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iR-Drop Effects in Self-Powered and Electrochromic Biosensors Miguel Aller Pellitero, Antón Guimerà, Rosa Villa, and Francisco Javier del Campo J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b11906 • Publication Date (Web): 16 Jan 2018 Downloaded from http://pubs.acs.org on January 16, 2018

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The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

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The Journal of Physical Chemistry

iR-Drop Effects in Self-Powered and Electrochromic Biosensors. Miguel Aller Pellitero1, Antón Guimerá1,2, Rosa Villa1,2, and F. Javier del Campo1*

1

Instituto de Microelectrónica de Barcelona, IMB-CNM (CSIC); Esfera UAB; Campus de la

Universitat Autónoma de Barcelona; 08193-Bellaterra, Barcelona, Spain. 2

CIBER de Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN).

Corresponding author email: [email protected]

ACS Paragon Plus Environment

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ABSTRACT

This article proposes the exploitation of ohmic drop in the development of novel electrochromic devices. Electrochromic materials enable the construction of more efficient selfpowered biosensors incorporating the ability to display information without the involvement of silicon-based electronics. Numerical simulations are employed to describe the behavior of a model system based on the combination of a second-generation biosensor and a Prussian bluebased display. The results show that concentration profiles can be used to model color behavior in electrochromic devices, but more importantly, how iR-drop is a critical a variable to consider in the design, construction, and study of electrochromic devices, but also self-powered electrochemical sensors and power sources in general.


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1. Introduction

Ohmic, or iR-, drop is an undesirable effect in electrochemical experiments. It stems from electrolyte resistance and results in uneven current distributions and deviations in applied potential.1-2 The consequences of these deviations differ from one application to another, but in general they can be very detrimental. In electroanalytical systems, ohmic drop results in determination errors. In bulk electrolysis systems, uneven current distributions result in poor process control, and in batteries and fuel cells ohmic drop (a form of internal resistance) directly translates into energy and power losses. By definition, the most common approaches to avoid ohmic drop involve decreasing solution resistance between electrodes,3-4 avoiding the passage of large currents through the system,5-6 or a combination of both.7-8 In contrast, here we present a case where internal resistance may be beneficially exploited. We are presenting a new class of self-powered sensors incorporating electrochromic materials, and in which ohmic drop assists in the conversion of chemical information into an easy to interpret visual readout. The device is an electrochromic display in which the charge storage layer9 at the counter electrode is an enzymatic biosensor, so the color switch is controlled by the charge exchanged between a wired enzyme and the analyte. Moreover, the device is configured as a galvanic cell with shifted electrodes, as depicted in Figure 1. By controlling iR-drop inside the device, we have demonstrated that it is possible to induce this color change along the current path. The length of the resulting line, which can be directly observed and interpreted de visu by the user, is found to be proportional to an analyte concentration, hugely simplifying device construction and usage.


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This shifted electrode construction differs from that used in conventional electrochromic devices, such as displays, glasses and mirrors. These rely on the so-called “sandwich” configuration,9-11 where anode and cathode face each other, separated by a gap of a few microns that contains an electrolyte to minimize ohmic losses and ensure a rapid and homogenous color switch.

Figure 1. (a) Schematic representation of the self-powered electrochromic device. (b) Side view of the device. The charged consumed at the cathode increases with time or with higher analyte concentrations, creating a discoloration along the electrochromic display that follows the path of least resistance. (c) Reactions sequence taking place in a general second generation glucose biosensor. (d) Representation of the electrochromic reaction at the transparent ITO electrode.

Electrochromic materials have also been used in the construction of self-powered electroanalytical devices, mostly relying on this standard sandwich configuration. Crooks et al, for instance, proposed a biosensor where the presence of glucose above a certain threshold concentration resulted in bleaching of a Prussian blue spot.12 More recently, Zloczewska et al presented another sensor where Prussian blue was bleached in the presence of ascorbic acid, allowing its determination with the aid of an external reading system.13 The electrochromic


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couple Prussian blue (PB)/Prussian white (PW) is perhaps the most popular electrochromic material used in electroanalysis due to its excellent properties, among which we find a high extinction coefficient, low redox potential, electrochemical reversibility, lack of toxicity, and ease of preparation by different means.14-15 However, other electrochromes have also been successfully used in the construction of electroanalytical devices.16-18 All these devices exploit electrochromic color-changes to indicate the presence/absence of a certain analyte. However, because of their construction, these systems require the aid of external detection systems to read color intensity changes quantitatively. In this work, we demonstrate how the use of a horizontal electrode configuration, be it co-planar, or shifted as seen in Figure 1a, enables the interpretation of chemical information in terms of the length of a color line or band. This co-planarity provides the necessary control over the current path along the device, and we take advantage of the internal resistance to generate a colorimetric signal readable by the naked eye without the aid of external equipment (Fig. 1b). As in any other self-powered device, the reduction potential of the anode process, in this case a biosensor, must be lower than that of the cathode process, in this case an electrochrome, and the device will work as long as the actual cell potential is positive. We use numerical simulations to understand the factors controlling the operation of this type of device, to explore its limitations, and to use them as a design tool to successfully predict the behavior of related systems prior to their fabrication. The model and the results presented here can be of help to those working on the development of electrochemical applications, and particularly fuel cells, sensors and electrochromic devices. 2. Theory


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Figure 1a presents a schematic representation of the device, which has a rectangular geometry resembling a channel cell with two coplanar electrodes.19 In line with other self-powered sensors,20 and electrochemical power sources in general, only two electrodes are needed: anode and cathode. The small separation gap between them prevents short-circuits and introduces a minimum internal resistance to prevent display activation in the absence of analyte (i.e.:glucose). Our system is based on a second-generation biosensor.21 Second-generation biosensors rely on redox mediators to shuttle electrons between the electrode and the enzyme in charge of the biorecognition function, as depicted in Figure 1c. These mediator species diffuse inside the biosensing layer in order to carry the charge to-and-fro. The electric current generated by the biosensor is transported through the electrolyte to the electrochromic display, which is then reduced switching from blue to colorless (Fig. 1d). The model presented here considers (i) chemical reaction of the analyte and the redox mediator with the enzyme, (ii) diffusion of the mediator to the electrode surface, (iii) electron transfer between the redox mediator and the electrode and between the electrochromic species and the electrode, and (iv) ion conductivity through the electrolyte between electrodes. 2.1 Biosensing anode: enzyme kinetics. The enzyme reaction has been modeled according to the Michaelis-Menten mechanism22-23 (1)

this is a homogeneous reaction taking place inside a domain corresponding to the biosensing layer coating the electrode.


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G represents the analyte, i.e.: glucose, Eox the oxidized form of the enzyme active site, EG would be an intermediate enzyme-substrate complex, Ered the reduced form of the enzyme active site, and GAc the product of the enzyme reaction, i.e.: gluconic acid. The regeneration of the enzyme active site following the conversion of glucose, Ered, is modeled by the following reaction

2 + 2 +

(2)

where O represents the oxidized form of a reversible redox mediator, and R its reduced form. The rate of the enzymatic reactions (1) and (2) is given by24

=

1 + +

(3)

where the Michaelis-Menten constant is defined as = ( + 1 )/" , = / and Etot = Eox + Ered + EG. CG and CO represent the concentrations of glucose and the oxidized redox mediator respectively. The value of was experimentally determined, and the values of

and k were taken from the literature (Table 1).23-26 2.2 Mass transport

The present model does not involve convection or migration of the electroactive species, which are only subject to diffusion according to Fick’s laws


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#$ = &$ ∇( $ #%

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(4)

where i represents a generic species, and Ci and Di its concentration and diffusion coefficient, respectively. 2.3 Electrode processes At the electrode, mediator species R is oxidized back to O

⇌ + *

(5)

This electrode process determines the anode potential. The presence of a catalytic homogeneous process (enzymatic reaction) coupled to an electrode process means that the actual anode response may be controlled by the enzyme reaction or the electrode process depending on the conditions. In fact, during the experiments, control shifts from enzyme to electrode kinetics as will be discussed below. At the cathode, the model assumes that electrochromic material is homogeneously distributed across the electrode surface, and it is modeled by a simple one-electron redox process

+ + * ⇌ ,

(6)

where P and Q are surface-bound species. The electrode reactions both at the anode and the cathode are assumed to follow a Nernstian behavior27


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= - +

. 1/ /0

(7)

where Cox and Cred represent the bulk concentration of the redox mediator and the surface concentration of the electrochromic species at their respective oxidation states. - represents the formal potential of the electrochromic species (see Table 1), n the number of electrons involved in each electrode reaction, T is the temperature, and F and R are the Faraday and the universal gas constants respectively. Electron transfer is modeled assuming Butler-Volmer kinetics both at the anode and the cathode.1 More specifically, our model uses the so-called current-overpotential equation which allows the current to be expressed as a function of the exchange current while considering the concentration gradient of electroactive species at the electrode surface:

−80( − - ) (1 − 8)0( − - ) 2 = 2 3 *45 6 9 − : exp 6 9>

.

.

(8)

where 2 is the exchange current density, 8 is the charge transfer coefficient, CR and CO are the

surface concentrations of the reduced and oxidized form of the redox mediator, and ′ its formal

potential. On the other hand, a linearized version of the Butler-Volmer equation was used to describe the electron transfer rate at the anode in the cases where the details of the electrode process were unimportant


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2 = 2

0 ( − - )

.

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(9)

The two cases where this was used were when either a fixed current or fixed potential was applied at an (unmodified) anode, or at the cathode during the biosensor chronoamperometric simulations. The overall passing current can be obtained by integrating the current density along the electrode boundaries. In the case of our 2-dimensional domain, this is done according to DE

?@ = A@ B 2 C4 D

(10)

where J is the current density vector normal to the electrode surface boundary. A 3 mm electrode width (Welec), akin to the experimental device, was defined to integrate the current densities of the system. 2.4 Ion conductivity Current is carried by ions in the electrolyte, and is described by the sum of fluxes of all charged species present

2 = F G$ 02$

(11)

$

where zi and Ji correspond to the charge and flux of species i, respectively. In the absence of convection, the Nernst-Planck equation describes mass transport of species i, as


10

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2$ = −&$ ∇H$ −

G$ 0 & H ∇I

. $ $

(12)

where Ji is the flux vector, Di, ci, and zi are its diffusion coefficient, concentration, and charge, respectively, and −∇I the electric field. Substituting eq. 12 into eq. 11, we find that

0 ( ∇I 2 = −0 J∇ F G$ &$ H$ K − F G$( &$ H$

. $

(13)

$

Our model assumes the electroneutrality condition, which states that

F G$ H$ = 0

(14)

$

This means that there is no charge separation within the solution, and neutrality is maintained everywhere. Although electroneutrality is known to break down in the very close proximity of the electrodes, where the electric field gradient is greatest28, this has been neglected in our model because we are neither interested in studying events occurring at the nanoscale, nor in a timescale of nanoseconds. An important implication of the electroneutrality condition is the simplification of Poisson’s equation into the Laplace equation

∇( I = 0

(15)

On the other hand, the electrolyte conductivity is given by

0( M= F G$( &$ H$

.

(16)

$


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Combination of these equations leads to the expression of Ohm’s law for electrolytes

2 = −M∇I

(17)

For the sake of simplicity and ease of calculation, our simulations assume electrolyte conductivity, M, to be a constant value. Solving these equations enables the determination of the electric field in the solution and, ultimately, the value of the actual electrochemical potential across the simulation domain. 3. Computational procedure and model geometry We are presenting a complex model involving a biosensor and an electrochromic display, which are combined to yield a galvanic cell that is half-way between a fuel cell and a battery. This is so because the system operation depends primarily on the concentration of a fuel analyte (consumed at the anode), but will only work as long as there is oxidized electrochromic material left at the cathode. Our approach consists in first validating separately the models for anode and cathode, which in the actual device correspond to a glucose biosensor (anode) and a Prussian blue display (cathode), respectively.29 Once these models are validated using experimental data, they are combined to facilitate the study of the complete device. Note that the model geometry presents anode and cathode shifted on opposite sides of a channel, in line with the working prototype, but the results are equally valid for the case of perfectly coplanar electrodes. Finite element simulations have been run using the commercial software COMSOL Multiphysics 5.3 (COMSOL, SE) on a PC (Intel Core® i7-4790 , 16 Gb RAM) running Windows 7.


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The model is inspired by an actual device reported elsewhere,29 and its dimensionality has been simplified from 3 to 2 dimensions, considering the plane of symmetry along the device midsection. Figure 2 shows a schematic representation of the 2D model, including the various subdomains and boundaries involved, which are as follows. The channel height, Hch, was set at 127 µm to match the dimensions of the experimental device, and different dimensions were also simulated ranging from 50 to 300 µm. The glucose biosensor was modeled by a 5 µm domain resting on top of the anode domain. This 5µm domain represents the polymeric membrane layer containing the enzyme and the mediator, and its thickness is in line with similar reported polymeric membranes.30 The values of other parameters utilized in the model are summarized in Table 1. Table 1 Parameters used in the simulations, and their values.

Figure 2. Two-dimensional representation of the different model domains. The values for each magnitude can be found in Table 1. The anode and the cathode boundaries are highlighted in green and blue, respectively.

Parameter

Value

Channel height, Hch

127 µm

Biosensor thickness, Hbio

5 µm


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Anode length, Lano

3 mm

Cathode length, Lcat

15 mm

Electrodes width, Welec

3 mm

Gap between electrodes, Lgap

4 mm

Exchange current density in anode, N,P

1 x 102 A m-2

Exchange current density in cathode, N,

2 x 104 A m-2

′ PB/PW formal potential, QR/QS

0.15 V

Redox mediator formal potential, T /

-0.05 V

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Initial concentration of the oxidized form of mediator, 5 x 10-2 mol L [O] 0 Initial concentration of the reduced form of mediator, 1 x 10-6 mol L [R] 0 Diffusion coefficient of glucose and redox mediator 10-6 cm2 m-1 inside the polymeric membrane, D=DGLUC=DMED PB superficial concentration, [PB] sup

2.3 x 10-4 mol m2


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Maximum rate of enzymatic reaction, Vmax

5 x 10-2 mol/L

Michaelis-Menten constant for the substrate, KM

9 x 10-3 mol/L

Michaelis-Menten constant for the mediator, K0

0.08 mol m-3

Turnover number, kcat

800 s-1

4. Results and Discussion Here we show that the models set-up to simulate the biosensing anode and the electrochromic cathode are in good agreement with experimental data. We then proceed to combine these models into a galvanic system, and look at the role played by iR-drop in its behavior. We use the model to gain further understanding of the system operation, with the ultimate aim to use it as a design tool for further experimental developments. 4.1 Glucose biosensor / Anode The anode under study is a glucose biosensor that relies on glucose oxidase to catalyze the oxidation of glucose to gluconic acid, and a low oxidation potential (E0’= -0.05 mV vs Ag/AgCl) redox mediator to shuttle electrons between the enzyme and the electrode (see SM for a more detailed description of the fabrication of the biosensor). The initial concentrations of the redox mediator and glucose oxidase used in the model were taken from experimental values, assuming the enzyme concentration (and activity) to be constant throughout the experiment. A steady supply of glucose to the biosensor was simulated by setting a constant concentration boundary


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condition at the interface between the biosensing layer and the electrolyte. This was done because the experiment relied on a continuous supply of glucose to the biosensor by means of a lateral flow membrane. Simulation of lateral flow is complex, but our results show that in this case it could be successfully approximated more simply by a constant value boundary condition. Regarding mass transport properties, it was found that the values of the diffusion coefficients of glucose and the redox mediator inside the biosensing layer did not have a significant effect on the biosensor response, so an arbitrary value of 10-6 cm2 s-1 was assigned to the species inside the membrane.31-32 Last, we assumed fast electrode kinetics (Nernstian behavior) by assigning an arbitrarily high exchange current density value, J0=103 A m-2 both at the anode and the cathode. Although this means that the model could actually be simplified further, the possibility to act on the exchange current also enables the simulation of cases with sluggish electrode kinetics. The biosensor transient response was simulated using a fixed polarization potential of 0.4 V. Figure 3 shows a comparison of the experimental and simulated current results taken at t=30s. The excellent agreement between both datasets supports the validity of the model.


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Figure 3. Comparison of the experimental amperometric calibration curve (blue triangles) and the simulated curve (black circles).

4.2 Electrochromic display / Cathode The cathode consists of a modified electrode featuring a reversible electrochromic coating. Experimentally, this was a thin, homogeneous Prussian blue layer electrodeposited33 on the surface of a transparent ITO electrode. PB is a well-known inorganic electrochromic material displaying several electrochemical equilibria and their corresponding color changes.34 In this case, our work focuses on the change occurring at a potential around 0.2 V vs. Ag/AgCl, and which corresponds to the beginning of the reduction from the characteristic blue form to a colorless state. Experimentally, this process involves not only electron transfer at the electrode, but also cation exchange with the solution, as represented in the following equilibrium equation


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0* UUU 0* UU (V)W + * + X ⇋ ( 0* UU 0* UU (V)W Prussian blue

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(18)

Prussian white

A surface-bound reversible redox system was implemented in the model to represent the PB coating. The diffusion coefficient of the electrochromic species was fixed at 10-10 cm2 s-1, according to previous works.27 Experimental voltammetric data was used to determine the surface concentration of electroactive material on the electrode. The charge under the oxidation and reduction peaks recorded at a scan rate of 5 mV s-1, divided by the electrode surface area yielded the surface concentration that was subsequently used in the simulations. The exchange current density, J0, was adjusted by fitting the experimental data of the cyclic voltammograms of Prussian blue and the experiments under constant current to the simulations. A value of 2·104 A m-2 was implemented, reflecting the particular high electron transfer rate of the adsorbed system. 4.2.1 Data interpretation: relating simulation and experiment. Because we want to discuss iR-drop effects on the color definition of the system, at this point it is important to clarify the link between our simulations results, consisting of concentration profiles, and those from experiments, which involved using image analysis software as described elsewhere.29 Electrochromic materials change color as a function of electrochemical potential, which relates to the concentration of different oxidation states through the corresponding Nernst equations. These species at different oxidation states are the material color centers so, knowledge of the concentration profiles for the surface oxidized or reduced species suffices to establish a relation with the colors observed experimentally. Figure 4 shows the effects of electrolyte


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conductivity, iR-drop and current distribution on the way in which the electrochromic material (surface-bound electroactive species) undergoes reduction or oxidation. Figure 4a and Figure 4b show concentration profiles of surface-bound electroactive species at three different times during the simulation of a constant-current experiment under different iR-drop conditions. In this case, iR-drop was controlled through the electrolyte volume extending over two coplanar electrodes. The resistance inside the channel is defined as

=

11 MZ

(19)

where σ is the conductivity of the electrolyte, l is the length of the conductor, and A is the crosssectional area of the channel. Increasing the volume of solution over the electrodes increases the section area, A, and the resistance is lowered.

Figure 4. Concentration profiles of PB for (a) low, (b) moderate, and (c) high iR-drop. (d) Plot of the derivative of the superficial concentration of PB corresponding to the displays with low (A), moderate (B) and high (C) internal resistance. (e) Schematic representation of the electrochromic display at time 0 (deep blue), and after operation under cases of low (A), moderate (B) and high (B) internal resistance corresponding to the derivative curves in subfigure (c).


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Figure 4a shows the concentration profiles obtained for an “infinite” solution volume; that is, the current lines are unrestricted and distribute rather homogeneously over the entire electrochromic electrode. Under these circumstances the bound electroactive species is consumed at nearly the same rate across the entire electrode surface, and the concentration profiles are almost flat (Figure 4a). There is a slight concentration drop towards the x-axis origin because current density is higher at the electrode edge than anywhere else. If the solution volume over the electrode decreases, solution resistance increases, and we observe that the concentration profile shows the progressive consumption of material along the path of least internal resistance (Figure 4b for a case of moderate resistance, and Figure 4c for a case of high resistance). In fact, the concentration drops to almost zero in certain areas, indicating the quantitative conversion of the electroactive species along the electrode length with time.

In the following, we use these concentration profiles to determine the position of the color front and its width, which we use to represent the color smearness. The position of the color front is determined by means of the first derivative of the concentration profile curve (Fig. 4d), which is related to current density by the familiar expression1

# [ = #4 /0&Z

(20)

where C is the concentration of the electrochromic species, x represents the direction normal to the electrode inside the medium where the electroactive species is confined, which in this case is a thin coating rather than a solution. i is current, n is the number of electrons involved, F is


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Faraday’s constant, D the diffusion coefficient of the electroactive species inside the electrochromic coating, and A the electrode area. Thus, the peak appearing in this representation shows the point where current density is maximum at the electrode, which we believe can be a way to define the color front position more objectively. The peak shape, on the other hand, provides a qualitative image of the iR-drop distribution at the color front. Thus, sharp peaks with a short tail are a sign of “significant” iR-drop, while cases of “moderate” iR-drop are related to broad peaks with a long tail, as shown in Figure 4 d-B. To describe color front width, on the other hand, we have taken the region where the concentration of the surface-bound electroactive species ranges between 30 and 90%. The explanation for this arbitrary span can be found in the color analysis of actual Prussian blue electrodes, and correspond to the region displaying a linear color gradient (see SM for a detailed description). Figure 4e shows the way in which color may be perceived by an observer in each of the two three cases depicted in Figure 4d. Accuracy in the determination of the maximum current density area or color edge is thus affected both by the magnitude of iR-drop present in the system, but also and equally important, by the user’s perception. Whilst the latter can be easily overcome by means of image analysis software, improving accuracy can be a much harder challenge, particularly in cases of relatively low iR drop caused by, for instance, at the lower concentration end of the device dynamic range. Out of the many design possibilities available, one might think about narrowing the working range of the devices or introducing more advanced geometries, which is beyond the scope of this work.


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Some of the above seems to imply that the higher the iR-drop the better, because sharper color fronts are favored, it is important to bear in mind that too high an iR-drop is likely to render the self-powered device inoperative, as the magnitude of the iR-drop exceeds the potential difference between cathode and anode, as discussed below. 4.2.2 Galvanostatic experiment.


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This section aims to (i) show that concentration profiles are a straightforward way to interpret electrochromic phenomena, and (ii) to study the effect of iR-drop on applied potential under constant current conditions. Thus, a constant current experiment was simulated in which current was injected through the anode and the depletion of the electroactive material on the cathode was studied. In this case, the simulations considered the case of an electrolyte conductivity of 1 S m-1, equivalent to that of supporting electrolyte solutions commonly used in bioanalytical experiments (ionic strengths ca. 0.1M). To validate the numerical model for the electrochromic display, different current levels were simulated, corresponding to the currents registered in the amperometric experiment displayed in Figure 3. As the electric current flows through the system, the PB on the cathode is progressively bleached to PW. The full conversion of the display under


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a maximum applied current of 40 µA took place after 30 seconds, and the color front position was determined at this time on passage of lower current levels. Figure 5 shows the plot of distance converted of the display against applied current. Barring some minor differences arising from experimental error, theory and experiment seem to be in excellent agreement. During these constant current experiments, the cathode potential is free to take whatever value is required in order to overcome the iR-drop at each point on the electrode surface and sustain the current. This is in line with experiment, and results in the observation of large potential

Figure 5. Plot of the distance converted of the display for different levels of current. Experimental data (blue triangles), simulated data (black circles).

differences between electrodes, and even from one position to another within a given electrode. Note that while this is not a problem in our simulations, which are only concerned with one redox process (the conversion from Prussian blue to Prussian white), care must be taken when


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dealing with real experimental conditions, where other processes may be involved. This may lead to the onset of unwanted reactions that may damage the device. Figure 6a shows the distance converted of the display with time and the respective cell voltage change under a constant applied current of 40 µA. As expected from Ohm’s law, the transient evolution of length converted and the cell voltage follow a linear relation. Moreover, because we are dealing with a homogeneous electrolyte of constant conductivity, the potential drop in the zone where the color switch happens is constant throughout the experiment, and a homogeneous color front is always obtained. This is shown by the peaks of the derivative curves in Figure 6b, which are nearly identical. Galvanostatic operation of electrochromic devices enables a really strict control over the regions of color switch, but more importantly about the rate at which these changes occur, which shows a linear dependence with time. However, the main drawback of this approach is that control over applied potential is obviously lost, so the risk of irreversible electrochromic material damage needs to be taken seriously. One way to overcome or at least control this type of risk is by setting appropriate voltage cutoff values that enable shutting the current when these voltages are reached. In summary, the color front under constant-current conditions advances at a constant rate, and its width depends on the magnitude of the applied current, as described in the previous section. However, the current in the final device does not remain constant throughout the experiment, but will be affected by analyte concentration and also by changes in iR-drop, as will be discussed next.


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Figure 6. Galvanostatic (a-b) and potentiostatic (c-d) experiments. (a) Plots of the distance consumed of the display (black squares) and the potential the boundary electrolyte-electrode (blue triangles) with time. (b) Evolution of the superficial concentration of PB with time and the correspondent derivatives. (c) Plots of the distance consumed of the display (black squares) and the current intensity (blue triangles) with time. (d) Evolution of the superficial concentration of PB with time and the correspondent derivatives.

4.2.3 Potentiostatic experiment. iR-drop between anode and cathode affects the degree of conversion inside the cell in two ways. First, it controls the rate of advance of the color front, as we have shown in the previous section under conditions of constant applied current. The other effect acts on the width of the front, which becomes blurrier with decreasing currents (lower iR-drop across the color front), and is more likely to hamper a clear reading in a real device. This section addresses the case of a potentiostatic experiment, which is a closer approximation to what happens in an actual self-


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powered device. This is because it considers the effect of an increasing internal resistance on the electrochemical processes taking place at the cathode under a constant applied potential difference between electrodes. In contrast to galvanostatic experiments, potentiostatic operation of electrochromic devices results in higher stability and possibly more longevity, as it prevents damages caused by extreme overpotentials. On the other hand, under potentiostatic conditions, the rate of color conversion along the display electrode is proportional to the square root of time, so the appearance of color gradients or shades can be expected –an is in fact confirmed by both simulation and experiment-. A constant voltage of 1V was arbitrarily applied from the unmodified anode to induce the conversion of PB into PW at the cathode. Figures 6c and 6d show the evolution of the current passing through the device as well as the evolution of the bleached cathode region. The resulting behavior is markedly different from the case of constant current. In the galvanostatic experiment, the potential at the cathode was free to adjust until all the electroactive material was consumed. On the other hand, in the potentiostatic experiment, the material at the cathode is consumed until the internal resistance offsets the electrochemical potential at the cathode, and the electrode process stops. The color front does not progress following a linear relationship anymore, as shown in Figure 6c. This is because as the internal resistance increases, the potential observed by the cathode changes, affecting the conversion rate of the electrochromic material. A situation is eventually reached in which the internal resistance has increased dominated by electrolyte resistance across a long inter-electrode distance, causing the current to drop as a result of an insufficient electrochemical potential. Then the iR-drop decrease is driven by the diminishing current in spite of the large electrolyte resistance, widening the color front as shown by the peaks represented in Figure 6d. A similar behavior is observed at the self-powered device, where the


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color front slows its advance at different positions but the overall behavior is controlled by the analyte concentration at the biosensor. The following section addresses the effect of iR-drop on the potential applied to both anode and cathode when combined into a single system.

4.3 Self-powered electrochromic biosensor. After studying the two components of the device independently, the behavior of the self-powered device was also simulated, evaluating the color switch of the electrochromic display after 30 seconds, as was done with the actual device. The simulation was done by poising both electrodes at a constant potential value of 0 V. This means that the system is shorted, and that it delivers its maximum current. The experiment was simulated under conditions of constant medium conductivity of 1 S m-1 and different glucose concentrations to match the actual experimental conditions. Figure 7 shows that, despite slight discrepancies likely due to error in the visual determination of the color front position, the agreement between both curves is still remarkable. It is worth noting that the color front advances a maximum of 6mm after 30s, despite the favorable experimental conditions (the cathode is 15mm long, containing plenty of electrochromic material available for reaction, and glucose is abundantly available to the biosensor). This is because the potential difference between the cathode and the anode reactions is around 0.5V, and is rapidly affected by the increasing internal resistance. The resistance growing inside the cell affects the actual potential observed at both electrodes, as presented in the previous section, diminishing the cell


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potential (see equation 21 below) as the experiment progresses. This also affects the maximum current the system can deliver, with decreases with increasing internal resistance. Eventually, the iR-drop across the cell is so large that the system no longer works and the color front stops its advance.

Figure 7. Calibration curves for the self-powered electrochromic device. Experimental (blue triangles) and simulated (black circles).

Figure 8 shows a number of linear sweep voltammograms for these same anode and cathode, simulated under different electrolyte conductivities. These conductivities range from 100 S m-1, a high value that results in virtually no iR-drop effects, down to 0.1 S m-1, a low value under which


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iR-drop is very significant. These voltammograms show that, as expected,1, 35 the electrochemical response at both electrodes is heavily influenced by the magnitude of the iR-drop present. On one hand, the current peak potentials shift towards each other. On the other hand, the peak currents decrease with increasing internal resistance. Figure 9 show a graph of maximum current as a function of medium conductivity for the galvanic system depicted in Figure 8. These voltammograms and maximum current plots were obtained for a system modeled with a homogeneous current distribution, using the electrolyte conductivity as main parameter affecting internal resistance. However, the results can be extrapolated to our model system in which conductivity is constant but internal resistance changes as a function of distance. The effective potential observed by both electrodes shifts as the experiment progresses, causing the ∆Ecell to decrease, and dragging the current down. This current decrease slows the conversion, and results in a widening of the color front as a result of the low iR value.


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Figure 8. Simulated linear sweep voltammograms of the anode (black line) and cathode (blue line) responses.


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Figure 9. Limiting current density plot as a function of supporting electrolyte conductivity.

4.3.1 Outlook: design aspects in self-powered devices So far we have seen the huge impact of iR-drop effects on the behavior of an electrochromic display, and how much it can affect the performance of the self-powered sensor we are describing. Simulations have enabled us to understand the system behavior and they also allow us to use the same model as design tool. The model, and the design parameters studied here can be of use not only for the development of this particular type of sensor, but we believe it can be an aid to those developing electrochromic devices and electrochemical power sources alike.


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When configured as a self-powered biosensor, we have shown that the device behavior is controlled by the internal resistance inside the cell, which affects both conversion rate and colorfront width. The device cell voltage is defined as

\@@ = − P − [

(21)

where Ecat and Eano is the potential of the cathode (display) and anode (biosensor) respectively, and iR is the ohmic drop inside the cell. An electric current flows at positive cell voltages, turning the PB into PW while the mediator at the biosensing anode is oxidized. As the electrochromic material on the display is consumed, the electrolyte resistance between the PB and the redox mediator increases, reaching a point where the cell potential approaches zero. At this point the current drops and the color front becomes blurrier until the system appears to have come to a halt. Although the electrode processes continue, their rate is hugely diminished due to the small overpotential, causing the current to drop to almost zero. Equations 19 and 21 point at three ways to control device performance: (i) by choosing adequate electrode processes, (ii) by selecting the right electrolyte conductivity, and (iii) by a suitable cell geometry design. The following results were obtained from simulations using a fixed glucose concentration of 5 mol m-3, falling in the lower range of concentrations where the current output is low, and a sluggish and less clear colorimetric response is obtained. The response time is fixed as in the previous experiments at 30 seconds. The effect of formal cell potential


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Figure 10a shows the effect that increasing formal potential of the electrochromic species, Ecat, has on the colorimetric response. In these simulations, the formal potential of the cathode process was changed. As expected, with higher formal potentials, and thus higher cell voltages, the cathode region undergoing color change becomes larger, as the cell is able to sustain higher internal resistance levels. Once this internal resistance becomes equal to or higher than the potential difference between cathode and anode reactions (eq. 21), the regeneration of the redox mediator is stopped, and the enzymatic reaction ceases, in line with the potentiostatic experiment described above. The maximum current, which is controlled by the biosensing anode, will decrease as described earlier unless the formal potential remains sufficiently high throughout the experiment (Fig. S2). In this particular case in which the internal resistance is overcome throughout the experiment, the biosensor operates at its maximum current level and the color front width remains essentially unaltered, in line with the results of the galvanostatic experiment. As seen with the error bars representing the size of the color gradient of the switch, the color front remains essentially unaltered and relatively narrow regardless of the overall cell potential, as the iR-drop at the color front is almost constant (Fig. S3a).On the other hand, a clear improvement can be observed in the distance converted as it increases with the cell voltage reaching a maximum at around 600 mV, a value that current biofuel cells can achieve.36-38 The onset of the oxygen reduction process sets a natural limit at the anode, so using redox mediators with formal potentials below -0.2 to -0.3V vs SCE probably does not make much sense in oxidase-based systems (the formal potential of the FAD group in glucose oxidase is around -0.5V vs SCE39). The case of the cathode is different; in this case it may be possible to find electrochromic materials with higher formal potentials than the Prussian blue/ Prussian white system, although they may not be so friendly to work with34, 40.


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The effect of electrolyte conductivity Figure 10b shows the effect of electrolyte conductivity on a system with formal cell potential of 200 mV, according to the experiment. The conductivities covered in our study range between 0.1 S m-1, characteristic of solid-gel polymeric electrolytes41, and 1.25 S m-1, which is more typical of conventional liquid electrolytes. Conductivity variations translate into changes in the internal resistance, as seen in equation 18, which ultimately affect the behavior of the display. Higher electrolyte conductivities result in lower internal resistance, which facilitates higher degrees of color conversion in the cell, however, the lower internal resistance generates a wider color front In other words, in the case of a sensing device, conductivity provides a trade-off between sensitivity and accuracy. As we have shown for galvanic systems, a high internal resistance damages device performance because it lowers the effective cell potential and results in lower currents. Lower conductivity media, which leads to narrower color fronts at high current levels, may be a feasible choice in cases in which power availability is not an issue, but should be ruled out in self-powered devices (and power sources in general). Although lower conductivities result in higher resistances that keep the current more focused, they will also require larger potential differences between electrodes to overcome the correspondingly high iR-drop levels (Fig. S3b), which can be a problem.


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The effect of cell geometry Last, cell geometry covers several design parameters such as electrode size and shape, interelectrode separation, and channel aspect ratio. We evaluated these last two parameters since they play a key role in the behavior of the electrochromic display. The height of the channel containing both electrodes was studied using values up to several hundreds of microns, which are typical magnitudes in displays, and in miniaturized devices in general. Changing the height of the channel containing the electrodes affects the current distribution inside the device, and therefore the current path inside the channel. The results in this case are similar to those obtained when electrolyte resistance was changed. As the crosssectional area of the device is increased internal resistance decreases, facilitating the flow of electric current and thus achieving larger extensions of color conversion, as seen in Figure 10c. However, the current is more homogeneously distributed across the electrode surfaces, and the color front becomes more diffuse (Fig. S3c).


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Figure 10. Plots of the length converted and the color front definition against the parameter evaluated: (a) Formal potential of the electrochromic species, (b) Electrolyte conductivity, (c) Paper thickness and (d) Anode-cathode separation distance. Black circles represent the length of the PB display converted into PW, and blue squares represent the front definition deduced from the peak height of the derivative curve of the superficial concentration of PB on the display. Error bars represent color front width.

Last, the effect that the anode-cathode separation distance has on the device performance was also studied. In our present case this is interesting because the resistance of this gap can be used as a “switch” to prevent the activation of the display in the absence of analyte. Different distances were tested ranging from a few hundred microns up to a few millimetres. As the separation distance increases, the iR-drop inside the channel increases too, leading to a more sluggish conversion of the PB display (Figure 10d). As in the first case, where the formal potentials were tested, the internal resistance at the switching zone remains almost constant due to the small contribution of the increasing length between the PB and the anode in equation 18, which leads to an unaltered color front (Fig. S3d).


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The importance of cell geometry is that it can help the designer to overcome certain limitations imposed by the materials, the sensing anode, the device work environment, or the fabrication processes. 5. Conclusions and outlook This work has shown how iR-drop can be used as a design factor in electrochromic devices, as a means to control the degree of color conversion. The present work has presented a numerical tool intended for the exploration of the effects of internal resistance on the performance of a selfpowered devices based on the combination of electrochromic materials and biosensors. However, the scope of this work goes much farther, as it can serve as a design tool of interest not only in the design of this type of devices, but also in the design of other devices involving electrochromic materials, such as displays and smart glass, and in miniaturized power generation devices in general, where internal resistance losses are clearly detrimental to performance. Some fundamental insight can be gained already from equation 19 and particularly equation 21, which provide a first approach to both understanding the behavior of these systems and their design. However, these simplifying approaches fall short in complex systems like the one described here, where the net observed behavior results from the combination different phenomena occurring in each system component. This is when finite element tools bring a significant advantage by providing solutions that better reflect these interactions. The model presented here accounts for three key design parameters, namely electrode processes, electrolyte resistance, and cell geometry. The model enables the exploration of different conditions so that specific applications can be better designed, considering the limitations imposed by materials and fabrication processes. In the case of the self-powered electrochromic biosensors studied here,


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this tool can serve to design devices that can operate within a desired concentration range, ensuring that the resulting color changes can be observed easily and unambiguously by the naked eye. The limitations facing these self-powered devices may be solved mainly through geometric design and the choice of materials with suitable formal potentials. On the other hand, conventional electrochromic devices, such as displays and smart windows, which account for most of the applications involving electrochromic materials, can also benefit from inclusion of iR-drop as design parameter for the fabrication of multicolor devices, or for the modulation of the radiation filtering abilities in smart glass. Supporting Information Contains experimental details including chemicals and materials involved in the construction of the actual device. Description of the color front position and width determination from , experimental data. Additional simulation results showing Current transients as a function of

internal resistance as a function of several parameters including channel geometry, formal potentials, and electrode separation, and current density distribution in the channel as a function of electrolyte conductivity. The COMSOL 5.3 file for the self-powered device and the model report are also provided for convenience.

Acknowledgements This work was supported by a 2016 BBVA Foundation Grant for Researchers and Cultural Creators. The authors would like to thank Edmund Dickinson, from the COMSOL support team


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for his patience and insightful comments, some of which were crucial in the setting up of the self-powered system simulations. References. 1. Bard, A. J.; Faulkner, L. R., Electrochemical Methods. Fundamentals and Applications, Second ed., 2000. 2. Dickinson, E. J. F.; Ekström, H.; Fontes, E., Comsol Multiphysics®: Finite Element Software for Electrochemical Analysis. A Mini-Review. Electrochem. Commun. 2014, 40, 7174. 3. Nam, J. Y.; Kim, H. W.; Lim, K. H.; Shin, H. S.; Logan, B. E., Variation of Power Generation at Different Buffer Types and Conductivities in Single Chamber Microbial Fuel Cells. Biosens. Bioelectron. 2010, 25, 1155-9. 4. Dickinson, E. J. F.; Limon-Petersen, J. G.; Rees, N. V.; Compton, R. G., How Much Electrolyte Is Required to Make a Cyclic Voltammetry Experiment Quantitatively "Diffusional"? A Theoretical and Experimental Investigation. J. Phys. Chem. C 2009, 113, 11157-11171. 5. Forster, R. J., Microelectrodes: New Dimensions in Electrochemistry. Chem. Soc. Rev. 1994, 23, 289-297. 6. Arrigan, D. W., Nanoelectrodes, Nanoelectrode Arrays and Their Applications. Analyst 2004, 129, 1157-65. 7. Amatore, C.; Maisonhaute, E.; Simonneau, G., Ultrafast Cyclic Voltammetry: Performing in the Few Megavolts Per Second Range without Ohmic Drop. Electrochem. Commun. 2000, 2, 81-84. 8. Rees, N. V.; Klymenko, O. V.; Maisonhaute, E.; Coles, B. A.; Compton, R. G., The Application of Fast Scan Cyclic Voltammetry to the High Speed Channel Electrode. J. Electroanal. Chem. 2003, 542, 23-32. 9. Eric Shen, D.; Österholm, A. M.; Reynolds, J. R., Out of Sight but Not out of Mind: The Role of Counter Electrodes in Polymer-Based Solid-State Electrochromic Devices. J. Mater. Chem. C 2015, 3, 9715-9725. 10. Andersson Ersman, P.; Kawahara, J.; Berggren, M., Printed Passive Matrix Addressed Electrochromic Displays. Org. Electron. 2013, 14, 3371-3378. 11. Kawahara, J.; Ersman, P. A.; Engquist, I.; Berggren, M., Improving the Color Switch Contrast in Pedot:Pss-Based Electrochromic Displays. Org. Electron. 2012, 13, 469-474. 12. Liu, H.; Crooks, R. M., Paper-Based Electrochemical Sensing Platform with Integral Battery and Electrochromic Read-Out. Anal. Chem. 2012, 84, 2528-32. 13. Zloczewska, A.; Celebanska, A.; Szot, K.; Tomaszewska, D.; Opallo, M.; JonssonNiedziolka, M., Self-Powered Biosensor for Ascorbic Acid with a Prussian Blue Electrochromic Display. Biosens. Bioelectron. 2014, 54, 455-61. 14. Kong, B.; Selomulya, C.; Zheng, G.; Zhao, D., New Faces of Porous Prussian Blue: Interfacial Assembly of Integrated Hetero-Structures for Sensing Applications. Chem. Soc. Rev. 2015, 44, 7997-8018. 15. Karyakin, A. A., Prussian Blue and Its Analogues: Electrochemistry and Analytical Applications. Electroanalysis 2001, 13, 813-819.


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16. Pinyou, P.; Conzuelo, F.; Sliozberg, K.; Vivekananthan, J.; Contin, A.; Poller, S.; Plumere, N.; Schuhmann, W., Coupling of an Enzymatic Biofuel Cell to an Electrochemical Cell for Self-Powered Glucose Sensing with Optical Readout. Bioelectrochemistry 2015, 106, 22-7. 17. Liana, D. D.; Raguse, B.; Gooding, J. J.; Chow, E., Toward Paper-Based Sensors: Turning Electrical Signals into an Optical Readout System. ACS Appl. Mater. Interfaces 2015, 7, 19201-9. 18. Chow, E.; Liana, D. D.; Raguse, B.; Gooding, J. J., A Potentiometric Sensor for Ph Monitoring with an Integrated Electrochromic Readout on Paper. Aust. J. Chem. 2017, 70, 979984. 19. Cooper, J. A.; Compton, R. G., Channel Electrodes – a Review. Electroanalysis 1998, 10, 141-155. 20. Katz, E.; Bückmann, A. F.; Willner, I., Self-Powered Enzyme-Based Biosensors. J. Am. Chem. Soc. 2001, 123, 10752-10753. 21. Wang, J., Electrochemical Glucose Biosensors. Chem. Rev. 2008 108, 814-825. 22. Liaudet, E.; Battaglini, F.; Calvo, E. J., Electrochemical Study of Sulphonated Ferrocenes as Redox. J. Electroanal. Chem. 1990 293, 55-68. 23. Cass, A. E. G.; Davis, G.; Francis, G. D.; Hill, H. A. O.; Aston, W. J.; Higgins, I. J.; Plotkin, E. V.; Scott, L. D. L.; Turner, A. P. F., Ferrocene Mediated Enzyme Electrode for Amperometric Determination of Glucose. Anal. Chem. 1984, 56, 667-671. 24. Battaglini, F.; Calvo, E. J., Digital Simulation of Homogeneous Enzyme Kinetics for Amperometric Redox-Enzyme Electrodes. Anal. Chim. Acta 1992, 258, 151-160. 25. Yokoyama, K.; Kayanuma, Y., Cyclic Voltammetric Simulation for Electrochemically Mediated Enzyme Reaction and Determination of Enzyme Kinetic Constants. Anal. Chem. 1998, 70, 3368-3376. 26. Kulys, J.; Tetianec, L.; Bratkovskaja, I., Pyrroloquinoline Quinone-Dependent Carbohydrate Dehydrogenase: Activity Enhancement and the Role of Artificial Electron Acceptors. Biotechnol. J. 2010, 5, 822-8. 27. García-Jareño, J. J.; Sanmatías, A.; Navarro-Laboulais, J.; Vicente, F., Chronoamperometry of Prussian Blue Films on Ito Electrodes: Ohmic Drop and Film Thickness Effect. Electrochim. Acta 1999, 44, 4753-4762. 28. Dickinson, E. J. F.; Limon-Petersen, J. G.; Compton, R. G., The Electroneutrality Approximation in Electrochemistry. J. Solid State Electrochem. 2011, 15, 1335-1345. 29. Pellitero, M. A.; Guimera, A.; Kitsara, M.; Villa, R.; Rubio, C.; Lakard, B.; Doche, M. L.; Hihn, J. Y.; Javier Del Campo, F., Quantitative Self-Powered Electrochromic Biosensors. Chem. Sci. 2017, 8, 1995-2002. 30. Harrison, D. J.; Turner, R. F. B.; Baltes, H. P., Characterization of Perfluorosulfonic Acid Polymer Coated Enzyme Electrodes and a Miniaturized Integrated Potentiostat for Glucose Analysis in Whole Blood. Anal. Chem. 1988, 60 2002-2007. 31. Harnisch, F.; Warmbier, R.; Schneider, R.; Schroder, U., Modeling the Ion Transfer and Polarization of Ion Exchange Membranes in Bioelectrochemical Systems. Bioelectrochemistry 2009, 75, 136-41. 32. Sel, O.; To Thi Kim, L.; Debiemme-Chouvy, C.; Gabrielli, C.; Laberty-Robert, C.; Perrot, H., Determination of the Diffusion Coefficient of Protons in Nafion Thin Films by AcElectrogravimetry. Langmuir 2013, 29, 13655-60.


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TOC GRAPHIC


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Lgap

Lcat Hch

Hbio Lano



5 0

4 0

3 0

I / µ A

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

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2 0 E x p e r im e n t S im u la tio n

1 0

0 0

1 0

2 0

3 0


[G lu c o s e ] / m o l· m

4 0 -3

5 0

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Figure 4. Concentration profiles of PB for (a) low, (b) moderate, and (c) high iR-drop. (d) Plot of the derivative of the superficial concentration of PB corresponding to the displays with low (A), moderate (B) and high (C) internal resistance. (e) Schematic representation of the electrochromic display at time 0 (deep blue), and after operation under cases of low (A), moderate (B) and high (B) internal resistance corresponding to the derivative curves in subfigure (c). 97x46mm (300 x 300 DPI)



2 0

1 5

D is ta n c e / m m

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

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1 0

5 E x p e r im e n t S im u la tio n

0 0

1 0

2 0

3 0

I / µ A


4 0

5 0

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a)

b)

c)

d)



7 6 5 4

D is ta n c e / m m

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

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3 2 E x p e r im e n t S im u la tio n

1 0 0

5

1 0

1 5

2 0


2 5

[G lu c o s e ] / m o l· m

3 0 -3

3 5

4 0

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100 S·m-1

Current density / μA·cm-2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1 S·m-1

0.1 S·m-1

E/V



2 0 0

-2

1 5 0

J / µ A ·c m

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

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1 0 0

5 0

0 0 .0 1

0 .1

1

σ/ S

· m

-1


1 0

1 0 0

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a)

b)

c)

d)


iR Drop Effects in Self-Powered and ... - ACS Publications

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