Conductivity and Voltammetry in Liquid andSupercritical Halogenated Solvents
Scott A. Olsen† and Dennis E. Tallman*
Department of Chemistry, North Dakota State University, Fargo, North Dakota 58105-5516
A previous study of the voltammetry of ferrocene in liquidand supercritical chlorodifluoromethane revealed elec-trochemically reversible behavior. However, shifts in thehalf-wave potential as a function of fluid conditions wereobserved which were tentatively attributed to ohmicdistortion due to changes in fluid resistance. To morecompletely understand the voltammetry in this fluid,conductivity measurements have been made for a rangeof fluid conditions. Additionally, a second referencecouple, cobaltocenium hexafluorophosphate, has beenintroduced, and the difference in half-wave potentialsbetween the two redox couples has been examined as afunction of fluid conditions. In the liquid, the differencein the half-wave potentials of the two couples correctedfor ohmic distortion decreases as the fluid temperatureincreases (25-85 °C) at constant pressure (5.2 MPa).In the supercritical fluid at constant temperature (115°C), the difference in the half-wave potentials correctedfor ohmic distortion is constant at 1.276 ( 0.005 V overa considerable range of fluid pressure (10-30 MPa). Ionaggregation in the supercritical fluid is indicated both bythe conductivity measurements and by the rather largehydrodynamic radius of cobaltocenium computed fromthe voltammograms. Preliminary voltammetry in super-critical trifluoromethane is also presented.
Supercritical fluid chromatography was first demonstrated byKlesper and co-workers,1 who used halocarbon solvents to elutenickel etioporphyrins. In the intervening years, supercritical fluidshave been used to study solvation effects,2-4 to perform chroma-tography of complex mixtures,5 and more recently as the basisfor extended electrochemical studies.6-10 Two of these applica-tions have come together in the development of electrochemicaldetection for supercritical fluid chromatography.11-20
Supercritical carbon dioxide, the most common mobile phasefor chromatography and extraction, is a rather poor solvent forpolar analytes such as phenols. Chlorodifluoromethane (CDFM)has been demonstrated to be a superior supercritical solvent forthe chromatography21,22 and extraction22-24 of polar analytes, inpart because CDFM possesses a higher dielectric constant thancarbon dioxide. At the critical point (96.15 °C, 4.97 MPa), CDFMhas a dielectric constant of 2.31, which can be increased byincreasing the fluid density (pressure). In contrast, carbon dioxidehas a dielectric constant of 1.18 at the critical point (31 °C, 7.39MPa), and its dielectric constant cannot be increased substantiallyby increasing the density.25
The modest dielectric constant of supercritical CDFM, com-bined with its readily accessible critical temperature and criticalpressure, makes it an attractive solvent for supercritical fluidelectrochemistry (SFEC) and an ideal candidate mobile phase forsupercritical fluid chromatography with electrochemical detection(SFC/EC). We have previously demonstrated that voltammetrycan be performed at unmodified microelectrodes in a hom*oge-neous supercritical fluid of CDFM containing a millimolar con-centration of a supporting electrolyte.26 Ferrocene behaves verynearly reversibly in liquid and supercritical CDFM, with onlymodest ohmic distortion. Similar voltammetry in supercriticalcarbon dioxide can be achieved only by employing microelec-trodes modified with ionic films at the electrode surface, the actualelectrochemistry occurring within the film.12-15,17-19
In our previous report,26 we observed shifts in the ferrocenehalf-wave potential with temperature in the liquid and with density(pressure) in the supercritical fluid. At least a portion of thesewave shifts was attributed to ohmic distortion, a result of variationsin fluid resistance with temperature and pressure, and ion-pairingwas suggested as one mechanism leading to increased resistance.
† Current address: Department of Chemistry, Monash University, Clayton,Australia.(1) Klesper, E.; Corwin, A. H.; Turner, D. A. J. Org. Chem. 1963, 27, 700.(2) Kajimoto, O.; Futakami, M.; Kobayashi, T.; Yamasaki, K. J. Phys. Chem.
1988, 92, 1347.(3) Zagrobelny, J.; Bright, F. V. J. Am. Chem. Soc. 1992, 114, 7821.(4) Roberts, C. B.; Zhang, J.; Chateauneuf, J. E.; Brennecke, J. F. J. Am. Chem.
Soc. 1993, 115, 9576.(5) Chester, T. L.; Pinkston, J. D.; Raymie, D. E. Anal. Chem. 1994, 66, 106R.(6) Crooks, R. M.; Fan, F.-R. F.; Bard, A. J. J. Am. Chem. Soc. 1984, 106, 6851.(7) McDonald, A. C.; Fan, F.-R. F.; Bard, A. J. J. Phys. Chem. 1986, 90, 196.(8) Crooks, R. M.; Bard, A. J. J. Electroanal. Chem. 1988, 243, 117.(9) Cabrera, C. R.; Garcia, E.; Bard, A. J. J. Electroanal. Chem. 1989, 260, 457.
(10) Flarsheim, W. L.; Bard, A. J.; Johnston, K. P. J. Phys. Chem. 1989, 93, 4234.(11) Philips, M. E.; Deakin, M. R.; Novotny, M. V.; Wightman, R. M. J. Phys.
Chem. 1987, 91, 3934.(12) Niehaus, D.; Philips, M.; Michael, A.; Wightman, R. M. J. Phys. Chem. 1989,
93, 6232.
(13) Michael, A. C.; Wightman, R. M. Anal. Chem. 1989, 61, 270.(14) Michael, A. C.; Wightman, R. M. Anal. Chem. 1989, 61, 2193.(15) Niehaus, D. E.; Wightman, R. M.; Flowers, P. A. Anal. Chem. 1991, 63,
1728.(16) Di Maso, M.; Purdy, W. C.; McClintock, S. A. J. Chromatogr. 1990, 519,
256.(17) Sullenberger, E. F.; Dressman, S. F.; Michael, A. C. J. Phys. Chem. 1994,
98, 5347.(18) Sullenberger, E. F.; Michael, A. C. Anal. Chem. 1993, 65, 3417.(19) Sullenberger, E. F.; Michael, A. C. Anal. Chem. 1993, 65, 2304.(20) Dressman, S. F.; Michael, A. C. Anal. Chem. 1995, 67, 1336.(21) Ong, C. P.; Lee, H. K.; Li, S. F. Y. Anal. Chem. 1990, 62, 1389.(22) Li, S. F. Y.; Ong, C. P.; Lee, M. L.; Lee, H. K. J. Chromatogr. 1990, 515,
515.(23) Yeo, S. K.; Ong, C. P.; Lee, H. K.; Li, S. F. Y. Environ. Monit. Assess. 1991,
19, 47.(24) Hawthorne, S. B.; Langenfeld, J. J.; Miller, D. J.; Burford, M. D. Anal. Chem.
1992, 64, 1614.(25) Michels, A.; Michels, C. Philos. Trans. R. Soc. London, Ser. A 1933, 231,
409.(26) Olsen, S. A.; Tallman, D. E. Anal. Chem. 1994, 66, 503.
Anal. Chem. 1996, 68, 2054-2061
2054 Analytical Chemistry, Vol. 68, No. 13, July 1, 1996 S0003-2700(95)01115-2 CCC: $12.00 © 1996 American Chemical Society
In this work, we further explore supercritical CDFM as anelectrochemical solvent. The conductivity of supercritical CDFMcontaining the electrolyte tetra-n-butylammonium tetrafluoroborate(TBATFB) has been measured at several pressures and iscompared with selected conductivity measurements performedin liquid CDFM. The measured fluid resistances are used toremove the ohmic distortion from the measured half-wavepotentials. Cobaltocenium hexafluorophosphate has been intro-duced as a second reference couple so that the previously reportedshifts in the oxidation potential of ferrocene as a function oftemperature and pressure can be more critically examined. Thediffusivities of ferrocene and cobaltocenium as a function ofsupercritical fluid pressure have been determined and are usedto estimate the respective hydrodynamic radii. These resultssupport the notion of ion aggregation in supercritical CDFM.
Finally, since the long-term availability of chlorofluorocarbons(CFCs) and hydrochlorofluorocarbons (HCFCs, of which CDFMis a member) is in question,27 alternative fluids of modest polarityshould be considered. A number of fluorocarbons would appearto be viable candidates for supercritical fluid electrochemistry,including 1,1,1,2-tetrafluoroethane (HFC-134a) and trifluoromethane(or fluoroform, CHF3). We present a preliminary voltammetriccharacterization of trifluoromethane as an electrochemical solvent.
EXPERIMENTAL SECTIONReagents. The CDFM manufactured by du Pont had a listed
minimum purity of 99.8%. An oxygen trap (J&W Scientific) andan in-line water trap, prepared by filling a cylinder with anhydrouscalcium sulfate and potassium hydroxide, were placed in-linebetween the CDFM tank and the pump. The supporting electro-lyte was TBATFB from Fluka (puriss) and was recrystallized twicefrom 95% ethanol, dried in a vacuum oven, and stored in a vacuumdesiccator. Cobaltocenium hexafluorophosphate (Aldrich) witha listed purity of 98% was used as received and was stored in avacuum desiccator. The CHF3 from Mattheson was of semicon-ductor purity (99.995 wt %) and was used without furtherpurification.
Electrodes and Instrumentation. The fabrication of thevoltammetric electrodes used in these experiments has beendescribed in detail.26 Briefly, either 10-µm- (Goodfellow) or 25-µm- (Aesar) diameter platinum wires or 10-µm-diameter carbonfibers were sealed into θ capillaries (World Precision Instruments).The finished capillary was epoxied into a stainless steel tube(0.125-in. o.d., 0.085-in. i.d., Alltech) with Torr-Seal (Varian). Allexperiments were performed in the two-electrode mode, for whichthe stainless steel tube (and the supercritical fluid cell with whichit is in electrical contact) acted as the quasi-reference/auxiliaryelectrode. The voltammetric waveform, supplied by a PAR Model175 universal programmer, was applied to the cell via a potentiostatbuilt in-house, and the current flow was measured with a Kiethley487 picoammeter. A block diagram illustrating the layout andconnections of the system has been published previously.26
Conductivity electrodes were constructed in the followingmanner. A 3 3/4-in. length of type 316 stainless steel tube (1/16-in. o.d., 0.030-in. i.d.) was epoxied inside a 3 1/4-in. length of largerstainless steel tube (1/8-in. o.d., 0.085-in. i.d.) with Torr-Seal. Toensure concentric placement of the inner tube, a small jig wasmilled which had a short 1/16-in. hole drilled at the bottom of ashort 1/8-in. hole. The 1/8-in. tube was filled with Torr-Seal and
placed in the jig, and the center tube was inserted. When theepoxy had cured, the jig was removed, and the end was sandedflat, exposing a concentric ring-ring electrode. The cell constantof this electrode assembly, determined from impedance measure-ments in an aqueous 0.0100 m KCl solution, was 260 ( 3 m-1.Impedance measurements were made with a BAS 100B/Welectrochemical workstation (BioAnalytical Systems) equippedwith an impedance module. All conductivities were calculatedfrom the real part of the impedance at a frequency of 950 Hz.
Procedures. To initiate a voltammetric experiment, microliteraliquots of ferrocene and cobaltocenium standards, prepared inacetonitrile, were dispensed into the cell, and the solvent wasallowed to evaporate. A weighed amount of TBATFB electrolytewas placed directly in the cell. The cell was assembled and purgedat ambient temperature with gaseous CDFM for ∼10 min,following which the exit valve (valve 3 in Figure 2 of ref 26) wasclosed, the cell placed in a Faraday cage, and the pump cylinderfilled with liquid CDFM. The cell was brought to operatingtemperature, after which the pressure was increased to the initialoperating pressure. Voltammograms were recorded at the desiredpressures, typically allowing about 45 min for fluid equilibrationafter each pressure adjustment. Experiments utilizing CHF3 asthe working fluid were carried out in an identical manner. Priorto each experiment, the electrode assembly was resurfaced on600-grit sandpaper, polished to a mirror finish with 1- and 0.3-µmalumina (Buehler), rinsed with deionized water (Millipore Milli-Q), wiped dry, and stored in a vacuum oven until used.
Impedance experiments were conducted in a manner similarto that described above for the voltammetric experiments, exceptthat an aliquot of 1.00 M TBATFB standard prepared in acetonitrilewas dispensed into the cell. The conductivity electrode waspolished on 1.0-, 0.3-, and 0.05-µm alumina. The electrode wasthoroughly rinsed with deionized water and wiped dry with aKimwipe. The cell and the freshly polished conductivity electrodewere placed in a room temperature vacuum oven to removeacetonitrile from the cell and water from the electrode. After 1h, the oven was opened, the electrode was inserted into the cell,and the assembled cell was placed in the vacuum oven for anadditional hour. The cell was then removed from the vacuumoven, connected to the syringe pump, and purged with CDFM,and the system was sealed. The pump cylinder was filled withliquid CDFM, the cell was brought to temperature, and thepressure was increased to the desired level. Sufficient time wasallowed between changes in the fluid pressure for the contentsto reach equilibrium. Under the conditions used in this work,the solutes and electrolyte are completely soluble, and the liquidand supercritical fluid phases are hom*ogeneous.26 The safetyissues surrounding these experiments were also discussed in theprevious report.26
RESULTS AND DISCUSSIONConductivity Measurements. Microelectrodes have been
used to perform voltammetry in media of low conductivity.28,29
However, voltammograms obtained in highly resistive media, evenemploying a microelectrode, may be subject to ohmic distortion,and it is useful to perform conductivity measurements in themedium of interest to obtain supporting data for the voltammetry.
(27) Chem. Eng. News 1993, 71 (Aug 16), p 15.
(28) Bond, A. M.; Mann, T. F. Electrochim. Acta 1987, 32, 863.(29) Pena, M. J.; Fleischmann, M.; Garrard, N. J. Electroanal. Chem. 1987, 220,
31.
Analytical Chemistry, Vol. 68, No. 13, July 1, 1996 2055
To that end, a number of conductivity measurements have beenmade in liquid and supercritical CDFM containing 10.0 mMTBATFB, with the results summarized in Tables 1 and 2. Themeasurements in liquid CDFM indicate that, as the fluid temper-ature is increased at constant pressure, the equivalent conductivityof the electrolyte decreases. This most likely results from thedecrease in density (and, thus, dielectric constant) which ac-companies the temperature increase (Table 1). At a constantelectrolyte concentration, the equivalent conductivity increasesas the fluid pressure is increased (Table 2). This is in contrastwith most nonaqueous liquid solvents, where an increase inpressure causes a decrease in the equivalent conductivity due tofluid viscosity increases with pressure.30 For comparison, theequivalent conductivities of the supercritical fluid at 115 °C andat pressures of 10.0 and 24.0 MPa are included in Table 1. Theconductivities of the supercritical fluid at 10.0 and 24.0 MPa arecomparable to the conductivities of the liquid (5.2 MPa) at 85 and70 °C, respectively. The correspondingly similar densities sug-gests that the bulk fluid density, and thus the dielectric constant,controls the conductivity of the fluid.
Figure 1 illustrates the equivalent conductivity of TBATFB insupercritical CDFM as a function of concentration at a constantfluid temperature of 115 °C at four different fluid pressures. Asin liquid CDFM, the equivalent conductivity at a constantelectrolyte concentration increases with fluid pressure. Such anincrease in equivalent conductivity is attributed to an increase inthe bulk fluid dielectric constant with fluid pressure, whichreduces the degree of ion-pairing in the supercritical fluid. Overthe concentration range investigated, the equivalent conductivityof the fluid increases (albeit slightly) with electrolyte concentra-
tion. Reliable conductivity measurements could not be made atconcentrations below 5 mM because the imaginary part of theimpedance became significant and the BAS 100B/W does notpossess a sufficiently high frequency range to permit increasingthe frequency to reduce the imaginary impedance.
In polar solvents, the equivalent conductivity typically de-creases with an increase in electrolyte concentration, in accordwith the Onsager equation,31 a consequence of the relaxation andelectrophoretic effects. In the absence of ion aggregation (e.g.,ion pair or triple formation), the equivalent conductance ispredicted to decrease linearly with the square root of concentration(Kolrausch’s limiting law).31 Departure from this linear behaviorusually signifies the formation of ion aggregates. An increase inequivalent conductivity with the square root of electrolyte con-centration, as observed in Figure 1, is indicative of the formationof higher ion aggregates, e.g., triple ions of the type (+)(-)(+)or (-)(+)(-), as predicted by the Fuoss-Kraus equation.32 Suchbehavior has been observed in other media of low dielectric andimplies that electrolytes present in supercritical CDFM undergoion association. Since cobaltocenium was added as the hexafluo-rophosphate salt, cobaltocenium should also take part in ionaggregation equilibria. The diffusion-limited currents measuredduring voltammetric experiments (vide infra) support this conclu-sion.
The measured fluid conductivities permit a determination ofthe expected uncompensated solution resistance for a microelec-trode. The expression for the resistance at a microdisk with aremote reference electrode was given by Newman:33
where Ru is the uncompensated resistance, F is the resistivity of
(30) Glugla, P. G.; Byon, J. H.; Eckert, C. A. J. Chem. Eng. Data 1981, 26, 80.
(31) Onsager, L. Phys. Z. 1927, 28, 277.(32) Kraus, C. A.; Fuoss, R. M. J. Am. Chem. Soc. 1933, 55, 21; 476; 1019.(33) Newman, J. J. Electrochem. Soc. 1970, 117, 198.
Table 1. Equivalent Conductivity (Λ) of 10.0 mMTBATFB in Liquid (5.2 MPa) and in Supercritical (10.0,24.0 MPa) CDFM at Selected Temperaturesa
P (MPa) T (°C) F (g/mL) Λ (×10-4 S m2 mol-1) Ru (MΩ)
5.20 25.0 1.209 9.84 ((0.05) 2.035.20 40.0 1.150 8.70 ((0.23) 2.305.20 55.0 1.084 6.49 ((0.13) 3.085.20 70.0 1.002 4.55 ((0.11) 4.395.20 85.0 0.889 2.82 ((0.12) 7.02
10.00 115.0 0.812 1.89 ((0.01) 10.5724.00 115.0 1.020 4.49 ((0.08) 4.46
a Fluid densities (F) were calculated from the equation of state inref 51. The uncompensated resistance (Ru) was computed for amicroelectrode of 25 µm diameter. The values of Λ and the standarddeviations (in parentheses) were computed from a minimum of 10measurements on two different solutions.
Table 2. Equivalent Conductivity (×10-4 S m2 mol-1) of10.0 mM TBATFB in Liquid CDFM as a Function ofPressure at Several Temperaturesa
pressure (MPa)
T (°C) 5.0 10.0 15.0 20.0 25.0
40.0 8.83 9.96 11.0 11.9 12.755.0 6.41 7.60 8.53 9.40 10.270.0 3.86 5.03 5.95 6.77 7.5485.0 2.76 4.24 5.33 6.29 7.18
a Each value is the average of at least four measurements.
Figure 1. Equivalent conductivity of supercritical CDFM at 115 °Cas a function of the square root of TBATFB concentration. The points(error bars) are the averages (standard deviations) of 5-6 measure-ments. Data at four densities are shown corresponding to fluidpressures of 10.0 (b), 14.0 (2), 18.0 (9), and 24.0 MPa ([).
Ru ) F4ro
) 14roCΛ
(1)
2056 Analytical Chemistry, Vol. 68, No. 13, July 1, 1996
the fluid, ro is the radius of the disk microelectrode, C is theelectrolyte concentration, and Λ is the equivalent conductivity ofthe fluid. The majority of microelectrodes constructed for thisresearch had a radius of 12.5 µm, the value used to calculate theRu values presented in Table 1. The uncompensated resistancein liquid and in supercritical CDFM is on the order of severalmegaohms, sufficient to cause several millivolts of ohmic distortionin voltammetric waves when measuring currents on the order ofnanoamperes. Of course, the highest resistance (and greatestdistortion) is expected in the supercritical fluid at lower fluidpressure (lower density and dielectric constant, Table 1). Thus,to minimize ohmic distortion, it is preferable to operate atpressures of 10.0 MPa or greater. The data presented in thispaper was recorded at pressures g10.0 MPa and show onlymoderate ohmic distortion. In the following sections, theseconductivity results are used to minimize the influence ofuncompensated solution resistance on measured half-wave po-tentials.
Voltammetry in Liquid CDFM. In our previous report, shiftsin the ferrocene half-wave potential with pressure and temperaturewere observed, and it was not clear whether such shifts were dueto changes in the quasi-reference electrode potential, changes influid resistance, solvation effects, or some combination of thesefactors. To better understand the origin of such potential shifts,the cobaltocenium-cobaltocene (Cc+/Cc) couple has been intro-duced, and the difference in half-wave potential between fer-rocene-ferrocenium (Fc/Fc+) and Cc+/Cc has been investigatedas a function of fluid conditions. An additional goal of this part ofthe work was to assess the suitability of the Fc/Fc+ and Cc+/Cccouples as internal potential references in liquid and supercriticalCDFM. The second reduction wave, corresponding to the Cc/Cc- couple, was partially obscured by the CDFM solvent reductionwave and was not employed in this study.
The similarities between ferrocene and cobaltocenium havemade them the focus of many electrochemical studies.34-38 Ofrelevance to this work, Stojanovic and Bond39 have reported theuse of cobaltocenium-cobaltocene as a reference couple in aproticorganic media. They found that, in acetonitrile, the potentialdifference between the ferrocene oxidation and the cobaltoceniumreduction appeared to be independent of electrode material andelectrolyte, that difference being 1.350 ( 0.003 V at both macro-and microelectrodes. When the solvent is dichloromethane, thepotential difference between the ferrocene oxidation and thecobaltocenium reduction is 1.357 ( 0.007 V at macroelectrodesand 1.351 ( 0.004 V at microelectrodes. These results suggestthat, in aprotic media, the potential difference between these twoprocesses is relatively constant at 1.35 ( 0.01 V, despite changesin the dielectric constant of the media, suggesting that cobalto-cenium may be a useful alternative reference couple when theferrocene couple would overlap another couple of interest. Aslightly different value was reported by Koepp and co-workers,who obtained 1.32 V in each of the solvents water, methanol,acetonitrile, and formamide.40 CDFM is an aprotic, low dielectric
medium which is expected to be similar to dichloromethane insolvation properties.
Figure 2 shows a voltammogram of liquid CDFM containingboth Fc and Cc+ at equal concentrations. Both the Fc oxidationwave and the Cc+ reduction wave are Nernstian under theseconditions (25.0 °C, 5.20 MPa). At higher temperatures, ohmicdistortion of the wave becomes more apparent. For example, at85 °C and 5.20 MPa, the highest temperature examined in liquidCDFM (thus, the greatest fluid resistivity, see Table 1), a plot ofE versus ln((id - i)/i) for the cobaltocenium wave has a slope of0.0342, compared to the Nernstian value of 0.0309. The agreementbetween the measured slope and the Nernstian slope improvesat lower fluid temperatures, where ohmic distortion is less. Thus,it appears that both cobaltocene and ferrocene are reversible inliquid CDFM.
Table 3 lists the observed differences between the ferroceneoxidation and the cobaltocenium reduction half-wave potentialsin the liquid as measured directly, ∆E1/2, and after correction forohmic distortion, ∆E1/2(corr), using the expression
which applies to steady-state voltammograms, where Ru is inmegaohms and the diffusion-limited currents are the absolutevalues in nanoamperes. We note that the use of eq 1 for lowelectrolyte concentrations may lead to an overestimation of iRu
for electrolysis of a neutral compound.41 However, the correctionsare generally small (a few millivolts), and any overestimation islikely to be insignificant.
At 25 °C, the corrected potential difference is 1.320 V, a valuesimilar to that reported by Stojanovic and Bond39 and in excellentagreement with the values reported by Koepp et al.40 The slightdecrease in ∆E1/2(corr) values as temperature increases could
(34) Geiger, W. E.; Smith, D. E.;J. Electroanal. Chem. 1974, 50, 31.(35) Gennett, T.; Weaver, M. J. J. Electroanal. Chem. 1985, 186, 179.(36) Krishtalik, L. I.; Alpatova, N. M.; Ovsyannikova, E. V. Electrochim. Acta
1991, 36, 435.(37) Amatore, C.; Deakin, M. R.; Wightman, R. M. J. Electroanal. Chem. 1987,
225, 49.(38) Cooper, J. B.; Bond, A. M. J. Electroanal. Chem. 1991, 315, 143.(39) Stojanovic, R. S.; Bond, A. M. Anal. Chem. 1993, 65, 56.
(40) Koepp, H. M.; Wendt, H.; Strehlow, H. Z. Elektrochem. 1960, 64, 483.(41) Myland, J.; Oldham, K. B. J. Electroanal. Chem. 1993, 347, 49.
Figure 2. Voltammograms of ferrocene and cobaltocenium in liquidCDFM. Conditions: 125 µM Fc, 125 µM Cc+, 11.0 mM TBATFB; 25.0°C, 5.20 MPa; 25-µm-diameter Pt disk electrode; scan rate, 10 mV/s. The initial potential was -0.20 V, with the ferrocene wave recordedfirst.
∆E1/2(corr) ) ∆E1/2 -Ru[iL(Fc) + iL(Cc+)]
2000(2)
Analytical Chemistry, Vol. 68, No. 13, July 1, 1996 2057
result from the concomitant decrease in dielectric constant,reflecting a difference in solvation energetics (Born charging),as described by the Born equation.42 However, the rather constant∆E1/2 observed in previous work39,40 for a range of liquid solventsof widely varying dielectric constant would argue against thisexplanation. We conjecture that this small temperature depen-dence of ∆E1/2 reflects differences in the entropy change for thetwo redox systems. The ∆∆S0 (defined as ∆S0
Fc - ∆S0Cc, where
each ∆S0 is defined for the corresponding reduction) required toaccount for the observed temperature dependence is approxi-mately -33 J K-1 mol-1, a not unreasonable value for solvationeffects. Since only a difference in entropy change is obtained,we can only conclude that reducing Cc+ to Cc results in greaterdisorder than does the reduction of Fc+ to Fc in liquid CDFM.
The ratio of the diffusion coefficient of cobaltocenium to thatof ferrocene is computed from the measurements of Stojanovicet al. to be ∼0.81 in acetonitrile and 0.72 in dichloromethane.39
The average ratio in liquid CDFM over the temperature range25-85 °C is 0.75, similar to that for dichloromethane. Thehydrodynamic radii of Fc and Cc+ can be estimated from theStokes-Einstein equation:
where D is the diffusion coefficient, R is the universal gas constant,T is the absolute temperature, η is the viscosity of the fluid, No isAvogadro’s number, and a is the hydrodynamic radius of theanalyte. Using computed values of viscosity (Table 3), thehydrodynamic radii of Fc and Cc+ were estimated from eq 3 andare tabulated in Table 3. For comparison, the hydrodynamic radiiat 25 °C in acetonitrile and in dichloromethane were alsocomputed from literature values of viscosity43 and diffusioncoefficients.39,44 Ferrocene has an estimated hydrodynamic radiusof 2.8 Å in acetonitrile and 4.0 Å in dichloromethane. Cobalto-cenium has an estimated hydrodynamic radius of 3.5 Å inacetonitrile and 5.5 Å in dichloromethane. Our values for the radii
in liquid CDFM fall within the range defined by these two solvents.Additionally, there is some uncertainty in the estimated CDFMfluid viscosity due to the presence of electrolyte. To the best ofour knowledge, the viscosities of liquid CDFM-electrolyte solu-tions at high temperatures and pressures have not been published.
The crystallographic measurement of the Fe-C bond distancein ferrocene is 2.05 Å.45 The hydrodynamic radius of a moleculein a solvent represents the molecule and its solvent shell, andthe values in Table 3 for ferrocene are consistent with this notion.Interestingly, the hydrodynamic radius of Cc+ is significantlylarger than that of Fc in each of the solvents, even though thesespecies are isoelectronic. The difference is somewhat larger inthe solvents of lower dielectric constant. We conjecture that thisis the result of ion aggregation of the Cc+ with electrolyte ions,resulting in a larger hydrodynamic radius.
Voltammetry in Supercritical CDFM. Figure 3 comparesthe forward sweeps of six cyclic voltammograms in supercriticalCDFM at 115 °C and at 12.0, 20.0, and 30.0 MPa, each sweeporiginating from -0.20 V. Two interesting changes in the wavesfor ferrocene oxidation and cobaltocenium reduction are observedas the pressure (density) is increased: (1) both waves shift tomore negative potentials, but close inspection reveals that themagnitude of the shift is not identical for the two waves, and (2)the limiting current for Fc decreases with pressure, whereas thatfor Cc+ remains rather constant.
First, we consider the potential shifts in the waves. Thepotential of the quasi-reference electrode is very likely a functionof pressure, but any change in reference electrode potential wouldshift each wave by identical amounts and should not have an effecton ∆E1/2. For this reason, we consider the effect of pressure onlyon ∆E1/2. Although the total change in the potential differencebetween the ferrocene and cobaltocenium waves (i.e., ∆∆E1/2)over the pressure range investigated is not large (∼40 mV), thebehavior is reproducible from experiment to experiment.
(42) Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: NewYork, 1992.
(43) CRC Handbook of Chemistry and Physics, 64th ed.; CRC Press: Boca Raton,FL, 1983; p F-39.
(44) Wipf, D. O.; Wightman, R. M. Anal. Chem. 1990, 62, 98. (45) Dunitz, J. D.; Orgel, L. E.; Rich, A. Acta Crystallogr. 1956, 9, 373.
Table 3. Difference between Ferrocene andCobaltocenium Half-Wave Potentials as a Function ofTemperature in Liquid Chlorodifluoromethane asMeasured, ∆E1/2, and after Correction for OhmicDistortion, ∆E1/2(corr)a
T(°C)
F(g/mL) ε
η(cP) ∆E1/2 (V)
∆E1/2(corr)(V)
Fcradius
(Å)
Cc+
radius(Å)
25 1.209 6.31 0.165 1.324 ( 0.002 1.320 ( 0.002 3.4 4.140 1.150 5.70 0.143 1.322 ( 0.002 1.317 ( 0.002 3.2 4.955 1.084 5.09 0.125 1.320 ( 0.002 1.313 ( 0.002 3.4 4.370 1.002 4.48 0.110 1.322 ( 0.002 1.308 ( 0.002 3.3 4.685 0.889 3.79 1.323 ( 0.002 1.299 ( 0.003
a Conditions: 125 µM Fc, 125 µM Cc+, and 10.0 mM TBATFB. Alsotabulated are density (F, ref 51), dielectric constant (ε, ref 52) andviscosity (η, ref 53), each computed from appropriate expressionsprovided in the indicated references, and the computed hydrodynamicradii of Fc and Cc+ (see text).
Figure 3. Comparison of ferrocene and cobaltocenium wavesas a function of pressure in supercritical chlorodifluoromethane.Conditions: 90 µM Fc, 90 µM Cc+, 10.0 mM TBATFB; 115 °C; 25-µm-diameter Pt disk electrode; scan rate, 20 mV/s. For clarity, onlythe forward sweep of each voltammogram is displayed, with theferrocene wave recorded first and the cobaltocenium wave im-mediately after, each wave originating from -0.20 V.
D ) RT6πηNoa
(3)
2058 Analytical Chemistry, Vol. 68, No. 13, July 1, 1996
A number of factors could explain the shift in ∆E1/2 withpressure, including (1) variations in activity coefficients and/ordiffusion coefficients, (2) differences in the standard molar volumechange upon reaction,46,47 (3) differences in solvation energies asdescribed by the Born model,42,48 and (4) differences in the ohmicdistortion of the waves due to the observed differences in currentflow (Figure 3). Based on the similarities between Fc and Ccand between Fc+ and Cc+, variations in ∆E1/2 due to the first threeof the above four explanations should be very small. Indeed, thevariation in ∆E1/2 with pressure is due largely to the variation influid resistance with pressure (Figure 1, Table 1) and theconcomitant variation in ohmic distortion of the voltammograms.Figure 4 illustrates the pressure dependence of ∆E1/2(corr) forboth liquid CDFM (70 °C) and supercritical CDFM (115 °C), alldata corrected for ohmic distortion using the conductivity of thefluid measured under identical conditions. Within experimentaluncertainty, ∆E1/2 appears to be independent of fluid pressure inboth the liquid and the supercritical fluid. Pooling all data inFigure 4 gives ∆E1/2 ) 1.298 ( 0.004 V for liquid CDFM at 70 °Cand ∆E1/2 ) 1.276 ( 0.005 V for supercritical CDFM at 115 °C,the difference in these values being attributed to the temperature(entropy) effect described in the previous section.
Now we address the pressure dependence of the limitingcurrent as exemplified in Figure 3. Figure 5 displays a plot ofthe diffusion current as a function of pressure, where the limitingcurrent for Fc oxidation is seen to decrease with increasingpressure, whereas that for Cc+ reduction remains relatively
constant. This experiment was repeated at various analyteconcentrations, and, with one exception, the limiting current wasobserved to vary linearly with concentration at each pressuredisplayed in Figure 5, verifying complete solubilization of theanalytes. The one exception was the data point for Cc+ at 10 MPa,where the behavior indicated incomplete and/or slow solubiliza-tion of the Cc+ salt. A diffusion coefficient at each pressure wasextracted from the concentration dependence using Saito’s equa-tion,49 id ) 4nFDCRD, and the results are presented in Table 4.The hydrodynamic radii of Fc and Cc+, computed at each pressurefrom the measured diffusion coefficients and from estimates ofsupercritical fluid viscosity, are also provided in Table 4. Theviscosity was estimated from equations describing the viscosityof CDFM vapor at high temperatures and pressures.50 To thebest of our knowledge, no one has measured the viscosity ofsupercritical CDFM. Additionally, we assume that contributionsto the current due to migration of Cc+ is negligible since theTBATFB electrolyte concentration is at least 50-fold higher thanthat of Cc+.37
(46) Cruanes, M. T.; Drickamer, H. G.; Faulkner, L. R. J. Phys. Chem. 1992, 96,9888.
(47) Krasinski, P.; Tkacz, M.; Baranowski, B.; Galus, Z. J. Electroanal. Chem.1991, 308, 189.
(48) Sawyer, D. T.; Roberts, J. L., Jr. Experimental Electrochemistry for Chemists;John Wiley and Sons: New York, 1974; p 186.
(49) Saito, R. Rev. Polarogr. Jpn. 1968, 15, 177.(50) Nabizadeh, H.; Mayinger, F. DKV-Tagungsber. 1989, 16, 411.(51) Kohlen, R.; Kratzke, H.; Muller, S. J. Chem. Thermodyn. 1985, 17, 1141.(52) Uematsu, M.; Franck, E. U. Ber. Bunsenges. Phys. Chem. 1989, 93, 177.(53) Kumagai, A.; Takahashi, S. Int. J. Thermophys. 1991, 12, 105.
Figure 4. Difference in half-wave potentials of ferrocene andcobaltocenium corrected for ohmic distortion,∆E1/2(corr), as a functionof fluid pressure. Liquid CDFM conditions: 70 °C; 10 mM TBATFB;25-µm-diameter Pt disk electrode; scan rate, 10 mV/s. Supercriticalfluid conditions: 115 °C; 11 mM TBATFB; 25-µm-diameter Pt diskelectrode; scan rate 20 mV/s. Each point is the average of four (liquiddata) or seven (supercritical fluid data) independent measurementswith Fc/Cc+ concentrations ranging from 30 to 125 µM.
Figure 5. Variation of the diffusion-limited currents of ferrocene andcobaltocenium with pressure in supercritical CDFM. Conditions: 100µM Fc (b), 100 µM Cc+ ([), 10.2 mM TBATFB; 115 °C; 25-µm-diameter Pt disk; scan rate, 20 mV/s.
Table 4. Diffusion Coefficients of Ferrocene andCobaltocenium as Functions of Supercritical FluidPressure (P), Density (G), and Viscosity (η) at 115 °Ca
P(MPa)
F(g/mL)
η(cP)
104 DFc(cm2/s)
Fcradius (Å)
104 DCc+
(cm2/s)Cc+
radius (Å)
10.0 0.985 0.0691 1.16 3.512.0 1.006 0.0752 1.04 3.7 0.6014.0 1.024 0.0800 0.94 3.8 0.66 5.416.0 1.040 0.0840 0.89 3.8 0.66 5.118.0 1.055 0.0873 0.85 3.8 0.66 4.920.0 1.069 0.0903 0.81 3.9 0.66 4.822.0 1.081 0.0929 0.77 4.0 0.65 4.7
a Densities and viscosities were calculated as described in Table 3.Also tabulated are the computed hydrodynamic radii of Fc and Cc+
(see text).
Analytical Chemistry, Vol. 68, No. 13, July 1, 1996 2059
The diffusion current and diffusion coefficient for ferrocenedecrease rapidly with pressure over the lower end of the pressurerange (Figure 5 and Table 4) due to the higher compressibilityof the fluid over this range and the resulting rapid increase indensity and viscosity with pressure. As the fluid becomes lesscompressible at higher pressures, the density and viscosity changeless rapidly with pressure, and this, in turn, results in a smallerchange in diffusion current and diffusion coefficient with pressure.The hydrodynamic radius of Fc in the supercritical fluid issomewhat larger than that in the liquid and increases withpressure, perhaps reflecting an increase in the solvent sheathsurrounding the Fc. The number of solvent molecules around aneutral solute has been shown to vary with solvent density.2
The pressure dependence of the limiting current and diffusioncoefficient of Cc+ is markedly different from that of Fc. Ignoringthe point at 10 MPa for reasons discussed above, the limitingcurrent (Figure 5) and diffusion coefficient (Table 4) are virtuallyindependent of pressure. As observed in liquid CDFM (Table3), the hydrodynamic radius of Cc+ in supercritical CDFM issignificantly larger than that of Fc and decreases with pressure.These observations are consistent with the formation of Cc+ ionaggregates. As the pressure is increased, the diffusion coefficientshould decrease as the viscosity of the solution increases, asobserved with Fc. However, the dielectric constant of the fluidalso increases with pressure, favoring dissociation of ion ag-gregates and reducing the average size of the diffusing Cc+
species, as reflected in the hydrodynamic radius. These effectsoffset one another, leading to the weak pressure dependenceobserved. At the liquid-like densities of the high-pressure fluid,the diffusion coefficients of Fc and Cc+ approach one another(Figure 5) with a ratio (DCc+/DFc ) 0.84) comparable to thatobserved in liquids (see earlier discussion).
Typically, complexation of a reducible ionic analyte such asCc+ (or complexation of the ionic product from oxidation of aneutral analyte such as Fc) is manifested by a shift in E1/2 to morenegative potential. However, ion associations involving Cc+ andFc+ are expected to be very similar, and both waves shouldexperience a very similar shift, resulting in little dependence of∆E1/2(corr) on factors influencing such ion associations (e.g.,electrolyte concentration or pressure).
Voltammetry in Fluoroform. Trifluoromethane (CHF3 orfluoroform, referred to here as TFM), is a fluid that is widely usedin supercritical fluid studies of solvation.4 It also possesses a verymild critical temperature of 25.1 °C and a critical pressure of 4.75MPa. TFM is slightly more polarizable than CDFM, whichsuggests that TFM should also be a suitable electrochemicalsolvent. Preliminary examinations of the voltammetry of neatTFM, of TFM containing added electrolyte, and of ferrocene inTFM have been performed. Figure 6 shows the voltammogramof the neat supercritical fluid and also the voltammogram ofsupercritical TFM containing 10 mM TBATFB, illustrating thepotential limits under these two conditions.
In the absence of electrolyte, no discernible oxidation processis observed out to a potential of +7 V. However, two reductionprocesses are observed as the potential is swept negatively,yielding a small peak at -2.5 V superimposed on a larger increasein current. The small peak is attributed to oxygen reduction(diagnosed as described previously26), while the general increasein background current is attributed to the onset of fluid reduction.Since the oxygen wave is observed without intentionally added
electrolyte present, there is the exciting prospect that electro-chemical detection in neat supercritical TFM may be possible withproper electrode/cell design.
In the presence of 10 mM TBATFB electrolyte, the reductionwaves shift to more positive potentials (lower ohmic distortion),and an oxidation process is now observed which is attributed tothe oxidation of TBATFB. The potential window within whichthe current density is less than 1.0 mA/cm2 is from +2.65 to-1.62 V, without removing the oxygen from the fluid. Thispotential window of∼4.3 V in TFM is very similar to that of CDFM(+2.8 to -1.5 V) and does not appear to change significantly asthe pressure is increased at 35.0 °C. The conductivity of TBATFBin fluoroform has not yet been measured.
Figure 7 displays a voltammogram of ferrocene recorded inTFM at 35.0 °C and 7.70 MPa, which is nominally in thesupercritical fluid region. The voltammogram was recorded inan optical cell similar to that previously described26 so that thehom*ogeneity of the phase could be ascertained. There was no
Figure 6. Background voltammograms of supercritical CHF3.Both voltammograms were obtained at a 25-µm-diameter Pt diskelectrode with a 20 mV/s scan rate. Neat fluid (‚‚‚) at 35.0 °C, 9.50MPa. Fluid containing 10.0 mM TBATFB (s) at 35.0 °C, 7.00 MPa.
Figure 7. Voltammogram of ferrocene in supercritical CHF3.Conditions: 35.0 °C, 7.70 MPa; 50 µM Fc, 8.69 mM TBATFB; 25-µm-diameter Pt disk; scan rate, 10 mV/s.
2060 Analytical Chemistry, Vol. 68, No. 13, July 1, 1996
evidence of a second phase, as was observed with near-criticalCDFM.26 A plot of E versus ln((id - i)/i) for the voltammogramhas a slope of 0.0285, which is comparable to the Nernstian slopeof 0.0266, indicating only modest ohmic distortion. The lowoperating temperature of this moderately polar supercritical fluidmakes it an attractive solvent for further electrochemical study.
CONCLUSIONSSupercritical fluids of modest polarity, such as the halogenated
methanes of this study, show promise for use in supercritical fluidchromatography/electrochemistry. Such fluids have sufficientlylow polarity as to possess readily accessible critical temperatureand pressure, compatible with chromatographic conditions, yetsufficiently high polarity as to dissolve millimolar concentrationsof electrolyte, providing ample conductance for supporting elec-trochemistry at unmodified electrodes. Ion-pairing (and possiblyhigher ion aggregate formation) occurs in CDFM, and uncom-pensated resistances of several megaohms can be encountered,leading to some ohmic distortion of voltammograms and shifts inhalf-wave potential of up to several tens of millivolts. However,knowledge of the equivalent conductivity of the fluid under theexperimental conditions of interest permits removal of such ohmiceffects from the data. A smaller microelectrode than that usedin this study would further ameliorate the ohmic distortion.
Reference electrodes of well-defined potential for use insupercritical fluids are difficult to develop, and internal referenceredox couples are usually employed. The ferrocene and colbal-tocenium systems appear to be excellent choices for such potentialreferences in CDFM, since the difference in their half-wave
potentials is independent of fluid pressure over a considerablerange and only slightly, but predictably, dependent on fluidtemperature. Furthermore, their waves are sufficiently separatedfrom one another that one of the two systems will likely sufficefor any given experimental situation. We anticipate that thisbehavior observed in CDFM will carry over to other halocarbonsolvents such as trifluoromethane.
Finally, in addition to the electrochemistry of the organome-tallic systems reported here, we note that we have observedpreliminary voltammetry in supercritical CDFM of organic (as-sorted phenols) and inorganic (copper bis(diethyldithiocarbam-ate)) species as well, illustrating the general utility of CDFM asan electrochemical solvent. This work will be reported in duecourse.
ACKNOWLEDGMENTWe thank Dr. Ulrich Herman for assistance in translating refs
40 and 50. This research was supported by the National ScienceFoundation through Grant CHE-9108921, by the North DakotaASEND/NSF EPSCoR Program, by the U.S. Department ofInterior/North Dakota Water Resources Research Institute throughGrant 14-08-0001-G158, and by the S. C. Johnson Wax Co.
Received for review November 10, 1995. Accepted March21, 1996.X
AC9511152
X Abstract published in Advance ACS Abstracts, May 1, 1996.
Analytical Chemistry, Vol. 68, No. 13, July 1, 1996 2061
