Electrochemical Chromatic Change of Deionized Latex Suspensions

Well-deionized suspensions of polystyrene sulfonate latex are known to exhibit iridescence, where color changes with the voltage applied to transparen...
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Langmuir 2001, 17, 7371-7377

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Electrochemical Chromatic Change of Deionized Latex Suspensions Koichi Aoki* and Chengming Wang Department of Applied Physics, Fukui University, 3-9-1, Bunkyo, Fukui-shi, 910-8507 Japan Received April 16, 2001. In Final Form: August 14, 2001 Well-deionized suspensions of polystyrene sulfonate latex are known to exhibit iridescence, where color changes with the voltage applied to transparent electrodes. The reflection spectra were blue-shifted at voltages more positive than 1.0 V, whereas the spectra were red-shifted at voltages more negative than -1.2 V. They were invariant to voltages from -1.2 to 1.0 V. The wavelength versus voltage curve was similar to the current versus voltage curve, and hence electrode reactions may participate in the chromatic change. The spectra in the quiescent suspension varied gradually for 1 min, whereas those in the stirred suspension were stable after the voltage application. The thickness of the layer exhibiting the chromatic change grew with time and was proportional to the square-root of time, suggesting a diffusion-controlled process. The diffusion coefficient was on the order of 10-4 cm2 s-1 for the 2.0 V application. This implies that the diffusion of H+ was generated electrochemically from water. The generation of H+ was monitored with pH chemical indicators and was found to be the diffusion-controlled process. The H+ should be compensated with anions to keep electric neutrality. There is only one kind of anion: the sulfonic latex particles. The latex particles are then accumulated near the electrode and, hence, exhibit the blue-shifted chromatic change. This elucidation contrasts with the conventional understanding that the external electric field causes the dilution or the accumulation of the latex particles.

1. Introduction Colloidal suspensions of monodispersed spheres, typically a polystyrene latex, have been used for a simplified model of particles dispersed with complicated interactions. This work includes a model of electrolyte solutions,1 the phase transition and the scaling approach near critical points,2,3 pattern formation by molecular interaction,4-7 a model of proteins and nucleic acids,8 and charge-charge interaction of polyelectrolytes.9,10 Advantages of using the monodispersed latex for the models are ascribed not only to the optically visible size of the particle,11 but also to an easy control of the interaction energy by varying the ionic strength of the dispersion as well as the concentrations of the latex.3 An interesting feature of monodispersed latexes is that they exhibit a well-ordered arrangement of particles in deionized suspensions.12-17 The ordering can readily be * To whom correspondence should be addressed. E-mail: [email protected]. (1) Schmitz, K. S. Macroions in Solution and Colloidal Suspension; VCH Publishers: New York, 1993; Chapter 1. (2) Mandel, M. In Polyelectrolytes; Hara, H., Ed.; Marcel Dekker: New York, 1993; Chapter 1. (3) Arora, A. K.; Rajagopalan, R. In Ordering and Phase Transitions in Charge Colloids; Arora, A. K., Tata, B. V. R., Eds.; VCH Publishers, Inc.: New York, 1996; Chapter 1. (4) Grier, D. G.; Murray, C. A. Ordering and Phase Transitions in Charge Colloids; Arora, A. K., Tata, B. V. R., Eds.; VCH Publishers, Inc.: New York, 1996; Chapter 4. (5) Pieranski, P.; Strzelecki, L.; Pansu, B. Phys. Rev. Lett. 1983, 50, 900. (6) Pansu, B.; Pieranski, P.; Strzelecki, L. J. Phys. 1983, 44, 531. (7) Van Winkle, D. H.; Murray, C. A. Phys. Rev. A: At., Mol., Opt. Phys. 1986, 34, 562. (8) Bloomfield, V.; Carpenter, I. L. In Polyelectrolytes; Hara, H., Ed.; Marcel Dekker: New York, 1993; Chapter 2. (9) Schmitz, K. S. Macroions in Solution and Colloidal Suspension; VCH Publishers: New York, 1993; Chapter 4. (10) Jo¨nsson, B.; Åkesson, T.; Woodward, C. E. In Ordering and Phase Transitions in Charge Colloids; Arora, A. K., Tata, B. V. R., Eds.; VCH Publishers, Inc.: New York, 1996; Chapter 11. (11) Ise, N.; Ito, K.; Matsuoka, H.; Yoshida, H. In Ordering and Phase Transitions in Charge Colloids; Arora, A. K., Tata, B. V. R., Eds.; VCH Publishers, Inc.: New York, 1996; Chapter 5.

recognized with a striking iridescence similar to precious opals18 when the interdistance between the closest neighboring particles is of the order of the wavelength of visible light.19,20 The iridescence has been analyzed quantitatively with the diffraction theory21 similar to that for X-rays by molecular crystals. It has been widely recognized that the ordering is ascribed to the repulsion of charged latex particles from which counterions are dissociated. The ordering has been quantitatively explained by PoissonBoltzmann cell models,22 Poisson-Boltzmann jellium models,23,24 density-functional theories,25,26 and molecular dynamics27,28 by the use of Yukawa’s potential.29 In contrast, the attractive force seems to participate in the ordering according to the detailed analysis of the distributions of the particles30,31 and has been supported by the (12) Williams, R.; Crandall, R. S. Phys. Lett. 1974, 48A, 208. (13) Hachisu, S.; Kobayashi, Y.; Kose, A. J. Colloid Interface Sci. 1973, 42, 342. (14) Hachisu, S.; Kobayashi, Y. J. Colloid Interface Sci. 1974, 46, 470. (15) Fujita, H.; Ametani, K. Jpn. J. Appl. Phys. 1977, 16, 1091. (16) Monovoucas, Y.; Gast, A. P. J. Colloid Interface Sci. 1989, 128, 533. (17) Sirota, E. B.; Ou-Yang, H. D.; Sinha, S. K.; Chaikin, M. P.; Axe, J. D.; Fujii, Y. Phys. Rev. Lett. 1989, 62, 1528. (18) Alfrey, T.; Bradford, E. B.; Vanderhoff, J. W.; Oster, G. J. Opt. Soc. Am. 1954, 44, 603. (19) Luck, W.; Klier, M.; Wesslau, H. Ber. Bunsen-Ges. Phys. Chem. 1963, 67, 75. (20) Luck, W.; Klier, M.; Wesslau, H. Naturwissenschaften 1963, 50, 485. (21) Krieger, I. M.; O’Neill, F. M. J. Am. Chem. Soc. 1968, 90, 3114. (22) Alexander, S.; Chaikin, P. M.; Grant, P.; Morales, G. J.; Pincus, P. J. Chem. Phys. 1984, 80, 5776. (23) Smith, B. B.; Chan, D. Y. C.; Mitchell, D. J. J. Colloid Interface Sci. 1985, 105, 216. (24) Ha¨rtl, W.; Versmold, H. J. Chem. Phys. 1988, 88, 7157. (25) Salgi, P.; Rajagopolan, R. Langmuir 1991, 7, 1383. (26) Sengupta, S.; Sood, A. K. Phys. Rev. A: At., Mol., Opt. Phys. 1991, 44, 1233. (27) Kremer, K.; Robbins, M. O.; Grest, G. S. Phys. Rev. Lett. 1986, 57, 2694. (28) Rosenberg, R. O.; Thirumalai, D. Phys. Rev. A: At., Mol., Opt. Phys. 1987, 36, 5690. (29) Griffiths, D. J. Introduction to Electrodynamics, 2nd ed.; Prentice Hall: London, 1989; pp 109-110.

10.1021/la010556f CCC: $20.00 © 2001 American Chemical Society Published on Web 10/20/2001

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theory based on Sogami’s potential32 and the Monte Carlo simulation.33,34 There is still much controversy on the properties of the interaction potential.31,35 Interactions in the latex particles have been influenced by some physical stimulations such as magnetic fields,36-40 variations of surface charges on a wall,5,7,40,41-45 gravity,46-49 irradiation of laser,50-54 and electric fields.55-61 The effect of electric fields has been observed as a color change in iridescence when a voltage of more than a few volts is applied to electrodes in a deionized suspension. It is different from the other physical stimulations because of a possibility of participating in electrochemical reactions. A change in ionic charges by electrode reactions may disturb the electric field near the latex particles. In fact, the application of ca. -1.0 V in the suspension of the polystyrene sulfonate latex causes the electrochemical reduction of the hydrogen ion62-64 to disturb the electric neutrality condition near a latex particle.65,66 However, the electric field effect has been, so far, thought to be a simple electrostatic force acting on a latex particle55-61 without electrochemical complications. This work was motivated by the question of why electrode reactions have not been taken into account for the re-arrangement of latex particles. The two following (30) Ise, N.; Matsuoka, H.; Ito, K.; Yoshida, H. Faraday Discuss. Chem. Soc. 1990, 90, 153. (31) Dosho, S.; Ise, N.; Ito, K.; Iwai, S.; Kitano, H.; Matsuoka, H.; Nakamura, H.; Okumura, H.; Ono, T.; Sogami, I. S.; Ueno, Y.; Yoshida, H.; Yoshiyama, T. Langmuir 1993, 9, 394. (32) Sogami, I.; Ise, N. J. Chem. Phys. 1984, 81, 6320. (33) Takano, K.; Hachisu, S. J. Chem. Phys. 1977, 67, 2604. (34) Tara, B. V.; Sood, A. K.; Kesavamoorthy, R. Pramana-J. Phys. 1990, 34, 23. (35) Overbeek, J. Th. G. Faraday Discuss. 1990, 90, 183. (36) Gast, A. P.; Fermigier, M. J. Colloid Interface Sci. 1992, 154, 522. (37) Fermigier, M.; Gast, A. P. J. Magn. Magn. Mater. 1993, 122, 46. (38) Wirtz, D.; Fermigier, M. Phys. Rev. Lett. 1994, 72, 2294. (39) Sohn, D.; Russo, P. S.; Da´vila, A.; Poche, D. S.; McLaughlin, M. L. J. Colloid Interface Sci. 1996, 177, 31. (40) Bubeck, R.; Neser, S.; Bechinger, C.; Leiderer, P. Prog. Colloid Polym. Sci. 1998, 110, 41. (41) Van Winkle, D. H.; Murray, C. A. J. Chem. Phys. 1988, 89, 3885. (42) Clark, N. A.; Ackerson, B. J.; Hurd, A. J. Phys. Rev. Lett. 1983, 50, 1459. (43) Ackerson, B. J.; Taylor, T. W.; Clark, N. A. Phys. Rev. A: At., Mol., Opt. Phys. 1985, 31, 3183. (44) Murray, C. A.; Van Winkle, D. H. Phys. Rev. Lett. 1987, 58, 1200. (45) Zahn, K. Phys. Rev. Lett. 1997, 79, 175. (46) Crandall, R.; Williams, R. Science 1977, 198, 293. (47) Furusawa, H.; Tomotsu, N. J. Colloid Interface Sci. 1983, 93, 504. (48) Okubo, T. Prog. Polym. Sci. 1993, 18, 481. (49) Okubo, T. J. Phys. Chem. 1994, 98, 1472. (50) Chowdhury, A. H.; Ackerson, B. J.; Clark, N. A. Phys. Rev. Lett. 1985, 60, 833. (51) Ackerson, B. J.; Chowdhury, A. H. Faraday Discuss. Chem. Soc. 1987, 83, 309. (52) Burns, M. M.; Fournier, J.-M.; Golovchenko, J. A. Science 1990, 249, 749. (53) Loudiyi, K.; Ackerson, B. J. Physica 1992, 184A, 26. (54) Chakrabati, J.; Krishnamurthy, H. R.; Sood, A. K. Phys. Rev. Lett. 1995, 75, 2233. (55) Fujita, H.; Ametani, K. Jpn. J. Appl. Phys. 1979, 18, 753. (56) Tomita, M.; van de Ven, T. G. M. J. Opt. Soc. Am. A 1984, 1, 317. (57) Tomita, M.; van de Ven, T. G. M. J. Phys. Chem. 1985, 89, 1291. (58) Okubo, T. J. Chem. Soc., Faraday Trans. 1 1987, 83, 2487. (59) Okubo, T. J. Chem. Soc., Faraday Trans. 1 1988, 84, 3377. (60) Okubo, T.; Ishiki, H. J. Colloid Interface Sci. 1999, 211, 151. (61) Ito, K.; Hayakawa, R. Colloids Surf., A 1999, 148, 135. (62) Roberts, J. M.; Linse, P.; Osteryoung, J. G. Langmuir 1998, 14, 204. (63) Roberts, J. M.; O’dea, J. J.; Osteryoung, J. G. Anal. Chem. 1998, 70, 3667. (64) Aoki, K.; Lei, T. Electrochem. Commun. 1999, 1, 101. (65) Aoki, K.; Roberts, J. M.; Osteryoung, J. G. Langmuir 1998, 14, 4445. (66) Aoki, K.; Baars, A.; Jaworski, A.; Osteryoung, J. G. J. Electroanal. Chem. 1999, 472, 1.

Aoki and Wang

Figure 1. Instrument for the reflection measurement composed of a white light source (S), a lens (L), the cell (C), a photonic multichannel analyzer (D), and a microscope (M). The multichannel analyzer was mounted so that the incident angle was identical with the reflecting one.

observations hint about the participation of electrode reactions: (i) The application of a few volts56,60 always brings about electrode reactions even without adding a supporting electrolyte.62,67-70 (ii) The change in the iridescence occurs at a threshold voltage55,60 like an electrode reaction, rather than being a continuous variation with the voltage. Therefore, here we examine the effect of electrode reactions on the structural change in the ordered arrangement of polystyrene sulfonate latex in suspensions without salt. 2. Experimental Section The polystyrene sulfonate latex was synthesized by the technique previously reported.64 It was purified and deionized more elaborately than the previous latex.64 Concentrations of H+ included in the latex particle were determined by titration of NaOH under a monitoring of the conductivity. The diameter was evaluated with a dynamic light scattering instrument, DLS7000 (Otsuka Electronics, Osaka). The electrochemical cell was a plastic optical cell (10 × 10 × 42 mm3). The working and the counter electrodes were the indium-tin oxide-coated (ITO) glass plate or the platinum plate. The working electrode and the counter electrode adhered to the inner wall of the cell so that they faced each other. The reference electrode was a platinum coil. A saturated calomel electrode was also used only for examining the reproducibility of the Pt reference electrode. A use of the saturated calomel electrode for more than 1 min decreased spectrum bands, probably because of a leak of KCl into the suspension. The potentiostat used was NPOT-2501 (Nikko Keisoku, Atsugi). Reflection measurements were made with a homemade instrument (Figure 1) composed of a white light source (S), a lens (L), the cell (C), a photonic multichannel analyzer (D) (PMA11, Hamamatsu Photonics, Hamamatsu), and a microscope (M) with a CCD camera (Pico Scopeman, Moritex). The light source was from an incandescent lightbulb. The multichannel analyzer provides a spectrum by averaging 16 spectra, ranging from 300 to 820 nm in 5 s. The anionic (Dowex, 1-X4, OH- form) and the cationic (Dowex, 50W-X4, H+ form) exchange resins were contained in the cell during measurements to keep exhaustively the deionized conditions from ionic contamination by the air (oxygen and carbon dioxide) and the electrolysis.

3. Results and Discussion The TEM photograph clearly displayed the dispersed spheres, and no aggregation of particles was found. The diameter, 2a, of the latex particles was found to be 0.155 (67) Morris, S. E.; Ciszkowska, M.; Osteryoung, J. G. J. Phys. Chem. 1993, 97, 10453. (68) Ciszkowska, M.; Osteryoung, J. G. J. Phys. Chem. 1994, 98, 3194. (69) Ciszkowska, M.; Osteryoung, J. G. J. Phys. Chem. 1994, 98, 11791. (70) Ciszkowska, M.; Zeng, L.; Stejskal, E. O.; Osteryoung, J. G. J. Phys. Chem. 1995, 99, 11764.

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Table 1. Dependence of pH Values of the Suspensions at vf ) 1.13 × 10-3 on Concentrations of KCl by pH meter [KCl]/mM pH

0 5.17

0.005 5.03

0.02 4.86

0.1 4.61

calculated 1.0 4.39

5.0 4.37

sufficient 4.35

( 0.002 µm by dynamic light scattering (DLS). The TEM image of the particles showed full circles in the projected shape, of which the diameter agreed with the value by the DLS. By inserting this value into the Stokes-Einstein relation, we evaluated the diffusion coefficient to be 2.93 × 10-8 cm2 s-1 at 25 °C for the value of water viscosity. The uniformity ratio71 was 1.004. If the sulfonic group on the latex works as a strong acid, the number of NaOH molecules, NOH, for the titration should be identical with the product of the number of latex molecules, N, and the charge number, Z, per particle. Since the titration curve, conductivity versus the titrated volume of NaOH, was composed of two straight lines without curvature, the sulfonic group can be regarded as a strong acid.62 Since N dried particles with weight w and density d are satisfied with the relation, w ) N(4/3)πa3d, Z is expressed by

Z ) NOH/N ) NOH(4πa3/3)d/w

Figure 2. Dependence of spectra on the electrode voltage, E ) (a) 0.0, (b) 0.7, (c) 1.2, (d) 1.7, and (e) 2.0 V versus Pt in the fully deionized latex suspensions at vf ) 0.10. The spectra were measured in the order from (a) to (e) succeedingly.

(1)

Combining this relation with the known values of a (77.5 nm) and d (1.05 g cm-3) for polystyrene72 and the measured values of NOH and w, we obtained Z ) 1.66 × 104 (negative charge). If the charge is distributed uniformly on the latex surface, the surface area occupied by one -SO3 is calculated to be 4.55 nm2 ((2.13 nm)2). This value may be so large that the sulfonic acidity is not altered by the interaction due to the immobilization. When the hydrogen ions are dissociated fully from the sulfonic substituent, a pH value of the suspension is calculated to be 4.35 for vf ) 1.13 × 10-3, where vf is the volume fraction defined by (4πa3/3)N/V in the volume V of the suspension. Values of pH were obtained in the suspension to which KCl was deliberately added and are listed in Table 1. Insertion of a pH meter into the suspension gradually decreased the pH values because KCl leaked out from the saturated calomel electrode of the pH meter. Thus, the value without KCl includes ambiguity. The pH values decreased with an increase in the concentration of KCl. The decrease suggests the release of H+ from the electrostatic immobilization of the latex into the water phase due to the replacement of H+ by K+. The pH value at high concentrations of KCl was very similar to the value calculated on the assumption of exhaustive dissociation (Table 1). The release and, hence, the increase in the concentration of H+ in the water phase has been found in the reduction current of H+ controlled by both electric migration and diffusion.63,64 The ratio of [H+] without KCl to [H+] at the high value of [KCl] is 10-5.17/10-4.37 ) 0.16, whereas the ratio of the reduction currents without KCl to those at high values of [KCl] was 0.023.63 If only the dissociated hydrogen ions participated in pH values, these ratios should be identical. The smaller ratio for the pH values may be ascribed to a leak of KCl from the saturated calomel electrode. When positive voltages were applied to the ITO electrode in a yellow-like iridescent suspension, the suspension near the electrode became green, whereas the suspension near the counter electrode became red. Figure 2 shows varia(71) Juang, M. S.; Krieger, I. M. J. Polym. Sci. 1976, 14, 2089. (72) Barthet, C.; Armes, S. P.; Lascelles, S. F.; Luk, S. Y.; Stanley, H. M. E. Langmuir 1998, 14, 2032.

Figure 3. Dependence of the wavelength of the band and the current on the electrode voltage when E changed step-by-step with time in the fully deionized latex suspensions at vf ) 0.10. Each point was sampled 1 min after the voltage step increment. The counter electrode was the ITO.

tions of reflection spectra at several voltages. As the voltage was more positive than 0.7 V, the band shifted in the blue direction, associated with a decrease in the optical intensity and a broadening of the band shape. Figure 3 shows the dependence of the wavelength of the band at the maximum, λmx, on the voltage when the voltages were varied step-by-step with time. There is a hysteresis in the λmx versus E curve, depending on periods of the sampling time. For E < -1.8 V, the ITO electrode changed gray irreversibly, probably because of electrochemical reduction of the ITO. Figure 3 also shows the current, I, on the right ordinate, which was obtained at the same time as the measurement of the spectra. The domain of E where λmx varies largely is close to that of E where the current varies largely. The similarity between λmx and I suggests their participation in electrode reactions. If the chromatic change were to be attributed to the electric field in the suspension,55-61 λmx should vary monotonically with E because of a simple relation between the electric field and the applied voltage. Electrode behavior of polystyrene sulfonic acid at an ITO electrode has not been known, whereas the Pt electrode reduces hydrogen ions at a negative voltage to exhibit the limiting current even without adding a

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Figure 6. A model of (A) interference by reflection lights at parallel layers and (B) nonparallel orientation to the electrode with defects. Figure 4. Plots of the current density against E at the Pt (open circles) and the ITO (full circles) electrode in the latex suspension at vf ) 0.10. Each point was sampled 1 min after the voltage application.

in Figure 6A. The light beam incident with angle θ normal to the layer is reflected on several layers. The reflected beams are interfered to generate spectra when the difference in optical path lengths is equal to m (integer) times the wavelength (see Figure 6A). The difference of the geometrical lengths reflected on the first layer, k ) 1, and on the (K + 1)th layer is expressed by

AB + BC ) Kl (sec(θ) + sec(θ) cos(2θ)) ) 2Kl cos(θ) (2) The optical length for AB + BC, that is, n(AB + BC) ) 2nKl cos(θ) (n is the refractive index of water), is equal to λmx, and hence we obtain

λmx ) 2(nK/m)l cos(θ)

(3)

Let the distance between the closest particles be 2b or the radius of the unit crystalline sphere be b and the packing fraction be p.73 The volume fraction is defined by the ratio of the volume of the particle to the volume of the unit cell, which is expressed by (4π/3)b3/p. Thus, we obtain vf ) (4π/3)a3/[(4π/3)b3/p] ) p(a/b)3 or Figure 5. Reflection spectra of the suspensions at vf ) (a) 0.0629 and (b) 0.0140. Band a1 is the primary peak, bands a2 and b2 are the secondary peaks, and band b3 is the third peak.

supporting electrolyte.62-64 We compared the current density, j, versus voltage curves at the ITO with that at the Pt electrode, and we show them in Figure 4. The reduction wave at the Pt for E ) -0.5 V is attributed to the reduction of oxygen dissolved in the suspension. Currents at the Pt for E < -1.5 and E > 1.0 are attributed, respectively, to the reduction of water or H+ and the oxidation of water or OH-. Although the sensitivity of the current at the ITO was much smaller than that at the Pt, the shapes of the curves resemble each other. Thus, the reaction mechanism at both electrodes may be common. To examine whether λmx represents a unit length of a crystalline structure, the reflection spectra were observed at different volume fractions. With a decrease in the volume fraction, the band shifted in the red direction. When the volume fraction decreased to 0.09 at which the band shifted up to 680 nm, a new band appeared at 340 nm. The original (band a1 in Figure 5) and the new band (a2) still shifted in the red direction with the decrease in the volume fraction. The original band was out of the scale of the available wavelength (from 300 to 820 nm) for vf < 0.05. Only one band was observed for 0.02 < vf < 0.05. The further decrease in vf gave a third band (b3 in Figure 5). It is assumed that particles in the suspension are arranged in layers regularly, each separated by l, as shown

b ) a(p/vf)1/3

(4)

Since the latex particle has no orientation or no directional bonding, it may take on a hexagonal or cubic closed-packed structure in the suspension. The shortest distance in the closed-packed unit cell is x8b. Then, l corresponds to x8b, and eq 3 is rewritten as

λmx ) 2x8(nK/m)(p/vf)1/3a cos(θ)

(5)

To estimate m and n, we measured λmx for various values of vf and plotted λmx against vf-1/3 in Figure 7. Three proportional lines are found. Bands a1, b2 (or a2), and b3 in Figure 5 belong to the top, the second, and the third lines in Figure 7, respectively. Ratios of the slopes are s2/s1 ) 0.490 and s3/s1 ) 0.327. By comparing these ratios with eq 5, the top, the second, and the third lines correspond to m ) 1, 2, and 3, respectively. Inserting values of p ) 0.740 for the closed packing, a ) 77.5 nm, m ) 1, n ) 1.33, and θ ) 16.5° into eq 5 yields λmxvf1/3 ) s1 ) 503 nm for K ) 1. This value is larger than the experimental value (s1 ) 297 nm) in Figure 7. Three possible reasons for the deviation can be considered: (i) Interference of light beams reflecting on the electrode surface (k ) 0 in Figure 6A) and on the first (73) Atkins, P. W. Physical Chemistry, 6th ed.; Oxford University Press: Oxford, 1998; p 638.

Deionized Latex Suspensions

Figure 7. Plot of λmx against the inverse of the cubic root of the volume fraction in the deionized latex suspension without application of voltage.

layer (k ) 1) of the ordered particles rather than on successive layers (k ) 1 and k g 2). This interference may occur if the first layer is different in structure from the succeeding layers owing to the surface effects such as adsorption on or repulsion from the electrode. Specific features of the first layer should have been deviated from the proportionality in the plot of λmx against vf-1/3. Therefore, the surface specificity is unlikely to occur. (ii) Nonparallel orientation of the ordered structure toward the electrode. The orientation in the bulk does not always direct parallel with or normal to the walls of the electrodes, as illustrated in Figure 6B. Thus, defects occur near the electrode surface. The structure of the defects should depend on the orientation in the bulk, which is almost random. Experimental values of λmx were highly reproducible, without randomness. Therefore, a difference in the orientations is unlikely to occur. (iii) Deviation from the close-packed structure. A structure slightly looser than close packing is body-centered packing, of which the packing fraction is x3π/8 ) 0.6802. The length of the unit cell is l ) (4/x3)b. We then obtain

λmx ) (8/x3)b(n/m) cos(θ) ) (8/x3)(n/m)(p/vf)1/3a cos(θ) (6) The theoretical value of λmxvf1/3 or s1 for n ) 1 and m ) 1 is 300 nm, which agrees with the experimental value (297 nm) in Figure 7. Therefore, the ordered structure is in the body-centered packing rather than in the cubic close packing. This result looks strange because the particle has no oriented bonding, and hence the most stable structure should be close packing. A role played in the oriented bonding is the surface by which symmetric interaction is destroyed. Therefore, eq 6 may not express the bulk structure. Okubo’s work74,75 has suggested both cubic close packing and body-centered packing structures. The proportionality in Figure 7 was also observed when voltages were applied to the electrode. However, the reproducibility of λmx was poor because the spectra varied gradually with time. Indeed, the hysteresis curve of λmx versus E in Figure 3 depended on periods of the voltage applications. To know the time dependence in detail, we measured the time variations of the spectra. Figure 8 shows the variation of λmx with the time when the voltage (74) Okubo, T. J. Chem. Soc., Faraday Trans. 1 1986, 82, 3163. (75) Okubo, T. J. Chem. Soc., Faraday Trans. 1 1986, 82, 3175.

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Figure 8. Variation of λmx with the time after the voltage application at 2.0 V for 20 s and then at 0.0 V in the suspension of vf ) 0.10.

Figure 9. Reflection spectra at (a) 0, (b) 20, (c) 40, (d) 65, (e) 70, and (f) 75 s after the voltage application (2.0 V). The suspension was stirred with N2 bubbling at 20 s after the voltage application. The flow rate of the gas was 1.3 cm3 s-1.

was stepped up to 2.0 from 0.0 V for 20 s and then stepped back. The wavelength decreased rapidly after a 5 s delay and continued to decrease even after 1 min (not shown in Figure 8). The 5 s delay is an artifact of the measurement because of the 5 s time window of the photonic multichannel analyzer. The response back to 0.0 V showed a gradual increase in the wavelength and did not reach the initial wavelength in 5 min. The relaxation curve reminds us that a time variation of the electrochemical charge is caused by a diffusion-limiting process. Figure 8 also shows a chronoamperometric curve responding to the above potential step. The current value for t > 20 s was actually zero, implying that the gradual increase in λmx should be diffusional relaxation. The chronoamperometric current for t < 20 s was plotted against t-1/2 in the inset of Figure 8. It deviated from the line and did not pass the origin, implying that it should not be controlled by the diffusion of reactants. It is frequently observed that the distribution of products is controlled by diffusion, whereas that of reactants is controlled by a charge-transfer step rather than diffusion. If the suspension is stirred, the effect of diffusion may not be significant. Figure 9 shows variations of λmx with the time when the suspension was stirred with the bubbling of N2 gas 20 s after the voltage (2.0 V) application. The increase in the band height from (b) to (c) was independent of the stirring and, hence, is in the ordering

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Figure 10. Time-dependence of λmx under the conditions of Figure 9 (full circles) and under the condition of stirring long before the voltage application (open circles). The flow rate of the gas was 1.3 cm3 s-1.

Figure 11. Photograph taken from the lateral side of the electrode 420 s after the 2.0 V application in the vf ) 0.10 suspension.

process. The stirring caused the red shift from (c) to (f), in which some bands or some ordering structures appeared. The band f did not change with further stirring. The variation of λmx with time is shown in Figure 10 (full circles). There are some ordering states during the period between 20 and 90 s. When the suspension was stirred long before the voltage application, λmx varied only slightly (open circles). Of interest is a thickness of the domain with the color change. We observed the domain from the lateral side of the ITO electrode (see Figure 1) through a microscope with a CCD camera. When a voltage of 2.0 V was applied to the electrode, the domain grew from the electrode to the bulk, exhibiting a boundary, as shown in Figure 11. If the color change were caused by a constant electric field throughout the cell, it should be continuous without any boundary. The thickness, d, of the color domain was defined as a distance of a point with the most significant color variation from the electrode and was evaluated at various times after the voltage (2.0 V) was applied. Figure 12 (full circles) shows the dependence of d on the square root of the time. A linear relation was found, indicating a diffusion control. The line did not pass through the origin, probably because of underestimation of determining the slightly vague boundary. From the intuitive relation for the thickness of the diffusion layer, xDt ) d, the slope gives D ) 2.1 × 10-4 cm2 s-1. This value is too large for the diffusion coefficient of the latex particle, 2.93 × 10-8 cm2 s-1, evaluated from the Stokes-Einstein equation. It

Aoki and Wang

Figure 12. Plots of the thickness of the colored domain in the suspension at vf ) 0.10 (b) and in 1.4 mM KCl aqueous solution including pH indicators (O) (thymol blue and bromphenol blue) against the square of the time after the voltage (2.0 V) application.

is ca. twice the D value of the hydrogen ion (D ) 0.93 × 10-4 cm2 s-1). The twice is within errors to be permitted, because we roughly estimated the diffusion coefficient in time measurements too long to cause natural convection. Hydrogen ions generated at the electrode seem to cause the chromatic variation. If the latex particles diffuse to generate the color domain, values of d calculated from the diffusion coefficient of the latex should be 0.04 mm at 10 min, as shown in the dotted line in Figure 12. Therefore, the diffusion of the latex is not a rate-determining step for the growth of the boundary. The generation of hydrogen ions can be confirmed with chemical pH indicators. We applied 2.0 V to the ITO electrode in the latex suspension including a pH indicator. However, the color change by the indicator was killed by the background color of the latex suspension. We used the HCl solution without the latex, of which the concentration was the same as the total amount of H+ in the latex suspension. The color change was also vague owing to the coloration by the bulk HCl. When we used 1.4 mM KCl solution including pH indicators (thymol blue and bromphenol blue) without latex, we found a clear boundary for the coloration responding to the application of 2.0 V. The color changed from blue to yellow. A pH value at the turning point is ca. 3 for these indicators. The distance of the yellow domain from the electrode is plotted against the square root of time in Figure 12 (open circles). The linear variation was found, of which the slope is similar to that for the latex. Therefore, the color change in the suspension should be provided by the pH variation caused by the electrode oxidation of water or OH-. On the basis of the pH variation as well as the diffusioncontrolled process of H+, the coloration in the latex suspension by the voltage application can be explained as follows. The electrochemical generation of H+ requires counterions to satisfy the electric neutrality. However, the suspension is deionized exhaustively. The only anion present in the suspension is the sulfonic group on the latex particles. Thus, the generation and accumulation of the positive charge (H+) should be compensated with the accumulation of sulfonic ions supplied from the bulk (Figure 13). Consequently, the interdistance, 2b, in the bulk is reduced to 2b′ (Figure 13), and hence λmx decreases according to eq 6. In contrast, OH- is generated at the counter electrode at the negative voltage. It decreases the concentration of the latex near the counter electrode, repelling the latex to the bulk. The amount of the repelled

Deionized Latex Suspensions

Langmuir, Vol. 17, No. 23, 2001 7377

Faradaic potential domain (Figure 4) and, hence, should not cause any chromatic change, according to our conclusion. We consider that their chromatic change is ascribed to the local deviation of latex particles by the alternating current which is caused by the diffuse double layer. Latex particles move back and forth to the electrode, depending on positive and negative currents. Thus, their chromatic change is time-dependent and is different from our chromatic change by the generation of H+ and OH- under the almost steady-state conditions.

Figure 13. Illustration of the accumulation and the repulsion of the latex particles by the electrochemical generation of H+ and OH-, respectively.

latex should be compensated with that of the accumulated latex at the working electrode. We estimate a degree of the condensation by the application of positive voltages by using the bands shifted from 625 to 548 nm in Figure 2. By the use of the relation λmxvf1/3 ) 297 nm for s1 in Figure 7, the shift is equivalent to the variation of the volume fraction from 0.107 to 0.159, which corresponds to the change in the molar concentration of the latex from 0.093 to 0.139 µM or to the change in the condensation by 1.5 times. Fujita and Ametani observed time variations of the reflected optical intensity when they applied alternating voltages with 0.2-15 V amplitude at frequencies larger than 15 Hz.55 Amplitudes less than 1.3 V are in the non-

4. Conclusion The long-term electric effect of the ordered latex suspension on the light interference is not due to the electric field but to the generation of H+ and OH- by electrode reactions. The generation of the ions requires counterions to satisfy the electric neutrality. The latex particle plays a role in the neutrality because there are no other counterions in the deionized suspension. This conclusion has been deduced from the time dependence of the colored layer as well as from the comparison of diffusion coefficients. The growth of the colored layer is controlled by the diffusion of H+. The ordered structure is the simple cubic packing rather than the close packing. The deviation from the close packing may be due to a loss of symmetric interaction at the electrode surface. Consequently, values of b or concentrations from eq 6 do not always represent those in the bulk. The ordered structure at the voltage application is unknown at present because of the instability of the structure. Acknowledgment. K.A. thanks Prof. M. Nomura and Mr. K. Fujita for instructions on TEM techniques. LA010556F