advances in molecular relaxation processes 235 elsevier publishing

Advances in Molecular Relaxation Processes Elsevier Publishing Company, Amsterdam. Printed in the Netherlands

235

RELAXATION TECHNIQUES IN FAST REACTION KINETICS

H. STREHLOW Max-Planck-Institut fiir biophysikalische Chemie (Karl-Friedrich-Bonhoeffer-Institut), CGttingen (West Germany)

CONTENTS

I. Introduction ................................ II. Chemical relaxation .............................

A. Temperature-, pressure- and field-jump techniques .............. 1. Temperature-jump technique ...................... 2. Pressure-jump technique ........................ 3. Field-jump technique ..........................

III. Stationary methods ............................. IV. The evaluation of relaxation times. ...................... V. Mean life times as obtained from NMR line broadening and chemical relaxation times

A.NMR .................................. 1. Advantages .............................. 2. Disadvantages .............................

B. Chemical relaxation ........................... 1. Advantages .............................. 2. Disadvantages .............................

VI. A practical comparison of NMR line broadening and a relaxation technique applied to the same chemical reaction ..........................

References ...................................

235 236 236 238 239 239 240 240 241 243 243 246 246 246 246

246 248

I. INTRODUCTION

In the early nineteen-fifties, two different kinds of relaxation techniques were developed which both proved to be very useful in the investigation of rapid chemical reactions. One of these techniques is nuclear magnetic relaxation in systems with rapidly exchanging magnetic nuclei. It was first introduced by Gutowsky et al.’ and has since been used in many laboratories. The other relaxation method has been called chemical relaxation. It was mainly developed by Eigen et al.’ and also has found widespread application. Chemical relaxation will mainly be covered in this review. The advantages and drawbacks of both techniques will be compared and a specific example will shortly be given of a chemical reaction which has been investigated by NMR line broadening3 and by the pressure-jump relaxation method4.

Advan. Mol. Relaxation Processes, 2 (1972) 235-249

236 H. STREHLOW

II. CHEMICAL RELAXATION

Chemical equilibrium constants depend on external parameters such as temperature, pressure or electric field strength. If such parameters are rapidly changed, momentarily the system will not be in equilibrium. Therefore, a chemical reaction occurs which re-establishes equilibrium conditions. As long as the relative change in the equilibrium constant is small - and in practice this is always the case - the re-adjustment of the concentrations to their new equilibrium values occurs at a rate which is proportional to the deviation of the momentary concentration from its equilibrium value. By measuring the change of concentration as a function of time, the rate constants of the chemical reaction may be obtained. Aside from these transient methods, the stationary state of a reacting system under the influence of a periodically changing external parameter is also changed by chemical relaxation and may be used for the investigation of fast chemical reactions (ultrasonic absorption, dielectric relaxation).

A. Temperature-, pressure- andfield-jump techniques

The most simple situation prevails if the external parameter is changed as quickly as possible from one constant value to another. Ideally, the parameter, e.g. the pressure on the reacting system

A+B %c (1) kz

will be subjected to a step function in time (Fig. l(a)).

Fig. 1. Principle of pressure-jump relaxation.

The equilibrium constant is changed according to

din K

dp __g,-_AE

cpp RT


RELAXATION TECHNIQUES IN FAST REACTION KINETICS 237

(where K is the equilibrium constant, AV the volume of reaction, a the coefficient of thermal expansion, c,, the specific heat, p the density, and AH the enthalpy of the reaction) and the concentrations will approach their new equilibrium values (Fig. l(b)). We shall now evaluate the rate law for this approach assuming a reaction of type (1).

If cA, c, and cc are the instantaneous concentrations of A, B and C, re- --

spectively, which change with time to their equilibrium values c,, , cB, and cc after the pressure jump, we have the equation

The deviations of the actual concentrations from their equilibrium values will be designated as

Aci E ci-c (4)

With the mass balance equation

Ac,+Ac, = 0 (9

and the stoichiometric equation

AC, = AC, = AC (6)

we obtain from eqn. (3)

dAc

dt - kl(G+QAc+k2A c+k,(Ac)2+k, CACB-k2C, (7)

k, (AC)” is small compared with the other terms, as long as the shifts in concentration are much smaller than the concentrations. This term may, therefore, be neglected. The last two terms vanish, since the 5 refer to equilibrium conditions. Therefore, we are left with a linear differential equation, the solution of which is

AC = Ac(t = 0) exp (-t/z) (8)

with

1 - = k,(c,+c,)+k, r

(9

r is the relaxation time for the reaction, which may be determined experimentally by measuring the change of the concentrations as a function of time.

If the outlined principle is to be realized for the measurement of fast chemical reactions, three problems have to be solved.

(I) How to effect a very sudden jump in temperature, pressure or electric field.

(2) How to measure the fast-changing, very small concentration differences.


238 H. STREHLOW

(3) How is the measured relaxation time connected with the rate constants and concentrations of the reactants? (Equation (9) is only a special case referring to system (l).)

The first two experimental problems will be discussed with the description of different chemical relaxation apparatus. The theoretical question of the dependence of r on the reaction mechanism, the concentrations, and the equilibrium values involved will then follow.

I. Temperature-jump technique

Fast temperature jumps have been realized by two different techniques, the first of which has been used very extensively in the investigation of chemical relaxa- tions. A high-voltage condenser is discharged through a solution containing the chemical system to be investigated. The switching of the circuit is performed by a spark gap. The temperature jump thus obtained is given by

AT=g [I-exp(-&)I (10)

with C the capacity of the capacitor, U the voltage, R the resistance, cP the specific heat, p the density, and V the volume of the solution. Typical values are U = 50 kV, C = 0.1 yF, p = 1 g cmP3, V = 5 cm3, cP = 4.19 joule/grad, R = 40 R. Under these conditions temperature jumps of 5 “C can be achieved in about RCj2 = 2 psec. With temperature jumps as high as this, relatively large shifts of the equilibrium constants

AInK=- AH AT RT2

result and optical detection methods with their inherent advantages may be used. Absorption spectrometry is the technique most often used for the detection

of the concentration changes with time. If the reacting species involved in the chemical reaction to be measured do not change the absorption of light sufficiently, it is possible to couple another chemical reaction to the system which does absorb light and is fast enough not to be rate-determining. pH indicators are often used as coupled systems, since in many reactions proton transfer occurs.

Besides light absorption, optical rotation and fluorescence spectrometry have been used, though less frequently, for the detection of concentration changes in temperature-jump relaxation equipment.

Another way to perform fast temperature jumps is the absorption of light either from a fast flash light6 or from a giant pulse laser7. Values of AT of roughly 1 “C in 2 psec have thus been obtained. A similar technique is the absorption of intense microwave pulses (AT - 0.7 “C in 2 psec)*.

Aduan. MO!. Relaxation Processes, 2 (1972) 235-249


With these techniques, electrical conductance has been used as a monitor of the concentration changes after the temperature jump. However, detection by optical absorption has also been used in combination with the microwave pulse technique’.

2. Pressure-jump technique

Different kinds of pressure-jump apparatus have been described in the litera- ture. In the most often used version, pressure (of the order of 100 atm) is applied to the system to be investigated in an autoclave”. The autoclave is closed by a metal membrane which bursts spontaneously at this pressure. In about 50 psec the pressure falls to 1 atm. Thus, relaxation times 2 100 psec can be measured. The concentration changes are followed by conductivity measurements. A relative change of resistance of 10e5 is about the limit of detectability. However, a general drawback of conductivity measurements in relaxation techniques is the appreciable loss in sensitivity if the solution contains non-relaxing electrolytes e.g. buffers.

Another version of the pressure-jump apparatus” follows the course of the reaction by measuring the temperature with a rapidly indicating thermistor (NTC resistor), thus taking advantage of the heat of reaction. The range of relaxation times which can thus be measured is about 10-2-100 sec.

A third type of pressure-jump apparatus works with an increasing pressure step12. As in gas shock wave technique, a shock wave may be produced in liquids resulting in a very sudden pressure jump (N 1 psec) at the end of the shock tube. This jump is much sharper than in the normal pressure-jump apparatus.

The time available for measurement is 21/v, where 1 is the length of the tube and v the velocity of sound. 21/v is of the order of 14 msec. This version of the pressure-jump technique is, therefore, a useful tool for measuring reactions which are too fast for the more conventional pressure-jump apparatus. The concentration changes are either followed by conductivity or - with a pressure jump of the order lo3 atm - with absorption spectrophotometry13.

3. Field-jump technique

If, during a reaction, the electric moment changes, e.g. in the dissociation of a weak electrolyte, the equilibrium constant is shifted by the application ofan electric field jump, E, according to

d In K AEVE

dE =E (11)

where AE is the change of the dielectric constant due to the chemical reaction. Rather high electrical fields, of the order of 104-lo5 V cm-‘, are necessary to cause a detectable shift in equilibrium. Therefore, only solutions with a low conductivity may thus be investigated, because otherwise, in highly conducting media, the

Adoan. Mol. Relaxation Processes, 2 (1972) 235-249

240 H. STREHLOW

electric field collapses too soon. The electric field is applied in pulse form either from a large condenser with a switch-on and a switch-off spark gap14, or from the discharge of a coaxial high voltage cable into the celli’. Rather fast reactions can thus be studied, either with conductivity or with absorption spectrometry as the concentration monitor.

III. STATIONARY METHODS

Instead of a stepwise perturbation of the chemical equilibrium, as discussed in Section II, a periodical perturbation may also be applied as in an ultrasonic wave or in an alternating electric field. If the reaction is very fast compared with the frequency (l/z >> w) the system will respond in phase and no energy absorption will occur. The energy absorbed in a half-wave by the system is dissipated in the next half-wave of the oscillation. With very slow reaction (l/r << 0) there is a phase shift of 90” but again no energy absorption, since the response of the slow reaction cannot follow the excitation and its amplitude therefore vanishes. With l/r = w a maximum of energy is absorbed with a phase shift of 45”. Therefore, chemical relaxation adds to the absorption of energy in ultrasonic16 and electric high-frequency fields l4 the maximum effect occurring at a frequency o = l/z. In the case of the chemical contribution to dielectric relaxation, eqn. (11) shows that AlnK- A(,!?‘). Therefore, the equilibrium is shifted only sufficiently if the high frequency field is superimposed with a high, constant electric field. With periodica perturbation techniques, relaxation times as short as lo- lo set may be determined

IV. THE EVALUATION OF RELAXATION TIMES

As demonstrated above (eqn. (9)) an expression for the relaxation rate may be derived for a given reaction. In more complicated types of reaction systems, more than one relaxation time will be observed. Without derivation, some expres- sions for relaxation times for some practically important reactions are given below.

Type of reaction Relaxation time

A$B kz

A+B SC kz

1 - = k,+k, T

1 - = k,(c,+c,)+k, r

(12)

(13)

ktz kz3

A+B +AB+C 1

~ =$[~k&(~k)‘-4rrk] kz1 ksz Tl,Z


(14)


where

c k = k,,(G+c,)+k,,+k23+k32 and

nk = kl2(CA+~)(k23+k32)+k21 k,, km 1 kzs G+G) A+B+ABSC -= _ +k

k32 r l+K(EJ4:+c,) 32 (15)

(+ indicates that the equilibrium A + B 4 AB is very fast compared with AB+C; eqn. (15) is obtained from eqn. (14) with k,,, k,, >> k,,, k32; K E cAB/cAcB.

The following characteristics of these equations are noteworthy. The relaxation times depend on both the forward and backward rate constants in an additive manner. In general, they are functions of the concentrations which are different for different types of reaction. Therefore, proposed mechanisms may be tested by the determination of the concentration dependence of r. However, it should be mentioned that only if the rate can be measured over a rather large range of concentration are the conclusions unambiguous, A considerable degree of experimental precision is required for that purpose. In many cases, modern equipment really affords this precision provided that a careful evaluation of z is performed18. In eqns. (12)-(15) for the sake of simplicity, the influence of the activity coefficients has been neglected. With higher concentrations this is, of course, not permissible. In principle, equilibrium constants may also be evaluated from the concentration dependence of r. In most cases, however, more precise results are obtained by combining relaxation measurements with conventionally determined equilibrium constants.

Another way of obtaining equilibrium constants should be mentioned. The amplitude of the relaxation effect, i.e. Ac(t = 0) in eqn. (8), provides information on equilibrium constants which are sometimes not easily obtained with other techniques. Though this method cannot be considered to be very precise, it may supply important semi-quantitative data on equilibrium constants in complicated chemical systemsi9.

V. MEAN LIFE TIMES AS OBTAINED FROM NMR LINE BROADENING AND CHEMICAL RELAX-

ATION TIMES

For the sake of simplicity, we shall only compare the data for the most simple reaction of type shown in eqn. (12) assuming that each of the species A and B contains at least one nucleus with magnetic moment, e.g. a proton. Therefore, we shall rewrite

AHSBH kz

(12a)


242 H. STREHLOW

This most simple case is sufficient to demonstrate the differences in the two techniques. If the proton experiences a chemical shift v,--v, in the state AH with respect to the state BH, chemical exchange manifests itself in increasing the line widths in the NMR spectrum. If the mean life times of the proton in the states AH and BH, rA and zn respectively, are very long compared with (v~-v~)-’ and with T,, two lines of line widths ~/XT, are observed (assuming a magnet of ideal homogeneity). The only kinetic information provided in this case is an upper limit for the rate of exchange. For T, > zA, zB > (v~-v~)-~, two broadened lines are observed with the additional line widths

(16)

It is this “slow case” with two broadened, not yet overlapping, lines which supplies especially useful kinetic information.

If r-l E (zi 1 +z, ‘) is of the order vA-vB, a single broad line with a line width of the order vA-vB is observed. With decreasing r, this line sharpens again and an exchange broadening of the coalesced single line is given by

Av+ exchange = 4n(vA - vB)2it &A+ zB) (17)

where p, is the proton fraction in state AH andp, that in state BH. With extremely fast reactions, the exchange broadening vanishes (rA, zB + 0 in eqn. (17)). In this latter case, only a lower limit for the exchange rate is supplied provided that the chemical shift is known or can be estimated.

The proton fractions and the life times are connected by

PA~B = PB~A

The rate constants and the average life times are given by

dCm _ k c CAH 1 AH=- ’ k : -_=

dt 1

TA TA

(18)

(19

and

_ d%H _ k c CBH ’ k

dt - 2BH=- : -_= 2 (20)

TB TB

In the “slow case”, eqn. (16) the single rate constants are thus obtained directly. In the case of chemical relaxation, only the sum of the two rate constants is determined

1 - = k,+k, = k,(l+K) r

Only with additional information about the equilibrium constant, K = kJk2, can the single rate constants be obtained. Correspondingly for the measurement of

Adoan. Mol. Relaxation Processes, 2 (1972) 2?5-249


activation parameters not only the temperature dependence of z must be evaluated in chemical relaxation but also that of K, i.e. the enthalpy of the reaction must be known from equilibrium measurements.

In the “slow case”, NMR measurements of the area under the line of AH and BH, respectively, supplies the proton fractions pA and pB . Their ratio, pA/pB, is independently obtained from the ratio of the life times, r&n, so that the consis- tency of the measurement may be contrclled. From measurements of zA and zs as a function of temperature, we obtain most directly the rate constants k, and kz and the concentrations pA andp, at different temperatures as well as the two energies of activation and the enthalpy of the reaction. The latter can be obtained independently either from the temperature dependence of the areas under the two absorption lines or from the difference between the two activation energies.

Thus, in the “slow case”, the NMR information is more direct and more abundant than that obtained from chemical relaxation.

However, in the “fast case”, eqn. (17) NMR line broadening supplies less information than chemical relaxation. Equation (17) contains the sum of z, and ze and, furthermore, the mole fractions pA and pB and the chemical shift (vA-vB) which cannot be taken from a high resolution spectrum with coalesced absorption lines. Therefore, as with chemical relaxation, additional information on the equilibrium constant must be available and an estimation of the chemical shift has to be made. The latter difficulty is overcome with a suitable application of the spin-echo technique”.

We are now in a position to list the advantages and the drawbacks of the two compared techniques.

A. NMR

1. Advantages In the “slow case”, very direct and precise information is obtained on the

single rate constants, on equilibria and on activation parameters. In the “fast case” with the application of the spin-echo technique the directness of information is comparable to that of chemical relaxation. NMR technique is the only method which allows the measurement of fast exchange reaction with no change in the composition of the system, e.g. of the reaction

NH; + NH3 5 NH, + NH; k

or the kinetic measurement of hindered molecular rotation. Of course, chemical relaxation cannot be applied to such cases, since the equilibrium constant is unity under all conditions.

Another advantage of NMR is the need for only a fraction of a cm3 of solution, the concentration of which, however, should be as high as possible.


244

TABLE 1

SURVEY OF CHEMICAL RELAXATION TFSHNIQUES

Technique AT, Ap, AE Detection of Ac by Time range Volume of produced by Zower limit Upper limit solution

(see) (set) needed (cm3)

Temperature-jump Discharge of capacitor

Flash light Conductivity

Laser

Microwave

Pressure-jump

Field-jump

Stationary, ultrasonic

Autoclave with rupture disc

Shock wave in liquids

Capacitor switch-on switch-off

Cable discharge

Ultrasonic wave

Stationary, dielectric

High electric field with superimposed high-frequency field

Optical absorption (rotation, fluorescence)

Conductivity

Conductivity, optical absorption

Conductivity, thermometry, optical absorption

Conductivity, optical absorption

Conductivity

Optical absorption

Dissipation of acoustical energy

Phase angle in conductivity bridge

Dielectric loss

5 x 10-6

2x10-5

2x10-6

2x10-6

1o-4 lo-2 10-b

2 x 10-e 2 x 10-G

10-7

5 x 10-a

lo-‘0

10-7

5 x10-9

0.2

2x10-2

2 x10-2

2 x 10-Z

10 100

1

2x10-3 4x10-3

10-a

5 x 10-S

10-S

10-a

10-e

3-10

0.3

0.01

0.1

0.3 50

5

0.1 5

10

2

2%1000

0.1

1



Type of reactions Advantages Disadvantages ReJ

Biochemical reactions, Very widely applicable High electrolyte concentration 5 complex formation, necessary proton transfer

Ionic reactions Fast, simple, small volumes

Possibility of flash photolysis 6

Ionic reactions

Ionic reactions

Ionic reactions, bio- Simple, small volume, chemical reactions sensitive

Ionic reaction, proton transfer

Dissociation of weak electrolytes, proton transfer

Dissociation of ueak High dilution possible, electrolytes, proton very fast. Measurements transfer in non-aqueous media

Ionic reactions, association of un- charged molecules, biochemical reactions

Very fast Not sensitive large volumes. A series of apparatus for a time range 1O-9-1O-5 set

Ionic reactions Fast, small volume Cumbersome to use.

Biochemical reactions, hydrogen bonding reactions

Very fast, extremely small volumes

Conductivity and optical absorption possible, gentle disturbance of equilibrium

Fast, small volume, Fast, small volume

Time per experiment high 12 Rates are measured at high pressures 13

High dilution possible, High dilution necessary. very fast Sophisticated equipment

Very fast Experimentally difficult

Not simple in application 7

Expensive equipment 8, 9

Not very fast Rather slow Not very fast

10 11

14

High dilution necessary. Sophisticated equipment

15

16

21

17


246 H. STREHLOW

2. Disadvantages Only compounds with magnetic nuclei must be used. The sensitivity of NMR

is much inferior to that of chemical relaxation techniques. However, with modern equipment this drawback of NMR will become much less serious. In the most informative “slow case”, only a small range of average life times from about 1 set to at most (depending on the chemical shift), 5 x lo- 3 set is accessible. In many cases the time range is considerably smaller. The equipment is rather expensive and the whole technique is more sophisticated than with chemical relaxation. This is particularly true if spin coupling is involved or in cases where the chemical shifts are small, or if the “intermediate case” (zA N (vA-va)- ‘) is investigated.

Another disadvantage is that the concentration ratio, pAlpa, should not differ too much from unity. Similar arguments, however, apply also to chemical relaxation.

B. Chemical relaxation

1. Advantages These techniques are applicable over a larger time range (although only with

an arsenal of different relaxation apparatus; see Table 1). With many techniques, solutions with small concentration may also be investigated. The apparatus is less complicated and expensive than NMR equipment. For most reactions at least one relaxation technique may be found which is especially suited for the problem and supplies precise data.

2. Disadvantages As with NMR, irreversible reactions cannot be investigated. Most equipment

is not available commercially. The exponential decay curves may often be disturbed by heat exchange processes or other artefacts. Therefore, it is difficult to get a relaxation time with a precision better than about f 5 %.

A definite advantage of both NMR line broadening and chemical relaxation techniques is the simplicity of the mathematical treatment. All kinetic differential equations are linearized. Therefore, advantage should be taken of chemical relaxation techniques also in the case of slow reactions, where conventional techniques are applicable.The increased simplicity in evaluation of the rate laws oftenwill com- pensate for the change in experimental technique.

VI. A PRACTICAL COMPARISON OF NMR LINE BROADENING AND A RELAXATION TECH-

NIQUE APPLIED TO THE SAME CHEMICAL REACTION

The kinetics of hydration of pyruvic acid were investigated by the pressure-

Aduan. Mol. Relaxation Processes, 2 (1972) 235-249


jump technique 4. It was concluded that the reaction proceeds as kz3

CH,COCOO - + H,O + + CH,COCOOH+ H,O + CH,C(OH)$ZOOH (21)

By using eqn. (15) the rate constants could relaxation times. The reaction was found to be

kz3 = k&+k&cn

and

k 32 = k;2+k;2cH

be evaluated from the measured acid-catalyzed

(22)

(23) The two k” were much higher than the corresponding values for the hydration of acetaldehyde, This fact was explained by assuming an inner-molecular acid catalysis.

In aqueous solutions of pyruvic acid, the methyl groups in the hydrated and the unhydrated form of the acid show two lines in the proton NMR spectrum. From the intensity of the lines the equilibrium constant and from the line widths the kinetics may be evaluated. With small concentrations of H30f ions the reaction is rather slow and the absorption lines are broadened to only a small extent. Pre- liminary measurements of the equilibrium and the rate constants for reaction (21) with NMR led to rate constants about 3 times as large as the corresponding values obtained by the pressure-jump technique. These NMR investigations22 have been performed with high concentrations of pyruvic acid (344) and with the addition of a high concentration of HCl in order to obtain (easily measurable) large and broad signals. In order to explain this discrepancy, further NMR measurements were performed with varied concentrations of pyruvic acid (0.14-10 M) and of HCl (0.1-5 M) at different temperatures3. The results of these investigations may thus be summarized: from the measurement of the equilibrium constant KH = kz3/ k,, at different concentrations, it became clear that the reaction (21) had to be rewritten as

CH,COCOO- + H30+ + 2H20 + CH,COCOOH+ 3H,O + CH,C(OH),COOH .2H,O (21a)

A trihydrate is formed, the structure of which was proposed to be as shown in Fig. 2.

“1 ..”

“P ‘0 \

_-b F-0

H ‘“....O/~-o\H "'H 'C-H

H'

Fig. 2. Proposed structure of pyruvic acid trihydrate3.


248 H. STREHLOW

The above-mentioned difference in the rate constants was due to activity coefficients very different from unity in the concentrated solutions. Both NMR and chemical relaxation measurements lead to consistent results when a small correction is applied for the fact that a trihydrate was formed. The measurements of Kn at low concentrations with uv absorption photometry, which were used in the evaluation of the pressure-jump experiments, did not show the existence of a trihydrate. An interesting effect was observed in the line width measurements. With only small concentration of HCl, it was found that the concentration ratio, as obtained from the area under the absorption line and from the ratio of the line widths, did not agree. The reason is that the line width of the hydrate is not only due to the kinetic broadening according to eqn. (19) but is also enlarged by hindered rotation of the methyl group. The two water molecules forming a hydrogen-bonded ring between the carboxylic proton to one of the geminal OH oxygen atoms make the molecule rigid with the consequence that hindered rotation of the methyl group occurs. Thus, from a pure kinetic argument, the proposed structure of the trihydrate has been strengthened. Besides, the relatively large negative entropy of hydration sug- gests more than one molecule of water in the hydrate.

In Table 2, the data as obtained by the two techniques are collected. The table clearly shows the usefulness of applying different techniques to the same system. Whereas the measurements at low concentrations of H+ ions are very imprecise with NMR and rather reliable with chemical relaxation, the activation parameters and the thermodynamic data are better evaluated by NMR techniques.

TABLE 2

THERMODYNAMIC AND KINETIC DATA FORTHE HYDRATION REACTIONOF PYRUVICACID

k” kH &I AH: ASf: AH AS Method (set- ‘) (M-‘see- ‘) (kcallmole) kcaljmole callgrdmole kcal/mole callgrd mole

Hydration 0.55kO.05 6.310.7 9.0*0.6 Relaxation (0.5&0.4) 5.0*1.5 10.0&0.5 9.4 -24 -7.1 -23 NMR

Dehydra- 0.22&0.02 2.5*0.3 Relaxation tion (l*l) 2.010.8 17.3*0.5 16.7 +1 +7.1 +23 NMR

-._____

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D. PAPADOPOULOS, Ber. Bunsenges., 75 (1971) 106. 20 Z. Luz AND S. MEIBOOM, J. Chem. Phys., 39 (1963) 366; A. ALLERHAND AND H. S. GUTOWSKY,

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