Effect of Electrolyte Concentration on the Viscosity and Voltammetry of

Anal. Chem. 2005, 77, 6702-6708

Effect of Electrolyte Concentration on the Viscosity and Voltammetry of Supercritical Solutions Andrew P. Abbott,* Eric G. Hope, and Donna J. Palmer

Chemistry Department, University of Leicester, Leicester, LE1 7RH, U.K.

The viscosity of a supercritical electrolyte solution is measured for the first time using a modified quartz crystal microbalance, and it is shown that ionic solvation leads to a significant structuring of the solvent and an appreciable increase in solution viscosity. Voltammetric investigations in the electrolyte solutions are used to confirm the magnitude of the viscosity changes, and these account for the appreciably lower than expected peak currents. Relatively few investigations have been carried out on the effects on viscosity of solutes dissolved in supercritical (sc) fluids. The majority of high-pressure viscosity studies have been concerned with the dissolution of biomolecules or polymers and have been conducted at subcritical pressures. The reason for this is the experimental difficulties faced with working at both high temperatures and pressures. Despite this, a range of techniques are available to study high-pressure viscosities including the oscillating disk viscometer,1 vibrating wire viscometer,2 highpressure capillary viscometer,3-5 magnetoviscometer,6 and vibrating quartz crystal viscometer.7 The most common is the fallingbody type viscometer.8-20 Several research groups have examined the changes in viscosity of sc fluids upon the addition of cosolvents or modifiers.21,22 It was found that in dilute solutions viscosities * To whom correspondence should be addressed. E-mail: [email protected]. Fax: UK + 116 252 3789. (1) Yokoyama, C.; Takahashi, M. Int. J. Thermophys. 1997, 18, 1369. (2) Padua, A. A. H.; Fareleria, J. M. N. A.; Calado, J. C. G. J. Chem. Eng. Data 1996, 41, 1488. (3) Yener, M. E.; Kashulines, P.; Rivzi, S. S. H.; Harriott, P. J. Supercrit. Fluids 1998, 11, 151. (4) Tuan, D. Q.; Zollweg, J. A.; Harriott, P.; Rizvi, S. S. H. Ind. Eng. Chem. Res. 1999, 38, 2129. (5) Kashulines, P.; Rizvi, S. S. H.; Harriott, P.; Zollweg, J. A. J. Am. Oil Chem. Soc. 1991, 68, 912. (6) Et-Tahir, A.; Boned, C.; Lagourette, B.; Xans, P. Int. J. Thermophys. 1995, 16, 1309. (7) Vieira dos Santos, F. J.; Nieti de Castro, C. A. Int. J. Thermophys. 1997, 18, 367. (8) Cook, R. L.; King, H. E. Jr.; Peiffer, D. G. Macromolecules 1992, 25, 2928. (9) Mertsch, R.; Wolf, B. A. Macromolecules 1994, 27, 3289. (10) Dindar, C.; Kiran, E. Rev. Sci. Instrum. 2002, 73, 3664. (11) Sen, Y. L.; Kiran, E. J. Supercrit. Fluids 1990, 3, 91. (12) Kiran, E.; Sen, Y. L. Int. J. Thermophys. 1992, 13, 411. (13) Dindar, C.; Kiran, E. Ind. Chem. Eng. Chem Res. 2002, 41, 6354. (14) Xiong, Y.; Kiran, E. Polymer 1995, 36, 4817. (15) Kiran, E.; Gokmenoglu, Z. J. Appl. Polym. Sci. 1995, 58, 2307. (16) Kiran, E.; Sen, Y. L. ACS Symp. Ser. 1993, 514, 104. (17) Xiong, Y.; Kiran, E. Polymer 1997, 38, 5185. (18) Yeo, S. D.; Kiran, E. J. Supercrit. Fluids 1999, 15, 261. (19) Yeo, S. D.; Kiran, E. Macromolecules 1999, 32, 7325. (20) Yeo, S. D.; Kiran, E. J. Appl. Polym. Sci. 2000, 75, 306.

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and densities increase with solute size, polarity, and concentration of cosolvent. A significant number of studies have been carried out on biomaterials in sc fluids. Peter and Jacob23 examined the viscosities of coexisting phases of sc ethane and sc CO2 with a number of fatty acids including pelargonic acid, oleic, acid and linoleic acid. It was found that the viscosity of the sc phase increased with increasing pressure and the viscosity of liquid phase decreased. More recently, Harriott et al. have measured and modeled the viscosities of several sc CO2/lipid mixtures by high-pressure capillary viscometry.3-5 They explored the viscosities of solubilized methyl oleate and oleic acid as a function of concentration up to 5 wt % and temperatures were from 313 to 333 K. Relative viscosities, which are the ratio solution viscosity and pure solvent (ηr ) η/ηo), increased linearly with concentration and were found to be no greater than 1.21 for either solute. It was concluded that the addition of oleic acid causes a 3-fold increase in viscosity when compared to the addition of the same weight percent of methyl oleate.4 The viscosity dependence on methyl oleate mass fraction in sc CO2 was measured at 313 K and pressures ranging from 106 to 115 bar.. This dependence was found to be linear, and a viscosity increase of 35% was measured for the system with 9% mass fraction at 115 bar.5 Prior to this, the group had investigated the viscosities of several fatty acid and fatty acid esters saturated with sc CO2.3 At temperatures of 313 and 333 K, oleic acid and linoleic acid were assessed at pressures ranging from 85 to 350 bar and methyl oleate and methyl linoleate at pressures from 90 to 170 bar. In addition, they evaluated anhydrous milk fat (AMF) at 313 K and from 100 to 130 bar. Results showed that, at the viscosities of the liquid phase, methylated fatty acids decreased by a factor greater than 10 as the pressure was increased. Both the fatty acids and AMF also experienced a viscosity reduction; however, in comparison with the methylated fatty acids, this was lower at higher pressures. At constant pressure, the viscosities of fatty acids and AMF decreased with increasing pressure whereas the methylated fatty acids experienced an increase in viscosity. The synthesis and modification of polymers using sc fluids is a growing area of research. To successfully design new processes, knowledge of transport properties such as viscosity and diffusivity is essential. However, it is only in the past three decades that (21) Llave, F. M.; Chung, F. T. H.; Burchfiled, T. E. SPE Reservoir Eng. 1990, 47. (22) Tilly, K. D.; Foster, N. R.; Macnaughton, S. J.; Tomasko, D. L. Ind. Eng. Chem. Res. 1994, 33, 681. (23) Peter, S.; Jacob, H. J. Supercrit. Fluids 1991, 4, 166. 10.1021/ac050883i CCC: $30.25

© 2005 American Chemical Society Published on Web 09/13/2005

research into high-pressure polymer solution viscosity has been conducted. Kiran and Sen have done the most extensive work in this area. Employing a falling-body type viscometer, they reported the temperature and pressure dependence of viscosity and density of several high-pressure alkanes11,12 and progressed to research the effect on solution viscosity of several polymers in both subcritical and sc alkanes and sc CO2. Studies include the following: poly(dimethylsiloxane) (PDMS) in sc CO2,13,14 polyethylene (PE) in n-pentane,14,15 and polystyrene (PS) in near-critical and sc n-butane,16 subcritical n-hexane,12 subcritical methylcyclohexane,17 and toluene with sc CO2.18,19 Activation energies and activation volumes were calculated from the respective temperature and pressure dependencies. Density dependencies of viscosity have also been examined using a free-volume relationship. The effect of temperature and pressure are unified when plotted as a function of density and close-packed volumes are calculated.12-15 Solutions of sc CO2/PDMS at 1, 2, and 5 wt % polymer compositions were investigated at pressures between 400 and 600 bar and temperatures of 380, 400, and 420 K. The corresponding relative viscosities ranged from approximately 1 to 1.50 at the highest PDMS weight percent.13 More recently, work has been carried out at the critical polymer concentrations of 5.5 wt % for PDMS in sc CO2 and 5.75 wt % PE in subcritical n-pentane. Pressures up to 500 bar were evaluated, and temperatures ranged from 328 to 373 K for PDMS solutions and were 413 and 423 K for PE solutions. At these temperatures and pressures, the corresponding relative viscosities were ∼2 for sc CO2/PDMS solutions and ranged from 18 to 26 for n-pentane/PE solutions.14 PS in sc n-butane was evaluated at temperatures from 395 to 445 K and pressures up to 700 bar. Viscosities again followed the general trend of increasing with pressure and polymer concentration and decreasing with temperature.16 All of the systems studied to date have been carried out in nonpolar sc fluids and have reported modest increases in viscosity. The solutes studied to date have also been nonpolar and hence would be expected to cause only modest ordering in the sc solution. In the current investigation, the effect of a quaternary ammonium electrolyte upon the viscosity of sc difluoromethane is quantified using a quartz crystal microbalance (QCM) as a viscometer, and the viscosities obtained are verified by measuring the diffusion coefficient of ferrocene using voltammetry. EXPERIMENTAL SECTION Electrochemical investigations were carried out using the highpressure cell shown in Figure 1. The cell was constructed from 316 stainless steel with an internal volume of ∼40 cm3 and was rated to 300 bar. The electrical feedthroughs consisted of microwave cable (RS Components Ltd.) sealed by Swagelok fittings. Prior to each measurement, the cell was purged with the appropriate gas and the pressure was applied using a model P50series piston controlled pump (Thar Technologies, inc., Pittsburgh, PA). The pressure was monitored ((2 bar) using a Swagelok manometer. At the center of the cell, the tip of an iron/constantan thermocouple was in contact with the solvent and a constant temperature ((0.5 °C) was retained using a CAL 9300-controlled heater. The solvent CH2F2 (Ineos Fluor >99.99% purity) was used as received. For the voltammetric experiments, a PGSTAT 20 potentiostat (Ecochemie) was employed. The working electrode was a 1-mm

Figure 1. Schematic diagram of the cell used to simultaneously measure solution viscosity and voltammetry. 1, working electrode; 2, reference electrode; 3, counter electrode.

diameter Pt disk, a Pt wire counter electrode was employed, and potentials were quoted against a Ag wire reference electrode. The electrodes were sealed in Scotch-Weld epoxy resin, which was covered with a glass sleeve to make it impermeable to the supercritical fluid. The electrolyte tetrabutylammonium tetrafluoroborate (TBABF4; Fluka, electrochemical grade) and ferrocene (Fluka) were used as received. The concentration of ferrocene was 1 mM, and the sweep rate was 10 mV s-1 in all cases. Prior to each measurement, the Pt electrode was polished to a mirror finish with 1-µm alumina paste. To make the viscosity measurements, a modified 10-MHz ATcut gold quartz crystal resonator (International Crystal manufacturing) was used. The shift in oscillating frequency of the crystal, ∆F, can be related to the viscosity of the surrounding solvent, ηs, by an extension to the Saurebrey equation24

∆F ) F03/2(ηsFs/πµQFQ)1/2

(1)

where F0 is the crystal frequency under ambient conditions, Fs is the solvent density, and FQ and ηQ are the density and shear modulus of the quartz. The oscillating frequency was measured at 10 MHz and 500 kHz range by a E5061 Network Analyzer (Aligent Technologies), and readings were taken as an average of three measurements. The area of the crystal was 0.3 cm2 and had a thickness of 60 bar), it is not possible to have one side of the crystal exposed to solution and the other to air. Therefore, it was necessary to modify the crystal to allow only one side to be exposed to the supercritical solution. This was done by thinly coating one side of the crystal with an epoxy resin (RS Components). The epoxy resin was not found to swell significantly when the cell was pressurized, and hence, it was assumed to have a relatively constant reference oscillating frequency. Prior to each high-pressure measurement, the oscillating frequency of the crystal under ambient temperature and pressure was recorded. To account for any frequency shifts due (24) Buttry, D. A.; Ward, M. D. Chem. Rev. 1992, 92, 1355.

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to temperature, a measurement of the crystal frequency at each appropriate temperature under ambient pressure was also recorded. All frequency shifts are quoted as the difference between the frequency under ambient conditions and under conditions of the system under investigation and are normalized to the ambient value. The quartz crystal was calibrated from literature viscosity and density data for CH2F2,25 water, and sucrose solutions26,27 at 25 °C. Measurements carried out under high pressure are difficult and should only be attempted by suitably qualified personnel using apparatus specifically designed for the operating conditions. RESULTS To ensure that the electrolyte was soluble and that the resultant solution was homogeneous, the system was viewed in a tubular high-pressure cell with sapphire windows at either end such that the entire volume could be viewed. TBABF4 (0.086 g) was put in a 10-mL cell, and the pressure of CH2F2 was varied from 15 to 300 bar. When CH2F2 (15 bar) was first introduced to the cell at 90 °C, the electrolyte immediately liquefied to form a dense liquid at the base of the cell despite the CH2F2 being in the gaseous state. The volume of the liquid phase was not too dissimilar to that of the solid electrolyte; however, it is unlikely to be a simple melting of the electrolyte as the cell temperature was 70 °C below the melting point of the electrolyte (159-162 °C). Such effects have also been observed by other groups with CO2 and ethane; however, the effect is not fully understood.28-32 In the case of TBABF4 with CH2F2, it is assumed that the electrolyte could form a clathrate, with the gas molecules coordinating strongly to the ions, decreasing the lattice energy, and causing the complex to melt. This has previously been observed with the same electrolyte with nonpolar liquids such as toluene.28 The observation that this occurs with a gaseous fluid demonstrates the high affinity of the electrolyte for CH2F2. This dense liquid phase remains until the pressure is raised above 80 bar in the supercritical region whereupon it becomes completely miscible and the whole solution becomes transparent. Pressurizing the cell to 300 bar did not induce any further phase changes, and hence, all further studies were confined to pressures above 100 bar where the fluid was known to be homogeneous. The cell shown in Figure 1 was used to quantify the effect of electrolyte concentration on viscosity of the sc fluids as a function of pressure. The cell had two complementary techniques that could both be used to measure the effect of viscosity, viz. QCM and an electrochemical cell that could be used to measure diffusion coefficients using voltammetry. With the QCM, the change in crystal admittance was related to the solution viscosity and this was carried out using a variety of liquids with known viscosity to calibrate the apparatus. Figure 2 shows a calibration plot obtained using pure CH2F2, water and aqueous sucrose solutions. The viscosities of these liquids were (25) Tillner-Roth, R.; Yokozeki, A. J. Phys. Chem. Ref. Data 1997, 26, 1273. (26) Hardy, R. C.; Cottington, R. L. J. Res. NBS 1949, 42, 573. (27) James, C. J.; Mulcahy, D. E.; Steel, B. J. J. Phys. D: Appl. Phys. 1984, 17, 225. (28) Van Welie, G. S. A.; Diepen, G. A. M. J. Phys. Chem. 1963, 67, 755. (29) Rodrigues, A. B. J.; Kohn, J. P. J. Chem. Eng. Data 1967, 12, 191. (30) McHugh, M. A.; Yogan, T. J. J. Chem. Eng. Data 1984, 29, 112. (31) Kazarian, S. G.; Sakellarios, N.; Gordon, C. M. Chem. Commun. 2002, 1314. (32) Leitner, W. Private communication, 2005. (33) Pickett, C. J. J. Chem. Soc., Chem. Commun. 1985, 323.

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Figure 2. Calibration curve ∆F ) 0.00121 ((3.8 × 10-5)ηF1/2 + 5.72 × 10-4 ((2.28 × 10-5).

Figure 3. CH2F2 solution viscosity as a function pressure and TBABF4 concentration at 90 °C.

taken from the literature and this gave a line of best fit of

∆A/A0 ) 0.00121((3.8 × 10-5)ηF1/2 + 5.72 × 10-4 ((2.28 × 10-5) (2) where ∆A is the change in admittance from the quartz crystal resonator in contact with the electrolyte solution compared to the value obtained in contact with air, A0, F is the solution density, and η is the solution viscosity. Good correlation was observed for all data to eq 1 (r ) 0.98). The data for CH2F2 solutions containing various concentrations of TBABF4 were obtained as a function of pressure, and these are shown in Figure 3. It can be seen that the incorporation of quaternary ammonium electrolytes results in a significant increase in solution viscosity even at relatively low concentrations. Given that in pure CH2F2 the viscosity ranges from 0.056 to 0.092 cP over the pressure range 100-260 bar, the data in Figure 3 represent relative viscosities in the range from 8 to 32 depending on the pressure and concentration. Figure 3 shows that the addition of 0.03 mol dm-3 electrolyte increases the viscosity such that it is more akin to a liquid solution. The increase in relative viscosity is considerably greater that those studied previously for fatty acids in scCO2.23 However, this is not surprising given that CO2 has no dipole moment and that the solute is relatively nonpolar such that solvent-solute and solute-solute interactions will be weak and it would not cause significant changes in the

Table 1. Physical Properties and Molar Conductivity of CH2F2 (90 °C) and CH2Cl2 (25 °C, 1 bar) p/bar

η25/ g cm-1 s-1

40

V25/ cm3 mol-1

Λ039/ S cm2 mol-1

λ0+/ S cm2 mol-1

λ0-/ S cm2 mol-1

A/ cm1/2 mol-1/2

Vfree/ %

100 150 200 260 CH2Cl2

0.0563 0.0698 0.0787 0.0919 0.401

7.39 8.29 8.99 9.59 8.93

77.3 67.4 63.0 59.8 64.5

0.770 0.622 0.551 0.499 0.108

0.202 0.163 0.145 0.131 0.028

0.568 0.459 0.406 0.368 0.080

0.501 0.473 0.454 0.416 0.505

59.7 53.7 50.5 47.9 30.0

solution structure. With TBABF4 dissolved in CH2F2, considerable solvent structuring will be required to solvate the ionic species and ion-ion interactions will also cause the solute to aggregate; hence, it is not surprising that this ionic solute causes an increase in solution viscosity. High relative viscosities of this magnitude are not unprecedented and have been observed with polymers in sc fluids.14 Precedent has also been set using quaternary ammonium electrolytes in nonpolar liquid solvents where relative viscosities up to 3.5 were reported over the same concentration range as that studied here.34 The effect of solute-solute interactions on the viscosity of electrolyte solutions has commonly been quantified using the Dole Jones equation35

ηr ) 1 + Ac1/2 + Bc

(3)

where ηr is the relative viscosity (ηr ) η/η0), c is the electrolyte concentration, and A and B are constants. The A constant accounts for the stiffening effect that the ions impart on the solution from Coulombic interactions, whereas the B constant is somewhat empirical and describes the effect of the electrolyte on the solvent structure. Negative B values result from the electrolyte breaking up the solvent structure, whereas positive values imply the solution is more ordered than the pure liquid. While the effect of electrolytes on the viscosity of aqueous solutions has been extensively investigated, the comparative studies in nonaqueous solvents are far less common, but the area has recently been reviewed by Jenkins and Marcus et al.36 Primarily polar solvents such as acetonitrile and dimethyl sulfoxide have been used in these studies because of their high solubility for electrolytes. Nonpolar solvents have received comparatively little attention, and the only study with a solvent of comparable dielectric constant to CH2F2 was that by Svorstøl et al.,37 who studied CH2Cl2 under ambient conditions. No studies have been carried out on nonaqueous sc electrolyte solutions. Svorstøl et al. studied a variety of quaternary ammonium salts in CH2Cl2 and concluded that the A factors were negligible because plots of ηr versus c were linear and intercepted the Y axis at 1. Hence eq 3 was simplified to

ηr ) 1 + Bc

(4)

The A coefficient can be predicted using the Falkenhagen-Vernon equation38

A)

0.2577Λo η(Τ)1/2λo+ λo-

[

1 - 0.6863

(

)]

λ0+ - λ0Λ0

2

(5)

where λo+ and λo- are the limiting molar conductivities of the

cation and anion respectively, Λo ) λo+ + λo-, and  is the dielectric constant. In the sc state, where , η, λo+, and λo- all vary significantly with pressure and are considerably different from those in the liquid state, it may be thought that the A values would be noticeably different, but Table 1 shows that using Λo,39 η,25 and 40 data from the literature the A parameters are all relatively similar to the values for liquid CH2Cl2. The data in Figure 3 do not give linear correlation to either eq 3 or 4 at any pressure (see Supporting Information). Equation 3 is probably invalid because the solute does not exist solely as dissociated ions, but rather, it is predominantly present as neutral pairs and charged aggregates. While this is also true in CH2Cl2, the main difference in the sc state is that the free volume of the fluid is considerably greater under sc conditions despite the fact that the molar volumes are relatively similar. The molecular volumes of the species were calculated41 to be V(CH2Cl2) ) 74.96 Å3 and V(CH2F2) ) 51.79 Å3. From these values, the free volume of the fluids can be calculated using the molar volumes from the literature.25,42 Table 1 shows the percentage free volume for the systems studied here, and this is clearly related to the viscosity of the pure fluids. In CH2F2, the percentage free volume at 100 bar, 90 °C is twice that in CH2Cl2 at ambient conditions, showing that the molecules have far more freedom to move around under sc conditions. Dissolution of the electrolyte will cause a significant change in the structure of the sc fluid. We propose that the charged species (both single and triple ions) will have the predominant effect on solution viscosity because electrostriction will produce a large increase in the local solvent density around the ions. This is already evident from the clathrate formation with the gas-phase CH2F2 shown earlier. The concentrations of single ions Is and triple ions It can be obtained using the ion pair, Kp and triple ion Kt dissociation constants,

Is ) (Kpc)1/2

(6)

It ) (Kpc)1/2c/Kt

(7)

The Kp and Kt data for this electrolyte system have been reported (34) Abbott, A. P.; Griffith, G.; Harper, J. C. J. Chem. Soc., Faraday Trans. 1997, 93, 577. (35) Robertson, C. T. Educ. Chem. 1973, 10, 219. 112. (36) Jenkins, H. D. B.; Marcus, Y. Chem. Rev. 1995, 95, 2695. (37) Svorstøl, I.; Sigvartsen, T.; Songstad, J. J. Acta Chem. Scand. 1988, B42, 133. (38) Sacco, A.; De Giglio, A.; Dellatti, A.; Petrella, M. J. Chem. Soc., Faraday Trans. 1, 1981, 77, 2693. (39) Abbott, A. P.; Eardley, C. A. J. Phys. Chem. B 2000, 104, 9351. (40) Abbott, A. P.; Eardley, C. A.; Tooth, R. J. J. Chem. Eng. Data 1999, 44, 112. (41) Spartan Pro, Wavefunction Inc., Irvine, CA.

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Figure 4. Relative viscosity and ionic strength as a function of pressure at 90 °C.

previously.39 Hence the relative viscosity should be related to the ionic strength, (I ) Is + It). Equations 6 and 7 are valid when ion concentrations are negligible compared to the electrolyte concentration. Figure 4 shows a plot of ηr versus I for the data shown in Figure 3, and good correlation is observed for all pressures. It has previously been suggested that the association of the electrolyte can be accounted for by splitting the contribution of the electrolyte into ionic Bi and nonionic components Bp viz.43-46

ηr ) 1 + A(Rc)1/2 + BiRc + Bp(1 - R)c

(8)

where R is the degree of dissociation. It has been found that in some water-based systems this nonionic contribution can be ignored,44,46 which would mean that amalgamating the ionic contributions eq 8 could be written as

ηr ) 1 + A(I)1/2 + BiI

(9)

which since A is small would account for the response shown in Figure 4. Several authors47-49 have noted a relationship between the B parameter and the dipole moment, µs, and molar volume, Vs, of the solvent.

B ) RVs + βµs

(10)

These have been difficult to independently relate in liquid solvents because of the interdependence of the terms, but in supercritical fluids, this is attainable as the molar volume can be varied with pressure. Figure 5 shows a good linear correlation between BI and Vs, and this confirms that the ionic component is largely responsible for the increase in viscosity. The unusual result may seem surprising given that only ∼10% of the electrolyte is in the (42) Svorstøl, I.; Sigvartsen, T.; Songstad, J. J. Acta Chem. Scand. 1987, B41, 318. (43) Tominaga, T. J. Phys. Chem. 1975, 79, 1664. (44) Davies, C. W.; Malpass, V. E. Trans. Faraday Soc. 1964, 60, 2075. (45) Crudden, J.; Delaney, G. M.; Feakins, D.; O’Reilly, P. J.; Waghorn, W. E.; Lawrence, K. G. J. Chem. Soc., Faraday Trans. 1 1986, 82, 2207. (46) Quintana, C.; Llorente, M. L.; Sanchez, M.; Vivo, A. J. Chem. Soc., Faraday Trans. 1 1986, 82, 3307. (47) Lawrence, K. G.; Bicknell, R. T. M.; Sacco, S.; Dell’Atti, A. J. Chem. Soc., Faraday Trans. 1 1985, 81, 1133. (48) Thompson, P. T.; Fischer, B.; Wood, R. H. J. Solution Chem. 1982, 11, 1. (49) Petrella, G.; Sacco, A. J. Chem. Soc., Faraday Trans. 1 1978, 74, 2070.

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Figure 5. Bi parameter as a function of molar volume for the data shown in Figure 4.

form of charged species, but the effect of solvation can be appreciated when the relative size of the solvent and solute species is considered. Given that the TBA+ ion has a surface area of 372 Å2 and the radius of a CH2F2 molecule is 2.41 Å, a significant number of solvent molecules will be required to fill the solvation sheath (between 20 and 60 depending on the model used). The solvated TBA+ ion will have a minimum radius of 9 Å, and this ignores the triple ions whose contribution to the viscosity increase will be even larger. Hence, the qualitative comparison between supercritical CH2F2 and liquid CH2Cl2 explains the observed changes in relative viscosity. In the sc state, there is a large free volume and a small solvent molecule, which is easily transported; hence the fluid has a low viscosity. When an electrolyte is added, a significant proportion of the solvent is used to solvate the ions and these large solutes have considerable difficulty moving. Long-range electrostatic interactions have the effect of ordering the fluid. In liquid CH2Cl2, the free volume is less and the solvent molecules are larger hence the fluid will be more viscous than its sc counterpart. The addition of the electrolyte has an effect similar to that in the sc state, but compared to the pure fluid, the effect is less. To confirm these unusually large viscosity increases caused by dissolving an electrolyte in a sc fluid, electrochemical studies were carried out to ascertain the diffusion coefficient of a standard redox couple. Since the initial work by Silvestri et al.,50 relatively few electrochemical studies have been carried out in supercritical fluids. By far the most comprehensive study is that carried out by Bard et al.51-54 using polar supercritical fluids such as water, ammonia, and acetonitrile. The work concentrated mainly on the effect of fluid viscosity upon electrochemical response. Considerably fewer investigations have been made in nonpolar supercritical fluids primarily because of the low solubility of electrolytes and the associated high solution resistance. Some studies have, however, been carried out in CO2,55,56 chlorodifluoromethane,57 (50) Silvestri, G.; Gambino, S.; Filardo, G. Cuccia, C.; Guarino, E. Angew. Chem., Int. Ed. Engl. 1981, 20, 101. (51) Crooks, R. M.; Bard, A. J. J. Electroanal. Chem. 1988, 243, 117. (52) Cabrera, C. R.; Bard, A. J. J. Electroanal. Chem. 1989, 273, 147. (53) Liu, C.; Snyder, S. R.; Bard, A. J. J. Phys. Chem. B 1997, 101, 1180. (54) Farlsheim, W. M.; Bard, A. J.; Johnston, K. P. J. Phys. Chem. 1989, 93, 4234. (55) Abbott, A. P.; Harper, J. C. J. Chem. Soc., Faraday Trans. 1996, 92, 3895. (56) Abbott, A. P.; Harper, J. C. Phys. Chem. Chem. Phys. 1999, 1, 839.

Figure 6. Voltammetric response of ferrocene at a 1-mm-diameter Pt disk electrode in sc CH2F2 at 90 °C as a function of pressure at 30 mM TBABF4 concentration.

and trifluoromethane.58 It was found that electrochemical artifacts are observed as the relative permittivity decreases even when microelectrodes are used. Investigations in nonpolar fluids such as carbon dioxide are hampered by the low solubilities of electrolytes. Voltammetry using conventional electrolytes could only be observed by the addition of polar modifying solvents such as acetonitrile or water.59,60 Grinberg and Mazin61 reviewed the very limited literature on electrochemical processes in modified sc CO2, and Compton has reviewed high-pressure electrochemistry.62 A recent study63 has investigated the double layer structure in liquid and supercritical difluoromethane and showed that as the pressure is decreased the thickness of the double layer increases until the diffuse layer collapses at pressures close to the critical pressure. We have also shown how ionic association in the supercritical state affects the redox behavior of ferrocene and ferrocene carboxylate ions in sc CH2F2.64 Figure 6 shows the voltammetric response of ferrocene at a 1-mm-diameter Pt disk electrode in sc CH2F2 at 90 °C and a variety of pressures. It is evident that the oxidation current, and hence the diffusion coefficient, is not changed by pressure to the same extent as the viscosity of the pure fluid (viscosity changes from 0.0563 to 0.0919 cP over the same pressure range). It was also observed that repeating the experiment using different electrolyte concentrations affected the oxidation current, which would not normally be expected. As the concentration of electrolyte is increased from 10 to 30 mM, the oxidation current decreases (see Supporting Information for data). These preliminary findings confirm that the electrolyte concentration could change the viscosity of the solvent, which backs up the viscosity results obtained using a QCM. Qualitatively the trends in oxidation current follow those in viscosity shown in Figure 3 and in the Supporting Information. (57) Olsen, S. A.; Tallman, D. E. Anal. Chem. 1994, 66, 503. (58) Olsen, S. A.; Tallman, D. E. Anal. Chem. 1996, 68, 2054. (59) Philips, M. E.; Deakin, M. R.; Michael, A. C.; Wightman, R. M. J. Phys. Chem. 1987, 91, 3934. (60) Neihaus, D.; Philips, M. E.; Michael, A. C.; Wightman, R. M. J. Phys. Chem. 1989, 93, 6232. (61) Grinberg, V. A.; Mazin, V. M. Russ. J. Electrochem. 1998, 34, 223. (62) Giovanelli, D.; Lawrence, N. S.; Compton, R. G. Electroanalysis 2004, 16, 789. (63) Abbott, A. P.; Eardley, C. A. J. Phys. Chem. B 1999, 103, 6157. (64) Abbott, A. P.; Durling, N. E. PCCP 2001, 3, 2579.

A caveat must be applied to the use of electrochemical studies in supercritical fluids, as they are somewhat prone to artifacts. Two such factors were noted about the voltammetric response in Figure 6; the reverse scan does not follow the forward scan even at slower scan rates (see Supporting Information for data), and the current decreases slightly with each successive scan such that after seven scans the current decreases to effectively zero. This is expected behavior at an electrode where linear diffusion dominates mass transport. The former artifact is thought to be due to the slow polarization of the double layer caused by quaternary ammonium electrolyte adsorption. This artifact has previously been demonstrated to be present in nonaqueous solutions.65 It could also be caused by the effect of migration in these fluids as noted by Corti.66 The observation that the current decreases with subsequent scans can be accounted for as optical inspection of the continuously cycled electrode reveals the growth of an electrolyte crystal on the electrode surface. The lack of a reverse wave, the decrease in current on successive scans, and the observation of a deposit on the electrode surface suggests that the ferrocene oxidation product forms an insoluble salt with the electrode. Such effects have also been noted by Olsen and Tallman in sc chlorodifluoromethane.37 This may also be induced by the adsorption of the electrolyte or a slight temperature differential brought about by the thermal conductivity of the electrode. All of the voltammograms shown in Figure 6 show the response for the first cycle of a freshly polished electrode. Care also needs to be taken when analyzing the voltammograms in Figure 6 because the elevated temperature and the low viscosity of the solvent mean that the contributions of both linear and spherical diffusion need to be accounted for when modeling the overall current. Under conditions where both linear and spherical diffusion are significant the current, i, at a planar disk electrode is given by67

i ) nFADo1/2c0σ1/2π1/2χ(σt) + nFADoRo-1φ(σt) (11) where n is the number of electrons, F the Faraday constant, A is the electrode area, Do is the diffusion coefficient, c0 is the bulk concentration of electroactive species, σ ) nFυ/RT, υ is the sweep rate, χ(σt) is the normalized current and Ro is the electrode radius. Figure 7 shows the voltammetry of Fc at 100 bar in CH2F2 containing 30 mM TBABF4. The figure also shows the theoretical response obtained by assuming the solution viscosity is the same as the bulk viscosity of the pure solvent. It is clear that the current expected is almost three times larger than that observed. It has previously been shown that in the absence of electrolyte the diffusion coefficient at a microelectrode corresponds to the value expected from the viscosity of the pure fluid.68 The diffusion coefficient has, however, never been measured in solvents using typical electrolyte concentrations. In addition, it is noticeable that the current is significantly greater than that observed at any pressure presented in Figure 6. It is also noted that the electrolyte (65) Abbott, A. P.; Harper, J. C.; Stimsom, G. J. Electroanal. Chem. 2002, 520, 6. (66) Corti, H. R.; Goldfarb, D. L.; Longinotti, M. P. J. Electroanal. Chem. 2001, 509, 155. (67) Bard, A. J.; Falkner, L. R. Electrochemical Methods; Fundamentals and Applications; Wiley: Chichester, 1980; p 218. (68) Goldfarb, D. L.; Corti, H. R. J. Phys. Chem. B 2004, 3363.

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This large discrepancy in D can only be explained by a larger than expected increase in solution viscosity. Figure 7 shows the voltammogram calculated using eq 11 and a diffusion coefficient of 4.22 × 10-6 cm2 s-1 calculated using eq 12 and assuming a viscosity of 1.79 cP. Good agreement between the maximum current for the measured and calculated voltammograms is obtained corroborating the viscosity data obtained using the QCM. This demonstrates for the first time that the dissolution of ionic solutes has a significant structuring effect on supercritical fluids. This leads to large relative viscosities in the electrolyte solutions and gives mass transport characteristics that are akin to liquid rather than supercritical fluids. Figure 7. Comparison of the voltammetric response of ferrocene in sc CH2F2 at 90 °C and 100 bar containing 30 mM TBABF4, the theoretical voltammetric response for 100 bar assuming solution viscosity is the same as that of pure solvent and the calculated voltammetric response using eq 11.

concentration has a significant effect upon the oxidation current, which could arise from a decrease in the diffusion coefficient of the electroactive species. The theoretical diffusion coefficient, D, can be calculated using the Stokes-Einstein equation

D ) kT/6πηr

(12)

Where k is the Boltzmann constant, η is the viscosity, and r is the radius of the diffusing species. Assuming that the radius of ferrocene is 3.8 Å41 and the viscosity of the fluid is that of the pure solvent (0.056 cP), a diffusion coefficient of 1.35 × 10-4 cm2 s-1 was calculated. The diffusion coefficient calculated using the measured voltammogram in Figure 7 was 8.60 × 10-6 cm2 s-1.

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CONCLUSIONS A partially coated QCM has been shown to be an accurate analytical method for the measurement of solution viscosities in sc fluids. The addition of electrolytes causes an increase in the viscosity of CH2F2 of between 8- and 32-fold. These remarkable increases in solution viscosity were confirmed using voltammetric measurements and are explained in terms of the structuring of the solvent that is brought about by the solvation of ionic aggregates and the equilibria that occur between neutral and charged species. ACKNOWLEDGMENT The authors thank EPSRC and Impact Faraday for funding the work, Prof. Hillman for use of the network analyzer, and Ineos Fluor for providing the CH2F2. Received for review May 20, 2005. Accepted July 26, 2005. AC050883I