Understanding Electrophoretic Displays: Transient Current Characteristics of Dispersed Charges in a Non-Polar Medium

Transcription

1 Understandng Electrophoretc Dsplays: Transent Current Characterstcs of Dspersed Charges n a Non-Polar Medum Yoocharn Jeon, Pavel Kornlovtch, Patrca Beck, Zhang-Ln Zhou, Rchard Henze, Tm Koch HP Laboratores HPL Keyword(s): e-paper, reflectve dsplays, electrophoretc, charge, non-polar, experments, modelng, transent current Abstract: Transent currents of reverse mcelles n a non-polar solvent from voltage step stmul were studed to nvestgate the electrophoretc behavor of the charges. It showed varous tme-dependent transents dependng on the appled voltage and the charge content. A one-dmensonal drft-dffuson model could reproduce the behavors for varous condtons. External Postng Date: September 2, 2 [Fulltext] Approved for External Publcaton Internal Postng Date: September 2, 2 [Fulltext] To be publshed and presented at Internatonal Dsplay Workshops, Fukuoka, Japan. Dec, 2 Copyrght Internatonal Dsplay Workshops, 2

2 Understandng Electrophoretc Dsplays: Transent Current Characterstcs of Dspersed Charges n a Non-Polar Medum Yoocharn Jeon, Pavel Kornlovtch*, Patrca Beck, Zhang-Ln Zhou, Rchard Henze, and Tm Koch* Hewlett-Packard Co., HP Labs, 5 Page Mll Road, Palo Alto, CA, 9434, USA * Hewlett-Packard Co., IPG, NE Crcle Blvd. Corvalls, OR, 9733, USA ABSTRACT Transent currents of reverse mcelles n a non-polar solvent from voltage step stmul were studed to nvestgate the electrophoretc behavor of the charges. It showed varous tme-dependent transents dependng on the appled voltage and the charge content. A one-dmensonal drft-dffuson model could reproduce the behavors for varous condtons.. INTRODUCTION Electrophoretc control of charged partcles has been used for reflectve dsplays and s gettng ncreasng attenton. Snce charge moton results n an electrc current, the transent current s a useful tool to understand how the charges move n the dsplay cell. Prevous efforts [] to nterpret the transent current behavors and to extract useful nformaton have not resulted n a thorough understandng of all the phenomena. In ths talk we wll present transent current measurement data for varous voltages and surfactant concentratons and compare them wth numercal smulatons of a one-dmensonal model. 2. EXPERIMENTS Dspersons of poly-sobutylene succnmde (OLOA, Chevron) n an so-paraffnc solvent n varous concentratons were used as model electrophoretc fluds. Accordng to a popular nterpretaton, reverse mcelles formed by the OLOA dsproportonate nto the charged speces n ths system. The test cells used had a parallel-plates geometry. The current through the test cells was measured after applcaton and removal of a voltage step of varous magntudes. 3. NUMERICAL MODELING A one-dmensonal model has been bult and solved numercally usng COMSOL Multphyscs. The charge flux s a sum of the drft and dffuson contrbutons. The concentraton of -th speces, c, satsfes the local mass conservaton equaton, c / t D c ( ) c, where D s the dffuson coeffcent, the electrophoretc moblty, and the electrostatc potental. The electrostatc potental s governed by the Posson equaton, q ( c c r ), where s the delectrc constant of vacuum, r the relatve delectrc constant of the soluton, and q the elementary charge. It s assumed that the mobltes of the postve and the negatve charges are dentcal and that each charge has one elementary charge only. Lnear elastc compresson s assumed for charges closer than 5 nm to one another. 4. RESULTS AND DISCUSSION Fg. shows transent currents from 3 wt% OLOA dsperson for varous voltages. After the voltage s appled, the current shows a sharp peak wth a heght proportonal to the voltage and then decreases to zero. After 5 seconds the voltage s brought down to zero volts. The reverse transent current that follows shows a dfferent behavor from the forward transent dependng on the magntude of the step voltage. When the voltage s lower than.5 V, the reverse current decays monotoncally n a smlar way to the forward current. At step voltages hgher than.5 V the reverse current develops a broad hump. The peak of the hump shfts to later tmes as the voltage ncreases up to V. After that, the shape and the poston of the peak does not change sgnfcantly. Prevous attempts to explan the orgn of the delayed hump [,2] were not conclusve. The one-dmensonal drft-dffuson model has been solved for a system wth varous amounts of charge and a gven electrophoretc moblty. All mportant phenomena n the transent current of the experments have been reproduced, ncludng the delayed hump n the reverse transent as shown n Fg. 2. The forward transent behavor can be easly explaned by a seres resstor-capactor model wth a lmted charge content. At the early stage of the transton all charges n the cell are moved by the appled electrc feld, whch produces a hgh peak current wth a magntude proportonal to the voltage. As the charges arrve at the collectng electrodes, they develop space charge layers that generate an electrc feld aganst the appled feld, whch lowers the drvng electrc feld n the mddle of the cell. The accumulated charges do not contrbute to the current anymore because the dffuson flux developed by the accumulated charge balances the

3 electrophoretc drft. The current decreases to zero ether when the space charge completely screens the appled feld at low voltages, or when all moble charges are accumulated at the electrodes at hgh voltages. At equlbrum, the dffuson and drft fluxes completely balance each other throughout the length of the cell. When the appled voltage s removed (at t = 5 s), the balance between the drft and dffuson s broken, whch gves rse to a reverse current. The drvng force for the drft s the electrc feld generated by the accumulated charges. At the early stages of the reversal the current from the charges movng away from the electrodes s small because most of the charges are stll held near the electrodes where they are beng pushed aganst the electrodes by local electrc felds generated by the spatal dstrbuton of the charges, as shown n Fg. 3 (t = 5. s). The charges dffuse toward the cell center where they are more susceptble to the local electrc feld that pushes them toward the opposte electrodes (t = 5.43 s), whch results n ncrease n the reverse current. As charges of two opposte polartes mx n the bulk of the cell, the space charge, whch s the man drvng force of the reverse transent, dmnshes wth tme. The charge dstrbuton becomes more even throughout the cell, whch also reduces the dffuson fluxes. Fg. 6 shows the drft flux whch s the product of the local electrc feld and the charge concentraton at the center of the cell. Ths agrees closely wth the external current. In the early stage of the reversal the ncrease n current s manly drven by the ncrease n the charge concentraton rather than by the change n the local electrc feld. In the later stage (t > 5.43 s), the current decreases because the electrc feld decreases faster than the charge concentraton ncreases. When the appled voltage s not large enough to polarze the entre populaton of charged speces, a sgnfcant amount of charge s left n the mddle of the cell. As a result, t can contrbute to the electrophoretc drft from the begnnng of the reversal, whch produces a hgh ntal reverse current.(v = -.5 V n Fg.4(a) and (b)) As the polarzaton becomes more complete wth ncreasng bas, less charge s avalable for the ntal drft and t takes longer to reach the peak current.(v = V n Fg.4(a) and (b)) However, once the voltage reaches the value that s suffcent to polarze the entre charge n the system, no further ncrease n the bas wll change the charge dstrbuton n the cell. The reverse current response stops changng because the entre process s determned by the ntal charge dstrbuton profle.(v = 2 V n Fg.4(a) and (b)) Therefore, the degree of the reverse peak development s a good measure of the completeness of polarzaton. Indvdual charge nteracton plays an mportant role n charge compacton at the electrodes. Though the model descrbes the overall behavor very well, t starts to devate from the expermental data f the charge-to-charge nteracton s gnored. As seen n Fg.4 and Fg.5, the reverse peak postons appear earler than the model wthout nter-charge nteracton predcts. Ths s because the model assumes pont charges, whch permts unrealstcally hgh local charge concentratons n the vcnty of the electrodes. Ths makes t underestmate the electrc feld buldup and predct complete polarzaton at a lower voltage than realty. And the lower electrc feld estmaton from the space charge slows down the rse of the reverse drft, whch ends up wth the shft of the peak poston to a later tme. Ths error gets worse as the charge content ncreases as n Fg.5. The model wth pont-charge assumpton predcts later appearance of the peak as the total charge content ncreases whle the expermental data shows that the peak stops shftng as the charge concentraton ncreases hgher than.3-5 C/cm 3. However, when lnear elastc compresson s assumed when the charges are compacted closer than 5nm to one another,(fg.4(a) and Fg.5(a)) the model fts the expermental results very closely. The charge concentratons used n the model was determned from expermental data accordng to the method descrbed below and the electrophoretc moblty was calculated from the conductvty from the ntal forward transent current usng the charge concentraton. Under complete polarzaton, the tme ntegral of the forward or reverse transent current s equal to the half of the total charge content (Fg. 7). Therefore, one can easly estmate the charge content by ntegratng the expermental data under a suffcently large voltage. The expermental data of the 3 wt% OLOA dsperson showed the exact same trend as predcted by the model (Fg. 7) for whch the sngle polarty charge concentraton of C/cm 3 s obtaned. Usng the conductvty of S/cm obtaned from the ntal forward currents, whch s n agreement wth mpedance spectra measurements, the moblty of the charge carrers s estmated as. -5 cm 2 /Vs. A good agreement between the model and the expermental results confrms the absence of any sgnfcant charge generaton or charge njecton, as assumed n the model. 5. SUMMARY Step-voltage transent current responses of surfactant dspersons have been measured and analyzed. At step voltages above a certan value, the reverse current shows a broad hump after voltage s removed. The behavor can be reproduced by a one-dmensonal drft-dffuson model. It s explaned as a competton between an ncreasng number of charges avalable for drft and a decreasng electrc feld resultng from mxng of opposte charges. From the measurement data the total charge content and the electrophoretc moblty has been determned.

4 Normalzed Quanttes (a.u.) Normalzed Quanttes (a.u.) Current Densty Normalzed Normalzed Normalzed Current Densty Current Densty Current Densty Current Densty REFERENCES [] Novotny and M. A. Hopper, J. Electrochem. Soc., 26(6), 925 [2] T. Bert, H. De Smet, F. Beuns, and F. Strubbe, Opto-electroncs Rev., 3(4), 28 [3] F. Beuns, F. Strubbe, K. Neyts, T. Bert, H. De Smet, A. Verschueren, and L. Schlangen, EuroDsplay 25, 34 2.E-7.E-7.E+ 2.E-7.E-7.E+ 3E Tme (s) Fg. Transent current responses of 3 wt% OLOA dsperson The currents were measured wth parallel-plates electrodes. The dstance between the electrodes was cm Tme (s) x -5 C/cm 3 Partcle Interactons (d < 5nm) Fg. 2 Transent currents from -D drft-dffuson model Parameters used: total charge concentraton C/cm 3, charge moblty -5 cm 2 /Vs, electrode spacng cm, elastc partcle nteractons when closer than 5nm.E+ -5.E-8 -.5E-7.E2-5.E-8 -.5E-7.E+ -5.E-8 -.5E (a) Wth partcle nteractons (d < 5nm).5 2 (b) OLOA Expermental data Tme (s) (c) No partle nteracton Fg. 4 Reverse transent currents from experments and models for varous appled voltages E-6.9E-5 2.9E-5 3.9E-5 (a) Wth partcle nteractons (d<5nm) 7.8E-6.3E-5 2.4E-5 4.E-5 (b) OLOA expermental data Tme (s) 9.6E-6.9E-5 2.9E-5 3.9E-5 (c) No partcle nteracton Fg. 5 Reverse transent currents from experments and models for varous charge concentratons.2 2E E.8 E+.6 Current Drft Flux -E Charge (5.s) Charge (5.43s).4 Charge Conc Electrc Feld E E Feld (5.s) E Feld (5.43s).2 E.E+ 5.E-5.E-4.5E-4 2.E-4 Dstance from Electrode (cm) Fg. 3 Normalzed postve charge concentraton and electrc feld near an electrode Same parameters as Fg. 2. The appled voltage s 2 V Tme (s) Fg. 6 Two major contrbutons to reverse transent current behavor The reverse transent current s compared wth the drft flux at the center of the cell. 2 V s removed at 5 s..

5 Charge Conc. (C/cm3) 6E-5 5E-5 4.6x -5 C/cm 3, used n the model 4E-5 3E-5 2E-5 E-5 E+ Model - Forward Model - Reverse Experments - Forward Experments - Reverse Fg. 7 Charge concentratons from transent current ntegral of -D model and experments Same parameters as Fg. 2, the total sngle-polarty charge concentraton of C/cm 3 was used. Expermental data are from 3 wt% OLOA dsperson