Effect of Quaternization of the Glucose Oxidase “Wiring” Redox

Feb 29, 1996 - Electrochemical Glucose Sensors and Their Applications in Diabetes Management. Adam Heller , and Ben .... Electroanalytical Application...
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J. Phys. Chem. 1996, 100, 3719-3727

3719

Effect of Quaternization of the Glucose Oxidase “Wiring” Redox Polymer on the Maximum Current Densities of Glucose Electrodes Ravi Rajagopalan, Atsushi Aoki,† and Adam Heller* Department of Chemical Engineering, The UniVersity of Texas at Austin, Austin, Texas 78712 ReceiVed: July 28, 1995; In Final Form: NoVember 1, 1995X

Redox polymers based on the poly(vinylpyridine) complex of [Os(bpy)2Cl]+/2+ were quaternized with methyl iodide, and the quaternized polymers were used to “wire” glucose oxidase. Quaternization enhanced both the rate of electron transport in cross-linked redox hydrogels containing glucose oxidase and the strength of the electrostatic complex formed between the polycationic redox polymer and the polyanionic glucose oxidase. Quaternization with methyl groups also decreased the number of pyridine rings available for cross-linking by the water soluble cross-linker poly(ethylene glycol) diglycidyl ether. The current densities of glucose electrooxidation increased with the degree of quaternization of the “wires” until one-third of the pyridine rings were quaternized, and the activation energies decreased until one-half of the rings were quaternized.

Introduction Glucose electrodes based on the “wiring” of glucose oxidase (GOX) via redox hydrogels based on poly(vinylpyridine)1,2 and poly(vinylimidazole)3-6 have no leachable components, do not require oxygen for their operation, and have been subcutaneously implanted.7-9 In the case of glucose oxidase, where the active centers are deeply buried within an insulating protein shell,10,11 the formation of an electrostatic complex between the redox polymer and enzyme in the gel was found to enhance the electrical communication between the two. The rate of electron transport through cross-linked redox hydrogels is controlled by segmental motion of the polymer chains.12 It was significantly enhanced upon increasing the charge density on the backbone of the polymer “wires” through quaternization of the pyridine nitrogens. Here, we extend the study of the effect of increased charge density on the polymer backbone, and the resulting enhancement in the rate of electron transport,12 to actual glucose electrodes. Figure 1 shows schematically the steps in the transduction of the concentration of the analyte into a current in “wired” enzyme electrodes. These are

analytebulk f analytehydrogel

(1)

Eox + analyte f Ered + product

(2)

Ered + relayox f Eox + relayred

(3)

relayred + relayox f relayox + relayred

(4)

relayred f relayox + e-

(5)

In the above scheme, E represents the enzyme and “relay” represents an electron relaying center of the hydrogel. The analyte partitions into the cross-linked redox polymer-enzyme hydrogel (eq 1) and is oxidized by the enzyme (eq 2), which in turn is oxidized by the redox centers (eq 3). The electrons are transported to the electrode by a self-exchange reaction in the cross-linked polymer/enzyme film (eq 4). This electron trans† Present address: Department of Molecular Chemistry and Engineering, Faculty of Engineering, Tohoku University, Aramaki-Aoba, Aoba-Ku, Sendai 980-77, Japan. X Abstract published in AdVance ACS Abstracts, January 15, 1996.

0022-3654/96/20100-3719$12.00/0

Figure 1. Schematic representation of the “wired” enzyme electrode. Ered and Eox are the reduced and oxidized forms of the enzyme; Dapp, Dp, and Ds, the diffusion coefficients of electrons, product, and substrate, respectively. Dpb and Dsb refer to the bulk phase. Rox and Rred are the oxidized and reduced forms of the relays.

port is represented by an electron diffusion coefficient. Finally, the reduced relay centers at the electrode surface are oxidized (eq 5), and this oxidation is measured as a current. One or more of the above reactions (eqs 1-5) determine the overall rate, and hence the current densities and the activation energies. The rate-limiting step for “wired” enzyme electrodes varies with the composition of the hydrogels on the electrodes and their operating environment. Under some conditions, diffusion of electrons away from the enzyme reaction center contacting the relay of the hydrogel is rate determining.2 In this case, only one or, at most, a few redox centers approach the active center in the enzyme, and these redox centers constitute a point source of electrons. The observed linear increase in current densities with film thickness was invoked to discount the possibility that, in thin hydrogel films, glucose and/or electron transport was rate limiting. The activation energy for electron diffusion in the hydrogel formed by crosslinking poly(4-vinylpyridine) complexed with [Os(bpy)2Cl]+/2+ and partially quaternized with ethylamine functions, POsEA, as measured by chronoamperometry, was about 62 kJ mol-1, practically identical to the activation energy for glucose electrooxidation at high concentrations.1,2 This suggested that a process involving the diffusion of electrons in the hydrogel was rate limiting. Activation energies of the electron diffusion current through the hydrogels, in the absence of glucose or glucose oxidase, as measured by the interdigitated array (IDA) method, yield lower values of 38 kJ mol-1 for POsEA and 36 kJ mol-1 for redox hydrogels derived from poly(vinylimida© 1996 American Chemical Society

3720 J. Phys. Chem., Vol. 100, No. 9, 1996 zole).13 The steady state IDA method provided more relevant activation energies because, in actual sensors, the concentration of glucose is transduced into a steady state current. This gave cause for further examination of the suggestion that in thin enzyme-rich films, and at high glucose concentrations, electron diffusion from a point source is rate limiting. Katakis and Hauser,14 following Leypold and Gough,15-19 solved analytically coupled differential equations for the transport and reaction rates in “wired” enzyme electrodes for the limiting case of low enzyme loading and thin sensing films. Experiments confirmed that when the sensing film was sufficiently thin and the enzyme loading was low, the transfer of electrons from the active center of the enzyme to the redox center on the polymer constituted the rate-limiting step. In the case of glucose electrodes, an electrode with less than 10 wt % glucose oxidase, and with less than 70 µg cm-2 of total immobilized solids, operated in this kinetically limited regime. The rate-limiting steps for cases of more practical interest, i.e. thicker electrodes with high enzyme loadings, were not determined. “Wired” enzyme electrodes exhibit a maximum in current density as the enzyme loading is increased. The maximum lies at about 40 wt % GOX for POsEA-based redox hydrogels,2 at 40 wt % GOX for redox hydrogels based on poly(vinylimidazole) (PVI) complexed with [Os(bpy)2Cl]+/2+, and at 12 wt % for PVI complexed with [Os(dme-bpy)2Cl]+/2+.4 To explain this maximum, Surridge et al.20 proposed that the kinetics of electron transfer from the enzyme active center to the redox centers on the “wire” is rate limiting at enzyme loadings in the domain where the value of the current density in the plateau reached at high glucose concentration, jmax, increases with the enzyme loading; the transport of electrons through the crosslinked redox hydrogels takes over as the rate-determining step at high GOX loadings, where jmax decreases with the enzyme loading. Equations 1-5 can be used to analyze the effects of an increased charge density on the polymer backbone on current densities obtained from “wired” glucose electrodes. Equation 1 relates to the partitioning of the analyte from the bulk solution into the redox hydrogel. Increasing the charge density on the polymer backbone makes the redox polymers, and hence the enzyme-immobilized redox hydrogel, more hydrophilic, enhancing the partitioning and permeation of hydrophilic analytes such as glucose. Equation 2 defines the intrinsic kinetics of the enzyme, a parameter that is unlikely to be affected by the nature of the polymeric “wire”. Equation 3 represents the transfer of electrons from the active center of the enzyme to the redox centers on the polymer. It has been postulated by Degani and Heller21 and shown by Katakis, Ye, and Heller22 that the formation of an electrostatic complex between the redox polymer and an enzyme such as glucose oxidase,10,11 whose active site is insulated by a protein shell, enhances electrical communication between the two. The efficiency of electrical communication correlates with the strength of the electrostatic complex. Increasing the charge density on the polymer backbone increases the strength of the electrostatic complex between the polymer and the polyanionic glucose oxidase and thus the glucose electrooxidation rate, i.e. the current density. Equation 4 represents the transport of electrons through the enzymeimmobilized redox polymer film. The increase of charge density on the polymer backbone was also shown to increase the rate of electron transport through cross-linked redox polymer films.12 In all of these studies, poising the electrode at a sufficiently oxidizing potential relative to that of the electron relay on the

Rajagopalan et al. polymer ensured that the electrooxidation of the relays (eq 5) was not rate limiting. In summary, the rates of three of the five steps in the electrooxidation of glucose on a redox hydrogel modified electrode are enhanced upon increasing the extent of quaternization, and the remaining two steps are unaffected. We expected, therefore, that the current density will increase with the extent of quaternization. However, our cross-linking reaction, whereby pyridine nitrogens are reacted with a diepoxide, also quaternizes the polymer. Beyond a certain degree of quaternization, further quaternization becomes slow and difficult. Hence, the heavily quaternized redox polymers were poorly cross-linked under conditions where the enzyme was not damaged. When the cross-linking i.e. immobilization of the enzyme polymer complex on the surface, was inadequate, part of the enzyme, polymer, or both dissolved off the rotating electrodes. There existed, therefore, an optimum extent of quaternization, at which persistent maximum current densities were obtained in electrodes rotating at 1000 rpm. Measurement of Electron Diffusion Coefficients in Crosslinked Redox Polymer Films. Transient techniques are frequently used in determining the rate of electron transport in redox polymer films. The results of the transient techniques are, however, difficult to interpret because of variations in the resistance of the redox polymer films and migration of ions.23 Results obtained with interdigitated array (IDA) electrodes, developed by Murray and co-workers, for the measurement of the electron diffusion coefficient, Dapp, are easier to interpret, because they are not affected by macroscopic ion migration and because the technique does not demand accurate knowledge of the film thickness or of the redox center concentration in the polymer films.24-28 We have found that highly quaternized redox polymers may swell to approximately 50 times their original volume in water.12 Swelling can drastically reduce the concentration of the electron-relaying redox centers in the hydrogels. Incorporation of glucose oxidase also affects the swelling. We found it most difficult to measure accurately the wet film thicknesses of swollen redox hydrogels. Surridge et al. measured dry film thicknesses of redox polymer films containing immobilized enzyme by step profilometry.20 For a constant amount of polymer, they found little variation in the film thickness with increasing enzyme loading. It remained uncertain, however, whether dry film thicknesses can be used to predict the thickness of swollen films, because swelling also depended on cross-linking, acidity, ionic strength, and other parameters. Through the use of the IDA electrode measurements, electron transport rates in cross-linked redox hydrogels can, however, be measured.12,29 Reasonably accurate estimates of the electron diffusion coefficients can be made when the spacing between the fingers, that is, the gap and finger width, is narrowed to micron dimensions, the arrays are made with a large number of fingers, and the polymer films are either thin enough or not more conductive than about 0.1 Ω cm. In this case, Dapp is calculated from eq 6:

Dapp )

Iss N gap (w + gap) ωQ N-1

(6)

where Iss is the steady state current plateau reached in the generator-collector experiment, ω is a correction factor for the microscopic counterion displacement,30,31 w and gap are the finger and gap widths, respectively, Q is the charge on the IDA as measured by integrating the anodic current of a cyclic voltammogram at a scan rate of 1 mV s-1, and N is the number of fingers on the IDA.12 In deriving eq 6, it was assumed that

Maximum Current Densities of Glucose Electrodes

J. Phys. Chem., Vol. 100, No. 9, 1996 3721 for poly(4-vinylpyridine) in which one pyridine ring in six is complexed with [Os(bpy)2Cl]+/2+ and the counterion is Cl- is C, 61.83; H, 4.82; N, 11.63; Cl, 5.36; Os, 15.80. Found: C, 61.33; H, 3.88; N, 11.21; Cl, 5.90; Os, 18.20. This polymer is labeled POs. The quaternization of POs was carried out as previously reported.12,32 One gram of poly(4-vinylpyridine) complex of [Os(bpy)2Cl]+ (bpy ) 2,2′-bipyridine) chloride was dissolved in 40 mL of ethanol, and to this solution was added an appropriate amount of iodomethane. The mixture was heated in a sealed tube overnight at 75 °C. The mixture was then concentrated by evaporating part of the ethanol, and the polymer was precipitated by dropwise addition to a rapidly stirred solution of ethyl ether (2 L). 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 then evaporated, and the residue was dried under vacuum overnight. The structures and nomenclature for the quaternized redox polymers are shown in Figure 2. The elemental analyses, summarized in Table 1, showed that the quaternization reactions proceeded until all the quaternizing methyl iodide was exhausted. The diepoxide used for cross-linking the quaternized POs polymer was poly(ethylene glycol) diglycidyl ether (Polysciences), PEGDGE. Unless otherwise noted, the experiments were performed in a (pH ) 7.0) 20 mM phosphate buffer solution containing 0.1 M NaCl. All chemicals were reagent grade and were used without further purification. Apparatus. A Pine Instruments RDE-4 bipotentiostat with an 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 argon. Electrochemistry. Electrochemistry was performed on 3 or 4.6 mm diameter glassy carbon (V-10 vitreous carbon 3 mm rods from Atomergic) electrodes. Electrochemical cells were conventional three-electrode cells with an SCE reference electrode and a Pt counter electrode enclosed in a Teflon sleeve with a Vycor tip. Cells were thermostated at 21.3 ( 0.1 °C unless otherwise stated. Electrodes were polished on four grades of alumina slurry (20, 5, 1, and 0.3 µm) with sonication and rinsing between grades. They were pretested in the electrolyte solution by scanning between potentials of interest (-50 to 500 mV vs SCE) to ensure that in this region the voltammograms were featureless. A Princeton Applied Research (PAR) 173 or 273 potentiostat interfaced to an IBM PC controlled with PAR M270 software or a PINE bipotentiostat with a Kipp and Zonnen x-y-y′ recorder was used depending on the experiment. Rotating electrodes, encased in Teflon, were fitted on an AFMSRX rotator from PINE Instruments. The electrochemical cells were of various configurations, usually of 50-100 mL capacity. Modified electrodes were prepared by depositing sequentially on the electrode surface appropriate aliquots of the redox polymer solution (5 mg mL-1), glucose oxidase solution in 10 mM HEPES buffer (2 or 5 mg mL-1), and PEGDGE dissolved in deionized water. The solutions were mixed, the water was allowed to evaporate, and the films were cured on the electrode surface at ambient temperature for 24 h. The total amount of

Figure 2. Structure of the redox polymer POs, partially quaternized with the function R. In POs, one ring in six is complexed with [Os(bpy)2Cl]+/2+.

the concentration gradient of the oxidized or reduced species between the generator and the collector electrodes is linear. The linearity, however, may be distorted because of macroscopic counterion displacement and the dependence of the local polymer fluidity on the state of oxidation/reduction of the redox species. The coimmobilization of polyanionic glucose oxidase in the polycationic redox polymer network of the hydrogel, in all likelihood, gives rise to local variations in the fluidity of the redox polymer chains because of electrostatic cross-linking of the polymer by the enzyme. We do not, however, correct for nonlinearities in the concentration gradients or local variations in polymer fluidity; rather, we consider the Dapp values that we derive as an average for electron transport over the entire region between the generator and the collector electrodes. The microscopic correction factor is usually negligible and is taken to be unity. Glucose electrooxidation currents are measured for the various “wires” at different enzyme loadings. The curves are plotted as Eadie-Hofstee plots, and the values of jmax, the current density at infinite glucose concentration, and the apparent Michaelis constant, Ks, are obtained from the plots. In this study, the activation energies, Eact, for glucose currents are measured in the temperature range 10-40 °C. The efficiency of the different polymers in “wiring” glucose oxidase is related to the parameters jmax, Ks, and Eact, and the trend in the electron diffusion coefficients is qualitatively compared to the trends in jmax and Ks. Experimental Section Reagents. The nonquaternized redox polymer used in this study, poly(4-vinylpyridine) partially complexed with [Os(bpy)2Cl]+/2+, was prepared as described earlier.1,12 Poly(4-vinylpyridine) (2.939 g) and cis-bis(2,2′-bipyridine-N,N′)dichloroosmium(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 the solution to ethyl acetate (4 L). The supernatant liquid was then decanted, and the polymer was dried under vacuum overnight. The yield was 6.2 g. Elemental analysis, calculated TABLE 1: Elemental Analysis for the Polymers calculated

found

polymer

C

H

N

Cl

Os

C

H

N

Cl

Os

POs (C62H58N10Cl2Os1) POs-Me1 (C63H61N10Cl3Os1) POs-Me2 (C65H64N10Cl4Os1) POs-Me3 (C65H67N10Cl5Os1)

61.83 60.30 58.89 57.57

4.82 4.87 4.91 4.95

11.63 11.17 10.73 10.33

5.36 8.49 10.89 13.10

15.80 15.17 14.58 14.04

61.33 58.95 58.19 57.70

3.88 4.49 4.30 4.69

11.21 10.85 10.64 10.13

5.90 8.65 10.54 13.26

18.20 17.07 16.33 15.19

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Rajagopalan et al.

Figure 3. Collector cyclic voltammograms of POs-Me3 at (A) 0 wt % GOX, (B) 40 wt % GOX, and (C) 70 wt % GOX. The films were crosslinked with 10 wt % PEGDGE and the collector poised at 0 V (SCE). Reduction current is seen at the collector. The generator-generator (broken lines) and generator-collector (solid lines) cyclic voltammograms were run at 5 mV s-1 (20 mM phosphate buffer, 0.1 M NaCl, and in air).

material deposited was varied in the experiments. The crosslinker used was 10% by weight of the combined amounts of the polymer and the enzyme. The electrodes were rotated in buffer for at least 30 min before use. Quasi steady state cyclic voltammograms, i.e. voltammograms at 1 mV/s, were taken for each electrode, and the currents were integrated to determine the amount of electrooxidizable/electroreducible polymer on the electrode. Current integration to obtain the charge was performed with the PAR M270 software. IDA Electrodes. The IDA consisted of 200 (N), 2.0 mm long, 5.0 µm wide gold fingers (w), separated by 5.0 µm gaps (gap). A contact pad (2.5 mm × 2.5 mm) was connected to each electrode via a lead (11.0 mm long × 0.2 mm wide). The entire 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 predicted33-35 voltammogram shapes, steady state currents, and the collection efficiencies were used. The IDAs were coated by pipetting 0.5 µL aliquots of the variously modified POs polymer solutions (5.0 mg/mL), various amounts of glucose oxidase solution, and selected volumes of 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 described.29 In the generator-collector 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, which translates into a steady state current (Iss) that is measured at both the generator (oxidation current) and collector (reduction current) electrodes, is set up between the generator and the collector electrodes. A well-defined steady state current was measured for all polymers except at high enzyme loading, where the electron diffusion rate and thus the currents were small. The current at 0.6 V was used to determine Dapp. In the generatorgenerator 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 at a scan rate

of 1 mV s-1 were integrated to calculate the charge (Q) in the redox polymer film. Electrophoresis. Electrophoresis was performed with a Multiphor apparatus and a Multidrive XL power supply from Pharmacia LKB.36 A refrigerated VWR water bath was used to keep the plate temperature at 10 °C. Agarose, Gelbond, Coomassie Blue, Ampholines, Pharmalyte, glass plates, and electrode wicks were purchased from Sigma. In-house molds giving a gel thickness of ∼0.3 mm were used for IEF (isoelectric focusing). Agarose (1%) and 2% ampholines (pH 2.5-9.5) were used for the gels, which were left in a humidity chamber for at least 4 h at 4 °C. IEF conditions were voltage limited (500 V) for 700 Vh, at which time the focusing was complete. The samples, which consisted of solutions of the redox polymer and glucose oxidase, were applied 4-4.5 cm from the cathode corresponding to a pH of ∼7.5. About 4 µL of sample was applied. The gels were then fixed, washed, dried, stained, and destained according to standard methods.36 Results and Discussion Effect of Enzyme Loading on the Electron Diffusion Coefficient. Figure 3 shows IDA cyclic voltammograms at the collector electrode for the POs-Me3 polymer (the structure of which is defined in Figure 2) as a function of enzyme loading. 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 current in the generator-collector experiment represents the oxidation of [Os(bpy)2vpyCl]+ (vpy ) vinylpyridine) at the generator, the transport of electrons across the gap through the redox polymer, and the reduction of [Os(bpy)2vpyCl]2+ at the collector. The limiting currents obtained at the generator and collector were identical, indicating the establishment of a steady state concentration profile of redox species. The steady state current decreases with increase in enzyme loading, indicating a decrease in the rate of charge propagation. The collector current at 0.6 V, for the generator-collector experiment, was used to calculate the electron diffusion coefficient according to eq 6. Figure 4 shows the dependence of Dapp on enzyme loading for redox polymers differing in their extent of quaternization by methyl groups and for POsEA. A best-fitting exponential curve is drawn only as an aid to the eye, not to suggest that the electron diffusion coefficient decays exponentially with the weight fraction of glucose oxidase in the film. Dapp is highest

Maximum Current Densities of Glucose Electrodes

J. Phys. Chem., Vol. 100, No. 9, 1996 3723

Figure 4. Dependence of the electron diffusion coefficient on enzyme loading for POs-Me3 (solid circles), POs-Me2 (open circles), POsMe1 (solid triangles), and POsEA (open triangles). The solid lines represent an exponential curve fit through the data points. All IDA electrodes were made with 2.5 µg of polymer and 10 wt % PEGDGE. The IDA voltammograms were run at 5 mV s-1 (20 mM phosphate buffer, 0.1 M NaCl, and in air).

TABLE 2: Values of the Apparent Electron Diffusion Coefficients for Redox Hydrogels Made of Polymers Varying in Their Extent of Quaternization without GOX and at 60 wt % GOX polymer

Dapp, cm2 s-1 (0 wt % GOX)

Dapp, cm2 s-1 (60 wt % GOX)

POsEA POs-Me1 POs-Me2 POs-Me3

5.1 × 10-9 9.2 × 10-9 2.19 × 10-8 3.79 × 10-8

5.72 × 10-10 1.06 × 10-9 4.55 × 10-9 5.13 × 10-9

for POs-Me3 and lowest for POsEA at the various enzyme loadings. The data at 0 wt % and 60 wt % GOX loading are summarized in Table 2. A similar dependence of Dapp with enzyme loading has been observed by Surridge and co-workers for a redox polymer based on poly(vinylpyridine) complexed with [Os(bpy)2Cl]+/2+.20 Dahms-Ruff theory,37,38 which requires a “mean-field” approximation to hold, predicts a linear decrease in Dapp with decreasing concentration of redox centers. This approximation is applicable to the extreme case of redox mediators that diffuse freely in solution. At the other extreme, theory based on rigorously fixed redox centers and extended electron transfer predicts an exponential decay of Dapp with decreasing redox center concentration.39 In between these two extremes is the case of a redox center that is tethered, i.e. is free to move within a small radius, about an equilibrium position. This seems to be the most realistic picture of our redox polymer system, particularly in the case of POs-Me3, where the polymer film swells considerably, increasing its volume by a factor as high as 50,12 and where there is local segmental motion of the polymer chains. Blauch and Saveant40 developed a “bounded” diffusion model to predict values of Dapp for this case. The expression for Dapp, for the limiting case where the displacement of the redox centers is rapid and extensive, is given by

Dapp ) kex(δ2 + λ2)CRT/6

(7)

where kex is the rate constant for electron transfer between redox centers, δ is the distance over which electron transfer takes place, λ is the maximum displacement of the redox center about the equilibrium position, and CRT is the total concentration of the redox centers. Simulations for certain cases (e.g. Dphys/De ) 0.01) show a dependence of Dapp on CRT that is close to the

actual dependence seen in Figure 4. A similar observation was made by Surridge et al.20 The decrease in Dapp upon increasing the weight fraction of enzyme can be explained either by electrostatic bonding of the polycationic redox polymer by the polyanionic GOX, leading to a more rigid network, or by the decrease in the concentration of the osmium centers upon dilution of the network with GOX. Complex formation between GOX and the redox polymers, POsMe1 and POs-Me3, was indeed observed by agarose gel electrophoresis,14 as shown in Figure 5. The redox polymers are polycations at any pH, their positive charge originating in their complexation with osmium and quaternization; GOX is a polyanion at pH 7.0 (pI ) 4.0). As is seen in Figure 5, up to 85 wt % of GOX can be bound to POs-Me1 (as seen from the absence of free enzyme migrating toward the anode in the gel), and 90 wt % of GOX is retained in the complex with POsMe3. Thus, both redox polymers form strong electrostatic complexes with GOX, that of POs-Me3 being stronger than that of POs-Me1. The effect of enzyme loading on the thickness of the polymer films at a constant amount of polymer, and hence the concentration of the redox centers, is unclear. Surridge et al. measured the dry film thickness of a POs film (one-third of the pyridines complexed for [Os(bpy)2Cl]+/2+ with varying GOX loadings).20 Film thickness remained practically constant between 40 and 64 wt %.GOX (t ) 5800 Å at 40% GOX and 6400 Å at 64% GOX). It should be kept in mind that dry film thicknesses were measured. In summary, the decrease in Dapp upon increasing the weight fraction of glucose oxidase in the hydrogel/enzyme film is caused by dilution of the redox centers and by lesser segmental mobility of the polymer network of the hydrogel. Glucose Response Curves. Figure 6A shows typical response curves for 3 mm vitreous carbon electrodes with 0.5 µg POs-Me3 and 10 and 80 wt % GOX. The response curve can be phenomenologically described by the simplified MichaelisMenten equation, which can also be expressed in the form of the Eadie-Hofstee equation:41,42,43

j)

jmax 1 + (Ks1/Cs1) + (Ks2/Cs2)

(8a)

When the term is much smaller than Ks2/Cs2, the equation is simplified to

j ) jmax - Ks(j/Cs1)

(8b)

where j is the steady state current density, jmax is the current density at infinite glucose concentration, Ks1 and Ks2 are apparent Michaelis constants for the substrate and the oxidizer, respectively, and Cs1 and Cs2 are the concentrations of the substrate and the oxidizer, respectively. Eadie-Hofstee plots, i.e. plots of j vs (j/Cs1), are thus straight lines with a slope Ks and intercept jmax. Eadie-Hofstee plots, shown in Figure 6B, are linear at low enzyme loadings and nonlinear at the higher enzyme loadings, particularly at low glucose concentrations. This shows that the simplification is, as expected, not valid when the glucose concentration is too low and at the same time the enzyme concentration is very high, i.e. when the redox relays are greatly diluted. The linear portions of the plots were used to obtain values of jmax and Ks. Activation energies were obtained by plotting log i vs 1/T in the range 10-40 °C. Dependence of Ks on Enzyme Loading. Figure 7 shows the dependence of Ks, the apparent Michaelis constant of the electrode, on the enzyme weight fraction in the film. It is seen that the value of the apparent Ks decreases approximately linearly with increase in enzyme loading. It is also seen that,

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Rajagopalan et al.

Figure 5. Agarose gel of the complex formation between GOX and POs-Me1 (A) and POs-Me3 (B). Free enzyme at the anode is seen at 85 wt % GOX for POs-Me1 and at 90 wt % for POs-Me3. The tracks are (from the top) standard; 0, 10, 20, 30, 40, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, and 100 wt % GOX (20 µg total of redox polymer + GOX); standard.

among the polymers, the value of Ks increases from POsEA to POs-Me1 to POs-Me2 and then decreases slightly, reflecting the variation in the apparent electron diffusion coefficient, Dapp. The Michaelis constant calculated is a composite parameter, a function of the different steps involved in the transduction of glucose concentrations into a current by the “wired” enzyme electrode, and therefore is only a qualitative measure of the efficiency of the “wiring” of the enzyme by the redox polymer. If all the enzyme molecules were “wired” with equal efficiency, Ks would remain constant upon increasing the weight fraction of enzyme in the film. The decrease in Ks values with enzyme loading suggests that the “wiring” efficiency decreases as the weight fraction of the enzyme increases. Possible reasons for this include, in addition to the already discussed lower electron diffusion coefficients, poorer cross-linking of the film and a lesser fraction of the enzyme having redox centers close enough to the active site for electron transfer. Dependence of jmax on Enzyme Loading. Figure 8 shows the dependence of jmax on the weight fraction of enzyme in the film. For the various polymers jmax increases with weight fraction at low enzyme loading, reaches a maximum at 30-40 wt % GOX, and then decreases, consistent with observations in previously studied polymers.3,5,14 jmax is consistently the highest for POs-Me2, with the values for POs-Me1, POs-Me3, and POsEA being close to each other for the GOX loadings considered. The level of quaternization of POsEA roughly equals that of POs-Me1. At 40 wt % GOX, the values of jmax are 944, 722, 624, and 548 µA cm-2, respectively, for the four polymers when thin films are applied, i.e. approximately 65 µg

cm-2 of solids deposited on the electrode surface. As discussed, jmax depends on the permeability of the hydrogel to glucose, on the strength of the electrostatic complex formed between the polymer and the enzyme, and the electron diffusion coefficient in the films. The rates increase with increasing charge density on the polymer backbone, and hence it is expected that jmax, for a fixed weight fraction of enzyme, would increase with increasing charge density on the polymer backbone, i.e. with the degree of quaternization. However, an anomaly immediately becomes apparent: POsMe3, quaternized to the highest extent in the series here, gives lower current densities than POs-Me2. We explain this behavior as an effect of quaternization on the rate of cross-linking by the diepoxide, PEGDGE. Cross-linking by PEGDGE occurs by the reaction of the pyridine nitrogens and the amine functions of the enzyme, and the polymer in the case of POsEA, as shown in Figure 9. As the polymer is quaternized with methyl groups, the rate of further quaternization by PEGDGE, leading to crosslinking, decreases. In fact when POs-Me4, a redox polymer with two-thirds of the pyridine rings quaternized, is used, the polymer-enzyme complex cannot be immobilized by PEGDGE cross-linking. Inadequate cross-linking led to the loss of a part of the film from our electrodes that rotated at 1000 rpm. The retention of the redox polymer, as measured by the charge, i.e. integration of the current in slow scan voltammograms, decreased in electrodes made with increasingly quaternized polymers when the amount of polymer initially deposited on the electrode was fixed. This is seen in Table 3. Assuming that all of the material deposited on the surface of the electrode

Maximum Current Densities of Glucose Electrodes

J. Phys. Chem., Vol. 100, No. 9, 1996 3725

Figure 8. Dependence of jmax on GOX loading for POs-Me3 (solid circles), POs-Me2 (open circles), POs-Me1 (solid triangles), and POsEA (open triangles). Electrodes were made with 2.5 µg of polymer and 10 wt % PEGDGE (argon; 0.5 V (SCE); 1000 rpm).

Figure 6. Glucose response curves (A) and Eadie-Hofstee plots (B) for electrodes with 2.5 µg POs-Me3 and 10 wt % (solid circles) and 80 wt % (open circles) GOX (Ar atmosphere, 0.5 V (SCE), 1000 rpm). The crosses indicate points that have not been omitted when calculating the slope.

Figure 9. Cross-linker, PEGDGE (a), and its reactions with pyridine (b) and the primary amine of POsEA (c).

Figure 7. Dependence of Ks on enzyme loading for POs-Me3 (solid circles), POs-Me2 (open circles), POs-Me1 (solid triangles), and POsEA (open triangles). Electrodes were made with 2.5 µg of polymer and 10 wt % PEGDGE (argon; 0.5 V (SCE); 1000 rpm).

is retained and that all of its redox centers are electroreduced/ electrooxidized, the surface concentrations of the redox centers would have been POsEA, 2.67 × 10-8 mol/cm2; POs-Me1, 2.81 × 10-8 mol/cm2; POs-Me2, 2.69 × 10-8 mol/cm2; and POsMe3, 2.61 × 10-8 mol/cm2. Coulometry showed that in the case of POsEA, which remained cross-linkable, since quaternization added cross-linkable amine groups, more than 85% of the deposited polymer was retained on the electrode surface. For the highly quaternized POs-Me3, less than 60% of the polymer was retained. Calculation of the current densities normalized for the charge retained on the electrode surface, i.e. the current density per unit charge, takes into account the loss of material from the electrode surface. The maximum current density per unit charge plotted against the GOX weight fraction, with that of POs-Me3

at 30 wt % GOX being defined as unity, is plotted in Figure 10. Now the trend is distinctly different from that in Figure 8. The normalized maxima for the current densities now follow the sequence POs-Me3 ∼ POs-Me2 > POs-Me1 > POsEA, increasing with charge density on the polymer backbone and then leveling off. In fact, the highest current density now obtained is for POs-Me3 at an enzyme loading of 30 wt %. This result, however, does not provide a rigorous basis for comparison because GOX contains far fewer cross-linkable lysyl groups per kilodalton of enzyme (∼0.2) than the number of pyridine groups per kilodalton of the redox polymer (∼5) and is more difficult to cross-link. Material, particularly enzyme, is thus lost from the electrode surface at excessive enzyme loadings, and actual enzyme loadings can differ from those expected from the loadings applied. Dependence of the Activation Energy on Enzyme Loading. The dependence of the activation energy on enzyme loading for the various redox polymers is shown in Figure 11. The activation energies cluster together in two distinct zones, at ∼47 ( 4 and ∼55 ( 3 kJ mol-1, those for POs-Me2 and POs-Me3 being lower than those for POs-Me1 and POsEA. Thus, the

3726 J. Phys. Chem., Vol. 100, No. 9, 1996

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TABLE 3: Effect of Quaternization of the Polymers and the Weight Fraction of GOX on τ, the Surface Density of Electroactive Osmium Centers wt % GOX

τ × 108 mol/cm2 (POsEA)

τ × 108 mol/cm2 (POs-Me1)

τ × 108 mol/cm2 (POs-Me2)

τ × 108 mol/cm2 (POs-Me3)

10 20 30 40 50 60 70 80

2.46 2.56 2.51 2.36 2.14 2.58 2.29 1.70

1.77 1.76 1.84 2.04 2.49 1.89 1.86 1.91

2.32 2.04 2.11 2.07 1.95 1.92 1.72 1.11

0.649 1.19 1.44 1.42 1.54 1.60 1.23 0.601

Figure 10. Dependence of normalized current densities per unit charge on GOX loading for POs-Me3 (solid circles), POs-Me2 (open circles), POs-Me1 (solid triangles), and POsEA (open triangles). Electrodes were made with 2.5 µg of polymer and 10 wt % PEGDGE (argon; 0.5 V (SCE); 1000 rpm).

Figure 11. Dependence of activation energy on GOX loading for POsMe3 (solid circles), POs-Me2 (open circles), POs-Me1 (solid triangles), and POsEA (open triangles). Electrodes were made with 2.5 µg of polymer and 10 wt % PEGDGE (argon; potential 0.5 V (SCE); 1000 rpm).

lower activation energy systems are those made with redox polymers that have a higher degree of quaternization. At 40 wt % GOX, the activation energies are POsEA, 55 kJ/mol; POsMe1, 54 kJ/mol; POs-Me2, 46 kJ/mol; and POs-Me3, 45 kJ/ mol. The reasons for higher activation energies at both low and high GOX loadings for all the redox polymers remain unexplained. The trend in activation energies is slightly different from the trend observed in jmax and Ks values, where POs-Me2 electrodes gave the highest current densities. The observation that POsMe3 electrodes have activation energies comparable to POsMe2, despite lower values of jmax and Ks as compared to POsMe2, supports the suggestion that the cause of low jmax in the case of POs-Me3 is loss of material from the rotating electrode.

Figure 12. Dependence of jmax on film thickness for POs-Me2 (open circles), POs-Me1 (solid triangles), and POsEA (open triangles). Electrodes were made with 40 wt % GOX and 10 wt % PEGDGE (argon; 0.5 V (SCE); 1000 rpm).

Figure 13. Dependence of activation energy on film thickness for POsMe2 (open circles), POs-Me1 (solid triangles), and POsEA (open triangles). Electrodes were made with 40 wt % GOX and 10 wt % PEGDGE (argon; 0.5 V (SCE); 1000 rpm).

The activation energy data also support the suggestion that the reaction rate barrier of the rate-limiting step in the overall reaction scheme (eqs 1-5) is reduced when the extent of quaternization is increased. Dependence of jmax and Eact on Film Thickness. To determine the maximum current densities obtainable with the redox polymers, the thickness of the films was optimized with the weight fraction of enzyme held constant at 40 wt %. Figure 12 shows the dependence of jmax on the surface density of electroactive relays. A maximum current density of 1.08 mA cm-2 is obtained with POs-Me2, the highest for “wired” glucose electrodes based on glucose oxidase. Figure 13 shows the dependence of activation energies on the surface density of the electroactive sites. The activation energies are highest for POsEA (∼56 kJ/mol), lower for POs-Me1 (∼53 kJ/mol), and lowest for POs-Me2 (∼46 kJ/mol).

Maximum Current Densities of Glucose Electrodes Conclusions Quaternization, whereby charge is added to the redox polymers, enhances the hydration, swelling, and fluidity of segments of the cross-linked polymer network. Segmental fluidity in the hydrogel enhances the rate of electron-transferring collisions between chain segments, leading to higher electron diffusion coefficients. Because a larger fraction of electronrelaying redox centers interact in the more fluid structures with the active centers of the enzyme, the rate of electron transfer from glucose oxidase to the redox polymer is enhanced. Quaternization also enhances the electrostatic interaction between the redox polymer and the enzyme, enhancing the flow of electrons from the enzyme to the polymer. Excessive quaternization diminishes subsequent cross-linking by diepoxides. When the film is poorly cross-linked, the redox polymer and the enzyme are leached from the hydrogel. Optimal performance is reached at a level of quaternization where the polymer is still easily cross-linked. When one third of the pyridines are quaternized with methyl iodide and the enzyme “wiring” polymer has about one [Os(bpy)2Cl]+/2+ redox center per six pyridine rings, i.e. when about half of all pyridine rings are quaternized or complexed, the performance is optimal. Glucose electrodes made with such a polymer, 40 wt % GOX and 10 wt % GOX, have ∼46 ( 2 kJ/mol activation energies and reach current densities of ∼1 mA cm-2, and their apparent Michaelis constant, in the absence of a diffusion-limiting membrane, is 15 mM. Acknowledgment. This work was supported by the National Institutes of Health (No. 1 RO1 DK42015-01A1), Office of Naval Research, and the Welch Foundation. We thank Dr. Ling Ye for help in the fabrication of IDAs and Dr. Ioannis Katakis for very useful discussions. References and Notes (1) Gregg, B. A.; Heller, A. Anal. Chem. 1990, 95, 5970. (2) Gregg, B. A.; Heller, A. Anal. Chem. 1990, 95, 5976. (3) Ohara, T. J.; Rajagopalan, R.; Heller, A. Anal. Chem. 1993, 24, 3512. (4) Ohara, T. J.; Rajagopalan, R.; Heller, A. Anal. Chem. 1994, 94, 2451. (5) Rajagopalan, R.; Ohara, T. J.; Heller, A. In Diagnostic Biosensor Polymers; Usmani, A., Akmal, N., Eds.; ACS Symposium Series 556; American Chemical Society, Washington, DC, 1994; p 355. (6) Taylor, C.; Kenausis, G.; Katakis, I.; Heller, A. J. Electroanal. Chem. 1995, 396, 511. (7) Csoregi, E.; Quinn, C. P.; Schmidtke, D. W.; Lindquist, S. E.; Pishko, M. V.; Ye, L; Katakis, I.; Hubbell, J. A.; Heller, A. Anal. Chem. 1994, 66, 3131. (8) Csoregi, E.; Schmidtke, D. W.; Heller, A. Anal. Chem. 1995, 34, 1240.

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