5102
J. Phys. Chem. 1995, 99, 5102-5110
Effect of Quaternization on Electron Diffusion Coefficients for Redox Hydrogels Based on Poly(4-vin ylp yridine) Atsushi AokiJ Ravi Rajagopalan, and Adam Heller* Department of Chemical Engineering, The University of Texas at Austin, Austin, Texas 78712-1062 Received: September 27, 1994; In Final Form: January 19, I995@
The effect of partial quarternization of pyridine rings on the electron transport characteristics in redox-conducting hydrogels of cross-linked poly(4-vinylpyridine), partially complexed with [Os(bpy)2Cl]+”+, was studied using steady-state voltammetry at interdigitated array (IDA) electrodes. The apparent electron diffusion coefficients, D,,, and their pH dependence were mapped for redox hydrogels varying in the (a) extent of quatemization of their pyridine rings, (b) nature of quatemizing groups, (c) degree of cross-linking, and (d) loading with [O~(bpy)2Cl]+’~+ centers. In gels made with polymers that were not quatemized, high electron diffusion coefficients were observed only when the pyridine rings were protonated. However, in gels made with substantially quatemized redox polymers, high and pH independent electron diffusion coefficients were observed. When one-half of the pyridine rings were quatemized, the electron diffusion coefficients were cm2 s-’. Excessive cross-linking decreased completely independent of pH and reached a value of 3.9 x the electron diffusion coefficients. At a fixed level of quartemization the electron diffusion coefficients increased with the density of redox centers. This increase resulted, however, from the added charge; when the density of electrostatic charge per macromolecule was fixed, i.e., when the degree of quatemization was increased to compensate for a lower loading of redox centers, the electron diffusion coefficients were the same. It was concluded that the rate of electron transport is determined by the segmental motion of the polymer chains in cross-linked redox hydrogels.
Introduction The design of redox hydrogels with high electron diffusion coefficients is of relevance to electrocatalysis and to electrochemical biosensors, where both enhanced electron transport and permeability to water-soluble reactants and products are sought.’ In a previous study,2 it was shown that the apparent electron diffusion coefficient (Dapp) in a redox hydrogel, based on poly(4-vinylpyridine) complexed with Os(bpy)2Cl2, increased upon protonation of the pyridine rings of the redox polymer chains. Because most enzyme electrodes are operated near neutral pH, Le., close to physiological pH, and because the activity of enzymes is pH dependent, we sought redox hydrogels in which D,, is high and pH independent. Here we describe redox hydrogels with pH-independent Dappvalues in excess of cm2 s-l. These are attained by quatemizing the pyridine rings on the poly(4-vinylpyridine) backbone. We find that electron diffusion through the redox hydrogel increases with the fluidity, i.e., the segmental motion of the polymer backbone. We also found that there was no difference in the values of Dappbetween two polymers differing by a factor of 2 in their loading of redox sites as long as the electrostatic charge, resulting from both quatemization and complexation, on the polymer molecule was fixed. Charge propagation through a redox polymer, where redox species are coordinately or covalently fixed on the polymer backbone, is thought to involve three proce~ses,~ Le., a bimolecular electron self-exchange reaction between nearby redox centers (kex),segmental motion of polymer chains leading to electron-transferring collisions, and displacement of counterions required to maintain electroneutrality in a defined spatial element of the polymer layer. These processes have been carefully Resent address: Department of Molecular Chemistry and Engineenng. Faculty of Engineering Tohoku University. Aramaki-Aoba. Aoba-Ku, Sendai 980-77, Japan. Abstract published in Advance ACS Absrracrs. March 15. 1995.
*
0022-365419512099-5102$09.00/0
described by several re~earchers.~-’OAndrieux and Sav$ant8 considered in detail the charge propagation process, taking into account the ionic association between the redox site and the counterion. Fritsch-Faules’ and Blauch12suggest an extended electron transfer process. The rate of electron transport in a redox polymer is controlled by one or more of these processes. An expression for electron diffusion coefficient, D,,, for freely diffusing redox species in solution was derived by D a h m ~and ~ ~Ruff et al.4b3c In this case, the rate of electron transport was enhanced by electron transfer between the oxidized and reduced species in solution. The expression (eq 1) combines terms due to physical diffusion and electron hopping.
+
Dapp= Dphys ke,a2C16 where Dphys is the diffusion coefficient for the physical displacement of the freely diffusing redox species, k,, is the bimolecular rate constant for electron self-exchange, C is the total concentration of redox species, and a is the center-to-center distance between redox centers at the time of electron transfer. Andrieux and SaveanP and Laviron4“ examined the behavior of redox polymer systems in which the redox centers were immobile and where physical diffusion of redox centers did not contribute to electron transport. Their equation was for electron exchange between monolayers of redox polymer and has been taken as the limiting case of eq 1, when Dphys = 0. D,, = k,,a2C/6 Equation 2 predicts that DaPpis proportional to the concentration of redox sites in the redox polymer. For many redox polymers studied previously, this was found to be valid! However, in some redox polymer system^,^^^.'^ the values of Dappincreased more steeply with the concentration of redox sites than predicted by eq 2. This excess increase was explained by the effect of 0 1995 American Chemical Society
J. Phys. Chem., Vol. 99, No. 14, 1995 5103
Redox Hydrogels Based on Poly(4-vinylpyridine)
the redox centers lack macroscopic mobility in the polymer film, but physical displacement of the redox centers around anchoring points is possible; this physical displacement is termed as “bounded diffusion”. In the limiting case, when the displacement of redox centers is rapid and extensive, the expression for D,, becomes
I+
I
POS POs-Me1 POs-Me2 POs-Me3 POs-Me4 POs-Acl POs-Ac3
POs3
Dapp= ke,(a2
R
[OS(bpy)&l]+Cl-
Figure 1. Structure of the redox polymer POs, partially quatemized with the function R. In POs one ring in six is complexed with [O~(bpy)2Cl]+’*+.
TABLE 1: Elemetal Analysis for the PolymeM found
polymer
C
H
N
C1
Os
C
H
N
C1
Os
POs POs-Me1 POs-Me2 POs-Me3 POs-Me4 POS-Acl POs-Acf POs3
61.83 60.30 58.89 57.57 56.36 59.22 55.00 52.49
4.82 4.87 4.91 4.95 4.98 4.78 4.72 4.57
11.63 11.17 10.73 10.33 9.96 11.88 12.27 10.45
5.36 8.49 10.89 13.10 15.16 8.21 11.96 7.56
15.80 15.17 14.58 14.04 13.54 14.67 12.82 20.27
61.33 58.95 58.19 57.70 57.99 57.76 55.34 52.19
3.88 4.49 4.30 4.69 4.05 5.00 5.68 4.47
11.21 10.85 10.64 10.13 10.39 11.49 11.34 10.17
5.90 8.65 10.54 13.26 13.88 7.97 12.75 8.28
18.20 17.07 16.33 15.19 13.67 17.76 14.88 20.24
‘Calculated represents the values assuming complete reaction. electric field,899 ionic association,lo extended electron translocal polymer fluidity,l4,l5and perc01ation.l~Note that eqs 1 and 2 predict linear variation of the apparent diffusion coefficient with the concentration of the redox species. Fritsch-Faules and Faulkner’l and Blauch12 developed a microscopic model based on extended electron transfer describing a system where there is no physical diffusion of redox species. Blauch and Saveant13developed a “bounded diffusion” model to describe the intermediate case between the extremes of freely diffusing and immobile redox centers. In this model,
l
~
*
a
a
.
s
0 0.2 0.4 0.6 Potential, V vs SCE
a
,
I
~
.
0
.
0.2
.
.
0.4
.
S
0.6
Polentlal, V vs SCE
(3)
where A characterizes the amplitude, Le., the range of redox site motion from equilibrium position. This expression was derived neglecting the effects of extended electron transfer, counterion displacement, and ionic association. We use this model to explain our results. Note, however, that this model is still incomplete, since we do not find the linear dependence of D,, on the concentration of redox centers that this model predicts. In the experiments described in this paper, we varied both the redox site concentration and the charge density on the polymer backbone affecting the segmental motion of the polymer chains. Our results suggest, in agreement with the results of Oh and Faulkner16 and Vos and co-workers,17 that the rate of electron transport is determined by the segmental motion of the polymer backbone leading to electron transfer between segments. In contrast with the results expected from eqs 1-3 and their models, we also find that D,, does not increase linearly with the concentration of redox sites; on the contrary, D,, increases even as the concentration of the redox sites decreases. Of the several electrochemical techniques for measuring apparent electron diffusion coefficients of redox polymers, transient electrochemical methods are the most frequently used. The results of the transient methods are, however, difficult to interpret because of variations in the resistance of the redox polymers and the migration of ions.8 The interdigitated array (IDA)-based method, developed by Murray and co-workers,18 for the measurement of D,,, gives results that are easy to interpret, because they are not affected by macroscopic ion migration and because the technique does not demand a knowledge of film thickness andor redox site concentration, parameters that are difficult to determine accurately for the redox hydrogels studied here. Reasonably accurate electron diffusion coefficients can be estimated when the spacing between the fingers, that is gap and finger width, is narrowed down to micron
= 5. n =O, o = 1 = 4, n = 1, o = 1, R = CH3 : m = 3, n = 2, o = I, R = CH3 : m = 2, n = 3, o = 1, R = CH3 : m = 1, n = 4, o = 1, R = CH3 : m = 4. n = 1. o = 1, R = CHzCONH2 : m = Z n =3,o = 1, R = CH2CONH2 : m = 2, n = 0, o = 1 :m :m
calculated
+ 3A2)C/6
,
L
.
6
0
.
0.2
.
*
0.4
.
.
,
0.6
Potentlal, V vs SCE
0
(Dl
0.2
Potentlal, V
0.4 VI
0.6
SCE
(A) (6) (C) Figure 2. Cyclic voltammograms of nonquatemized and partially methyl-quatemized POs: (A) POs (nonquatemized), (B) POs-Me1 (one ring in six quatemized), (C) POs-Me2 (one-third of the rings quatemized), and (D)POs-Me3 (half the rings quatemized). The IDA generator-collector voltammograms are represented by solid lines, and the generator-generator voltammograms are represented by broken lines. The polymers are cross-linked with 10 wt % PEGDGE (20 mM phosphate buffer, pH 7.0, with 0.1 M NaC1; 5.0 mV s-l scan rate).
5104 J. Phys. Chem., Vol. 99, No. 14, 1995
I
Aoki et al.
A- B1 ,
1.0 PA
,
.
--
....
:...I.....
.. . .* . .,.*
-
.. , -..*. .., ... ....-. ._ I
. ' .
collector
,
f
i
0
e
','
a
1
.
.
.
*
t
,
t
&
0
0.2 0.4 0.6 Potential, V VI SCE
I
I
,
*
.
~
,.---
-..:
. ,.
-__.
,...
I .
...*..--
I
I
.
.
I
.
.........
#
I
I
0.2
I
0.4
Polentlal, V
VI
I
I
1
0.6
8
1
SCE
1
1
0.2
0
1
4
Polenllal, V
'
1
0.8
0.4
SCE
VI
(4 (6) (C) Figure 3. Cyclic voltammograms for POs cross-linked with 5 wt % PEGDGE in solutions differing in their pH: (A) pH 7.0, (B) pH 4.0, and (C) pH 2.0. The generator-collector (solid lines) and generator-generator (broken lines) voltammograms were run at 5.0 mV s-I scan rate (20 mM phosphate solutions with 0.1 M NaCl).
dimensions, the arrays are made with a large number of fingers, and the polymer films are either thin enough or not too conductive. In this case, Dappis calculated from eq 4:
4s
4 p p
= -gap(w UQ
N
+ gap)-N - 1
(4)
where Iss is the steady-state current plateau reached in the generator-collector experiment, w is a correction factor for microscopic counterion displacement, Q is the total charge, calculated by the integration of the voltammogram in the generator-generator experiments, N is the number of fingers, and w and gap are the finger and gap widths, respectively. In deriving eq 4, it was assumed that the concentration gradient of the oxidized or reduced species between the generator and collector electrodes is linear. The linearity, however, may be distorted by microscopic counterion displacement and the dependence of the local polymer fluidity on the state of oxidatiodreduction of the redox species. Here we do not correct for nonlinearities in the concentration profiles. Rather, we consider the DqP values that we derive as an average for electron transport over the entire region between the generator and the collector electrodes.
Experimental Section Reagents. The nonquatemized redox polymer used in this study was prepared as described.lg Poly(4-vinylpyridine)(2.939 gj and cis-bis(2,2'-bipyridine-N,K)dichloroosimium(II) (3.38 g) were heated under nitrogen at reflux in 120 mL of ethylene glycol for 1 h. After the solution was cooled to room temperature, the polymer was precipitated by adding ethyl acetate, the solution was then decanted, and the polymer was dried under vacuum overnight. The yield was 6.2 g. Elemental analysis, calculated for poly(4-vinylpyridine) in which one pyridine ring in six is complexed with [Os(bpy)2Cl]+/*+(bpy = 2,2'-bipyridine) and the counterion is C1- is as follows: C, 61.83; H, 4.82; N, 11.63; C1,5.36; Os, 15.80. Found: C, 61.33; H, 3.88; N, 11.21; C1, 5.90; Os, 18.20. This polymer is labeled POs. The quatemization of POs was carried out as previously reported.20 One gram of the poly(4-vinylpyridine) complex of [O~(bpy)2Cl]+'~+ was dissolved in 40 mL of methanol, and to this solution was added an appropriate amount of iodo-
TABLE 2: Correction Factors for Microscopic Counterion Displacement' polymer
n
z
z'
z"
f
w
POS POs-Me1 POs-Me2 POs-Me3 POs-Me4 POs-Ac1 POS-AC~ POs3
1 1 1 1 1 1 1 1
2 2 2 2 2 2 2 2
-1 -1 -1
0 1 1 1 1 1 1 0
0 1 2 3 4 1 2 0
1.114 1.067 1.048 1.037 1.030 1.067 1.048 1.114
-1 -1
-1 -1
-1
n is the number of electrons transferred in the charge propagating reaction; z is the charge on the oxidized redox centers, 2 for (i
[Os(bpy)2Cl]+"+; z' is the number of charges on the C1- counterion; z" has a value of 1 when a pyridine ring is quatemized and 0 when it is not; f is the number of equivalents of quaternized pyridines per repeating unit as defined in Figure 1; w is the calculated correction factor for microscopic counterion displacement.
methane or 2-bromoacetamide. The mixture was heated in a sealed tube (ACE glass) ovemight at 75 "C. The mixture was concentrated, and the polymer was precipitated by dropwise addition to a rapidly stirred solution ethyl ether. The polymer was then dissolved in water, ion exchanged with AG1-4X chloride ion exchange resin, and filtered to remove the resin. The solution was evaporated, and the residue was dried under vacuum ovemight. The structures and nomenclature for the quatemized redox polymers are shown in Figure 1. The elemental analyses are summarized in Table 1. The elemental analyses showed that the quatemizationreactions proceeded until all the quatemizing methyl iodide or bromoacetamide was exhausted, except in the case of POs-Me4. The diepoxide used for cross-linkingthe quatemized POs polymer was poly(ethy1ene glyco1)diglycidyl ether (Polysciences, PEG400). Unless otherwise noted, the experiments were performed in a (pH = 7.0) 20 mM phosphate buffer solution containing 0.1 M NaC1. All chemicals were reagent grade and were used without further purification. Apparatus. A Pine Instruments RDE-4 bipotentiostat with a x-y-y' Kipp and Zonnen recorder was used. The singlecompartment water-jacketed electrochemical cell had Pt auxiliary and saturated calomel electrode (SCE) reference electrodes. The experiments were carried out under N2 at room temperature (20 f 1 "C).
Redox Hydrogels Based on Poly(4-vinylpyridine)
J. Phys. Chem., Vol. 99,No. 14, 1995 5105
5.0 wt%
.-'a
-7.5
-
17-3 n=4
-7.5
A
"5 0 P
'a
n=2
-8
-
n=l
-8
-
4.5
-
sm
0
-8.5
-
20
30
n=O
t
I -Q
1
2
3
4
5
6
7
1
8
2
3
4
5
8
7
8
PH
PH
Figure 4. Variation of the apparent electron diffusion coefficient,Dw, with pH for POs (nonquaternized, solid circles), POs-Me1 (one ring in six quaternized, open circles), POs-Me2 (one-third of the rings quaternized, solid triangles), POs-Me3 (half the rings quaternized,open triangles), and POs-Me4 (two thirds of the rings quatemized, solid squares).5 wt % PEGDGE cross-linked polymers in 20 mM phosphate, 0.1 M NaC1. at 5.0 mV s-I scan rate.
Figure 6. Dependence of the apparent electron diffusion coefficient, D,, on the extent of cross-linking of nonquatemized POs. Conditions are as in Figure 4, except for the weight percent cross-linker in the films,which is shown.
-7.5
-7.5
n=3
A
c
-8
'a
"Eu a P
-8
-
n=l
e
-
-8.5
UI
0
-8.5
-9
n=O
1 -9
2
3
4
5
6
7
8
1 Figure 7. Dependence of the apparent electron diffusion coefficient, PH
1
2
3
4
5
6
7
8
Daw,on the density of redox sites and on the total charge on the cross-
PH
Figure 5. Variation of apparent electron diffusion coefficient, DYp, with pH for POs (nonquatemized,solid circles), POs-Ac1 (one ring m six quatemized with acetamide groups, open circles), and POs-Ac3 (half the rings quaternized with acetamide groups, solid triangles), with conditions as in Figure 4. TABLE 3: Electron Diffusion Coefficients of 5 wt % Cross-Linked Redox Polymer Films in Which a Varying Fraction of the Pyridine Rings Was Quaternized with Methyl Groups, at pH 2.0 and pH 7.0 redox fraction of Dw, cm2 s-l polymer quartemized pyridines 3H 2.0 uH 7.0 POS 016 1.6 x 2.3 x POs-Me1 116 1.6 x 10-8 9.2 x 10-9 POs-Me2 113 3.4 x 10-8 2.2 x 10-8 POs-Me3 112 3.9 x 3.8 x POs-Me4 213 3.3 x 3.2 x ~
IDA Electrodes. The IDA consisted of 200 (N), 2.0 mm long, 5.0 p m wide gold fingers (w),separated by 5.0 pm gaps (gap). A contact pad (2.5 x 2.5 mm2) was connected to each electrode via a lead (11.O mm long x 0.2 mm wide). The entire
linked polymer. POs (nonquatemized, one-sixth of the rings [ 0 s ( b p ~ ) U J +complexed, ~+ solid circles), POs3 (one-thirdof the rings [O~(bpy)~Cl]+~+complexed, open circles), and POs-Me1 (one-sixth of the rings [Os(bpy)~Cl]+~+ complexed, solid triangles). POs3 and POsMe1 have the same electrostatic charge when the osmium centers are reduced (5 wt % cross-linking, conditions as in Figure 4). surface with the exception of the finger and contact pad areas was coated with silicon dioxide. The metalization consisted of titanium primed gold. The IDAs were tested by running cyclic voltammograms in 0.5 mM ferrocenemethanol at a scan rate of 5.0 mV/s. Only the IDAs having theoretically predicted21 voltammogram shapes, steady-state currents, and the collection efficiencies were used. The IDAs were coated by pipetting 0.5 p L aliquots of the variously modified POs polymer solutions (5.0 mg/mL) and the selected volume of the PEGDGE solution (2.0 mg/mL) onto both the finger and the internal gap areas and then allowing the water to evaporate at room temperature. The electrodes were then left to cure in air at room temperature for 24 h. The generator-collector and the generator-generator voltammograms were run as describeda2 In the generator-collector
5106 J. Phys. Chem., Vol. 99, No. 14, 1995
Aoki et al.
Redox Hydrogels Based on Poly(4-vinylpyridine).
J. Phys. Chem., Vol. 99, No. 14, 1995 5107
Figure 8. Scanning electron micrographs showing the swelling of the redox polymers POs-Me1 (a) and POs-Me3 (b) in water. The film thickness under dry (left) and swollen (right) conditions are shown. POs-Me1 was cross-linked with 10 wt % PEGDGE, and POs-Me3 was cross-linked with 5 wt % PEGDGE. The images were obtained with an environmental scanning electron microscope (ESEM). The water vapor pressure of the chamber was maintained between 2.0 and 4.5 Torr and is indicated by the fourth number at the bottom of the micrographs.
5108 J. Phys. Chem., Vol. 99, No. 14, 1995
experiments, the cyclic voltammograms were obtained by scanning the potential of the generator from 0.0 V (SCE) to 0.6 V (SCE) at various scan rates, while maintaining the potential of the collector at 0.0 V (SCE). At steady state, a concentration gradient of oxidized (or reduced) osmium centers is set up between the generator and the collector electrodes, which translates into a steady state current (Iss)that is measured at both the generator (oxidation current) and collector (reduction current) electrodes. A well-defined steady state current was measured for all polymers except POs, where the electron diffusion rate and thus the currents were small. The current at 0.6 V was used to determine Dapp.In the generator-generator experiments, the voltammograms were obtained by simultaneously scanning the potentials of IDA finger pairs from 0.0 V (SCE) to 0.6 V (SCE) at various scan rates. The anodic areas of the generator-generator voltammograms were integrated to calculate the charge ( Q ) in the redox polymer film. Imaging of the Swelling in the Cross-Linked Redox Hydrogels. Environmental SEM (ESEM) was used to determine the swelling of the redox hydrogels. The cross-linked redox hydrogel was cast on a glass slide using 5.0 p L aliquots of a 5.0 mg/mL solution of the redox polymer and a selected amount of PEGDGE solution (2.0 mg/mL). The film was allowed to cure at room temperature for 24 h. The slide was then scribed and broken to expose a vertical section of the polymer film. This section was examined by SEM, the chamber of which was maintained between 2.0 and 4.5 Torr water vapor pressurc;. The instrument was described by Danilatos.22 After measuring the thickness of the ‘‘dry‘’ f i i s , the film was hydrated with drops of water, and the swollen film thickness was measured after the 45 s pump-down of the environmental SEM. Hence, some of the water may have evaporated, and the actual thickness of the fully swollen films may have been greater than the values reported here. Results and Discussion Voltammetry of the Quaternized POs Polymer Based Hydrogels. Cyclic voltammograms for POs polymers quaternized to differing degrees with methyl groups, as measured with IDA electrodes, are shown in Figure 2. The voltammograms were normalized by dividing the currents by the coulometrically estimated osmium coverage. The voltammograms of the generator-collector experiments are shown as solid lines and those of the generator-generator experiments as broken lines. The steady state currents in the generator-collector experiment represents the oxidation of [Os(bpy)zvpyCl]+ at the generator, the transport of electrons across the gap through the redox polymer, and the reduction of [Os(bpy)2~pyCl]~+ at the collector. The limiting currents obtained at the generator and collector were identical, indicating the establishment of a steady state concentration profile of the redox species between the generator and collector electrodes. At the employed sweep rate of 5.0 mV s - l , steady state concentration profiles of the redox centers were not established except at the limiting currents; this led to a difference between the forward and the backward potential sweeps at the collector electrodes. Experiments by FritschFaules and Faulkner14 and Goss and Majda15 show the local diffusion coefficient to be a function of the local fluidity of the redox species. The concentration profile developed between the generator and the collector becomes nonlinear when the charge propagation through redox polymer is influenced by hydrophobic interactions between the redox species or when electrostatic interaction between the redox species and counterion becomes significant. This could lead to nonuniform electron diffusion coefficients through the polymer film. As indicated
Aoki et al. earlier, we ignore such effects and calculate only an average Dapp for the entire polymer film. Quatemization of the polymers decreased the concentration of redox sites in the film because swelling increased with the extent of quatemization,as will be discussed later. Nevertheless, it is apparent that the segmental motion of the polymer increased with swelling. In terms of eq 3, , Iincreases with swelling. This increased the rate of effective electron-transfemng collisions between chain segments in the swollen matrix, more than compensating for the decrease in the density of redox sites. D,, increased rather than decreased when the concentration of redox sites was reduced upon the swelling of the films. The voltammograms in the generator-generator experiments exhibited well-defined surface waves at both IDA electrodes and were almost symmetricalz3except in the case of the POs (Figure 2A). D,, of this polymer was very low, and at high sweep rates, the voltammogram exhibited diffusional tailing. The voltammogram, however, became symmetrical at slow sweep rates, indicating a surface wave. Cyclic voltammetry c o n f i i e d that the [Os(bpy)zvpyCl]+centers were completely oxidized both on the fingers and in the internal gaps The contribution of microscopic displacement of the countenon to current ( w ) was estimated using Saveant’s theory9 as follows: 2
0
=
2
zn‘ [- y1F + (yo + y1 + l)(y, - 7,) - YOYl In;]
(5)
where n is the number of electrons transferred in the charge propagation reaction (1 in our case), z is the number of charges of the oxidized form for [Os(bpy)~vpyCl]+/~+ (2 in our case), z’ is the number of charges on the mobile counterion (-1 for Cl-), zff is the number of charges of the counterion fixed in the redox polymer (1 in our case, the charge on the N atom of the pyridine due to quaternization), a n d f i s the number of equivalents of quatemized pyridine molecules per repeat unit as defined in Figure 1, which varied with the extent of quatemization. The values of w for the quatemized redox polymers are summarized in Table 2. Using Zss, Q and w , DaPpwas calculated by eq 4.It is seen that w decreased with quatemization, but the effect of w on Dap, is small even in the nonquatemized POs polymer. Increasing the extent of quaternization reduced the contribution of the microscopic counterion displacement to the current response, increasing the value of D,. Dependence of D., on pH. In Figure 3, cyclic voltammograms of the redox polymer, POs, are shown at pH 7.0, 4.0, and 2.0. The generator-collector voltammograms (solid lines) depend strongly on the solution pH. This pH effect on Dapp mirrored the effect of quatemization. Lowering of the pH led to the protonation of the pyridine rings and increased D,,, in close resemblance with the effect of the added positive charge on the backbone upon quatemization of the rings. The generator-generator voltammogram exhibited a distorted surface wave at pH 7.0 because of interaction between redox but shifted to a well-defined surface wave as the pH was lowered. As proposed earlier,z protonation caused swelling of the film. This led to an increase in the distance between redox sites and hence to lesser interaction between the sites. The variation of D,,, with pH for polymers with varying fractions of methyl-quarternized pyridine rings is shown in Figure 4. At pH 7.0, DaPpdepends on the extent of quaternization. While Dappwas a function of pH in the case of non-
Redox Hydrogels Based on Poly(4-vinylpyridine) quartemized POs, and remained pH dependent for polymers with a low degree of quatemization (POs-Me1 and POs-Me2), it increased with increasing quartemization and became pH independent when l/2 to 2/3 of the pyridine rings were quartemized with methyl groups (POs-Me3 and POs-Me4). Thus, both quartemization and protonation enhanced the rate of collisional charge transfer between chain segments. However, only quatemization led to a high D,, value across the entire 2.0-7.0 pH range. The D,, values are summarized in Table 3. The Dappvalue for POs-Me3 was almost identical to that of cmz s-l, the maximum for our series. POs-Me4 near 3.9 x In order to assess whether the increase in Dappwas unique for quatemization by methyl groups, quatemization by the larger acetamide groups was studied. The results, similar to those with methyl groups, are shown in Figure 5. Dappincreased with quatemization, its highest value being only marginally smaller than that observed with methyl groups. Dependence of Dappon Cross-Linking. The dependence of D,, on the weight fraction of cross-linker in the film for nonquatemized POs is shown in Figure 6. At pH 7.0 the Dapp did not vary significantly with the extent of cross-linking. Evidently, in the case of the redox polymer that was neither protonated nor quatemized, the rate of charge propagation was low and was not influenced by the extent of cross-linking. However, at pH 2.0, where the polymer was protonated, Dapp decreased with the extent of cross-linking. At very high crosslinking, Dappremained low and almost independent of pH. The results show that high values of Dappare difficult to attain at excessive cross-linking. Increasing the extent of cross-linking lowers the fluidity of the polymer, i.e., makes the polymer more rigid. A, in eq 3, becomes smaller as the extent of cross-linking is increased. Note here that cross-linking by epoxidation quatemizes the pyridine rings.25 Evidently, the favorable effect of such quatemization is more than negated by the reduced fluidity of the polymer chains. Dependence of Dsppon Osmium Loading. The effect of redox center loading on Dappwas studied by comparing D,, for POs with that of POs3, a poly(4-vinylpyridine)polymer with l/3 pyridine rings complexed with O~[(bpy)2Cl]+’~+. Plots of the dependence of Dappon pH for POs, POs3, and POs-Me1 polymers are shown in Figure 7. D,, increased with the loading of redox sites, consistent with the predictions of eqs 1-3. However, an increase in the loading of the redox sites also led to an increase in the charge on the polymer backbone. Though the loading of POs3 was twice that of POs, the total charge on reduced POs3 was also twice that on POs. In order to distinguish between the effects of charge and redox center loading on Dapp,the D,, values for POs, POs3, and POsMe1 were compared. POs3 and POs-Me1 have the same electrostatic charge, but the loading of redox sites in POs3 is about twice that on POs-Mel. As seen in Figure 7, when the polymers were not substantially protonated, (pH L 4.0), the Daw values of POs3 and POs-Me1 were nearly identical. At pH 2.0, the Dappvalues for all the three polymers converged. It is therefore concluded that in the redox hydrogels, at the redox center loadings studied here, the electrostatic charge on the polymer backbone rather than loading of redox sites determines the value of Dapp. The hydrogels differ in this respect from the very highly cross-linked electropolymerized po1y[M(bpy)z(vpy)2l2+ (M = Ru, Os, Fe) polymers studied by Murray and co-workers.26In the latter, segmental motion was severely restricted, and electron hopping by self-exchange along the redox polymer chains
J. Phys. Chem., Vol. 99,No. 14, 1995 5109
determined Dapp, unlike the systems in this paper. Therefore, D,, depended on the concentration of redox sites in the polymer. Dependence of the Hydrated Film Thickness on Quaternization. Figure 8 shows the film thickness, both dry and hydrated, for the redox polymers POs-Me1 and POs-Me3. The highly quatemized POs-Me3 hydrogel swells considerably to 50 times its original thickness (-4.0 p m dry vs >250 pm when swollen), whereas POs-Me1 swells only to -2.2 times its dry thickness (-2.5 p m dry vs -5.5 p m when swollen). The swelling of POs-Me3 films was apparent to the naked eye, which was not the case with POs-Mel. The extent of swelling correlates very well with the extent of quatemization.
Conclusions Electron transport through cross-linked redox hydrogels is significantly increased upon increasing the charge density of the polymer backbone. This increases the swelling of the hydrogels, decreases the concentration of the redox centers, and facilitates the motion of the polymer chain segments, leading to an increase in the rate of the electron transferring collisions between the segments. At the redox center loadings considered, the rate of electron transport was a stronger function of the charge density and segmental motion than of the distance between redox centers. When about half the pyridine rings were quartemized, D,,, reached a value of 3.9 x cm2 s - l and became pH independent. The quatemized redox hydrogels, in which electrons diffuse more readily, are likely to lead to higher current density enzyme electrodes and thus to their further miniaturization.
Acknowledgment. This work was supported by the National Institutes of Health (No. 1 RO1 DK42015-01Al), Office of Naval Research, and the Welch Foundation. We thank Dr. Ling Ye for help in the fabrication of the IDAs and for providing the POs3 polymer and both Dr. Ling Ye and Dr. Ioanis Katakis for very useful discussions. We also thank Dr. Jeffrey Hubbell for suggestingEnvironmental SEM as a technique for measuring swelling in cross-linked redox hydrogels, Dr. J. M. White for use of the Environmental SEM, and Jeff Armstrong for the swelling measurements. References and Notes (1) (a) Heller, A. J. Phys. Chem. 1992,96,3579 and references therein. (b) Rajagopalan, R.; Ohara, T.; Heller, A. In Polymeric Materials in Biosensors and Diagnostics; Usmani, A., Akmal, N., Eds.; ACS Symposium Series 556; American Chemical Society: Washington, DC,1994. (c) Ohara, T. J.; Rajagopalan, R.; Heller, A. Anal. Chem. 1994, 66, 245 1. (2) Aoki, A.; Heller, A. J. Phys.Chem. 1993, 97, 11014. (3) Majda, M. Dynamics of Electron Transport in Polymeric Assemblies of Redox Centers. In Molecular Design of Electrode Surjaces; Murray, R. W., Ed.: Techniques in Chemistry; Wiley: New York, 1992; p 159. (4) (a) Dahms, H. J. Phys. Chem. 1968, 72,362. (b) Ruff, I.; Friedrich, V. J. J. Phys. Chem. 1971, 75, 3297. (c) Ruff, I.; Friedrich, V. I.; Demeter, K.; Csaillag, K. J. Phys. Chem. 1971, 75,3303. (d) Andrieux, C. P.; SavCant, J. M. J. Electroanal. Chem. 1980, 111, 377. (e) Laviron, E. J. Electroanal. Chem. 1980, 112, 1. ( 5 ) Facci, J. S.; Schmehl, R. H.; Murray, R. W. J. Am. Chem. SOC. 1982, 104, 4959. (6) Surridge, N. A.; Sosnoff, C. S.; Schmehl, R.; Facci, J. S.; Murray, R. W. J. Phys. Chem. 1994, 98, 917. (7) Forster, R. J.; Vos, J. G. Langmuir 1994, 10, 4330. (8) Andrieux, C. P.; SavCant, J. M. J. Phys. Chem. 1988, 92, 6761. (9) (a) SavCant, J. M. J. Electroanal.Chem. 1988, 242, 1. (b) SavCant, J. M. J. Electroanal. Chem. 1987, 238, 1. (10) (a) Anson, F. C.; Blauch, D.N.; SavCant, J. M.; Shu, C.-F. J. Am. Chem. SOC. 1991, 103, 1922. (b) Sadant, J. M. J. Phys. Chem. 1988, 92, 4526. (c) SavCant, J. M. J. Phys. Chem. 1988, 92, 1011. (1 1) Fritsch-Faules, I.; Faulkner, L. R. J. Electroanal.Chem. 1989,263, 237. (12) Blauch, D. N.; SavCant, J.-M. J . Phys. Chem. 1993, 97, 6444.
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