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Effect of Counterion Species on Colloidal Crystal Hideki Matsuoka,* Taisuke Yamamoto, Tamotsu Harada, and Takashi Ikeda Department of Polymer Chemistry, Kyoto University, Kyoto 615-8510, Japan Received November 15, 2004. In Final Form: March 22, 2005 The effect of counterion species on the colloidal crystal structure in a dispersion was carefully investigated as a function of the degree of neutralization (R) by the ultra-small-angle X-ray scattering technique. The nearest neighbor interparticle distance (2Dexp) first increased with decreasing R, and then decreased after passing through the maximum. This behavior was confirmed for K+, Li+, Ca2+, TMA+ (tetramethylammonium) as a counterion, and Na+ in our previous report (Harada, T.; Matsuoka, H.; Ikeda, T.; Yamaoka, H. Langmuir 2000, 16, 1612). However, the R value of the maximum position (Rmax) largely depended on the counterion species, and it was in the order K+ < Na+ < TMA+ ∼ Li+. This behavior was well characterized by the specific features of each ion: the Rmax map could be well superimposed in the Stokes radius-crystal ion radius relationship of counterions. The Rmax dependence on Stokes radius was very similar to that of the B coefficient by Jones and Dole except in the case of Ca2+. In principle, the smaller the value for B, the smaller Rmax, indicating that a water structure breaker such as K+ can more easily destroy the colloidal crystal structure. In other words, the effect of the counterion species on colloidal crystal stability follows the Hofmeister series. Including Ca2+, the relationship was linear for the Rmax values plotted as a function of the limiting equivalent conductivity of small ions. A counterion with larger conductivity would be a stronger breaker for the colloidal crystal structure.
Introduction The mechanism of colloidal crystal formation at a low ionic strength and hence the interparticle interaction at these conditions are still a mystery.1,2 For 10 years, we have been investigating the colloidal crystal structure as a function of salt concentration and the degree of neutralization by applying the ultra-small-angle X-ray scattering (USAXS) technique.3-7 As a result, we have clarified the following points, which are not consistent with classical and contemporary concept/theory for colloidal particle interaction: (1) The interparticle distance in colloidal crystal increases with increasing added salt concentration in the region of κa < 1.3 (κ-1 is the Debye length4; a is the particle radius), but decreases in the region of κa > 1.3.3,4 (2) A solidlike colloidal crystal is formed in κa < 1.3, but the structure in κa > 1.3 is liquidlike. The former is well described by the three-dimensional paracrystal theory and the latter by the rescaled mean spherical approximation (RMSA).5,7 (3) The behavior at κa > 1.3, i.e., a decreasing interparticle distance, agrees with the DLVO (DerjaguinLandau-Verway-Overbeek) theory, while that for κa < 1.3 does not. Hence, a novel mechanism and interparticle interaction must be considered for colloidal crystal formation.4,6 (4) The colloidal crystal structure is different when H+ is replaced by Na+ as a counterion. Hence, the driving * To whom correspondence should be addressed. E-mail:
[email protected]. (1) Matsuoka, H.; Harada, T.; Ikeda, T.; Yamaoka, H. Colloids Surf., A 2000, 174, 79-98. (2) Harada, T.; Matsuoka, H. Curr. Opin. Colloid Interface Sci. 2004, 8, 501. (3) Matsuoka, H.; Harada, T.; Yamaoka, H. Langmuir 1994, 10, 4423. (4) Matsuoka, H.; Harada, T.; Kago, K.; Yamaoka, H. Langmuir 1996, 12, 5588. (5) Harada, T.; Matsuoka, H.; Yamaoka, H. Langmuir 1999, 15, 573. (6) Harada, T.; Matsuoka, H.; Ikeda, T.; Yamaoka, H. Langmuir 2000, 16, 1612. (7) Harada, T.; Matsuoka, H.; Ikeda, T.; Yamaoka, H. J. Polym. Sci. B, Polym. Phys. 2001, 39, 78.
force of colloidal crystal formation depends on the counterion specis.6 In this study, to obtain further information of the effect of counterions on the colloidal crystal formation, its structure, and interparticle interaction, we have investigated the colloidal crystal structure as a function of the degree of neutralization with changing the counterion species such as Li+, K+, Na+, Ca2+, and tetramethylammonium (TMA+) ions. Experimental Section The methyl methacrylate latex particles named MS-32, MS-34, and MS-45 were synthesized and purified in the same manner as in our previous studies.3-7 The characteristics of these latex particles were also determined in the same way and are summarized in Table 1. The details of USAXS instruments, experiments, and data analysis have been fully described elsewhere.3-7 The method of sample preparation was as reported previously.6 The latex concentration was 4 vol % for all experiments.
Results Figures 1-3 show examples of USAXS profiles for colloidal crystals at different degrees of neutralization (R) with various bases of different small cations. As in our previous study,6 R ) 0 means that all counterions are protons and R ) 1 means that all of them were replaced by other small cations such as Li+, K+, Na+, Ca2+, and TMA+. In any case, the peak position shifted toward smaller q (scattering vector defined by q ) 4π (sin θ)/λ, where 2θ is the scattering angle and λ is the wavelength of the X-rays) until a certain R, but it came back to larger q by further addition of base, as was observed in our previous study using NaOH as a base.6 In addition, the peak became broader with increasing R, which means that the colloidal crystal was destroyed by neutralization. However, the R value where the peak appears at the smallest q seems to be dependent on the cation species. The amount of the shift may seem to be very small, but this is physically meaningful as shown in our previous studies,3-7 in which only a small shift corresponding to a
10.1021/la0472044 CCC: $30.25 © 2005 American Chemical Society Published on Web 06/28/2005
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Table 1. Characteristics of Latex Particles Used in This Study surface charge/particleb code no.
diama
polydispersitya
(Å)
(%)
MS-32 MS-34 MS-45
2840 2690 2530
6 6
charge no.
charge density (µC/cm2)
6840 2910 8940
4.4 2.1 7.1
a Determined by USAXS. b Determined by conductometric titration.
Figure 3. USAXS curve of MS-34 latex dispersion neutralized by TMAOH with various degrees of neutralization. Arrows and notes are same as Figure 1.
Figure 1. USAXS curve of MS-32 latex dispersion neutralized by NaOH with various degrees of neutralization. The numbers in the figure are the concentrations of LiOH; those in parentheses are the degree of neutralization R. The arrows indicate the peak position, which corresponds to the first diffraction peak of fcc lattice when the structure is solidlike. Latex concentration is 4 vol %. The curves are shifted upward for clarity.
Figure 4. Degree of neutralization (R) dependence on interparticle distance in colloidal crystal (2Dexp) for MS-32 latex dispersion. The horizontal straight line in the figure indicates the average distance calculated from the concentration (2D0).
Figure 5. Degree of neutralization (R) dependence on interparticle distance in colloidal crystal (2Dexp) for MS-34 latex dispersion. Figure 2. USAXS curve of MS-32 latex dispersion neutralized by KOH with various degrees of neutralization. Arrows and notes are same as Figure 1.
change within 10% of the interparticle distance was systematically interpreted as a function of salt concentration3-5 or R,6 although the quality of USAXS profiles is not as good as in our previous studies.3-6 In some profiles in Figures 1-3, an additional peak was observed at a lower q than the peak indicated by an arrow typically in those for low a conditions. This additional peak was also observed in our previous studies, and its origin is still unknown.8,9 However, it was clarified that the distance
calculated from this additional peak is unrealistic for particles with a colloidal crystal origin.8,9 Figures 4-6 shows the R dependence of the nearest interparticle distance in a colloidal crystal (2Dexp) calculated from the peak position in USAXS profiles by using the Bragg equation assuming a face-centered-cubic (fcc) lattice for the three latexes used. Although it may be difficult to determine the lattice system from present (8) Matsuoka, H.; Ikeda, T.; Yamaoka, H.; Hashimoto, M.; Takahashi, T.; Agamalian, M. M.; Wignall, G. D. Langmuir 1999, 15, 293. (9) Harada, T.; Matsuoka, H.; Yamamoto, T.; Yamaoka, H.; Lin, J. S.; Agamalian, M. M.; Wignall, G. D. Colloids Surf., A 2001, 190, 17.
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Figure 6. Degree of neutralization (R) dependence on interparticle distance in colloidal crystal (2Dexp) for MS-45 latex dispersion.
USAXS profiles, assuming an fcc lattice can be justified since all of our previous studies at similar conditions indicated an fcc lattice formation.3-9 As was the case for Na+ ions in our previous study,6 the 2Dexp value takes a maximum at a certain R value below unity. The maximum 2Dexp values are close to the 2D0, which is the average interparticle distance calculated from latex concentration assuming a uniform distribution throughout the dispersion. The R value at the maximum 2Dexp is clearly dependent on the counterion species; i.e., it is different for Li+, Na+, K+, Ca2+, and TMA+ ions. The maximum R, Rmax, was determined from Figures 4-6, and will be discussed with the characteristics of each cation in the next section. For MS-45 latex (Figure 6), 2Dexp values have a plateau region since this latex particle is highly charged (see Table 1). For this latex, the smallest R value in the plateau region was used as Rmax. In the R region above Rmax, the 2Dexp value decreases and the Bragg peak becomes broader. Hence, this process corresponds to a melting of solidlike colloidal crystal. The Rmax value means how easily the crystal structure is destroyed by replacing counterions from H+ to other small cations.6 Discussion In this study, we used five small cations, i.e., Li+, Na+, K+, TMA+, and Ca2+. These ions are generally categorized into three groups:10 Class I ions have a small crystal ion radius (ion radius in salt crystal) and high charge density. The Stokes radius is large due to hydration. The structure maker for water by the concept of Frank and Wen11 and the Jones-Dole viscosity B coefficient is positive.12,13 Class II ions have a medium crystal ion radius and low charge density. The Stokes radius is smaller than the crystal ion radius. The structure breaker for water due to negative hydration,14 and hence the B coefficient is negative. Class III ions have a very large crystal radius. The Stokes radius is also large and comparable to the crystal radius. The B coefficient is positive. Typical examples are tetraalkylammonium ions, which are hydrophobic structure makers for water.15 (10) Ohtaki, H. Ion no Suiwa (Ion hydration); Kyoritsu: Tokyo, 1990; in Japanese. (11) Frank, H. S.; Wen, W.-Y. Discuss. Faraday Soc. 1957, 24, 133. (12) Kaminsky, M. Discuss. Faraday Soc. 1957, 24, 171. (13) Robinson, R. A.; Stokes, R. H. Electrolyte Solutions, 2nd rev ed.; Butterworth: London, 1959; Chapter 11 (Dover Publications: Mineola, NY, 2002). (14) Samoilov, O. Ya. Discuss. Faraday Soc. 1957, 24, 141.
Figure 7. Superimposed plots of relations between crystal ion radius and Stokes radius and between crystal ion radius and Rmax. See text for details.
Li+, Na+, and Ca2+ are categorized into class I, K+ is categorized into class II, and TMA+ is categorized into class III. Figure 7 shows a representative diagram of the relationship between crystal ion radius and Stokes radius. For the same valent ions, this relationship is well characterized by a concave-upward curve. In this diagram, the values of Rmax were superimposed on those of the crystal radius. Rmax also shows an excellent concave-upward relationship. This means that Rmax is dominated by Stokes radius to some extent. Although Rmax for Ca2+ is almost the same as that for Na+, it might be safe to say that size is not the only dominant factor. The viscosity of aqueous electrolyte solution (η) sometimes increases but sometimes decreases with electrolyte concentration c depending on the ion species. Jones and Dole16 proposed the following equation:
η ) 1 + Axc + Bc η0
(1)
where η0 is the viscosity of pure solvent. In this JonesDole equation, A is the constant, which is always positive. B is called the viscosity B coefficient, and its sign and magnitude depend on the character of the ions. B values were measured by Kaminsky.12 In principle, a negative B value means that the ion is a structure breaker of water. The B value itself is strongly related to the Stokes radius as is shown in Figure 8. In this diagram, Rmax values were superimposed and an excellent linear correlation with positive slope could be found, except for calcium ion. This means that Rmax is related to the B coefficient as shown in the inset in Figure 8. An excellent linearity was found both for MS-32 and MS-45 (and also MS-34 although with only two data points) as is shown in the figure by dotted lines. As was the case of Stokes radius, Rmax for Ca2+ deviated from linearity for single-valent cations. However, if we take the B coefficient in liters per equivalent instead of liters per mole, the data point comes closer to a straight line (arrow in inset). These observations suggest that the structure breaker cations have a higher ability to break the colloidal crystal structure since Rmax is smaller. In this sense, it can be said that the effect of counterion species on colloidal crystal obeys the Hofmeister series,17 which (15) Franks, F. Water; Royal Society of Chemistry: London, 1983; Chapter 10. (16) Jones, G.; Dole, M. J. Am. Chem. Soc. 1929, 51, 2950.
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Figure 8. Superimposed plots of relations between JonesDole B coefficient and Stokes radius and between Rmax and Stokes radius. Inset is plot of Rmax vs B coefficient.
was spotlighted recently again.18 Since at least the dielectric constant of water and small ion mobility in water should be influenced by the structure of water, our observation here is reasonable when the electrostatic interaction and motion of small counterions are accepted as important factors for colloidal crystal formation. As pointed out previously, in the colloidal crystal region, which has a limited size, an anomalous overlap of counterion cloud should occur.5 Schmitz et al.19,20 and Schmidt et al.21 proposed similar concepts as “temporal aggregate” or “temporal cluster (domain)”. Hence, it is not unnatural to think that the structure of water inside the crystal region is different from that in bulk and has a highly ordered arrangement. Finally, let us consider the relationship between Rmax and the limiting equivalent conductivity λ0 of small ions. A surprisingly excellent linear correlation with a negative slope was obtained even for Ca2+, as shown in Figure 9. The larger the limiting conductivity of countercations, the stronger the power to destroy the colloidal crystal structure. This observation may mean that the driving force to form colloidal crystals in dispersion is related to the dynamic nature of counterions. However, an explanation for the trend observed in Figure 9 is unknown at this stage. Classical theories, such as DLVO, cannot explain our present observation for the effect of counterion species since it assumes a point charge for small ions. However, recent developments on theory and simulation on colloidal interaction and phase transition in colloidal dispersion, such as density functional theory (DFT),22-25 simulations with three-body26 or many-body27 interaction, and a Monte (17) Hofmeister, F. Arch. Exp. Pathol. Pharmakol. (Leipzig) 1888, 24, 247. (18) Kunz, W.; Henle, J.; Ninham, B. W. Curr. Opin. Colloid Interface Sci. 2004, 9, 19. (19) Schmitz, K. S.; Lu, M. Biopolymers 1984, 23, 797. (20) Schmitz, K. S.; Mei, L.; Gauntt, J. J. Chem. Phys. 1983, 78, 5059. (21) Fo¨rster, S.; Schmidt, M.; Antonietti, M. Polymer 1990, 31, 781. (22) Chakrabarti, J.; Krishnamurathy, H. R.; Sengupta, S.; Sood, A. K. In Ordering and Phase Transitions in Charged Colloids; Arora, A. K., Tata B. V. R., Eds.; VCH: New York, 1996; Chapter 9. (23) Yu, Y.-X.; Wu, J.; Gao, G.-H. J. Chem. Phys. 2004, 120, 7223.
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Figure 9. Limiting equivalent conductivity dependence of Rmax.
Carlo simulation taking hydrated ion sizes into account,28 will help to give a theoretical backbone for our observation here, which is earnestly desired. Conclusion We clarified that solidlike colloidal crystals were formed at κa < 1.3 in dispersion and that the salt concentration dependence of the structure in this region could not be interpreted by current theories and concepts. After a systematic investigation, we have proposed an “electrodynamic” interaction as a driving force of colloidal crystal formation. To further investigate the essence of this novel interaction, we investigated the effect of counterion species on the colloidal crystal structure in this study. All cations used, i.e., Li+, Na+, K+, TMA+, and Ca2+, destroyed the solidlike colloidal crystal formed with H+ as a counterion, but the efficiency was different for each ion. The effect follows the Hofmeister series; i.e., it was stronger for ions with a smaller Jones-Dole B coefficient and with larger limiting equivalent conductivity. Hence, the structure of water and ion transport process inside the crystal region might play an important role as the driving force of colloidal crystal formation. Acknowledgment. We would like to express our sincere gratitude to Professor Junpei Yamanaka (Nagoya City University) and Dr. Priti Sunder Mohanty (currently at Kyoto University) for fruitful discussions. This work was financially supported by a Grant-in-Aid for Scientific Research (B12450386) from the Ministry of Education, Science, Culture, Sports and Technology of Japan, to whom our sincere gratitude is due. This work was also supported by the 21st Century COE Program, COE for a United Approach to New Materials Science. LA0472044 (24) Li, Z.; Wu, J. Phys. Rev. E 2004, 70, 031109. (25) Gunnarsson, M.; Abbas, Z.; Ahlberg, E.; Nordholm, S. J. Colloid Interface Sci. 2004, 274, 563. (26) Russ, C.; Gru¨nberg, H. H. Phys. Rev. E 2002, 66, 011402. (27) Dobnikar, J.; Chen, Y.; Rzehak, R.; Gru¨nberg, H. H. J. Chem. Phys. 2003, 119, 4971. (28) Quesada-Pe´rez, M.; Martı´n-Molina, A.; Hidalgo-A Ä lvarez, R. J. Chem. Phys. 2004, 121, 8618.
