Demagnetizing field - Journal de Physique II

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76.60J. Demagnetizing field effects on high resolution. NMR spectra in solutions with paramagnetic impurities. E. Belonzky (I), P. H.. Fnes. (2), W. Gorecki. (I) and.
Phys

J.

(1991)

II1

527-541

1991,

MAT

527

PAGE

Classification

Physics

Abstracts

75 20

76.60J

Demagnetizing solutions E.

Grenoble,

(associk

Physique

M.

Jeann~n

CNRS),

au

Cedex, France (Equipe Chimie de

Chimie

DRF

and

(I) Joseph

Umversitb

Coordination),

85X,

BP

Founer,

38041

Grenoble

France

(Received 21

appliqub,

champ

le

expnme

magnktiques

moments

accepted

1990,

December

On

Rksi~mk. aux

Spectromktne

(I)

Gorecki

spectra in

NMR

on

(2), W.

Fnes

H.

Samt-Martin-d'Hdres

38402

CEN

Cedex,

P.

de

Laboratoire

87,

BP.

high resolution impurities

effects

paramagnetic

with

Belonzky (I),

(I) (2)

field

February 1991)

4

dbmagnbtisant

klectromques

la

comme

des

molkcules

d'un

somme

de

diamagnbtique, dfi par le champ paramagnbtiques Les

tenure

solution

la

mduits

klectronJques des impuretbs opposbs, rbsonance nuclbaire les de sont ces signes sur raies calculbs fonction de la su~sceptibihtb dJarnagnbtique de la solution, de la concentration en en molbcules paramagnktiques et de la gbombtne de l'bchantillon direction du rapport I la par champ La thbone est illustrke par une btude de la RMN des protons de (CH~)( en solution dans D~O et couplks I des ions Mn~+ de spin dlevb. Des dbplacements de raies et des klargissements observbs, lorsque la gbomktne du tube est modifibe et, considbrables de plusieurs p p m sont bchantillon sphdnque, les raies observbes dissymbtnques. La thbone et sauf dans le cas d'un sont l'expbnence sont en bon accord effets

d'un

et

de

The

Abstract.

molecular and

of

a

contnbutions,

field

magnetic

ansing

term

from

the

spins

de

demagnet1zlng

electronic

contributions

expressed

is

of

moments

electronic

of

opposite susceptibility of the

two

des

provenant

tenure

deux

signs

on

the

as

the

solution

spins of the the NMR

of

sum

which

paramagnetic line

are

diamagnetic induced by

a

are

impunties. calculated

term

the

The

as

a

due

to

extemal

effects function

the field

of these of

the

and diamagnetic of the molecules solution, of the concentration paramagnetic theory is of the sample with the extemal field The illustrated respect geometry to m D~O solutions coupled with by a study of the (CH~)I spectroscopic Protons manganous Mn~+ high spin shifts and hnewidths of several Considerable paramagnetic are ions. p-p m observed when of the modified and, except for sphencal samples, the the vessel is geometry lJneshape is asymmetncal with the theory is obtained. A good agreement

Introduction.

1.

It

is

to

well

shape of perfectly field

known

relative

axis,

the

that

vessel

containing

was

coaxial shown

of

introduction

sh~fts

cyhndncal it

the

frequency

«

of the

vessels

the

paramagnetic

NMR

solution

l~nes and

positioned

impunties

of the the

field

parallel

and

on

iq

liquid

solutions

g~ves

nse

depend on the Typically, for long and direction. perpendicular w~th respect to the

solvent

nuclei

which

[1, 2] that «j

«~

2 =

arx~~~~,

(1)

where

x~~~~

impurities The

Beconsall

oxygen

under

susceptibility

volume

solution

method

dissolved tubes

the

by

described

[4, 5]

the

is

m

Th~s al. [3]

et

brought is

property as

titration

a

benzene

m

and

field

order

to

authors

several

the

measure

contained

solutions

5

paramagnetic method », first

axis

developed by

was m

of

presence

called

so

al. [2, 6]

hexafluorobenzene

and

by the

the

method et

M

II

about

in

used

improved by Delpuech

was

PHYSIQUE

DE

JOURNAL

528

in

of

titration

sample

sealed

pressure.

diamagnetic solutions or liquids, there are also considerable the NMR l~nes of the liquid nuclei together with This is magnetic sample shape dependent due dipolar to are induced interactions of the with the electronic diamagnetic by the studied nuclei moments demagnetizing field extemal applied magnetic field Then, we have a classical mhomogeneous effect which of l~quid samples. The theory of this investigated m h~gh resolution NMR was mhomogeneous broadening was performed and successfully compared w~th expenmental results tetramethylammonium in heavy water the NMR of protons of solution conceming ions Recently, we have shown [7] important frequency sh~fts « of broaden~ng of the l~nes which

and

of

benzene

pure

purely

in

that

[7]

paramagnetic the study to solutions extend containing previous we field of inhomogeneous demagnetizing the two opposite is sum of the of molecules contributions arising from the field induced diamagnetic moments one : induced of the impurities the solution and the other from the field moments paramagnetic of the impurities with should be It noticed that usually the interact paramagnetic spins solution, through the d~polar nuclear of the diamagnetic molecules of the only not spins scalar interactions responsible for the demagnet~zing field, but also through short range effects which play an hyperfine interactions. these It is very useful to separate two important the

In

present Here

impurities.

role

relaxation

the

in

which

there

paramagnetic But,

effects.

and

a

we

species, in will show

in

D~O

order

to

relaxation

between

investigated

observed

sample

the In

2 the

concern~ng solution are

water

and

and

free

and

to

for

separating

separation

systems and

nuclei the

of

is

dipolar dipolar

the

master

in

the

fundamental

radical

like

electronic

spins

erratic

because

somewhat

were

studied

(CH~)~P+ /free radical an pair ion possible interpret the it not to was by only considenng the dipolar coupling

Indeed,

the

hnewidths

the

Furthermore,

[8]. no

care

the

taken

was

of

geometry

section

results

nuclei

shifts

chemical

Th~s

chosen

have

wa

of

of ~H, ~~C and ~~P nuclei

rates

work

carrying

ions

behaviour

solution).

this

present

are

study the dynam~c

longitudinal the

latter

the

the

hyperfine interaction powerful method is a

any

technique

our

when

In

systems

between

avoid

to

that

(electrolytic

solution

these

repulsion order

interactions

importance

of

mechanisms

coulombic

is

scalar

in

paper the

theory of the

the

NMR

of

discussed

m

broadening (CH~)~NCI in

inhomogeneous of

protons section

presented The of Mn~+ presence

experimental

is

ions

heavy

m

3.

Theory.

2.

We

are

interested

gyromagnetic

contain~ng

xd,a,

H,

ratio

m

yj

m

field H, diamagnetic

local

the a

paramagnetic

impunties

at

sites

of

solution, w~th

equJvalent

with

volume

volume

nuclei

of

diamagnetic

susceptibility

xpara

spin

I

and

of

susceptib~l~ty The

local

field

is

H,

=

Ho(I

ha

+

H~,~

(2)

independent of the shift which chem~cal f§ is the applied field. ha is the usual is the molecule which from the susceptibility It takes into the field contribution account m field by dipolar given the shape. proton is located and is independent of the sample lid,~ is

M 5

DEMAGNETIZING

FIELD

~

where

is

~~ number

w~th

respect paramagnetic

~~

and

~~

~s order

these

the

to

reference the

of

SOLUTIONS

~

)

~~~~)

~~~~

~

of a g~ven the is position of r~~ spin I. Similarly, ~s

nuclear

th~s

lIa~

w~th

respect

the

to

(gs

S

spin

the

is

nucleus

the

m

diamagnet~c

the

g~ MB S is the Landk factor) and discussed

As

I.

529

~~~

molecule

moment

with

impunty

spin approximated of

are

PARAMAGNETIC

=

moment

position

relative

diamagnetic molecules) and

electronic

the

density of

IN

)

~~~~l'~~~~

~dtP

(N

EFFECTS

m

liquid moment

electronic

r~s is reference

the

[7]

point dipoles

as

the The Lorentz method. volume of the hqu~d sample is use centered sphere the reference nucleus, of radius 1lo much larger two pans : at a than the minimum distance of approach b of two molecular but much smaller than the centers, macroscopic sample size ; (ii) the volume outside is the sum of two the sphere. The field H~~~ electronic moments terms Hj,~ + H][~. The first, II~~~ is the field produced by the induced inside second Hj[~ by those (both diamagnetic and paramagnetic) the sphere 1lo and the of the local of the hquJd outside the sphere. According to the rotational structure invanance Notice around the studied nuclei, it is clear that Hj~~ 0 that in the case of a sphencal solid distnbution of the relative sample with an uniform electron~c 0. Here, the moments, Hj~~ uniform ~pair equihbnum distribution of the w~th~n the sphere 1lo is not molecules interacting isotropic because of the random diffusing motions of the correlation effects), but it remains In

div~ded

calculate

to

we

(I)

in

=

=

molecules. In

order

calculate

to

of the

distnbution

ll~[~

the

use

we

electronic

classical We

moments.

M

as

the

magnet~zation

total

(Xd>a

"

volume

unit

per

method

We

N~ g)

where

N~ is the field

density of

number

l§,

in

have

we

th~s

»( S(S

paramagnetic

=

the

6~ and

the

integration vessel

intemal

H$,~

=

taken

is

S.

where

z

the

zk =

vessel

~k

unit

and

div

Denoting by equation (3)

to

~

r~ volume

be

can

H][~

Oz)

radius

=

M,

w~th N,,

"

l~ =

S

of the

~

r~

N~,)

the

spherical

surface

[10]

rewntten

~'~~

~~° r

and dS, dSJ llo. Finally, we ~

d~rection

(6)

between

V

~

r

to

the

dV,

=

parallel sphere So of

z

r

dV

vector

the

~~~

~(

M;

I)

species.

the

Equation (6)

(4)

'

~ ~~

M-

over

v

S of

+

according

v

where

uniform

continuous

have

3 kT

direct~on

H][~

a

Xpara)1i0

+

~P~"

applied

considenng

[9]

define

S

are

l,

(7)

r

onented

outside

the

surface

obtain,

(8a)

(8b)

JOURNAL

530

Hence,

the

N,~.

H][~ and

For

on

spherical

a

field

local

the

the

in

sample shape (external

the

sample

it

well

is

a

From

by

Denoting

YI H>

"

the

vo

H0

YI

"

ii

uniform

(Xda

+

to

para) St

+ X

simply have « ha we cylinder sample w~th heigh be parallel to the cylinder axis It

consider

we

A"

"

sample

sphencal

Now,

tr)

sh~ft "

For

=

diameter

and

h

easy

is

~2

at

distance

a

c

b)

=

a

N~~ while

ii

from

the

~"~~"'~

=

4

h

+

on

~2c

the

axis

~

j~~

that

the

the

at

field

direct center

of the

-1/2

(12)

~

h

center,

(~

I

ar

First,

d.

show

to

,

of

the

cylinder,

0

«

c

«

h/2,

~ ~~l' i~ h~2c j~~

~~~

~~~~

For an arbitrary point inside the cylinder N~; must be nunlencally calculated from equation (8b). Th~s has been done for a large number of nuclear positions m a rectangular sect~on of the cylinder containing the central axis for various values of the ratio hid. As an example we obtained values of N== for hid I report m figure I the =

Then, distribution

we

have

f(Si)

performed for

vanous

numencal

a

values

of

mtegrat~on

hid

The

order

m

to

obtain

technique

numencal

is

the

normalized

explained

in

the

appendix z

Ho 2,24

3,68

6,95

axe

Fig. axis

I

of the

Values

of N==

cylinder

m

a

rectangular

section

of

a

cylinder

with

hid

I =

The

field Ho

is

parallel

to

the

DEMAGNETIZING

M 5

FIELD

f

EFFECTS

PARAMAGNETIC

IN

531

SOLUTIONS

h/d=lO.O

S~

2.

I.

1.

0.

0. -8.-6.-~.-2.

0.

2.

6.

~.

(a

8.

S~

O.

f

f

h/d=I.OO

S~

h/d=O.

S~

3~

0.

0.

0.

0.

o.

o.

o. -8.-6.-~.-2.

0.

2.

~.

(b Fig 2 the

-8.-6.-~.-2.

8.

6.

ratio

Theoretical

hid,

when

dipolar the

field

shifts

and

llj

parallel

is

0.

2.

~.

(c

S~ line

shapes f(Si) to

the

axis

for of the

6.

8.

S~ a

cyhndncal cylinder

sample for

various

values

of

JOURNAL

532

figure m (flat cylinder). axis of the cylinder.

We

hid

represent

0 34

2

the

th~s

In

has

work

san~e

=

f(Si)

d~stnbution

the

The

case

PHYSIQUE

DE

have

we

N~~=

hid

for

done

been

II

lK° 5

(thin

10

=

when

cylinder), hid I, llo is perpendicular

and

=

field

the

to

:

1@

(14a)

r

S

and

Si We

report

m

figure

3

corresponding

the

~

N~~

=

"

(14b)

distribution

f(Sr)

function

hid

for

1. =

1.

f

S~ )

h/d=I.OO

0.

0.

0.

0.

-8.-6.-~.-2.

0.

2.

6.

~.

8.

S~ Fig

Normalized

3

of the

ams

For

a

relaxation,

f(Si) for

dJstnbution

a

cyhndncal sample

the field Ho is

when

perpendicular

to

the

cylinder

g~ven the

of species normalized

neglecting

nuclei,

mhomogeneous

line

the from homogeneous broadening ansing shape F(v equation (9) and is, according to

(I1)

~~

f (Sf) V0(Xd>a

In

th~s

equation,

v

=

2

~

v~

Au,

where

Xpara)

+

v~

is

yi

v~

and

~

=

YJ

the

Ho

f (Sf)

H0(Xd>a

resonant

(l

1T

ha

~~~~ +

Xpara)1

frequency

for

a

sphencal

sample (16)

M

DEMAGNETIZING

5

From is

(15),

equation

that

see

we

EFFECTS

FIELD

F(

v

is

PARAMAGNETIC

IN

proportional

to

f(Si)

SOLUTIONS

Furthermore,

533

relative

the

sh~ft

by

gJven

"d

@

~~ "

"

s

"

Sf(Xdia

+

(18)

Xpara)

~0

applied field I§

parallel to the axis of the cylinder. For ( x~~ + x ~~~) < 0. It can be seen from we figure 2a that the theoretical line f(Sr) for a thin cylinder (hid 10 ) is displaced towards the low Si values with the low frequencies towards respect to the ong~n (sphencal sample)~ i e v(hv » 0) The line is dissymmetncal w~th a slower the h~gh frequencies decrease towards For hid dissymmetncal I, the line is and centered around Si= 0 but is considerably broadened (Fig 2b) Finally, for a flat cylinder (hid 0.34 ) the line is very dissymmetncal and displaced towards the h~gh values of Si, i.e towards the h~gh frequencies The broadening also larger than in the (Fig 2c). For higher of concentrations paramagnetic is prev~ous cases impurities, when (xd,a + xpara) »0 we must have shifts m the opposite direction that to observed the We also and the asymmetry of the line shape must be inverted. m previous case predict from equation (17) the existence of a cntical of impurities concentration paramagnetic for which (xdia + x para) 0 leading to the absence of any sh~ft and broadening of the line For th~s the line is posit~oned at the frequency for all sample shapes. The concentration same line for a cyhndncal sample must be very for a sphencal sample. resonance narrow as We

consider

low

the

where

situation

of

concentrations

the

impunties

paramagnet~c

is

have

=

=

=

=

3.

Experiment

discussion.

and

performed using a h~gh resolution WM200 Spectrometer have Brucker expenments working for the proton at a frequency of 200 MHz, with a direct field homogeneity of about The diameter 10 Hz, i e 0.05 ppm mtemal of the r f coil is 25 mm and its height is 40 mm three of.pyrex vessels d We used kinds sphencal one w~th internal diameter 21mm, a a thin tube with internal diameter 40 mm (hid 10 ), and a partially d 4 mm and height h filled tube with d and h varying between 5.5 and 7 5 mm (0 26 « hid « 0 36 ). We 21 mm, of have analysed the hneshift the and line broadening NMR spectra for the twelve equivalent of Mn~+ of (CH~)~N+ ions (CH~)~NCI of D~O solution the protons presence m m obtained dissociation of Mncl~. (S impurities from the 512) paramagnetic of (CH~)~NCI m our The solution 0.I mole l~ ~, and that of MnC12 was concentration was varied from 0 (diamagnetic solution) to 0.12 mole l~ reference Usually, the chemical shifts studied by locking the rf frequency on a ha are nucleus (deutenum of D~O). the locking frequency is affected, m the Because way as same independently of the studied the nuclei by the sample shape effect, ha constant, remains different hneshapes and broaden~ng according to the sample shape, although one observes Here, m order to observe the sh~fts and the broadening of the l~nes due to the geometry nucleus for a dipolar inhomogeneous fields, it is necessary to lock the rf field on the deutenum sphencal sample and to keep this locking frequency for all constant geometnes. consider the diamagnetic solution The observed represented m First, we spectra are figure 4 For a sphencal sample we observe a symmetncal, line (Fig 4a) w~th a half narrow height hnewidth of 0.07 ppm. The satellite line displaced by 1.6 ppm with respect to the main residual line is due to HDO m D~O. For the thin cylinder (hid 10 ) the line is displaced by 2.95 ppm w~th a slight towards high frequencies as expected (Figs 4b and 2a) asymmetry For a flat cylinder (hid 0.34 broad (about 2.5 ppm at half height) and the the line is very displaced peak towards frequencies by h~gh Theoretically, if 3 4 ppm (Fig 4c) maximum is ~ (cgs) [I I], the volume take susceptibil~ty of D~O be 0.72 10~ obtain a to we x~~~ x we We

=

=

=

=

=

=

=

=

=

JOURNAL

DE

PHYSIQUE

II

-T

"

5

MM

>WI

,7

JOURNAL

534

PHYSIQUE

DE

M

II

5

b

a

I

25

is

20

S

lo

25

20

is

PPm

5

lo

PPm

c

25

20

is

lo

5

PPm

Fig 4 ~b) thin

Observed

cylinder

resonance

(hid

displaced by maxbnum peak larger expenmental

=

l~ne the

Now,

Mn~+ T

=

is

introduce

ions.

From

lines of

protons

(c) flat

cylinder

of

(CH~)~NCI

(hid

,

0 34 =

cylinder.

m

D~O

200

at

MHz

:

(a) sphencal

sample,

)

cylinder

the displacement of height of 1.5 ppm. The a linewidth value is probably due to the interference with the HDO peak. the paramagnetic impurities with a concentration C~ (mole l~~) of for (5) we obta~n S=512, g~=2 and equation temperature a

2.92

we

293 K

10)

ppm

predicted

for

to

thin

the

be 3 0 ppm

For

the

linewidth

w~th

flat

at

half

:

xpara

15.0 =

x

10~

~

C~ (cgs)

(19)

DEMAGNETIZING

lK° 5

Then,

sh~fts

relative

the

EFFECTS

FIELD

~~ «~

535

by

g~ven

are

SOLUTIONS

PARAMAGNETIC

IN

=

Si(-

=

0.72

C~) 10~~.

15

+

(20)

Us

The

cntical

concentration

susceptibilit~es than

C~

for

is

then

for

Cl =

diamagnetic

the

For C~

increases.

which

0.048

solution,

Cl

the

we

have l~ ~.

but

w~th

position of

For

C~ < decreasing

the

lines

Cl

must

=

diamagnetic

of the

cancellation

mole

shifts be

the

expect

we

and

same

paramagnetic

20

b

5

lo

15

spectra

narrowing of the l~nes as a independent of the sample shape and

a

25

of

kind

S

lo

15

20

25

ppm

ppm

c

I 25

20

lo

15

5

ppm

Fig

5.

Observed

paramagnetic

C~

=

0, (b) C~

impunties =

0.04,

lJneshapes Mn~+

(c) C~

=

of

proton

with

vanous

0.12

resonance

lines

concentrations

of

(CH3)4NCl

C~ (mole

l'~)

m

in

a

D20 m sphencal

presence

of

sample (a)

JOURNAL

536

PHYSIQUE

DE

lK° 5

II

broadening mhomogeneous vanishes For values of C~ » Cl, the sh~fts increasing proportionally to C~ and m direction for the observed must opposite to the shifts increase diamagnetic solution. Simultaneously, the broadening of the lines for cyhndncal samples must with C~, but the with respect to a diamagnetic solution. Notice asymmetry is reversed increase that for sphencal samples the position of the l~ne is independent of C~, but the l~newidth w~ll because of the contribution relaxation effects homogeneous of due the to increase impurities. paramagnetic

and

the

First, confirms 0 07

ppm

checked

have

we

sphencal

sample to

remains

absence

the

0.4

of any the

and

ppm

represented

have

that at

for a

C~