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A semi-empirical model for the charging and discharging of electric-paint displays
Electrochemistry Communications 4 (2002) 963–967 www.elsevier.com/locate/elecom
A semi-empirical model for the charging and discharging of electric-paint displays M.O.M. Edwards b
a,*
, T. Gruszecki b, H. Pettersson b, G. Thuraisingham a, A. Hagfeldt
a,1
a Department of Physical Chemistry, Uppsala University, Box 532, S-75121 Uppsala, Sweden IVF Industrial Research and Development Corporation, Argongatan 30, S-43153 M€olndal, Sweden
Received 29 August 2002; received in revised form 15 October 2002; accepted 15 October 2002
Abstract Electrochromic displays based on porous nanostructured films, ‘‘electric-paint displays’’, are promising for electronic-paper applications due to their prominent paint-on-paper qualities. We have investigated the charge–discharge kinetics of electric-paint displays by chronocoulometry experiments. Whereas the charging curves are exponential, Að1 et =sÞ, up to about 1 s, the discharging (when bleaching the display) cannot be described properly by a single exponential expression in the 0–1 s time regime. A semi-empirical model, in which the display is treated like a serial RC-circuit with a capacity step function, was developed and fitted to the experimental chronocoulometry curves with successful results. The general features of both the charging and discharging curves, as well as their dependences on the applied voltage, are reproduced in the 0–1 s regime by the suggested model. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Electrochromic display; Viologen; Titanium dioxide; Charging kinetics; Semi-empirical model
1. Introduction There is a growing industrial interest in electrochromic display technologies for usage in e.g., electronic-paper applications. This is triggered by the recent progress in the development of ‘‘electric-paint displays’’ [1–6] and the black-and-white metal electrodeposition displays [7]. Several teething troubles with previous electrochromic displays [8] have been overcome. Most attractive with the new generation electrochromic displays are the excellent optical properties: the bright white reflectors, the wide viewing angle regimes, and, for electric-paint displays, the possibility of using different sharp colors. Other common features are the rapid switching, the long color memory in open circuit, the high stability, and the good prospects of low production costs. Passive-matrix driving of electrochromic displays has been demonstrated [7,9,10]. In spite of the relatively far technical develop*
Corresponding author. Fax: +46-18-508542. E-mail addresses: [email protected] (M.O.M. Edwards), [email protected] (A. Hagfeldt). 1 Also corresponding author.
ment, detailed information about the functioning of the new electrochromic displays can hardly be found in the literature. We will in the present paper be concerned with ‘‘electric-paint displays’’, which have coloring electrodes of a porous film of metal-oxide nanoparticles on conductive glass with electrochromic molecules attached to the huge inner surface of the nanoparticles in the film. The electrochromic molecules are electrically addressed from the back contact on the conductive glass via the nanoparticle network. Real devices consist, in addition to the semi-transparent or transparent coloring electrode, of a counter electrode and an electrolyte between the electrodes. In reflective devices a layer of lightscattering titanium dioxide particles is incorporated between the front and counter electrodes. Several variants of electric-paint displays have been presented [1–6]. We have developed a ÔcapacitiveÕ electric-paint concept with an organic electrolyte without redox-active species and a counter electrode that also consists of a highly porous film of nanoparticles, however, without attached molecules [4–6,11]. Charge is stored capacitively at the counter electrode interface (opposite charging on either
1388-2481/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 1 3 8 8 - 2 4 8 1 ( 0 2 ) 0 0 5 0 8 - 8
964
M.O.M. Edwards et al. / Electrochemistry Communications 4 (2002) 963–967
side of the interface) in such displays, as in electrochemical capacitors [12]. Suitable materials for the counter electrode are e.g., carbon and doped metal oxides. We report on a semi-empirical model for the charging kinetics of capacitive electric-paint displays during color switches. As the degree of coloration is closely related to the charging, the model is believed to be a valuable tool for simulations of the display operation. Furthermore, by varying the geometry and the composition of the display one should be able to isolate the effects from different display components on the model parameters, and in this way pinpoint limiting factors for the switch time. This will be the subject of future investigations.
2. Experimental The experimental investigations were carried out on displays with the following configuration: a coloring electrode of a semi-transparent titanium dioxide film with attached viologen molecules, a film of antimonydoped tin oxide particles as counter electrode, a white reflector of light-scattering titanium dioxide particles on top of the counter electrode film, as well as an organic electrolyte of 0.2 M lithium triflate in 3-methoxypropionitrile. We used the same preparation methods as in [5], which briefly will be summarized here. The electrodes were prepared by screen-printing pastes of metal-oxide particles on conductive glass and baking the printed electrodes at 450 °C. The coloring electrodes were then dyed by viologen molecules (bis-2-phosphonoethyl)-4,40 bipyridinium dichloride) [13] in a bath. Pairs of coloring and counter electrodes were glued together and filled with electrolyte. The cell gaps and the film thicknesses were approximately 100 and 10 lm, respectively. The size of the rectangular counter electrode films were 33 41:5 mm2 , whereas the coloring electrodes consisted of 35 circular pixels of 3 mm in diameter that were homogeneously spread over the counter electrode area in 5 rows and 7 columns. The total film areas of the counter and coloring electrodes were 13.7 and 2:5 cm2 , respectively. None of the electrodes were electrically structured, i.e., the color of the pixels could not be individually controlled. Cyclic voltammetry (CV) and chronocoulometry (CC) studies were performed with a potentiostat (Autolab pgstat 10 from EcoChemie) with the coloring electrode as working electrode and the display counter electrode as both reference and counter electrode. The CV measurements were performed in the current integration mode, i.e., by integrating the charge during each voltage step and calculating the current by dividing the step charge by the step time. The presented charge and current values are divided by the total geometric area of the TiO2 pixels throughout the paper. As the display is
bleached in the rest state at zero voltage we refer to the charging reactions during coloring and bleaching as charging and discharging, respectively.
3. Results and discussion The viologen molecules are reduced from the colorless +2 state to the deep blue +1 state at negative voltages [2,4,6,11]. The charge of the viologen molecules is counterbalanced by opposite ion charging in the surrounding electrolyte volume. As can be seen in the CV curve (Fig. 1) the on-set voltage for the coloration is about )0.6 V, a value which can vary between different devices and also can depend on the previous operation history. At negative voltages there are a couple of side reactions that can take place at the coloring electrode, e.g., capacitive charging of the TiO2 –electrolyte interface, ion adsorption and intercalation, and a second viologen reduction step to a faint yellow color. The bluecoloring of the viologen molecules, and the mentioned side reactions, are counterbalanced by, mainly, capacitive charging of the counter electrode. One should also bear in mind that reactions due to unwanted redoxactive species in the inert electrolyte could take place. The optical switch times of the present display configuration are about 200 ms for coloring and 250 ms for bleaching when the voltages )1.15 and 0.20 V, respectively, are applied. The switching can be speeded up by applying higher voltages for sufficiently short time periods. Expressions that quantitatively describe the coloration kinetics and the dependence on applied voltages would be of great value in the engineering of electricpaint displays. In this work we have studied the kinetics
Fig. 1. Cyclic voltammogram of an electric-paint display recorded with a scan rate of 50 mV/s (solid line). The displayed curve is the third CV cycle (stable conditions are attained after the first cycle). The ratio between the integrated anodic and cathodic currents is 92%. Also shown is the theoretical curve of an ideal serial RC-circuit for a low scan rate (dotted line). The scan directions are indicated by arrows.
M.O.M. Edwards et al. / Electrochemistry Communications 4 (2002) 963–967
of the charging of the display, which is intimately related to the coloration, by CC experiments. The result of a typical CC experiment is shown in Fig. 2 along with the applied sequence of alternating charging (when colored) and discharging (when bleached) pulses of, in this example, the voltages )1.15 and 0.2 V, respectively. The discharging is essentially completed within half a second, when there is a kink in the curve and a rather flat plateau is reached, whereas the charging declines smoothly without reaching a final value in, at least, 10 s. The kink and the plateau in the discharge curves are explained by the absence of reactions at positive voltages in the CV (Fig. 1). Furthermore almost all of the transferred charge during the charging pulses is
returned in the discharges, a signature of reversible accumulative processes. The rapid discharging indicates that the charge is accumulated at the electrode–electrolyte interface (viologen coloration, capacitive charging at the metal-oxide surfaces, etc.) rather than inside the electrode materials (intercalation). The flat discharge plateau gives us a well-defined reference charging level of the display. In the studies of the charging, the charging pulses were immediately preceded by a 5 s 0.2 V pulse to adjust the display to the reference charging level. It is more difficult to find a proper zero adjustment procedure for the discharging studies. We used two sequential pulses: 5 s 0.2 V and 1 s )1.15 V. The intention was to apply the non-damaging coloration voltage )1.15 V until a reasonably low charging current was attained (to get high accuracy), however, not so long that the influence from side reactions subsequent to the coloration becomes significant. Attempts of fitting exponential [Að1 et=s Þ] and power-law (Atb ) expressions to an experimental charging CC curve are displayed in Fig. 3(a). A very good agreement is obtained up to 1 s with the former, whereas the latter, with different exponents, fail to reproduce the experimental data in the 0–1 s time window. The initial phase of the discharging (before the kink) can be reproduced by the same exponential expression, but the kink and the plateau cannot be accounted for (Fig. 3(b)). The charging of a serial RC-circuit of ideal resistive and capacitive elements is described by an exponential expression, QðtÞ ¼ ðU U 0 ÞC½1 expðt=RCÞ;
Fig. 2. Chronocoulometry response (top) for a voltage sequence of alternating )1.15 and 0.20 V pulses (bottom).
965
ð1Þ
where Q is the charge, t is the time, U the applied voltage, and U 0 the voltage of the capacitor before charging. The present electric-paint displays can be viewed as non-ideal serial RC-circuits with high capacitances at the electrode–electrolyte interfaces and resistances in the conductive glass, the electrode materials,
Fig. 3. Attempts of fitting exponential and power-law expressions (lines) to charging (a) and discharging (b) chronocoulometry curves (squares) with applied voltages of )1.25 and 0.5 V, respectively.
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and in the electrolyte. The main contributions to the capacity are the viologen charging and the high doublelayer capacity of the counter electrode. R and C for the displays depend on the voltage and frequency of applied electric fields as well as the history of display operation. In spite of this, the good agreement between the exponential expression and the experimental charging curve (Fig. 3(a)) indicate that the displays, at least under certain conditions, may be treated in a similar way as ideal serial RC-circuits. This is our starting point in the development of a model for the charging kinetics. The voltage dependence of C is reflected by the current in a cyclic voltammogram, however, for a proper analysis the CV scan rate must be taken into account [14]. The CV curve of an ideal serial RC-circuit is, for a sufficiently low scan rate, rectangular with constant negative and positive currents in the two different scan directions (cf. Fig. 1). A striking difference between the CV curves of the ideal serial RC-circuit and the electricpaint display is that the current, and therefore the capacity, almost completely vanishes at voltages higher than the on-set for coloration. Thus it is reasonable that the serial RC-circuit would be a better equivalent circuit for the display if a step is introduced in the capacity function, i.e., approximating the capacity of the electricpaint display by a constant value C at voltages lower than a certain cut-off voltage Ucut and zero at voltages higher than Ucut . This modification of the ideal serial RC-circuit result in four distinguishable cases: (a) Expression (1) is still valid for switches between two colored states with different coloration strength (U 0 < Ucut , U < Ucut ). (b) No charge is exchanged if the voltage of the bleached state is changed without accompanying color changes (U 0 > Ucut , U > Ucut ). (c) U 0 in (1) is replaced by Ucut for switches from the bleached state to a colored state (U 0 > Ucut , U < Ucut ),
QðtÞ ¼ ðU Ucut ÞC½1 expðt=RCÞ:
ð2Þ
(d) The bleaching of a colored state (U 0 < Ucut , U > Ucut ) is initially described by (1), however, at a certain characteristic time the discharging is suddenly interrupted. This occurs when all the charge of the initial colored state, ðU 0 Ucut ÞC, has been discharged. A validity test of the developed ‘‘capacity-step model’’ was performed by fitting the above expressions to a series of experimental charging and discharging CC curves (Figs. 4(a) and (b)). Expression (2) was fitted simultaneously to charging curves with U 0 fixed as 0.2 V and U ranging from )2.0 to )0.9 V. A good agreement was obtained in the 0–1 s interval rather uniquely for R ¼ 72 X, C ¼ 3:1 mF=cm2 , and Ucut ¼ 0:6 V. Similarly, expression (1) and the level of the plateau, ðU 0 Ucut ÞC, were both fitted simultaneously to discharging curves with U between 0.0 and 2.0 V. The slightly different plateau levels of the 0.0–1.0 V curves are due to parasitic capacitances, of which the origin will be discussed elsewhere. The plateau fit was optimized for the 0.0–0.5 V curves in the 0.5–1.0 s regime. A deviation from the capacity-step model is seen for the 2.0 V curve, which, due to side reactions, does not flatten out after the kink. The parameter values of the discharging fit in Fig. 4(b) are R ¼ 64 X, C ¼ 2:7 mF=cm2 , Ucut ¼ 0:5 V, and U 0 ¼ 1:0 V. The initial voltage U 0 is not well determined by the zero adjustment (see above) and was therefore kept as a freely varying parameter in the fit. Rough estimates of the uncertainties for both the charging and discharging fits are 10 X (R), 0:3 mF=cm2 (C), and 0.05 V (Ucut and U 0 ). Evidently the capacitystep model correctly reproduces the general features of the display charging kinetics that cannot be described by an ideal serial RC-circuit, including the voltage dependence as well as the kink and the plateau in the
Fig. 4. Fits of the ‘‘capacity-step model’’ (lines) to charging (a) and discharging (b) chronocoulometry curves (symbols) for applied voltages from )2.0 to )0.9 V and from 0.0 to 2.0 V, respectively. The experiments with applied voltages )2.0, )1.4, and 2.0 V were interrupted before 1.5 s to avoid electrochemical damage.
M.O.M. Edwards et al. / Electrochemistry Communications 4 (2002) 963–967
discharges. Moreover, the two sets of fitted parameter values agree rather well between themselves. We conclude therefore that the suggested model is justified for simulations of the general charge–discharge characteristics under realistic operation conditions for the displays (switches shorter than 1 s). All parameter values are reasonable following simple physical arguments: R is somewhat greater than the serial resistance of the two conductive glass pieces. The magnitude of C agrees with typical surface roughness values of nanostructured metal-oxide films (100–1000) and reported molecular coverage areas (about 1 nm2 ) of similar viologen molecules [2]. Ucut equals roughly the observed coloration onset in the CV curve (Fig. 1), and U 0 is as expected somewhat larger than the applied coloring voltage in the zero adjustment. A detailed analysis of the fitted parameter values and the implications for the optimization of display components are beyond the scope of the present work. 4. Conclusions A semi-empirical model has been developed for the charging kinetics in color switches of electric-paint displays. In the model, the display is treated like a serial RC-circuit with a capacity step function. In spite of its simplicity, the model describes well the general characteristics of the charging.
967
Acknowledgements This work was supported by the Swedish Research Council and the Swedish Agency for Innovation Systems.
References [1] A. Hagfeldt, L. Walder, M. Gr€atzel, Proc. Soc. Photo-Opt. Instrum. Eng. 2531 (1995) 60. [2] P. Bonh^ ote, E. Gogniat, F. Campus, L. Walder, M. Gr€atzel, Displays 20 (1999) 137. [3] M. Gr€atzel, Nature 409 (2001) 575. [4] M.O.M. Edwards, G. Boschloo, R. Sohlberg, A. Hagfeldt, T. Gruszecki, H. Pettersson, Proc. of SID 2001 (2001) 1058. [5] H. Pettersson, T. Gruszecki, L.-H. Johansson, A. Norberg, M.O.M. Edwards, A. Hagfeldt, Proc. of SID 2002 (2002) 123. [6] U. Bach, D. Corr, D. Lupo, F. Pichot, M. Ryan, Adv. Mater. 14 (2002) 845. [7] K. Shinozaki, Proc. of SID 2002 (2002) 39. [8] T. Oi, Annu. Rev. Mater. Sci. 16 (1986) 185. [9] M.O.M. Edwards et al., in preparation. [10] N. Leventis, C. Muguo, A.I. Liapis, J.W. Johnson, A. Jain, J. Electrochem. Soc. 145 (1998) L55. [11] M.O.M. Edwards, G. Boschloo, T. Gruszecki, H. Pettersson, R. Sohlberg, A. Hagfeldt, Electrochim. Acta 46 (2001) 2187. [12] B.E. Conway, Electrochemical Supercapacitors, Plenum Publishing, New York, 1999. [13] R. Cinnsealach, G. Boschloo, S. Nagaraja Rao, D. Fitzmaurice, Sol. Energy Mater. Sol. Cells 55 (1998) 215. [14] W.G. Pell, B.E. Conway, J. Power Sources 96 (2001) 57.
A semi-empirical model for the charging and discharging of electric-paint displays M.O.M. Edwards b
a,*
, T. Gruszecki b, H. Pettersson b, G. Thuraisingham a, A. Hagfeldt
a,1
a Department of Physical Chemistry, Uppsala University, Box 532, S-75121 Uppsala, Sweden IVF Industrial Research and Development Corporation, Argongatan 30, S-43153 M€olndal, Sweden
Received 29 August 2002; received in revised form 15 October 2002; accepted 15 October 2002
Abstract Electrochromic displays based on porous nanostructured films, ‘‘electric-paint displays’’, are promising for electronic-paper applications due to their prominent paint-on-paper qualities. We have investigated the charge–discharge kinetics of electric-paint displays by chronocoulometry experiments. Whereas the charging curves are exponential, Að1 et =sÞ, up to about 1 s, the discharging (when bleaching the display) cannot be described properly by a single exponential expression in the 0–1 s time regime. A semi-empirical model, in which the display is treated like a serial RC-circuit with a capacity step function, was developed and fitted to the experimental chronocoulometry curves with successful results. The general features of both the charging and discharging curves, as well as their dependences on the applied voltage, are reproduced in the 0–1 s regime by the suggested model. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Electrochromic display; Viologen; Titanium dioxide; Charging kinetics; Semi-empirical model
1. Introduction There is a growing industrial interest in electrochromic display technologies for usage in e.g., electronic-paper applications. This is triggered by the recent progress in the development of ‘‘electric-paint displays’’ [1–6] and the black-and-white metal electrodeposition displays [7]. Several teething troubles with previous electrochromic displays [8] have been overcome. Most attractive with the new generation electrochromic displays are the excellent optical properties: the bright white reflectors, the wide viewing angle regimes, and, for electric-paint displays, the possibility of using different sharp colors. Other common features are the rapid switching, the long color memory in open circuit, the high stability, and the good prospects of low production costs. Passive-matrix driving of electrochromic displays has been demonstrated [7,9,10]. In spite of the relatively far technical develop*
Corresponding author. Fax: +46-18-508542. E-mail addresses: [email protected] (M.O.M. Edwards), [email protected] (A. Hagfeldt). 1 Also corresponding author.
ment, detailed information about the functioning of the new electrochromic displays can hardly be found in the literature. We will in the present paper be concerned with ‘‘electric-paint displays’’, which have coloring electrodes of a porous film of metal-oxide nanoparticles on conductive glass with electrochromic molecules attached to the huge inner surface of the nanoparticles in the film. The electrochromic molecules are electrically addressed from the back contact on the conductive glass via the nanoparticle network. Real devices consist, in addition to the semi-transparent or transparent coloring electrode, of a counter electrode and an electrolyte between the electrodes. In reflective devices a layer of lightscattering titanium dioxide particles is incorporated between the front and counter electrodes. Several variants of electric-paint displays have been presented [1–6]. We have developed a ÔcapacitiveÕ electric-paint concept with an organic electrolyte without redox-active species and a counter electrode that also consists of a highly porous film of nanoparticles, however, without attached molecules [4–6,11]. Charge is stored capacitively at the counter electrode interface (opposite charging on either
1388-2481/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 1 3 8 8 - 2 4 8 1 ( 0 2 ) 0 0 5 0 8 - 8
964
M.O.M. Edwards et al. / Electrochemistry Communications 4 (2002) 963–967
side of the interface) in such displays, as in electrochemical capacitors [12]. Suitable materials for the counter electrode are e.g., carbon and doped metal oxides. We report on a semi-empirical model for the charging kinetics of capacitive electric-paint displays during color switches. As the degree of coloration is closely related to the charging, the model is believed to be a valuable tool for simulations of the display operation. Furthermore, by varying the geometry and the composition of the display one should be able to isolate the effects from different display components on the model parameters, and in this way pinpoint limiting factors for the switch time. This will be the subject of future investigations.
2. Experimental The experimental investigations were carried out on displays with the following configuration: a coloring electrode of a semi-transparent titanium dioxide film with attached viologen molecules, a film of antimonydoped tin oxide particles as counter electrode, a white reflector of light-scattering titanium dioxide particles on top of the counter electrode film, as well as an organic electrolyte of 0.2 M lithium triflate in 3-methoxypropionitrile. We used the same preparation methods as in [5], which briefly will be summarized here. The electrodes were prepared by screen-printing pastes of metal-oxide particles on conductive glass and baking the printed electrodes at 450 °C. The coloring electrodes were then dyed by viologen molecules (bis-2-phosphonoethyl)-4,40 bipyridinium dichloride) [13] in a bath. Pairs of coloring and counter electrodes were glued together and filled with electrolyte. The cell gaps and the film thicknesses were approximately 100 and 10 lm, respectively. The size of the rectangular counter electrode films were 33 41:5 mm2 , whereas the coloring electrodes consisted of 35 circular pixels of 3 mm in diameter that were homogeneously spread over the counter electrode area in 5 rows and 7 columns. The total film areas of the counter and coloring electrodes were 13.7 and 2:5 cm2 , respectively. None of the electrodes were electrically structured, i.e., the color of the pixels could not be individually controlled. Cyclic voltammetry (CV) and chronocoulometry (CC) studies were performed with a potentiostat (Autolab pgstat 10 from EcoChemie) with the coloring electrode as working electrode and the display counter electrode as both reference and counter electrode. The CV measurements were performed in the current integration mode, i.e., by integrating the charge during each voltage step and calculating the current by dividing the step charge by the step time. The presented charge and current values are divided by the total geometric area of the TiO2 pixels throughout the paper. As the display is
bleached in the rest state at zero voltage we refer to the charging reactions during coloring and bleaching as charging and discharging, respectively.
3. Results and discussion The viologen molecules are reduced from the colorless +2 state to the deep blue +1 state at negative voltages [2,4,6,11]. The charge of the viologen molecules is counterbalanced by opposite ion charging in the surrounding electrolyte volume. As can be seen in the CV curve (Fig. 1) the on-set voltage for the coloration is about )0.6 V, a value which can vary between different devices and also can depend on the previous operation history. At negative voltages there are a couple of side reactions that can take place at the coloring electrode, e.g., capacitive charging of the TiO2 –electrolyte interface, ion adsorption and intercalation, and a second viologen reduction step to a faint yellow color. The bluecoloring of the viologen molecules, and the mentioned side reactions, are counterbalanced by, mainly, capacitive charging of the counter electrode. One should also bear in mind that reactions due to unwanted redoxactive species in the inert electrolyte could take place. The optical switch times of the present display configuration are about 200 ms for coloring and 250 ms for bleaching when the voltages )1.15 and 0.20 V, respectively, are applied. The switching can be speeded up by applying higher voltages for sufficiently short time periods. Expressions that quantitatively describe the coloration kinetics and the dependence on applied voltages would be of great value in the engineering of electricpaint displays. In this work we have studied the kinetics
Fig. 1. Cyclic voltammogram of an electric-paint display recorded with a scan rate of 50 mV/s (solid line). The displayed curve is the third CV cycle (stable conditions are attained after the first cycle). The ratio between the integrated anodic and cathodic currents is 92%. Also shown is the theoretical curve of an ideal serial RC-circuit for a low scan rate (dotted line). The scan directions are indicated by arrows.
M.O.M. Edwards et al. / Electrochemistry Communications 4 (2002) 963–967
of the charging of the display, which is intimately related to the coloration, by CC experiments. The result of a typical CC experiment is shown in Fig. 2 along with the applied sequence of alternating charging (when colored) and discharging (when bleached) pulses of, in this example, the voltages )1.15 and 0.2 V, respectively. The discharging is essentially completed within half a second, when there is a kink in the curve and a rather flat plateau is reached, whereas the charging declines smoothly without reaching a final value in, at least, 10 s. The kink and the plateau in the discharge curves are explained by the absence of reactions at positive voltages in the CV (Fig. 1). Furthermore almost all of the transferred charge during the charging pulses is
returned in the discharges, a signature of reversible accumulative processes. The rapid discharging indicates that the charge is accumulated at the electrode–electrolyte interface (viologen coloration, capacitive charging at the metal-oxide surfaces, etc.) rather than inside the electrode materials (intercalation). The flat discharge plateau gives us a well-defined reference charging level of the display. In the studies of the charging, the charging pulses were immediately preceded by a 5 s 0.2 V pulse to adjust the display to the reference charging level. It is more difficult to find a proper zero adjustment procedure for the discharging studies. We used two sequential pulses: 5 s 0.2 V and 1 s )1.15 V. The intention was to apply the non-damaging coloration voltage )1.15 V until a reasonably low charging current was attained (to get high accuracy), however, not so long that the influence from side reactions subsequent to the coloration becomes significant. Attempts of fitting exponential [Að1 et=s Þ] and power-law (Atb ) expressions to an experimental charging CC curve are displayed in Fig. 3(a). A very good agreement is obtained up to 1 s with the former, whereas the latter, with different exponents, fail to reproduce the experimental data in the 0–1 s time window. The initial phase of the discharging (before the kink) can be reproduced by the same exponential expression, but the kink and the plateau cannot be accounted for (Fig. 3(b)). The charging of a serial RC-circuit of ideal resistive and capacitive elements is described by an exponential expression, QðtÞ ¼ ðU U 0 ÞC½1 expðt=RCÞ;
Fig. 2. Chronocoulometry response (top) for a voltage sequence of alternating )1.15 and 0.20 V pulses (bottom).
965
ð1Þ
where Q is the charge, t is the time, U the applied voltage, and U 0 the voltage of the capacitor before charging. The present electric-paint displays can be viewed as non-ideal serial RC-circuits with high capacitances at the electrode–electrolyte interfaces and resistances in the conductive glass, the electrode materials,
Fig. 3. Attempts of fitting exponential and power-law expressions (lines) to charging (a) and discharging (b) chronocoulometry curves (squares) with applied voltages of )1.25 and 0.5 V, respectively.
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and in the electrolyte. The main contributions to the capacity are the viologen charging and the high doublelayer capacity of the counter electrode. R and C for the displays depend on the voltage and frequency of applied electric fields as well as the history of display operation. In spite of this, the good agreement between the exponential expression and the experimental charging curve (Fig. 3(a)) indicate that the displays, at least under certain conditions, may be treated in a similar way as ideal serial RC-circuits. This is our starting point in the development of a model for the charging kinetics. The voltage dependence of C is reflected by the current in a cyclic voltammogram, however, for a proper analysis the CV scan rate must be taken into account [14]. The CV curve of an ideal serial RC-circuit is, for a sufficiently low scan rate, rectangular with constant negative and positive currents in the two different scan directions (cf. Fig. 1). A striking difference between the CV curves of the ideal serial RC-circuit and the electricpaint display is that the current, and therefore the capacity, almost completely vanishes at voltages higher than the on-set for coloration. Thus it is reasonable that the serial RC-circuit would be a better equivalent circuit for the display if a step is introduced in the capacity function, i.e., approximating the capacity of the electricpaint display by a constant value C at voltages lower than a certain cut-off voltage Ucut and zero at voltages higher than Ucut . This modification of the ideal serial RC-circuit result in four distinguishable cases: (a) Expression (1) is still valid for switches between two colored states with different coloration strength (U 0 < Ucut , U < Ucut ). (b) No charge is exchanged if the voltage of the bleached state is changed without accompanying color changes (U 0 > Ucut , U > Ucut ). (c) U 0 in (1) is replaced by Ucut for switches from the bleached state to a colored state (U 0 > Ucut , U < Ucut ),
QðtÞ ¼ ðU Ucut ÞC½1 expðt=RCÞ:
ð2Þ
(d) The bleaching of a colored state (U 0 < Ucut , U > Ucut ) is initially described by (1), however, at a certain characteristic time the discharging is suddenly interrupted. This occurs when all the charge of the initial colored state, ðU 0 Ucut ÞC, has been discharged. A validity test of the developed ‘‘capacity-step model’’ was performed by fitting the above expressions to a series of experimental charging and discharging CC curves (Figs. 4(a) and (b)). Expression (2) was fitted simultaneously to charging curves with U 0 fixed as 0.2 V and U ranging from )2.0 to )0.9 V. A good agreement was obtained in the 0–1 s interval rather uniquely for R ¼ 72 X, C ¼ 3:1 mF=cm2 , and Ucut ¼ 0:6 V. Similarly, expression (1) and the level of the plateau, ðU 0 Ucut ÞC, were both fitted simultaneously to discharging curves with U between 0.0 and 2.0 V. The slightly different plateau levels of the 0.0–1.0 V curves are due to parasitic capacitances, of which the origin will be discussed elsewhere. The plateau fit was optimized for the 0.0–0.5 V curves in the 0.5–1.0 s regime. A deviation from the capacity-step model is seen for the 2.0 V curve, which, due to side reactions, does not flatten out after the kink. The parameter values of the discharging fit in Fig. 4(b) are R ¼ 64 X, C ¼ 2:7 mF=cm2 , Ucut ¼ 0:5 V, and U 0 ¼ 1:0 V. The initial voltage U 0 is not well determined by the zero adjustment (see above) and was therefore kept as a freely varying parameter in the fit. Rough estimates of the uncertainties for both the charging and discharging fits are 10 X (R), 0:3 mF=cm2 (C), and 0.05 V (Ucut and U 0 ). Evidently the capacitystep model correctly reproduces the general features of the display charging kinetics that cannot be described by an ideal serial RC-circuit, including the voltage dependence as well as the kink and the plateau in the
Fig. 4. Fits of the ‘‘capacity-step model’’ (lines) to charging (a) and discharging (b) chronocoulometry curves (symbols) for applied voltages from )2.0 to )0.9 V and from 0.0 to 2.0 V, respectively. The experiments with applied voltages )2.0, )1.4, and 2.0 V were interrupted before 1.5 s to avoid electrochemical damage.
M.O.M. Edwards et al. / Electrochemistry Communications 4 (2002) 963–967
discharges. Moreover, the two sets of fitted parameter values agree rather well between themselves. We conclude therefore that the suggested model is justified for simulations of the general charge–discharge characteristics under realistic operation conditions for the displays (switches shorter than 1 s). All parameter values are reasonable following simple physical arguments: R is somewhat greater than the serial resistance of the two conductive glass pieces. The magnitude of C agrees with typical surface roughness values of nanostructured metal-oxide films (100–1000) and reported molecular coverage areas (about 1 nm2 ) of similar viologen molecules [2]. Ucut equals roughly the observed coloration onset in the CV curve (Fig. 1), and U 0 is as expected somewhat larger than the applied coloring voltage in the zero adjustment. A detailed analysis of the fitted parameter values and the implications for the optimization of display components are beyond the scope of the present work. 4. Conclusions A semi-empirical model has been developed for the charging kinetics in color switches of electric-paint displays. In the model, the display is treated like a serial RC-circuit with a capacity step function. In spite of its simplicity, the model describes well the general characteristics of the charging.
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Acknowledgements This work was supported by the Swedish Research Council and the Swedish Agency for Innovation Systems.
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