2) H and (139) La NMR Spectroscopy in Aqueous Solutions at Geochemical Pressures.

TL;DR: A new NMR probe designed for solution spectroscopy at geochemical pressures allows experiments on aqueous solutions to pressures corresponding roughly to those at the base of the Earth's continental crust.

Abstract: Nuclear spin relaxation rates of (2) H and (139) La in LaCl3 +(2) H2 O and La(ClO4 )3 +(2) H2 O solutions were determined as a function of pressure in order to demonstrate a new NMR probe designed for solution spectroscopy at geochemical pressures. The (2) H longitudinal relaxation rates (T1 ) vary linearly to 1.6 GPa, consistent with previous work at lower pressures. The (139) La T1 values vary both with solution chemistry and pressure, but converge with pressure, suggesting that the combined effects of increased viscosity and enhanced rates of ligand exchange control relaxation. This simple NMR probe design allows experiments on aqueous solutions to pressures corresponding roughly to those at the base of the Earth's continental crust.

Summary

1. INTRODUCTION

• A common geochemical model of electrolyte solutions, the Helgeson-Kirkham-Flowers (HKF) model, describes the partial molar properties of solutes using an expression containing the dielectric constant of water and solutespecific variables derived from fits to experimental data.
• These new pressure and temperature limits inspired the design of a nuclear magnetic resonance (NMR) probe for examining solute speciation at higher pressures (Pautler et al., 2014; Ochoa et al., 2015).
• In contrast, the design described in the present paper has a 10–15 microliter sample volume (Fig. 1) and can reach pressures of 2.0 GPa.
• The CsCl and LaCl3 solutions were chosen because Jonas’ group not only measured the T1 values for these solu- tions, but also measured viscosities via the rolling-ball method at high pressures.

2. EXPERIMENTAL METHODS

• All cesium chloride (CsCl) solutions were prepared by dissolving the anhydrous salt into deuterium oxide solvent (D2O).
• This highpressure NMR probe is distinct from previous designs (e.g., Ballard et al., 1996, 1998) because it employs a small solenoid coil made of Berylco-25 wire wrapped around cylindrical capsule of PEEK (Polyether ether ketone) tubing containing 10–15 lL experimental solution.
• The cylindrical capsule is sealed at each end (Fig. 1.A) with waterproof epoxy.
• Pressure was monitored in situ using ruby fluorescence where movement of the R1 peak with pressure (Piermarini et al., 1975; Mao et al., 1986) could be monitored using an Ocean Optics HR4000 UV–vis spectrometer.
• Temperature in the probe was checked with a Type T thermocouple.

3. SOLUTION NMR

• Rapid tumbling of small molecules in a strong magnetic field causes the longitudinal and transverse relaxation times to become equivalent (T1 = T2).
• Here estimates in the pressure-variation of viscosity can be determined via measurements of the diffusion coefficient of H2O using the alternative expression: D ¼ kT 6pgr ð3Þ where D is the self-diffusion coefficient of molecules in the solvent, r is the hydrodynamic radius of the molecule and all other variables retain their usual definitions (Edward, 1970).
• In the PGSE experiment, the apparent signal-decay time constant is measured with a spin-echo experiment as function of the strength of the applied magnetic-field gradient pulses.
• These intensity data are then fit to Eq. (4) in order to calculate D, the apparent diffusion coefficient, with uncertainties established as the precision of four trials.
• An assumption is made that the scaling does not vary with pressure, which is reasonable since controls of the magnetic-field gradients are exterior to the probe.

4.1. 2H and 133Cs NMR relaxation rates in CsCl solutions compared to LaCl3 solutions

• The results using the microcoil probe are bracketed by the previous work at near temperatures (Fig. 2.B).
• The maximum in T1 values with pressure has generally been interpreted to indicate pressure-enhanced structuring of the solvent.
• The microcoil design has much less precise control over pressure at P < 0.4 GPa than the large-volume design of Lee et al. (1974), but it can recapture the characteristic maxima in 2H T1 values observed for all CsCl solutions.

4.2. Diffusion coefficients for H2O at pressure

• As described above, the viscosity can be estimated from measurement of an apparent diffusion coefficient using the PGSE pulse sequence.
• The apparent diffusion coefficients for H2O in both pure water and in a 1.0 m CsCl solution measured here are shown in Fig. 4.A.
• Note that the D values for both solutions decrease uniformly with pressure and that these trends match well the pressure variation of T1 values shown in Figs. 2 and 3. Solutions viscosities were calculated via Eq. (3) and are reported in Table 1.
• If changes in viscosity alone caused the measured variation in T1 values with pressure, then the ratio of D/T1 would be independent of pressure.
• As one can see, the ratios for all conditions lie within 10 % of each other and are independent of pressure, within experimental error.

4.3. Evidence for suppressed freezing

• Pressure was applied to all CsCl solutions until they froze, which was inferred from the disappearance of the 133Cs NMR peak, or when the 2H linewidth increased beyond the bandwidth of the detector.
• The estimated pressures when each solution froze are reported in Fig. 5, with respect to various phase boundaries.
• Ice-V and Ice-VI phase boundaries were reproduced from the results of Wagner et al. (1994).
• Lines in Fig. 5 also identify the solid–liquid phase boundary in the presence of different NaCl concentrations in H2O (Journaux et al., 2013).
• The points plotted on Fig. 5, however, correspond to a crude estimate of the actual freezing pressure – the authors cannot identify frozen samples in their NMR probe.

5.1. Relaxation in fully dissociated electrolytes

• The differences in T1 relaxation values at ambient conditions for solutions of various CsCl and LaCl3 concentrations are expected since these electrolytes affect the structure of water differently.
• Electrolytes are classified as ‘structure-breaking’ or ‘structure-making’ according to their effects on NMR relaxation and the structure of water (Cox and Wolfenden, 1934; Hribar et al., 2002; Marcus, 2009).
• Structure-breaking ions, like Cs+, allow solvent molecules to rotate more freely when added to pure water and structure-making ions, like La3+, restrict the rotation of solvent molecules by binding tightly to the bulk solvent lattice.
• Pressure eliminates the differences in T1 values for different solutions.

5.2. Viscosity of aqueous solutions at pressure and NMR spectroscopy

• The broadening with pressure of these signals can, under ideal circumstances, be interpreted to indicate pressure-induced changes in reaction rates and thus activation volumes.
• The contribution of viscosity will be increasingly important as high pressures are reached.
• As one can see in Tables 1 and 2, the increases in solution viscosities with pressure are monotonic and can probably be predicted from a simple regression.
• This agreement is important because the data in Table 2 were measured by Jonas’ group using a completely different method.
• They employed a rolling sphere to estimate the viscosity from optical measurements.

5.3. Suppressed freezing and metastability

• There are two causes of the apparent overpressurization of these solutions.
• The figure demonstrates solution freezing at 1.75 GPa after 15 min, as gauged by the slow disappearance of the NMR signal.
• As mentioned above, temperature estimates seem to be accurate and indicate that the sample is not heated by the radio frequency pulse in the saturation-recovery pulse sequence.
• Similar over-pressurization of the samples is observed when either fluorocarbon liquid or Daphne 7373 oil is used as the pressure medium.
• The simplest explanation for the relatively high freezing pressures is that higher pressures ure for pure H2O and 4.5 m CsCl in D2O at 10 C and 30 C (Jonas ed in Table 1 that were measured independently via NMR methods, can be reached via the combined effects of freezing-point depression by the electrolyte and solution metastability.

6. CONCLUSIONS AND IMPLICATIONS FOR GEOCHEMISTRY

• There are several important geochemical results from this study.
• As mentioned in the Introduction, the range of geochemical models for solution thermodynamics was recently extended via moleculardynamic estimates of the dielectric properties of water to 6.0 GPa and 1200 C (Pan et al., 2013; Sverjensky et al., 2014).
• It is reasonable to expect a similar effect to that which is found for NaCl solutions (Journaux et al., 2013).
• Finally, transport properties of molecules can be measured easily at pressure, such as the diffusion coefficients shown in Fig.
• At the high pressures of this study, contributions to the NMR linewidth from increased solvent viscosity are appreciable, but can be estimated directly and easily (Fig. 5).

Figures

Table 1 Diffusion coefficients and calculated viscosities for pure water and for 1.0 m CsCl solution at 20(±0.5) C. Diffusion coefficients in this table are estimated by dividing the measured value at ambient pressure by an accepted diffusion coefficient value for water at 20 C of 2.025 10 9 m2/s (Holz et al., 2000). Uncertainties are reported as an estimated standard deviation. Uncertainties in the pressure estimates are ±0.03 GPa.

Fig. 4. (A): Self-diffusion coefficients for H2O in water and aqueous solutions of 1.0 m CsCl, 4.5 m CsCl, or 1.0 LaCl3 at 20 (±0.5) C. (B): The diffusion coefficients divided by the 1H T1 measurements for pure H2O and for aqueous 1.0 m CsCl. Uncertainties from pressure were determined by propagating a ±0.01 nm (±30 MPa) estimated uncertainty in the peak position through the equations relating the R1 fluorescence of the ruby to pressure (Dewaele et al., 2008). Error estimates assigned to diffusion coefficient values are the estimated standard deviation from four repeated PGSE trials. The lines are merely to guide the eye and are not regressions.

Table 2 Viscosity measurements via the rolling-ball method as a function of press et al., 1976). Note that these values are about the same size as those report and that the change is similar with pressure.

Fig. 5. Estimated minimum freezing pressures of the experimental solutions relative to various phase boundaries for water. These pressures are inferred from the disappearance of liquid-like NMR behavior. Curves for Ice-V and Ice-VI were constructed from Wagner et al. (1994). The curve for metastable ice, labeled ‘New Ice’ was reproduced from Whittaker et al. (1998). The curves describing the salt-effected freezing of NaCl solutions are shown as various lines labeled: ‘4.0 m’, ‘2.5 m’ and ‘1.0 m’ (from Journaux et al., 2013). A sample of 1.0 m LaCl3 showed liquid-like NMR spectra all the way to 1.86 GPa and the final pressure is shown as an ‘ ’.

Fig. 1. The microcoil geometry, showing the 1-mm-diameter ruby sphere that is attached to a fiberoptic cable for pressure measurements and calibration. (A): Solenoid and ruby before a solution sample has been placed in the 10–15 lL PEEK tubing container, and before trimming, with no Stycast added to seal the berylliumcopper feedthrough. The coil length is 3.4 mm and the coil diameter is 2.7 mm. (B): The solenoid ready for an experiment. The sample is sealed into the tubing and the assembly is sealed with Stycast mixed with Al2O3 powder.

Fig. 6. Sequential 133Cs NMR spectra for 3.0 m CsCl at 1.75 GPa. The signal loss after 930 s indicates freezing. The remaining small peaks seen at 930 s are noise.

Fig. 3. T1 values for 133Cs for various CsCl solutions in D2O at 25 (±0.5) C. Errors assigned to pressure (±30 MPa) for 1.0 m, 2.0 m, and 3.0 m solutions, were determined by propagating a ±0.01 nm estimated uncertainty in the R1 fluorescence peak position through the equations relating the ruby fluorescence shift to pressure (Dewaele et al., 2008). Uncertainties for the 4.5 m CsCl solution (±100 MPa) were determined using a standard curve relating hydraulic press force to pressure measured in separate samples from ruby fluorescence (Ochoa et al., 2015). Uncertainties in the T1 values correspond to a single estimated standard deviation of triplicate measurements.

Fig. 2. (A): 2H T1 values as a function of pressure for various solutions at 25(±0.5) C. (B): 2H T1 data values as a function of pressure for pure D2O compared with previous data (Lee and Jonas, 1972). (C): Values of 2H T1 for CsCl and LaCl3 solutions (Ochoa et al., 2015) at 25(±0.5) C. Errors assigned to pressure (±30 MPa) was determined by propagating a ±0.01 nm estimated uncertainty in the R1 fluorescence peak position through the equations relating the ruby fluorescence shift to pressure (Dewaele et al., 2008). Uncertainties in the T1 values correspond to the estimated standard deviation of triplicate measurements.

Full text

UC Davis
UC Davis Previously Published Works
Title
(2) H and (139) La NMR Spectroscopy in Aqueous Solutions at Geochemical Pressures.
Permalink
https://escholarship.org/uc/item/1m07t5hs
Journal
Angewandte Chemie (International ed. in English), 54(51)
ISSN
1433-7851
Authors
Ochoa, Gerardo
Pilgrim, Corey D
Martin, Michele N
et al.
Publication Date
2015-12-01
DOI
10.1002/anie.201507773
Peer reviewed
eScholarship.org Powered by the California Digital Library
University of California

NMR spectroscopy of some electrolyte solutions to 1.9 GPa
Gerardo Ochoa
a
, Christopher A. Colla
b
, Peter Klavins
c
, Matthew P. Augustine
a,
⇑
,
William H. Casey
a,b,
⇑
a
Department of Chemistry, University of California, Davis, 1 Shields Ave, Davis, CA 95616, USA
b
Department of Earth and Planetary Sciences, University of California, Davis, 1 Shields Ave, Davis, CA 95616, USA
c
Department of Physics, University of California, Davis, 1 Shields Ave, Davis, CA 95616, USA
Received 14 May 2016; accepted in revised form 8 August 2016; Available online 13 August 2016
Abstract
Nuclear-magnetic resonance (NMR) spectra of CsCl and LaCl
3
in D
2
O/H
2
O solutions were collected up to pressures of
1.9 GPa using a new NMR probe design that considerably extends the pressure range available for geochemical experiments.
The longitudinal-relaxation times (T
1
) for
2
H compare well with those reported in the previous studies of Lee et al. (1974),
who examined lower pressures, and indicate that the probe functions properly. In some experiments,
133
Cs and
1
H NMR spec-
tra could be taken on solutions to pressures well beyond the nominal freezing pressure of D
2
OorH
2
O to form Ice VI (near
0.9 GPa). Freezing to form the high-pressure ice is kinetically slow on an experimental time scale (minutes to hours). The data
indicate that the electrolyte concentrations increase the freezing pressure of the solution. This result means that solution NMR
spectra can be collected at pressures that are nearly twice the nominal freezing pressure of pure D
2
OorH
2
O. Pulsed-magnetic-
field-gradient NMR methods are used to independently measure the self-diffusion coefficient of H
2
O in these solutions, which
yields estimates of solution viscosity via the Stokes–Einstein relation. The increased viscosity accounts for the pressure vari-
ation of T
1
values as rates of molecular tumbling are affected. Accounting for such changes is essential if NMR spectral line
widths are used to infer pressure-enhanced rates of geochemical reactions, such as interconversion of aqueous complexes.
Ó 2016 Elsevier Ltd. All rights reserved.
Keywords: NMR; Aqueous geochemistry; High-pressure spectroscopy; Electrolyte solutions; Diffusion; Viscosity
1. INTRODUCTION
A common geochemical model of electrolyte solutions,
the Helgeson-Kirkham-Flowers (HKF) model, describes
the partial molar properties of solutes using an expression
containing the dielectric constant of water and solute-
specific variables derived from fits to experimental data.
When this model is coupled to thermodynamic data for
minerals, it can be used to estimate solubilities and
speciation information at high pressures and temperatures
(Shock and Helgeson, 1988; Tanger and Helgeson, 1988;
Shock et al., 1989; Anderson and Crerar, 1993; Shock
and Koretsky, 1995; Sverjensky et al., 1997, 2014; Schulte
et al., 2001). Recently the HKF model was extended to
6.0 GPa and 1200 °C via molecular-dynamic estimates of
the dielectric constant of water (Pan et al., 2013;
Sverjensky et al., 2014). These new pressure and tempera-
ture limits inspired the design of a nuclear magnetic reso-
nance (NMR) probe for examining solute speciation at
higher pressures (Pautler et al., 2014; Ochoa et al., 2015).
There is a rich literature on high-pressure NMR spec-
troscopy, but this earlier work is generally limited to pres-
sures less than 0.5 GPa (see Ballard et al., 1996), with
heroic exceptions (Jonas, 1980; Lang and Lu
¨
demann,
http://dx.doi.org/10.1016/j.gca.2016.08.013
0016-7037/Ó 2016 Elsevier Ltd. All rights reserved.
⇑
Corresponding authors at: Department of Chemistry, Univer-
sity of California, Davis, 1 Shields Ave, Davis, CA 95616, USA
(W.H. Casey).
E-mail addresses: maugust@ucdavis.edu (M.P. Augustine),
whcasey@ucdavis.edu (W.H. Casey).
www.elsevier.com/locate/gca
Available online at www.sciencedirect.com
ScienceDirec t
Geochimica et Cosmochimica Acta 193 (2016) 66–74

1993; de Langen and Prins, 1995; Ballard et al., 1998).
These earlier designs generally employed milliliter-sized
samples. In contrast, the design described in the present
paper has a 10–15 microliter sample volume (Fig. 1) and
can reach pressures of 2.0 GPa. The early work was direc-
ted at detailing solvent motions and relaxation mechanisms
(Lee and Jonas, 1971; Lee et al., 1974; Akai and Jonas,
1976; Jonas et al., 1976; Defries and Jonas, 1977; Jonas,
1980; Lamb et al., 1981; Lamb and Jonas, 1981; Lang
and Lu
¨
demann, 1993; Ballard et al., 1998). High-pressure
NMR was then extended to estimate the activation volumes
of homoleptic reactions (Merbach and Vanni, 1977; Asano
and Noble, 1978; Ducommun et al., 1979a,b, 1980;
Monnerat et al., 1981; Swaddle and Merbach, 1981;
Meyer et al., 1982; Hugi-Cleary et al., 1985, 1987; Cossy
et al., 1987; Minirale, 1989; Pittet et al., 1990; Takagi
et al., 1994; Drljaca et al., 1998a; Swaddle et al., 2005;
Dees et al., 2007) with an intent of assigning mechanisms
to ligand-exchange reactions (Helm and Merbach, 2005).
The work has been reviewed several times (Asano and
Noble, 1978; Eldik et al., 1989; Drljaca et al., 1998b).
Diamond-anvil technologies, of course, can reach much
higher pressures but are limited to nanoliter sample vol-
umes or less, which are too small for studying solutes in
water (e.g., Meier et al., 2015).
In this paper, the NMR spectroscopy of a fully disso-
ciated electrolyte (CsCl, LaCl
3
) is studied in order to
reproduce the earlier work of Lee et al. (1974) and to
demonstrate the utility of the new probe design. Time
constants for the longitudinal relaxation (T
1
)of
2
H were
measured on aqueous CsCl in D
2
O and compare well
with the original work. In addition, values of T
1
were
determined for
133
Cs and
2
H NMR in the solutions and
were compared to previous work on LaCl
3
(Lee and
Jonas, 1971; Lee et al., 1974; Ochoa et al., 2015). The
CsCl and LaCl
3
solutions were chosen because Jonas’
group not only measured the T
1
values for these solu-
tions, but also measured viscosities via the rolling-ball
method at high pressures. Knowing the viscosity of an
experimental solution is important because this controls
rates of molecular tumbling and thus affects the widths
of NMR spectral peaks.
2. EXPERIMENTAL METHODS
All cesium chloride (CsCl) solutions were prepared by
dissolving the anhydrous salt into deuterium oxide solvent
(D
2
O). Lanthanum chloride (LaCl
3
) solutions were made
similarly but in H
2
O with a resistance of 18 MX. Solution
compositions were verified by coulometric titration for
the chloride ion. All pD and pH measurements were made
with a combination electrode and calibrated using standard
buffers in H
2
O. The pD values were calculated using:
pD = pH + 0.4 (Krȩzel and Bal, 2004).
The design of the high-pressure NMR probe is described
in earlier papers (Pautler et al., 2014; Ochoa et al., 2015)
and only the highlights are mentioned here. This high-
pressure NMR probe is distinct from previous designs
(e.g., Ballard et al., 1996, 1998) because it employs a small
solenoid coil made of Berylco-25 wire wrapped around
cylindrical capsule of PEEK Ó (Polyether ether ketone) tub-
ing containing 10–15 lL experimental solution. The cylin-
drical capsule is sealed at each end (Fig. 1.A) with
waterproof epoxy. The solenoid is fabricated from 28 gauge
beryllium-copper wire and fed through small holes in the
assembly where it is sealed with StycastÓ epoxy mixed with
a small amount of Al
2
O
3
powder (Fig. 1.B). A ruby
attached to a 200 lm fiber-optic cable is also passed
through the feedthrough, just below the RF coil, and
sealed. Pressure was monitored in situ using ruby fluores-
cence where movement of the R1 peak with pressure
(Piermarini et al., 1975; Mao et al., 1986) could be moni-
tored using an Ocean Optics HR4000 UV–vis spectrometer.
To ensure that the lowest-pressure measurements were
accurate, we confirmed the ruby-fluorescence calibration
via a four-wire resistance measurement on manganin wire
(Supplemental Information). The correlation is nearly exact
(Supplemental Information) but we use the fluorescence
estimates of pressure throughout this paper because they
can be made in situ.
The
133
Cs and
2
H NMR data were acquired using a
300 MHz (7.0 T) Oxford Instruments 78-mm-bore super-
conducting magnet interfaced to a spectrometer controlled
by Tecmag Orion
Ò
software. The
2
H T
1
measurements were
acquired using a standard inversion-recovery pulse
sequence with a calibrated p/2 time of 15.8 ls and a relax-
ation delay of 3 s (applied peak-to-peak radiofrequency
voltage of 130 V with a circuit Q  11). The
133
Cs T
1
mea-
surements were acquired using a saturation-recovery pulse
sequence with a calibrated p/2 of 9 ls and a relaxation
delay of 100 ms. The probe includes a cooling jacket
through which water was circulated at 25(±2) °C from an
external water bath. The two degree range corresponded
to a diurnal variation. Temperature in the probe was
checked with a Type T thermocouple. The experimental
range in temperature during an experiment was much smal-
ler at 25 °C (±0.5 °C).
Fig. 1. The microcoil geometry, showing the 1-mm-diameter ruby
sphere that is attached to a fiberoptic cable for pressure measure-
ments and calibration. (A): Solenoid and ruby before a solution
sample has been placed in the 10–15 lL PEEKÓ tubing container,
and before trimming, with no StycastÓ added to seal the beryllium-
copper feedthrough. The coil length is 3.4 mm and the coil diameter
is 2.7 mm. (B): The solenoid ready for an experiment. The sample is
sealed into the tubing and the assembly is sealed with StycastÓ
mixed with Al
2
O
3
powder.
G. Ochoa et al. / Geochimica et Cosmochimica Acta 193 (2016) 66–74 67

The self-diffusion coefficients of H
2
O in aqueous solu-
tions were measured using
1
H NMR on a permanent-
magnet-based Aspect Imaging MR-100 instrument at
43.7 MHz (1.0 T) that is interfaced to a Tecmag Apollo
Spectrometer. A standard pulsed-gradient spin-echo
(PGSE) pulse sequence was used with a field-gradient pulse
length of d = 10 ms and a gradient-pulse spacing of
D = 100 ms (Stilbs, 1987; Antalek, 2002). The p/2 pulse
time was calibrated to 15 ls for all solutions. Parameters
were extracted from the measured data with a Matlab code
by fitting the signal intensity to an exponential decay
(Stejskal and Tanner, 1965; Tanner and Stejskal, 1968).
Temperature in the bore of this magnet was also monitored
via a type-T thermocouple.
3. SOLUTION NMR
Rapid tumbling of small molecules in a strong magnetic
field causes the longitudinal and transverse relaxation times
to become equivalent (T
1
= T
2
). In this ‘‘extreme narrow-
ing” limit, the longitudinal relaxation rates of quadrupolar
nuclei (I > ½), such as
2
H and
133
Cs can be determined from
(Harris, 1986):
1
T
1Q
¼
1
T
2Q
¼
3
10
p
2
2I þ 3
I
2
ð2I  1Þ
hv
2
is
c
ð1Þ
where I is the spin of the nucleus, s
c
is the reorientation time
of the molecule, and hv
2
i is the mean square of the zero-
average quadrupolar-coupling constant.
The reorientation time of the molecule, s
c
, depends upon
solution viscosity and can be described using the Stokes–
Einstein equation as:
s
c
¼
gjV
m
kT
ð2Þ
where g is macroscopic viscosity, V
m
is hydrodynamic vol-
ume, and j is a theoretical constant that describes the ratio
of intermolecular torques on the solute molecule to the
intermolecular forces of the solvent molecules (McClung
and Kivelson, 1968; Kivelson et al., 1970). The value for
j is typically set to unity, so that V
m
can be treated as the
effective hydrodynamic volume. In these experiments, that
volume would be D
2
O, H
2
O, or a single Cs
+
or La
3+
ion
in solution.
The solution viscosity increases with pressure, which
originally motivated (Lee et al., 1974) to directly measure
viscosity in the high-pressure solutions. Here estimates in
the pressure-variation of viscosity can be determined via
measurements of the diffusion coefficient of H
2
O using the
alternative expression:
D ¼
kT
6pgr
ð3Þ
where D is the self-diffusion coefficient of molecules in the
solvent, r is the hydrodynamic radius of the molecule and
all other variables retain their usual definitions (Edward,
1970). In evaluating Eq. (3), a hydrodynamic radius for
water of 1.379 A
˚
is used (Woessner, 1964; Rahman
and Stillinger, 1971) and assumed to be independent of
pressure.
The diffusion coefficient of H
2
O was measured via a
variation of a method employed by Akai and Jonas
(1976) that is well developed for ambient pressure
(Stejskal and Tanner, 1965; Tanner and Stejskal, 1968).
In the PGSE experiment, the apparent signal-decay time
constant is measured with a spin-echo experiment as func-
tion of the strength of the applied magnetic-field gradient
pulses. The Akai and Jonas (1976) method employed a sta-
tic gradient. For the work reported here, the PGSE pulse
sequence is a standard p/2-pulse followed by a p-pulse. Fol-
lowing the first p/2-pulse, an initial magnetic-field gradient
pulse is applied with length d. Subsequently, at a time D
later than the initial gradient, a second gradient pulse with
an identical length d is applied. The apparent diffusion coef-
ficient is determined by fitting the measured intensity data
to the following equation (Stejskal and Tanner, 1965;
Tanner and Stejskal, 1968):
S ¼ S
0
exp c
2
G
2
d
2
D 
d
3

D

ð4Þ
where S
o
is signal intensity in the absence of a gradient, c is
the gyromagnetic ratio, G is the strength of the gradient
pulse in Tesla/m, and D is the apparent diffusion coefficient.
During the field gradient pulse, the signal intensity, S,
decreases exponentially as a function of time and as a func-
tion of G. These intensity data are then fit to Eq. (4) in
order to calculate D, the apparent diffusion coefficient, with
uncertainties established as the precision of four trials. This
value is ’apparent’ because the actual magnetic-field gradi-
ents affecting the microcoil sample are not known with cer-
tainty, only the field gradients produced by the
spectrometer. Conventionally, such geometry-specific
effects are eliminated by using a well-accepted standard to
scale the measurements. An accepted value for the diffusion
coefficient of H
2
Oat20°C is 2.025  10
9
m
2
/s (Holz et al.,
2000). This value is used to scale the apparent measure-
ments, which are within a factor of two of this number at
ambient pressures. An assumption is made that the scaling
does not vary with pressure, which is reasonable since con-
trols of the magnetic-field gradients are exterior to the
probe. The coil and sample are also not considerably
deformed by the hydrostatic pressure.
4. RESULTS
4.1.
2
H and
133
Cs NMR relaxation rates in CsCl solutions
compared to LaCl
3
solutions
The T
1
values for
2
H in various solutions at 25 °C are
shown in Fig. 2.A. The values for pure D
2
Oat25°C (this
paper) and at 10 °C and 30 °C from Jonas’ group (Lee
et al., 1974) are shown in Fig. 2.B. The results using the
microcoil probe are bracketed by the previous work at near
temperatures (Fig. 2.B). The similarity between the T
1
val-
ues reported here and those reported previously indicates
that the microcoil sample is not being heated by repeated
pulsing and that the NMR probe design is trustworthy.
The maximum in T
1
values with pressure has generally been
interpreted to indicate pressure-enhanced structuring of the
solvent. The microcoil design has much less precise control
68 G. Ochoa et al. / Geochimica et Cosmochimica Acta 193 (2016) 66–74

over pressure at P < 0.4 GPa than the large-volume design
of Lee et al. (1974), but it can recapture the characteristic
maxima in
2
H T
1
values observed for all CsCl solutions.
Lee et al. (1974) report the maximum at about
0.3–0.5 GPa. Comparison of
2
H T
1
values in a 4.5 m CsCl
and LaCl
3
solutions indicate that the steady decline in T
1
values with pressure is similar (Fig. 2.C). Beyond the
0.5 GPa maxima, the T
1
values for all D
2
O solutions
decrease uniformly (Fig. 2) and this decrease has been inter-
preted as resulting from an increase in solution viscosity
(Lee et al., 1974).
The
133
Cs T
1
values of CsCl solutions (Fig. 3) also
decrease uniformly with pressure and the rate of decrease
is nearly, but not completely, independent of solution com-
position. These results contrast with previous work on
LaCl
3
solutions where the
139
La T
1
values vary consider-
ably with electrolyte concentrations at ambient pressures
(Ochoa et al., 2015). For example, at ambient pressures,
an increase of LaCl
3
concentration from 1.0 m to 4.5 m is
accompanied by a large decrease in the T
1
values from
1.11(±0.02) ms to 0.18(±0.09) ms (Ochoa et al., 2015). In
contrast, T
1
values for
133
Cs decrease only from 11.6
(±1.2) s to 8.5(±0.4) s over a similar range in concentra-
tion. The difference is also manifested in the properties of
the solvent. For example, the T
1
values for
2
H in 1.0 m
and 4.5 m LaCl
3
are 0.27(±0.02) and 0.18(±0.005) s,
respectively. This difference is much larger than in similar
CsCl solutions, where the
2
H T
1
values are 0.43(±0.04) s
and 0.47(±0.02) s for 1.0 m and 4.5 m CsCl solutions,
respectively.
4.2. Diffusion coefficients for H
2
O at pressure
As was originally concluded by the Jonas group, pres-
sure variations in T
1
values reflect changes in viscosity of
the solution. As described above, the viscosity can be
estimated from measurement of an apparent diffusion coef-
ficient using the PGSE pulse sequence. The apparent diffu-
sion coefficients for H
2
O in both pure water and in a 1.0 m
CsCl solution measured here are shown in Fig. 4.A. Note
that the D values for both solutions decrease uniformly
with pressure and that these trends match well the pressure
variation of T
1
values shown in Figs. 2 and 3. Solutions vis-
cosities were calculated via Eq. (3) and are reported in
Table 1.
If changes in viscosity alone caused the measured varia-
tion in T
1
values with pressure, then the ratio of D/T
1
would be independent of pressure. Such a ratio is shown
as Fig. 4.B. As one can see, the ratios for all conditions
lie within 10 % of each other and are independent of pres-
sure, within experimental error.
Fig. 2. (A):
2
H T
1
values as a function of pressure for various
solutions at 25(±0.5) °C. (B):
2
H T
1
data values as a function of
pressure for pure D
2
O compared with previous data (Lee and
Jonas, 1972). (C): Values of
2
H T
1
for CsCl and LaCl
3
solutions
(Ochoa et al., 2015) at 25(±0.5) °C. Errors assigned to pressure
(±30 MPa) was determined by propagating a ±0.01 nm estimated
uncertainty in the R1 fluorescence peak position through the
equations relating the ruby fluorescence shift to pressure (Dewaele
et al., 2008). Uncertainties in the T
1
values correspond to the
estimated standard deviation of triplicate measurements.
Fig. 3. T
1
values for
133
Cs for various CsCl solutions in D
2
Oat25
(±0.5) °C. Errors assigned to pressure (±30 MPa) for 1.0 m, 2.0 m,
and 3.0 m solutions, were determined by propagating a ±0.01 nm
estimated uncertainty in the R1 fluorescence peak position through
the equations relating the ruby fluorescence shift to pressure
(Dewaele et al., 2008). Uncertainties for the 4.5 m CsCl solution
(±100 MPa) were determined using a standard curve relating
hydraulic press force to pressure measured in separate samples
from ruby fluorescence (Ochoa et al., 2015). Uncertainties in the T
1
values correspond to a single estimated standard deviation of
triplicate measurements.
G. Ochoa et al. / Geochimica et Cosmochimica Acta 193 (2016) 66–74 69

Frequently asked questions

Q1. What have the authors contributed in "Nmr spectroscopy of some electrolyte solutions to 1.9 gpa" ?

The longitudinal-relaxation times ( T1 ) for H compare well with those reported in the previous studies of Lee et al. ( 1974 ), who examined lower pressures, and indicate that the probe functions properly. 

Q2. What are the future works in "Nmr spectroscopy of some electrolyte solutions to 1.9 gpa" ?

These pressures, however, are well beyond the current capabilities of conventional hydrothermal solution spectroscopies, yet through judicious choice of nonmagnetic, high-strength alloys ( e. g., Uwatoko et al., 2002 ), it should not be difficult to extend the 2. Furthermore, and most interestingly, the crystallization of high-pressure ices from these solutions at pressure is sufficiently slow that NMR spectra can be acquired. The authors, of course, know nothing of the phases that precipitate when they lose liquid-like NMR signals from these solutions, but these questions await further experimentation. Finally, transport properties of molecules can be measured easily at pressure, such as the diffusion coefficients shown in Fig.