Anal. Chem. 1991, 63, 2955-2960
in saving chromatographic interpretation time, in tracking down compounds of important elements, and in directing the attention of the analyst to interesting substances, it should serve neither as a final arbiter of elemental identity nor as an inscrutable, infallible "black box". Perhaps more than other types of analytical results, CONDAC chromatograms require an analyst fully aware of their conditional nature. In conclusion, the simple conditional-access approach can be employed-with just a few or perhaps even with only one wavelength selection-for obtaining specific chromatograms from resolved peaks of most if not all of the FPD-active elements. This study deliberately used a worst-case scenario in terms of separation efficiency and noise levels. With capillary separations of larger peaks on cleaner baselines, the CONDAC algorithm will work just that much better. Registry No. Cr, 7440-47-3; Co, 7440-48-4; Fe, 7439-89-6; Pb, 7439-92-1;Mn, 7439-96-5;Os, 7440-04-2;Re, 7440-15-5;Ru, 7440-18-8; C, 7440-44-0; HP, 1333-74-0; P, 7723-14-0; S,7704-34-9;
2955
n-C9Hzo,111-84-2; Co(CgHS)2,1277-43-6; Re2(CO)lo,14285-68-8; ( ~ - B U ) ~110-06-5; S ~ , O S ( C ~ H ~1273-81-0; )~, Mn(CH3C5H,)(C0)3, 12108-13-3; Mn(CSHS)(CO)3,12079-65-1; Fe(CSHS)2,102-54-5; Cr(CO)6,13007-92-6; R u ( C ~ H ~1287-13-4. )~,
LITERATURE CITED (1) Body, Sam S.; Chaney, John E. J . Gas Chromfogr. 1966, 4 , 42-48. (2) Dressier, M. Selectke Gas Chromafogmphic Defectors; Journal of Chromatogrephy Library; Elsevier: Amsterdam, 1988; Voi. 36. (3) Joonson, V. A.; Loog, E. P. J . Chromatcgr. 1976. 720, 285-290. (4) Aue, Waiter A.; Milller, Brian; Sun, Xun-Yun. Ana/. Chem. 1990, 62, 2453-2457. (5) Aue, Walter A.; Miliier, Brian; Sun, Xun-Yun. 73rd CIC Conference, Halifax. NS, July 1990. (6) This section was added in response to the reviewers' requests for additional information.
RECEIVED for review June 19,1991,Accepted September 19, 1991. This study was supported by NSERC Operating Grant A-9604, and was presented in part at the 73rd CIC Conference, July 1990.
Interdigitated Array Electrode Diffusion Measurements in Donor/Acceptor Solutions in Polyether Electrolyte Solvents Hiroshi Nishihara,' Frank Dalton? and Royce W. Murray* Kenan Laboratories of Chemistry, University of North Carolina, Chapel Hill,North Carolina 27599-3290
A steady-state interdigitated array (IDA) electrode method Is introduced for measurement of the dtffusivity of charge in mixed-valent donor/acceptor solutions In polyether solvents. The method lo based on establishment of steady-state c r d conccmtratkn gradients d donor and acceptor solutes In the 15-pm gap between the IDA finger electrodes. Apparent dtffusion coefficients D,,, are determined for the couples [c~,Fe]+'~,[Cp, Fe]'", TMPD'", TCNQo'-, and DDQo'- in poly(ethyiene glycol dimethyl ether) (MW = 400 and 1000) with lithium perchlorate electrolyte. The D,, values are In the range 10-10-104 cm2/s and exhibit strong variations with solute concentration. The changes are lnterpreted in terms of the concentration dependencies of the and of the electron self-exsolute physical coeffkient DPHYS change reactions between donor and acceptor. The IDA 0, measurements can also be employed to track the crystallization kinetics of the polyether solutions.
The dissolution of metal salts by poly(ethy1eneoxide) (PEO) and its polyether analogues to form ionically conductive polymer electrolytes (I) has spawned considerable research aimed at understanding ionic mobilities in these polymeric solids (2, 3). Our interests (4-8) in this family of polymer electrolyte are in their use as solvents in studies of the methodology of solid-state voltammetry and of the chemistry of redox monomer solutes in rigid or near-rigid solvents. Investigations of polymer-phase rates and mechanisms of transport of molecular redox solutes has been an important part of these studies. Molecular diffusion rates in the poly-
'
On leave from Department of Chemistry, Keio University, H i yoshi, Yokohama 223, Japan. *Present address: Grove City College, Grove City, PA 16127.
ether phases are typically much slower and more sensitive to the chemical nature of the diffusant than in more familiar monomeric fluid solvents. Methodology we have adapted for diffusive transport measurements in polymer phases includes potential sweep voltammetry (4-6), chronoamperometry (5), and ac voltammetry (7), all at microelectrodes and with consideration given to linear vs radial transport geometry effecta (5,9). Studies of redox molecule transport mechanisms have included the concentration dependencies of physical diffusion (5b,c)of diffusion-plasticization effects (4), and of coupled diffusion-electron self-exchange reactions (5b,c, 6). Except for electron self-exchange processes, such concentration dependencies are also known (5b, 10) from ionic conductivity measurements. This paper presents an investigation of interdigitated array (IDA) electrodes for redox diffusivity measurements in polyether solvents. The method is based on coating the IDA (fingers and gaps) with a 1:l mixed-valent polymer solution of a redox molecule of concentration C = C, = CRED and thickness h- Applying a potential bias between the electrode finger pairs electrolytically establishes steady-state concentration gradients of the oxidized and reduced forms of the redox species in the interfinger gap (d, cm). The limiting current iLIMflowing under this condition is related to the apparent diffusion coefficient DAppof the donor-acceptor couple by DAPP
=
~ L I M ~
nFCLhfi,(N - 1)
where N , L, and h , are the number of fingers, finger length, and height of the IDA (11). We apply the IDA experiment to mixed-valent solutions of the donor-acceptor couples tetracyanoquinodimethane (TCNQOI-),2,3-dichlor&,6-dicyanyano-p-benzoquinone(DDQo/-), tetramethylphenylenediamine (TMPD+Io), ferrocene
0003-2700/91/0383-2955$02.50/00 1991 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 63, NO. 24, DECEMBER 15, 1991
(Cp2Fe+/O), and decamethylferrocene (Cp,*Fe+/O), in the short-chain polyethers, poly(ethy1ene glycol dimethyl ether), MW = 400 (MezPEG-400)and MW = lo00 (Me2PEG-1000). The diffusion coefficients of these redox species vary with concentration in a manner semiquantitatively consistent with the coupling of electron self-exchanges to physical diffusion and are correspondingly labeled DApp values (12). The diffusion coefficients are also very sensitive to the phase state of the polymer, as ilIustrated by diffusivity differences between the solvent Me2PEG-400 (a clear amorphous, highly viscous liquid) and Me2PEG-1000(a soft white, partly crystalline wax at room temperature), by the time course of crystallization events in the polymer, and by effects of thermal history. EXPERIMENTAL SECTION Chemicals. LiClO, was dissolved at O/Li ratio of 16:l (CLicIo, = 1.7 M) in poly(ethy1ene glycol dimethyl ether), MW = 400 (MezPEG-400)and MW = lo00 (Me2PEG-1000)(Polysciences), that had been predried in a vacuum oven. The electrolyte solution was vacuum-dried at 50 "C over Pz05for 3 days before use with redox species. The MezPEG-1000 solution is a soft white wax at room temperature; it melts to a highly viscous clear liquid at 32 "C, as determined by differential scanning calorimetry. Ferrocene (Cp2Fe), bis(pentamethylcyclopentadieny1)iron (Cpz*Fe),N,N,","-tetramethyl-p-phenylenediamine (TMPD), tetracyanoquinodimethane (TCNQ), and 2,3-dichloro-5,6-dicyano-p-benzoquinone (DDQ) were obtained from commercial sources, and their corresponding redox couple salts, [Cp,Fe](BF,) U3), [Cpz*FeI(BF,) (131, [TMPDl(C104) (14L(Li)[TCNQI (15), and (Et4N)[DDQ] (161, were prepared by literature methods. Fabrication of Polymer-Coated IDA. Transport measurements were made with interdigitated array electrodes (Microsensor Systems, Inc., P.O. Box 90, Fairfax, VA 22030) having 25 fingers on each electrode side ( N = 50) with finger width w = 45 pm, length L = 0.51 cm, and height h, = 0.1 pm, and interfinger gap d = 15 pm. The IDAs were rinsed with acetone, sonicated in carbon tetrachloride to improve wettability, again rinsed in acetone, and dried before use. Individual IDAs were quite durable and could be used repeatedly in diffusivity experiments. A 1:l mole ratio mixture of a donor/acceptor pair (Le., 4.1 mg of [Cp,Fe](BF,) and 2.8 mg of CpzFe) was mixed with a known amount of predried Me,PEG/LiClO, polymer electrolyte in a controlled-atmosphere enclosure. The mixture was homogenized by heating to 40 "C (above the MezPEG-1000polymer melting temperature) with stirring for 1 h or by dissolving it in acetonitrile (Burdick and Jackson, dried over 4-A molecular sieves). IDAs were coated by carefully spreading a droplet of the polymer melt or of its acetonitrile solution over the entire finger area (5.1 mm X 3.0 mm). Acetonitrile in the polymer was allowed to evaporate and the IDA was heated at 40-50 "C for 10 min to further dry the polymer and ensure a homogeneous film. All of these steps were carried out in a glovebox since water contaminant in the polymer affects its transport characteristics. The electrode enclosure consisted of four pairs of copper wire feedthroughs sealed in 24/40 glass stoppers, capping a flask with four 24/40 necks and a two-way stopcock. An IDA could be hung from each stopper, making electrical connections with alligator clips soldered to the feedthroughs. The sealed flask equipped with four polymer-coated IDAs could be removed from the glovebox, allowing electrochemical measurements to be carried out on the benchtop. The two-way stopcock was connected to an argon line to regulate the flask pressure during controlledtemperature experiments. Electrochemical Measurements. Two-electrode IDA voltammetry was performed with a potentiostat and waveform generator of local construction, scanning the potential between 0.5 and -0.5 V at various rates. When voltammograms with well-defined steady-state limiting currents could not be obtained by potential scan rates as slow as 1 mV/s, steady-state voltammograms were measured point by point, holding the potential constant at each value until the current became constant (ca. 5-30 min.). Repetitive experiments (5-10) were carried out at each donor-acceptor concentration to counter the relatively poor reproducibility of the measurement. In experiments where the temperature or time dependency of the limiting current (i.e., DmP)
Figure 1. Change in cyclic voltammetry of 0.05 M Cp,Fe and 0.05 M Cp,Fe+ in Me2PEG1000/LiCi0, film on IDA (hnm= ca. 0.5 mm, scan rate 2 mVls) as (and after) melted film cooled down to room temperature: (a) first three scans, (b) after 2.2 h, and (c) after 19 h. Circles (0)represent steady-state, constant-potential current. S = 1 PA (a); S = 0.2 p A (b and c).
was observed, the current was monitored continuously at a potential bias of 0.3 V, which was sufficient to obtain a limiting current. RESULTS AND DISCUSSION Measuring Dmp: IDA Voltammetry of Cp,Fe+/O in Me2PEG-1000/LiC104. Me2PEG-1000containing 1 6 1 (0:Li) LiC10, is a white soft wax, i.e., a partly crystalline polymer, which melts a t 32 "C to an amorphous, highly viscous, clear solution. Figure l a shows the result of applying a slow voltage bias scan to an IDA following spreading of a droplet of MezPEG-1000/LiC104 melt containing 0.05 M each of Cp,Fe and [Cp,Fe] (BF,) onto an interdigitated electrode. The film in this case is relatively thick, h,, = ca.0.5 mm. As (and after) the film is cooled to room temperature, each succeeding scan produces a smaller current; this change continues for a protracted period (Figure lb,c). Both the diminishing currents and the increased tendency to produce peaked currents that settle to plateaus reflect a time-dependent slowing of diffusion that in turn reflects the formation of ordered regions within the polymer and its gradual solidification (partial crystallization). Transport in polyethers occurs much more rapidly through amorphous (nonordered) than through crystalline regions (2). After an equilibrium state is reached, the voltammogram does not change further upon repeated scans. The time required to reach an equilibrium transport rate varied with the donor/acceptor couple and its concentration as discussed in a later section. I t is from 5 to 10 h for samples like that in Figure 1. Long recrystallization times following melting are a well-known property of polymers including polyethers (2). The 0 points in Figure 1 represent fixed-potential, steady-state currents for the thermally equilibrated polymer. Limiting currents employed for DApp measurements were typically obtained in this way. When a polymer film is cast onto the IDA, the film covers both the 45-pm-wide electrode fingers and the 15-km-wide interfinger gaps. DMp evaluation using eq 1 is conceptually most straightforward when the polymer film thickness hah and the IDA finger height hrmg(0.1 pm) are the same, since this gives a parallel plate cell arrangement for the part of the film resting in the interfinger gap. Drop-casting a known
ANALYTICAL CHEMISTRY, VOL. 63,NO. 24, DECEMBER 15, 1991
2957
'\
/
Figure 4. Plots of steady-state current vs A€ for 0.2 M TMPD/O.2 M TMPD' (A)and 0.15 M WQ10.15 DDQ- (0)in Me2PEG1000/UCi04. Lines represent ideal Nerstian behavior based on eq 3. S = 0.1 pA (TMPD); S = 0.2 p A (DDQ).
anode
j
j cathode
~-w/~-+I-~-JCW/~~ Schematic Cross-sectional view of IDA fingers and mixed-valent film, showing relative dimensions of fingers, gaps, and O.8-pm film. The cross-hatched part of the Rim Is, in effect, in between the two electrode fingers; crossed concentration gradients are generated in this part of the film during a diffusivtty experiment. (B) Schematic view of the steady-state concentration profile (-) and current profile (---) at an IDA based on ref 17. Numbers represent the ratio of ,C to CTOTAL. Flgure 2. (A)
tionality to hfil,would suggest. In these thicker films, the film dimension is no longer negligible compared to that of the interfinger gap, resulting in extension of the region of concentration polarization (which for the thin films is confined to the gap) beyond the edges of the 15-pm gaps into the strips of film resting on top of the 45-pm-wide fingers. This effectively increases the gap width and lowers the concentration gradient and thus the current. A calculation based on the theory by Aoki et al. (17) for a very thick film and a quasiinfinite diffusion condition is shown in Figure 2B. The solid lines are for isoconcentration values of CRED/CmAL and the dashed lines are isoflux lines, which have the smallest values when they are far from the gap; i.e., the polymer regions far from the fingers contribute little to the overall steady-state current. DApPvalues can be estimated for the very thick f i i using the im relation proposed by Aoki et al. when d/(w d) < 0.85 where x is finger width
(In,
+
DAPP
=
nFNCL(0.637 In [2.55(1
him,
~m
of I,, vs h , for 0.05 M Cp,Fe/0.05 M Cp,Fe+ (0), 0.2 M Cp2Fe/0.2M Cp,Fe+ (n), and 0.2 M Cp,'Fe/O.2 M Cp,*Fe+ (A)in Me2PEG1000/LiCi0,. Flgure 3. Plots
quantity of polymer to form a uniform film of such a small thickness was difficult to achieve, however, and typically films of a larger average thickness (0.8 pm) were used (Figure 2A). The desired situation is that in which, at im,all redox solutes in the strips of film resting on electrode finger tops are either reduced or oxidized according to whether the finger is biased with a negative or positive potential. As long as the film thickness is much less than the interfinger gap (15 pm), these strips of polymer film effectively act as vertical extensions of the IDA electrode finger, so that the walls of the parallel plate cell are htil, high; i.e., hfw in eq 1becomes h* This leads to the prediction that iLIMshould be proportional to heh, which is explored in Figure 3 for three different seta of donor/acceptor films. im appears to be satisfactorily linear with hnh for small film thicknesses, 2 pm and below. The average DApp values for 0.1 and 0.4 M [Cp,Fe]+/O and for 0.4 M [Ch*Fe]+/Oobtained from Figure 3 and eq 1for filmswhere hfb = 0.8 and 1.7 pm are 6.2 (f2.0) X 10-lo, 1.6 (f0.9) X l P , and 8.6 (f2.3) X 10-lo cmz/s. We observe in Figure 3 that films thicker than ca. 2 pm exhibit currents less than the small film thickness propor-
+ w/d)] - 0.19(d/(w + d))2}
(2) For our IDA dimensions, the term in braces in eq 2 is 1.47, which for a very thick film corresponds to a limiting value of hfmg= 11pm in eq 1. This relation was applied to the iLIM result (e.g., Figure 1)for ca. 0.5-mm-thick films containing 0.05 M [Cp2Fe] and 0.05 M [Cp2Fe]+to give a DApp = 6.0 cm2/s that agrees with the value, 6.2 X (f1.9) X cm2/s, obtained above from thin films of this composition. This agreement reenforces the validity of the IDA method. Shape of Steady-State Voltammograms. Steady-state, point-by-point, room-temperature voltammograms of 1:l TMPD+/Oand DDQo/- mixed-valent solutions in 0.8-pm-thick M%PEG-1000/LiC1O4filmsare presented in Figure 4. These films had been prepared from drop-cast polymer melts in a glovebox followed by thermal equilibration at room temperature for 15 h. The steady-state currents were measured following application of each potential value for a 2-min period. They are compared to the ideal wave shapes (solid lines) predicted by the Nernst equation for this twin-electrode thin-layer18 cell-like situation. exp(nFV/2RT - 1) i = ' rLmexp(nFV/2RT 1) (3)
+
The calculated voltammograms are similar to the experimental ones for both donor/acceptor pairs. This very long lived and nearly ideal voltammetric behavior indicates that the mixed-valent Me2PEG/LiC104polymer solutions are stable (under rigorously dry and oxygen-free conditions), and that the voltammetric changes in Figure 1are indeed due to diffusivity as opposed to chemical decay changes.
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ANALYTICAL CHEMISTRY, VOL. 63,NO. 24, DECEMBER
15, 1991
Table I. DAppof Redox Couples in Me#EG/LiClO,
redox couple (lit. kex,~omo, M-I s-l; solvent) [CpzFeIC/O( 5 X IO6;CH,CN)'
[Cp,Fe]+/O(5 X IO6;CH3CN)a
[Cp*zFe]t/o(4 X IO'; CH3CN)"
TMPD+/O(1 X log;CH,CN)b
TMPD+/O(1 X lo9; CH3CN)b
TCNQo/-(5 X IOB;CH,CN)'
TCNQo/-(5 X lo9; CH,CN)'
DDQo/-
MezPEG MW 400
lo00
lo00
400
lo00
400
IOOO'
lo00
cox + CRED, M
0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.4 0.05 0.1 0.15 0.2 0.3 0.4 0.1 0.2 0.3 0.4 0.05 0.1 0.2 0.3 0.4 0.01 0.02 0.03 0.05 0.01 0.02 0.03 0.05 0.1 0.2 0.3 0.05 0.1 0.3
DAPP,cmz/s 2.6 (h1.7) X 2.4 (f2.3) X 1.7 (h1.3) X 1.5 (hl.0) X 6.2 (h2.0) X 6.5 (h2.0) X 1.3 (h0.3) X 1.6 ifo.gj x 1.1 (h0.2) x 1.3 (ho.3) x 2.1 (ho.6) x 1.6 (h0.3) X 1.5 (f0.3) X 8.6 (h2.3) X 2.6 (hO.9) X 2.2 (f2.0) x 2.3 (f1.7) X 2.4 (hl.1) X 4.3 (h0.3) X 3.9 (f2.7) X 2.6 (f1.4) X 1.3 (f0.5) X 2.0 (f1.5) X 2.3 (f2.4) X 3.2 (h2.3) X 3.1 (i0.1) x 4.4 (f2.5) x 1.8 (h0.6) X 4.9 (h0.7)X 6.8 (h2.8) X 8.5 (h4.3) X 3.1 (h1.4) X 4.8 (f1.9) X 3.5 (f2.4) x 6.9 (12.3) X 4.8 (h2.8) X 1.0 (h0.1)x
no. of expta
10" 10"
calc kex! M-'
5 5 5 4 10 10 6 16 9 6 8 4 6 5 4 6 7 6 2 9 6 8 8
lo4 10-9 lo-ge
10-9 10-9 lo4
10-8
IO4 lo4 lo4 IO4 IO4
2 x 106 2 x 108 2 x 106 2 x 106 7 x 106 2 x 108
5 5
lo-' 10-7 10-7
3 x 109 2 x 109 3 x 109
2 6 4 4 7 8 6 6 6 4 4 4
10" 10"
lo4 10-9
IO4 10-8
s-l
I x 109 1 x 109 I x 109
3 x 107 2 x 107
s in calculation of kex. 'These data were Reference 25. Reference 26. dApproximate values; see text. e D p ~ y assumed a Reference 24. obtained for samples that had been cooled to room temperature for 15-20 h, which according to Figure 7 might not have sufficed for complete crystallization.
Concentration Dependence of DMP.By use of the above procedure, and 0.8-pm films, DAppwas measured for several concentrations of each of the donor/acceptor pairs. For TMPD+/O and TCNQOI-, DApp was measured in both the amorphous, viscous liquid Me2PEG-400 and the soft wax Me2PEG-1000. These data are listed in Table I and are plotted in Figure 5. In each determination, the f i i thickness was estimated from the quantity of polymer applied, assuming uniform spreading. The observed scatter in D U p values probably originate (at least in part) from imperfectly uniform films;other contributing factors could be variations in thermal history (vide infra) and in heterogeneity of the distribution of Me2PEG-1000 microcrystallites between the electrode fingers. The DAppresults in Figure 5 display a number of features. First, values of DApp in the amorphous Me2PEG-400 (filled symbols) are 1 order of magnitude larger than those in the partly crystalline Me2PEG-1000 (open symbols). A difference of this magnitude is consistent with other studies (7)and is mainly due to the difference in polymer-phase state, and to a lesser extent to that in polymer molecular weight. Second, considering the DApp values a t the lowest concentrations in Me2PEG-1000,there is a substantial dispersion between the different species, a factor of 20X between the most rapidly transported TCNQOl- and the most slowly transported DDQo/-. Third, the values of DAppof Cp2Fe+fo,TMPD+fo,and TCNQo/fall in the same order as the values of literature k,, cited in the table (that of DDQo/- has not been reported). Fourth, in
-
-
-"-2
-1.5
-1
-0.5 -1.5 lOg(C, M)
-1
-0.5
Flgure 5. Plots of log Dcpp vs log CroTAL for [Cp Fe]"" (circles), [Cp2*Fe]+/0(hexagons),Th+lPD+/O(triangles),TCNQd- (squares),and DDQo'- (diamonds) in Me2PEG-1000/LiCI0, (open symbols) or In Me2PEG-400/LiCI0, (filled symbols).
both polymers, instances of DAppvalues both rising and falling with increasing donor/acceptor concentration can be seen. Let us first focus attention on the reasons for this last feature. There are precedents and rationales for transport rates of solutes in polyether solvents rising, and falling, a t increased
ANALYTICAL CHEMISTRY, VOL. 63, NO. 24, DECEMBER 15, 1991
solute concentration (5b,c). As for cases of decrease in DApp with increasing solute concentration, we have recently described (5b) the voltammetrically determined diffusivity of several ferrocene derivatives in a cross-linked (amorphous) polyether, network PEO. We observed that DAppvaried little at concentrations of
