Methodology for measuring current distribution effectsin electrochromic smart windows

Johnny Degerman Engfeldt,1,2,* Peter Georen,2

Carina Lagergren,1 and Göran Lindbergh1

1Applied Electrochemistry, School of Chemical Science and Engineering,KTH—The Royal Institute of Technology, SE-100 44 Stockholm, Sweden

2ChromoGenics AB, Märstagatan 4, SE-75323 Uppsala, Sweden

*Corresponding author: johnnyd@kth.se

Received 27 April 2011; accepted 21 August 2011;posted 2 September 2011 (Doc. ID 146673); published 3 October 2011

Electrochromic (EC) devices for use as smart windows have a large energy-saving potential when used inthe construction and transport industries. When upscaling EC devices to window size, a well-known chal-lenge is to design the EC device with a rapid and uniform switching between colored (charged) andbleached (discharged) states. A well-defined current distribution model, validated with experimentaldata, is a suitable tool for optimizing the electrical system design for rapid and uniform switching. Thispaper introduces a methodology, based on camera vision, for experimentally validating EC current dis-tribution models. The key is the methodology’s capability to both measure and simulate current distribu-tion effects as transmittance distribution. This paper also includes simple models for coloring (charging)and bleaching (discharging), taking into account secondary current distribution with charge transfer re-sistance and ohmic effects. Some window-size model predictions are included to show the potential forusing a validated EC current distribution model as a design tool. © 2011 Optical Society of AmericaOCIS codes: 230.0230, 230.2090.

1. Introduction

Electrochromic (EC) materials are of great technolo-gical interest for a variety of applications, for exam-ple, in highly interesting energy-efficient smartwindows [1–3]. An EC device can be viewed as a thin-film electrical battery whose charging state ismanifested in optical absorption, i.e., the optical ab-sorption increases with increased state of chargeand vice versa. As a result of this changeable absorp-tion, the transmittance of solar energy and visiblelight in windows can be controlled, hence the name“smart window” [2]. These unique properties of con-trolling light and solar energy transmittance throughwindows make the EC technology potentially able toincrease indoor comfort and save large amounts of en-ergy for buildings [2,3]. Most energy savings derive

from reducing the amount of solar energy passingthrough the windows, i.e., reducing the building’scooling needs. In fact, compared to an efficient low-emissivity window, the EC window shows annualpeak cooling load reductions of 19%–26% when theEC window is controlled to minimize solar heat gainsand lighting energy use savings of 48%–67%when theEC window is controlled for visual comfort [4].

Today, EC devices like small windows, car rear-view mirrors, and eyewear are being produced asprototypes by various companies [5]. To reach theconstruction market, it is crucial to be able to pro-duce large-area EC devices (from 1m2 upward) withsatisfactory performance and low cost. A challengewith upscaling is to design the electrical system ofthe EC device with a rapid and uniform coloration(charging) and bleaching (discharging) [1,3]. Al-though this is a well-known issue, little work hasbeen done to address and solve these problems [6,7].

0003-6935/11/295639-08$15.00/0© 2011 Optical Society of America

10 October 2011 / Vol. 50, No. 29 / APPLIED OPTICS 5639

The EC device electrical system design can beimproved either by decreasing the transparent con-ductor resistance or by optimizing the charge anddischarge procedures. Decreasing the transparentconductor resistance, i.e., increasing its thickness,will result in a significant increase of the overall de-vice cost since the transparent conductor material isvery expensive. To optimize the coloration andbleaching procedures, there has to be a well-foundedunderstanding of the current distribution effects inthe EC electrical and electrochemical systems. Afurther advantage of understanding the current dis-tribution effects is that the EC electrical system de-sign also can be optimized for low cost and lifetime,for example decreasing the amount of transparentconductor material to a minimumwithout sacrificingtoo much of the performance and lifetime. A currentdistribution model, validated with experimentaldata, is known to be a powerful tool for investigatingand understanding current distribution effects ofnovel designs such as the EC system.

This paper introduces a methodology, based oncamera vision, that makes it possible to validateEC current distribution models with experimentaldata. The methodology consists of two experimentalprocedures and one model simulation procedure. Thefirst experimental procedure enables the experimen-tal equipment to measure current distribution effectsas transmittance distribution during coloration andbleaching procedures. The second experimentalprocedure enables current distribution models to si-mulate transmittance distribution over time for dif-ferent coloration and bleaching procedures. Thesimulation procedure evaluates EC current distribu-tion models by comparing the model-simulatedtransmittance distribution data with the experimen-tally measured transmittance distribution data. Toshow this methodology’s ability to validate EC cur-rent distribution, some simple current distributionmodels are included. Moreover, some EC window-size coloration predictions are also included to showthe potential of using this methodology as a designtool for optimizing the EC system design. This paperis the starting point of the work to develop a well-defined mathematical model for EC systems.

2. Experimental

In this section the material and equipment used inthe methodology are presented. The actual proce-dures used in the methodology are presented inSection 3.

A. EC Device

The EC devices used in this study are made of flex-ible polyester foils with sputter-deposited transpar-ent electrical conductors [In2O3:SnO2 (ITO)], anodicEC material (NiO), and cathodic EC material (WOx)that are joined together with an ion-conducting elec-trolyte, illustrated in Fig. 1.

All EC devices have an ITO sheet resistancemeasured to 20Ohm=sq. Two different EC device

sizes are used in this study, 5 cm × 5 cm and20 cm × 5 cm, as shown in Figs. 1(c) and 1(d). The pur-pose of using two different EC device sizes is to usethe 5 cm × 5 cm devices for measurements where thecurrent distribution effects should be kept to a mini-mum and the 20 cm × 5 cm devices to study currentdistribution effects as transmittance distribution.The current distribution effects can be studied on de-vices with the width of only 5 cm since the currentcollector resistance is negligible, thus making thedistance between the current collectors the criticaldesign parameter.

B. Experimental Equipment

The equipment used in this study consists of a digitalcamera (Sony 10XCDV60CR), high-resolution optics(Goyo 80GMHR31614MCN) with a 532nm laser-linebandpass filter, a cold cathode fluorescent backlightpanel, a potentiostat (PAR EG&G Model 273A), ageneral-purpose interface bus (IEEE 488.1) control-ler for high-speed USB, and a computer with the soft-ware LabView 8.6. A schematic and an actual pictureof the experimental setup are shown in Fig. 2.

The camera (with an optical bandpass filtermounted) and the potentiostat are connected to thecomputer, with the backlight panel providing back-ground light for the camera. To minimize stray lightdisturbance, the camera and backlight panel areplaced in a closed cabinet. In addition, an opaquematerial, designed to only emit light within the di-mensions of the active EC surface, is placed on

Fig. 1. (a) Schematic illustration of an EC device (b) in cross sec-tion, (c) the 5 cm × 5 cm EC device, and (d) the 20 cm × 5 cm device.The current collectors are placed 0:5 cm from the active EC sur-face. The darker parts around the active EC surface in (c) and(d) are sealant materials.

5640 APPLIED OPTICS / Vol. 50, No. 29 / 10 October 2011

top of the backlight panel during calibration and thefollowing measurement(s). The camera is placedabout 80 cm from the backlight panel.

A LabView interface is programmed to simulta-neously control the coloration/bleaching (charge/discharge) of the device and to collect data from theEC device samples. A potentiostat is used for collect-ing electrical data (current, voltage, and charge),while a digital camera is used for collecting opticaldata (transmittance and location). As accurate elec-trical chargemeasurement is important, thepotentio-stat’s coulometer is used for charge measurements.Using a digital camera for optical measurementshas the advantage of freely choosing quantifyingpoints, lines, or contrast levels without modifying theexperimental setup.Yet another advantage is thepos-sibility to capture pictures of the EC surface asimages, which makes it possible to capture the actualcoloration/bleaching behavior and optical deviations(such as defects) over the EC surface. This study uti-lizes the option of quantifying discrete points fordetermining the local transmittance state and uti-lizes images for showing the actual coloration/bleach-ing behavior.

It is important to notice the use of an optical band-pass filter. This bandpass filter is the key to makingadequate and comparable optical light-transmit-tance measurements, independent of the backgroundlight spectrum. Using an optical bandpass filter, the

camera only detects wavelengths of 532nm, makingthe transmittance measurement easy to define andcompare with other transmittance measurements.The specific bandpass filter wavelength, 532nm, waschosen since EC applications often are see-throughapplications and the human eye is most sensitiveat around that wavelength. However, using a band-pass filter coloration/bleaching information for otherwavelengths is neglected, but since it is easy to mea-sure the light-transmittance spectrum at differentstates of charge (using a spectrometer), the neglectedinformation is possible to obtain anyway.

An Ocean Optics spectrometer was used for verify-ing the transmittance measurements.

C. Experimental Setup Accuracy and Precision

As the setup should be able to measure the change oftransmittance state and its distribution over a large-area device, the setup has to be optically calibrated toprocess accurate and precise location and transmit-tance data from the digital images.

The pixel-to-real-world coordinates are calibratedwith a calibration grid. The calibration results in alocation measurement accuracy within 1mm withvery high precision. The pixel size is about 0:4mmwith a camera distance of 80 cm.

The transmittance measurement is calibrated byfirst measuring the light intensities at 0% and 100%transmittance state for every measurement pointwith 50 iterations, followed by calculating the meanlinear relationship for every measurement point.Repeating with 50 iterations for every measurementpoint is important for increasing the accuracy since itminimizes influence of both the fluctuations of lightintensity and unevenness of light intensity over thebacklight panel area. However, since light scatteringand reflection make the camera detect light in-tensities from other pixels than desired, the calcu-lated linear relationship between the light intensityand transmittance has to be adjusted to give an accu-rate transmittance. This light scatter correctionprocedure is preformed by measuring the lightintensities and transmittance through a linearlystepped neutral density filter (11 transmittancestates in the range of 1%–91%) and calculating thecorrection coefficients for the linear relationship. Byusing the light scatter correction values of 0.92 forthe linear coefficient and 1.16 for the zero transmit-tance point, the transmittance measurement accu-racy is within �1% units and the precision within�1% [i.e., �ðT532nm × 0:01Þ% units] in the transmit-tance range 5%–85%. The limiting factors of this set-up’s accuracy and precision are the light intensityfluctuation over time and the unevenness over thebacklight panel.

The experimental setup sample rate for time, cur-rent, potential, charge, and transmittance points isabout 0:3 s.

Fig. 2. Experimental setup as (top) schematic illustration and(bottom) actual picture.

10 October 2011 / Vol. 50, No. 29 / APPLIED OPTICS 5641

3. Results

A. Experimental Results

1. Transmittance Distribution Measurements

The setup is able to measure the transmittance dis-tribution as pictures, which is shown in Fig. 3, wherea 20 cm × 5 cm EC device has been colored (charged)with a potential of 6:0V versus WOx for about 6 s.

Studying pictures like this, current distribution ef-fects are shown as uneven transmittance distribu-tion, i.e., a color gradient over the surface. Thiscolor gradient is seen in Fig. 3 as more colored areasnear the current collectors than in the middle. Byplacing the transmittance measurement points ac-cording to Fig. 3, current distribution effects canbe measured quantitatively as transmittance distri-bution, shown in Figs. 4 and 5.

The quantitative data show the same results as inFig. 3; i.e., the areas near the current collectors arecoloring/bleaching faster due to current distributioneffects. The transmittance is only plotted for half ofthe device as measurements showed that the trans-mittance distribution behavior during coloration/bleaching was symmetrical.

2. Correlation of Transmittance to State of Charge

To simulate transmittance distribution, using ECcurrent distribution models, this methodology usesexperimental data for correlating the transmittancestate to the state of charge (SOC). This correlationenables the model to simulate the charge distribu-tion as transmittance distribution, thus making itpossible to compare measured and model-simulatedtransmittance distribution data.

To correlate the experimental transmittance toSOC, small-area EC devices (5 cm × 5 cm) with a con-trolled coloration/bleaching algorithm are used. Thecontrolled coloration/bleaching algorithm consists ofa galvanostatic charge and discharge current of0:05mA=cm2, with the fully colored and bleachedstate limits of 15% and 55% transmittance, respec-tively. The small-area device and galvanostaticcoloration/bleaching algorithm are chosen to mini-mize the current distribution effects. If there aresignificant current distribution effects during thisexperimental procedure, the transmittance will notbe uniform over the EC surface throughout the pro-cedure, thus making it impossible to relate the SOCto the actual corresponding transmittance state. Thecurrent distribution effects are recorded by alwaysmeasuring the transmittance in nine evenly distrib-uted measurement points.

Fitting the experimental transmittance and SOCdata from this procedure results in the polynomialEq. (1),

T532nmðQÞ ¼ −0:00015Q3− 0:0002Q2 þ 0:05414Q

þ 0:547509; ð1Þ

where T532nm is light transmittance at wavelength532nm andQ is mC=cm2. This is illustrated in Fig. 6,where a comparison between some typical experi-mental data and polynomial fitted data is shown.

The comparison shows that the fitted data differ byno more than �0:0075% units from the measured

Fig. 3. EC surface and its transmittance measurement points fora 20 cm × 5 cm EC device with uneven transmittance distribution.The six outer measurement points to the left and right are placed15mm from its nearest current collector, and all other measure-ment points are evenly spaced between these outer points. TheWOx current collector outside on left side (not shown in the figure)is the origin point for all measurement points. The darker parts atthe very edges are sealant glue and mask material.

0 1 2 3 4 5 60.1

0.2

0.3

0.4

0.5

0.6

Tra

nsm

ittan

ce a

t 532

nm

Time / s

Fig. 4. Transmittance as a function of time when coloring (char-ging) a 20 cm × 5 cm EC device with 6:0V versus WOx. The mea-surement points are placed 15mm (squares), 37mm (crosses),60mm (circles), 82mm (asterisks), and 105mm (triangles) fromthe WOx current collector.

0 2 4 6 8 10 12 140.1

0.2

0.3

0.4

0.5

0.6

Tra

nsm

ittan

ce a

t 532

nm

Time / sFig. 5. Transmittance as a function of time when bleaching (dis-charging) a 20 cm × 5 cm EC device with −6:0V versus WOx. Themeasurement points are placed 15mm (squares), 37mm (crosses),60mm (circles), 82mm (asterisks), and 105mm (triangles) fromthe WOx current collector.

5642 APPLIED OPTICS / Vol. 50, No. 29 / 10 October 2011

data. This shows that the correlation procedure hashigh accuracy.

B. Model Simulation Results

1. EC Models

There are numerous local kinetic models for the col-oration and bleaching behavior of EC materials,especially WOx, including effects of charge transfer,diffusion, and local ohmic effects [8,9]. However,neither of these models includes effects of currentdistribution. The current distribution models pre-sented in this study are two-dimensional time-dependent models (one for coloring and one forbleaching) describing the potential, current, andcharge distribution over the EC device surface.Ohm’s law [Eqs. (2) and (3)] is used to describe cur-rent flow through the transparent conductor layers(ITO layers):

− σ1d2E1

dx2¼ j; ð2Þ

− σ2d2E2

dx2¼ −j: ð3Þ

These models describe secondary current distribu-tion as they include voltage losses in the electroche-mical reaction kinetics. The electrochemical reactionkinetics is described by a Butler–Volmer-based equa-tion. Moreover, the electrolyte is described as a resis-tance. However, the models do not include anydiffusion effects or electrical resistance effectsbetween the current collector and the transparentconductor. An addition to the discharge model isan electrode interface resistance. More details areshown in Appendix A.

Although this model relies on simple kinetics,there are numerous of kinetic models for the colora-tion and bleaching behavior of EC materials, espe-cially WOx, under different conditions [8].

2. Model Fitting and Verification

In the models, one parameter, S · i0, was used whenfitting the model to experimental results. All otherparameters where kept constant. More details areshown in Appendix A.

Figures 7 and 8 show both the measured and thesimulated data for one case of coloring (charging) andbleaching (discharging), respectively.

One could see that the simulated data catch thetransmittance distribution behavior fairly well, i.e.,that the areas near the current collectors color/bleach faster than the areas near the middle of thedevice. However, the coloring model shows a some-what better match than the bleaching model.

Notice that these results only show that the pre-sented models are validated for transmittance distri-bution for this particular case. Depending on thepurpose of the model simulations, the model shouldbe validated for different coloration/bleaching vol-tages, sizes, or other properties. The model could alsobe validated with the total current and charge re-sponse as these data are also available.

−10 −8 −6 −4 −2 00.1

0.2

0.3

0.4

0.5

0.6

Charge / mC/cm2

Tra

nsm

ittan

ce a

t 532

nm

Measured dataFitted data

Fig. 6. Comparison between some typical experimentally mea-sured data and the calculated data from the transmittance versusSOC polynomial.

0 1 2 3 4 5 60.1

0.2

0.3

0.4

0.5

0.6

Tra

nsm

ittan

ce a

t 532

nm

Time / s

Fig. 7. Transmittance as a function of time when coloring (char-ging) a 20 cm × 5 cm EC device with 6:0V versus WOx. The experi-mental (markers) and model simulation (solid lines) measurementpoints are placed 15mm (squares), 37mm (crosses), 60mm(circles), 82mm (asterisks), and 105mm (triangles) from theWOx current collector.

0 2 4 6 8 10 12 140.1

0.2

0.3

0.4

0.5

0.6

Tra

nsm

ittan

ce a

t 532

nm

Time / sFig. 8. Transmittance as a function of time when bleaching (dis-charging) a 20 cm × 5 cm EC device with −6:0V versus WOx. Theexperimental (markers) and model simulation (solid lines) mea-surement points are placed 15mm (squares), 37mm (crosses),60mm (circles), 82mm (asterisks), and 105mm (triangles) fromthe WOx current collector.

10 October 2011 / Vol. 50, No. 29 / APPLIED OPTICS 5643

3. Model Simulation Predictions

When having an EC current distribution model ableto simulate the transmittance distribution, the mod-el can be used as a design tool. A design tool wherenumerous parameters such as changed geometry,changed transparent conductor resistance, and dif-ferent coloration/bleaching voltage behaviors canbe evaluated. One example is to use the coloringmodel to compare the coloration behavior of a fullsize window at different coloration voltages (1:5V,3:0V, and 6:0V), shown in Figs. 9–11.

The model predicts that coloring a window with1:5V results in a relatively even transmittance dis-tribution throughout the coloration but slow overallcoloration (no point reaches 15% transmittance stateeven after 1800 s). A 3:0V coloring, on the otherhand, gives a relatively fast coloration but a ratheruneven transmittance distribution throughout thecoloration (the transmittance distribution becomesmore even with time). Finally a 6:0V coloring givesa very fast coloration but very uneven transmittance

distribution throughout the coloration (the transmit-tance distribution increases with time).

Comparing Figs. 7 and 9, the model prediction alsoshows that, by increasing the size more than threetimes (20 cm × 5 cm to 70 cm × 5 cm), the average col-oration speed decreases almost seven times at theedge (6:7%units=s down to 1%units=s) and morethan 13 times in the middle (2%units=s downto 0:15%units=s).

4. Discussion

It is known that a challenge for the EC technology isdesigning a window-size EC device with rapid anduniform coloration (charging) and bleaching (dis-charging). The presented methodology gives the pos-sibility of measuring and simulating transmittancedistribution over large-area EC devices, thus makingit possible to experimentally validate EC models.These models can then be used to optimize an ECwindow design for rapid and uniform coloration/bleaching. Even though this study only shows trans-mittance distribution measurements on a 20 cm ×5 cm EC device, the methodology could easily mea-sure the transmittance distribution up to the sizeof 70 cm × 5 cm by utilizing the whole backlight paneland measuring half of the device at a time. In fact,

0 300 600 900 1200 1500 18000.1

0.2

0.3

0.4

0.5

0.6

Time / s

Tra

nsm

ittan

ce a

t 532

nm

Fig. 9. Transmittance as a function of time when coloring (char-ging) a 70 cm × 5 cm EC device with 1:5V versus WOx. The modelsimulation measurement points are placed 15mm (squares),98mm (crosses), 180mm (circles), 263mm (asterisks), and345mm (triangles) from the WOx current collector. The colorationis stopped when the first point reaches 15% transmittance state.

0 50 100 150 200 250 300 3500.1

0.2

0.3

0.4

0.5

0.6

Time / s

Tra

nsm

ittan

ce a

t 532

nm

Fig. 10. Transmittance as a function of time when coloring (char-ging) a 70 cm × 5 cm EC device with 3:0V versus WOx The modelsimulation measurement points are placed 15mm (squares),98mm (crosses), 180mm (circles), 263mm (asterisks), and345mm (triangles) from the WOx current collector. The colorationis stopped when the first point reaches 15% transmittance state.

0 5 10 15 20 25 30 35 400.1

0.2

0.3

0.4

0.5

0.6

Time / s

Tra

nsm

ittan

ce a

t 532

nm

Fig. 11. Transmittance as function of time when coloring (char-ging) a 70 cm × 5 cm EC device with 6:0V versus WOx. The modelsimulation measurement points are placed 15mm (squares),98mm (crosses), 180mm (circles), 263mm (asterisks), and345mm (triangles) from the WOx current collector. The colorationis stopped when the first point reaches 15% transmittance state.

0 0.2 0.4 0.6 0.8 1−2

−1

0

1

2

SOC

Eeq

/ V

Fig. 12. Relation between Eeq and f (SOC) used in the models.

5644 APPLIED OPTICS / Vol. 50, No. 29 / 10 October 2011

even larger sizes are possible by simply using a lar-ger backlight panel.

Even though the accuracy and precision of thetransmittance measurements in this methodologyare good enough for the purpose, they could probablybe improved somewhat with a more stable backlightsource. Choosing a more stable and even light sourceover surface and time, the present light intensity un-evenness and fluctuations would be smaller. Thisfluctuation and unevenness are inevitable since thismethodology’s backlight panel has a single fluores-cent lamp as light source providing and distributinglight for the whole backlight surface. An example giv-ing more even light is using a backlight source withlight-emitting diodes (LEDs). Besides being stable,an LED backlight panel has the advantage of beingcapable of controlling the backlight spectrum, thusmaking it possible to utilize the camera’s possibilityto measure color coordinates, since with a more stan-dardized backlight spectrum the bandpass filter isnot needed. Measuring color coordinates and theirdistribution during charge and discharge could givemore information on the current distribution effects.However, a disadvantage with this type of LED back-light panel is that it is very expensive.

The model prediction results show the potential ofusing simulations as a design tool to investigate thecurrent distribution effects of large-area EC devices.The prediction results, such as from this study, can beused as foundation for developing large-area controlalgorithms. A first suggestion of a rapid and uniformcontrol algorithm strategy would be to use a gradu-ally increasing coloration voltage going from 1:5V tomaybe 3:0V. Hence, by starting at a lower voltage,the coloration is kept uniform, and by gradually in-creasing the voltage, the total coloration speed is in-creased. Suggestions like this are of course possibleto simulate and experimentally validate for more de-tailed and defined algorithms, which is another greatstrength of this methodology.

An interesting observation is that, even though thekinetic models presented are simple, model simula-tions fit the experimental data fairly well. This indi-cates that the current distribution effects over thetransparent conductors are the limiting factor for ra-pid and uniform coloration/bleaching of large-areaEC devices. This indication is plausible, consideringthat experimental and simulated data are obtainedat a relatively low sheet resistance, 20Ohm=sq,and relatively small EC device size, 20 cm × 5 cm.This is also what the model predicts; the colorationspeed goes down dramatically with increased EC de-vice size. Even if the results show that the simulationmodel fits the experimental data fairly well and thatthe transparent conductor may be the limiting factor,these models are limited and need further develop-ment. The models are based on Butler–Volmer ki-netics. This assumption may be appropriate for thecoloration process but may be not as appropriatefor the bleaching process, which may explain the bet-ter fit for the coloration model and the need of an

extra electrode interface resistance for the bleachingmodel. The current distribution model puts large de-mands on the local kinetic model, since neither localcurrent nor potential is constant.

With the capability to experimentally validate ECcurrent distribution models, future work shouldconcentrate on developing the kinetic models andvalidating the model for a larger matrix of experi-mental data. Based on already published findings,the kinetic models should be further developed to in-clude, e.g., diffusion and contact resistance.

5. Conclusions

A good understanding of the current distribution ef-fects is crucial when optimizing the EC window tech-nology for performance, low cost, and lifetime. Anexperimentally validated current distribution modelis a well-suited tool for increasing the understandingof current distribution effects for novel designs suchas the EC device system. This paper introduces amethodology that is clearly capable of measuringcurrent distribution effects as transmittance distri-bution over an EC device, correlating the transmit-tance state to the SOC with high accuracy so thatcurrent distribution models can simulate transmit-tance distribution over an EC device. This meth-odology can thus experimentally validate currentdistribution models. We conclude that this methodol-ogy is crucial for validating current distribution mod-els used to optimize the EC window technology.

The kinetic model is relatively simple, but themodel simulations still match the experimental datafairly well; this indicates that the electrical proper-ties of the transparent conductor layers constitutethe limiting factor for rapid and uniform coloration(charging) and bleaching (discharging) for large-areaECwindows. Although the simulations match the ex-perimental data fairly well, the local kinetic modelneeds to be developed further.

The potential of this methodology lies in the pos-sibility to both simulate and experimentally validatenew construction and control algorithms.

Appendix A

1. Model Equations

The model uses Butler–Volmer-based kinetics[Eqs. (A1)–(A6)]:

j ¼ S · j0

8<:e

�αaFϕΣRT

�− e

�αaFϕΣRT

�9=;; ðA1Þ

where

ϕΣ ¼ E1 − E2 −ΔEiR −ΔEeq ðA2Þ

(X1 is for WOx and X2 is for NiO),

10 October 2011 / Vol. 50, No. 29 / APPLIED OPTICS 5645

ΔEiR ¼ jdκel

; ðA3Þ

ΔEeq ¼ f ðSOCÞ¼ −0:5þ SOC · 1:9 − 10−3 · eð

1SOCþ0:15Þ ðA4Þ

(shown in Fig. 12),

SOC ¼ qðx; tÞqmax

; ðA5Þ

qmax ¼ 16mC=cm2: ðA6ÞThe potential drop and current flow in the trans-

parent conductors are described by Ohm’s law[Eqs. (A7) and (A8)]:

�−σdE

dx¼ i and −σ di

dx¼ j

�gives −σ1

d2E1

dx2¼ j;

ðA7Þ

− σ2d2E2

dx2¼ −j: ðA8Þ

The boundary conditions for the models are

x ¼ 0 and t ¼ t∶i2 ¼ 0 and E1 ¼ 0;

and for

x ¼ L and t ¼ t∶i1 ¼ 0 and E2 ¼ Vapp:

The model calculates the local SOC with integrat-ing the charge [Eq. (A9)],

dqdt

¼ j; ðA9Þ

where

qðx; 0Þ ¼ 0 ðbleached=discharged state;T ¼ 55%Þ;

qðx; 0Þ ¼ qc ðcolored=charged state;T ¼ 14:5%Þare used for the coloration and bleaching case, re-spectively.

For the bleach (discharge) model, a charge-dependent contact resistance at the electrode inter-face is added Eqs. (A10) and (A11)]:

ΔEiR ¼ j

�dκel

þ Ri

�; ðA10Þ

where

Ri ¼ 0:05ð1 − SOCÞ: ðA11Þ

2. Model Constants

The models use the following constants:

σITO ¼ σ1 ¼ σ2 ¼ 2 · 105 S=m.dITO ¼ 250nm (dITO and σITO give a sheet resis-

tance of 20Ohm=sq).κel ¼ 1 · 10−3 S=m.del ¼ 5 · 10−6 m.αa ¼ αc ¼ 0:5.T ¼ 298K.

3. Model Adjustment

The S · j0 parameter was fitted to the experimentaldata, where it was 1 · 10−15 A=m3 and 1 · 10−7 A=m3

for the color (charge) and bleaching (discharge) mod-els, respectively.

Financial support from the Swedish ResearchCouncil Formas is gratefully acknowledged.ChromoGenics AB is acknowledged for financialand material support.

References and Notes1. C. G. Granqvist, Handbook of Inorganic Electrochromic Mate-

rials (Elsevier, 1995).2. G. A. Niklasson and C. G. Granqvist, “Electrochromics for

smart windows: thin films of tungsten oxide and nickel oxide,and devices based on these,” J. Mater. Chem. 17, 127–156(2007).

3. C. M. Lampert, “Large-area smart glass and integratedphotovoltaics,” Sol. Energy Mater. Sol. Cells 76, 489–499(2003).

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