Effects of Mixed-Valent Composition and Bathing ... - ACS Publications

1992, 96,962-970. Effects of Mixed-Valent Composition and Bathing Environment on Solid-State Electron. Self-Exchanges in Osmium Bipyrldlne Redox Polym...
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J. Phys. Chem. 1992, 96,962-970

962

Effects of Mixed-Valent Composition and Bathing Environment on Solid-State Electron Self-Exchanges in Osmium Bipyrldlne Redox Polymer Films Nigel A. Surridge, Mary EUen Zvanuf,+F. Richard Keene,* Connie S . Sosnoff, Marvin Silver,+ and Royce W. Murray* Departments of Chemistry and Physics, University of North Carolina, Chapel Hill, North Carolina 27599-3290 (Received: February 15, 1991: In Final Form: September 12, 1991)

Rate constants for the electrical gradient driven, bimolecular electron-self-exchange reaction between 0 s " and Os111sites in dry, mixed-valent films of the undiluted, polymeric metal complexes poly[O~(bpy)~(vpy)~](BF,), and poIy[Os(~bpy)~](BF~),,, in interdigitated array electrodes and in sandwich electrodes are measured as a function of m. Linear potential sweep and ac impedance measurements show that the reaction follows the expected, but in solid-state materials, seldom evaluated, bimolecular rate law from Ca(III)/Ca(II)= 6 to 0.1. Comparison of rate constants for poly[O~(bpy)~(vpy)~](BF,),), and poly [Os(vbpy),] (BF,), self-exchanges driven by electrical and concentration gradients, measured in a variety of bathing environments,shows that electron hopping rates decrease in the order liquid solvent > solvent vapor > dry N2bathing environment, and in each environment, the rate constant for the former complex is larger. It appears that the electron hopping rate is affected by the rigidity of the polymeric matrix; matrices that are more rigid by virtue of the absence of solvent or through enhanced cross-linking (as in the vbpy complex) exhibit slower rates. The results imply that electron hopping involves (short range) nuclear displacement of the pendant osmium site from its equilibrium location in solvent-wetted polymers and is slowed when polymer rigidity inhibits such displacement.

Electron hopping between diffusively immobile donor and acceptor molecular sites embedded within (attached to) polymer films has been an active research topic in recent years. Polymer films in which the counterions of a mixture of donor and acceptor sites are mobile, making the polymers mixed (both electron and ion) conductors, can be investigated using electrochemical approaches.' We have been interested in comparisons of electron hopping rates in solvent-wetted vs dry mixed-valent polymers and rates in polymer films vs solutions of analogous monomers.2 The effects of site concentration? counterion m~bility,'*~*~ and reaction free energy for cross-reactions at polymer-polymer interfaces5have also been studied. In films of electroreductively polymerized poly[Os(bpy),( v p ~ )(X), ~ ] (vpy = 4-vinylpyridine, bpy = 2,2'-bipyridine), sandwiched between two electrodes, the polymer-phase electron hopping transport can be written as the bimolecular self-exchange reaction poiy-os2+

+ poiy-oS3+

-

poiy-oS3+ + poiy-oS2+

(1)

which repeated through successive layers of metal complex sites transports the electron between the electrodes. When the polymer is a mixed conductor (i.e., counterions diffuse in the film) but the electrodes are counterion-blocking, limiting concentration gradients develop by electrolysisunder an applied voltage bias. The resulting limiting current measures the electron hopping rate as the phenomenological electron diffusion coefficient, De, and as the electron-self-exchange rate constant, k,,, through the CT

ilim= wonFADe-

d

CT2 = 103wonFAk,,,c626d

(2)

where kwc (M-] s-l) denotes a concentration gradient derived rate constant and CT is the total site concentration (mol/cm3), d the film thickness ( d = r T / c T where rT, mol/cm2, is the electrochemically determined coverage), 6 (cm) the average intersite separation, and wo a small (1.07) numerical factor accounting for electrostatic coupling between electron and counterion motions.6d Alternatively, freezing outZathe counterion (X-) transport in mixed-valent films of poly[O~(bpy)~(vpy)~] (X)2,5by using either fast experimental time scales or low temperatures leads to electron transport (reaction 1 ) that is driven by sustained, 104-106 V/cm Department of Physics. *On Approved Special Studies Program from James Cook University, Department of Chemistry and Biochemistry, Townsville, QLD 481 1 Australia.

electrical (rather than concentration) gradients within the bulk polymer film. Deriving the reaction free energy for reaction 1 from the potential difference (4) between adjacent sites imposed by the applied voltage AE is formally related to electron drift mobility in other materials' derived by transient measurements, in that the electron conductivity increases a t higher applied voltages. Current-voltage curves for 200-500-nm-thick poly[O~(bpy)~(vpy)~](BF~)~,~ conformzBto the following relation, based on Marcus* theory i = io(exp[-nFp4/2RT] - exp[nFp4/2RT]j

(3)

whereg the average intersite voltage, 4, is AE divided by the (1) (a) Surridge, N. A.; Jernigan, J. C.; Dalton, E. F.; Buck, R. P.; Watanabe, M.; Wooster, T. T.; Zhang, H.; Pinkerton, M. L.; Facci, J. s.; Murray, R. W. Faraday Discuss. Chem. Soc. 1990,88, 1. (b) Dalton, E. F.; Surridge, N. A.; Jernigan, J. C.; Wilbourn, K. 0.;Murray, R. W. Chem. Phys. 1990, 141, 143 and references therein. (c) Murray, R.W. Annu. Rev. Mater. Sci. 1984, 14, 145. (2) (a) Jernigan, J. C.; Sumdge, N. A.; Zvanut, M. E.; Silver, M.; Murray, R. W. J . Phys. Chem. 1989, 93, 4620. (b) Jernigan, J. C.; Murray, R.W. J . Phys. Chem. 1987, 91, 2030. (c) Jernigan, J. C.; Murray, R. W. J . Am. Chem. Soc. 1987,109, 1738. (d) Jemigan, J. C.; Chidsey, C. E. D.; Murray, R. W. J. Am. Chem. Soc. 1985,107,2824. ( e ) White, B. A.; Murray, R.W. J . Am. Chem. Soc. 1987,109,2576. (3) (a) Facci, J. S.;Schmehl, R. H.; Murray, R. W. J. Am. Chem. SOC. 1982, 104, 4959. (b) Facci, J. S.Ph.D. Dissertation, University of North Carolina, Chapel Hill, NC, 1982. (c) Fritscfi-Fades, I.; Faulkner, L. R. J . Electroanal. Chem. 1989, 263,237. (d) Chidsey, C. E. D.; Murray, R. W. J. Phys. Chem. 1986,90, 1479. (e) Hurrell, H. C.; Abruna, H. D. Mol. Cryst. Liq. cryst. 1988, 160, 377. (f) Ofer, D.; Wrighton, M. S . J . Am. Chem. Soc. 1988, 110, 4467. (g) Kelly, J. M.; Long, C.; OConnell, C. M.; Vos, J. G. Inorg. Chem. 1983, 22, 2818. (4) Bruns, M. W.; Fritsch-Faules, I.; Faulkner, L. R. J. Electrochem. Soc., Ext. Abs. 1989, 89, 722. (5) Leidner, C. R.; Murray, R. W. J . Am. Chem. Soc. 1984, 106, 1606. (6) (a) Laviron, E. J . Electroanal. Chem. 1980, ZZ2, 1. (b) Andrieux, C. P.; Saveant, J. M. J. Electroanal. Chem. 1980, 111, 377. (c) Buck, R.P. J. Phys. Chem. 1988,92,4196. (d) Saveant, J. M. J . Electroanal. Chem. 1988, 242, 1. (7) (a) Pai, D. M.; Yanus, J. F.; Stolka, M.; Renfer, D. S.;Limburg, W. W. Philos. Mag. B 1983,48, 505. (b) Stolka, M.; Yanus, J. F.; Pai, D. M. J . Phys. Chem. 1984,88,4707. (c) Pai, D. M. J. Appl. Phys. 1975,46,5122.

(d) Mort, J.; Pai, D. M. Photoconductivity and Related Phenomena;Elsevier: New York, 1976. ( 8 ) (a) Marcus, R.A. Annu. Reu. Phys. Chem. 1964.15, 155. (b) Marcus, R. A. J . Chem. Phys. 1965, 43, 679. (c) Sutin, N. Acc. Chem. Res. 1982, 15, 275. (9) (a) The number of monolayers is calculated from rr/I'- where ris taken as 1.0 mol/cm*. q5 is taken as negative at the electrode at which a

(positive) reduction current flows; is., electron hops in the direction of increasingly positive charge are favored.lb This convention was not made clear in the earlier paper.*

0022-365419212096-962%03.00/0 0 1992 American Chemical Society

Electron Self-Exchange between Os” and OS”’

The Journal of Physical Chemistry, Vol. 96, No. 2, 1992 963

number of monolayers of osmium complex sites between the two electrodes, and the current represents the difference between forward and reverse electron hopping rates. p is a fitting parameter whose value is ideally one but in real samples exceeds one (vide infra). io, the intersite exchange current density (A/cm2) when AGmn= AE = 4 = 0, is related to the bimolecular reaction rate constant and the concentrations of donor and acceptor sites by io = (1O3/

~

~

~

~

~

~

~

~

1 (4)1

denotes an electrical gradient derived rate constant. where The electron conductivity u at small 4 can be linearized u = d ( i / A E ) (ohm-I cm-I);

.(io) = pionF6/RT

(5)

but at large 4 is nonlinear given the form of eq 3. Consideration of the reverse electron hopping rate is necessary because, although the electrical gradient may be large, it amounts to a modest intersite driving force; i.e., for a lo5 V/cm gradient and intersite spacing (6) of 1.2 nm, 4 is only 26 mV (210 cm-’, 0.6 kcal/mol, or ca. kTZg8). This paper describes further studies of mixed-valent poly [Os(bpy)2(vpy)2](BF4), films (bpy = 2,2’-bipyridine; vpy = 4vinylpyridine) and of a related polymer poly[Os(vbpy)3] (BFI), (vbpy = 4-methyl-4’-vinylbipyridine)that address the following points. A. Equations 3-5 show that, at a fmed total concentration (CT) of redox sites, Q depends on the electron acceptor and donor concentration product (i.e., C~~(III)C~~(II) or C~S(II)[CT - Cos(11)1), but k,, should not. All previous electrochemical concentration gradient based measurements of D, and k,, in redox polymers rely6J0on this bimolecular model and assume that the electronself-exchange rate constant k,, is invariant with the product cd,,,ca,. In our previousZastudy, only 1:1 Os(III):Os(II) mixed-valent films were employed (Le., Cos(III) = Cos(lI):? = 2.5). There are, in fact, few data that address the validity of the bimolecular rate law ass~mption’~”-~~” in redox polymer materials, and in all of the available data, the observed k,, is relatively constant near C,, = Cd,, but decreases as either C,, or Cd,, becomes greatly in excess. To further investigate this problem, we have carried out electrical gradient based electron transport measurements on the undiluted polymers poly [Os(bpy),(vpy),](BF4), and poly[O~(vbpy)~](BF,),in films where m is varied between 2 and 2.5 in the former and between 2 and 3 in the latter. The total osmium site concentration is constant at CT = 1.3 M. The rate law expressed in eqs 2-4 proves to be satisfactory when m is near 2.5, Le., at mixed-valent compositions near 1:1, but as in the previous studies deviations occur at more extreme ratios. The deviations may represent experimental uncertainties at very low or high mixed-valent ratios, rather than breakdown of the bimolecular model. B. Our previous measurements” were based on current-voltage curves derived from sweeps of AE sufficiently fast as to be sweep rate independent, indicative of avoiding counterion motion. Here, we support those experiments with an ac impedance study of poly[Os(bpy)2(vpy)z](BF4), films in which both frequency and temperature are varied. C. A fitting parameter p > 1 was necessary in the previous study2ato fit eq 3 to experimental current-voltage responses of poly[Os(bpy)2(vpy)2](BF4)2.5 films. The parameter may reflect overestimation of the interelectrode film distance and/or a dispersion in the electron-transfer barrier height.1a*”.7bThe problem is clarified here, in part, by defining the interelectrode dimension with an interdigitated electrode. Equations 2 and 4 contain a geometrical factor6cof 6 which was unfortunately omitted in the previous studies? The values of k,, (nit those of io or b) should properly bemultiplied by 6. When making comparisons of present and previous electron-transfer rate constants for the polymer poly[Os(bpy),(10) In electrochemical 0, measurements, where a concentration gradient profile exists, the total cdom + c,, = cTconcentration may be constant, but the relative values of Cd, and C., in any region of the film will vary widely. (11) Wilbourn, K.; Murray, R. W. J . Phys. Chem. 1988, 92, 3642.

( ~ p y ) , ] ( X ) ~ the , ~ . previousZadata have been corrected for the geometrical factor.

~

Experimental Section The ligand 4-methyl-4’-vinyl-2,2’-bipyridine(vbpy) was synthesized in two steps based on a modificationI2”of a literature method.lZb [O~(bpy)~(vpy),] [PF,], was prepared as described earlier. ~ ~ ~ 1 ~ ~ ~ e X , ~ Synthesis of~ [Os(vbpy),1PF6],. Vbpy (0.222 g; 1.133 mmol) was added to (NH4),0sC16 (0.164 g; 0.375 mmol) in 8 mL of ethylene glycol under N2 and the mixture heated under reflux for 3 h. The solution was cooled to room temperature, and an equal volume of water added, followed by NH4PF6 (0.1465 g; 0.899 m o l ) to precipitate the product, which was filtered, washed with water and ether, and air-dried. The product was chromatographically purified on an alumina column using 1:l CH3CN: toluene as eluent. The faster moving (major) band, the desired product, was collected and the solvent evaporated to give a dark green solid: yield 0.385 g; 96%. Anal. Calcd for OSC~~H~~N P, ~5.81. P ~ Found: F ~ ~ : P, 6.03. No C1 was found by elemental analysis. ‘HNMR. This complex can exist as two isomers: a “facial” or cis form with C3symmetry and a “meridional”or trans form with CI symmetry. The splitting observed in both the methyl and vinyl resonances is consistent with the statistically preferred meridional isomer, with no evidence for the facial isomer. A slower moving second band collected from the column exhibits aliphatic NMR resonances suggestive of a polymerized complex. Electroehemistry. Film deposition and three and four-electrode voltammetry were performed with a Pine Instruments RD4 bipotentiostat. Acetonitrile (CH3CN) and CH2Clz(Burdick & Jackson) solvents were used as received and stored over 4-A molecular sieves. The electrolyte was 0.1 M tetrabutylammonium tetrafluoroborate (Bu4NBF4, Fluka), unless otherwise noted. Potentials were measured vs saturated sodium chloride calomel (SSCE), 0.01 M Ag+/Ag, or Ag-wire quasi-reference electrodes and are reported vs SSCE. Deposition of P~ly[Os(bpy)~(vpy),](BF~)~ and Poly[Os(~bpy)~](BF~), F b . These were electrochemically polymerized from 0.2 to 0.8 mM monomer solutions in 0.1 M Bu4NBF4/ CH3CN onto polished tips of Pt wires sealed in glass or onto Pt interdigitated array electrodes (vide infra), in an inert-atmosphere enclosure (dry N2), by cyclically scanning the electrode potential between -1 .O and -1.75 V vs SSCE at 150 or 200 mV/s. The electroactive film coverage, rT,was determined by integrating the charge under the Os(III/II) voltammetric wave (20-50 mV/s) observed in monomer-free, 0.1 M Bu4NBF4/CH3CN. This voltammetry is like that in our previous publication.ls2 Sandwich Eaectmdes. Films deposited on (0.002 or 0.0013 cm2) Pt wire tip electrodes were used to prepare Pt/polymer/Au “sandwich” electrodes, as previously14described, by evaporation of a porous, ca. 300 A Au film overcoat onto the polymer. Electrical contact to the Au film was made by allowing the evaporated Au film to overlap the surrounding glass insulator, and a nearby, bare Pt wire also sealed in the glass. IDA Electrodes. Interdigitated arrays” consisted of 100 interdigitated, 3-pm-wide Pt figers (50 per electrode side) separated by either 5- or 2-pm gaps, on SiOZ/Sisubstrate. The Pt finger height was 1700 A as measured by a Tencor Alpha Step 100 surface profilometer. Pt tracks overcoated with an insulator lead to contact pads at the top end of the wafer slice, where contact was made with copper wire and Ag paint and insulated with a coat of quick-drying epoxy. Electropolymerizationonto IDA electrodes was conducted with the two sets of fingers of the array (12) (a) Reed, R. Unpublished results, University of North Carolina. (b) Abruna, H. D.; Breikers, A. I.; Collum, D. B. Inorg. Chem. 1985, 24, 987. (13) (a) Kober, E. M.; Caspar, J. V.; Sullivan, B. P.; Meyer, T. J. Inorg. Chem. 1988, 27, 4587. (14) Pickup, P. G.; Kutner, W.; Leidner, C. R.; Murray, R. W. J . Am. Chem. soc. 1984, 106, 1991. (15) Aoki, K.; Moritz, M.; Niwa, 0.;Tabei, H. J . Electrounul. Chem. 1988, 256, 269.

The Journal of Physical Chemistry, Vol. 96, No. 2, 1992

Surridge et al.

shorted together as the working electrode and potential scanned in the same way as the Pt wire tip electrodes, in a solution of 0.4 mM [Os(vbpy ),I 2+. Preparation of Dry,Mixed-Valent Polymer Films. The metal complex polymer films, Os" as-prepared, must be converted to an mixed-valent form for two-electrode electron transport rate measurements as dry, N2-bathed films. The previously described2"J4procedure was modified as follows: Immersing the Pt/polymer/Au sandwich or polymer-coated IDA in 0.1 M Bu4NBF4/CH2C12with the two electrode terminals shorted together, a potential is applied vs reference electrode to electrolyze the polymer to the desired mixed-valent composition. The sandwich or IDA electrode assembly is raised from the solution, rinsed with pure CH2CI2,and placed in a dry N2 atmosphere for 15 min to evaporate the residual solvent, after which the potentiostat is disconnected. The specimen was (typically) immediately used in electron transport studies. Sandwich electrodes containing 0s"' states, when in CH3CN, tend to corrode the Au contact, presumably via 0s"'-mediated oxidation of Au in the strongly coordinating solvent. Reliable generation of mixed-valent filmsZ has thus relied on a brief electrolysis period with continuous potential control until the film has been rinsed and dried, after which the Au corrosion ceases. We have found that using the less strongly coordinating CH2C12 in the electrolysis alleviates the Au corrosion problem considerably. The change to CHZCl2was crucial in the present study, permitting individual sandwich electrode specimens to be repeatedly reelectrolyzed to different mixed-valent compositions. Electron Transport (Conductivity) Measurements. Electron transport measurements can be made's2 with the sandwich (or IDA) electrode immersed either in an electrolyte solution or in a dry N2 atmosphere. In electrolyte solutions, four electrodes are employed: a reference and auxiliary electrode and the two sandwich or IDA electrodes whose potentials are each controlled vs Eref.Some of the initially all-Os" film undergoes electrolysis to 0s"' states when appropriately negative, and positive potentials are applied to the two contacting electrodes (vs Emf),at the positive (Pt) electrode to 0s"' but maintaining Os" at the negative (Au) electrode. Films used in dry Nz atmosphere owing to ion budget restrictionszdmust be first rendered mixed valent (vide supra). In both environments, after a short period, electrolysis develops linear concentration gradients of Os" and 0s"' sites across the film, and the initially large currents decrease to steady values given by eq 2, from which De and keXvc are obtained.2 In two-electrode, electrical gradient based electron transport measurements on N2-dry, mixed-valent films (vide supra), fast time scales and/or lowered temperatures are employed (based on previous work2") to render interfacial electrolysis and diffusion of the film's counterions unimportant on the experimental time scale. These measurements are carried out in two ways: (a) linear cyclical voltage sweeps are made at sufficiently large rates that the current-voltage pattern and amplitude are sweep rate independent, or (b) an ac voltage is applied at a series of frequencies, measuring the resulting ac current amplitude and phase angle. We refer to these two procedures, the results from which will be compared, as the fast linear sweep and the ac impedance methods, respectively, and label rate constants thus derived as kex,E,LS and kex,E,AC, respectively. In the fast linear sweep method, f 3 to 4 V triangular wave AE are applied to sandwich electrodes using a PAR 174 universal programmer or a Wavetek function generator, at sweep rates up to 1000 V/s. Current measured as a voltage across a 30-2500ohm series resistor is recorded with a Nicolet 2090 digital storage oscilloscope. In experiments using smaller amplitude triangular waves (f0.6 V) and sweep rates ( solvent vapor > dry N2. The variations with bathing environment span about a factor of 10, and their order and rough magnitude are similar to2a that observed with Pt/poly[Os(bpy)2(vpy)21 (BF4)2,$/Au sandwiches* Trairpport in ~ / ~ o l y [ o s ~ v b p Y ~ 3 1 ~ -cb ~~4~2.5/~~ Electrodes, Using Electrical Gradients, by Fast Linear Sweep Method. Upon imposingfast potential sweeps on dry, N2-bathed Pt/ply[Os(vbpy)3](BF4)2,/Au sandwiches, the currents are much larger, are independent of potential sweep rate, and rise exponentially with voltage (out to irreversible film breakdown). Analogous responses are obtained by lowering the temperature; counterion diffusivity is more readily thermally quenched than is electron hopping.2a-bFigure 1A displays the 266 K currentvoltage curve for a 1:1 mixed-valent Pt/poly[Os(vbpy),](BF4)2*5/Au sandwich that was cooled to 187 K and subjected

-

(16) F't/poly[Os(~bpy),](BF~)~ 5/Au sandwiches approach steady state much more slowly than do previously studied" pt/qoly[Os~bpy)~(vpy)~](BF,)z,,/Au sandwiches. This and other current experiments' indicate that counterion transport is slower in the former polymer. (17) Surridge, N. A,; Murray, R. W. Unpublished results, 1990.

The Journal of Physical Chemistry, Vol. 96, No. 2, I992 965

Electron Self-Exchange between Os" and 0 s " '

TABLE I: Collected Electron Transport Data for R/poly[Os(vbpy)d(BFI),dAu Suidwicbcs in CH2C12/Bu4NBF4 in CH2CI2vapor batch no. 1 2 3 4 5 6 7

no. of samples 4 1 3 2 3 4 5

108rT/ mol/cm2 0.85 2.2 1.2 2.5 1.4 2.1 1.7

lo9&, cm2/s 3.4 8.2

M-l s-l 1.1 i 1.0 2.6

3.7 4.3 8.2b 10.6b

1.2 1.4 2.6b 3.4b

109De, cm2/s 2.1

10-5kex,c,

M-'

s-I

6.6 i 1.0

109De, cm2/s 0.93 9.8

"The polymer film thickness (d)is given by rT/CT where CT is total site concentration, 1.3

CH3CN/Bu4NBF4. 3.36

AE (V) 0

1.68

-1.68

-3.36

0.002 r

I

in dry N2 10-5kex,c, M-l s-l 3.0 i 0.8 31

X

104i0, A

P

3.3 10.4 12.7

3.0 6.3 3.1

10-5kexe~, M-I ;-'I 1.3 & 0.3 6.6 3.7

mol/cm3. For batch 1 , d = 65 nm.

20/

*O

h

7

15-

6

c

I

8

tI

-O'Ool -0.002 I 0.02

00.00

I

I

0.01

-0.01

0

Q

1

IR

1

3

-0.02

(V/monolayer)

-2

-3

10-

5

4

6

1000/T (K-')

Figure 1. (A) Current-voltage curve (0) for a Pt/poly[Os(vbpy)J(BFJlj/Au film in dry N2 at 266 K. rT= 2.2 X mol/cm2. (-) is calculated from eq 3 for io = 1.9 X l P A and p = 6.5. (B) Arrhenius plot of similarly obtained io values for the film in panel A; linear, least-squaresfit gives EA = 9.1 kcal/mol, u, = 29.3 C1cm-I (eq 5 ) , and ,k = 6 X lo9 M-I s-I (eq 4).

0.25

0.50

0.75 0

1.00

1.25

1.50 0

Eapp (V vs Ag)

Figure 2. Anodic branch (-) of room temperature cyclic voltammogram film (20 mV/s, background subtracted) of Pt/poly[Os(vbpy),](BF4),/Pt onto 2-pm gap IDA electropolymerized from 0.1 M Bu4NBF4/CH2C12 electrode. (The cathodic branch is a mirror image.) Total electroactive mol. Simulation (---) of the voltpolymer on the IDA is 1.3 X ammetric wave; see text. ( 0 )are conductivities derived from io (Table 11) measured with fast potential sweeps (e.g., Figure 3) after electrolyzing the film at different E,, to set the mixed valency (m)and drying in N2.

in the actual film thickness is at least part of the answer. Results for the temperature dependence of the exchange current parameter io are given in Figure 1B. The Arrhenius plot is linear over the range examined and gives an activation barrier of ca. 9.1 kcal/mol (0.39 eV) for the electron hopping reaction. This barrier is similar to that obtained by ac impedance measurements described below. The fitting parameter p required in the current-voltage analysis with eq 3, 5.8-6.8 (average 6.3), is independent of temperature. Electron T ~ p o r itn Solvent-Wetted Pt/P~ly[Os(vbpy)~](BF4)2/Pt Films IDA'S, Using C~nceotratiOnGrrdienQ. A film of poly[O~(vbpy)~](BF~)~ was deposited on a Pt IDA electrode (2-pm gaps) from a 0.4 mM monomer solution by potential cycling for 15 min. Loosely attached material was removed by brief sonication'* in CH3CN, leaving a relatively smooth film but ca. 10-20% of the finger area uncovered. Figure 2 (-) shows the anodic branch of the Oslll/lr cyclic voltammetry in 0.1 M Bu4NBF4/CH3CNwhich gave a charge, Q,of 1.88 X C. Application of 0 V vs SSCE to one set of Pt fingers and + 1.37 V to the other to produce the limiting current ilimfor Oslll/rl transport gave De = 1.9 X cm2/s using the relationI9

to f3-V potential sweeps as the film slowly warmed. Figure 1A also shows the satisfactory fit of eq 3 to the experimental curve; similarly good fits were obtained at lower temperatures. The current-voltage response in Figure 1A resembles that found for Pt/p~ly[Os(bpy)~(vpu)~](BF~)~.~/Au sandwichesaband reflects electrical gradient driven electron hopping as opposed to selfexchange promoted by concentration gradients between the Os complex sites. Analysis by eq 3 produces two parameters: the exchange current io (and through eq 4 the self-exchange rate De = ( $ m G P / Q ) ( N / [ N - 11) (6) constant kcx,E,LS) and the fitting parameter p, which are shown where G is the interelectrode gap, p the (finger width interefor room-temperature experiments in Table I (batches 1-3). lectrode gap), and N the number of fingers. By eq 2, this corresults with those obtained in conComparison of the kcx,E,LS responds to kqc = 6 X 106 M-' s-', which is close to the sandwich centration gradient experiments (kcx,c)for the same R/polyresult in Table I (batches 6 and 7). The ca. 0.005 cm2plan area [Os(~bpy),](BF~)~~/Au electrodes (Table I, rhs, batchs 1 and 2) of the IDA, the above charge, and 1.04 nm/monolayer indicate shows that the latter is larger by ca. 2-4 times. Such a difference was found for Pt/p~ly[Os(bpy)~(vpy)~] (BF&/Au sandwiches.& Ideally, the rate of electron hopping should not depend on whether (18) Both the cyclic voltammetric charge and ib, were larger on the film prior to sonication, but by similar amounts (32% vs 22%), sa that the value the reaction free energy is supplied by electrical or by concentration of 0, was little different, 1.9 X lo-* cm*/s. gradients. Possible reasons for the difference between kcx,bLsand (19) (a) Chidscy, C. E. D.; Feldman, B. J.; Lundgren, C.; Murray, R. W. kqc were conjectured" for WP~Y [ ~ ~ ( ~ P Y ) Z ( ~ ~ Y ) ~ I ( B F ~Anal. ) ~ .Chem. ~ / A 1986,58,601. U (b) Feldman, B. J.; Murray, R. W. Awl. Chem. sandwiches, and of them, as shown here (vide infra), uncertainty 1986, 58, 2844.

+

~

~

~~

966

The Journal of Physical Chemistry, Vol. 96, No. 2, 1992

Surridge et al.

TABLE II: Conductivity Measurements on Pt/poIy[Os(~bpy)~](BF,),/Pt IDA Electrode io b

Enpp - EO," V

-3.30 X -8.20 X -7.80 X -6.00 x 6.00 X 8.40 X 1.06 X 2.94 X 3.89 X

lo-' loT2 10-3

10-I 10-1 lo-'

Cos(IlI)/Cos(II)

5.34 x 1.56 X 1.71 X 8.73 X 1.10 4.00 5.75 1.28 X 6.12 X

104 lo-' 10-1 10-1

lo2 lo2

A/cm2

Pb

5.7 x 10-9 4.0 X 4.0 X 8.3 X 9.7 x 10-2 6.9 X 9.1 X 4.7 x 10-2 2.9 X

3.4 3.4 3.8 3.4 3.4 3.5 3.4 3.6 3.8

o(io),E W cm-l

9.2 x 6.6 X 7.2 x 1.3 X 1.6 X 1.2 x 1.5 x 8.1 x 5.3 x

kcx.E L3:.

M-I' s-l

(3.3)

10-14

1 . 1 x 105

0.96 x- 105 1.0 x 105 1.2 x 105 1.3 x 105 2.2 x 105 (1.9 X lo6) (5.5 x 106) av 1.3 (k0.3) X lo5

10-7 10" 10" 10" 10" 10-7 10-7

"Measured from Eo' for the Os"/"' couple. bFitted parameters from eq 3, finger edge area = 3.5 X lo4 cm2. e Calculated from eqs 4 and 5, using io obtained by fit of eq 3 to curves like Figure 3. an average film thickness of ca. 2000 A, larger than the ca. 1700 AE ( V I Assuming that the gaps have been adequately 0 - 1 9.23 -38.46 38.46 19.23 filled with polymer, this film was employed to study the effect of mixed-valent composition in dry films, as described next. Electron Transport in Dry P~/PO~Y[~S(V~P~)~](BF~),,,/P~ Films on IDA'S, as a Function of m, Using Electrical Gradients,by Fast Linear Sweep Method. As noted above, our previous2a,bstudies were exclusively of 1:1 mixed-valent O S ~ ~ ' :films; O S ~according ~ to eq 4, this is the most conductive state. One objective of the present study (section A, Introduction) is to examine films containing an excess of 0s"' or Os", at canstant Cos(II) + where according to eq 4 conductivity u but no kex,Eshould vary with the excess. Another objective (section C, Introduction) is to use an IDA with a well-defined interelectrode distance to examine the 1 I effect of interelectrode separation. -10' 0.02 0.01 0 -0.01 -0.02 The above polymer-coated IDA was electrolyzed in 0.1 M Bu4NBF4/CH2C12with the Pt finger sets shorted together, at $ (V/monoIayer) selected potentials on the wave to prepare various mixFigure 3. Example of current-voltage curve (0,shown for fast forward ed-valent compositions. After each electrolysis, the film was k36 V) analyzed with eq 3 to produce and reverse linear sweeps at withdrawn from solution, rinsed, allowed to dry in a N2 atmoconductivity data for F't/poly[Os(~bpy)~](BF~),,,/Ptfilm in Figure 2 and sphere, and subjected to a fast cyclical potential sweep, producing = 1 for the film shown. (-) is the Table 11; in N2,CoscIl)/Cos(rIl) current-voltage curves like that shown for a 1:1 mixed-valent film theoretical curve from eq 3 for io = 2.9 X loe5 A and p = 3.4. in Figure 3. Figure 3 also shows a nonlinear least-squares fit according to eq 3, which yields p = 3.4 and io = 8.3 X 1W2 A/cm2. face-confined species21 (Figure 2, - - -), is good over the central Taking the Pt finger height as the cross-sectional area of the film ca. f80 mV region and deviates somewhat further out on the wings through which electron transport occurs gives kex,E,LS = 1.0 X IO5 of the wave. Fits to the cathodic branch of the voltammogram M-l s-I using eq 4. (not shown) were similar. Values of C ~ ~ ( I I I ) / Cfrom ~ ( I such I ) fits Results from experiments like Figure 3 are summarized in Table are given in Table I1 as are values of kcx,E,LS calculated from eq I1 ( i o ,p, and conductivity u(io)from eq 5 ) and are presented in 4. Figure 2 ( 0 )as a function of the electrolysis potential used to The results in Table I1 show that kcx,E,LSis independent of prepare the mixed-valent state. The potential axis for the elecmixed-valent composition for electrolysis potentials ca. f85 mV trolysis and for the cyclic voltammetry curve (-) is the same, from Eo' or from C~(III)/C~(II) ca.6 to 0.1. This is an important and the film conductivity .(io) and the voltammetric current both result, showing the electron hopping rate law expressed in eq 4 pass through a maximum a t E O ' . This agrees with eq 4 in that to be adequately obeyed within this range. That is, these results conductivity should be maximal when CO~(III) = C+(II). confirm the presumption of eqs 1-3, that the electron conductivity Analysis of the Table I1 and Figure 2 data to derive values of of these materials is a solid-state, bimolecular reaction between keX,E,Lsfrom io requires converting the electrolysis potential to diffusively immobile sites. and Cos(II)compositions. This is a thorny step the actual Cos(III) Further examination of the kex,E,udata in Table I1 shows that because these films, like most redox polymers,lc*zo do not exactly kcx,E.LS is larger at CCa(III)/CCh(II) and at ~ 0 8 ( 1 ! I ) / ~ O a ( I I ) follow the Nemst equation, which predicts that the voltammetric < 0.1. Both these experimental regimes have difficulties. The wave should at 298 K be symmetrical with A E f w h m = 90.6 mV. conductivities in poly-Os%ich films are subject to several exThe wave in Figure 2 (-) is slightly broader on the positive side perimental problems, most notably the ex rimentally demonstrable (vide infra) reactivity of the poly-Os' sites in the films. and has AEfwhm= 185 mV. The electrolysis potential was converted to film composition with the modified20 Nernst relation Reversion of even small quantities of p01y-Os~~'sites to poly-Os" ), large apparent values sites would, at large Ca(III)/Ca(IIcause of a(io) and kcx,E,u as observed. The deviation a t low Ca(III)/ (7) probably reflects an inaccuracy in converting electrolysis potential to film composition with eq 7 at potentials far from E O ' . that approximates the wave broadening with a nonideality factor Two other significant observations can be made by com ring g, obtainable from an experimental voltammogram as U f w h m = the kcx,E,LSresults in Table I vs 11. Firstly, a t 1:l Osp" 3.53RT/gnF. The Figure 2 voltammogram produced g = 0.55 composition, kcx,E,u= 1.3 X lo5 M-I s-I (IDA, Table 11) is in and 0.42 for the sides of the wave negative and positive of E O ' , very good agreement with that for the smallest film thickness respectively. The fit of eq 7, written for current due to a sur-

A Pt finger height.

'

r

(20) (a) Ikeda, T.; Leidner, C. R.; Murray, R. W. J . Elecrroanal. Chem. 1982, 138, 343. (b) Albery, W. J.; Boutelle, M. G.; Colby, P. J.; Hillman, A. R. Ibid. 1982, 133, 135.

(21) (a) See eq 12.5.11 in: Bard, A. J.; Faulkner, L. R. Electrochemical Merhods; Wile : New York, 1980; p 522. (b) Ratio of activity coefficients of Os" and Osh is assumed to be unity.

The Journal of Physical Chemistry, Vol. 96, No. 2, 1992 967

Electron Self-Exchange between Os" and 0 s " '

TABLE III: Conductivity Measurements on Pt/poly[ (bpy)20s(vpy)2](BF2)m/Au slndwichea Eapp- EO,' V

-0,190 -0.157 -0,113 -0.060

-0.055 -0.038 -0.033 0.0000

0.014 0.0 16

io,b

A/cm2 4.6 X lo4

~ a c l l l ~ / ~ a ~ l l ~

1.22 x 10-3 3.92 x 10-3

1.85 X 1.18 x 10-1 1.43 X lo-'

2.57 X 10-1 3.20 X 10-1 1.oo 1.48 1.60

7.8 X lo4 3.3 x 10-3 6.0 X 2.5 X lo-* 1.8 X 10-1 1.9 X 10-1 4.6 X 10-1 3.4 x 10-1 4.1 X lo-'

kcx,E LS?

Pb

(4.8) (4.7) (7.2) 6.4

6.5 6.0 5.9 5.5 5.8

5.8 av 6.0 (10.3)

.(io),

k c x 3 AC, M-I's-l

M-1 's-l

W cm-1

(0.5 x 105) (0.3 x 105) (0.5 x 105) 1.8 x 105 0.5 x 105

(1.1 x 105) (0.6 x 105) (0.6 x 105) 2.0 x 105 0.7 x 105 3.3 x 105 3.1 x 105 5.7 x 105 4.3 x 105 5.3 x 105 3.5 (11.2) x 105

2.8 X 2.7 x 4.2 x 3.8 x 4.1 x

1.0 x 10-8

4.4 x 10-9

1.8 X lo-* 1.1 x 10-7 1.8 X lo4

8.9 8.9

7.7 x 10-7 5.0 X 10"

10' 105 105 105

105

2.8 (f1.2) x 105

5.2 X lod 1.2 x 10-5 9.3 x 104 1.1 x 10-5

X X

lo4

1.7 X 5.9 x 4.2 X 4.3 x 8.8 X

10"

10-7 10" lo"

10" 8.1 X 10" 8.6 X 10"

"Measured from Eo' for the Osll/ll' couple. bFitted parameters from eq 3. 'Calculated from a(ac) = d/R,J. -2.0 0 ' 11.2 samples (sandwich, Table I, batch 1, kcx,E,s = 1.2 X lo5 M-l s-' )* The film dimension over which the applied potential A,!? drops -1.5 is 2 pm in the IDA result and ca. 100 nm for the sandwich - 1 .o electrode result, a 20-fold difference. Changing sample thickness g-0.5 in conductivity measurements is a classical criterion for differv entiating interfacial from bulk resistances, and the present result .- 0.0 confirms that the bulk film resistance is the dominant effect. 0.5 Second, data in the tables, and other recent show that 1 .o agreement between kex,E,s and kex,cis best, and the fitting parameter p is closest to its ideal value of one, when using sandwich 1.5 electrodes that contain the thinnest polymer films ( p = 3-4), as 2.0 1 compared to sandwiches containing thicker polymer films, where 0.2 0.4 0.6 0.8 1 .o 1.2 p = 4-7. As discussed previously,2aif the amount of mixed-valent Eapp(V "3 As) polymer that is actually present between the electrodes of a Figure 4. Cyclic voltammogram (-, 50 mV/s) for Pt/poly[Os(bpy),sandwich is less than that estimated from the voltammetric rT, mol/", in 0.1 M (V~~)~(BF,),/AU sandwich, rT 2.2 X the underestimation of film thickness would appear as a multiplier Bu4NBF4/CH2C12, and conductivities of this and a similar film after of intersite voltage, i.e., as p4. Recent ellipsometric and scattering electrolyzing the film at E, vs Ag and drying in N2: (0)conductivity electron microscopic studies23of poly[O~(bpy)~(vpy)~] (X), films a(io) derived from io obtained €rom fast potential sweeps and fit to eq show that, while they are smooth and dense up to ca. 100 nm, 3; (0,A, A) conductivity a(ac) derived from ac impedance measuredeposition of further material tends to occur as a rough, fibrous ments. (0,0 , and A are from the same film, data given in Table 111.) layer, which in making the sandwich electrode is thus potentially penetrated by evaporated Au to yield a smaller effective Pt-Au interelectrode spacing,especially for the thicker films. In contrast, the IDA interelectrode spacing is predetermined by the microlithography, and the uncertainty there is a different one: whether the deposited film perfectly fills the interelectrode gap. Note that eqs 2 and 3, 4 have differing dependencies on the value of the interelectrode gap (4,and so that an error in it would cause measured ke,,c and kcx,Evalues to diverge. These combined observations lead us to surmise that the fitting parameter p, and the differences between kex,cand kex,E at least in part, is an artifact 8 arising from underestimation of the exact dimensions of the thicker 4 versions of the sandwich polymer filmsz4employed in these studies. 0.0 0.0 0.5 1.0 1.5 2.0 This observation does not, however, exclude contributions from other, additional, energy barrier dispersive factors as previously Z r e d (kn) discussed.2a Figure 5. Cole-Cole ac impedance plot (1-lo6 Hz) for Pt/poly[OsElectron Transport in Dry F't/P~ly[OS(bpy)~(vpy)~(BF~),,,/Au (bpy)2(vpy)2(BF4)2,21/A~ sandwich where rT= 2.3 X mol/cm2 and and Pt/Poly[Os(~bpy)~](BF~)~.~/Au Sandwich Electrodes, as a C~~II)/C,-,,(~,) = 0.26. The low (right-hand) frequency limit indicates an RB 2130 0,corresponding to kcx,EhC = 2.8 X lo5 M-' s-I (see entry Function of m and of Temperature, Using Electrical Gradients, 6, Table III), and a least-squares fit (not shown) gives c b = 90 pF, CY = by Fast Sweep and by Ac Impedance Methods. Previous2"electron 0.8, and Rb 2000 a. transport measurements in dry Pt/p~ly[Os(bpy)~(vpy)~](BF4)2,5/A~ sandwich films were confined to a 1:l C~S(III)/C~S(~~) the Figure 2, results for poly[Os(vbpy),] (BF.,),,,, the electron ratio. Extending these measurements to varied m, using the fast hopping conductivity rises as Os"' sites are introduced, to an potential sweep method and eqs 3 and 5, gave results for io, p, apparent maximum at C~(~II)/COS(II) = 1. Converting the io data and .(io) shown in Table 111and Figure 4 (0).Film compositions to kcx,E,s values with eq 4 and the electrolysis potentials to with CoS(ln)/Cos~n) > 1 were not studied. As anticipated from mixed-valent composition with eq 7, as above, gives the results = 1 film, in Table 111. The rate constant for the Co~(l,l)/Ca(ll) (22) Sosnoff, C. S. Master's Thesis, University of North Carolina, 1990. kex,E,s = 5.6 X lo5 M-' s-I, is in satisfactory agreement with the (23) McCarley, R. L.;Thomas, R. E.; Irene, E. A.; Murray, R. W. J . previous study,28 kcx,E,s= 1.0 X lo6 M-'s-I, for films prepared Electrochem.,Soc. 1990, 137, 1485. in an inert-atmosphere enclosure. (24) It is worth noting that error in sandwich electrode film thickness has Conductivities were also measured by ac impedance for the no particular tearing on previousz" investigationsthat depended on observing relatiue values of 0, and k,, for a giuen sandwich electrode specimen as a same series of film compositions (Pt/poly[O~(bpy)~(vpy),]function of environmental conditions and that emphasized a ca. 2X experi(BF4),/Au with m = 2-2.5) and over a range of lowered temmental scatter which is consistent with the present observations. These two peratures for poly[Os(~bpy)~](BF~)~.5 films where m = 2.5. The points were made previo~sly;~*'~ the present results serve to suggest an origin ac experiment had not previously been applied to electrical gradient of the experimental scatter and to suggest the use of the thinnest practical film thicknesses in sandwich electrodes. driven electron hopping in these mixed-valent films, and the h

J

J

J

The Journal of Physical Chemistry, Vol. 96, No. 2, 1992

968

Surridge et al.

I

1E7 1

1 E-5 A

c

I

1E-6

6

c

&

1E-7

v

b

.-'5 c) 0

1 E2 1EO

1El

1E2 1E3 1E4 Frequency ( H z )

1E5

1E-8

1E6 1000/T (K-l)

-

Figure 7. Arrhenius plots of u(ac), conductivity derived from ac impe-

1 E7

poly[Os(bpy)2(vpy)2](BF,)2.~ dance, in N2 for sandwiches containing (0) at rT = 2.1 x 1W8mol/cm2 (EA 8.3 kcal/mol (0.36 ev), u, 6.0Srl cm-l) and ( 0 )poly[Os(~bpy),](BF~)2,~ at r T = 2.5 X lo-" mol/cm2 (EA = 9.9 kcal/mol (0.43 eV), u, = 42 cm-I).

1 E6 h

C

v

8 1E5

C .M

.I

1E4

V

1 E3 20

1 E2 1EO

1El

1E3 1E4 1E5 1E6 Frequency ( H r ) Figure 6. (A) Room temperature Rb obtained from the inverse of the real part of ac admittance (Y) of the film in Figure 5, as a function of see Table 111. At 20 OC, frequency, at selected values of CO~(III)/CO~(I~); the low-frequency limiting resistance is 2200 Q, which corresponds to kmEAC = 2.0 X lo5 M-'S-I. (B) Rb of a similar film (rT = 2.1 X 1W8 mol/cm2) at selected temperatures at Ca(III)/Ca(ll)= 1 .

1E2

purpose here was to confirm the fast potential sweep results. Figure 5 is a representative ac impedance (Colecole) plot of Zrealvs Zimagfor a room temperature Pt/poly[O~(bpy)~( ~ p y ) ~ l ( B F ~ ) ~ sandwich , ~ ~ / A u electrode (Le., Ca(lII)/Ca(rr)= 0.26). Results at frequencies from 1 to 106 Hz (increasing to the left in Figure 5) form a slightly sunken semicircle whose equivalent circuit is a parallel resistor (Rb),capacitor ( c b ) , and dispersive elementZSRb/(iwr)a.23Following the results above, we take the resistance and capacitance to represent the bulk film properties. The bulk resistance.to electron hopping is related to conductivity by u(ac) = d/ARb, where d and A are film thickness and cross-section area; u(ac) is translated to electron-self-exchange rate constant kcx,E,AC with eqs 4 and 5. Values of Rb for poly[O~(bpy)~(vpy)~](BF~),,, films are shown as a function of ac frequency in Figure 6A at room temperature and m = 2-2.62 and in Figure 6B form = 2.5 at varied temperature. There is some decrease in the resistance at high frequency (we return to this dispersive effect below), but Rb is frequency independent at lower becomes < frequencies and strongly increases as Cos(III)/Ca(II) 1:l and as the film temperature decreases. The increase in Rb reflects a decrease in the electron hopping rate: the change in mixed-valent composition (presumably) effecting diminution in reactant pair population (eq 4) and the change in temperature which provide decreasing the populations of vibronic the activation pathway for electron exchange. The low-frequency Rb results, expressed as conductivity u(ac), are given in Table I11 and as (A,A, 0 ) in Figure 4. These ac data were obtained from the same p~ly[Os(bpy)~(vpy)~](BF~), films that were examined by fast potential sweeps in Table 111. and kcsEAcresults (Table 111, Figure 4) are in excellent The -k agreement, which is gratifying in light of the different basis of (25) a measures the dispersion which can be taken as a distribution of time constants (a nondispenive element has (I = 1). a in this study ranged from 0.6 to 0.8 over m = 2-2.5. (26) (a) Holstein, T. In Tunnelling in BidogiccrlSystems; Chance, B., Ed.; Academic Press: New York, 1979 p 129. (b) Sutin, N. h o g . Inorg. Chem. 1983, 30, 441.

the two methods, one being a small-voltage-amplitude method (ac) and the other a large-amplitude one (fast potential sweep).27 Inspection of the Table I11 results for the effect of CwIII)/Ca(II) ratio on k c x , ~and , ~ ~kex,~,~~ for pol~[Os(b~~)~(vp~)2l(BF4)m fih produces much the same conclusions as drawn from the analogous Table I1 experiments. The electron-self-exchangerate constants seem to be independent of the CwIII)/Ca(II) ratio for electrolysis potentials between Eo' and those ca. 60 mV more negative, Le., from Ca(IIl)/CwII)ca. 2 to 0.1. The result demonstrates that electron hopping reactions in this polymer, like poly [Os(~bpy)~](BF,),,,,follow a bimolecular rate law over this central composition range. As seen in Table 11, the rates in Table I11 decrease at low Ca(IIl)/Ca(II).While experiments at low Ca(III)/Ca(II)are probably less reliable (vide supra), it is appropriate to note that analogous discrepancies are found in measurements of De in a poly[Os(bpy)2(vpy)2](C104), film contacted by liquidMCH3CN and in conductivities of films of poly(vinylferrocene)1b,28and of the ladder polymer" BBL as a function of mixed-valent c o m p sition. That is, in both solvent-wetted and dry mixed-valent polymers, the bimolecular character of the electron-self-exchange reaction is, strictly speaking, only confirmed for OX/REDvalues inside the range ca. 0.1-10, and thus, strictly speaking, the issue of proper bimolecular behavior outside that range remains an open question. With respect to understanding of the electronic prop erties of very lightly or very heavily 'doped" molecular materials, this remaining issue is a significant one. Ac results for Rb in poly[O~(bpy)~(vpy)~](BF,)~.~films at low temperature (Figure 6B) show that the electron hopping rate decreases strongly at lowered temperature, are frequency-independent at low frequencies, and exhibit some dispersion at higher frequency. The low-frequency Rb results for poly[Os(~bpy)~](BF412.5 and poly [ O ~ ( ~ P Y ) ~ ( (BF412.5 V P Y ) ~film, ~ expressed as u(ac), follow Arrhenius behavior (Figure 7) as expected for thermally activated electron hopping and from previous observations".b for poly[Os(bpy)2(vpy)z](BF4)2.s. Figure 7 gives activation barriers E, = 8.3 kcal/mol (0.36 eV) for poly[Os( b p ~ ) ~ ( v p y[BF4]2*s, )~] in agreement with the previous study (8.5 kcal/mol), and -9.9 kcal/mol (0.43 eV) for poly[Os(vbpy),][BF4]2,s,in agreement with the barrier (9.1 kcal/mol) derived in Figure 1B from potential sweep IDA experiments. The ac impedance measurements also yield the bulk capacitance for poly[Os(bpy)2(vpy)2](C104),,, films as a function of C~III)/CwII) = 0.003-0.26 (Figure 8A) and temperature (Figure 8B) at m = 2.5. The results show that c b changes with mixedvalent composition and temperature, but to a quite minor degree (2-4 times) compared to the changes in Rb. (Note:Rb is displayed (27) While the u(P) results in Table I11 represent the small 4 region, they are calculated from values of io and p (eqs 4 and 5) which were obtained by potential sweeps to large voltages (4 3). (28) Pittman, C. U.; Suryuarayanan, B.; Sasaki, Y. Adu. Chem.Ser. 1976, No. 150, 46.

The Journal of Physical Chemistry, Vol. 96, No. 2, 1992 969

Electron Self-Exchange between Os" and OS"' ~

Clll/CII

400 h

0.0035

--

0

0.26

0.14

A

* o O '

0

o

LL

Q

v

300 -

u C

Y

200

0

-

Q

0

100-

I

04 1EO

1El

1E2

1E3

1E4

1E5

1E6

Frequency ( H t )

0.50 0

5

10

time

n

LL

Q

Y

u

2ool .O0I 500

- 35 b

-

20 oc

Bl

15

20

25

hind

Figure 9. Potential vs SSCE of two Pt/poly[O~(vbpy),](BF~)~,~/Au sandwich films, previously electrolyzed at 0.751 V vs SSCE (EO' for the Os"/"'couple), upon exposure to 0.1 M Bu4NBF4/CH2C12. The areas of evaporated Au contacts exposed to the solution are 0.28 cm2 (0)and 0.06 cm2 (W).

poly[O~(bpy)~(vpy)~] (BF4)z.s polymeric complexes, the rates are slower in the former polymer. The difference is by factors between 0 2- and 10-fold and appears in all forms of measurement: with a solvent-wetted concentration gradient [keXc= 3 X lo6 M-' s-' u (Table I, batchs 6 and 7) vs 2 X lo7 M-' s-1,2arespectively, in 100 CH3CN], in dry Nz with concentration gradient = 3 X lo5 M-' s-' (Table I, batch 1) vs 6 X lo6 M-' respectively], or 04 I with electrical gradient [kex,E,LS = 1 X lo5 M-' s-' (Tables I and (EO 1El 1E2 1E3 1E4 1E5 1E6 11) vs kex,E,m= 4 X lo5 M-' S-' (Table 111), kex,E,AC = 3 X los Frequency (Hz) M-' s-' (Table 111), and 1 X lo6 M-' respectively]. The Figure 8. (A) Room temperature capacitance (yi/w, where Y , is the difference in activation barrier observed for Pt/poly[Osimaginary part of the admittance) of the film in Figure 6A, at indicated ( ~ b p y ) ~ ] ( X(9.1 ) ~ , ~and 9.9 kcal/mol, Figures 1B and 7) vs C~1II)/C~(II). C, = 90 pF, e, = 9. (B) Capacitance of the film in Figure poly[Os(bpy)z(vpy)2](X)z,s (8.3 kcal/mol, Figure 7, and 8.3 6B at C~(~~I)/CO,(II) = 1 for indicated temperatures. C, = 105 pF, e, = kcal/molza) in the case of the dry films is consistent with the 10. smaller rate constant for the ostensibly more highly cross-linked tris-vbpy polymeric complex. in Figure 6 on a log scale.) cb approaches a high-frequency Second, the environmental effects on the rate constants for both limiting value of ca. 90 pF from which the effective dielectric polymers, derived here and show that k,(liquid C H F N constant of the mixed-valent medium can be estimated as t 9 or CH2C12)> k,,(vapor) > k,,(dry N2). These polymer-phase from t = Cb/td, where to is the permittivity of free space. This rates range from nearly equal to (in the case of poly[Os(bpy),value presumably represents the response of the osmium metal (vpy)2](BF4)u in liquid CH3CN) to 70-fold smaller than (in the complex sites, and their counterions, as polarizable dipoles. case of dry poly[O~(vpy)~] (BF4)2,5) the k,, rate constant for Regarding the frequency dependence in Rb and c b seen in monomer [ O ~ ( b p y ) ~ ] ~ exchange + / ~ + in solutions.30 Third, we also Figures 6 and 8, the decrease in Rb at higher frequency is most pronounced for the most resistive films, Le., at small C ~ ( I I I ) / C ~ ( I I )have established" that the diffusivity of C1- counterion is smaller in acetonitrile-wetted Pt/poly[Os(vbpy),] (BF4)2,5, as compared and at low temperature. Parallel electron hopping resistance and to that of the, ostensibly, less highly cross-linked Pt/poly[Osfilm capacitance should ideally display no such frequency dis(bpy)2(vpy)Z1(BF4)2,5* persion, so this effect reflects some nonideal chemical process that These observations are consistent with a definite influence on is superimposed upon the primary dependency of Rbon compothe electron hopping rate in the polymer of the rigidity by the sition and temperature. Given the characteristics of the ac and polymeric matrix. Matrices which are more rigid by virtue of linear sweep methods, it appears likely that the dispersion in the the absence of solvent or through enhanced cross-linking lead to ac results and the fitting parameter p found in the linear sweep slower rates. The inference drawn is that the electron-transfer experiments (vide supra) have common origins, such as a dispersion hopping rate is aided by circumstances allowing some nuclear in the energy barrier for the electron-self-exchange reaction. As displacement of the osmium sites away from their equilibrium discussed before,%an energy barrier dispersion could arise from locations (Le., short-range oscillations of pendant sites) and/or structural nonidealities of the polymeric material, but until it distortion of the vinyl polymer framework holding the sites tobecomes possible to systematically manipulate details of the gether, and the hopping rate is slowed when polymer rigidity polymer structure, it will be difficult to assess this hypothesis. inhibits such displacement or distortion. That is, the polymer Analogous dispersive effects are common in time-of-flight oblattice can, under rigidified circumstances, impose an 'innerservations, and while they have been modeled exten~ively,2~ their sphere"-like barrier. molecular basis also remains obscure. C 0

.-

.u 0

Conclusions These experiments collectively show that the electron transport dynamics in Pt/poly[Os(~bpy)~](BF,), and p~ly[Os(bpy)~( v p ~ )(BF,), ~] films follow a bimolecular rate law provided the film composition is within the range ca. 0.1-6 Oslll:Osll. Further, while the electron-transfer rate behavior of Pt/poly[Os(~bpy)~](BF,),,,films is generally similar to that of the related%.b (29) Abkowtiz, M.; hi, D.M. Philos. Mag. 1989, 53, 193.

Stability of 0s"' in a Mixed-Valent Sandwich Electrode We noted (ExperimentalSection) the instability of mixed-valent films when using CH3CN rather than CHzClzas the electrolysis >> solvent and when attempting to generate films where The following experiments demonstrate that Os"'-driven oxidation of the evaporated gold film electrode is the source of this effect. Two nominally identical Pt/poly[O~(bpy)~(vpy)~](30)Chan, M A . ; Wahl, A. C. J . Phys. Chem. 1982,86, 126.

970

J . Phys. Chem. 1992, 96, 970-975

(BF4)z 5 / A sandwiches ~ were prepared, each containing rT = 2.0 x IO-$ mol/cm2 deposited on 0.002-cm2 Pt wire tip electrodes, with evaporated gold overlayer contacts that covered the film and spread out onto the surrounding glass shroud to different extents (28 and 6 mm2 of Au in area). Each sandwich was immersed in 0.1 M Bu4NBF4/CHZCl2and electrolyzed a t E O ' , so as to = then poproduce a mixed-valent film where Cos(nI) tentiostatic control was released, and the potential of each film (Pt electrode) vs a SSCE reference electrode was monitored vs time. In both cases, Efilmdecayed with time in a direction indicating loss of Os111states (Figure 9), and the decay was faster for the sandwich electrode having the larger area of Au exposed to the solution. This result shows that either oxidation of Au or of some trace solution component at the Au surface occurs to discharge the Os"' states. The dimensions are such that less than 1 X 1O-Io equiv/cmz of charge (less than one molecular layer) must pass across the Au/solution interface in order to completely discharge the Os"' layer.

Our experience indicates that effects such as Figure 9 are greatly retarded in films dried of solvent, which is the reason that, in preparing mixed-valent films, it is important to retain potential control of the film until it has been raised from the solution, rinsed, and dried.

Acknowledgment. This research was supported in part by grants from the National Science Foundation. We gratefully acknowledge the Pt IDA'S supplied for this research by Masao Morita and Osamu Niwa of the NTT Basic Research Laboratories, Nippon Telegraph and Telephone Company, Tokai, Ibaraki, 319-11, Japan. R&tW NO. Vbpy, 74173-48-1; BFC, 14874-70-5; ([Os(bpy)2( [OS(V~PY)J(BF~)~+)~, 138089-55-1; (vPY)~] ( B F ~ ) Z - ~138062-06-3; )~, [OS(Vbpy),](PF6)2, 130728-19-7; (NH4)2OSCI,, 12 125-08-5; NHdPF,, 16941-1 1-0; CH2C12, 75-09-2; CH$N, 75-05-8; Bu~NBF~, 429-42-5; ([OS(~PY)Z(VPY)ZI(BFS)~)~, 13806247-4; ([OS(V~PY),I(BF~)Z)~, 138062-08-5; Pt, 7440-06-4; Au, 7440-57-5.

Transfer Energetics of Tetraalkylammonium Ions in Aquo-Organic Systems and the Solvent Effect on Hydrophobic Hydration Himansu Talukdar and Kiron Kumar Kundu* Physical Chemistry Laboratories, Jadavpur University, Calcutta- 700 032, India (Received: June 13, 1991, In Final Form: August 20, 1991)

The solvent effect on hydrophobic hydration has been studied by measuring the solubilities of some tetraalkylammonium tetraphenylborate (R.,N+PbB-) salts with R = methyl (Me), ethyl (Et), n-propyl (Pr),and n-butyl (Bu) spectrophotometrically at 25 OC in some aqueous mixtures of tert-butyl alcohol (TBA) and acetonitrile (ACN). The observed results, which yield standard free energies of transfer (AGlo) of KN+P4B- from reference solvent water to these cosolvents, have been dissected into individual ion contributions using the preevaluated values of P4B- which are based on the widely used tetraphenylarsonium tetraphenylborate (TATB) reference electrolyte (RE) assumption. The AGlo(i) values of &N+ cations were then combined with the previously evaluated standard enthalpies of transfer (Ml0(i)) based on the same RE assumption, to give standard entropies of transfer (ASto(i)). The AGto(i) values were analyzed in light of the cavity effect and electrostatic effect and the rest in light of the hydrophobic hydration (HH) effect, which was found to decrease with cosolvent. The corresponding A S W H O values when analyzed in light of Kundu et ala'sfour-step transfer process and the marked influence on water structure by the three-dimensional (3D) structure promoter TBA and 3D structure breaker ACN molecules reflect the respective solvent effect on hydrophobic hydration as induced by R4N+cations.

Introduction Hydrophobic solutes or ions with apolar residues induce water molecules around them to organize in a way similar to clathrate hydrates,' causing hydrophobic hydration (HH)'-' and resulting in a significant increase of free energy and decrease of entropy of the system.' The phenomena of hydrophobic hydration and the related hydrophobic interactions (HI)693camong apolar sites are of great significance in the realms of micelles, mixed micelles, microemulsions, bilayer membranes, and particularly biopolymers including protein^.^ Studies on thermodynamic and transport b e h a v i ~ r ~ . ~of, ~aqueous . ~ - ' ~ solutions of tetraalkylammonium salts (1) Wen, W. Y. Water and Aqueous Solutions; Horne, R . A,, Ed.; Wiley-Interscience: New York, 1972; p 613. (2) Conway, B. E. Ionic Hydration in Chemistry and Biophysics; Elsevier: Amsterdam, 1981; Chapters 20 and 24. (3) (a) Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological Membranes; Wiley-Interscience: New York, 1980. (b) Faraday Symp. Chem. SOC.1982,17. (c) Kauzmann, W. Adu. Protein Chem. 1959, 14, 1. (4) Abraham, M. I+.; Matteoli, E. J. J. Chem. SOC.,Faraday Trans. 1 1988, 84, 1985 and relevant references therein. ( 5 ) Privalov, P. L.;Gill, S.J. Pure Appl. Chem. 1989, 61, 1097. (6) Ben-Naim, A. J. Chem. Phys. 1971, 54, 1387, 3696. (7) Engberts, J. B. F. N.; Nusselder, J. J. H. Pure Appl. Chem. 1990.62,

47. (8) Cox, B. G.; Waghorne, W. E. Chem. SOC.Rev. 1980, 9, 381.

with and without ionic and nonionic cosolutes/cosolvents and salient features of hydrophobic hydration have been reported. We have shown recentlyI5 that tetraalkylammonium picrates and especially the corresponding hydrophobic cations induce more hydrophobic hydration in aqueous sodium nitrate solutions than in pure water. Analysis of the observed standard free energies (Acto) and entropies (Uto) of transfer data specifically indicated the alteration of water structure around the incoming ions and thus provided measures of the salt effect on hydrophobic hydration. It should be equally important and interesting to understand the systematic behavior of these tetraalkylammonium salts in various aquc-organic solvent systems. Various thermodynamic studies2~8-'2J4 on these salts have been made particularly from calorimetric measurements, which helped evaluate standard enthalpies (9) (a) Heuvelsland, W. J. M.; de Visser, C.; Somsen, G. J. Phys. Chem. 1978, 82, 29. (b) Heuvelsland, W. J. M.; Bloemendal, M.; de Visser, C.; Somsen, G. J. Phys. Chem. 1980,84, 2391. (IO) Juillard, J. J. Chem. SOC.,Faraday Trans. 1 1982, 78, 37, 43. (11) Miyaji, K.; Morinaga, K. Bull. Chem. SOC.Jpn. 1983, 56, 1861. (12) Carthy, G.; Feakins, D.; Waghorne, W. E. J. Chem. SOC.,Faraday Trans. 1 1987.83.2585. (13) Nakayama, H.; Kuwata, H.; Yamamato, N.; Akagi, Y.; Matsui, H. Bull. Chem. Soc. Jpn. 1989,62, 985. (14) Feakins, D.; Mullally, J.; Waghorne, W. E. J . Chem. Soc., Faraday T r a m 1 1991, 87, 87. (15) Talukdar, H.; Kundu, K. K. J. Phys. Chem. 1991, 95, 3796.

0022-365419212096-970$03.00/00 1992 American Chemical Society