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Langmuir 1999, 15, 4198-4202
Reentrant Order-Disorder Transition in Ionic Colloidal Dispersions by Varying Particle Charge Density† Junpei Yamanaka,*,‡,§ Hiroshi Yoshida,‡,| Tadanori Koga,‡,⊥ Norio Ise,¶ and Takeji Hashimoto‡,# Hashimoto Polymer Phasing Project, ERATO, Japan Science and Technology Corporation, 15 Morimoto, Shimogamo, Sakyo, Kyoto 606-0805, Japan, Central Laboratory, Rengo Company, Ltd., 186-1-4, Ohhiraki, Fukushima, Osaka 553-0007, Japan, and Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan Received August 31, 1998. In Final Form: March 2, 1999 The influence of the effective particle surface charge density, σe, on the order-disorder phase transition was examined for aqueous dispersions of charged colloidal silica and polymer latex particles (diameters ) 0.11-0.13 µm). The σe value of the silica particle was continuously tuned by changing the concentration of added NaOH. The three-dimensional phase diagram of the order-disorder transition for the silica system was determined as a function of σe, particle volume fraction φ, and salt concentration Cs, by observing iridescence due to Bragg diffraction from the ordered structure, and further by applying an ultra-smallangle X-ray scattering method. With increasing σe, the disordered dispersion became ordered and thereafter reentered into the disordered state. The presence of the reentrant disordered phase at high σe conditions was observed for ionic polymer latex systems. The reentrant phase transition was not explainable in terms of the Yukawa potential and charge renormalization model.
I. Introduction The ionic colloidal systems undergo the order-disorder phase transition (ODT) with varying magnitude of an electrostatic interparticle interaction.1 The colloidal systems have substantial experimental advantages for studying ODT, since the interaction can be easily tuned over a wide range. Major experimental variables that determine the interaction, and thus the dispersion state, are the effective surface charge density of the particles σe, the particle volume fraction φ and the salt concentration Cs.1 The phase diagram of ODT has extensively been studied.1-6 Usually, φ and Cs have been adopted as variables, and the charge dependence has been examined only in recent studies by Palberg et al.5 and by us.6 In both studies, the Cs value at the transition point (Cs,ODT), which was determined at a fixed φ and at relatively small σe’s, † Presented at Polyelectrolytes ’98, Inuyama, Japan, May 31June 3, 1998. * To whom correspondence should be addressed. ‡ Hashimoto Project. § Present address: Faculty of Pharmaceutical Sciences, Nagoya City University, 1-3 Tanabe-dori, Mizuho, Nagoya 467-8603, Japan. | Present address: Hitachi Research Lab., Hitachi Ltd., 7-1-1 Omika, Hitachi, Ibaraki 319-1292, Japan. ⊥ Present address: Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York 11794-3400. ¶ Rengo Co., Ltd. # Kyoto University.
(1) For review articles, see: (a) Sood, A. K. In Solid State Physics; Ehrenreich, H., Turnbull, D., Eds.; Academic Press: New York, 1991; Vol. 45, p 1. (b) Schmitz, K. S. Macroions in Solution and Colloidal Suspension; VCH: New York, 1993. (c) Ordering and Phase Transitions in Charged Colloids; Arora, A. K., Tata, B. V. R., Eds.; VCH: New York, 1996. (2) Wadachi, M.; Toda, M. J. Phys. Soc. Jpn. 1972, 32, 1147. (3) Hachisu, S.; Kobayashi, Y. J. Colloid Interface Sci. 1974, 46, 470. (4) Monovoukas, Y.; Gast, A. P. J. Colloid Interface Sci. 1989, 128, 553. (5) Palberg, T.; Mo¨nch, W.; Bitzer, F.; Piazza, R.; Bellini, T. Phys. Rev. Lett. 1995, 74, 4555. (6) Yamanaka, J.; Koga, T.; Ise, N.; Hashimoto, T. Phys. Rev. E 1996, 53, R4317.
increased with σe. Here we investigated much broader charge conditions than in the previous studies and found that the disordered state became ordered and thereafter reentered into the disordered state with increasing σe.7,8 To examine the charge density dependence systematically, we used aqueous dispersions of colloidal silica particles.6-9 The surface of the silica particle is covered by weakly acidic silanol groups (Si-OH).10 By adding a Brφnsted base, such as NaOH, the degree of dissociation of the silanols, and thus the σe value, was continuously increased. The three-dimensional phase diagram of the order-disorder transition was determined as a function of σe, φ, and Cs, by observing iridescence due to Bragg diffraction from the ordered structure, and further by applying an ultra-small-angle X-ray scattering (USAXS) method. The reentrant transition was also confirmed for dispersions of ionic polymer latex particles having various charge densities, by direct observation of their internal structures with a confocal laser scanning microscope (CLSM).7,8 The ODT of ionic colloids has often been claimed to be explainable in terms of the Yukawa-type interaction potential1,11 and charge renormalization concept.12 The phase boundary determined in the present study showed a close agreement with the theoretical one at low charge conditions. However, the reentrant transition, which was found to take place at higher charge densities, was not explainable within the framework of these theories. (7) Yamanaka, J.; Yoshida, H.; Koga, T.; Ise, N.; Hashimoto, T. Phys. Rev. Lett. 1998, 80, 5806. (8) Yoshida, H.; Yamanaka, J.; Koga, T.; Koga, T.; Ise, N.; Hashimoto, T. Langmuir 1999, 15, 2684. (9) Yamanaka, J.; Hayashi, Y.; Ise, N.; Yamaguchi, T. Phys. Rev. E 1997, 55, 3028. (10) For a review article, see: Iler, R. K. The Chemistry of Silica; Wiley: New York, 1979. (11) Kremer, K.; Robbins, M. O.; Grest, G. S. Phys. Rev. Lett. 1986, 57, 2694. Robbins, M. O.; Kremer, K.; Grest, G. S. J. Chem. Phys. 1988, 88, 3286. (12) Alexander, S.; Chaikin, P. M.; Grant, P.; Morales, G. J.; Pincus, P. J. Chem. Phys. 1984, 80, 5776.
10.1021/la9811315 CCC: $18.00 © 1999 American Chemical Society Published on Web 04/24/1999
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Table 1. Characteristics of the Colloidal Particles Used sample silica KE-P10W SI-80P latex SS-10 SS-16 N-100 SS-19
diameter (µm)
analytical charge density (σa) (µC/cm2)
0.12 0.11 0.12 0.11 0.12 0.13
effective charge density (σe) (µC/cm2)
analytical charge number (Za)
effective charge number (Ze)
0.07 0.23 1.7 3.9 5.3 7.2
II. Experimental Section The colloidal silica particles, Seahoster KE-P10W and Cataloid SI-80P, were purchased from Nippon Shokubai Co., Ltd. (Osaka, Japan) and Catalyst & Chemicals Co., Ltd. (Tokyo Japan), respectively, in the form of aqueous dispersions. Ionic polymer latex particles having strongly acidic groups, SS-10, SS-16, and SS-19, were synthesized by an emulsifier-free emulsion polymerization method. N-100 latex was purchased from Sekisui Chemicals Co., Ltd. (Osaka, Japan). Diameters of the particles are shown in Table 1. These particles were first purified by dialysis against purified water, and then by ultrafiltration using an ultrafiltration cell (Model 8400, Amicon Inc., Beverly, MA) and 0.05 µm pore size membranes (Type VM, Millipore, Bedford, MA). After these processes, ion-exchange resin beads (AG501-X8 (D), Bio-Rad Laboratories, Hercules, CA) were introduced and the dispersions were kept standing for at least 1 week. Water used was purified by a Milli-Q system (Type XQ or SP-TOC, Millipore, Bedford, MA), and had a conductivity of 0.40.6 µS/cm. Aqueous solutions of NaOH were prepared using analytical grade NaOH (Merck, Darmstadt, Germany) just prior to use; the concentrations were determined by conductometric titrations with HCl solutions. The electrical conductivity was measured by employing a conductivity meter (DS-12, Horiba, Japan) and two kinds of conductance cells each having a pair of parallel platinum electrodes (cell constants: 1.00 and 1.28 cm-1). The temperature was controlled at 25.00 ( 0.05 °C. Samples for the measurements were prepared under an argon atmosphere to minimize ionic contamination by carbon dioxide. To avoid ionic impurities from the glass wall, plastic bottles and apparatuses were used. A USAXS apparatus having Bonse-Hart optics was applied, as described in detail elsewhere.13 A sample dispersion was introduced into a quartz capillary with an inner diameter of 2 mm and a thickness of 0.02 mm. The measurements were performed at 25 ( 0.1 °C. An inverted type CLSM (LSM410, Carl-Zeiss, Germany) was employed. The observations were carried out in a reflection mode at 24 ( 1 °C, using an argon laser (wavelengths ) 488 and 364 nm) as a light source. Further details of the sample preparations, the USAXS measurement, and the CLSM observation have been fully described elsewhere.8
III. Results A. Effective Charge Density. Counterions of the colloidal particle are partly condensed near the particle surface due to a strong electrostatic field, which reduces the net surface charge of the particle. Therefore, the effective charge density of the particle σe is quite different from the analytical (bare) charge density σa. When particles are dispersed in liquids, it is σe, not σa, that determines the interparticle interaction, and consequently the state of the dispersion. We determined σe values for the silica and latex particles by applying conductometry. The surface charge density of the silica particle was altered by partly neutralizing their surface silanol groups by adding NaOH to the system. We note that the (13) Hart, M.; Koga, T.; Takano, Y. J. Appl. Crystallogr. 1995, 28, 568. Koga, T.; Hart, M.; Hashimoto, T. Ibid. 1996, 29, 318.
0.28 0.42 0.50 0.70
200 510 4 400 10 300 13 800 22 000
720 1 100 1 300 2 100
counterions of the silica particle are H ions in the absence of NaOH and that they are gradually replaced by Na ions by addition of NaOH. The electrical conductivities of the dispersions were measured at various concentrations of added NaOH (hereafter designated simply as [NaOH]) in the pH range of 6 < pH < 8. [NaOH] was 5.0 × 10-5 to 4.5 × 10-4 M. Under this condition, we can safely assume that most of the counterions were Na ions, since [H+] was much smaller than [NaOH]. Furthermore, the concentration of excess NaOH in bulk was negligibly small, because [OH-] was less than 10-6 M. Thus, in the present condition, the σa value is simply determined by the ratio of [NaOH] to total particle surface area in the dispersion, which leads to a linear relationship between σa (µC/cm2) and [NaOH] (M) as
σa ) (10-3/3)NAeap[NaOH]/φ
(1)
where NA is Avogadro’s number and ap is the particle radius (cm). The electrical conductivity of the silica dispersion, K, under a salt-free condition is given by
K ) 10-3 (λcCc + λpφ) + Kb
(2)
where λc and λp are the equivalent conductivities of the counterion (50.10 (S cm)/mol for Na+ at 25 °C in water) and the particles. Kb is the background conductivity, which was calculated as the sum of conductivities of ionic impurities in water (2 µM) and excess NaOH estimated from the pH value. Cc is the concentration of counterions, which is related to σe by
σe ) (10-3/3)NAeapCc/φ
(3)
The value of λp was determined by comparing conductivities of silica dispersions having potassium and sodium ions as counterions, assuming that the degree of dissociation of the silanols, and thus the σe value, was the same in both cases.8 The transport number of the particles, tp (≡λpφ/(λcCc + λpφ)) did not significantly vary with φ in the range of φ ) 0.01-0.03 and was 0.50 ( 0.02 for the Na-type silica.8 Figure 1a shows the σe versus σa plot for KE-P10W silica particles. σe was estimated from the measured conductivites by applying eqs 2 and 3, while σa was calculated from [NaOH] by using eq 1. Our previous results for latex systems9 are also shown. (The diameters of the latex particles were 0.08-0.13 µm, except for two samples (0.6 µm, σa ) 0.7 µC/cm2; 1 µm, σa ) 1.6 µC/cm2 cf. Table 1 of ref 9). It is clear that σe was always smaller than σa, and more significantly different from σa at larger σa’s. This trend is reasonably attributable to counterion condensation, which is expected to be more pronounced at higher surface potentials. We have reported earlier that the relation between σe and σa for ionic polymer latex systems obeyed a power law.9 A double-logarithmic plot
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Figure 2. Three-dimensional phase diagram for the orderdisorder transition of an aqueous dispersion of KE-P10W silica particles as a function of the effective charge density σe, the particle volume fraction φ, and the salt concentration Cs. The order-disorder phase boundary was shown by rectangles, and dashed lines are guides for the eye.
Figure 1. Relationships between σe and σa for salt-free aqueous dispersions of KE-P10W silica (filled circle; φ ) 0.02) and latex particles (open circle; extrapolated value to φ ) 0; taken from ref 9), represented in (a) linear and (b) double logarithmic scales. The full lines show an empirical relationship, ln σe ) 0.51 ln σa - 1.0. In Figure 1a, the broken curve shows the renormalized charge density σ*, and the dot-dashed curve represents σe ) σa.
of σe and σa (Figure 1b) for the presently examined silica dispersions showed a good linearity, which implied that the power law also held for the silica systems. For the latex systems,9 coefficients C1 and C2 in an empirical relationship
ln σe ) C1 ln σa + C2
(4)
were (C1, C2) ) (0.49, 1.0). The coefficients obtained for the present silica system were (0.51, 1.0), which showed close agreement with those for the latex. In the absence of NaOH, σe for the silica particles was estimated by eqs 2 and 3 from measured conductivities, using the equivalent conductivity of H+ (349.82 (S cm)/ mol at 25 °C in water) and the λp value obtained above. For the latex particles, which had strongly acidic groups (counterion: H+), σa was determined by conductometric titrations by NaOH solutions. σe values for the latex particles were determined by performing conductivity measurements and by using eqs 2 and 3. The charge densities thus determined are compiled in Table 1. The analytical and effective charge numbers (Za, Ze) are also shown. B. Phase Diagram for Silica System. Figure 2 is the three-dimensional phase diagram for the KE-P10W silica as a function of σe, φ, and Cs, which was constructed by observing iridescence from the ordered structure. Cs values were estimated from the sum of concentrations of coexisting NaCl, ionic species in the water used (2 µM), and excess NaOH, if any. The region whose Cs is smaller than Cs,ODT (shown by rectangles) corresponds to the ordered state.
Figure 3. Variation of the USAXS profiles with increasing σe showing the reentrant order-disorder phase transition: (a) σe ) 0.07, (b) 0.36, and (c) 0.72 µC/cm2. φ ) 0.03 and Cs ) 10 µM in all cases.
With increasing φ at fixed σe’s, Cs,ODT increased monotonically, as reported previously.1-4 On increasing σe for φ g 0.02, the phase boundary first shifted toward higher Cs due to an augmented electrostatic interaction. However, with a further increase in σe, a maximum was observed at around σe ) 0.4-0.5 µC/cm2, after which Cs,ODT decreased. In other words, there existed a reentrant disordered state in the high σe region. C. USAXS Studies. The phase diagram was further examined by applying the USAXS method. Figure 3 shows the scattering intensity versus scattering vector q, at φ ) 0.03, Cs ) 10 µM, and at three σe’s, which corresponded to the disordered, ordered, and reentrant disordered states in the phase diagram (Figure 2). In the disordered state (profile a; σe ) 0.07 µC/cm2), a broad peak due to interparticle interference, which resulted from an electrostatic interaction, was observed in addition to the form factor of an isolated particle. In the ordered state (b; 0.36 µC/cm2), sharp peaks were observed. The ordered structure consisted of grains, which increased in size when the order-disorder boundary was approached.6,8 Under the present condition, the Cs value was close to Cs,ODT (about
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15 µM) and the sizes of the ordered grains were as large as the width of the incident X-ray beam (approximately 1 mm). Relative peak positions of the sharp peaks with respect to the first peak position were integers from 1 to 4. This suggests that these peaks can be ascribed to the first to the fourth orders of Bragg diffraction. When measurements were performed by rotating the sample with respect to the capillary axis, similar scattering profiles were observed at each multiple angle of 60°. This result implies that the ordered structure had a 6-fold symmetry. As discussed by Konishi et al.,14 this scattering profile can be attributed to the diffraction from (110) planes of a “single” body-centered cubic (bcc) lattice, which were maintained parallel to the capillary axis with the [11 h 1] direction being vertically upward. At σe ) 0.72 µC/cm2 (c), again a scattering profile due to the liquidlike particle arrangement was observed, which confirmed the presence of the reentrant disordered state. D. Phase Diagram of the Latex System. Internal structures of the latex dispersions were observed by LSCM. Figure 4 is a phase diagram determined from the LSCM images for four kinds of latex particles at Cs ) 2 µM and under relatively dilute conditions. The data for the two kinds of silica in the absence of NaOH (σe ) 0.07 and 0.23 µC/cm2) are also shown. Clearly, there exists a disordered state at high σe’s, not only when φ and/or σe are small. Thus, the reentrant transition was confirmed for latex systems. We note that coexistence of the ordered and disordered states was observed in the “ordered” state near the phase boundary. Detailed studies concerning the location of the order-disorder coexistence regime have been reported elsewhere.8 IV. Discussion Here we compared the observed phase boundary with theoretical studies. The interaction between charged colloidal particles has often been claimed to be explainable in terms of the pair potential having the Yukawa form UY(r),
UY(r) ) A[(Ze)2/4π] exp(-κr)/r
(5)
where r is the interparticle distance, Z is the charge number, e is the elementary charge and A ) [exp(κap)/(1 + κap)]2 is a geometrical factor.1 1/κ is the Debye screening length defined as
κ2 ) 4πe2(Cc + 2Cs)/kBT
(6)
where Cc is the concentration of counterions and is the dielectric constant of the medium. Robbins et al.11 have performed a numerical simulation study for systems interacting via the Yukawa potential, and determined a phase diagram for ODT. UY(r) is derived from the linearized Poisson-Boltzmann (P-B) equation with Debye-Hu¨ckel (D-H) approximation.1 In practice, especially under the low salt conditions examined here, the D-H approximation is not valid. Even then, it has been considered that the use of UY(r) was justified, if one introduces a renormalized charge density σ*, proposed by Alexander et al.12 In fact, several authors have reported that the observed phase diagrams showed a close agreement with that calculated by Robbins et al. by using σ*.4,5 Furthermore, Palberg et al.5 reported that the renormalized charge was close to the effective charge determined by conductivity measurements. We note that these (14) Konishi, T.; Ise, N.; Matsuoka, H.; Yamaoka, H.; Sogami, I.; Yoshiyama, T. Phys. Rev. B 1995, 51, 3941.
Figure 4. Phase diagram determined by confocal laser scanning microscopy for polymer latex (circle) and colloidal silica (square) dispersions: (open symbols) ordered state; (filled symbols) disordered state. Cs ) 2 µM.
Figure 5. Comparison between observed phase boundary (rectangles) and the numerical simulation results by Robbins et al. with σ* (broken curve) and with σe (full curve). φ ) 0.03.
conclusions have been drawn for relatively small charge particles (σa < 0.63 µC/cm2 in ref 5). σ* values calculated for the silica system (φ ) 0.02) by the method in ref 12 were also shown in Figure 1a (broken curve). At small σa’s, the observed σe value was close to σ*, as reported in the previous studies. However, at higher σa’s, the σ* value tended to level off, while σe kept increasing, obeying the power law. In Figure 5, the experimental phase boundary in the (Cs, σa) coordinate is compared with that calculated from the numerical simulation results by Robbins et al. using σ* (φ ) 0.03). At small σa’s, the predicted boundary (broken curve) was close to the observed one, as reported in the previous studies. However, at higher σa’s, Cs,ODT became constant, due to the saturation of σ*. Thus, the reentrant transition was not in accord with the theoretical treatment based on the Yukawa potential and charge renormalization concept. When σe was used instead of σ* (full curve in Figure 5), Cs,ODT increased with σa and showed a maximum at around σa ) 6 µC/cm2. The calculated phase boundary is also represented in the (Cs, σe) coordinate in Figure 6 (dotdashed curve). In this case, the occurrence of the maximum is attributed to an increase of the screening effect with σa. The ionic strength of the dispersion, I (≡Cs + (1/2)Cc), increases with σa. Since κ is proportional to I1/2, the screening effect becomes more pronounced at higher σa’s, resulting in a reentrant order to disorder transition. However, both the predicted maximum position and Cs,ODT at the maximum were much higher than those observed. Furthermore, the validity of the effective hard sphere model1-3 was examined. The ODT of the ionic colloids has often been regarded as the Kirkwood-Alder (K-A) transition,15 which was originally found for hard sphere (15) Alder, B. J.; Wainwright, T. E. J. Chem. Phys. 1959, 31, 459.
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aeff ) ap + (1/2)
Figure 6. Phase boundaries calculated from the numerical simulation results by Robbins et al. and two effective hard sphere (HS) models. The observed phase boundary is shown by rectangles. φ ) 0.03.
(HS) systems. In this case, ODT occurs due to the excluded volume effect, and the transition point from the disordered state to the order-disorder coexistence state lies at φ ) 0.494. For ionic colloids, the particle size is enlarged by introducing the effective particle radius aeff, so that the effective volume fraction φeff
φeff ) φ(aeff/ap)3
(7)
is as large as the φ value for the K-A transition. Usually, aeff is defined as the sum of the Debye screening length and the bare radius, that is,
aeff ) ap + 1/κ
(8)
In Figure 6, the phase boundary calculated by this model (hereafter designated as HS I model; full curve) is compared with the observed phase boundary. Cs,ODT was determined from eqs 6-8 so that the condition φeff ) 0.494 was satisfied. The HS I model predicts the monotonic decrease of Cs,ODT with σe, which is due to a decrease in 1/κ with σe and does not reproduce the observed rentrance. A more elaborate estimation of aeff has been reported by Baker and Hendersen (B-H)16 by applying the perturbation theory and by assuming UY(r) for interparticle interaction, which gives (16) Baker, J. A.; Henderson, D. J. Chem. Phys. 1967, 47, 2856.
∞ [1 - exp{-UY(r)/kBT}] dr ∫r)2a p
(9)
The phase boundary calculated with aeff as defined in eq 8 (HS II; dashed curve) is also presented in Figure 6. The calculated phase boundary reproduces the observed trends, but the overall agreement is not satisfactory. Although the effective hard sphere model has been reported to successfully explain some of the experimental results,2,3 in our opinion, its physical background is rather vague, especially under the low salt (large 1/κ) conditions examined here. As seen above, both the numerical simulation study based on the Yukawa potential and the effective hard sphere models did not reproduce the phase boundary determined here. These discrepancies appear to be partly attributed to, e.g., neglect of the many-particle interaction in the theory, which is more significant in strongly interacting systems such as the present one. In our opinion, the Yukawa potential, in which only Coulombic repulsion between two particles is assumed, does not duly account for the phase behavior in low-salt dispersions: Recent experimental results suggest the presence of net attraction in ionic colloidal systems in low-salt conditions. For example, spontaneous formation of void structures,17 where vapor and liquid states are coexisting, seems to be difficult to explain without assuming a net attraction. We would like to point out that the void structure is favored for highly charged particles,18 for which the reentrant disordered state was observed here. V. Conclusions In the present study, we examined the order-disorder phase transition in dispersions of ionic colloidal silica and polymer latex particles. Both systems showed a reentrant order-disorder transition with increasing surface charge density, which was not explainable in terms of a numerical simulation study based on the Yukawa potential and renormalized charge model. We may reasonably conclude that the argument in terms of the theories is not applicable for highly charged colloidal systems. The effective hard sphere models also did not reproduce the observed phase boundary. LA9811315 (17) Ito, K.; Yoshida H.; Ise, N. Science 1994, 263, 66. (18) Yoshida, H. et al. Preprints of The 49th Meeting on Colloid and Surface (Tokyo), The Chemical Society of Japan: Tokyo, 1996; p 145 (in Japanese).
