pubs.acs.org/Langmuir © 2011 American Chemical Society
Heating-Induced Freezing and Melting Transitions in Charged Colloids Akiko Toyotama* and Junpei Yamanaka Faculty of Pharmaceutical Sciences, Nagoya City University, 3-1 Tanabe, Mizuho, Nagoya, Aichi 467-8603, Japan Received December 8, 2010. Revised Manuscript Received December 29, 2010 We examine influence of temperature on the phase behavior of dilute aqueous dispersions of charged colloidal silica and polystyrene particles. They undergo either freezing or melting transitions with increasing temperature. Freezing occurs in the case of low-charge, low-salt colloids, and melting is observed in the case of high-charge, high-salt colloids. All of these phase transitions are thermoreversible. These intriguing behaviors can be qualitatively explained in terms of the decrease in the permittivity of water at elevated temperatures.
Dispersions of uniformly shaped, submicrometer-sized charged colloidal particles undergo a freezing transition from a disordered “liquid” state to an ordered “crystal” state upon increasing the magnitude of the electrostatic interparticle interaction.1-6 In the crystal state, the particles are regularly arranged in a facecentered-cubic (fcc) or body-centered-cubic (bcc) lattice. In the disordered state, liquidlike ordering of the particles is observed. Aqueous dispersions of charged polystyrene (PS) and colloidal silica particles have frequently been used to study the freezing and melting transitions. The effect of temperature on the phase behavior of charged colloids, however, remains to be clarified, although temperature is one of the fundamental parameters governing phase transitions in atomic systems. In this letter, we report that aqueous charged colloids undergo both freezing and melting at elevated temperature. Freezing is found to occur in the case of low-charge, low-salt colloids, and melting is observed in the case of high-charge, high-salt colloids. Phase transitions in charged colloids have been discussed in terms of the interaction potential between two colloidal particles under the mean-field approximation,1,2,5 according to which the liquid medium surrounding the colloidal particles is assumed to be a dielectric continuum characterized by the permittivity, ε. When the pair interactions are sufficiently weak, the potential can be approximated as a Yukawa-type screened Coulomb potential U(r),2 Z 2 e2 expð - KrÞ ð1Þ UðrÞ ¼ GðK, ap Þ r 4πε Here, r is the center-to-center distance between the two particles; ap is the particle radius; Z is the charge number of the particle; and e is the elementary charge. The Debye length κ-1 is a measure of the degree of electrostatic screening by small ions in the liquid medium. For univalent ions with a number concentration of ni (i = 1, 2,..., N), N P n i 2 e2 i¼1 2 ð2Þ K ¼ εkB T *To whom correspondence should be addressed. E-mail: toyotama@ phar.nagoya-cu.ac.jp. (1) Russel, W. B.; Saville, D. A.; Schowalter, W. R. Colloidal Dispersions; Cambridge University Press: New York, 1989. (2) Sood, A. K. Solid State Physics; Ehrenreich, H., Turnbull, D., Eds.; Academic Press: New York, 1991. (3) Anderson, V. J.; Lekkerkerker, H. N. W. Nature 2002, 416, 811–815. (4) Yethiraj, A.; van Blaaderen, A. Nature 2003, 421, 513–517. (5) Ise, N.; Sogami, I. Structure Formation in Solution; Springer: Berlin, 2005.
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where kB is the Boltzmann constant and T is the absolute temperature. For salts formed from univalent positive and negative ions such as NaCl, the salt concentration Cs is related to ni as N 1X ni Cs ¼ ð3Þ 2 i ¼ 1 1000NA where NA is Avogadro’s number. The geometric factor G(κ, ap) exp(2κaP)/(1 þ κaP)2 represents the effect of the finite particle size. The phase behaviors of uncharged hard-sphere (HS) colloids are governed only by the particle volume fraction φ; therefore, the phase transitions of the HS colloids are completely entropic and athermal.7,8 For colloids interacting via soft potentials, the phase transitions are governed by enthalpy changes as well as φ and are hence temperature-dependent. For example, dispersions of polymer-modified particles undergo thermally induced phase separation because of the temperature dependence of the miscibility between the polymer and the dispersion medium.9 The phase behavior of charged colloids is also more or less temperature-dependent. It should be noted, however, that in the expressions for κ-1 and the reduced potential U(r)/kBT, T is introduced as εT. When T increases, ε decreases drastically and hence the temperature dependence of the phase transitions becomes very weak.10,11 In particular, for noninteracting dipolar liquids, ε(T) obeys the Curie law (ε ≈ 1/T), and hence the product εT is independent of T;11 in this case, the phase transition should be athermal. However, for many polar liquids, including water, ε decreases more rapidly than does 1/T. Therefore, the εT values decrease with an increase in T; for example, when T is increased from 0 to 100 °C, the relative permittivity of water decreases from 87.74 to 55.72, resulting in a 3% reduction in εT. On the basis of this fact, Robbins et al. stated that charged colloids might freeze upon heating under appropriate conditions.11 In previous experimental studies,12-15 however, it has been reported that charged colloids (6) van Blaaderen, A. MRS Bull. 2004, 29, 85–90. (7) Pusey, P. N.; van Megen, W. Nature 1986, 320, 340–342. (8) Chen, Z.; Russel, W. B.; Chaikin, P. M. Nature 1999, 401, 893–895. (9) Vrij, A.; Penders, M. H. G.; Rouw, P. W.; de Kruif, C. G.; Dhont, J. K. G.; Smits, C.; Lekkerkerker, H. N. W. Faraday Discuss. Chem. Soc. 1990, 90, 31–40. (10) Chaikin, P. M.; Pincus, P.; Alexander, S.; Hone, D. J. Colloid Interface Sci. 1982, 89, 555–563. (11) Robbins, M. O.; Kremer, K.; Grest, G. S. J. Chem. Phys. 1988, 88, 3286–3313. (12) Schaefer, D. W.; Ackerson, B. J. Phys. Rev. Lett. 1975, 35, 1448–1451. (13) Williams, R.; Crandall, R. S.; Wojtowicz, P. J. Phys. Rev. Lett. 1976, 37, 348–351. (14) Okubo, T. J. Chem. Phys. 1991, 95, 3690–3698. (15) Okubo, T. J. Chem. Phys. 1992, 96, 2261–2269.
Published on Web 01/06/2011
DOI: 10.1021/la104878r
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Toyotama and Yamanaka Table 1. Charged Colloids Used and Their Melting or Freezing Temperatures
sample
particle
ap (nm)
PS #1 PS #2 PS #3 PS #4 PS #5 silica #1 silica #2 silica #3 silica #4 silica #5
#5043 SS-22 SS-22 SS-09 #5010A KE-W10 KE-W10 KE-W10 KE-W10 KE-W10
234 58 58 46 48 54 54 54 54 54
[NaOH] (μM)
Z
φ
Cs (μM)
Tm (°C)
75 40 27.5 22.5 25
4498 1017 1017 870 735 528 390 336 314 325
0.02 0.01 0.01 0.01 0.01 0.035 0.035 0.035 0.035 0.035
5.4 12.0 11.0 13.3 10.8 14.5 7.0 4.0 2.0 2.0
16-25 30-38 25-30 15-25 25-30 5-25
exhibit only melting transitions at elevated T. In the present study, we report that charged colloids undergo both melting and freezing transitions upon heating. We note that variations in Z, Cs, and φ with T also lead to thermally induced phase transitions. For example, colloidal silica crystallizes upon heating in the presence of a weak base, pyridine, because of the increase in Z with T.16,17 The crystallization of thermoresponsive spherical microgels that undergo volume phase transitions at elevated T has been studied extensively.18,19 However, as will be explained later, we believe that the temperature dependence of Z, Cs, and φ at elevated T need not be taken into account when investigating the phase behavior of the colloids discussed in this study. Dilute (φ = 0.01-0.035) aqueous dispersions of PS and colloidal silica particles with various values of Z were used. Table 1 shows the compositions of the samples that exhibited melting and freezing transitions and the characteristics of the colloidal particles. Two types of PS particles, SS-22 and SS-09, were synthesized by emulsifier-free polymerization. PS #5010A and #5043 were purchased from Duke Co. Ltd. The silica particles, Seahoster KE-W10, were obtained from Nippon Shokubai Co., Ltd., Tokyo, Japan. The particle radii were determined by using a dynamic light scattering apparatus (type DLS7000, Photal, Osaka, Japan). All of these colloids were purified by dialysis and ion exchange, as reported in our previous study.20 The Cs values of the samples were set close to the value at the liquid-crystal phase boundaries. Cs values thus chosen were high for large Z because of the stronger screening effect required to melt the crystals. The PS particles had strongly acidic groups on their surfaces, and the silica particles had weakly acidic silanol (Si-OH) groups on their surfaces. Their Z values were determined by electrical conductivity measurements performed in a previously described manner.21 The as-purified silica particles had a small number of surface charges (Z = 207 at 25 °C) owing to the selfdissociation of the silanol groups (Si-OH f Si-O- þ Hþ).22 The addition of sodium hydroxide (NaOH) enhanced the dissociation of the silanols (Si-OH þ NaOH f Si-O- þ Naþ þ H2O) and thus resulted in an increase in Z.21,23 We adjusted Z to a (16) Yamanaka, J.; Koga, T.; Yoshida, H.; Ise, N.; Hashimoto, T. In Slow Dynamics in Complex Systems; Tokuyama, M., Oppenheim, I., Eds.; American Institute of Physics: Woodbury, NY, 1999; p 144. (17) Toyotama, A.; Yamanaka, J.; Yonese, M.; Sawada, T.; Uchida, F. J. Am. Chem. Soc. 2007, 129, 3044–3045. (18) Alsayed, A. M.; Islam, M. F.; Zhang, J.; Collings, P. J.; Yodh, A. G. Science 2005, 309, 1207–1210. (19) Brijitta, J.; Tata, B. V. R.; Joshi, R. G.; Kaliyappan, T. J. Chem. Phys. 2009, 131, 074904. (20) Wakabayashi, N.; Yamanaka, J.; Murai, M.; Iwayama, Y.; Yonese, M. Langmuir 2006, 22, 7936–7941. (21) Yamanaka, J.; Yoshida, H.; Koga, T.; Ise, N.; Hashimoto, T. Phys. Rev. Lett. 1998, 29, 5806–5809. (22) Iler, R. K. The Chemistry of Silica: Solubility, Polymerization, Colloid and Surface Properties, and Biochemistry; Wiley: New York, 1976; Chapter 6 . (23) Yamanaka, J.; Hayashi, Y.; Ise, N.; Yamaguchi, T. Phys. Rev. E 1997, 55, 3028–3036.
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Tf (°C)
5-25 15-20 30-35 5-10
Figure 1. Temperature dependence of the Z values for the SS-22 PS particles (blue) and KE-W10 silica particles at [NaOH] = 20 μM (red). Broken lines and bars represent averaged values and standard deviations.
relatively low charge regime (Z e 528 at 25 °C). The temperature dependence of Z was examined for the KE-W10 silica ([NaOH] = 20 μM; Z = 303) and SS-22 PS particles by means of electrical conductivity measurements in the range of T = 5-45 °C. The experimental details of the Z-value determination are provided in Supporting Information A. Figure 1 shows the Z versus T plot for the two colloids. The Z values decreased slightly with an increase in T, and the plots could be approximated by linear relations with slopes of -1 and -6% when T was increased from 5 to 45 °C. The freezing and melting transitions of the colloids were examined by microscopy and spectroscopy. Optical micrographs were recorded using an inverted optical microscope (TE2000-S, Nikon, Japan, Plan Fluor 100 objective) equipped with a thermally controlled transparent glass plate. Reflection spectra were measured by means of a multichannel spectrophotometer equipped with a Y-branch optical fiber probe (type USB2000; Ocean Optics Inc., Dunedin, Florida, USA). After 2 mL of the colloidal sample was introduced into a poly(methyl methacrylate) cell (1 1 4.5 cm3), argon gas was blown into the cell to prevent contamination from airborne carbon dioxide, which would otherwise produce carbonic acids when dissolved in the sample. Then the cell was tightly sealed with plastic film and the spectra were measured after maintaining the cell in the thermostated baths controlled at various temperatures for more than 10 min. We used purified water (conductivity ∼0.5 μS/cm) obtained by using a Milli-Q waterpurification system (Millipore Co., Ltd.). The concentration of ionic impurities in the water was estimated to be 2 μM, which was added when calculating the Cs values. Figure 2 displays the optical micrographs of PS #1 at two values of T showing the arrangements of individual colloidal particles. The ordered crystal structures formed at T = 16 °C melted when T was elevated to 25 °C. The Bragg diffraction wavelengths of crystals other than PS #1 were in the visible region and could be determined by reflection spectroscopy. Figure 3a shows the reflection spectra of PS #5 (Z = 735) for various temperatures. The crystals that formed at temperatures below T = 25 °C, which Langmuir 2011, 27(5), 1569–1572
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Figure 2. Optical micrographs showing the melting transition of PS #1 upon heating. (a) Disordered liquid state (T = 25 °C) and (b) ordered crystal state (T = 16 °C).
Figure 4. (a) T-Z phase diagrams of the silica colloids at φ =
0.035 and Cs = 2 μM. Circles and crosses represent the crystal and liquid states, respectively; the phase boundary, which is a guide to the eye, is represented by a broken red curve. The dotted-dashed curve is the phase boundary when the T dependence of Z is considered. The solid red curve represents the theoretical phase boundary determined on the basis of the numerical simulation result of Robbins et al. (b) Theoretical phase diagram in the parameter space of T, Z, and Cs (ap = 50 nm, φ = 0.035). The regions shown in red and green represent the crystal and liquid states, respectively. The red curves drawn on the interface between the crystal and liquid phases are the phase boundaries at constant values of Cs from 0 to 30 μM in 5 μM steps.
Figure 3. Reflectance spectra of aqueous charged colloids undergoing (a) melting and (b) freezing transitions upon heating. Samples: (a) PS #5 and (b) silica #4. The spectra are shifted vertically for clarity. (c) Changes in the reflectance spectra of silica #4 upon successive variations of T. The blue and red curves represent the spectra at T = 5 and 50 °C, respectively.
were characterized by sharp Bragg peaks, melted upon heating to T = 30 °C or higher. Melting of the crystals at high T was observed for all of the PS dispersions used and for silica #1, which had a relatively high charge number (Z = 528). Their melting temperatures Tm are compiled in Table 1. All of these melting transitions were thermoreversible; that is, the melted colloid froze to form a crystal structure upon cooling to below Tm. The behavior of colloids having low Z values was in contrast to that described earlier. Figure 3b shows the spectra of silica #4 (Z = 314). Clearly, the sample froze upon heating to T = 35 °C. This freezing transition was also reversible with changing T and was reproducible. Figure 3c demonstrates changes in the reflection spectra when T was varied repeatedly between 5 and 50 °C, with a time interval of approximately 20 min. The liquid (T = 5 °C, shown in blue) and crystal (T = 50 °C, red) states were observed alternately. Freezing was also found for silicas #2 and #3. We note that the silica colloids thus exhibited both the melting and freezing Langmuir 2011, 27(5), 1569–1572
transitions, depending on the Z and Cs values. The freezing temperatures Tf of these samples are shown in Table 1. Figure 4a presents the phase diagram of the silica colloid at φ = 0.035 and Cs = 2 μM, presented by using Z and T as the parameters. (Data for silicas #4 and #5 (Z = 325) are included in Figure 4a.) The circles and crosses represent the observed crystal and liquid phases, respectively; we assumed that the Z values are constant with changing T, and we used the Z values obtained at 25 °C. The broken curves (which are a guide to the eye) represent the phase boundaries. The dotted-dashed curve in Figure 4a is the phase boundary drawn by taking the temperature dependence of Z into account (-1% from T = 5 to 45 °C), which did not significantly vary from that obtained by assuming Z = const with T. The aforementioned results clearly indicate that freezing and melting occur in the case of low-Z (low-Cs) and high-Z (high-Cs) colloids, respectively, at elevated temperatures. Here we examine whether these behaviors are in accordance with theoretical predictions that consider the temperature dependence of the permittivity of water. Robbins et al.11,24 reported a numerical simulation study on the crystallization phase diagram of charged colloids based on U(r) in eq 1. Elaborate simulation studies have recently been reported by several authors.25,26 It has been reported that the (24) Stevens, M. J.; Robbins, M. O. J. Chem. Phys. 1993, 98, 2319–2324. (25) Hamaguchi, S.; Farouki, R. T.; Dubin, D. H. E. Phys. Rev. E 1997, 56, 4671–4682. (26) Hynninen, A. -P.; Dijkstra, M.; van Roij, R. Phys. Rev. E 2004, 69, 061407/ 1–061407/8.
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Figure 5. Phase diagram defined by kBT/U(a) and λ. The circles and crosses correspond to the crystal and liquid states observed upon elevating the temperature from 5 to 45 °C. The inset shows the magnified diagram at low λ.
phase boundaries obtained by Robbins et al. were in close agreement with the experimental results when the interparticle interactions were sufficiently weak.1 In Figure 4a, the crystallization phase boundary determined on the basis of the results reported by Robbins et al. is shown by a solid curve. Here, we set φ=0.035 and Cs =2 μM, which were the experimental conditions that we used, and we calculated the Z values at the crystallization point as a function of T, taking into account the temperature dependence of the ε value of water. We note that the Z value at the phase boundary is constant with changing T if ε is proportional to 1/T. It is clearly seen that the lowcharge colloids are expected to freeze upon heating, although only for a narrow Z range. Figure 4b shows the calculated phase diagram plotted for a wider range of Z values. At high Z (high Cs), the colloids are expected to melt upon heating. Therefore, the results obtained by the present experiments are in qualitative agreement with the theoretical results. We discuss our experimental data by plotting them in the parameter plane reported by Robbins et al., which is defined by the reduced temperature kBT/U(a) and the coupling parameter λ=κa. Here a, which is defined as a=F-1/3, is the average distance between neighboring particles, where F is the number density of the particles. The two dashed curves in Figure 5 are obtained by fitting the results reported by Robbins et al. for liquid and crystal phases. We assumed that Z is constant with T. The circles and crosses denote the crystal and liquid states observed upon heating the sample from T = 5 to 45 °C, respectively. The inset shows a magnified view of the small-λ regime. The arrows next to the symbols indicate the directions of increasing temperature. At high T, κ is large and consequently λ is also large. kBT/ U(a) also increases with T because of the large increase in κ with T.
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The observed transition points lie around the theoretical phase boundaries, although they are not in good quantitative agreement except for PS #3. The observed difference between the experimental and theoretical boundaries may be due in part to the presence of trace amounts of ionic impurities, the effect of which will be discussed in Supporting Information B. It is worthwhile, however, to compare the slopes of the observed trajectories upon changing T with those of the tangents to the calculated boundaries. At small λ (low Cs), the former is smaller than the latter, whereas at large λ (high Cs), the latter has larger values than the former. This is in accordance with the observed trends in the freezing and melting transitions. Here we discuss whether factors other than ε would cause the thermally induced phase transitions. First, the thermal expansion of the aqueous medium should result in decreases in Cs and φ, which may result in freezing and melting transitions, respectively. However, upon increasing T from 5 to 45 °C, the decrease in these values is estimated to be approximately 1%, which is within the allowed experimental error range. The temperature dependence of Cs might also be caused by the dissolution of airborne carbon dioxide, which generates carbonic acid in water. In that case, the Cs values could change with T because of the temperature dependence of the solubility and the dissociation equilibrium of carbon dioxide. However, the crystallization phase diagram of the colloidal silica determined in air varied only slightly from that obtained under an argon atmosphere (Figure 4a). Therefore, the influence of carbon dioxide, if any, appears not to be significant. The decrease in Z with T (-1 and -6% for silica and SS-22 upon changing T from 5 to 45 °C, respectively) facilitates the decrease in Z upon heating, particularly for the PS colloids, although the freezing upon heating is not explainable in terms of this effect. The aforementioned quantitative discrepancy between the theoretical phase diagram and the experiments might be partially due to the temperature dependence of Z. In the present study, we have demonstrated that aqueous charged colloids undergo melting and freezing transitions upon heating. These behaviors can be explained qualitatively in terms of the fact that the permittivity ε of water decreases more rapidly with T than with 1/T. Temperature has a significant effect on the phase behavior of a variety of aqueous charged systems, including polyelectrolyte solutions and ionic vesicles. However, in many cases, the temperature dependence of other factors, such as miscibility and solvation number, is very strong, and hence the effect of the temperature dependence of ε becomes less pronounced. We believe that the findings of the present study would be useful for elucidating the phase behavior of various charged aqueous systems. Supporting Information Available: Experimental details for the determination of Z values and the calculation of the theoretical phase diagram. This material is available free of charge via the Internet at http://pubs.acs.org.
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