Nuclear magnetic relaxation by intermolecular quadrupole interaction, determination of the correlation time

Advances in Molecular Relaxation Processes, 9 (1976) 293--326 © Elsevier Scientific Publishing C o m p a n y , A m s t e r d a m - P r i n t e d in T h e Netherlands

NUCLEAR MAGNETIC RELAXATION BY INTERMOLECULAR DETERMINATION

OF THE CORRELATION

QUADRUPOLE

293

INTERACTION,

TIME

A. GEIGER AND H. G. HERTZ

Institut

f~r physikalische

Karlsruhe

(W. Germany)

(Received

IO December

Chemie und Elektrochemie

der Universit~t

1975)

ABSTRACT

Expressions

for the correlation

times corresponding

are presented which have been proposed results

for the 7Li magnetic

in the literature.

relaxation

rate solutions

and glycerol-d 8 as a function of the temperature cases a maximum for the relaxation

maxima occur at the same temperature

experiments

a realistic

and 133Cs dissolved

in water.

are reported.

In all

rate in the same solution. it is concluded

description

have been performed

Experimental

of LiCI in glycerol

rate is observed and is compared with

the maximum for the proton relaxation

model provides

to various models

that the electrostatic

of the relaxation

for solutions

As both

process.

Similar

of Cs + in glycerol and of 7Li

In all cases the electrostatic

model was

found to be satisfactory.

INTRODUCTION

Let us assume that by some means we have produced a ~erturbation the nuclear magnetization M in a static magnetic component

of

field such that Mz, the

of M in the direction of the static magnetic

field, differs

from

the equilibrium value M o. Then the nuclear magnetization moves back z towards the equilibrium value, and under suitable conditions the motion of the longitudinal

component obeys the differential

=

dt

T 1 is the longitudinal

i(< I1

relaxation

equation

[I]

(I)

time and I/T 1 is called the longitudinal

294 relaxation rate. moment Q.

Nuclei with a spin I > 1/2 have an electric quadrupole

This has the consequence

1/2 the nuclear magnetic type Eqn.

(I) is caused by the interaction

Dole moment with the electric electric

field gradient transitions,

at the nuclear site.

in the environment.

One important

is that in order to be effective

and thereby magnetic

relaxation,

This

of other nuclei and

feature of the electric

in inducing nuclear spin

it fluctuates with time.

such fluctuations with time are due to the molecular motion.

electrical

field gradient is a tensor quantity,

importance are the components system,

of the nuclear electric quadru-

field gradient

field gradient is produced by the distribution

of the electrons

course,

that in most cases for nuclei with I >

relaxation mechanism v~ich leads to an equation of

and the quantities

of this tensor in the laboratory

of

coordinate

the z axis of which is the direction of the static magnetic

Thus it is easy to imagine that the tensor components

Of The

field.

in the laboratory

system vary with time when the molecules perform rotational

B r o ~ i a n motions

In fact, the theory of nuclear magnetic relaxation caused bv intramolecular quadruDole

interaction

components

due to rotational molecular motion is well established

Hcwever,

and based on fluctuations

[I].

the situation becomes more difficult when we consider a nucleus

which resides in the centre of an ion the ion is of spherical symmetry, means of varying the electric is meaningless.

Obviously,

In the literature

with

a noble gas structure.

then the electric

essentially

mechanism because,

field gradient must in some

two mechanisms have been proposed in relaxation rate by quad-

The first mechanism we may call an electronic primarily,

distortions

There are two subversions

of the ion electron cloud are

of this hypothesis:

i) The ion collides with the surrounding collision

at its centre

effects.

order to account for the observed intermolecular rupole interaction.

Now, as

the concept of a rotation of the ion as a

field gradient at the nucleus

way be produced by intermolecular

involved.

of the field gradient

solvent molecules.

During the

the spheric~l symmetry of the ion is lost and consequently

an electric field gradient arises at the centre of the ion. mechanism was proposed by Deverel

This

[2,3].

ii)~he other version which is due to Mishustin and Kessler is suitable only for the relaxation of small and highly charged ion~

One example is Li +,

the nucleus of which is the subject of the present study. these authors Li + ions have highly symmetric, vation shells.

In such surroundings

presumably

of tetrahedral

According tetrahedral

symmetry - like

to sol-

295 spherical symmetry - the electric field gradient vanishes. exists,

Thus, if it

the field gradient at the nuclear site arises from distortions of

the common electronic system of Li + and the first solvation shell. maximum distortion

(and the maximum field gradient) corresponds

The

to the

breakage of one Li + -solvent molecule bond~ the "freed" molecule most probably is leaving the first solvation shell.

In this case the relaxation

rate is determined by exchange of molecules i.e. by the residence time of solvent molecules in the solvation shell. The second attempt to explain this quadrupolar relaxation rate of ion nuclei is based on an electrostatic model.

The electric field gradient at

the nuclear site is caused bv the electric point dipoles of the surrounding solvent molecules and the point charges of other ions present in solution. This model was derived by Valiev and coworkers

[5-8] and by Hertz

rq].

The

electronic distortion is taken into account not as a specific effect but as a universal multiplication [i0-II].

factor,

the antishielding or Sternheimer factor

Later an improved version of this model was applied to a number

of systems,

including aqueous and non-aqueous electrolyte

On the whole,

solutions

r12-2~.

so far the experimental data could be satisfactorilv inter-

preted in terms of the electrostatic

theory.

It is the purpose of the present paper to report results of a number of experiments which were performed in order to decide which of the proposed three models is the most realistic.

The basic principle underlying

these experiments is the direct measurement of the time constant, which determines

the fluctuation of the electric field gradient.

scopic time constant is usually termed the correlation time. shown,

This microAs will be

the different models lead to different predictions of the correla-

tion time and thus the measurement of this time will be useful.

In the

next section we shall present the quantitative expressions which are to be used in the experimental

section.

The system we have studied are solutions of Li + (7Li) and Cs + (133Cs) in glycerol,

since the molecular motions are slow enough for a nmr study

to be feasible.

In a rather short section some results for aqueous solu-

tions of some Li and Cs salts are added.

BASIC FORMULAS

RELAXATION RATES AND CORRELATION FUNCTIONS We shall study the relaxation behaviour of the two nuclei 7Li and 133Cs in the ions Li + and Cs +.

One difficult feature of these nuclei is

296 that both have a spin I > I, and, as the theory shows, general,

a relaxation

time T 1 is not strictly defined

~z = O at t = O the regrowth of the longitudinal

for such nuclei, [I, 21].

magnetization

in

Thus, if ~#z relative

to the equilibrium value

M °

-

z

H

z

= f (t)

M° Z is not an exponential Father,

function as it should be according

it is a superposition

of 7Li with f = 3/2 is comparatively formula

to eqn.

of a number of exDonentials simple.

r21].

(I). The case

Hubbard has derived the

[21]

-

z

M z

=

4

I

~ exp (-alt) + ~ ex D (-a2t)

(2)

M7 133Cs h a s t h e s p i n I equilibrium

= 7/2,

and t h e m o t i o n o f i t s m a g n e t i z a t i o n t o w a r d s + i s more c o n m l i c a t e d ; t h e r e f o r e Cs r e s u l t s w i l l o n l y be d i s c u -

s s e d on a q u a i i t a t i v e

level.

In eqn.

(2)

the constants

a 1 and a 2 a r e g i v e n

by t h e r e l a t i o n s 2 aI = I 6 a2

=

eQ

1 e Q -~ --~

J-22 (2~)

(3)

J-ll

(4)

2 (~)

where Jfk is the Fourier transform of the time correlation

G_kk(t) = vk(o)v-k(t )

k=l,

function

2

of the electric field gradient:

J-kk (~) = f wi th

~=2v 7~ zz

G-kk(t)

ex~ (-imt) dt

(5)

297

V~I = V

~2

t i V ~i

xz

(6)

= I (Vx-Vy)x y

+ i V

V Y ...... are the components of the field gradient tensor. The liquid xx ~j is an isotropic system; in such a system G_I I = G_22 and we may drop the subscripts

of G(t).

Vk(O) 2 # O.

G(t)

approaches

If the molecular motion is fast, then the time constant

the decay of the time correlation The time dependence Experiments very small.

of G(t)

eqn.

(2).

function is short; otherwise

In all the measurements

(2) from an exponential

behaviour.

Therefore we

function by a computer as an approximation

Thus we replaced eqn.

M°_M z z

is

to be reported here we were never able

from a simple exponential

the exponential

for

it is long.

is dependent on the model we are postulating.

show that the deviation of eqn.

to detect a deviation simulated

0 as the time goes on; in general

to

(2) by a law of time dependence

1

t]

(7)

z

and we may write for (I/Tl)ef f

~I

(

4 1 )eff = x 1 ~ a t + x2 ~ a 2

(8)

2 _ 30 i eQ ?~

[4 " x I J 22(2~) + x 2 J ll(m)]

is the nuclear magnetic applying.

resonance

frequency at the magnetic

The quantities Xl, x 2 are numerically

fitting of eqn.

(7) to the real behaviour

least mean square procedure of the computer.

field we are

unknown to us because

according

and x 2 should not differ very much from unity. we would have exactly

(9)

to eqn.

the

(2) is done by a

As will be shown below, x I, If the spin were I = I, then

[I] 2

I

_ I

eQ

[4 J_22(2~)

+ J ii(~)]

s T i.e. here x I = x 2 = I.

In the following we drop the subscript "eff" from

(I/Tl)ef f and simply write I/TI; we also do this in those cases where a

298 rigorous

1/71 is not defined.

N o w the simplest a s s u m p t i o n regarding the time c o r r e l a t i o n function is an exponential

G(t)

= V---~$(O)2 exp(-t/T ) e

T c is the c o r r e l a t i o n time, the quantity we wish to know.

transform

o f an e x p o n e n t i a l

is

the Lorentz

function,

that

The F o u r i e r

is

2T e J(~) = V(0)

2

i + 2

(1~)

2 c

and consequently, w i t h eqn.

(9) T

[4 X I

T C 2 + m2 C ] I + 4~2T I + ~2r 2 e c

If we consider the e x p r e s s i o n in the square brackets of e~n. function of the c o r r e l a t i o n time T

at a given frequency

(12)

(12) as a

(and for the

c moment w i t h x I = x 2 = i) then we find that this function has a m a x i m u m if

mT

c

= 0.62

(1B)

With our computer a p p r o x i m a t i o n for I/T 1 we found the m a x i m u m of the effective 1/71 to be

m~

e

= 0.55 + 0.02

(14)

Thus we see that x I and x 2 do not differ verv much from unity

(the weight

of the double resonance frequency term is slightly greater than that of the resonance frequency term). In the experimental procedure temperature.

T

is varied by the v a r i a t i o n of the c The m a x i m u m of the relaxation rate is determined. As the

resonance frequency is k n o w n at the temperature of m a x i m u m r e l a x a t i o n rate, T

c

can be determined f r o m eqn.

(14).

The nuclear m a g n e t i c resonance frequencies of typical nuclei to be c o n s i d e r e d here are about 10 7 Hz, thus ~ ~ 10 8 sec -I and at the r e l a x a t i o n

299 maximum •

c correlation

~ I0

-8

s.

We shall see that this order of magnitude of the

time implies that ordinary electrolyte

consideration;

only rather concentrated

can be investigated nesium salts.

solutions of LiCI, LiBr and Lil

and probably also some concentrated

The study of aqueous

presented here.

is glycerol.

CORRELATION

is

Thus, the majority of experiments

to be described use solutions of Li and Cs halides is glycerol.

use solutions

solutions of mag-

solutions of lithium halides

An organic solvent with which the desired study can be

made at room temperature

temperature

solutions must be cool-

Thus,

the majority

of Li and Cs halides

in glycerol.

of experiments

to be described

in glycerol.

FUNCTIONS FOR THE VARIOUE MODELS

We turn now to the discussion

of the correlation

times ~¢hich are to be

expected for the various models described briefly above.

DISTORTION OF THE ELECTRON

CLOUD OF THE ION DUE TO COLLISIONS WITH SOLVENT

MOLECULES

The follow;ng expression previously

for the correlation

function has been derived

[12a]:

P°Vro2 exp

[-(r~ 4- 1

1

(15)

p'--~ = .rb , Pa 4- Pb =1

Pa is the probability

(16)

that a solvent molecule,

during a collision,

ches the ion so closely that the electron cloud is distorted. electric

field gradient in this state of distortion;

the

In the state b

field gradient vanishes.

In both states

a and b the solvent molecule is a member of the first solvation is the probability are the residence the rotational

of finding the solvent molecule

shell; Pb

in state b; r a and,T b

times in state a and b, respectively;

correlation

aoproais the

ra the subscript a means

state a and the subscript r that the force is repulsive. the ion is no longer distorted;

V

Pb >> Pa"

TC

is

time of the vector connecting the ionic nucleus

with the collision partner. Now each collision of the ion with a solvent molecule ~roduces

a state

300 a.

If

gl

is the number of collisions ~er unit time, then T a =

room temperature

in liquid glycerol

and glycerol molecules -ii

of the order of I0 T -I/2

is approximately s.

7 x IO ll s -1, that is T

The term)erature

dependence

Tc* is of the order of 10 -8 s; consequently

From these values one sees that within 200 OK it should not be possible ing to ~ T

c

At

the number of collisions between Li + should be a is given by T a I/T a >> I/Tb, I/T c .

the temperature

range 400 oN > T >

to find a relaxation maximum correspond-

= I if the collision model is correct.

MODEL USING THE DISTORTION

OF THE COMMON ELECTRONIC

SYSTEM OF Li + AND THE

FIRST SOLVATION SHELL

Again,

in principle,

G(~):

however,

eqn.

gWsa2

(15),

(16) may be applied:

exp [-(--Ta + "rb

(17)

~c,)t]

now the state a is such that one of the solvent molecules has left

its tetrahedral distortion.

position. V is the field gradient in this state of sa In most cases, when the solvation sphere is in this activated

state a, a solvent molecule exchange

takes place.

Then

d

Ta z___

where d is the diameter of the solvent molecule and ~ is the mean thermal velocity of the solvent molecule. With d'5 ~ we find for glycerol T = -12 c 2 x I0 s. This again much shorter than Tb which is at least of the order of 10 -8 s at 25 °C.

We see that, if such a very short-lived

distorted

state of the solvation sphere were the source of the relaxation process, then in the temperature could not occur•

range 400 OK > T > 200 OK a maximum relaxation

We may also rewrite eqn.

~PaV 2 G(t)=

g

sa

(17) in the form

[l (l +Pb)+ J ] exp-

~b

Pa

If during the solvent exchange the replacement sive character,

rate

Tc*

(17a)

~

is slow, that is of diffu-

then Pa " Pb and the total effective

correlation

time

801

1

2

1

"7'cl = Vb

(18)

+ We*

is the fact of the order of iO

-8

s.

Of course such a situation can occur

only in the event of rather weak solvation. that the maximum of the relaxation

In this case we should expect

rate can be obtained in the temperature

range to be considered here.

THE ELECTROSTATIC

MODEL

For ions such as Li + the correlation G 1 and G 2.

function consists

G 1 is due to the first coordination

caused by the remainder of the solution.

of two Darts,

sphere of the ion; G 2 is

As has been shown elsewhere

[12a]

we have

GI = ns

2[9m(I+Y~)~2exD(-t/Tsl )

~5

[l-exp(-6 %) ]

r 4 o

24~ G 2 =-~-

[m(l + y ~ )p]2 r* 5

1

+ _I,

-

~sl

I Trl

;

Tcl

I

I exp(-t/Ts2) Csolv

-

rs2

1 rr

(19)

(20)

+ _ ,1 Tc2

(21)

where n

is the first solvation number of the ion; m the electric dipole s moment of the solvent molecule; y~ the Sternheimer factor [I0,II]; P the polarization

factor [12a]; ~ the distance between relaxing nucleus and o point dipole of solvent molecule in the first solvation sohere; r, the closest distance of approach of solvent dipole towards the central ion t the first solvation sphere; Csolv the solvent molecule concentr~ion

outside

(particles

cm-3);

first solvation quenching

% the parameter

sphere from cubic symmetry,

connecting

sphere;

relative

Tcl* the rotational

% > 0 (for X = 0 we have total

sphere;

in the first o time of the vector r °

in the first solvation sphere;

time of the solvent molecule

the first solvation

Trl the reorientation

to the vector ~ correlation

the ion with the solvent molecule

T r the reorientation r* outside

the degree of distortion of

of field gradient due to exact syrmnetry);

time of the solvent molecule solvation

describing

relative

to the vector

and Tc2 the rotational

correlation

302 time of the vector r* connecting, the first solvation sphere~

the ion with a solvent molecule outside

The total correlation

function

G = GI + G2

(2Oa)

is a sum of two exponentials. represents

Indeed,

only an approximation.

time as an effective quantity in eqn. actually

this is a suitable

any time dependence

given so far

Thus, if we introduce one correlation (Ii) or eqn.

(12) this means

average of the time costants

that

given in eqn.

c = ~ITsl + ~2Ts2

~i + ~2

(21):

(22)

= i

In the case of very weak solvation we may drop G 1 in eqn. we have to replace r, in eqn.

(20a).

Now

(20) by r . Then a comparison of e~n. (18) o time T c and Ts2 will be of the same

and (21) shows that the two correlation order,

i.e. approximately

10 -8 s.

Thus, in this particular

our present method one cannot distinguish distorted cormnon electronic model.

V

sa

the model of

state of solvation sphere and the electrostatic

But in the electrostatic

rate can be calculated,

formally between

situation using

whereas

theory the absolute in the electrostatic

value of the relaxation theory the quantity

is unknown.

CORRELATION

TIME CONNECTED WITH MAGNETIC DIPOLE-DIPOLE

By the statement

that the correlation

equal we have already postulated

that T

INTERACTION

times T and are about -8 c TS2 S. However, we wish to

= I0

c confirm this estimate experimentally ; so measured

the proton relaxation

rate of the solvent using the same solution for which the 7Li relaxation was measured. The proton relaxation

!

rate is given by the formula

rl]:

= 2 yi4~2I(i + I) [J(m) + 4J(2m)]

(23)

2

*)

If we write "rotational

correlation

time" this means "correlation

time of spherical harmonics of order two". identical with the correlation order.

"The reorientation

time" is

time of the spherical harmonics

of first

303

Here the spectral density J(m) is the Fourier transform of the time correlation function for the magnetic dipole-d~pole interaction g(t):

J(m) = f %

(24)

g(t) exp (-iwt) dt

The time correlation function

g(t)

contains a contribution due to the

intramolecular magnetic divole-dipole interaction and a contribution due to the intermolecular dipole-dipole interaction.

For glycerol in the

temperature and frequency region of main interest, the intramolecular contribution is about twice as large as the intermolecular one [22a].

The

effective correlation time characterizing the decay of the intermolecular correlation function is of the same order of magnitude, but it is longer than that of the intramolecular part.

Let us denote the rotational corre-

lation time of the glycerol molecule by ~2"

In fact z2 is not very well

defined because the glycerol molecule is not rigid [22,23].

Together with

the intermolecular contribution we get an effective correlation time

T2,' = T2(I + e)

where E is a quantity of order unity. T2 may be expressed in terms of the correlation time of the vector connecting the solvent molecule with the cation and the reorientation time of the solvent molecule relative to this vector.

For a solvent molecule residing in the first coordination suhere

of the cation we obtain

I T~l) 2*

I I (1 + E "-I) = T--el* + T r

(25a)

and with eqn. (21)

i = T2,~2)

I (I + c) -I Tsl

(25)

For a molecule residing in the second coordination svhere we have

-$" C2) = T * and with eqn. (21)

+ C2

(I + C) -I

(26a)

304

-

I T (2) c*

I

+T

(I +

(26)

2

and, finally, for the bulk of the liquid including the surroundings

of the

anions

1

= 3

~2 ,(3)

(27)

(I + E) -I

Tr

The quantity 3 (I/T r) in eqns.

(26a) and (27) appears because ~r and T 2 are

for first-order and second-order

spherical harmonics,

respectively

r4,24a].

In the first solvation sphere, when fast (jump like) solvent replacement occurs, the factor 3 is absent [1,24a].

The observed dipolar correlation

time r d is the average of the three correlation times given in eqns. (25), (26),

(27):

z d : ZIT2~I) + X2T2~2) + %3~2~3)

= (I + ~ )

X ITsl + X2

Ts2 T r + X3 ~ ) T r + 2Ts2

(28)

X1 + X2 + X3 = I where the 7(i are the mole fractions of solvent molecules occurlng in the ith region around the central cation.

The observed d~polar correlation

time according to eqn. (28) has to be compared with the observed quadrupolar correlation time as given in eqn. (22).

It will be seen that T

c

and T d are not exactly the same but TC/T d = I is to be expected. The time constant T d determines the correlation function

rl]

g(t) ~2566) exp (-t/Td)

(29)

which gives the Fourier transform I 4r d Jd (~) =15--~6 1 + 2 Td 2

b is the representative

intramolecular proton-proton

(30) separation in the

305 glycerol molecule. Then again,

the determination

varied by temperature

~d

change yields

of the maximum of I/T 1 when T d is T d via the relation

= 0.62

(14a)

In this way the effective

correlation

time of the dipol-dipole

can be compared directly with the effective

correlation

interaction

time of the quad-

rupole interaction.

EXPERIMENTAL

SECTION

All measurements of a home-made

were carried out on a Dulse sDectrometer

rf-transmitter

two other pulse spectrometers)

and receiver.

(Mineal 523, Dietz, Mulheim,

F.R.G.).

A re-entrant

[24b].

with three teletypes, a multitasking

This set of instruments

were connected

system is as follows

The organization

control

one for each spectrometer,

that are necessary

within the pulse sequences

(and

computer

of the commuter

steering routine eormnunicates and assembles

the input in the pulse

for the desired measurements

which are executed by a real time-operating

home-built

to a process

mode in several control strings which describe

sampling sequences

consist;ng

system.

and

The pulse distances

are generated by the executive by means of a

program-controlled

clock with a precision

of ~ l~s.

The pulse

lengths are produced via a 12-bit counter with a clock frequency of I0 MHz. The analog signals were read in by an analog-digital

converter having a

clock frequency of i00 MHz.

of the signal-to-noise

ratio accomplished improvement signals

Not only is improvement

by signal accumulation,

but also at the same time

has been achieved by integration

recorded.

over certain ranges of the

All proton relaxation measurements

as to give T I = 3.60 s for pure water at t = 25 °C. 7Li and 133Cs relaxation obtained previously

were standardized Correspondingly

times were compared with experimental

in this laboratory.

given as a function of the temperature.

results

All the reported measurements

are

The tenmerature was controlled by

a gas stream through a Dewar probe head which contained the sample. needed,

so

the

If

the gas was cooled by passing through a cooling coll inmaersed in

liquid nitrogen.

Within the Dewar probe head the gas was heated to the

desired temperature by variation

of the electric heating Dower.

The actual

temperature was measured in the gas stream by aid of the thermocouple

306 +

directly

in front of the sample.

Temperature

0.3 °C during the total measuring

time.

As a check,

also measured directly behind the samnle. observed a temperature

difference

points which corresponds sample sample.

to a temperature

~ith l o w gas flow rates we the two measuring

gradient of 1 °cm -I along the

of the sample" we took the mean value

on the assumption

linearly along the sample.

the temperature was

of up to 3 °C between

As the "temperature

of these temperatures

constancy achieved was -

that the temperature

varies

Of course, all samples were carefully

freed

from oxygen in the usual wav. All salts were of highest purity cormmercially available CsCI, CsBr,suprapur,LiI'2

H20 , ~erck AG Darmstadt).

at about 120 °C before use. weighting

The solutions

Normal glycerol,

according

a water content less than 0.I wt. %. ~urchased

in glycerol were prepared by

in the glove box under a dry N 2 atmosphere

P205 [22a].

form ~erck,

solutions was checked bv titration.

and in the presence of

to the producer

(Fluka, Basel), had

The fully deuterated

Sharp and Dohme, Canada;

deuteron content of better than 97 %.

(LiCI, LiBr,

The salts were dried

glycerol-d 8 was

the producer quotes a

The water content

in the glycerol

When the water content was greater

than 0.2 %, the sample was heated to IO0 °C and dry N 2 was bubbled through the liquid for about three hours For the solutions ent, ~erck)

r22a,b]; then the sample was sealed off.

in D20 , LiI'2 H20 was dissolved in D20 (99.9 % D20 cont-

and most of the protons were removed by a remeated solvent

evaporation and dissolution procedure.

The salt concentration was

determined by titration.

RESULTS

THE MAGNETIC RELAXATION OF 7Li IN GLYCEROL

CORRELATION

TIMES

The electric quadrupole moment of 7Li is comparatively the magnetic moment

is relatively

large.

small; however,

This leads to the expectation

that part of the relaxation is also due to magnetic dipole-dipole action

[4,14,25-27].

Therefore, with regard to the present problem, as

the first step one has to examine what is the contribution dipole-dipole

inter-

interaction relative

to the quadrupole

procedure

is straightforward.

solvent.

Then the difference of the relaxation

of the magnetic

interaction.

The

One dissolves Li + in the fullv deuterated rates in the normal

compound and in the deuterated one is the relaxation Dart caused by

3O?

magnetic dlpole-dipole interaction.

The results of the corresponding

experiments are shown in ~igs. I and 2. recognized from these drawings:

Two facts may immediately be

(i) In both solvents, glycerol and glycerol

-d 8 the relaxation rate has a maximum at a certain temperature;

(il) In the

range of the maximum which is the only region of interest in this section, the relaxation rates i n t h e

two solvents differ very little.

Thus the

magnetic dipole-dipole contribution is small compared with the quadrupolar part and for simplicity in the present section we shall take the total 7Li relaxation rate in the solvent glycerol as being caused bv ouadrupole interaction.

Then we chose as a weighted average at the maximum of the

total 7Li relaxation rate

~T

c

=

0.58

(14b)

We shall return to the discussion of the detailed features of Figs. I and 2 below.

1_ T1

TI

sec -1

sec-1

5O

5O

2O

20"

10

10

5

2

1

f 2B

5

2

3.0

3.2

3/* Fig. I.

3.6

38

I

40

loo,.o ~-oK-1 T

1 ~

o

K Fi(:J,2.

Fig. I

7Li relaxation rates in c = 4.9 m solution of LiBr in glycerol (O) and glycerol-d_ (e) as a function of the • temperature. Concentratlon is given in the aquamolality scale (moles salt/55.5 moles solvent). Lower smooth curve represents difference between two upper curves.

Fig. 2

7Li relaxation rates in c = 9.3 ~ solutions of LiCI in glycerol (O) and glycerol-d 8 (e) as a function of the temperature. F~r other details see legend of Fig. I.

T

308

iI

: ~ set-1

~"

30 MHz

1H

50

20

2

3b 3:2 3.'~ 3:6 ~:8t~.8 3.b 312 3'.4 J.6 3.'e ,:olT_ ~_ oK-~

2.8

Fig. 3

7Li relaxation rates (0, 16.4 ~; I, 6.8 ~; V, 2.9 m) ~nd proton relaxation rates (A, 16.4 ~; A, 6.8 ~ , Q , 4.9 F~;m, 2.9 ~; +, I ~) of various Li bromide solutions in glycerol as a function of the temperature.

sec -1 1

30 MHz

~ I

. ~.~ 1H 12 MHz

~

~

50

20

10 5" 2-

Fig. 4

-1 T 7Li relaxation rates ( 0 : 1 1 r~ (1:9.3 ~, e: 2.9 m--) and proton relaxation rates (A: l l r~, A: 9.3 ~, A: 6.9 N +: 1 ~) of various Li chloride solutions in glycerol as a function of the temperature.

309 In Figs.

3 and 4 we present further 7Li relaxation results to~ether

with proton relaxation rates in the same LiCI and LiBr solutions, as a function of the temperature for various concentrations and frequencies. may be shown that at the maximum the relaxation rates at different

It

frequen-

cies should satisfy the relation

(I/Ti)max

w' =

--

J

(i/Tl)ma x

In our case ~'/m = 2.5 and the ratios

(I/Tl)ma x /(i/Tl)~a x

lie between

2.25 and 2.54 which shows the quality of our measurements. The most important feature of these figures is the observation that in all cases the maxima of the 7Li relaxation and the proton relaxation are very close to each other. from eqns.

(14a),

T

At these maxima the correlation times as derived

(14h) are

c

= 7.7 X 10 -9 S for 7Li

T d = 8.2 x 10 -9 s for IH

when the frequency was v = ]2 MHz, and

= 3.1

x 10 -9

s

For

7Li

"rd = 3 . 3

x 10 -9

s

for

Itt

T

e

when the frequency was

v = 30 MHz.

In Fig. 5 we give temperatures at which the relaxation maximum occurs (which is also the temperature at which

Tc and Td, respectively, have the

values as given above) as a function of the salt concentration. be seen from Fig. 5 at all concentrations

the temperatures

As may

corresponding

to a given correlation time are almost the same when the correlation time represents a quadrupolar or a dioolar mechanism. given temperature,

Thus, reversely,

at a

the correlation time of the quadrupole interaction and

that of the dipole interaction are very close to each other. In order to present this result in a yet more distinct way we wish to transform all our correlation

times to one single temperature.

This can

310 T

-A~

12 M H z

30 M H z ii0

Fig. 5

i15

Temperatures of the maximum relaxation rate as a function of salt concentration for LiBr and LiCI solutions in glycerol. Open symbols, Maxima of Droton relaxation rate (O, LiBr; A, LicI) filled symbols, 7Li relaxation rate (quadrupolar mechanism, O, LiBr; A, LiCI).

only be done approximately.

I/T

should yield directly

At high

temperatures the slope of

I/T 1

versus

the activation energy

T

c T

because,

(Ea/kT)

= exp O C

according

to eqns.

J(~o) "+ 2T

(Ii),

(30)

V(O) 2 C

4 Jd(m) ÷ ~-Sb 6 T d when ~Tc, m~d become much less than I. a function of the temperature.

However,

In a suitable

E a / R = 4.8 x 103 for all systems.

i.e.

12 and 20 MHz, the resulting

Ea/R

= 6.5 - 8.5 x 103.

partly due to the fact that the time correlation exponential.

The functional

vary as the temverature

mind that the experimental difference

However,

function may

it should also be kept in

error may contribute somewhat

in activation energies.

This is

function is not strictly

form of the time correlation

decreases.

is itself

range we find

On the other hand, if we use the

(i/Tl)ma x values at the two frequencies activation energy is much larger,

in g l y c e r o l E a

temperature

to the great

In the present situation we chose a

311 mean value of E /R = 6 x 103 for the transformation of the correlatien a times to a common temperature. As the reference tem0erature we take the temperature at which (i/Tl~ax for 12 MHz occurs for pure glycerol [4], that is

T = 274 OK

(see also ref.

22).

Then IO00.~ [6(3.65 - T )] max

(31)

Td(C* ) = 8.2 x 10 -9 exp [6(3.65 - TI000.) ] max

(32)

T (C*) = 7.7 X 10 -9 exp c

and

The result is shown in Fig. 6.

It may be clearly seen that the correlation

time of the quadrupole interaction is the same as the correlation time of the magnetic dipole-dipole interaction.

At low concentrations

the quad-

rupolar correlation time is slightly longer than the dipolar one.

This

should be so, because the motion around Li + is slower than in the bulk and according to eqn.

(18) the proton relaxation rate measures

correlation time over the entire solution.

the mean

At higher concentrations

the two correlation times are virtually the same; here in eqn. Actually in eqn.

then

(28) X 1 "

I.

(28) instead of Tsl there should also be a combined

expression

Tsl T r Tr

with O
+ k'

~Is

This would make T d

<

Tsl , but obviously this effect is just

compensated by the factor 1 + g. Summarizing we arrive at the following result:

The correlation time

of the quadrupole relaxation is about the same as the rotational correlation time of the solvent molecules.

Consequently

the collision model and

the symmetric ion-solvent electronic state model with fast solvent molecule replacement can be excluded. Since a symmetric common electron state model with slow, diffusive,

312

10-8

sec

•C.c, -C'd

.

.

i.

C~

5 Fig. 6

10

15

ff~

Correlations time T A for magnetic dipole-dipole interaction (opens symbols) and~eorrelation time T for quadrupolar relaxation mechanism (filled symbols) ~s a function of the salt concentration in solutions of LiBr (0, e) and LiCl (A, A) in glycerol. The temperature is T = 274 OK.

313 solvent

replacement

should

have

about

the

same

corresponding to molecular reorientations

correlation

time

as

the

one

this latter possibility cannot

strictly be ruled out.

THE ABSOLUTE VALUE OF THE RELAXATION RATE

We have now to investigate whether the absolute value of the quadrupolar part of the total relaxation rate can be accounted for in terms of the electrostatic

theory.

If this should be so, then this fact would very

strongly support the validity of the electrostatic model. The procedure of calculating the absolute value of the quadrumolar relaxation was as follows: In eqns.

(2), (3), (4) we introduced the soectral

densities which were obtained from the correlation functions (2On).

Next the suitable numerical values were inserted,

(19), (20),

i.e. the nuclear

and electronic quantities

Q7Li = - 0.042 x 10 -24 cm 2

I + ¥o~ = 0.74

m =2.67 D

From the density of glycerol and from a molecular model we estimated the radius of the glycerol molecule:

Pgl = 2.8 ~; rLi+ = 0.7 ~.

Then for the

distance of the point dipole in the first solvation sphere from the central ion we estimate that r

= 3 R; for simplicity we set r, = ~ . Furthermore, o o we set P = i which implies the assumption that delocalized quenching effects of the field gradient are absent in glycerol solution [I]a,15]. mentioned,

As already

the correlation time in the first solvation sphere of Li~ differs

from that in the bulk; we set

Tsl = bTs2 = b~ d

Use of all these quantities in eqns.

l

o1= 26.7 x 108/

(3) and (4) gives

%2 1 + 4oJZrs22

+11.7 [I- exp(-6X)]

brs2 i s-2 I +4(~2Ts22b2 l (33)

314

a 2 = 26.7 x i08~~ !

TS2 - + ll.7[l-exp~6~] I +t~2 2 Ts2

With our value for the activation glycerol we set for Ts2 in eqns.

(33),

1 + O2Ts22b 2 I

3.0)] s

since the apparent activation energy of the quadruDole

interpreted

this deficiency

smaller,

smaller.

relaxation

(Ea /B = 5 x 103 ) we

in activation energy as being due to an

increasing symmetry quenching effect as the temperature means in terms of eqns.

motion of

(34)

in the range IO00/T < 3.2 K -I is somewhat

I becomes

~ s-2 04)

energy for the reorientational

Ts2 = 1.46 x i0 -I0 e x p [ 6 ( ~ -

However,

bTs2

(33),

decreases, which

(34) that at lower temperature

the parameter

By some preliminary

fitting attempts we were led to the

exD (- 0.8 103 --7- )

(35)

relation

I = I

o

With these data the motion of the magnetization

according

to eqn.

(2) was

computed with a first trial set of the two quantities b and I . Then by a o least mean square fit over a suitable range of time t the motion was approximated by a single exponential. corresponding

This gives the effective T 1

to the fact that in all cases only an ordinary exoonential

decay of M z o _ M z o was observed. the experimental

This commuted

one at all the temperatures

(Tl)ef f was compared with

investigated.

In the next

step a new set of the two parameters b and %o was tried, a new (Tl)ef f was found by least mean square fit to the computed motion of the magnetization, the result was again compared with the experimental optimal agreement with the experimental optimization procedure Bromin coincides

[28].

T 1 and so forth until

results was achieved using the

The results of this commutation

virtually with the solid line drawn through the experimental

points of Figs.

1 and 2; only at the lowest temperatures

results differ markedly

from the experimental

lines give the computed relaxation rate. are

LiBr:

b = 2.1; I

o

= 1.0

do the computed

behaviour;

here the dashed

The parameters

of the best fit

315 LiCI:

b = 2.7; % = 0.8 o

Are these values acceptable ? which we know already; 6.

Clearly the results for b are the values

to a good approximation they can be taken from Fig.

The temperature dependence of the interaction factor via the quenching

parameter % introduces a slight shift of the resulting T . With eqn. (35) c our result for % yields % = 0.055 at T = 273 OK which means that the field o gradient is reduced to 30 % of the value we had in the absence of local symmetry. %

Of course,

it may be considered as a very small deficiency that

is slightly smaller for the LiCI solution as the high ion concentration

o should in any case destroy local sym~netry around an ion.

In much of our

recent work, and also in non-aqueous solutions, we used the model of nonlocalized quenching of the field gradient, factor P # i.

From electrostatic arguments

is suggested and usually used.

that is we put the polarization !9,11ajl2a],

the figure P = 1/2

This would give a reduction to 25 % of the

field gradient without any correlation effect.

One sees that our results

for % is very reasonable and we can safely conclude that the electrostatic model is completely satisfactory.

IHE DIRECT ION-ION CONTRIBUTION

From the point of view of a naive electrostatic model one would expect that the ions themselves, being re~resented by point charges should give a distinct contribution to the quadruDolar relaxation rate.

In contrast to

this, insDection of Figs. I - 4 clearly shows that the absolute value of the relaxation rate at the temperature of the relaxation maximum is virtually a constant quantity and does not increase with the ion concentration.

As we see from eqn.

(12), if the ions contribute to the mean

squared field gradient V(O)2 I, such an increase of the relaxation rate must be observable.

Indeed, the observation that the ion contribution to

the quadrupolar relaxation rate is unmeasurably small is not unique.

In

aqueous solutions the halide nuclear magnetic relaxation rates in Li + solutions show very weak ion-ion effects up to appreciable concentrations [13], whereas the 7Li+ relaxation in the same solution suffers a strong increase over and above that which is to be exvected from correlation time effects

[14].

Obviously in glycerol the anions do not approach closely

towards the Li + ions.

Formulas

for the calculation of the ion-ion-

contribution have been given elsewhere [12b]°

A suitable evaluation yields

a fairly short correlation time for the ion-ion contribution

316

(T ' = 1.2 x 10 -9 s at T = 286 OK [29]) and at 300 OK the relaxation c contribution is only 1/30 of that due to the glycerol molecules [29].

In

Figs. 1 and 2 at the lowest temperature the experimental relaxation rate lies well above the computed one corresponding to the glycerol effect; possibly this additional relaxation effect is due to the ion-ion contribution with its short correlation time (and other fast processes).

THE MAGNETIC DIPOLE-DIPOLE CONTRIBUTION TO THE 7Li RELAXATION ~ATE

We shall now discuss the difference between the two under curves in Figs. 1 and 2 which reoresents the magnetic dioole-diDole contribution to the 7Li relaxation rate.

This contribution is caused by the magnetic

moments of the solvent urotons.

As we are concerned with an interaction

between different nuclei we should use the formula for "unlike nuclei" [I]

= KLi

*2 1+ (wl-~s) 2 rc

2 ]+~I

*2 Tc

1+(Wl+Ws) 2 rc.2 (36)

2

KLi = ~ y~y2~2 S(S

+

l)nH

(36a)

r6

where mI is the magnetic resonance frequency of 7Li (angular frequency); magnetic resonance frequency of IH (angular frequency); S the shin of proton (S = 1/2); YI' Ys the gyromagnetic ratios of 7Li and IH, respectively; r the distance between Li + and the centre of solvent molecules in the first coordination sphere; and

n H the number of urotons in the first

coordination sphere (nH = 8nq in glycerol).

In eqn. (36) the contribution

from all the solvent protons outside the first coordination sphere is neglected. Since

= 2.57~f we have

lLiH (

S

= KLi +

T

i + 2.48~i 2r *2 c 2TG* ]

I + 12.72~/TC'2 J

C

*

+ 1 + ~_r2r *2 c

(37)

317

and numerical evaluation shows that at the maximum of (I/T I)

LiH

at given

frequency

~0fTc

= 0.69

(38)

and

! ]eiH : Tl/max

(39)

KLi 0.77mI

It can be seen that the curve revresenting (I/TI)LiH for the LiCI solution (Fig. 2) is markedly shifted towards higher temveratures which corresponds to slower motion.

This effect is not so strong for the LiBr solution

which is of lower concentration (Fig. l.).

From Figs. I and 2 we find

(~a(LiBr) = 3.52 x 10 -3 °K-I

3.34 x 10 -3 °K-I

According to eqn. (38) at these temperatures~ 12 MHz).

*

= 9.2 x I0

-9

s (w/2~ =

When we transform this correlation time to our standard temper-

ature T = 274 OK (with Ea/R = 6 x 103 ) we obtain

T

= 2 x 10 -8 s for 4.9 m LiBr solution

c

e

= 6 x 10-8s for 9.3 m LiCI solution

Let us discuss these results.

For the situation of independent transla-

tional motion of the two pair partners we estimated * T

which gives rc glycerol.

*

c

12b,30

~ r 2 ~ --

3Dg I

= 3 x 10

-7

s.

D g I is the self-diffusion coefficient of

In the pure liquid Dg I = D gol o ~ 2.0 x I0-9 cm2/s at 274 OK [31]

at high salt concentration D g l ~ (I/2) Dgl, D L i + ~ D g l .

We see that this

time is one order of magnitude longer than T * for the LiBr solution. c Thus the model of independent translational motion is not correct; rather

318 we seem to h~ave short time fluctuating attachment of the small Li + ion to the surrounding glycerol molecules. In the more concentrated LiCI solution * r comes closer to the estimate corresponding to independent translational c .L~H motion. However, it should be kept in mind that (I/T1) is a rather small difference of two larger quantities and as such it has a relatively large exuerimental error. Lastly we compute r, the distance between the Li + ion and the uroton in the first solvation sphere. eqn.

Introduction of the nuclear quantities in

(36a) yields

KLi = 2.58 x 10 -38 and with

nil6 (r i n cm) r

"I/T l)max .LiH = 6.5 s -I we obtain from eqn. (39) with n H = 32 (~/2~ =

12 MHz)

r=3.3~ With

r = 2.8 ~ and g

Li + = 0.7 ~ this result is fullv satisfactory.

ION RELAXATION OF 133Cs DISSOLVED IN GLYCEROL

A relaxation mechanism based on distortions of the electron cloud may indeed not be expected to be very efficient for Li + because here the number of electrons is exceptionally small.

This situation is quite different for

Cs + with its many electrons and thus, in order to give support for the electrostatic model on a broader basis, we report some experimental results + concerning Cs dissolved in glycerol. Fortunately, the quadrupole moment of |33Cs is rather small, so that its magnetic relaxation time can be measured over wide ranges of temperature and in practically all organic solvents - if there are salts of sufficient solubility.

This is not so

easy or even impossible for other ions with noble gas structure and a high number of electrons.

Here under certain conditions

become extremely short present study.

[15,16,18,19].

the relaxation times

133Cs has another advantage for the

Its magnetic moment is small.

As a consequence the nuclear

magnetic relaxation is exclusively caused by quadrupole interaction. was already known from aqueous Cs + solutions

[32].

This

We checked the correct-

ness of the statement again by performing part of our measurements in fubly deuterated glycerol

(glycerol-d8).

the same as in normal glycerol.

The results in this solvent were almost The corresnonding ex-oerimental data are

319 presented in Figs.

7 and 8.

This behaviour shows that the dvnamical iso-

tope effect which occurs when the IH nuclei are replaced by 2H nuclei is small and may be neglected.

With our Li salt studies in glycerol we did

not apply any dynamic corrections regarding

isotope effects, and we find

the justifications for this omission in our 133Cs relaxation results. However,

133Cs has one appreciable

already mentioned in the introduction, Hubbard

disadvantage for our study.

As

the spin of 133Cs is I = 7/2.

r21] showed that in this case the variation of the magnetization

with time should be described by a combination of four exponentials. However,

explicit formulas are not available.

The only region which can

be studied quantitatively is the one for which the fre~uencv dependence of I / T I disappears;

this is the region of "extreme narrowlng " ,, [I]" here mT <
which for the Dresent system occurs at temperatures above room temperature. Thus, in the so-called dispersion range, i.e. in the range where I / T I is frequency dependent, we have to be content with a aualitative evaluation of our experimental

results.

The most important information we are seeking is the correlation time for the quadrupolar relaxations.

As before,

if we find a maximum of the

relaxation rate as a function of the correlation time (or as a function of the temperature),

then, at the maximum the correlation

time is determined

by the resonance frequency

~T

e

=

K"

But for 133Cs the constant K" is not known.

All we ean do is to estimate

K" = 0.55 so that we have the same interconnectlon between T

e

and m as for

7Li, the other qnadrnpolar nueleus we studied in this work. All our relaxation results in Cs halide-glycerol in Figs. 7 and 8.

solutions are shown

It may be seen from these figures that the maxima of

the quadrupolar relaxation of 133Cs occur in the same temperature range where they were observed for the 7Li relaxation;

furthermore,

at the

resonance frequency 12 MHz, the maxima have practically the same position on the temperature scale as the maxima of the proton relaxation rates in the same solution.

T

c

T

Again, at these maxima for the 12 MHz curves we have

= 7.3 x 10-9 s for Cs + 8.2

d

x

10 -9 s for IH

320 As w i t h t h e Li + s o l u t i o n s

t h e c h a n g e o f t h e r e s o n a n c e f r e q u e n c y f r o m 12 to

30 MHz shifts the maxima towards lower IO00/T values

(higher temperature):

= 2.9 X 10-9 S for Cs +

T C

Td

3.3 X 10 - 9 s f o r

1H

and the ratios of the maximum relaxation rates at low and high frequency are very close to 2.5 as they should be.

The maximum of the 133Cs

relaxation rate in the II m CsCI solution is markedly lower than those of these two other CsCI solutions.

This must be due to a systematic error

caused by some misadjustment of the apoaratus.

Here the oosition of the

maximum on the lO00/P scale should be taken as the only valid experimental result.

1 sec 1

r~ I0C

~4Hz

10£

12MHz x/

/

"°; 0

2'~ 2~ ~io J2 ~ JG 3!~ ,oj~,K, F~ 7

~\× MNZ

J6 218 ~'o ~'~ 3', j~ 3'8~'=., Fig. 8.

Fig.

7

133Cs r e l a x a t i o n r a t e o f a e = 4.9 ~ CsBr s o l u t i o n i n glycerol (0) and g l y c e r o l - d ~ (A) as a f u n c t i o n o f t h e t e m p e r a t u r e (12 ~fl~z). P r o t O n r e l a x a t i o n r a t e o f t h e same s o l u t i o n a t 12 t ~ = (O) and 30 ~ z ( x ) .

Fig.

8

133Cs r e l a x a t i o n r a t e o f v a r i o u s CsC1 s o l u t i o n s (O, 4.9 ~ ; , 9 . 0 ~; +, 11 ~) i n g l y c e r o l and a e = 4 . 9 ~ CsC1 s o l u t i o n i n g y c e r o l - d 8 (/~) as a f u n c t i o n , o f t h e t e m p e r a t u r e (12 MHz). Proton relaxation rate of a e = 9 ~ CsCI solution in glycerol at 12 MHz (O) and 30 MHz (x).

Apart from the coincidence of the temperature of the proton and Cs relaxation maxima the most striking feature of Figs.

7 and 8 is the fact

that now all these relaxation maxima occur at temperatures

lower than 274

OK (100/T = 3.65) which corresponds to the pure solvent glycerol.

In

contrast to this, for Li-halide solutions the maximum of relaxation occur+ This means that Cs causes an acceleration of

red at higher temperatures.

321 the molecular motion as compared with pure glycerol. known;

glycerol is one of the solvents

in which the so-called structure

breaking effect is produced by large inorganic of the most obvious manifestations observation

This effect is well

ions with low charge.

One

of the structure breaking effect is the

that the molecular motion becomes

faster than in the neat

liquid. From the temperature and 8 we computed

a fixed temperature eqns.

interaction

time of the magnetic

1~

Fig. 9

The result is given in Fig. 9 a n d i t

time of the quadrupolar

the correlation

rate taken from Figs.

7

times of the proton and Cs relaxation at

274 OK as a function of the salt concentration

(31) and (32).

correlation

of maximum relaxation

the correlation

is virtually

dipole-dipole

using

shows that the the same as

interaction.

¢* 115~ ~

Correlation time T d for magnetic dipole-dipole interaction (open symbols) and correlation time T for quadrupolar relaxation mechanism (filled symbols)Cas a function of salt concentration in solution of CsBr (O,e) and CsCI (A,A) in glycerol. The temperature is T = 274 °K.

Next we have to examine whether the absolute value of I/T I can be calculated

satisfactorily

in terms of the electrostatic

model.

At suffic-

iently high temperature we may apply eq. (12) with x I = x 2 = i. consider I/T I at T = 333 OK, i.e. IO00/T = 3.0 i.e. we set G 2 = O.

This corresponds

model defined by us previously

[16].

erature is 5 s-l; the correlation

Let us

First we use eqn.

(19) alone

to the FOS (Fully Oriented Solvation) The Cs relaxation

time is T

rate at this temp-

= 1.5 x iO -I0 s.

Then, with

c

the numerical

quantities

calculated r

= 3.9 ~.

as above and y~ = IIO, P = 1/2, n s = 6, % + oo we This is 15 % less than the sum of the ion radius

O

(= 1.65 ~) and the radius of glycerol of a non-orientated

solvation sphere

assumed to be 2.8 ~.

With the model

[16] (NOS model) we find r

= 3.6 ~, O

still a reasonable value.

In the NOS model the strict radial orientation

of the solvent electric dipoles in the first coordination by random orientation.

Finally,

sphere is replaced

the fully random distribution

[16]) which is described by the exDression G 2 according to eqn.

(FRD model (20) (r, =

ro) yields r ° = 2.54 ~ which indeed seems to be too small and which shows that the third model probably is not realistic.

322 Summarizing,

we have shown that for the nuclear magnetic relaxation of

133Cs + dissolved in glycerol

the electrostatic

model is also fully satis-

factory.

THE MAGNETIC RELAXATION OF 7Li ANDI33cs

The electrostatic rupolar relaxation ready indicated,

model yielded an acceptable

rates in aqueous

confirm the correctness

Li halides

conditions,

(apart from fluoride)

trated solutions temperature

of the quadAs a]-

at room temperature we are in the i.e. ~

of the electrostatic

of the correlation

explanation

solution at room temperature.

for aqueous solutions

domain of "extreme narrowing"

by a measurement

DISSOLVED IN WATER

<< I. We wished to c model for these solutions also

time ~overnin~

the relaxation mechanism.

are very soluble in water and the concen-

can be cooled down to temperatures

of about-lOO

control is more difficult at such temperatures.

°C.

The

Therefore,

our

results in the aqueous systems probably are less precise and evaluation of the data has been performed

100

in a more qualitative way.

see -1 J_ T1

50,

30

MHz

lo

/

,

i

' ~D

Fig.

10

44

48

52

56

I1- ~ - ° K -1

60

P r o t o n r e l a x a t i o n r a t e ( I 50 ~ z , 0 60 HHz) and 7Li r e l a x a t i o n r a t e (A) i n a e = 6.2 ~ L i I s o l u t i o n i n H20 , 7LI relaxation rate (A) in a o* = 6 ~ Lil solution in D20 ; both quantities are plotted as a function o~ the temperature. Lower smooth curve: difference of -Li relaxation rates in H20 and in D20.

Figure I0 shows the proton relaxation different relaxation

resonance

frequencies

rates in 6.2 m LiI solution at two

as a function of I/T.

Furthermore,

the 7Li

rate of the same solution and of a 6.2 m LiI solution in D20 is

given in the figure.

The 7Li relaxation

rate in the latter system is

323 caused by quadrupole interaction.

It may be seen that the maximum in the

relaxation rate is observable for all systems and that, for a given frequency (here v = 30 ~ z ) ,

the maximum due to the quadruuolar relaxation

occurs at very much the same temperature at that of the proton relaxation rate All pertinent data we obtained from these measurements are collected in Table I.

Table i

SOME RELAXATION AND DYNA~ICAL DATA IN AOUEOUS SOLUTION

Nucleus

iO00 T (°K-l)

Tc,Td

EA/R

(ns)

• * rLiH e

(I/T]~bX

(ns) (~)

inD20

(s-1)

max (I/Tl)al c in D20 F0S modelFRD model

(s-1)

iH

5.4 a)

3.3 b) --3xlO 3

(s-1)

3.~ ) 2.~ )

7Li

5.4 a)

2.9 d) ~ 3xlO 3

9

IH

4.6 c)

8.2 d) 74xlO 3

7L i

4.6 c)

7.3 d) =4xlO 3

30 e)

133Cs

4.7 e)

5.O d) Z4xlO 3

86

112

11.2

280 e)

28 e) 78 e)

a) at 30 MHz. b) at 185 °K. c) at 12 MHz.

d)

at 217 °K.

e) without relaxation contribution of ions.

We did not apply any correction taking into account dynamic isotope effect~

324 For instance the curve for the 7Li relaxation somewhat

towards lower temperatures

rate in D20 should be shifted

because molecular motions would be

faster if the solvent molecule were H20.

This dynamic effect is estimated

to cause a shift of IO - 30 % of the correlation

time.

A number of similar

results regarding Li halide solutions in water may be found elsewhere r34]. Finally,

in Fig.

Ii we present some data which show that 133Cs in

aqueous solution has qualitatively has the samebehaviour

the same behaviour

as the 7Li relaxation

(the experimental

taken from ref. 34).

The solution was a concentrated

whichCsCl was added;

the Cs + concentration was I.i m.

obtained for this solution are also presented that all relevant correlation

results are

LiCI solution

tc

The dynamical

in table I.

data

Again one sees

times are rather close to each other;

absolute value of the relaxation Concluding,

as in glycerol and

the

times can be computed satisfactorily.

we find that in aqueous solutions

as in glycerol

the electro-

static model yields a good description of the observed nuclear magnetic relaxation

rates.

150 ~-I sec-1 100

~

1

1o

I~'~'o Fig. II

Li

~'~ ' ~I~ •

i

, .o~__O_Oo~.~

Proton relaxation rate (0), 133Cs relaxation rate (e) and 7Li relaxation rate (A) in a solution containing 17.9 ~ LiCI and I.I ~ CsCI in H20 as a function of the temperature.

*) When we prepared Harmon

5'2

this paper we learned about a DaDer bv Nutter and

[33] in which the 7Li relaxation

as a function of the temperature.

in i0

These authors

relaxatin rate at about the same temperature

LiCI solution was studied found a maximum o # the

as we did.

However,

they

reported that the 7Li relaxatin rate in D20 is greater than in H20.

This

is in contrast to our finding and also in contrast to all other results so far reported in the literature.

325

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