Parallel NMR based on solution magnetic-susceptibility differences. Application to isotopic effects on self-diffusion

Article abstract of DOI:10.1021/je901031b

Different susceptibility NMR line shifts can be induced in distinct liquid solutions by dissolving different concentrations of complexes of paramagnetic lanthanide Ln³⁺ ions. We show how these solutions, put in capillaries, can be simultaneousl

Full text of DOI:10.1021/je901031b

2048
J. Chem. Eng. Data 2010, 55, 2048–2054
Parallel NMR Based on Solution Magnetic-Susceptibility Differences. Application
to Isotopic Effects on Self-Diffusion†
Pascal H. Fries* and Daniel Imbert
CEA, INAC, Service de Chimie Inorganique et Biologique (UMR-E 3 CEA UJF, FRE 3200 CNRS), 38054 Grenoble, France
Different susceptibility NMR line shifts can be induced in distinct liquid solutions by dissolving different
concentrations of complexes of paramagnetic lanthanide Ln3+ ions. We show how these solutions, put in
capillaries, can be simultaneously studied with a standard high-resolution spectrometer. After theoretical
justification the method is illustrated by an investigation of the effects of H/D substitution on self-diffusion
in heavy water. Non-Stokesian effects are observed.
method should be convenient because the accompanying change
of intermolecular potentials, which may affect D, is expected
to be rather modest. The applicability of the Stokes-Einstein
equation to molecular solutes can be questioned, first in the
simplest case of pure liquids for which the solute and solvent
molecules are the same species. For that purpose, an accurate
NMR spin-echo procedure was developed by Holz et al.13–15
For several liquids, they found a strong correlation between D
and the inverse of the square roots of the moments of inertia of
the molecule, indicating a translation-rotation coupling, but for
a few liquids they observed that D varies as the inverse of the
square root of the molecular mass as already predicted in dilute
gases.16 They concluded that the dependence of the diffusion
coefficients on the molecular mass was still an open question,
even in pure liquids. Liquid mixtures and solutions are the
second class of liquids concerned by the Stokes-Einstein
equation,17,18 in particular those in which the solvent and
diffusing solute have significantly different molecular masses.
For instance, Weinga¨rtner did not detect any isotopic effect on
the self-diffusion of water, methanol, and ethanol amid the much
heavier carbon tetrachloride molecules.17 Clearly, more numer-
ous experimental data are required to obtain a reliable overview
of the dynamic isotopic effect in liquids.15,19
Introduction
The transport or move of molecules from one place to another,
which is very common in physical and chemical processes, has
attracted much attention in the domain of electrolyte solutions.1
Under the action of external forces, macroscopic numbers of
particles flow with velocities proportional to these forces. The
proportionality factors, named mobilities, are themselves pro-
portional to the diffusion coefficients of the particles according
to the Einstein relation. Practical and reliable methods for
predicting the general transport phenomena, which are so
important in applied research, are still lacking despite notable
theoretical advances since the beginning of the 1990s.1,2 An
ubiquitous kind of transport at the molecular scale is self-
diffusion, that is, the random translational motion of a particle
due to its bombardment by the neighboring molecules. Self-
diffusion is one of the simplest properties, the macroscopic study
of which allows one to test molecular theories of time-dependent
phenomena in liquids.3,4 It is one of the key molecular factors
which govern the intermolecular NMR relaxation rates, and the
determination of which is necessary to properly interpret these
rates in terms of molecular interactions.5–8 A fundamental result
is the Stokes-Einstein eq 1 giving the self-diffusion coefficient
D of a spherical particle of radius a in a liquid of viscosity η.
We present a high-resolution NMR parallel method for fast
comparison of self-diffusion coefficients. The self-diffusion
coefficients of the molecules carrying the observable nuclear
spins are derived from pulsed (field-) gradient spin-echo
(PGSE) experiments,20,21 that is, from the attenuation of the
spin-echo NMR signal caused by the molecular Brownian
displacements. Parallelism is obtained by labeling the spins with
resonance frequency shifts due to prescribed paramagnetic
changes of the magnetic volume susceptibility of the solution.
Such changes result from the controlled dissolution of para-
magnetic solutes. They are at the basis of the Evans method
for determining the paramagnetic susceptibility of such solutes,
which simply requires a standard NMR tube containing one
capillary tube in a preferred coaxial position.22–25 Variants of
the Evans method have been used to study properties of
paramagnetic lanthanide Ln3+ complexes such as the crystal field
of their ligands or their concentration.26,27 Starting from the
theory of the demagnetizing field, already revisited to investigate
the effects of the geometry of the NMR sample on the line
shape,28 we show that parallel capillaries inside a standard NMR
D ) kBT/(6πaη)
(1)
This equation was initially derived for a diffusing macroscopic
solute which undergoes the frictional force of the neighboring
solvent molecules approximated as a viscous continuum.
However, it turns out to be surprisingly accurate even for a
molecular solute, if the viscosity is replaced by an effective
viscosity ftη where ft is a translational (t) microviscosity factor
depending only on the solute and solvent sizes.9–11 Perhaps,
one of the most remarkable features of the Stokes-Einstein
expression is that D is independent of the solute and solvent
masses, though it is a dynamical property which determines the
mean squared displacement 〈|R(t)|2〉 ) 6Dt of the solute as a
function of time. Isotopic substitution is a natural method for
studying the effect of the change of molecular mass on
diffusion.12 Accurate measurements are needed to quantify this
small effect and interpret it in terms of theoretical models. The
† Part of the “Josef M. G. Barthel Festschrift”.
* Corresponding author. Tel.: +33438783107; fax: +33438785090; e-mail:
pascal-h.fries@cea.fr.
10.1021/je901031b  2010 American Chemical Society
Published on Web 03/23/2010

Journal of Chemical & Engineering Data, Vol. 55, No. 5, 2010 2049
(rP - rI) · k
|rP - rI|3
1
4π
ij
zz
N (rI) ≡
dSP -
∫
Sup,j
(rP - rI) · k
|rP - rI|3
1
4π
dSP
(4)
∫
Slow,j
The main features of the susceptibility shift are conveniently
described in the simplest situation of n ) 2 molecules and
capillaries discussed hereafter. Let u be the symmetry axis of
the setup of the two capillaries C1 and C2. Denote by πu the
rotation of angle π about u. The demagnetizing coefficients
ij
N (rI) are purely geometrical quantities which are invariant
zz
jj
ii
ji
under πu so that we have N [πu(rI)] ) N (rI) and N [πu(rI)] )
zz
zz
zz
ij
N (rI). The shifts ∆iν(rI)/νI simplify to
zz
∆1ν(rI)
1
3
11
zz
12
zz
)
- N (rI) ꢀ1 - N (rI)ꢀ2
Figure 1. Capillary setup in a standard NMR tube.
(
)
νI
(5)
tube can become independent tracks where the race of the
diffusing molecules can occur. We explain why tiny variable
concentrations of paramagnetic lanthanide Ln3+ complexes are
particularly appropriate to yield the desired shifts. We apply
the method to methanol, tert-butanol (tBuOD), and tetraphe-
nylphosphonium (TPP) ions and some of their deuterated
derivatives in D2O.
∆2ν[πu(rI)]
1
3
12
zz
11
zz
) -N (rI)ꢀ1 +
- N (rI) ꢀ2
(
)
νI
and the shift difference becomes
∆2ν[πu(rI)]
∆1ν(rI)
1
3
11
zz
12
zz
-
)
- N (rI) + N (rI) (ꢀ2 - ꢀ1)
(
)
νI
νI
(6)
Demagnetizing Field and Capillary Setup
In an experimental setup, the height and diameter of the liquid
columns typically verify h g 32 mm and d e 1.6 mm, that is,
h/d g 20, the distance between the axes of the tubes is = 2
mm, and the length of the detection zone is l = 15 mm. Then,
a straightforward computation shows that the coefficient (1/3)
We wish to simultaneously investigate the self-diffusion
coefficients of n molecules Mi (1 e i e n) in n different solutions
soli of volume susceptibilities ꢀi. The different susceptibilities
obtained by varying the nature and/or concentrations of the
paramagnetic solutes can be written as
11
12
- N (rI) + N (rI) is equal to the value of 1/3 of the form
zz
zz
factor of a tube of infinite height with a precision better than
0.1 %, and eq 6 can be approximated as
ꢀi ) ꢀdia + ꢀpara,i
(2)
where ꢀdia and ꢀpara,i are the susceptibilities of the solvent and
solutes, respectively. To simplify the formulas and discussion,
we assume that the molecules Mi are derived from one another
by hydrogen/deuterium (H/D) isotopic substitution and that the
observed proton spins I on Mi have the same chemical shift in
all of the solutions. The formulas can be easily generalized to
account for chemical shift variations. The experimental setup
is sketched in Figure 1.
The solutions soli are put in identical glass or quartz capillaries
where they occupy cylindrical columns Ci of equal heights h
and diameters d. The capillaries are placed at the same height
in a standard NMR tube located in the uniform vertical magnetic
field B0 ) B0k of the cryomagnet of a high-resolution
spectrometer. The liquid columns are centered with respect to
the detection zone of the receiver coil, so that their upper and
lower surfaces Sup,i and Slow,i are at quite large distances from
the limits of the detection zone of length l. Consider a proton
I at the position rI in the capillary Ci. The local magnetic field
B(rI) at rI is B(rI) ) B0 + Bdip(rI), where Bdip(rI) is the dipolar
field due to the diamagnetic and paramagnetic moments of the
molecules in the various capillaries. Let γI be the gyromagnetic
ratio of the proton. According to the demagnetizing field
theory,28 the dipolar field induces a relative susceptibility shift
∆iν(rI)/νI of the proton resonance frequency νI ) -γIB0/(2π)
given by (SI units)
∆2ν[πu(rI)]
∆1ν(rI)
1
3
-
)
(ꢀ2 - ꢀ1)
(7)
νI
νI
This approximation extends to two points located in C1 and
C2 at the same height in the NMR tube in the case of two and
more capillaries. More generally, if two points rIi and rIj are
located at the same height in two capillaries Ci and Cj amid n
parallel capillaries, the difference of the relative frequency shifts
at these points is
∆jν(rIj)
∆iν(rIi)
1
3
1
3
-
)
(ꢀj - ꢀi) ) (ꢀpara,j - ꢀpara,i
)
νI
νI
(8)
Note that the possible small curvatures of the upper and lower
surfaces Sup,j and Slow,j due to the menisci and capillary bottoms
barely affect eq 8 because these surfaces are at quite large
distances (h - l)/2 . d from the limits of the detection zone.
Furthermore, this equation keeps accurate to within 1 % if the
heights of the liquid columns differ by less than about 20 %.
To sum up, the concentrations of paramagnetic solutes
dissolved in the different solutions containing the isotopically
substituted molecules Mi are chosen according to eq 8 so that
the resonance lines of the observed spins are well-separated and
do not overlap with the remaining parts of the spectra from the
various capillaries.
n
∆iν(rI)
1
3
ij
zz
)
δij - N (rI) ꢀj
(3)
∑
(
)
Susceptibility Frequency Shift Labeling with Ln3+
Complexes
We take advantage of the fact that lanthanide Ln3+ ions have
νI
j)1
ij
where the demagnetizing coefficients N (rI) are defined in terms
zz
of integrals over the upper and lower surfaces Sup,j and Slow,j of
the columns Cj of solutions as
nearly identical chemistry but magnetic properties which vary

2050 Journal of Chemical & Engineering Data, Vol. 55, No. 5, 2010
markedly with the number of their 4f inner electrons.29 First,
all paramagnetic Ln3+ ions, but not Gd3+, show different, very
short electronic relaxation times < 1 ps of their paramagnetic
moments,29,30 so that they weakly accelerate the intermolecular
relaxation rates of the surrounding nuclear spins, even at quite
large concentrations,26 cLn = 100 mM. In contrast, Gd3+ is an
ideal paramagnetic ion for magnetic resonance imaging (MRI)
contrast agents because of its long longitudinal electronic spin
relaxation time31–34 T1e at the MRI fields35 g 1 T. Secondly,
the heavy paramagnetic Ln3+ ions from Tb3+ to Yb3+ often shift
the resonance frequencies of the nuclei of their tightly bound
ligands to values outside the chemical shift range of the protons
on diamagnetic molecules.29 Moreover, Gd3+ and these heavy
Ln3+ ions to a lesser extent strongly accelerate the intramolecular
relaxation rates and broaden the lines of the nuclei of tightly
bound ligands,29,30 so that these lines tend to disappear in the
background noise of the NMR spectrum. Thus, the ligands
bound to the Ln3+ ions from Gd3+ to Yb3+ are often NMR silent.
Thirdly, the Ln3+ ions have significantly different effective
ω ) 0.40 in D2O, atom fraction D ) 0.995) were supplied by
Aldrich and used without further purification. Solvents and
starting materials for the organic syntheses were purchased from
Aldrich, Fluka, or Acros and used without further purification,
unless otherwise stated.
Organic Syntheses. 1H NMR spectra were recorded at
25 °C for characterization purposes on a Bruker Advance 200.
Chemical shifts are reported in ppm and were referenced
internally to the residual solvent resonance. Mass spectra were
run on a Thermo Scientific LXQ mass spectrometer equipped
with an electrospray source.
tert-Butanol CD2H(CD3)2COD. Single hydrogen tBuOD
CD2H(CD3)2COD, named tBu1OD (1 methyl proton), was
prepared as follows. Vaporized iodine crystal was introduced
into a flask equipped with stirrer and water-cooled condenser
and added to a suspension of Mg (382 mg, 15.9 mmol) in cooled
to 0 °C anhydrous Et2O (10 mL). A Grignard reagent was
prepared by adding slowly 2.19 g of methyl-d2 iodide (CD2HI,
15.2 mmol) in 15 mL of anhydrous Et2O (Aldrich). The mixture
was stirred at 0 °C for 15 min, heated to reflux for an additional
15 min, and cooled again at 0 °C, and a solution of 1.11 mL of
acetone-d6 (16.7 mmol) in 10 mL of anhydrous Et2O was added
slowly. The cooling bath was removed and the mixture left at
room temperature for 30 min. A solution of freshly prepared
ND4Cl (35 mL) was added. The organic and aqueous layers
were separated and the aqueous layer extracted 10 times with
diethyl ether. The organic layers were combined and dried with
Mg2SO4, and the major part of diethyl ether was evaporated
with caution. The resulting oil was distilled (84 °C) to yield
450 µL of tBuOD (5.6 mmol, 28 % yield), and the purity was
confirmed by NMR using two salts as reference [δH (200 MHz,
D2O) 1.28 (s, 1H)]. tert-Butanol CH3(CD3)2COD, named
tBu3OD (3 methyl protons) was prepared similarly.
magnetic moments µeff,Ln, for example, µ2eff,Gd ) 63, µ2eff,Tb
=
94.5, and µ2eff,Yb = 20.6. The volume paramagnetic susceptibility
of an Ln3+ complex with magnetic moment µeff,Ln and concen-
tration cLn (mM) is
µ2eff,Ln µ2B
ꢀpara,Ln ) cLn µ0NAvogadro
)
3kBT
5.27·10-9
298.15
µ2eff,LncLn
(9)
T
The frequency shifts of the solutions are conveniently
obtained by dissolving the two complexes TbL and/or YbL (L
) ligand) of short T1e at significant concentrations cTb + cYb g
5 mM and possibly the GdL complex of long T1e at small
concentrations cGd < 0.5 mM. The GdL complex acts as an agent
for paramagnetic relaxation (rate) enhancement (PRE) and serves
to balance the nuclear relaxation rates among the various
solutions. In all of the solutions the concentrations of the three
complexes are chosen so that their sums keep, as much as
H/D Substituted Tetraphenylphosphonium. The various steps
are sketched in Scheme 1.
2,4,6-d3-Aniline (1). To a 100 mL flask containing 20 g of
aniline hydrochloride (0.155 mol) and equipped with a stirrer
and a water-cooled condenser 50 mL of D2O (atom fraction
D ) 0.999) was added. The solution was heated to reflux under
nitrogen for 24 h. Water was then removed under reduced
pressure and the procedure repeated five times. Sodium hy-
droxide (1 mol ·L-1 in water) was then added to the crude dark
blue solution, the resulting mixture extracted four times with
200 mL of Et2O, the organic layers washed with brine and dried
with MgSO4, and the solvent removed. 1 was obtained as a
possible, a constant value csum
:
cTb + cYb + cGd ) csum
(10)
This requirement ensures that the isotopically substituted
molecules Mi move in quasi-identical solutions. In particular,
even if the complexes GdL are charged species, the self-
diffusion coefficients of ions Mi can be compared directly since
these ions undergo the same Coulomb interactions with the
complexes. Indeed, the transport properties of a given ionic
species often depend significantly on the charges and concentra-
tions of the various ions in the solution.1,2 Note that we cannot
replace YbL by a diamagnetic analogue such as LuL, the proton
NMR spectrum of which generally overlaps with the lines of
the molecules Mi.
1
colorless oil (7 g, 47 %). H NMR (200 MHz, CDCl3): δ )
3.69 (2H, br s, NH2), 7.19 (2H, s, CH); ES+-MS m/z: 97.1 [M
1
+ 1]+. The isotopic purity (mass spectroscopy and H NMR)
was found to be 97 %.
2,6-d2-4-Bromoaniline (5). Compound 5 was prepared ac-
cording to the same synthetic procedure described for the
synthesis of 1 by using the following: 12.5 g of 4-bromoaniline
hydrochloride (0.073 mol), 50 mL of D2O (atom fraction D )
0.999), and 4 g of DCl (mass fraction ω ) 0.35 in D2O, atom
fraction D ) 0.99). 5 was obtained as a colorless oil (9.53 g,
75 %). 1H NMR (200 MHz, CDCl3): δ ) 3.79 (2H, br s, NH2),
7.29 (2H, s, CH). ES+-MS m/z: 174 and 176 [M + 1]+. The
isotopic purity (mass spectroscopy) was found to be 98 %.
2,4,6-d3-Bromobenzene (2). 2,4,6-d3-Aniline (1, 3.64 g, 38
mmol) was dissolved in 48 % aqueous HBr (27 mL). After
cooling to 0 °C, sodium nitrite (2.7 g, 39 mmol) was added
very slowly to the stirred solution with the temperature being
kept within (0 and 5) °C. This diazonium salt solution was then
poured into a flask containing CuBr (7.69 g, 53 mmol) and 22
Experimental Section
Purchased Chemicals. Heavy water D2O (atom fraction D
) 0.999), methanol CH3OD (atom fraction D ) 0.99), methanol
CHD2OD (atom fraction D ) 0.99), tert-butanol (CH3)3COD
(atom fraction D ) 0.99), named tBu9OD (9 methyl protons),
were purchased from Eurisotop. TPP bromide, the hydrated salts
GdCl3 ·6H2O, TbCl3 ·6H2O, YbCl3 ·6H2O, triethylenetetraamine-
hexaacetic acid H6ttha, DCl (mass fraction ω ) 0.35 in D2O,
atom fraction D ) 0.99), hypophosphorous acid (mass fraction
ω ) 0.5 in H2O), hypophosphorous acid-d3 (mass fraction ω )
0.5 in D2O, atom fraction D ) 0.98), and NaOD (mass fraction

Journal of Chemical & Engineering Data, Vol. 55, No. 5, 2010 2051
Scheme 1. Synthesis of H/D Substituted Tetraphenylphosphonium Ions
mL of 48 % aqueous HBr. The solution was heated to reflux
for 5 h and then extracted three times with dichloromethane.
The organic layers were washed with 1 mol ·L-1 NaOH and
water and dried with MgSO4, and the solvent removed. The
yellow oil was distillated (51 °C, 27 mbar) to give a colorless
liquid (4.2 g, 69 %). 1H NMR (200 MHz, CDCl3): 7.31 (2H, br
s, CH).
Tri(3,5-d2-phenyl)phosphine (8). 580 mg (23.9 mmol) of
magnesium turnings, 20 mL of anhydrous Et2O, 3,5-d-bro-
mobenzene (6, 3.45 g, 21.7 mmol), PCl3 (993 mg, 7.2 mmol).
After sublimation, compound 8 was obtained as a white powder
(0.85 g, 44 %). 1H NMR (200 MHz, CDCl3): δ ) 7.45 (3H, br
s, CH), 7.61 (6H, br s, CH). ES+-MS m/z: 269.2 [M + 1]+.
Tri(3,4,5-d3-phenyl)phosphine (9). 334 mg (13.8 mmol) of
magnesium turnings, 7 mL of anhydrous Et2O, 3,4,5-d3-
bromobenzene (7, 2.0 g, 12.5 mmol), PCl3 (572 mg, 4.2 mmol).
After sublimation, compound 9 was obtained as a white powder
(0.67 g, 60 %). 1H NMR (200 MHz, CDCl3): δ ) 7.58 (6H, br
s, CH). ES+-MS m/z: 272.2 [M + 1]+.
3,5-d2-Bromobenzene (6). 2,6-d2-4-Bromoaniline (5, 3.0 g,
17 mmol) was dissolved in 50 % aqueous hypophosphorous
acid (3.73 g, 57 mmol) and heated to reflux for 15 min. After
cooling to -10 °C, sodium nitrite (573 mg, 8 mmol) was added
very slowly into the stirred solution with the temperature being
kept within (0 and 5) °C. The stirring was continued at 0 °C
for 3 h and then the mixture poured on ice, extracted three times
with dichloromethane, and dried with MgSO4. After evaporation
of the solvent, the dark oil was distillated (51 °C, 27 mbar) to
Tetra(2,4,6-d3-phenyl)phosphonium Bromide (4). To a 100
mL three-necked flask equipped with a stirrer and a water-cooled
condenser entirely flushed with argon, 1.09 g of compound 3
(4 mmol), 951 mg of anhydrous NiCl2 (4 mmol), 35 mL of
anhydrous benzonitrile, and 705 mg of compound 2 (4.4 mmol)
were added. The mixture was heated at 190 °C for 24 h. After
cooling to 120 °C, water was added (25 mL) and the mixture
stirred over a period of 8 h at 120 °C. The yellow mixture was
then cooled on ice and filtered and the solid washed with
chloroform. The aqueous layer was then extracted four times
with chloroform and the organic layers washed with water, dried
with MgSO4, and evaporated to dryness to give 750 mg a white-
yellow powder. After crystallization in water and drying 2 days
under vacuum at 100 °C, compound 4 was obtained as a white
1
give a colorless liquid (1.86 g, 66 %). H NMR (200 MHz,
CDCl3): 7.37 (1H, br s, CH), 7.56 (2H, br s, CH).
3,4,5-d3-Bromobenzene (7). Compound 7 was prepared
according to the same synthetic procedure described for the
synthesis of 6 by using the following: 2,6-d2-4-bromoaniline
(5, 3.0 g, 17 mmol), 50 % aqueous hypophosphorous acid-d3
in D2O (3.90 g, 57 mmol), and sodium nitrite (573 mg, 0.008
mol). After distillation (51 °C, 27 mbar), a colorless liquid was
1
obtained (2.40 g, 87 %). H NMR (200 MHz, CDCl3): 7.51
(2H, s, CH).
1
powder (470 mg, 27 %). H NMR (200 MHz, CDCl3): δ )
Tri(2,4,6-d3-phenyl)phosphine (3). To a 100 mL three-necked
flask equipped with a stirrer and a water-cooled condenser
entirely flushed with argon to remove the moist air, 592 mg
(24 mmol) of fine magnesium turnings and 15 mL of anhydrous
Et2O and iodide were added. A portion of 3.5 g of 2,4,6-d3-
bromobenzene 2 (22 mmol) was then added slowly over a period
of 30 min and the mixture heated to reflux for 30 min. After
cooling to -10 °C, PCl3 (1.01 g, 7.4 mmol) was added dropwise
to the stirred Grignard solution and the mixture allowed to warm
up at room temperature for 30 min. After cooling to 0 °C, water
(7 mL) was added, and the resulting mixture was extracted four
times with 50 mL of dry Et2O under argon atmosphere and dried
12 h over Na2CO3. After evaporation of the solvent, compound
3 was obtained as a white powder (1.2 g, 60 %) by sublimation
7.50 (8H, d, J ) 2.9 Hz, CH). ES+-MS m/z: 351.3 [M + 1]+.
Compounds 10 and 11 were prepared according to the same
synthetic procedure described for the synthesis of 4:
Tetra(3,5-d2-phenyl)phosphonium Bromide (10). 0.85 g of
compound 8 (3.2 mmol), 749 mg of anhydrous NiCl2 (3.2
mmol), 35 mL of anhydrous benzonitrile, and 552 mg of
compound 6 (3.5 mmol) were used. After crystallization in water
and drying under vacuum, compound 10 was obtained as a white
1
powder (260 mg, 19 %). H NMR (200 MHz, CDCl3): δ )
7.43 (4H, br s, CH), 7.68 (8H, br s, CH). ES+-MS m/z: 347.2
[M + 1]+.
Tetra(3,4,5-d3-phenyl)phosphonium Bromide (11). 0.65 g of
compound 3 (2.4 mmol), 567 mg of anhydrous NiCl2 (2.4
mmol), 25 mL of anhydrous benzonitrile, and 420 mg of
compound 7 (2.6 mmol) were used. After crystallization in water
and drying under vacuum, compound 11 was obtained as a white
1
(170 °C, 0.5 mbar). H NMR (200 MHz, CDCl3): δ ) 7.48
(6H, d, J ) 2.5 Hz, CH). ES+-MS: m/z 272.2 [M + 1]+.
Compounds 8 and 9 were prepared according to the same
synthetic procedure described for the synthesis of 3 by using
the following:
1
powder (390 mg, 38 %). H NMR (200 MHz, CDCl3): δ )
7.72 (8H, d, J ) 13.4 Hz, CH). ES+-MS m/z: 351.3 [M + 1]+.

2052 Journal of Chemical & Engineering Data, Vol. 55, No. 5, 2010
Table 1. Approximate Compositions of the Paramagnetic Solutions Sol1, Sol2, and Sol3 Containing the H/D Substituted Molecules of
Methanol, tert-Butanol, and Tetraphenylphosphonium in D2Oa
solute
Sol1
CH3OD
tBu9OD
Sol2
Sol3
methanol (50 mmol ·L-1
)
no
CHD2OD
tBu1OD
tert-butanol (50 mmol ·L-1
)
tBu3OD
TPPBr (20 mmol ·L-1
)
TPP
TP35DP
TP246DP
[Ybttha3-
]
7.6 mmol ·L-1
0 mmol ·L-1
0.4 mmol ·L-1
3.8 mmol ·L-1
4 mmol ·L-1
0.2 mmol ·L-1
0 mmol ·L-1
8 mmol ·L-1
0 mmol ·L-1
[Tbttha3-
[Gdttha3-
]
]
a The H/D substituted molecules are for tert-butanol CD2H(CD3)2COD (tBu1OD), CH3(CD3)2COD (tBu3OD), and (CH3)3COD (tBu9OD) and for
tetraphenylphosphonium the fully hydrogenated tetraphenylphosphonium (TPP), tetra(3,5-d3-phenyl)phosphonium (TP35DP), and
tetra(2,4,6-d3-phenyl)phosphonium (TP246DP). The three solutions contain identical concentrations of the substituted molecules, but different
concentrations of the paramagnetic Ybttha3-, Tbttha3-, and Gdttha3- complexes with ttha ) triethylenetetraaminehexaacetate leading to different
paramagnetic susceptibilities.
Liquid Sample Preparation. Hydrated salts LnCl3 ·6H2O were
used to prepare the Lnttha3- complexes. Stock solutions of
Tbttha3- (99.53 mM), Ybttha3- (100.3 mM), and Gdttha3- (5.0
mM) complexes were prepared by dissolving the appropriate
amounts of the hydrated salts LnCl3 ·6H2O with H6ttha in D2O
followed by adjustment of the pHread = 8 with NaOD solution
in D2O. The precise stoichiometries of the salts were determined
by colorimetric titration in acetate buffer (pH 4.5) using
standardized H2Na2EDTA solution (Merck) and a Xylenol
orange indicator. The Lnttha3- stock solution was prepared with
a slight relative excess of ligand to avoid the presence of free
Ln3+ aqua ions. Stock solutions of the various H/D substituted
molecules of methanol (500 mM), tBuOD (500 mM), and TPP
bromide (35 mM near the solubility limit) were also prepared
by dissolving the appropriate amounts of products. The solutions
for the diffusion studies with the desired concentrations of H/D
substituted molecules and Lnttha3- complexes were obtained
by diluting the appropriate volumes of stock solutions with D2O
in 1.5 mL Eppendorf tubes. The Pyrex capillaries (OD ) 1.9
mm, ID ) 1.5 mm) and the standard NMR tube (5 mm OD
precision tube with 0.38 mm wall thickness) serving as a
capillary holder were purchased from Wilmad-Labglass.
Diffusion Coefficient Measurement. The self-diffusion coef-
ficients DX of the various species X in D2O solutions were
measured by a PGSE sequence20,21 on a 500 MHz Bruker
Avance spectrometer equipped with a BBI probe with a triple-
axis gradient field. The bipolar stimulated spin-echo sequence
was applied to protons on X.21 Denote the proton gyromagnetic
ratio by γI, the strength of the gradient pulse by g, the duration
of this gradient by δ, and the diffusion delay by ∆. The self-
diffusion coefficient DX of a species X was calculated by fitting
of the theoretical expression of the proton signal intensity
I(δ,∆,g) ) I0exp[-(γIgδ)2(∆ - δ/3)DX], where I(δ,∆,g) and I0
are the intensities in the presence and absence of the gradient
pulses, respectively. The values chosen for δ and ∆ depend on
the magnitude of the measured diffusion coefficient. The values
of δ and ∆ were typically (4 and 80) ms, respectively. In the
experiments g was incremented from (1.18 to 35.4) G ·cm-1
triamine pentaacetate) form Ln3+ complexes with one coordinat-
ing water molecule37 which can be replaced by methanol.38 The
choice of LnL complexes such as Lnttha3- without coordinating
water avoids the formation of LnL-methanol ternary adducts
which could slightly modify the self-diffusion coefficient of
methanol and somewhat alter the dynamic isotope effects.
Because of its limited solubility, we did not use the uncharged
complex39 Lntpatcn (tpatcn ) (1,4,7-tris[(6-carboxypyridin-2-
yl)methyl]-1,4,7-triazacyclononane) which would not modify
the dynamics of the TPP+ ion by Coulomb interactions.1,2
The three solutions were put in three parallel capillaries inside
a standard NMR tube as discussed in the Experimental Section.
1
Their H 500 MHz spectrum is shown in Figure 2.
All of the lines are well-separated thanks to appropriate
susceptibility differences between the solutions. The frequency
shift is roughly proportional to the Tbttha3- concentration
because this concentration has the most notable variation and
Tb3+ has the highest effective magnetic moment. Note that the
shift variations between Sol2 and Sol1 are somewhat larger than
those between Sol3 and Sol2 because the actual Lnttha3-
concentrations in Sol2 are about 6 % larger than their target
values in Table 1. As predicted by eq 8, the frequency shift
variation between two solutions is nearly independent of the
observed protons H in all of the molecules but HOD. For
instance, the shift variation between Sol3 and Sol2 is ∆Sol3-Sol1νtBuOD
/
νH ) 0.958 ppm for the tBuOD protons, but ∆Sol3-Sol1 HOD/νH
ν
) 1.061 ppm for the HOD protons. The deviation from eq 8
can be explained by significant values of the pseudocontact
dipolar interaction Hpcd of the HOD proton with the complexed
Tb3+ ion.29,38 This interaction stems from the susceptibility
anisotropy of Tbttha3- and varies with the distance rH of the
HOD proton to Tb3+ as rH-3. The molecular pair distribution
function of the small polar water molecules with respect to the
highly charged Tbttha3- ion is expected to be strongly
anisotropic40–43 and to have high peaks for some water/Tbttha3-
collision geometries where rH is small so that Hpcd is large. Then,
the ensemble average of Hpcd over the molecular pair distribution
function can also be significant and induce an observable
additional relative frequency shift of the water protons. Small
values of Hpcd can explain the tiny differences of frequency shift
variation between two solutions for the observed protons H in
all of the molecules but HOD. The concentration cGd of the PRE
agent Gdttha3- is reduced from Sol1 to Sol3 to balance the
increase of the nuclear relaxation rates which is due to the Tb3+
Curie spin29,30 and grows with the concentration cTb of Tbttha3-.
Thus, for instance at 25 °C, all of the proton relaxation times
are in the range (250 to 800) ms, which is very appropriate for
the measurements of the self-diffusion coefficients DX.
with a step of 1.18 G ·cm-1
.
Results and Discussion
As a first illustration of the method, we prepared three
solutions Sol1, Sol2, and Sol3 containing the H/D substituted
molecules and the Lnttha3- susceptibility shift inducers. The
solute concentrations are reported in Table 1 for the three
solutions.
The ligand ttha6- was chosen because it completely wraps
around the Ln3+ ions so that water, and of course methanol,
cannot enter the first coordination sphere.36 In contrast, the
popular ligands L for MRI such as dtpa5- (dtpa5- ) diethylene
The measured values of DX are reported in Table 2. Clearly,
DX increases when the molecular mass of the H/D substituted

Journal of Chemical & Engineering Data, Vol. 55, No. 5, 2010 2053
Figure 2. 1H 500 MHz spectrum of the H/D substituted molecules of methanol, tBuOD, and TPP in D2O at 25 °C. The substituted molecules are dissolved
in three solutions Sol1, Sol2, and Sol3 having different paramagnetic susceptibilities and placed in three parallel capillaries inside a standard 5 mm OD NMR
tube.
Table 2. Self-Diffusion Coefficients DX of the H/D Substituted
the standard NMR tube containing the capillaries. Besides, the
use of capillaries should reduce the convection artifacts21 which
become important for nonviscous liquids. We hope that the
observation of non-Stokesian self-diffusion effects in simple
D2O by the present method and also in ionic liquids by Wachter
et al.44 will encourage renewed theoretical efforts toward a full
understanding of the diffusion process at the molecular level.
Beyond the application to self-diffusion, the aim of this work
was to show the experimental potential of the parallel NMR
(molecular imaging) method based on solution magnetic-
susceptibility differences. In this method, the various liquid
solutions are at the same temperature and undergo the same
NMR procedure so that the observable quantities can be
accurately compared when necessary. More generally, the
parallelism of the method leads to a high throughput of data
which should facilitate the engineering work. Finally, in the
MRI context, it should provide a fast determination of
the contrast efficiency of a Gd3+ complex GdL, simply by the
parallel measurements of the water proton relaxation rates in
several GdL solutions with different concentrations of GdL and
thus different susceptibilities. Should the susceptibility differ-
ences be insufficient, the GdL complexes could be supplemented
with the same amount of auxiliary TbL complexes which
marginally increase the longitudinal proton relaxation rate.
Molecules X in D2O at the Temperatures (5, 25, and 50) °C
DX/10-5 cm2 ·s-1
X
t/°C ) 5
t/°C ) 25
t/°C ) 50
TP246DP
TP35DP
TPP
CHD2OD
CH3OD
tBu1OD ) CHD2(CD3)2COD
tBu3OD ) CH3(CD3)2COD
tBu9OD ) (CH3)3COD
0.178
0.187
0.187
0.604
0.639
0.320
0.337
0.336
0.360
0.366
0.378
1.13
0.706
0.755
0.757
2.08
2.30
1.30
1.25
0.647
0.663
0.681
1.39
1.34
molecule decreases. Typically, the relative increase δDX/DX is
0.05 for tBuOD or TPP and 0.10 for methanol. The dynamic
isotopic effect is smaller for tBuOD or TPP, since the motion
of these species, which are significantly larger than the D2O
solvent molecule, should tend toward that of a macroscopic
solute for which the Stokes-Einstein expression is valid. Finally,
the effect seems to slightly increase with temperature. This work
presents preliminary results on self-diffusion. Even with NMR
experiments using a restricted number of eight scans, it was
possible to detect small variations of the self-diffusion coef-
ficients of rather dilute solutes. The uncertainty on the absolute
values of the self-diffusion coefficients DX measured with the
help of the present parallel PGSE experiment is similar to that
of the standard experiment with a unique NMR tube and of the
order of several percent because of the imprecise calibration of
the gradient and RF pulses. This impreciseness does not cause
more uncertainty on the differences of the self-diffusion
coefficients obtained by the parallel PGSE method and does
not affect the accuracy of their ratios under the reasonable
assumption that the solutions in the capillaries undergo the same
gradient and RF pulses. Then, the uncertainty on these ratios
should be intrinsically low and statistically decrease with the
number of scans. Note that the spatial homogeneity of the
gradient and RF pulses between two capillaries can be checked
by repeating the experiments at different rotated positions of
Acknowledgment
This work is a contribution to the EC COST Action D-38 and
European EMIL network. We thank P.-A. Bayle for his help to
use the INAC NMR facilities.
Literature Cited
(1) Barthel, J. M. G.; Krienke, H.; Kunz, W. Physical Chemistry of
Electrolyte Solutions; Springer: Darmstadt, 1998.
(2) Dufreche, J. F.; Bernard, O.; Durand-Vidal, S.; Turq, P. Analytical
theories of transport in concentrated electrolyte solutions from the
MSA. J. Phys. Chem. B 2005, 109, 9873–9884.
(3) Hansen, J.-P.; McDonald, I. R. Theory of Simple Liquids, 3rd ed.;
Academic Press: London, 2006.

2054 Journal of Chemical & Engineering Data, Vol. 55, No. 5, 2010
(4) Suarez-Iglesias, O.; Medina, I.; Pizarro, C.; Bueno, J. L. On predicting
self-diffusion coefficients in fluids. Fluid Phase Equilib. 2008, 269,
80–92.
(5) Sacco, A.; Belorizky, E.; Jeannin, M.; Gorecki, W.; Fries, P. H.
Effective forces between diamagnetic and paramagnetic ions in D2O
at low and moderate ionic strengths: An NMR relaxation study. J.
Phys. II 1997, 7, 1299–1322.
(6) Helm, L. Relaxivity in paramagnetic systems: Theory and mechanisms.
Prog. Nucl. Magn. Reson. Spectrosc. 2006, 49, 45–64.
(7) Kruk, D.; Kowalewski, J. General treatment of paramagnetic relaxation
enhancement associated with translational diffusion. J. Chem. Phys.
2009, 130, 174104.
(8) Bonnet, C. S.; Fries, P. H.; Crouzy, S.; Seneque, O.; Cisnetti, F.;
Boturyn, D.; Dumy, P.; Delangle, P. A Gadolinium-Binding Cyclo-
decapeptide with a Large High-Field Relaxivity Involving Second-
Sphere Water. Chem.sEur. J. 2009, 15, 7083–7093.
(9) Gierer, A.; Wirtz, K. Molekulare Theorie Der Mikroreibung. Z.
Naturforsch., A: Phys. Sci. 1953, 8, 532–538.
(10) Spernol, A.; Wirtz, K. Zur Mikroreibung in Flussigkeiten. Z. Natur-
forsch., A: Phys. Sci. 1953, 8, 522–532.
(11) Edward, J. T. Molecular Volumes and Stokes-Einstein Equation.
J. Chem. Educ. 1970, 47, 261–270.
magnetic susceptibility shifts in NMR spectra. Magn. Reson. Chem.
2001, 39, 723–726.
(28) Belorizky, E.; Fries, P. H.; Gorecki, W.; Jeannin, M. Demagnetizing
Field Effects on High-Resolution NMR-Spectra in Solutions with
Paramagnetic Impurities. J. Phys. II 1991, 1, 527–541.
(29) Peters, J. A.; Huskens, J.; Raber, D. J. Lanthanide induced shifts and
relaxation rate enhancements. Prog. Nucl. Magn. Reson. Spectrosc.
1996, 28, 283–350.
(30) Bertini, I.; Luchinat, C.; Parigi, G. Solution NMR of Paramagnetic
Molecules; Elsevier: Amsterdam, 2001.
(31) Kowalewski, J.; Kruk, D.; Parigi, G. NMR Relaxation in Solution of
Paramagnetic Complexes: Recent Theoretical Progresses for S g 1.
AdV. Inorg. Chem. 2005, 57, 41–104.
(32) Fries, P. H.; Belorizky, E. Electronic relaxation of paramagnetic metal
ions and NMR relaxivity in solution: Critical analysis of various
approaches and application to a Gd(III)-based contrast agent. J. Chem.
Phys. 2005, 123, 124510.
(33) Fries, P. H.; Belorizky, E. Relaxation theory of the electronic spin of
a complexed paramagnetic metal ion in solution beyond the Redfield
limit. J. Chem. Phys. 2007, 126, 204503.
(34) Aman, K.; Westlund, P. O. Direct calculation of 1H2O T1 NMRD
profiles and EPR lineshapes for the electron spin quantum numbers S
) 1, 3/2, 2, 5/2, 3, 7/2, based on the stochastic Liouville equation
combined with Brownian dynamics simulation. Phys. Chem. Chem.
Phys. 2007, 9, 691–700.
(12) Mills, R.; Harris, K. R. The Effect of Isotopic Substitution on Diffusion
in Liquids. Chem. Soc. ReV. 1976, 5, 215–231.
(13) Weingartner, H.; Holz, M.; Sacco, A.; Trotta, M. The Effect of Site-
Specific Isotopic Substitutions on Transport-Coefficients of Liquid
Methanol. J. Chem. Phys. 1989, 91, 2568–2574.
(35) Caravan, P. Strategies for increasing the sensitivity of gadolinium based
MRI contrast agents. Chem. Soc. ReV. 2006, 35, 512–523.
(36) Chang, C. A.; Brittain, H. G.; Telser, J.; Tweedle, M. F. pH
Dependence of Relaxivities and Hydration Numbers of Gadolinium(III)
Complexes of Linear Amino Carboxylates. Inorg. Chem. 1990, 29,
4468–4473.
(37) Caravan, P.; Ellison, J. J.; McMurry, T. J.; Lauffer, R. B. Gadolin-
ium(III) chelates as MRI contrast agents: Structure, dynamics, and
applications. Chem. ReV. 1999, 99, 2293–2352.
(38) Fries, P. H.; Giraud, M.; Belorizky, E. Determination of the rate of a
fast exchanging coordinated molecule in a lanthanide(III) complex
by proton NMR. Phys. Chem. Chem. Phys. 2008, 10, 5817–5821.
(39) Fries, P. H.; Gateau, C.; Mazzanti, M. Practical route to relative
diffusion coefficients and electronic relaxation rates of paramagnetic
metal complexes in solution by model-independent outer-sphere
NMRD. Potentiality for MRI contrast agents. J. Am. Chem. Soc. 2005,
127, 15801–15814.
(40) Fries, P. H.; Kunz, W.; Calmettes, P.; Turq, P. Molecular-Solvent
Model for a Cryptate Solution in Acetonitrile - a Hypernetted-Chain
Study. J. Chem. Phys. 1994, 101, 554–577.
(41) Fries, P. H.; Kunz, W.; Calmettes, P.; Turq, P. Small-Angle Neutron-
Scattering - a Critical-Study of the Contrast Approximation. J. Chem.
Phys. 1994, 101, 578–584.
(42) Richardi, J.; Fries, P. H.; Krienke, H. The solvation of ions in
acetonitrile and acetone: A molecular Ornstein-Zernike study. J. Chem.
Phys. 1998, 108, 4079–4089.
(43) Fischer, R.; Richardi, J.; Fries, P. H.; Krienke, H. The solvation of
ions in acetonitrile and acetone. II. Monte Carlo simulations using
polarizable solvent models. J. Chem. Phys. 2002, 117, 8467–8478.
(44) Wachter, P.; Zistler, M.; Schreiner, C.; Fleischmann, M.; Gerhard,
D.; Wasserscheid, P.; Barthel, J.; Gores, H. J. Temperature Dependence
of the Non-Stokesian Charge Transport in Binary Blends of Ionic
Liquids. J. Chem. Eng. Data 2009, 54, 491–497.
(14) Holz, M.; Weingartner, H.; Sacco, A. Isotope Effects Upon Transla-
tional Diffusion as a Probe for Translation-Rotation Coupling in
Molecular Liquids. Ber. Bunsen-Ges. 1990, 94, 332–336.
(15) Holz, M.; Mao, X. A.; Seiferling, D.; Sacco, A. Experimental study
of dynamic isotope effects in molecular liquids: Detection of transla-
tion-rotation coupling. J. Chem. Phys. 1996, 104, 669–679.
(16) Hirschfelder, J. O.; Curtiss, C. F.; Bird, R. B. Molecular Theory of
Gases and Liquids; Wiley: New York, 1954.
(17) Weingartner, H. Isotopic Effects on the Tracer Diffusion of Water,
Methanol and Ethanol Dissolved in Carbon-Tetrachloride at 25-
Degrees-C. J. Chem. Soc., Faraday Trans. 1 1985, 81, 1031–1035.
(18) Wittko, G.; Kohler, W. Influence of isotopic substitution on the
diffusion and thermal diffusion coefficient of binary liquids. Eur. Phys.
J. E 2006, 21, 283–291.
(19) Bagno, A.; Rastrelli, F.; Saielli, G. NMR techniques for the investiga-
tion of solvation phenomena and non-covalent interactions. Prog. Nucl.
Magn. Reson. Spectrosc. 2005, 47, 41–93.
(20) Callaghan, P. T. Principles of Nuclear Magnetic Resonance Micros-
copy; Oxford University Press: New York, 2003.
(21) Jerschow, A.; Muller, N. Suppression of convection artifacts in
stimulated-echo diffusion experiments. Double-stimulated-echo experi-
ments. J. Magn. Reson. 1997, 125, 372–375.
(22) Evans, D. F. The Determination of the Paramagnetic Susceptibility
of Substances in Solution by Nuclear Magnetic Resonance. J. Chem.
Soc. 1959, 2003–2005.
(23) Zimmerman, J. R.; Foster, M. R. Standardization of NMR High
Resolution Spectra. J. Phys. Chem. 1957, 61, 282–289.
(24) Loliger, J.; Scheffol, R. Paramagnetic Moment Measurements by NMR
- Micro Technique. J. Chem. Educ. 1972, 49, 646–&.
(25) Piguet, C. Paramagnetic susceptibility by NMR: The “solvent cor-
rection” removed for large paramagnetic molecules. J. Chem. Educ.
1997, 74, 815–816.
(26) Vigouroux, C.; Belorizky, E.; Fries, P. H. NMR approach of the
electronic properties of the hydrated trivalent rare earth ions in solution.
Eur. Phys. J. D 1999, 5, 243–255.
(27) Corsi, D. M.; Platas-Iglesias, C.; van Bekkum, H.; Peters, J. A.
Determination of paramagnetic lanthanide(III) concentrations from bulk
Received for review December 4, 2009. Accepted March 9, 2010.
JE901031B