J. Phys. Chem. 1994, 98, 13643-13650
13643
Electron Self-Exchange Rates in a Site-Dilutable Osmium Bipyridine Redox Polymer Connie S. Sosnoff,? Melani Sullivan,’ and Royce W. Murray* Kenan hboratories of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290 Received: June 22, 1994; In Final Form: October 5, 1994@
The metal complexes [Os(vbpy)3I2+ and [Zn(vbpy)3Iz+ have been electroreductively copolymerized as 70230 nm thick films in which the mole fraction of Os sites is varied from xoS = 1.0 to 0.49. Currentpotential data have been obtained from concentration-polarized, OsZ+l3+ mixed-valent films sandwiched between two electrodes and bathed in liquid CHzClZ, CHzClz vapor, and dry Nz.Electron transport data were also obtained for non-concentration-polarized films bathed in dry Nz and subjected to an electrical gradient. The electron self-exchange rate constants @EX) derived from the concentration gradient-based measurements are larger in liquid and vapor CH2Clz media than in dry Nz. EX values in dry N2 are the same whether obtained from concentration gradient measurements using a Fickian electron hopping theory or from electrical gradientbased measurements with analysis both by a modified Marcus relation and by a dispersive transport model due to Scher/Montroll/F’fister. All EX values, however derived, drop much more sharply, by 35-50-fold, with decreasing fraction of Os sites &os), than expected from simple bimolecular kinetic or static percolation models. The behavior of the copolymer kinetics is rationalized based on a dependence of activation barrier on Os site concentration and/or nonideal aspects of the microscopic structure of the copolymer.
Much work has been done in this laboratory’ and elsewhere2t3 to design redox polymers that probe the dynamics of electron hopping (self-exchange) transport through mixed-valent, solid state materials. The relationship between the concentrations of fixed electron carrier sites and the rates of electron hopping is an important but less widely e ~ p l o r e d ~component ~ ~ ~ , ~ of ~ ~this ,~ topic. Solid state concentration-rate relations can involve microscopic electron site and counterion mobilities, distance and medium effects on electron transfer, “inner-sphere’’ terms associated with counterion dipoles, etc. The solid state problem is more c o m p l e ~ ~ J Jthan ’ , ~ analogous homogeneous solution electron self-exchanges and can involve a dispersion in reaction rates. The understanding of concentration effects should be simplified by use of polymeric materials in which the redox site concentrations can be varied in a controlled fashion, unaccompanied by concurrent morphological changes in the polymer. This paper uses a system designed for such isostructurd redox site dilution, in a study of electron transport dynamics as a function of site concentration. We have previously describedleSi two polymer systems designed for a capability for isostructural redox site dilution. In one, solution mixtures of the metal complexes5 [Ru(bpy)z(p-cinn)2lZ+and [Os(bpy)z(p-cinn)~]~+ were electrochemically polymerized” to form thin, electroactive RdOs copolymer films on the electrode. More recently, mixtures of [Os(vbpy)3Iz+and [Zn(vbp~)3]~+ were electroreductively copolymerized.le In both cases, the ratios of [Ru(bpy)2(p-cinn)2I2+ and (Os(bpy)z(pc i n n ) ~ ] ~sites, + and of [Os(vbpy)3l2+and [Zn(vbpy)3Iz+ sites, were found to be equal in the copolymer films and in the monomer feed solutions. Such equality is a criterion6 for randomly distributed copolymer sites. This feature, and the matched metal complex structures, should in principle yield copolymer films in which Os complex sites are randomly and isostructurally diluted by sites of the other metal complex. In an Os2+13+mixed-valent state of the [Os(vbpy)3lZ+/Zn(vbpy)3]*+copolymer, the Os sites provide an electron conduct Present address: Centers for Disease Control and Prevention, Atlanta, GA 30333. Present address: Paul Scherrer Institut, Wurenlingen and Villigen, CH5232 Villigen PSI,Switzerland. Abstract published in Advance ACS Abstracts, November 15, 1994.
*
@
0022-3654/94/2098- 13643$04.50/0
tive pathway based on bimolecular electron self-exchanges, with rate constant k ~ x .
+
os3+ os2+
+
os2+ os3+
The Zn sites, being nonmixed valent, are electron transfer silent and act as diluent. This paper describes measurements of [Os(~bpy)3]~+/~+ electron self-exchange rates in thin (70-230 nm) films of the copolymerle [Os(~bpy)3]~+/[Zn(vbpy)3]~+,as the Os site mole fraction xoS is varied from 1.00 to 0.49. The objectives are threefold: to evaluate how the rate of reaction 1 depends (a) on dilution with [Zn(vbpy)#+ sites and (b) on the bathing environment of the conductive copolymer film and (c) to apply steady state sandwich electrode measurement methodsl~b~d~f that avoid possible electroneutrality coupling limitations1cs8of the transient chronoamperometric method that was used to study Os2+”+self-exchangerates in the earlier [Ru(bpy)z(p-cinn)2lZ+/ [0s(bpy)z(p-cinn)pl2+copolymer. The sandwich electrode methodld~f~h~k depends on fabrication of a thin copolymer film sandwiched between a solid Pt electrode (wire tip) and an evaporated Au film electrode. The evaporated Au film is tailored to be electrically continuous but porous, allowing access of solvent and electrolyte or solvent vapor to the polymer film, or drying of it in a N2 bath, while controlling the potentials applied to the electrodes. This arrangement allows preparation of mixed-valent OsZ+l3+film compositions and subsequent measurement of l c ~ xwith reaction 1 being driven either by gradients of concentrations of Os2+ and Os3+ sites in the film or, in the absence of concentration gradients, by gradients of electrical potential. We have reported analogous measurements previouslyla-dsf-hon redox polymers that were mixed valent but not site diluted. The reaction 1 concentration gradient-based k ~ measurex ments are made on copolymer films bathed in several environments: CH2C12 electrolyte solution, CH2ClZ vapor, and dry in Nz. The results reveal a pattern of bathing environment sensitivity analogous to that revealed in previous work. la,b,d,f-h The electrical gradient-based current-potential responses, all 0 1994 American Chemical Society
Sosnoff et al.
13644 J. Phys. Chem., Vol. 98, No. 51, 1994
obtained for films bathed in dry Nz,give km values agreeing with the concentration gradient-based results in dry Nz. All k ~ xresults, regardless of method employed or of copolymer bathing environment, reveal a steep, 50-fold decrease in the Os2+13+self-exchange rate constant as the Os site mole fraction xoSdecreases from 1.00 to 0.49. This site concentration dependency is steeper than expected from either static or dynamic percolation model^.^
1OG% OSMIUM
1.5
0.0 1.5
69% OSMIUM
Experimental Section Chemicals. Acetonitrile (Burdick and Jackson, UV quality) and dichloromethane (Mallinckrodt, Analytical Reagent grade) were dried and stored over 4A molecule sieves. Tetrabutylammonium tetrafluoroborate, B u m F 4 (Fluka), was used as received and stored in a vacuum desiccator. The ligand 4-methyl-4’-vinyl-2,2’-bipyridine (vbpy) was synthesized using a modification of a literature method, substituting aA-dichloroanisole for methyl chloromethyl ether.lO The complexes [Os(vbpy)3](BF4)2 and [Zn(vbpy)3](BF4)2 were prepared according to literature methods.1e,11v12 Electrochemical Experiments. A Pine Instrument Co. (Grove City, PA) Model RDE 4 bipotentiostat was employed to scan electrode potentials during electrochemical polymerization of films onto polished 0.0032 or 0.00203 cmz Pt wire tip electrodes, during electrolysis of thus prepared films in CH2C12 electrolyte solution to the 1.1 Os2+13+mixed-valent state, and during slow potential scan (concentration gradient) experiments with the mixed-valent electrodes bathed in CHzClz vapor and in dry N2. The current-potential curves were recorded using a Yokogawa Model 3025 X - Y recorder. Fast potential bias scans with the electrodes bathed in dry NZ(electrical gradient experiments) were accomplished with a Wavetek triangle wave generator, with current measured as a voltage drop across a (30-1000 ohm) series resistor and recorded on a Nicolet 2090 digital oscilloscope. Electrochemical Copolymerization and Film Characterization. Electropolymerizationwas accomplished as before, by cyclical potential scanning into the bpy ring reduction waves in sub-millimolar mixtures of the monomers [Os(vbpy)#+ and [Zn(vbpy)#+ in CH3CN solvent. The negative limit of the ca. &OS V cyclical potential scan was set at -2.15 V relative to the peak potential of the Os2+13+wave. This negative potential limit lies slightly past the second bpy ring reduction wave of the [Os(vbpy)3l2+complex and just at the first bpy ring reduction peak for [Zn(vbpy)3I2+. Under these conditions, steady growth of a current-potential envelope signaling electroactive film accumulation could be observed, both for Zn and Os homopolymer films and for ZdOs copolymer films. Use of more negative potentials during scanning can produce gradual film passivation, apparently due to labilization and demetalation of the Zn complex. Based on previousle analyses of copolymer film composition by XPS and by OsFe voltammetry (following replacement of Zn with Fe), the mole fraction xoS of Os and Zn sites in the copolymer films was taken as equal to that of the metal complex monomers in the solution used for the electropolymerization. Values of xoSare reliable to ca. 10% judging from the previous analytical uncertainties. Voltammetry of the Os2+13+ couple in five copolymer compositions (figure 1) shows (i) larger AEPEAK splittings for copolymers with lower Os site content, reflective of slower electron transport, (ii) voltammetric peaks broader ( E f ~ = b 165 mV for xoS = 1.0 and 175-185 mV for xoS < 1.0) than the ideal14E f ~ = h 90.6 mV, indicative of site-site interactions or a spread in formal potentiais,15 (iii) small charge-untrapping
1.0 0.5 VOLTAGE M
91% OSMIUM
1.0 0.5 VOLTAGE M
0.0
59% OSMIUM
f 1.5
1.0 0.5 VOLTAGE M
0.01.5
1.0
0.5
0.0
VOLTAGE M
49% OSMIUM
1.30
0.65 VOLTAGE (v)
0.00
Figure 1. Voltammetry (50 mV/s) of the Os*+”+ couple in copolymer f h s of indicated xoS on Pt wire tip electrodes in 0.1 M B-Fd 3.1 x loW4,1.5 x CHsCN. Current sensitivities SI-& = 1.3 x 9.9 x and 1.3 x A/cm2,respectively. peaksL6at the leading edge of the oxidation peak, and (iv) a hint of a minor electroactive constituent at more positive potentials which is most obvious at large xes. The latter two features have no significance in the electron transport measurements, which begin by exhaustive electrolysis of the film at the E” of the Os2+”+ wave, making the impurity states respectively empty and filled. The voltammetric peak broadening (ii) affects concentration gradient electron transport at low applied potential biases. Following Albery,lsa it is empirically accounted for’5b with a parameter “g” modifying the Nemst equation cOs(2+)lc0s(3+)
= exp[(gnF/Rq(Eo - E)]
(2)
which for the observed Ef~hmvalues ranges from 0.57 to 0.49 with an average value of 0.51. The coverages rOs (mol/cm2) of Os sites in the films, evaluated from charges Q under the OsZ+I3+peak in voltamto 3.0 x mograms as in Figure 1, ranged from 0.9 x mol/cm2. Since the number of “equivalent monolayers” of Os sites is roJl.3 x these films contain 61 to 230 equivalent monolayers of electron conductive, metal complex sites. Taking the total metal complex site concentration (Os Zn) as 1.3 M (value estimated for an undiluted Os homopolymer filmic), the copolymer film thicknesses ranged from 60 to 470 nm. We have no evidence for ordering in the films; the electrical gradient measurements (vide infra) are in fact consistent with disordered films. Experiments in electrolyte solution were carried out in a deareated 4 mL two-compartment cell with large area (> 1 cm2) Pt gauze counter electrode and Ag/AgCl reference electrode in the main and side compartments, respectively. Electrochemical polymerizations were carried out in a Vacuum Atmospheres glovebox, from mixtures of the two monomer complexes (at total concentration between 0.5 and 1.0 mh4) in 0.1 M BudNBFJCH3CN solutions. Films were electrolyzed to the 1:l
+
J. Phys. Chem., Vol. 98, No. 51, 1994 13645
Osmium Bipyridine Redox Polymer iwu
Os2+13+mixed-valent state (after Au film evaporation) in 0.1
M BUBFdCH3CN solutions and then transferred to CH2C12 as the organic solvent in order to minimizeId corrosion of the Au film by Os3+ sites. Electron Transport Measurements. Most of the sandwich electrodes were fabricated following procedures fvst reported by Pickup et al.'g*l7 Typically, copolymer films were deposited on six of the 12 polished Pt wire tips exposed at the end of a soft glass cylinder, and then a 300 8, Au overcoat was slowly evaporated onto the polished cylinder end. Pairs of polymer/ Au-coated and only Au-coated electrodes were isolated by scratching away Au on the intervening glass with a wooden tip, to produce a batch of six sandwich electrodes. Typically, 50% or more of the sandwiches proved to be shorted owing to minute imperfections in the thin films. For films with xoS= 1.O and 0.91, after polymer deposition, determination of Tosby cyclic voltammetry, Au film deposition, and electrolysis to the 1:1 mixed-valent Os2+13+state, the order of exposure to bathing environment for the electron transport experiments was B L @ J B F ~ C H ~solution, C ~ ~ CH2C12 vapor, and dry N2. For experiments in dry N2, the films were dried for 20 min and then subjected to slow potential scans to collect data in the concentration gradient mode, and finally the films were subjected to fast potential scans to collect data in the electrical gradient mode. In transfening 1:1 mixed-valent films from CH2Clz electrolyte to CHzClz vapor, the films were rinsed with pure CHzC12, dried in a N2 stream, and exposed for 10 min to a CH2Cl2-saturated N2 stream under zero bias to relax any Os2+13+ concentration gradients. Our experience has been that organic solvents evaporate very rapidly and completely from these thin films. For films at other xoS values, determination of electron transport rates followed the order: initial establishment of 1:1 Os2+13+mixed-valent film by electrolysis at E"' in B W F d CHzC12 solution with rinsingldrying steps and then concentration gradient and electrical gradient measurements in dry NZ as above, next repeated electrolysis at E"' in BuflBFdCH2C12 solution to refresh the 1:1 state (done conservatively not due to actual observation of its loss), and then concentration gradient measurements in BuDBFdCH2C12 solution and in CHzCl2 vapor.
91%
0.0 1.2
0.0 1.2
(VI
(VI
0.0 1.2
49%
OSMIUM
0.0 1.2
(VI
(V)
0.0 (v)
Figure 2. Steady state concentration gradient voltammograms, in liquid electrolyte, 0.1 M BuWFdCH2C12, at 5 mV/s, for Wcopolymer film/ Au sandwiches of indicated xes. EA"= 0.0 V vs Ag/AgCl as collector of Os3+states generated at Pt electrode, the potential (V) of which is scanned positively; current is measured at Au side of sandwich (is the same on Pt side but with charging currents). Current sensitivities SISs = 1.6 X loW2, 3.1 X 2.5 X 9.9 X and 1.6 X A/cm2. The differing current scales reflect changes in electron transport rates. 100% OSMIUM
0.6
0.3
0.0
91% OSMIUM
-0.6
-0.3
0.6
0.3
0.0
-0.6 0.6
-0.3
VOLTAGE
-0.6
5% OSMIUM
69% OSMIUM
0.6
0.0 -0.3 VOLTAGE M
0.3
VOLTAGE 0
M
0.0 -0.3 VOLTAGE M
0.3
-0.6
4996 OSMIUM
r-
Results and Discussion
I
Concentration Gradient-Based Measurements in B u ~ NBFdCH2Clz Electrolyte Solution, in CHzClz Vapor, and in Dry Nz Bathing Gases. At sufficiently large potentials and on time scales slow enough for the film's BF4- counterions to migrate across the film, electrolysis at the opposing electrode/ copolymer interfaces maximizes the Os3+ and Os2+ site concentrations at the positive and negative electrodes, respectively. The consequently maximized concentration gradient of Os2+13+sites and steady state limiting ~ u r r e n t are ' ~ ~related ~ ~ to kEx and the so-called electron diffusion coefficient DEby the re1ation~'~J~J~
>f
where DEis related to kEx through a cubic lattice model,lg A is the opposing sandwich electrode area, 6 is the average Os-Os intersite distance (estimated from CT as 6 = (CTNA)-'~= 1.2 nm center-to-center), CT is total Os site concentration (1.3 M when no Zn is present), and oois a small migration correction (1.067 for a 2+/3+ couple).*fs20
OSMIUM
OSMIUM
II;1
1.2
59%
69%
OSMIUM
OSMIUM
0.6
s5
0.0 -0.3 VOLTAGE M
0.3
-0.6
Figure 3. Steady state concentration gradient voltammograms,in CHzClz vapor, at 5 mV/s, for Wcopolymer film/Au sandwiches in 1:l O F 3 + mixed-valent state; current sensitivities SI-& = 3.1 x 6.3 x 2.5 x 9.9 x and 3.3 x A/cmz. Same sandwiches as used in Figure 2 ; V is voltage applied between Pt and Au. The differing current scales reflect changes in electron transport
rates. Results of concentration gradient experiments in different bathing media are displayed in Figures 2-4. Figure 2 shows current-potential curves in BWFdCHZC12 electrolyte solution where the potential of the R electrode of the sandwich was scanned positively through the Os2+I3+wave while holding that of the Au electrode at a reducing value. The current peaks in the lower xoSfilms reflect a delay in attaining steady state concentration gradients caused by the slower transport rates there; potential scans were halted after the peak to allow currents to decay to steady values. The current-potential curves shown
Sosnoff et al.
13646 J. Phys. Chem., Vol. 98, No. 51, 1994 10% OSMIUM
91% OSMIUM
b
0.6
0.3
0.0
-0.3
-0.6 0.6
0.3
VOLTAGE M
0.3
0.0
-0.3
-0.6
VOLTAGE M
69% OSMIUM
0.6
0.0
8
59% OSMIUM
-0.6 0.6
-0.3
0.0 -0.3 VOLTAGE M
0.3
VOLTAGE M
-0.6
49% OSMIUM
U
fi
.8
P
8 0.6
0.0 -0.3 VOLTAGE M
0.3
-0.6
Figure 4. Steady state concentration gradient voltammograms, in dry Nz,at 2-5 mV/s, for Wcopolymer film/Au sandwiches in 1:l mixed-valent state; current sensitivities &-& = 1.3 x lo+, 3.1 x 9.9 x 4.9 x and 1.6 x Alcmz. Same sandwiches as used in Figures 2 and 3. The differing current scales reflect changes in electron transport rates.
in Figures 3 and 4 were obtained with the same sandwich specimens as used in Figure 2, after electrolysis to the 1:1 mixed valent state and exposure to CHzClz vapor (Figure 3) and dry Nz (Figure 4). Steady state currents, reflecting redistribution of film counterions and production of stable Osz+"+ concentration gradients through the film, are again obtained most readily at larger xoSvalues. We have no data for films with xoSvalues smaller than 0.49, owing to difficulties of very slow electropolymerizations and attainment of steady state currents, brought on by extremely slow electron transport rates. Application of eq 3 to the limiting currents of Figures 2-4 gives the concentration gradient REX rate constants in the lefthand section of Table 1. The results show that the averageZL value of REX decreases in the progression of bathing media BQNBF4/CHZC12 > CHzC12 vapor > dry N2. This variation in electron self-exchange dynamics is quite similar to that observed previously using concentration gradient measurements with other 1:l mixed valent (but undiluted) redox polymer films, notably's [Os(bpy)z(vpy)~](C104)2 and poly(viny1ferrocene). The self exchange rate constants in CHzCl2 vapor are, at all xes, only slightly smaller than those in liquid CHZClz, indicating (as seen beforelh) that these polymers can incorporate sufficient organic solvent from a vapor stream to produce an internal solvation state nearly the same as that produced by immersion in the liquid form of the solvent. Examination of Table 1 also shows that REX in films with lower %osis less sensitive to bathing environment. The most dramatic aspect of the data in Table 1 is the large decrease in the rate constant REX as the mole fraction %osof Os sites in the copolymer film is decreased. A decrease in OsZ+l3+ site concentration of a factor of only 2-fold produces a decrease of about 50-fold in k ~ xin BwF4/CHzC12 solution and 35fold in dry Nz.A bimolecular rate expression for reaction 1 under conditions where the sites move about freely would
f
m .
k
Osmium Bipyridine Redox Polymer
J. Phys. Chem., Vol. 98, No. 51, 1994 13647
1M)x OSMIUM
4.0
2.0
0.0
-2.0
-4.0
VOLTAGE M
4.0
2.0 0.0 -2.0 VOLTAGE M
69% OSMIUM
4.0
2.0
0.0
Current-potential curves like those in Figure 5 were analyzed by two methods, as in recent papers.la,b One method is based on the Marcus relation22connecting electron transfer rate with reaction free energy,
91% OSMIUM
-4.0
59% OSMIUM
-2.0
-4.0 4.0
VOLTAGE M
0.0 -2.0 VOLTAGE M
2.0
-4.0
49% OSMIUM
/
4.0
0.0 -2.0 VOLTAGE M
2.0
-4.0
Figure 5. Electrical gradient current-potential curves. Fast potential bias scans (ranges from 6.4 x 104 to 80 V/s for curves 1-5) applied to 1:1 mixed-valent Wcopolymer fiMAu sandwiches bathed in dry N2; SI-& = 1.6, 1.3 x 4.9 x 2.5 x low3,and 6.3 x A/cm2. Same sandwiches as used in Figures 2-4.
predict no decrease in the rate constant upon dilution in donor and in acceptor reactants. A bimolecular reaction between sites rigorously stationary would predict an electron diffusion coefficient (or conductivity) decreasing linearly to near zero at a (static) percolation threshold9 of about xos 0.35. We will return to these observations later. Electrical Gradient-BasedMeasurements in Dry Nz Bathing Gas. Scanning the bias potential applied to the sandwich on a time scale rapid in comparison to that on which significant counterion migration and interfacial electrolysis can occur allows the bias potential to be dropped more or less linearly across the film bulk. In this case, the free energy for the electron selfexchange reaction (eq I), the intersite potential, 4, is modeledla& as the bias potential divided by the number of equivalent monolayers of Os sites in the film. The currents observed (Figure 5) in f 4 . 0 V scans in N2 bathing gas increase continuously with applied potential and are much larger than those in the concentration gradient mode (compare current scales to those in Figure 4; the same electrode samples are used). The results in bathing gases (Figures 2-5) are generally symmetrical about zero bias, indicating that Au and Pt provide similar injecting contacts. In N2 bathing gas, it was possible to manipulate experimental time scales over a range sufficient to make both concentration gradient and electrical gradient measurements on the same film. The criterion for counterion motion that is insignificant in comparison to the electron hopping rate, and thereby for insigificant copolymer electrolysis, is the disappearance of hysteresis in current-potential curves when the potential scan rate is increased above some value, which in N2 bathing gas was ca. 64 000 VIS for xoS= 1.0 films but only ca. 80 VIS for films with xoS= 0.49 and where the electron hopping rate is slowest. The results at these and higher potential scan rates are independent of scan rate.
-
and incorporates a fitting factor to account for the fact, observed here and in previous exampleslaqb.d,kof electrical gradient-driven electron self-exchange, that the experimental current-potential curves rise more steeply with increased applied potential than classical Marcus theory allows. This effect is thought to reflect dispersive transport in the mixedvalent material; i.e., not all of the electron hopping steps occur with the same rate constant. The parameter e, ideally one, ranged in this study from 1.8 to 4.0 and is smaller when data at large electrical gradients are analyzed. This analysis is referred to as @-modifiedMarcus. Figure 6 (top) illustrates fitting eq 4 to data obtained for xoS = 0.69; the fit is quite good with low residuals (Figure 6, bottom), as are those at other xoSvalues. Results for values of kEx, @, and the product @kEXare given in Table 1, center. As observed previously,laqb the product @kEx best reflects the “average” electron transport rate constant of the dispersive system. In Table 1, note that @kEXis in very good agreement with kEx values derived from concentration gradient measurements in dry N2 (sixth column from left of Table 1). This was seen before.la Since electron self-exchange rate constants are ideally i n d e ~ e n d e n of t ~ the ~ source of the free energy gradient for electron transfer, the agreement in Table 1 is gratifying. Figure 5 data were also analyzed based on a model presented by Scher and M o n t r ~ l l ,later ~ ~ modified by PfisterZ5 (SMP model), to account for non-Gaussian dispersive transport in electron time-of-flight experiments in xerographic and related transport films. In such experiments, it is common that the advancing front of electrons becomes spread out in a nonGaussian manner,24ba property of disordered solids plausibly attributed to a dispersion of hopping times between donor and acceptor locations, which differ (among other things) in nearestneighbor reactant distances. This model, in notationla consistent with the above, gives
where E meausres the rate constant dispersion ( E = 1 for an ordered material, in which case eq 5 reduces to the classical Marcus relation22),
and is the electronic overlap parameter in the rate-distance relationz6 (7)
In the original t h e ~ r y ,L~ (film ~ , ~ thickness) ~ is a time-scaling factor in a time-of-flight experiment; here, L is approximatedla as the average electron transport distance during one-quarter of a triangular potential sweep at frequencyf, with average electron hop frequency, CTkEx, and hop distance, 6,
Sosnoff et al.
13648 J. Phys. Chem., Vol. 98, No. 51, 1994
TABLE 2: Electron Self-ExchangeRate Constants for Os2+"+ in Poly-[Os(Zn)(vbpy)~]Copolymer Films, Calculated from Electron Conductivitiesat Low Potentials (Eq 9)
6 9 % Os 2.055
-
conc gradient 108, (ohm.cm)-'
electr grad
0x
1.0E-J
-
1.o 0.91 0.69 0.59 0.49
n
s c)
E8
O.OEO
-
a
4.0
-3.0
-2.0
-1.Q
0.0
1.0
2.0
3.0
4.0
voltage bias (v) 2.OE-5
-
1.OE-5 -
-e
h
s c
-1.OE-5
4.OE-7 3.OE-7
-
*
-
2.OE-7 1.OE-7 -
U
I
2.81-14 -1.OE-7
. I
.-E
(ohmvm)-'
k~x1(1 M-'
74 34 3.1
1.9 x 1.1 x 1.7 x 6.6 x 6.6 x
105 105
104 103 103
0.88 0.60
s-l
105 105 104 lo3 lo3
Assumes ideal form of eq 9 (q = 1).
conclude from this comparison of three modes of obtaining the average solid state electron self-exchange rate constant that the results in Table 1 represent a satisfactory determination of how the rate constant of reaction 1 changes with the concentration of Os sites in the copolymer films. It is additionally possiblela to extract electron transfer rates from current-potential curves like those in Figures 4 and 5, based on the i-E slopes in the low potential region, Le., the electron conductivity u,
-
-2.OE-5
z
2.8 x 1.5 1.5 x 5.7 5.6 x
(9)
a
0
. I
kEXlaM-' s-'
x 108,
O.OEO -
b
A
106 46 2.7 0.76 0.51
(5
-2.OE-7
4.OE-7 -
-3.057
-5.OE-7 4OE-7
'
4.0
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
4.0
voltage bias (V) Figure 6. Electrical gradient current-potential curves for %os = 0.69, fitted to eq 4 (top, for which e = 2.4 and kEx = 576 M-' s-*) and eq 5 (middle, for which E = 0.773, L = 61 nm, and kexL'-"' = 21 M-' SKI), Bottom shows residuals between experiment and theory. Film thickness 115 nm.
L=
S2CTkExFdEm, 48fdRT
Examination of this model shows that in eq 5 the dispersive rate constant for electron hopping is the product kEXL1-l". The units of lc~xare M-I s-l cm(l/€-l),a complication discussed by Pfi~ter.~~ Figure 6 (middle) illustrates fitting eq 5 to data obtained at xoS = 0.69. The fit of theory to data, here and at other xoS values, is good with small residuals (Figure 6, bottom). SMP results for k~xLl-l'', L, and E are given in Table 1, right side. The values of k~xL'-"' agree quite well with the and dry N2 concentration gradient results at all values of xes. We
The right-hand side of eq 9 represents the linearized form of the Nerst equation (eq 2), in which the nonideal broadening of the i-E wave is represented by q = g, where g = 0.51. Equation 9 is also the linearized, small 4, form of the Marcus equation (eq 4, in which case q = e). The similarities of the electron conductivities derived from Figures 4 and 5 prompt us to ignore the nonideality term q ;values of kEx thus calculated (Table 2) are in reasonable agreement with those obtained from eqs 3, 4, and 5 (Table 1). Rate-Concentration Dependence. Blauch and Saveantga have recently addressed the relation between electron hopping rates and site concentration for fixed-site redox materials under steady state transport conditions. Using a cubic lattice model, and neglecting other than nearest-neighbor (i.e., long distance) electron transfer, completely immobile sites correspond to a static percolationga situation in which electron transport rates (DE)fall approximately linearly with decreasing site concentration to near-zero rates at the percolation threshold xredox= ca. 0.35. Introducing a microscopic mobility of the fixed sites ("bounded d i f f u ~ i o n " )smears ~~ out the threshold, elevating electron transport rates at concentrations below the threshold. Figure 7 presents the dry N2 kEx rate constant data of Table (0, x, O), and the inset shows these results in the various bathing media as a log plot. The figure additionally displays earlier" (0)electron transport data as electron diffusion coefficients, based on the [Ru(bpy)2(p-~inn)~]~+/[Os(bpy)z(pcinn)2I2+ copolymer; these results are at -25 "C in a CH3CN electrolyte solution. The electron self-exchange rate constants in the present (0, x, 0 ) studies and the electron diffusion coefficients from the previousli (0)study behave similarly (Figure 7) with respect to xoS site concentration. The Table 2 conductivity data, if added to Figure 7, would closely resemble the KEXresults. All of these data, however presented (KEx, DE. or o),exhibit a steeper dependence on site concentration than expected from a static percolation model. All fall to very small values at higher xoSthan the static percolation threshold value. As noted above, bounded diffusionga would elevate rates below the static threshold, not depress them above it. It is apparent that contemporary theory does not yield a satisfactory representation
J. Phys. Chem., Vol. 98, No. 51, 1994 13649
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~inn)2]~+/[Os(bpy)2(p-~inn)2]~+ and [O~(vbpy)3]~+/[Zn(vbpy)31~+ copolymers make it plausible that activation barriers in the latter copolymer are also concentration dependent. That is, the decreases in EX in Figure 7 arise not only from a decreasing electron donor-acceptor site concentration but also from a decreasing reactivity of those sites with one another. This is neither anticipated nor is a part of the percolation model? which presumes a concentration-independent rate constant. We have that the change in reactivity may be associated with the increasing role of the polymer lattice dynamics, as site concentrations are lowered, such as in allowing microscopic motions of sites toward one another precedent to the electron transfer. Alternatively, the microscopic mobility of the matrix surrounding the reacting sites (that provides the fluctuating dipolar environment assisting surmounting of the electron transfer energy barrier)4 may assume a more important role as the average site-site spacing is lowered. These effects are potential sources of concentration-dependent reorganizational energy. We are not aware of available rigid media electron transport theories that incorporate effects of both site concentration and actual site-site reactivity as variables. Ion-pairing interactions are a second possible chemical complication, since the counterion population in a 1:1 mixedvalent copolymer changes with the concentration of redox sites.23bIon pairing should however depend strongly on whether the polymer film is solvent-wetted or dry. The Figure 7 inset shows that, while fluid solvent or solvent vapor-bathed [Os(~bpy)3]~+/[Zn(vbpy)3]~+copolymer lc~xvalues are larger than those in N2-dry films, they exhibit the same dependence on site concentration. We infer that ion pairing is less likely as the source of site concentration dependence in Figure 7. Innersphere barriers associated with ion dipoles could, on the other hand, be responsible for the kinetic differences between wet and dry films. Second, the bounded diffusion model of Blauch and Saveantg is based on a cubic lattice model, but the dispersive nature of the electron transport in the [O~(vbpy)3]~+/[Zn(vbpy)3]~+copolymer strongly suggests that this polymer has a disordered lattice. What are the consequences of disorder? We know little about the detailed microscopic structure of the electropolymerized polymers, except that the Os sites are randomly dispersed. The electropolymerized films accrete by precipitation or adsorption of small polymer clusters as they are formed in the solution layer around the electrode,16 so that the resulting films may contain some voids. More importantly, the precipitated clusters may themselves form a percolation lattice superimposed on the problem of electron percolation within the clusters. Either effect would dilute the population of adjacent electron donor and acceptor sites that exists at any moment and simulate a cubic lattice copolymer with a much smaller xes. The preceding rationales of Figure 7 are obviously speculative. Regardless of their merits, the results of Figure 7 point out real difficulties in delineating the elements of electron transfer rate control in fixed site, mixed-valent polymers and analogous redox materials. The materials that we have prepared, on the macroscopic level being ostensibly ideal isostructurally dilutable redox polymers, prove o n the microscopic scale to retain substantial complexity. Acknowledgment. This research was supported in part by grants from the National Science Foundation and the Office of Naval Research. References and Notes (1) (a) Sullivan, M. G.; Murray, R. W. J . Phys. Chem. 1994,98,4343. (b) Temll, R. H.; Sheehan, P. E.; Long, V. C.; Washbum, S.; Murray, R.
13650 J. Phys. Chem., Vol. 98, No. 51, 1994 W. J. Phys. Chem. 1994, 98, 5127. (c) Surridge, N. A.; Sosnoff, C. S.; Schmehl, R.; Facci, J. S.; Murray, R. W. J. Phys. Chem. 1994,98,917.(d) Sumdge, N. A.; Zvanut, M. E.; Keene, R. F.; Sosnoff, C. S.; Silver, M.; Murray, R. W. J. Phys. Chem. 1992,96,962. (e) Sumdge, N. A.; Keene, F. R.; White, B. A.; Facci, J. S.; Murray, R. W. Inorg. Chem. 1990, 29, 4950. (f) Dalton, E. F.; Surridge, N. A.; Jernigan, J. C.; Wilboum, K. 0.; Facci, J. S.; Murray, R. W. Chem. Phys. 1990, 141, 143. (g) Jernigan, J. C.; Surridge, N. A.; Zvanut, M. E.; Silver, M.; Murray, R. W. J . Phys. Chem. 1989, 93, 4620. (h) Jernigan, J. C.; Murray, R. W. J . Am. Chem. SOC. 1987, 109, 1738. (i) Facci, J. S.; Schmehl, R. H.; Murray, R. W. J. Am. Chem. SOC. 1982, 104, 4959. fj) Chidsey, C. E. D.; Murray, R. W. Science 1986,231, 25. (k) Jernigan, J. C.; Murray, R. W. J . Phys. Chem. 1987, 91, 2030. (2) Majda, M. In Molecular Design of Electrode Surfaces; Murray, R. W., Ed.; Wiley: New York, 1992. (b) Oyama N. In Molecular Design of Electrode Surfaces; Murray, R. W., Ed.; Wiley: New York, 1992. (c) Abkowitz, M. A.; Facci, J. S.; Limburg, W. W.; Yanus, J. G. Phys. Rev. B: Condens. Mater. 1992, 46, 6705. (d) Bommarito, S. L.; Lowerybretz, S. P.; Abruna, H. D. Synlett 1993 (June), 375. (e) Cmmbliss, A. L.; Cooke, D.; Castillo, J.; Wisianneilson, P. Inorg. Chem. 1993, 32, 6088. (f) Facci, J. S.; Abkowitz, M.; Limburg, W.; Kniwer, F.; Yanus, J.; Renfer, D. J . Phys. Chem. 1991, 95, 7908. (g) Facci, J. S.; Stolka, M. Philos. Mag. E 1986,54, 1. (h) Forster, R. J.; Vos, J. G. J . Electrochem. SOC.1992, 139, 1503. (i) Leddy, J.; Bard, A. J. J . Electroanal. Chem. 1985, 189, 203. Q) Abkowitz, M.; Facci, J. S.; Stolka, M. Chem. Phys. 1993, 177, 783. (k) Maidan, R.; Wang, D. L.; Heller, A. Sensors Actuators 1993, 13, 180. (1) Mirkin, M. V.; Fan, F. F.; Bard, A. J. Science 1992, 257, 364. (m) Shu, C.-F.; Wrighton, M. S. J. Phys. Chem. 1988, 92, 5221. (n) Stolka, M.; Yanus, J. F.; Pai, D. M. J. Phys. Chem. 1984, 88, 4707. (3) (a) Lin, R. J.; Onikubo, T.; Nagai, K.; Kaneko, M. J . Electroanal. Chem. 1993, 348, 189. (b) Blauch, D. N.; Saveant, J. M. J. Am. Chem. SOC.1992, 114, 3323. (c) Blauch, D. N.; Saveant, J. M. J . Phys. Chem. 1993,97,6444. (d) Oyama, N.; Tasuma, T.; Takahashi, K. J . Phys. Chem. 1993,97, 10504. (e) Anson, F. C.; Blauch, D. N.; Saveant, J. M.; Shu, C. J . Am. Chem. SOC. 1991, 113, 1922. (f) Buttry, D. A.; Anson, F. C. J . Electroanal. Chem. 1981, 130, 333. (g) Sharp, M.; Lindholmsethson, B.; Lind, E. L. J . Electroanal. Chem. 1993, 345, 223. (4) (a) Ratner, M. A.; Shriver, D. F. Chem. Rev. 1988, 88, 109. (b) Mikkelson, K. V.; Ratner, M. A. Chem. Rev. 1987, 87, 113. (5) p-cinn is N-(4-pyridyl)cinnamide; vbpy is 4-methyl-4'-vinyl-2,2'bipyridine, and bpy is 2,2'-bipyridine. (6) (a) Ham, G. E. In High Polymers Series; Wiley-Interscience: New York, 1964; Vol. 18, Chapter 1. (b) Hiemenz, P. C. Polymer Chemistry; M. Dekker: New York, 1984; Chapter 7. (7) (a) Another isostructural example based on mixtures of molten salt metal complex is under current study. (b) Velbquez, C. S.; Hutchison, J. E.; Murray, R. W. J . Am. Chem. SOC.1993, 115, 7896. (8) Andrieux, C. P.; Saveant, J. M. J. Phys. Chem. 1988, 92, 6761. (9) (a) Blauch, D. N.; Saveant, J.-M. J. Am. Chem. SOC.1992, 114, 3323. (b) Zailen, R. The Physics of Amorphous Solids; Wiley: New York, 1983; Chapter 4. (c) Ratner, M. A.; Nitzan, A. Faraday Discuss. Chem. SOC.1989,88, 19. (d) Blauch, D. N.; Saveant, J.-M. J . Phys. Chem. 1993, 97,6444. (10) Abruiia, H. D.; Breikss, A. I.; Collum, D. B. Inorg. Chem. 1985, 24, 987. (11) Gould, S.; O'Toole, T. R.; Meyer, T. J. J . Am. Chem. SOC.1990, 112, 9490. (12) Meyer, T. J.; Sullivan, B. P.; Casper, J. V. Inorg. Chem. 1987,26, 4145.
Sosnoff et al. (€3) Sosnoff, C. S. M. A. Thesis, University of North Carolina, Chapel, Hill, NC, 1990. (14) Murray, R. W. In Electroanalytical Chemistry; Bard, A. J., Ed.; M. Dekker: New York, 1984; Chapter 2. (15) (a) Albery, W. J.; Boutelle, M. G.; Colby, P. J.; Hillman, A. R. J . Electroanal. Chem. 1982, 133, 135. (b) Leidner, C. R.; Murray, R. W. J . Am. Chem. SOC.1984, 106, 1606. (16) Denisevich, P.; Abrunfia, H.D.; Leidner, C. R.; Meyer, T. J.; Murray, R. W. Inorg. Chem. 1982, 21, 2153. (17) Pickup, P. G.; Kutner, W.; Leidner, C. R.; Murray, R. W. J . Am. Chem. SOC.1984, 106, 1991. (18) The differing cment scales in Figure 1 simply reflect the differences in ra for these particular films. (19) (a) Andrieux, C. P.; Saveant, J.-M. J . Electroanal. Chem. 1980, I l l , 377. (b) Laviron, E. J. Electroanal. Chem. 1980, 112, 1. (20) Saveant, J.-M. J . Electroanal. Chem. 1988, 242, 1. (21) The uncertainties expressed for the data in Table 1 reflect primarily the difficulties of exactly reproducing multiple specimens of these ultrathin sandwiches. However, determination of kEx with a given electrode in a succession of bathing environments produces rather reproducible changes in kEx, so that the relative values of the kEx averages in Table 1 can be reliably compared. (22) (a) Marcus, R. A,; Sutin, N. Biochim. Biophys. Acta 1985, 811, 265. (b) Marcus, R. A. Annu. Rev. Phys. Chem. 1964,15,155. (c) Marcus, R. A. J. Chem. Phys. 1965, 43, 679. (d) Marcus, R. A. Discuss Faraday SOC. 1960, 29, 21. (23) (a) In the electrical gradient measurement, there is no activity gradient of counterions as there was in the concentration gradient measurement. The agreement between results from the two methods suggests that the changing populations of counterions across these f h do not particularly affect the electron transfer rates, at least under steady state conditions. In another redox polymer system,3e evidence was given that changing counterion populations can be important. (b) The steady state conditions mean that no macroscopic counterion migration is required for electron transport, and any mismatch between electron and counterion diffusivity is not of consequence. (24) (a) Scher, H.; Montroll, E. W. Phys. Rev. B 1975, 12, 2455. (b) Bottger, H.; Bryskin, V. V. Hopping Conduction In Solids; VCH Publishers: Deerfield Beach, FL,,1985; pp 218-236. (25) Pfister, G. Phys. Rev. B 1977, 16, 3676. (26) (a) Gamow, G. Z. Phys. 1928, 51, 204. (b) Miller, J. R. J . Chem. Phys. 1972, 56, 5173. (27) Sharply decreasing electron hopping rates can be caused by electroneutrality coupling when transient methods are employed for the measurement.8 We have recentlylC measured counterion diffusion rates directly to demonstrate that the earlier" chronoamperometric data on electron transport tin the [Ru(bpy)z@-~inn)2]~+/[Os(bpy)2@-cinn)~]*+ copolymer was not substantially influenced by the rates of counterion diffusion as had been proposed in a study of electroneutrality coupling.8 (28) Out of concem about resistive electrode-copolymer contacts, and about possible excess poly-[Zn(vbpy)#+ in the layer of polymer immediately adjacent to the electrode surface, electrodes were prepared in which a layer of pure poly-[O~(vbpy)3]~+ (Le., ~ 0 =% 1.0) was deposited on the electrode before deposition of a %os= 0.49 layer. The electron transport properties of such samples were indistinguishable from those prepared solely with a %os = 0.49 layer. (29) Fritsch-Faules, I.; F a u h e r , L. R. J . Electroanal. Chem. 1989,263, 237.
