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~