J . Phys. Chem. 1991, 95, 10191-10197
10191
Utility of Mlcroelectrodes in High-Pressure Experiments Janusz Golakt Harry G. Drickamer, and Larry R. Faulkner* School of Chemical Sciences and Materials Research Laboratory, University of Illinois, 1209 W.California St., Urbana, Illinois 61801 (Received: June 13, 1991)
A method for preparing platinum cylindrical microelectrodes for applications in high-pressure measurements is described.
Advantages of microelectrods of this geometry are illustrated with voltammetric and chronoamperometricexperimentsperformed at pressures of 1-8000 bar. Quantitative data on the pressure dependence of diffusion coefficients of K3Fe(CN)6 and O2 in 0.1 M KCl solutions are presented together with qualitative remarks on the behavior of these systems at higher pressure. The results for microelectrodes are compared to those obtained at large cylindrical Pt electrodes under the same experimental conditions.
Introduction Electrodes for which the smallest dimension, r, is on the order of microns have rapidly gained interest during the past decade or more.'-' First called microelectrodes, and more recently known as ultramicroelectrodes, they not only have introduced qualitative changes in electrochemical experiments but also have caused the development of new qualitative descriptions of electrode processes. The most characteristic feature that appears when the size of the electrode is diminished is the effect of nonplanar diffusion toward the electrode surface. This happens for 0 = Dt/$ >> 1, where t is the electrolysis time and D is the diffusion coefficient of the reduced or oxidized species. In a chronoamperometric experiment, the current-potential curve eventually becomes time independent and approaches steady state. In linear scan voltammetry, a steady-state current is attained when the radius, r, is much less than the distance (D/nfv)'/2,where f = F / R T and v is the scan rate. The limiting steady-state current depends also on the geometry of the electrode as follows: i, = anFrDC (1) where a = 47r for a sphere, 27r for a hemisphere, and 4 for a disk, and C is always the concentration of the electroactive species. The chronoamperometric response for cylindrical electrodess-I0 can be expressed in the form il = nFACR(0) (2) where A is the electrode area and R(0) is a time-dependent function describing the diffusion characteristics of the system. Again for 0 >> 1, one has a limiting form il = 2nFADC/[r In (4~9)] (3) and for 0
E w to.
T
TnA
2
0
4
6
6
10
p / kbar
Figure 4. Square wave voltammetry of 1 mM K,Fe(CN), in 0.1 M KCI; ( A E = 25 mV, f = 15 Hz, step E = 4 mV). Dependence of peak potential E, (curve 1) and half peak width u , , ~(curve 2 ) on pressure. I tO.0
t o ,500
I
I
-0.200
E/V
Figure 3. Cyclic voltammograms of 1 mM K,Fe(CN), in 0.1 M KCI obtained at Pt cylindrical microelectrode CI at I (curve I), 4000 (curve 2), and 8000 bar (curve 3). Scan rate u = 5 mV/s.
Before each experiment, the wire was soaked in a mixture of perchloric and sulfuric acid, rinsed with water in an ultrasonic bath, and finally heated in an electrical coil (-180 “C). A chromic acid bath was too aggressive toward the plastic materials. The length of the exposed Pt wire was adjusted to approximately 3-4 mm. To get a microdisk electrode, the Pt wire was cut off at the level of the seal with a microtome. The cross section was polished (without pressing) on a polishing wheel with polishing cloth (Buehler, Ltd.) and a water suspension of 0.05-pm alumina powder (Buehler, Ltd.). Each microelectrode could survive two or three series of high-pressure measurements before the internal connection broke. The large cylindrical Pt electrode was prepared by press-fitting platinum wire ( r = 0.05 cm) into Nylon. The surface of this electrode was polished with 0.05-pm alumina powder after chemical cleaning. Two platinum wires ( r = 0.05 cm) were press-fitted into the Nylon plug which closes the compression chamber of the cell. There is also one threaded opening in this plus which enables the expulsion of any air bubbles that remain in the cell after filling. The opening is then closed with a screw (Figure 1). One of the platinum wires was used as a counter electrode, and the other was electroplated with silver and then electrooxidized in HCI to form an AgCl coat. Comparisons of results obtained in two- and three-electrode systems indicated the possibility of eliminating the third (counter) electrode in our measurements. The potential of the reference electrode could be reasonably assumed to be constant with pressure, as proved in earlier experiments by CruaAes. Pressure was generated in a hydraulic intensifier, with the cell located in the high-pressure chamber. The pressure transmitting fluid was 90% methylcyclohexane and 10% isooctane. All electrochemical measurements were carried out with a BAS- lOOA electrochemical analyzer. In each series of experiments, all measurements were done for progressively increasing pressure. Solutions of 1 mM K3Fe(CN), in 0.1 M KCI were deaerated by purging with nitrogen immediately before transfer to the cell. In order to obtain oxygen-saturated solutions of 0.1 M KCI, oxygen was purged through each sample for h before closing the cell. The results discussed below were obtained with a set of platinum working electrodes: three cylindrical microelectrodes (Cl, C2, C3),one microdisk electrode (DI),and a large cylindrical electrode
0
2
6
4
8
c
10
p I kbar
Figure 5. Cyclic voltammetry of 1 mM K,Fe(CN), in 0.1 M KCI at Pt cylindrical microelectrode (u = IO mV/s). Dependence of formal po-
tential on pressure.
(LC). Fine platinum wire ( r = 12.5 pm, AESAR, Johnson Matthey) was used in making microelectrodes, and platinum rod ( r = 0.05 cm) was used for the large cylindrical electrode. The area of the surface was determined by measuring the dimensions (1) of each electrode and the following values were calculated: A,-, = 3.6 X IO-3 cm2 (I = 0.46 cm); AC2 = 2.4 X cm2 (1 = 0.30 cm); A3 = 2.9 X 10” cm2 (I = 0.37 cm); A,, = 4.9 X 10” cm2; ALC = 48.6 X IO-’ cm2 ( I = 0.13 cm).
Results and Discussion Chronoamperometric transients of K3Fe(CN),, obtained at ambient pressure, were used for an experimental determination of the effective area of the cylindrical microelectrode CI. The value Ac, = 3.7 X lo-’ cm2 (assuming D = 0.76 X IO” cm2/s) matched well the value determined earlier from geometry. This effective area was calculated according to the procedure suggested by eq 9. The value obtained, together with good agreement between the theoretically predicted slope of the voltammogram [n(EIl4- E!/4) = 56.5 mV] and the corresponding measured slope of 57 mV, indicated a good quality of surface on electrode C1. Curves for 1,4000, and 8OOO bar are presented in Figure 3. The slopes of the voltammograms confirm the reversible character of the process up to -4000 bar, given that values 57, 57, and 75 mV were obtained for curves 1,2, and 3, respectively. The latter value suggests a slowing of the kinetics for pressure above 4 kbar. This was also seen in Osteryound square wave voltammetry, as shown in Figure 4. The peak potential shifts steadily in the positive direction, and the half-width of the peak increased significantly for p > 4 kbar. Cyclic voltammograms also shifted toward more positive potential with pressure, as shown in Figure 5.
The reduction of Fe(CN)63- is favored by the pressure; hence, the total volume of the products must be smaller than the total
The Journal of Physical Chemistry, Vol. 95, No. 24, 1991
Microelectrodes in High-pressure Experiments
I
T
I
I
I
I
0
I &oo
I
10195
I
T t I msec
EIV
Figure 6. Cyclic voltammograms (u = 5 mV/s) and chronoampcrometric transients of oxygen (C = 1.24 mM) dissolved in 0.1 M KCl. At Pt cylindrical microelectrode C2 under 1 kbar (curves I , 3) and 8 kbar (curves 2, 4). TABLE I: Diffusion Coefficient of K3Fe(CN)‘ in 0.1 M KCI with Pressure, As Calculated from Chronoamperometry at Microelectrode C1
n/bar 1
500 1000 2000 3000 4000 5000 6000 7000 8000
10sD/
IOsD~E~/
Z.
BJB.
DJDn
cm2s-I
cm2s-I
1.00 0.99 0.96 0.93 0.91 0.89 0.87 0.85 0.84 0.83
1.00 0.97 1.00 1.00 1.00 0.92 0.92 0.86 0.84 0.75
1.00 0.96 0.96 0.93 0.91 0.82 0.80 0.73 0.70 0.62
0.76 0.73 0.73 0.71 0.69 0.62 0.61 0.56 0.53 0.47
0.37 0.37 0.38 0.39 0.41 0.41 0.43 0.44 0.45 0.43
volume of the reactants. If one assumed linear dependence of E”’ vs p (which in fact is not ideal, given that the linear correlation coefficient was 0.981 l ) , the standard volume of the reaction Ag(,, + CI- Fe(CN)63- AgCl + Fe(CN)64-
+
is equal to approximately A T = -2 cm3/mol. Looking at smaller segments of the pressure curve, one finds that this value changed from AVO -5.5 cm3/mol at 0.5 kbar to AVO -1.5 cm3/mol a t 8 kbar. Determination of the diffusion coefficient vs pressure was done according to the procedure described with eqs 9 and 10, and the results are collected in Table I. The diffusion coefficient decreased almost in half when the pressure was elevated from 1 to 8OOO bar. This effect is attributed mostly to the change of viscosity because D q,el (where qnl is the relative viscositys9)did not change greatly with pressure. The effective area of microcylinder C2 was determined from chronoamperometric measurements of K3Fe(CN), in 0.1 M KCI cm2 is under ambient pressure, and the value Acz = 2.4 X in excellent agreement with the earlier calculation from geometric parameters. A series of voltammetric and chronoamperometric measurements were performed for oxygen-saturated solutions of 0.1 M KCI. This procedure gave a basis for refining the estimate of the diffusivity for O2a t ambient pressure. The surface area of cylindrical microelectrode C3 was calibrated against oxygen via chronoamperometric measurements, assuming an oxygen diffusion coefficient D = 1.97 X lW5cm2/s, as obtained in the experiments with microelectrode C2 (see Table 11). The measured value of Ac3 = 2.8 X lo-’ cm2 was in agreement with cm2. the previously calculated value of Acs = 2.9 X Examples of voltammograms and chronoamperometric transients for 1 and 8000 bar obtained with the oxygen system at
-
-
TABLE II: Diffusion Coefficient of Oxygen in 0.1 M KCI with Pressure, As Calculated from Chronoamperometry at Microelectrodes C2 and C3
10sD/ Bo/Bn
p/bar
Z,, C2
1 500 1000 2000 3000 4000 5000 6000 7000 8000
1 0.99 0.96 0.93 0.91 0.89 0.87 0.85 0.84 0.83
1.00 0.97 0.89 0.88 0.84 0.80 0.69 0.63 0.53 0.48
C3 1.00 1.00 1.00 0.99 0.92 0.82 0.80 0.74 0.70 0.66
D,,/Do C2 1.00 0.96 0.85 0.82 0.76 0.71 0.60 0.54 0.45 0.40
cm2 s-I
C3 C2 1.00 1.97 0.99 1.89 0.96 1.67 0.92 1.61 0.84 1.49 0.73 1.40 0.69 1.18 0.63 0.99 0.59 0.89 0.55 0.79
C3 1.97 1.95 1.89 1.81 1.65 1.44 1.34 1.24 1.16 1.08
10s&ml/ cm2 s-l C2 0.96 0.95 0.86 0.89 0.89 0.92 0.85 0.78 0.76 0.73
C3 0.96 0.97 0.97 0.99 0.99 0.95 0.96 0.97 0.99 0.99
TABLE 111: Diffusion Coefficient of Oxygen in 0.1 M KCI with Pressure, As Calculated from Chromoulometry at the Large Cvlindrical Electrode
D,/Do
cm2 s-I
10s&d/ cm2 s-I
1.00 1.00 0.94 0.89 0.76 0.67 0.65 0.61 0.55 0.5 1
2.02 2.02 1.90 1.81 1.53 1.35 1.31 1.23 1.11 1.03
0.99 1.01 0.98 0.99 0.92 0.89 0.94 0.97 0.95 0.95
10sD/
p/bar 1 500
lo00 2000 3000 4000 5000 6000 7000 8000
Z,, 1.00 0.99 0.96 0.93 0.9 1 0.89 0.87 0.85 0.84 0.83
1.OOo 1.010 0.986 0.966 0.834 0.753 0.749 0.714 0.65 1 0.6 12
microelectrode C2 are shown in Figure 6. The voltammograms, which are kinetically determined, shifted toward positive potentials as the pressure increased; thus, the volume of the transition state is probably smaller than that of the reactants in the rate-determining step. From chronoamperometric data, the diffusion coefficients a t different pressures were determined, and the results are collected cm2/s was in Table 11. The obtained value of D = 1.97 X in the range of the published data for oxygen at ambient pressure. The diffusion coefficients decreased with increasing pressure, and the change was attributed to the changing viscosity of the solution. The values obtained were compared to those resulting from chronocoulometric measurements for the large cylindrical electrode LC. The calculations, based on charge measured within 100-ms range in oxygen-saturated 0.1 M KCI solution, gave the values
10196 The Journal of Physical Chemistry, Vol. 95, No. 24, 1991
GolaS et al. A
E -0.5
to.0
+O.
-0.800
T
-1.0
T 1
B
50nA
lOyA I. ."
~
t o .'so0
j
\
' , to.0
l
A
,
-0.5
,
,
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L
,
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to
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EIV EIV Figure 7. Cyclic voltammograms (u = 5 mV/s) of oxygen ( c = 1.24 mM/s) dissolved in 0.1 M KCI. At the large cylindrical Pt electrode under ambient pressure (curve I ) , 4 kbar (curve 2) and 8 kbar (curve
Figure 8. Cyclic voltammograms of oxygen (c = 1.24 mM/s) in 0.1 M KCI obtained at Pt microdisk electrode DI at 1 (curve A) and 8000 bar (curve B) for scan rate u = 200 mV/s.
liI\
3).
-
A
TABLE IV: Limiting Current for the Reduction of Oxygen at 1 and 8000 bar at the Pt Microdisk Electrode at -0.8 V i/nA ilnA time/s (p = 1 bar) (p = 8000 bar) 3.3 I I4 38.4 4.1 109 35.0 4.9 106 31.5 5.9 I03 31.0 6.5 101 31.0 1.3 99 29.8 8.0 98 29.8
for diffusion coefficient presented in Table 111. Diffusion coefficients were determined assuming planar diffusion (0 = 3 X IO4 >I) for t = 8 s.) This was also justified based on the current values (chronoamperometry) obtained at ambient pressure and 8 kbar (Table IV). Diffusion coefficients calculated assuming that only the disk surface was exposed were about 2 times too high for pressures less than 2 kbar. Voltammograms obtained at lower pressures also showed large hysteresis, which could suggest the influence
:
c21 c3 Di
$
2
3 7
1
0
10
"I F
F 2 0
1
10
p I kbar
Figure 9. Change of diffusion coefficient (A) and Dv (B) for oxygen in 0.1 M KCI with pressure. Values calculated from the chronoamperometric (for C2, C3, DI microelectrodes) and chronocoulometric (large
cylindrical electrode LC). of cylindrical diffusion. These voltammograms are shown in Figure 8. These effects disappeared with increase of pressure. One explanation would be to take into account the quality of the seal between the Teflon tubing and platinum microwave. It seemed very probable that there was also a side wall of Pt wire exposed to the solution. If the seal tightened around the wire when pressure increased, one could explain why results obtained for higher pressures were in very good agreement with those obtained at all other electrodes. A comparison of results for oxygen diffusion coefficients obtained at different electrodes during high-pressure experiments
10197
J. Phys. Chem. 1991, 95, 10197-10203 is shown in Figure 9. Considering the fact that all results were obtained during a series of time-consuming measurements and, that the surface of the electrode could be controlled only once before closing the cell, they are very self-consistent and clearly reflect the pressure dependence, which is mainly due to the change of viscosity of the solution (Figure 9B). The proposed procedure of making cylindrical microelectrode results in relatively durable electrodes of good quality. Such electrodes enable us to perform voltammetric experiments under high pressure, and these kinds
of studies are now being continued. Acknowledgment. We are grateful to the National Science Foundation for supporting this work under Grant CHE-86-07984 and the Materials Science Division of the Department of Energy under Contract DEFG02-91ER45439. We also thank Ann Zielinski for helpful editing of the manuscript. Registry No. Pt, 7440-06-4; K,Fe(CN),. 13746-66-2; 0, 7782-44-7; KCI, 7447-40-7.
Solvatochromic Study of the Effect of Chain Length, Chain Branching, and Polymethylation of Alkylbenzenes on Solvent Poiarizabllity Edward T. Ulrich and Peter W. Cam* Department of Chemistry, Kolthoff and Smith Halls, University of Minnesota, 207 Pleasant Street Southeast, Minneapolis, Minnesota 55455 (Received: January 29, 1991; In Final Form: June 24, 1991)
The contribution of solvent polarizability to solvatochromic measures of solvent strength, such as the Kamlet-Taft scale of solvent dipolarity-polarizability, is well recognized. In this work, we measured the A* values of 23 nonpolar aromatic solvents, including 10 n-alkylbenzenes (benzene to pentadecylbenzene), 5 branched-chain alkylbenzenes, and 8 di-, tri-, and tetramethylated benzenes. The A* values of n-alkane solvents increase monotonically with chain length. In contrast, the A* values of the aromatic liquids systematically decrease with homologue number. The direction of these changes is consistent with the increase in the polarizability of the n-alkanes and the decrease in the polarizability of the n-alkylbenzenes as homologue number increases. For both series of liquids, A* increases linearly with solvent polarizability; however, the slopes and intercepts of the relationships are quite different. We hypothesize that this difference in behavior is due to concentration of the phenyl groups of the long-chain alkylbenzenes in the cybotactic region of the very polar solvatochromic probes. Chain branching decreases A* of the alkylbenzenes,as it does for the alkanes. Ring methylation increases K* relative to that of the n-alkylbenzene of the same carbon number. However, when compared on the basis of polarizability, ring-methylated aromatics have a lower A* than the hypothetical n-alkylbenzeneof the same refractive index. The extent of this decrease is not related to the dipole moment of the polymethylated aromatic but does follow the extent of crowding of the methyl groups about the ring.
Introduction The Kamlet-Taft A* parameter is a well-established scale of solvent dipolarity-polarizability and has been used as the basis for a large number of correlations involving the effect of solvent dip01arity.l~ The A* scale of solvent strength was experimentally derived from the effect of solvent on the A to T * transition of a large number of judiciously chosen test solutes. The basic tenet of the Kamlet-Taft approach to the determination of A* is that some observed property of a solvent (j),such as its effect on the transition energy (vmJ of a suitable solute, will vary with solvent in accord with the linear solvation energy relationship vi4
= v0.j
+
(1)
Equation 1 has proven to be generally quite useful, but only if the type of solvent tested is limited to the so-called ‘select” solvents. These are defined as aliphatic, monodipolar, aprotic liquids. The parameters vo,, and si are established by least-squares fitting of the observed transition energies to eq 1 in a large number of select solvents. A numerical value is obtained by defining the A * ~scale to be zero for cyclohexane and unity for DMSO. The solute susceptibility parameter, si, varies with the nature of the process under study and with the specific probe solute. In general, the A * ~parameter of a very wide variety of liquids can be correlated with simple functions of solvent dielectric constant and refractive index. As shown in previous work, contributions from distortional polarization (solute dipole-solvent-induced dipole effects) to the A* scale are suppressed when one considers the select solvents as a single group. However, in the alkanes where distortional polarization is the only solute-solvent interaction that can lead to Author to whom correspondence should be addressed.
a solvent-induced change in the transition energy, we have shown that the measured A * ~values are well represented by the simple regression A*
= -1.11 (f0.03)
+ 5.75 (f0.12)
,
(2)
n = 12 r = 0.995 S D = 0.01 The term O(n2)represents the Onsager reaction field function of the refractive index
O(n2) = (nZ- l)/(2n2
+ 1)
(3)
and is used to measure the ability of nonpolar alkanes to interact with a solute dipole. Equation 2 predicts the A* of the gas phase (1) Kamlet, M. J.; Abboud, J. L.; Taft, R. W. Prog. Phys. Org. Chem. 1980, 13, 485-630.
(2) Kamlet, M. J.; Abboud, J. L.; Taft, R. W. J . Am. Chem. Soc. 1977, 99, 6027-38. (3) Fong, C. W.; Kamlet, M. J.; Taft, R. W. J . Org. Chem. 1983, 48, 822-5. (4) Kamlet, M.J.; Doherty, R. M.; Taft, R. W.; Abraham, M. H. J . Am. Chem. SOC.1983, 105, 6741-3. (5) Abraham, M. H.; Kamlet, M. J.; Taft, R. W.; Weathersby, P. K. J . Am. Chem. SOC.1983, 105, 6797-801. (6) Kamlet, M. J.; Abraham, M. H.;Doherty, R. M.; Taft, R. W. J . Am. Chem. SOC.1984, 106,464-6. ( 7 ) Kamlet, M.J.; Doherty, R. M.; Taft, R. W.;Abraham, M. H.; Koros. W. J. J. Am. Chem. SOC.1984, 106, 1205-12. (8) Taft, R. W.; Abboud, J. L.; Kamlet, M. J. J . Urg. Chem. 1984, 49, 2001-5. (9) Brady, J. E.; Carr, P. W . Anal. Chem. 1982, 54, 1751-7. (IO) Brady, J. E.; Carr, P. W . J . Phys. Chem. 1982, 86, 3053-7. (1 1) Brady, J. E.; Bjorkman, D.; Herter, C. D.; Carr, P. W. Anal. Chem. 1984, 56, 278-83. (12) Brady, J. E.; Carr, P. W . J . Phys. Chem. 1984, 88, 5796-9. (13) Brady, J. E.; Carr, P. W . J. Phys. Chem. 1985, 89, 1813-22.
0022-3654191 12095-10197%02.50/0 , 0 1991 American Chemical Society I
O(n2)
