump vector 0.7 A). NMR measurements  indicate nonArrhenius behavior of the exchange process at
A. Stoeckli et al. / Dynamics o f hydrogen bonds in carboxylic acids
low temperatures which may arise from excited state tunneling. Further experimental and theoretical investigations to clarify this question are in progress.
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