D. Vapor Liquid Equilibrium Measurements

and equipment intensive and are not commonly available in most typical laboratories. For most supercritical fluid solvent systems of interest the solvent

molecules are hydrocarbons (a notable exception is supercritical CO2 ). This

presents an opportunity for the use of high-pressure NMR to determine the

pressure–temperature–composition behavior of binary hydrocarbon solvents because of the ease of proton detection on the solvent molecules in both the vapor

and liquid phase simultaneously. In practice, the application of high-pressure

NMR for the determination of VLE phase behavior could be extended to any

1

spin one-half ( 2 ) nuclei of adequate sensitivity. A hydrocarbon-containing solvent system, ethylene/methanol, was investigated demonstrating the advantages

and limitations of high-pressure NMR for VLE determinations.

The VLE experimental data for the ethylene/methanol binary solvent system at 140◦ C is shown in Figure 3. The initial mole fraction of methanol at

the starting conditions of the NMR experiment was 0.54. This was determined

from the peak areas in the single-phase liquid region of the VLE phase diagram.

Liquid phase equilibrium data determined by McHugh et al. (37) is shown for

comparison in Figure 3. At pressures above the two-phase region only a single liquid phase was detected in the capillary cell. As pressure decreased the

two-phase region was entered, resulting in an NMR spectrum containing both

liquid and vapor phase. Figure 4A and 4B shows the two-phase and singlephase NMR spectra for the ethylene/methanol binary system at the pressures

of 130.0 and 269.5 bar, respectively. The vapor and liquid phases are readily

distinguished due to the differences in the chemical shifts between the two sepa-



Figure 3 Plot of the experimental phase behavior for ethylene/methanol at 140◦ C;

vapor phase (᭹), liquid phase (᭺), and liquid phase data (᭿) reported from McHugh

et al. (From Ref. 37.)



Copyright 2002 by Marcel Dekker. All Rights Reserved.



Figure 4 The high-pressure NMR spectra of the binary phase behavior of ethylene/

methanol at 140◦ C. Spectra A—ethylene/methanol at 130.0 bar; liquid phase: a , ethylene;

b , CH3 group in methanol; and c , OH group in methanol. Vapor phase: x , ethylene; y ,

CH3 group in methanol, and z , OH group in methanol. Spectra B—ethylene/methanol

at 269.5 bar in the single-phase region: a , ethylene, b , CH3 group in methanol, and c ,

OH group in methanol.



rate environments. The separately resolved peaks of the vapor and liquid phases

allow the simultaneous quantitation of the mole fraction of methanol in the

two phases.

A unique advantage of the NMR technique is the ability to determine the

behavior of the methanol protons in the two phases as a function of pressure.

The change in chemical shift, δ (ppm), was used to describe the dynamics and

extent of methanol–hydrogen bonding in the two-phase system as a function of

pressure. For the ethylene/methanol binary solvent system at 140◦ C, methanol

in the liquid phase exhibits a decrease in the extent of hydrogen bonding with

increasing pressure, but in the vapor phase methanol demonstrates an increase

in hydrogen bonding with increasing pressure (36). This is due to the change in

density of the two phases as one approaches the critical pressure. The density of

the liquid phase decreases, while the density of the vapor phase increases with

a concomitant decrease and increase, respectively, in the extent of methanol–

hydrogen bonding in the two phases. As pressure increases in the two-phase

region, the physical characteristics of the two phases become more similar (density, viscosity, and composition) by definition. As the liquid and vapor phases

merge to a single phase, the extent of hydrogen bonding and the chemical shifts

will merge to a single value. If the mole fraction of the binary modifier is near the

critical composition for the temperature and pressure under investigation, then



Copyright 2002 by Marcel Dekker. All Rights Reserved.



the change in the extent of hydrogen bonding in the two phases with pressure

can be used to determine the critical pressure of the binary solvent.



E. Diffusion Coefficient Measurements

Diffusion coefficients measured by the spin-echo technique provide a means

of investigating the translational motion of molecules under the extremes of

temperature and pressure. There have been numerous studies of the self-diffusion

coefficients of high-pressure liquids and supercritical fluids by NMR. As an

illustration of the potential of these physicochemical measurements, we will

focus on CO2 (3,28,33,38,39). The availability of a wide range of diffusion

coefficients and viscosities allows one to test the Stokes–Einstein equation at

the molecular level. From hydrodynamic theory,

D = (kB T )/(κπaη)



(6)



where kB is Boltzmann’s constant, T is temperature, κ is a constant equal to 4 for

slip boundary conditions and 6 for stick boundary conditions, a is the molecular

radius, and η is viscosity. Therefore, Eq. (6) relates the self-diffusion coefficient

to the viscosity of the solution. This equation is valid for a macroscopic sphere

moving in a solvent continuum and should apply only to solutions where the

solute is large in comparison with the solvent (stick condition). If the solute and

solvent are of comparable size, the slip condition should apply. It is interesting to

note that in past studies Eq. (6) has demonstrated its ability to provide reasonable

estimates of the diffusion coefficient for simple molecules (40). For CO2 , using

the slip condition and the assumption that the packing structure is arranged

as a cubic lattice with all CO2 molecules just touching, the predicted selfdiffusion coefficients were within ±5% of the experimentally determined values

for reduced densities greater than 1.5 (38). In their high-pressure CO2 diffusion

coefficient measurements, Lüdemann et al. (39) have shown that using a roughhard-sphere approximation to describe a in Eq. (6), results in the fluid becoming

more “sticky” as temperature increases. This is caused by the deviation of the

CO2 molecule from spherical symmetry as assumed in Eq. (6).

From Eq. (6), the self-diffusion coefficient can be related to the viscosity

of the solution in a simple manner. The measurement of solution viscosities at

high pressures and temperatures is a difficult, time-consuming task. Using highpressure NMR measurements of the diffusion coefficient under these extreme

conditions, the solution viscosity can be easily estimated from Eq. (6). Therefore, high-pressure NMR not only provides a very good estimate of solution

viscosity under extreme conditions of pressure and temperature but also provides an experimental method to test the different microscopic physicochemical

models of translational dynamics in solutions.



Copyright 2002 by Marcel Dekker. All Rights Reserved.



F. Quadrupolar NMR Measurements

The linewidth of a NMR absorption peak is dependent on the relaxation processes of the nuclei in solution. From the uncertainty principle,

E t∼



(7)



since E = h ν, and t can be related to the lifetime of the excited state

T2 , then ν ∼ 1/T2 . T2 represents all of the factors influencing the linewidth

(relaxation processes) and ν is the linewidth at half-height. When the relaxation

contributions are from spin-lattice effects, then T2 = T1 . Therefore, in units of

Hz the peak width at half-height ( ν1/2 ) of a NMR absorption is 1/π T1 . From

Eq. (5) for the quadrupolar relaxation rate of nuclei,

ν1/2 = 1/πT1 = (3π/10)(2I + 3/(I 2 (2I − 1)))(1 + ηs 2 /3)χ2 τc



(8)



where the parameters are the same as described in Sec. II.B. It is important

to note that ν1/2 is proportional to the rotational correlation time (τc ) of the

molecule containing the nuclei of interest. The molecular reorientation time in

a polar liquid has been described by Debye as

τ = 4πηa 3 /kB T



(9)



where the molecule is treated as a sphere of radius a in the viscous liquid

and τ involves the same motions as τc . Therefore, the rotational correlation

time depends on both the solution viscosity and temperature. From Eqs. (8)

and (9), it can be seen that the peak width at half height of the quadrupolar

nuclei is directly related to the viscosity of the solution. Thus, a decrease in the

linewidth of an NMR resonance undergoing a quadrupolar relaxation process

can be accomplished either through an increase in temperature or a decrease in

solution viscosity. This is critical, as the linewidth for a quadrupolar nucleus can

be very broad due to short relaxation times, and when coupled with low NMR

receptivity, peak detection is essentially impossible.

The advantage of supercritical fluids lies in their low viscosities as compared to liquids and in their variable solvating powers by changing density. The

study of quadrupolar nuclei naturally benefits from use of a supercritical fluid

solvent in terms of the decrease in viscosity, which contributes to a decrease

in linewidth. Studies have been reported investigating organic molecules containing 14 N and 17 O in supercritical fluids where the decrease in the linewidth

for the quadrupolar nuclei was substantial (41–43). In homogeneous catalysis

the organometallic compound can contain a transition metal that is a quadrupolar nuclei. The first report of the NMR investigation of such an organometallic compound (methylmanganesepentacarbonyl, 55 Mn) in supercritical ethylene

was by Jonas et al. (43). The line narrowing between the supercritical fluid

and a liquid solution for 55 Mn was reported to be a factor of 5.8. Rathke and



Copyright 2002 by Marcel Dekker. All Rights Reserved.



coworkers (44) were the first to exploit the line narrowing of quadrupolar nuclei in supercritical fluids to study in situ chemical reactions with high-pressure

NMR. Their work on the homogeneous catalytic activity of cobalt carbonyl

complexes in supercritical fluids is covered in Sec. III.D. While the number of

investigations of quadrupolar nuclei in supercritical fluid solvents have been few

(41–45), the distinct advantages of supercritical fluids for the investigation of

homogeneous catalysis and chemical synthesis in such systems should expand

in the future.



III. REACTIONS IN SUPERCRITICAL FLUIDS

NMR spectroscopy is routinely used in today’s organic synthesis laboratories to

identify and structurally characterize reaction products. Yet despite the enormous

structural information content of NMR and the availability of a variety of highpressure NMR techniques (3–13), it is little used for studying in situ chemical

reactions and solvent effects on chemical reactions in supercritical media.

Some advantages that are inherent to in situ NMR are as follows: (a) the

linewidth narrowing of quadrupolar nuclei in supercritical fluids allows NMR

measurements on nuclei with I ≥ 1; (b) in situ NMR conveniently provides

information on the phase behavior in the solution system; and (c) the nuclear

spin may be regarded as a label for reactive species. NMR spectroscopy can use

a variety of “labeling” techniques, such as a magnetization transfer experiment,

that manipulates the sample’s spin system with suitable pulse sequences. These

capabilities, which are unique to NMR spectroscopy, provide a wide array of

powerful means for studying chemical reactions. We hope the following sections

will capture some of the flavor of NMR’s ability toward the in situ investigation

of reactions in supercritical fluids.

A. Deuteration and Hydrogen Exchange Reactions

In supercritical water extremely weak acidic protons, such as aliphatic or aromatic protons, undergo substitution reactions. Hydrogen exchange of this class

of molecules in deuterium oxide can be studied by following the extent of

deuteration as a function of time. Evilia et al. (46–48) have studied deuteration reactions of various organic molecules in supercritical D2 O using ex situ

NMR. Their results have established that (a) the exchange reactions are base catalyzed, (b) for aromatic systems the inductive electron withdrawing of oxygenor nitrogen-containing functional groups may be stronger than resonance effects

resulting in preferential ortho deuteration selectivity, and (c) the substitution reaction most likely does not occur through hydride abstraction and the formation

of carbocations.



Copyright 2002 by Marcel Dekker. All Rights Reserved.



Hoffmann and Conradi (49) studied the deuteration of 4-ethylphenol in

supercritical D2 O at 460◦ C and 250 bar using high-pressure NMR. The methyl

protons were found to be stable under these conditions. The temperature was

raised to 500◦ C, and the deuteration of the methyl protons in conjunction with

decomposition reactions was monitored. From this investigation, the selective

deuteration of the different protons in 4-ethylphenol in supercritical D2 O could

be demonstrated.

Another investigation of the deuteration of resorcinol in supercritical D2 O

used a high-pressure NMR capillary cell as an in situ flow reactor (50). The

temperatures covered in these measurements ranged from 200◦ C to 450◦ C at a

pressure of about 400 bar. The deuterium exchange in resorcinol under these

conditions was observed using both proton and deuterium NMR as a function of

the resorcinol residence time in the capillary tubular reactor. The NMR results

indicate that H/D exchange in resorcinol for the ring protons was observed at

temperatures as low as 200◦ C. The activation energy of the H/D exchange of the

ortho/para ring protons on resorcinol was reported. The microvolume and low

thermal impedance of the capillary tubing contributes to the rapid temperature

equilibration in the flow-through reactor region in the NMR probe.

If the hydrogen exchange rate 1/τlife is comparable to the chemical shift

frequency difference, ωshift , of the spin exchanging sites, then lifetime broadening effects are visible in the NMR spectrum. Specifically, if hydrogen exchange

1, then one observes one sharp resonance. A

is fast, such that ωshift τlife

gradual slowing of the chemical exchange rate, to the regime of ωshift τlife ≈ 1,

results in resonance broadening. This eventually leads to the emergence of two

broad lines, each representing one of the two hydrogens. Finally, when hydrogen exchange is fast, such that ωshift τlife

1, two sharp lines are present in

the NMR spectrum. This was observed for a supercritical aqueous solution of

methanol when the density at a constant temperature of 400◦ C was gradually

decreased (49). Methanol in comparison with aliphatic or aromatic hydrocarbons

is a much stronger acid. At high densities and 400◦ C, hydrogen exchange is fast,

and one resonance line for the hydroxyl and water protons is observed. However,

with decreasing density the solvation characteristics of supercritical water and

methanol change. Hence, polar intermediates during hydrogen exchange, such

as H3 O+ , are less stabilized, which in turn slows the hydrogen exchange rate.

As a result, the hydrogen exchange rate at low, gas-like densities shows two distinct resonances for the hydroxyl and water protons. This example demonstrates

one of the major promises of supercritical fluids: reaction rates can be smoothly

altered at a fixed temperature by pressure-tuning (density-tuning) the solvation

characteristics of the supercritical fluid solvent.

Similar to lifetime effects based on chemical shift differences, the J coupling can be exploited to study changes in reaction rates as well (49). Using this

approach, the collapse of the J-coupling multiplets in ethanol (from the hydroxyl

proton coupling with the CH2 protons) was monitored as a function of pressure



Copyright 2002 by Marcel Dekker. All Rights Reserved.