Solid State Nuclear Magnetic Resonance, 1 (1992) 115-119

115

Elsevier Science Publishers B.V., Amsterdam

‘H NMR study of lithium D-lactate M.L. Buszko and E.R. Andrew Departments of Physics and Radiology, Unk~ersityof Florida, Gainesclille, FL. 32611, USA

(Received 3 January 1992; accepted 3 March 1992)

Abstract

Polycrystalline b-lactic acid lithium salt [CR)-2-hydroxypropanoic acid lithium salt, lithium o-lactate] has been investigated by pulsed proton magnetic resonance methods between 77 and 300 K at 25 MHz. The main relaxation mechanism is methyl rotation; the motion is characterized by an activation energy E, = 14.5 f 0.5 kJ/mol and time factor ~a = (1.5 f 0.5)~ lo-r3 s. The activation energy is higher than the potential barrier obtained by ESR and ENDOR techniques for methyl rotation in the lactate radical. The methyl rotation is also responsible for a reduction of the dipolar second moment, Below 100 K the reduction of the dipolar second moment is ascribed to quantum-mechanical tunneling; an excitation energy of 6.1+ 1 kJ/mol is derived from a contribution to the spin-lattice relaxation times from the tunneling. Keywords: lithium b-lactate; relaxation mechanism; methyl rotation

Introduction Contemporary interest in lactic acid and its salts is due to (i) the important role they play in energy metabolism [l], (ii) the application in synthesis of biodegradable, low-molecular-weight polymers [2,3], and (iii) the widespread use in pharmacy and in the food industry. Among many salts of lactic acid, the lithium salt is of especial interest due to its effects on immune functions [4]. Lithium lactate is also a convenient compound to study the effects of lithium on the emotional behavior, as well as to determine an hourly dosage of Li+ in human chromopsychiatry

El. Several spectroscopic methods have been employed in studying molecular dynamics of lithium lactate. Infrared spectra of lithium lactate have

Correspondence to: Professor E.R. Andrew, Department of Physics, University of Florida, Gainesville, FL 32611, USA.

0926.2040/92/$05.00

been recorded, and partly interpreted, by Ranade and Biswas [6] in their studies of some metal lactates. ESR and ENDOR measurements of free radicals CH,COHCOOformed by y irradiation of a crystal of lithium lactate have been presented by Clough and Poldy [7]; a splitting of the ground state due to tunnelling rotation of the methyl group was found and estimated to be 22 k 5 GHz. Finally, a new ENDOR technique [S] has been applied by Brustolon et al. [9] to this radical which enabled the values of the Arrhenius parameters (barrier height and preexponential factor) for the methyl jumping rate to be obtained; these values were E, = 1.3 _t 0.1 kJ/mol and ~a = (7 * 1) x lo-i3 s. These values are significantly different from the values of motional parameters of methyl rotation obtained in our NMR studies of solid L-lactic acid [lo]; the correlation time of methyl rotation was found to be characterized by an activation energy of 12.2 + 1 kJ/mol and a time factor of (3.5 f 1) x lo-‘” s. Above 220 K, the interpretation of the data of lactic acid - where the

0 1992 - Elsevier Science Publishers B.V. All rights reserved

116

h4.L. Buszko, E.R. Andrew/Solid

magnetization recovery is not single-exponential, and a small 1 x low8 T* decrease of the dipolar second moment is observed - was not clear. Similarly, deviations from simple BPP-type behavior were observed below 100 K; they were interpreted in terms of quantum-mechanical tunnelling characterized by an excitation energy of 6.2 k 1 kJ/mol. In order to clarify the question of methyl rotation of the lactic acid moiety, which is the principal aim of this paper, we have now extended the NMR studies to solid D-lithium lactate at temperatures 77-300 K. These studies, which exploit the proton spin-lattice Tl relaxation and the dipolar second moment, (i) confirm the results obtained for an isomeric form of solid lactic acid by the same NMR technique and (ii) compare the motional parameters of the methyl reorientation obtained for an intact molecule (by NMR) with those for a radical (by ESR and ENDOR). Clough and Poldy [7] have reported a preliminary X-ray structure investigation, finding a monoclinic unit cell containing four molecules. No full structure investigation has, however, been reported.

Experimental Polycrystalline o-lactic acid lithium salt, CH,CH(OH)COOLi, (RI-2-hydroxypropanoic acid lithium salt, was obtained from Fluka, Product No. 62551 (purity > 99%, ratio of enantiomers > 99 : l), and was studied without further purification. The sample for the study was sealed off in a glass ampoule after evacuation at 0.01 Pa for five days at room temperature. The NMR measurements were made on a variable frequency, home-built pulse NMR spectrometer incorporating a Varian electromagnet, a Nicolet 1180 Data System, a 293A Pulse Programmer, and a PTS 160 frequency synthesizer. The sample was placed in a temperature-controlled cryostat. The accuracy of the temperature measurements and the stability during data accumulation were both about 2 K. The saturation-recovery technique was used to measure Tl values, with a train of 32 90” pulses

&I-

e0 5

15

State Nucl. Magn. Reson. I (1992) 115-119

L

OLD__

I

0 0

________~_~_~_,_~~,_~__~~__~_~~~~~~~

t

tI

I

I 100

I

I

I

I

I 150

I1

I

Fig. 1. The temperature dependence for polycrystalline lithium D-lactate.

I

I

200

I

I

T(K)

I

I

I, 250

of the second momebt

separated by 300 ps intervals; the standard twopulse technique was employed in the vicinity of TImin. The magnetization recovery was inspected up to about 5 Tl. Eight to 64 FIDs were typically acquired to achieve a signal-to-noise ratio of over 80. Experimental values of Tl were obtained by non-linear least-squares routines fitted to an exponential recovery function. Below 100 K, where the recovery is significantly non-exponential, the data were fitted to the sum of two exponentials. Values of the second moment M, were determined from the initial shape of the full-bandwidth FID signals, sampled at a rate of 5 MHz, assuming a Gaussian lineshape. Errors in the determination of Tl were estimated to be about 5% and those in M2 about 15%.

Results The temperature dependence of the second moment is shown in Fig. 1. At 77 K the second moment is 8.0 X 1O-8 T2 and falls to a plateau value of 5.0 x lop8 T2 above 120 K. The temperature dependence of T, from 77 to 318 K at 25.0 MHz is shown in Fig. 2. A characteristic minimum of 23.8 ms at 169 K is displayed. Below 100 K the magnetization recovery is significantly non-exponential; in Fig. 2 the main (long) component of the bi-exponential recovery is shown in this temperature region. A progressive

M.L. Buszko, E.R. Andrew/Solid State Nucl. Magn. Reson. 1 (1992) 115-119

117

molecule and n is the number of protons in the methyl groups contributing to the relaxation process. Taking the commonly accepted protot-proton distance b in the methyl group, 1.79 A, and substituting the value of C from eqn. (2) in eqn. (11, we found the value of T, at the minimum where r, = 0.616/w,, - to be 23.9 ms at 25.0 MHz. This value is in a very good agreement with the experimental TImin = 23.8 ms, strongly identifying reorientation of methyl groups as the source of the spin-lattice relaxation above 120 K. For classical methyl reorientation, it is assumed that r, obeys an Arrhenius activation law: 3

5

7

13

11

9

103/T

(K-l)

Ea

Fig. 2. The temperature dependence of the proton spin-lattice relaxation time TI for polycrystalline lithium D-lactate at 25 MHz Larmor frequency. The solid line was calculated in the manner described in the text. The broken line corresponds to classical methyl reorientation.

departure from linear dependence of Tr versus T-’ (in a logarithmic scale) in this temperature region is observed.

Discussion To analyze the experimental results, we first consider the TI data above 120 K. In this temperature region, (i) a single, deep, and symmetrical minimum (of the type analyzed first by Bloembergen et aZ. [ll]) is observed, (ii) the magnetization recovery is single exponential, and (iii> the dipolar second moment reaches a well-established plateau. The data have been analyzed using the weak-collision theory of Kubo and Tomita [12]: 1 -c T,-

47, rc + 1+ W2,r2 1 + 4w2r2c 1 c i

For methyl group reorientation in the presence of rapid spin exchange the relaxation constant C in eqn. (1) has been shown to be [13,14]:

(2) where N is the total number of protons in the

I

Tc=7oexp i RT

Using the T, data above 120 K and the C value Ff (3/5) x 7.7 x lo9 sm2 (i.e., calculated for 1.79 A intramethyl proton-proton distance), we obtained an activation energy of E, = 14.5 k 0.5 kJ/mol and r. = (1.5 It 0.5) X 10-l” s in a leastsquares fitting procedure. Both the E, and the r. are typical values for classical methyl rotation, again confirming the identification of the relaxational mechanism. For comparison, the motional parameters in solid L-lactic acid were E, = 12.2 + 1 kJ/mol and TV= (3.5 + 1) X lo-l3 s [lo]. In the NMR study of hindered rotations in some methylbenzenes [15], Allen and Cowking noted that E, is directly proportional to the temperature of the Tlmin. Eguchi and Chihara [16] extended this observation to methyl rotation in many other compounds and found the proportionality constant to be EJRT,, = 10 f 1, depending somewhat on the Larmor frequency. In our case the ratio E,/RT,, = 10.3, i.e., the typical value. Further confirmation of a model of classical, thermally activated methyl rotation comes from the analysis of the second moment plateau of the value 5.0 x lo-’ T2 above 120 K. In the presence of this motion, making plausible approximations concerning the reduction of the dipolar interaction, the intramolecular contribution to the second moment is estimated to be 4.8 x low8 T2, in good agreement with the experimental average value above 120 K.

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M.L. Buszko, E.R. An&ti/Solid

No considerable changes in the second moment occur above 120 K; at room temperature the material is in the solid state and is stable. No melting point is reported for this salt. Lithium salts of the lower alkane carboxylic acids, and particularly lithium propanoate, melt at temperatures of the order of 500-600 K [17]. Although mesophases are observed when going from the solid to the liquid state, the temperatures of the phase transitions are high enough to be sure no melting effect influences the methyl dynamics at the temperatures within the range of our studies. Summarizing, the experimental results above 120 K exhibit in a clear manner the characteristic features of a model of classical, thermally activated methyl reorientation characterized by an activation energy of E, = 14.5 k 0.5 kJ/mol and a time factor of ~a = (1.5 f 0.5) X lo-l3 s. This behavior is similar to that for lactic acid. Although our data for lithium lactate are similar to those of lactic acid, they differ markedly from those for the lactate radical [7,9], for which the activation energy was reported to be much lower, 1.3 + 0.1 kJ/mol. This suggests that reorientation of the methyl group in the radiation damaged lactate is much less restricted. A reduction in activation energy for methyl reorientation has also been noted in the alanine radical [8,18] compared with the intact molecule [19l. We now consider the results for lithium lactate below 100 K. Within the model of the classical regime, the relaxation constant C in eqn. (1) is related to the reduction of the dipolar second moment. The minima of T, correspond therefore to [20,211: 1.05 ‘6Jg AM,= Y2’

(4) Tlmin

Substituting our experimental T,min, we obtain the second moment reduction AM, = 9.4 x lo-’ T’. Adding the average plateau value of 5.0 X lo-* T* we obtain 14.4 X lo-’ T2. This value compares favorably with the rigid second moment value calculated from the dipolar theory of Van Vleck [221; the intramolecular contribution to the rigid second moment is calculated to be 15.1 x

II

I

3

State Nucl. Map. Reson. 1 (1992) IIS-119

I

5

I

I

7

I

I

9

I

I

I

11

I

13

103/T(K-'1

Fig. 3. The temperature dependence of the correlation time of methyl reorientation for polycrystalline lithium o-lactate. The solid and broken lines were calculated from eqns. 6) and (3), respectively, using the parameters given in the text.

lo-’ T2, assuming a staggered conformation of methyl protons and a 1.79 A intramethyl proton-proton distance. Below 90 K, the average experimental value of the second moment M, of 8.0 x 10m8 T* is substantially lower than the rigid theoretical value. This implies motional narrowing at 77 K. Although the classical narrowing condition wdr, +z 1 is not satisfied - 7, at 77 K equals 1 x 10m3 s, Fig. 3 - such narrowing can be ascribed to quantum tunneling of the methyl groups. In an analysis of linewidths, both classical and tunneling theories lead to the same observable motionally narrowed spectrum [23]. However, an interpretation of the T, data at low temperature requires the temperature dependence of the correlation time rc to be modeled. After Clough et al. [24], the correlation of methyl tunneling and thermally activated reorientation led to a model which allows one to calculate the temperature dependence of T, by using the measured tunnel splittings as the only input parameters [25,261. The application of the theory to calculate a tunnel splitting for a methyl group of lithium lactate from the temperature of the observed Tlmin gives a value of the order of linewidth and is, therefore, small compared with the Larmor frequency. In the general case of tunneling, the expression for T, becomes more complicated than the

M.L. Buszko, E.R. Andrew /Solid

119

State Nucl. Magn. Reson. I (19921 115-119

conventional Kubo-Tomita equation [eqn. cl)] and involves (wO k w,) and (2w, k mt) terms [25]. However, for very low tunnel frequencies, i.e., for high barrier materials, we may safely apply eqn. (1) to calculate the temperature dependence of T,, modeling - after Takeda and Chihara [27] - the correlation time r, by adding an additional term in the temperature dependence of the correlation time:

Acknowledgment This work RR02278.

was supported

by NIH

grant

References 1 H.E. Whipple and P.E. Reyen, Ann. N.y Acad. Sci., 119

(1965) 851. 7,’

= TO’

exp( 2)

+r;l

exp[+)

(5)

where Eel is interpreted as the energy difference between the two lowest torsional states. Since E,, TV, only the first term on the right-hand side of eqn. (4) is significant at higher temperatures. However, at lower temperatures the second term becomes progressively more important and causes TVto rise less rapidly than the classical term would dictate and causes T, to rise less rapidly than otherwise. Despite some controversy in the interpretation of both E,, and T”], such modeling gives essentially the same characteristic shape of the temperature dependence of TV U~TSMS T- 1 as obtained by Clough et af. [25]. Adopting eqn. (5) and using the high temperature values of E, and TV, the experimental values are fitted very well, as shown in Fig. 2, with E,, = 6.1 + 1 kJ/mol and 701 = (2 & 1) x lOPa s. The temperature dependence of T, that corresponds to these parameters is presented in Fig. 3 as the solid line; the classical methyl correlation time is given by the broken line. The value of E,,, is almost half the value of E,, which hinders methyl rotation at higher temperatures; similar results were obtained in the solid state for CH,Cl [16], CH,SiCl, [27], and lactic acid CH,CH(OH)COOH [lo]. E,, - although relatively high - may correspond to a rotational oscillatory frequency. Expressed in wave-numbers units, E,,r equals 510 cm-‘. A broad 500 cm-’ band was reported without interpretation by Ranade and Biswas [6] in lithium lactate by IR absorption.

2 K. Imasaka. T. Nagai, M. Yoshida, H. Fukuzaki, M. Asano

and M. Kumakura, Macromol. C/rem., 191 (1990) 2077. 3 H. Fukuzaki, M. Yoshida, M. Asano, M. Kumakura, T. Mashimo, H. Yuasa, K. Imai and H. Yamanaka, Polymer, 31 (1990) 2006. 4 E. Lepri, M. Andrielli, L. Romani, A. Goldin and E. Bonmassar, Chemiother. Uncol., 5 (1981) 49. 5 C. Poirel and M. Belanger, J. Psychiatr. Bioi. Ther.. 23

(1986) 17. 6 A.C. Ranade and A.B. Biswas, J. Indian Chem. Sot., 44 (1967) 314. 7 S. Clough and F. Poldy, J. Phys. C, 6 (1973) 1953. 8 M. Brustolon. T. Cassol, L. Micheletti and U. Segre, Mol. Phys., 57 (1986) 1005. 9 M. Brustolon, T. Cassol. L. Micheletti and U. Segre, Mol. Phys.. 61 (1987) 249. 10 M.L.. Buszko and E.R. Andrew, Mol. Phys., (1991) in

press. 11 N. Bloembergen, E.M. Purcell and R.V. Pound, Phys. Rec.. 73 (1948) 679. 12 R. Kubo and K. Tomita, L Phys. Sot. Jpn.. 9 (1954) 888. 13 E.R. Andrew and B. Peplinska, Mol. Phys., 70 (1990) 505. 14 E.R. Andrew, W.S. Hinshaw, M.G. Hutchins and R.O.I. Sjoblom, Mol. Phys.. 34 (1977) 1965. 15 P.S. Allen and A. Cowking, L Chem. Phys., 49 (1968) 789. 16 T. Eguchi and H. Chihara. J. Magn. Reson., 76 (1988) 143. 17 A. Cingolani, G. Spinolo and M. Sanesi, Z. Naturforsch. Teii A. 34 (1979) 575. 18 I. Miyagawa and K. Itoh, J. Chem. Php., 36 (1962) 2157. 19 E.R. Andrew, W.S. Hinshaw, M.G. Hutchins, R.O.I. Sjoblom and PC. Canepa. Mol. Phys., 32 (1976) 795. 20 G. Soda and H. Chihara. J. Phys. Sot. Jpn., 36 (1974) 954 21 R. Sjoblom, in P.S. Allen, E.R. Andrew and C.A. Bates (Eds.), Proceedings of the 18th Ampere Congress, University of Nottingham. England, 1974, p. 485. See also R. Sjoblom. .I. Magn. Reson.. 22 (1976) 411. 22 J.H. Van Vleck, Phys. Ret,.. 74 (1948) 116X. 23 F. Apaydin and S. Clough, J. Phys. C, 1 (1968) 932. 21 S. Clough, A. Heidemann, 4.5. Horsewill, J.D. Lewis and M.N.J. P&y.

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25 S. Clough, A. Heidemann, A.J. Horsewiil, J.D. Lewis and M.N.J. Paley. J. Phyb. C, 15 (1982) 2495. 76 P.J. McDonald, G.J. Barker, S. Clough, R.M. Green and A.J. Horsewill, Mol. Phvs., 57 (1986) 901. 27 S. Takeda and H. Chihara, J. Magn. R~~oFI.,56 (1984) 48.