Biosensors are important devices for monitoring biological species in various processes of environmental, fermentation, food and medical concerns. The main challenges biosensors face include low sensitivity, poor specificity and proneness to fouling. The advent of nanotechnology presents some promising solutions for alleviating these problems. While many efforts have been devoted to improving the performances of biosensors by taking advantage of nanostructures or macrostructures with nanoscale features, the effort to elucidate the underlying mechanism governing the performances of biosensors enhanced with nanostructures is still scant.
This study intends to investigate the role of reaction kinetics and mass transport in biosensing when electrodes with nanoscale features are used. For this purpose, we used glucose biosensor as a model system. In a typical glucose biosensor, an enzyme such as glucose oxidase is immobilized onto the electrode surface [1,2]. The performance of such functionalized electrodes can be improved by either adjusting the spatial distribution of the enzyme or by modifying the morphology of the electrode surface. To achieve a high efficiency in immobilizing an enzyme onto the electrode surface, various techniques have been developed, such as the use of self-assembled monolayer [1-4], conducting polymers [5,6] and sol-gels . Among these methods, the self-assembled monolayer (SAM) approach offers a better control for enzyme distribution at the molecular level, a high degree of reproducibility in enzyme immobilization and a short distance between the immobilized enzyme and the electrode surface [1,4]. The SAM approach, however, is limited by the amount of the enzyme that can be immobilized onto the electrode surface, which in turn will affect the sensing performance of the biosensor . To increase the amount of immobilized enzyme various nanostructures such as nanotubes, nanoparticles and nanorods have been explored in order to increase the active surface area of the electrodes. For example, nanostructures like gold nanotubes , carbon nanotubes [5,9] and gold nanoparticles  have been incorporated into electrode surfaces and they exhibited better performance than conventional flat electrodes.
Recently Wang et al.  used nanostructured platinum electrodes functionalized with glucose oxidase for glucose detection. These electrodes showed a significant (two orders of magnitude) increase in glucose detection sensitivity as compared with a flat electrode, but the response of these electrodes to K4Fe(CN)6 was just 2.3 times that of the flat electrode. They attributed such sensitivity enhancements for glucose detection to the increased enzyme loading and improved retention of hydrogen peroxide near the electrode surface without examining systematically the role of reaction kinetics and mass transport. We believe that the electrical current response of these nanostructured electrodes is controlled by reaction kinetics, mass transport and the geometric topography of the nanostructures. Thus, to be able to understand the mechanism governing such an electrochemical process for the purpose of improving the performance of nanostructure based electrodes, it is necessary to investigate the role of reaction kinetics and mass transport in biosensing when nanostructured electrodes are used.
Nanopillar array electrodes (NAEs) with three different pillar heights were fabricated using a template method . In fabricating these electrodes, a layer of gold film about 150 nm thick was first sputter-coated onto one side of a porous anodic alumina (PAA) circular disc (d = 25 mm; Whatman Inc, Maidstone, England) having an average pore diameter of 150 nm using a SPI sputter coater (Structure probe Inc, West Chester, PA). Then, a thicker gold layer was electrodeposited on top of the sputtered gold film to form a strong supporting base in an Orotemp24 gold plating solution (Technic Inc, Cranston, Rhode Island) with a current density of 5 mA/cm2 for two minutes. This supporting base was masked with Miccrostop solution (Pyramid plastics Inc., Hope, Arkansas) for insulation. After that, gold nanopillars were electrodeposited through the open pores of the PAA disc from the uncoated side under an electrical current density of 5 mA/cm2 at 65°C. The deposition time was varied for achieving nanopillars of different heights. For this study, specimens with three different nanopillar heights were prepared with the electrodeposition time controlled at 1, 7 and 15 minutes. After nanopillar deposition, the PAA disc was dissolved in 2.0 M NaOH resulting in a thin gold sheet with arrays of vertically standing gold nanopillars. The fabricated specimens were cut into small square pieces (about 3.2 × 3.2 mm2) and they were grouped into specimens A, B and C by their nanopillar height. For connecting the electrodes, a copper tape were attached to the backside of an electrode with the exposed part of the copper tape insulated using Miccrostop. Of these small specimens, some were used for scanning electron microscopy (SEM) imaging analyses, and some for electrochemical experiments (bare and functionalized conditions). For controls, two flat gold electrodes (one for bare and one for functionalized condition) with the same geometric size were prepared by depositing a thin film (300 nm) of gold on a titanium coated glass plate using a thermal evaporator (built in house). Prior to the electrochemical experiments, all electrodes (NAEs and flat) were cleaned by running cyclic voltammetry (CV) in 0.3 M H2SO4 between -500 mV and 1500 mV until a stable CV curve was obtained for each specimen, and then washed with deionized water.
These electrodes were characterized in either bare or functionalized conditions. In the bare condition the cleaned electrodes were used directly, and in the functionalized condition the cleaned electrodes were further functionalized prior to use. To functionalize the electrodes, their surfaces were first modified with a SAM layer by placing them in a 75% ethanol solution containing 10 mM 3-mercaptopropionic acid. Then the SAM modified electrodes were rinsed in 75% ethanol and immersed in a 0.1 M 2-(N-morpholino) ethanesulfonic buffer solution (pH of 3.5) containing 2 mM 1-ethyl-3-(3-dimethylaminopropyl) carbodiimide hydrochloride and 5 mM N-hydroxysuccinimide for activation for two hours. After washing in phosphate buffer solution (PBS), the activated NAEs were placed in PBS solution at pH 7.4 containing 1 mg/ml of glucose oxidase for two hours under constant stirring. The reason for setting the immobilization time to two hours is that according to literature , enzyme loading reaches its maximum in about 2 hours and it saturates afterwards. From the electrochemical experiments, the amperometric current responses of both bare and functionalized NAEs along with flat controls were measured using a conventional three-electrode cell with an Ag/AgCl reference electrode and a platinum counter electrode with the Multistat 1480 (Solartron Analytical, Houston TX, USA) electrochemical system.
For the bare-electrodes, their amperometric current responses at different concentrations of K4Fe(CN)6 to each incremental addition of 80 μl of 1 M K4Fe(CN)6 to a 20 ml solution containing 0.5 M Na2SO4 (equivalent to a 4 mM increase in K4Fe(CN)6concentration) were measured at a constant electrode potential of 350 mV (vs. Ag/AgCl), and the change in the current response upon the change in K4Fe(CN)6 concentration for both the NEAs and flat electrode was determined. For the functionalized NAEs, the amperometric current responses to each incremental addition of 50 μl of 1 M glucose to a 20 ml PBS solution (equivalent to a 2.5 mM increase in glucose concentration) containing 3 mM p-benzoquinone as a mediator were measured at a constant potential of 350 mV (vs. Ag/AgCl). In all experiments, the background current of all electrodes was allowed to stabilize before drops of target species were added. Prior to these experiments the electrolyte solution was deaerated with nitrogen and during experiments the solution was blanketed with nitrogen and stirred constantly at 600 rpm.
For glucose detection, the electrode reactions in the present study can be described by the following cascading events . With the catalysis of glucose oxidase (GOX-FAD), glucose was first oxidized into gluconolactone with GOX-FADH2 as a by-product. The GOX-FADH2 was then converted back to its oxidized form (GOX-FAD) by the p-benzoquinone mediator in the solution. The mediator itself was converted back to its original form by oxidation at the electrode surface, through which free electrons were generated and picked up by the electrode to produce a current response. These cascading events can be expressed by the following reactions:
Glucose + GOX-FAD → Gluconolac tone + GOX-FADH2(1)
GOX - FADH2 + 2 Mediatorox → GOX - FAD + 2 Mediatorred + 2H+(2)
2Mediatorred → 2Mediatorox + 2e-(3)
Based on these enzymatic events and the current measurements from the functionalized electrodes, we performed an enzymatic-kinetics study to determine the enzyme activity in the functionalized electrodes by using the Michaelis-Menten equation:
Where Is is the steady-state current measured at each glucose concentration, Imax the maximum current attainable, Km the apparent Michaelis-Menten constant, and S the concentration of the target species (i.e., glucose in this case). The parameter Km describes the enzymatic activity of glucose: the smaller the Km value is, the more efficient the enzymatic reaction is. When Km of an enzymatic biosensor is larger than the Km value of the freely dissolved enzyme, it usually implies that the enzyme immobilized in the biosensor is less efficient in oxidizing glucose than the dissolved enzyme . In this study, the Km values for the functionalized electrodes were determined by performing nonlinear curve fit using Eq.4 to the measured current-concentration data.
To elucidate the effects of reaction kinetics and mass transport on the current response of bare and functionalized NAEs, we simulated such an electrochemical process using a finite element analysis method with commercial software COMSOL Multiphysics (COMSOL Multiphysics, Burlington, MA). To simplify the situation we considered two dimensional situations. As shown schematically in Figure 1, a set of NAEs (with a width and a spacing of 200 nm for the pillars, and an overall dimension of 5 μm × 4.3 μm for the electrode) was placed in a circular electrochemical cell containing a supporting electrolyte. In this simulation, a bare and a functionalized (with glucose oxidase) NAEs as well as a flat electrode with the same planar area (as a control) were considered.
For the electrode reaction at the functionalized NAEs, we assumed that glucose was consumed at a flux of Jg at the electrode surface to produce the mediator in its reduced-form at a flux of JM. Here Jg and JM can be described by the following equations:
Jglucose = kcG (5)
JM = kcG - k0cM exp(-αF(E - Estd)/RT)(6)
where k represents the rate constant for Eq. 1, cG the concentration of glucose, cM the concentration of mediator, k0 the standard rate constant, α the charge transfer coefficient, F the Faraday constant, E the electrode potential, and Estd the standard potential of the mediator. To simulate the actual event, the electrode was held at a constant overpotential of 350 mV. Under this condition, the reduced-form mediator was oxidized at the electrode surface to generate a current flux of Jc:
JC = -2k0cM exp(-αF(E - Estd)/RT)(7)
With these considerations, the amperometric current response of the electrodes in response to a drop of glucose was determined while the electrolyte solution was constantly stirred by a swirling vortex force applied at the center of the cell.
For the electrode reaction at the bare-electrode, we considered the redox of K4Fe(CN)6 with the reduction flux of K4Fe(CN)6 governed by:
JF = -k0FcF1 exp(-αF(E - Estd')/RT) + k0FcF2 exp(-αF(E - Estd')/RT)(8)
where k0F is the electron transfer rate for both ferrocyanide and ferricyanide (assumed to be the same), cF1 the concentration of ferrocyanide, cF2 the concentration of ferricyanide, E the electrode potential, and Estd' the standard potential of ferro- and ferri-cyanide.
Besides the reaction kinetics discussed above, the mass transport in these electrochemical processes was mainly governed by diffusion and convection for the mobile species such as glucose and K4Fe(CN)6. The electromigration was ignored because of the presence of the supporting electrolyte in a high concentration.
After these considerations, the diffusion/convection-controlled electrochemical reaction problems upon a step potential excitation (350 mV) at the electrode were solved using the combined Electrokinetic-Flow and Navier-Stokes applications in COMSOL Multiphysics. In the simulation process, two initial analyses were performed. First, a stationary nonlinear analysis in Navier-Stokes mode was performed for reaching a fully developed vortex flow inside the center inner circle (see Figure 1), and then a stationary nonlinear analysis in Electrokinetic-Flow mode was performed for producing a uniform initial concentration of glucose within the off-center inner circle (see Figure 1), much like dropping a small volume of glucose into the solution. After these initial steps, time dependent analyses were performed. For the kinetic constants, literature values  including the diffusivity of ferrocyanide and ferricyanide listed in Table 1 were used. The values for the diffusivity of glucose and the mediator, which are not readily available in the literature, were calculated using the following equation :
where A represents the solute (e.g., glucose or the mediator) and B the solvent (e.g., water), εB the association factor of the solvent, MB the molecular weight of the solvent, μ the viscosity of solution, VA the molar volume of solute glucose, and T the absolute temperature.