Thermosensitive Colloidal Crystals of Silica Spheres in the Presence

Department of Applied Chemistry, Gifu University, Gifu 501-1193, Japan, and Institute of. Applied Biochemistry, University of Tsukuba, Tsukuba 305-857...
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Langmuir 2002, 18, 6783-6788

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Thermosensitive Colloidal Crystals of Silica Spheres in the Presence of Gel Spheres of Poly(N-isopropyl acrylamide) Tsuneo Okubo,*,† Hiromi Hase,† Hiroshi Kimura,† and Etsuo Kokufuta‡ Department of Applied Chemistry, Gifu University, Gifu 501-1193, Japan, and Institute of Applied Biochemistry, University of Tsukuba, Tsukuba 305-8572, Japan Received April 3, 2002. In Final Form: June 7, 2002 Structure, crystal growth kinetics, and rigidity of thermosensitive colloidal crystals formed from mixtures of colloidal silica spheres (diameter, 103 nm) and gel spheres of poly(N-isopropylacrylamide) are studied mainly from reflection spectroscopy. The gel spheres change their hydrodynamic size transitionally at 35 °C from 72 nm (at 20 °C) to 28 nm (at 45 °C). The mixtures are deionized exhaustively with ion-exchange resins in aqueous suspensions. In the absence of gel spheres, intersphere spacings of the crystals, lobs, are quite insensitive to suspension temperatures ranging from 15 to 55 °C. In the presence of the gel spheres, on the other hand, the lobs value decreases transitionally at 35 °C when suspension temperature increases. The ζ-potential and the effective diameter of colloidal silica spheres determined by electrophoretic lightscattering measurements increase as the gel concentration increases. Addition of the gel spheres decreases the crystal growth rate and increases the rigidity of the mixtures. These results support strongly that the thermosensitive gel spheres adsorb weakly onto the surface of colloidal silica spheres.

Introduction Keen attention has been paid to colloidal crystals, that is, crystal-like distributions of colloidal particles in suspensions of aqueous and organic solvents. Generally speaking, most colloidal particles in an aqueous suspension get the negative charges on their surfaces by two mechanisms; one is the dissociation of ionizable groups, and the other is the preferential adsorption of ions from suspension. These ionic groups leave their counterions, and the excess charges accumulate near the surface forming an electrical double layer. When the suspension is exhaustively deionized with mixed beds of ion-exchange resins, the electrical double layers expand and the particles arrange regularly. In other words, an essential interaction for the colloidal crystallization is the interparticle electrostatic repulsion accompanied with the extended electrical double layers around the particles.1-18 Ise et al. has proposed the interparticle “attraction” as the important * Corresponding author. Phone: +81 58 293 2620. Fax: +81 58 293 2628. E-mail: [email protected]. † Gifu University. ‡ University of Tsukuba. (1) Luck, W.; Klier, M.; Wesslau, H. Ber. Bunsen-Ges. Phys. Chem. 1963, 67, 85. (2) Ottewill, R. H.; Shaw, J. N. Discuss. Faraday Soc. 1966, 42, 154. (3) Hiltner, P. A.; Krieger, I. M. J. Phys. Chem. 1969, 73, 2386. (4) Kose, A.; Ozaki, M.; Takano, K.; Kobayashi, Y.; Hachisu, S. J. Colloid Interface Sci. 1973, 44, 330. (5) Clark, N. A.; Hurd, A. J.; Ackerson, B. J. Nature 1979, 281, 57. (6) Pieranski, P. Contemp. Phys. 1983, 24, 25. (7) Vanderhoff, W.; van de Hul, H. J.; Tausk, R. J. M.; Overbeek, J. Th. G. Clean Surfaces: Their Preparation and Characterization for Interfacial Studies; Marcel Dekker: New York, 1970; p 15. (8) Williams, R.; Crandall, R. S.; Wojtowicz, P. J. Phys. Rev. Lett. 1976, 37, 348. (9) Mitaku, S.; Ohtsuki, T.; Enari, K.; Kishimoto, A.; Okano, K. Jpn. J. Appl. Phys. 1978, 17, 305. (10) Lindsay, H. M.; Chaikin, P. M. J. Chem. Phys. 1982, 76, 3774. (11) Ottewill, R. H. Ber. Bunsen-Ges. Phys. Chem. 1985, 89, 517. (12) Aastuen, D. J. W.; Clark, N. A.; Cotter, L. K.; Ackerson, B. J. Phys. Rev. Lett. 1986, 57, 1733. (13) Okubo, T. Acc. Chem. Res. 1988, 21, 281. (14) Lowen, H.; Palberg, T.; Simon, R. Phys. Rev. Lett. 1993, 70, 1557. (15) Stevens, M. J.; Falk, M. L.; Robbins, M. O. J. Chem. Phys. 1996, 104, 5209. (16) Pusey, P. N.; van Megen, W. Nature 1986, 320, 340.

interaction for colloidal crystallization for more than 10 years. However, quite recently, they seem to withdraw their idea in their own paper and supported “repulsion” including the Alder transition and Yukawa potential19 instead. Colloidal crystallization has also been reported for mixtures of colloidal spheres and neutral water-soluble polymers hitherto.20-23 The polymers used were poly(vinyl alcohol) (PVA), poly(ethylene glycol) (PEG), poly(vinyl pyrrolidone) (PVP), hydroxypropyl cellulose (HPC), and poly(acrylamide) (PAAm). The lattice spacing increased by the addition of PEG and PVA, while it decreased with PVP, HPC, and PAAm. The order was PEG > PVA > none > PVP ∼ HPC > PAAm for the same sphere concentration. This effect of neutral polymer was explained beautifully by the intersphere repulsion from the electrical double layer interaction, which is influenced by the adsorption of the polymer on the colloidal surface due to hydrophobic and/or dipole-dipole interactions. Several types of thermosensitive spheres including the core-shell type have been reported hitherto.24-27 Quite recently, thermosensitive colloidal crystals of N-isopropylacrylamide (NIPAAm) derivative polymer hydrogel have been prepared.28-30 We succeeded in preparing the (17) Russel, W. B.; Saville, D. A.; Schowalter, W. R. Colloidal Dispersions; Cambridge University Press: Cambridge, U.K., 1989. (18) Sood, A. K. Solid State Phys. 1991, 45, 2. (19) Shinohara, T.; Yoshiyama, T.; Sogami, I. S.; Konishi T.; Ise, N. Langmuir 2001, 17, 8010. (20) Okubo, T. Curr. Top. Colloid Interface Sci. 1997, 1, 169. (21) Okubo, T. J. Chem. Soc., Faraday Trans. 1 1987, 83, 2497. (22) Okubo, T. Colloid Polym. Sci. 1987, 265, 597. (23) Okubo, T. Polym. Bull. 1990, 23, 211. (24) Murray, M. J.; Snoedon, M. J. Adv. Colloid Interface Sci. 1995, 54, 73. (25) Pelton, R.; Wu, X.; McPhee, W.; Tam, K. C. In Colloidal Polymer Particles; Goodwin, J. W., Buscall, R., Eds.; Academic Press: San Diego, 1995; p 81. (26) Kawaguchi, H. In Biomedical Functions and Biotechnology of Natural and Artificial Polymers; Yalpani, M., Ed.; ATL Press: Shrewsbury, MA, 1996; p 157. (27) Kawaguchi, H. In Microbeads, Microcapsules and Liposomes; Arshady, R., Ed.; STN Books: London, 1998; p 233. (28) Pelton, R. Adv. Colloid Interface Sci. 2000, 85, 1. (29) Xia, Y.; Cates, B.; Yin, Y.; Lu, Y. Adv. Mater. 2000, 12, 693. (30) Xia, Y. Adv. Mater. 2001, 13, 369.

10.1021/la020315n CCC: $22.00 © 2002 American Chemical Society Published on Web 08/08/2002

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thermosensitive colloidal crystals simply by mixing colloidal silica spheres with NIPAAm gel spheres in the aqueous suspension state as described below in detail. Experimental Section Samples. Monodisperse colloidal silica spheres (CS-82, 103 nm in diameter) were a gift from Catalyst & Chemicals Ind. Co. (Tokyo). The stock suspension has been deionized with ionexchange resins (Bio-Rad, AG501-X8(D), 20-50 mesh, Richmond, CA) more than 8 years. Poly(N-isopropylacrylamide) gel spheres were prepared in the same manner as described in the previous papers.31,32 The gel concentrations, w, ranged from 0 to 0.02 g/mL. Water used for the purification and for suspension preparation was purified by a Milli-Q reagent grade system (Milli-RO5 plus and Milli-Q plus, Millipore Co., Bedford, MA). The sample suspensions were prepared in the cell with the ion-exchange resins 1 week before the measurements. Dynamic Light-Scattering (DLS) and Electrophoretic Light-Scattering (ELS) Measurements. DLS measurements were made on a DLS spectrophotometer (DLS-7000, Otsuka Electronics, Hirakata, Osaka) at 25 ( 0.02 °C in a cylindrical vat containing silicone oil. A 5 mL sample suspension was prepared in a Pyrex tube cell (12 mm outside diameter and 130 mm long). Data analysis was made with the cumulant analyses. ζ-Potential was measured on an electrophoretic light-scattering spectrophotometer (ELS-6000, Otsuka Electronics). Reflection Spectroscopy. The reflection spectra of the suspension at various temperatures, at an incident angle of 90° through the quartz glass of the bath, the water in the bath, and the quartz glass of the optical cell, were recorded on a multichannel photo detector (MCPD-7000G3, Otsuka Electronics) connected to a Y-type optical fiber cable. A test tube (8 mL, 10 mm in inner diameter and 100 mm high; NN-13, Maruemu Co., Osaka) was set in the water bath of quartz glass. The temperature of the water was controlled from 15 to 55 °C by the circulating water from a thermostat (RTE-211, Neslab Instruments, Newington). Crystal growth rate was measured from the growth in the reflection peaks with time after the suspensions were mixed and left to stand still. The rigidity of the crystals was determined from the reflection spectroscopy in the sedimentation equilibrium. The observation cell was made from a Pyrex glass tube (10 mm in inner diameter and 100 mm high), which was set in a test tube support. A sample suspension of 6 cm3 volume was introduced into the cell. Circa 0.5 cm3 of a mixed bed of ion-exchange resins [Bio-Rad, AG501-X8(D)] was added. Then the cells were left to stand. The reflection spectra at various heights at an incident angle of 90° were recorded for 2 months on the multichannel photodetector.

Figure 1. Change in the gel diameter as a function of temperature: O, raising temperature; ×, lowering temperature.

Figure 2. Reflection spectra of the mixtures of CS-82 and gel spheres. φ ) 0.032. (a) w ) 0 g/mL, (b) w ) 0.008 g/mL, (c) w ) 0.017 g/mL, (d) w ) 0.020 g/mL; solid line, T ) 20 °C; dashed line, T ) 45 °C.

Results and Discussion Temperature Dependence of Gel Sphere Size. The size of NIPAAm gel spheres was evaluated from the DLS measurements between 15 and 55 °C. Figure 1 shows the hydrodynamic diameter, dh, of NIPAAm gel spheres as a function of suspension temperature, T. The diameter decreased transitionally at ca. 35 °C when the temperature was raised. The diameter decreased from 72 nm at 20 °C to 28 nm at 50 °C, which corresponds to a volume change by a factor of 17. The size changed reversibly when the temperature increased and then decreased. Reflection Spectroscopy of the Suspension Mixtures of CS-82 and NIPAAm Gel Spheres. Typical examples of the reflection spectra of CS-82 and NIPAAm gel mixtures at 20 and 45 °C are shown in Figure 2. Interestingly, the peaks at 45 °C shifted significantly toward shorter wavelengths and became broad when the (31) Hu, Z.; Lu, X.; Gao, J. Adv. Mater. 2001, 13, 1708. (32) Ito, S.; Ogawa, K.; Suzuki, H.; Wang, B.; Yoshida, R.; Kokufuta, E. Langmuir 1999, 15, 4289.

concentration of gel spheres increased. On the other hand, the peaks at 20 °C shifted to longer wavelengths, though the broadening of the peak occurred at low concentrations compared with the experiments at 45 °C. These changes in the peak wavelengths indicate clearly that the expansion and contraction of the crystal lattice occur at 20 and 45 °C, respectively, by the addition of the gel spheres. The lattice spacing, that is, the nearest-neighbor intersphere distance, in face-centered cubic (fcc) and bodycentered cubic (bcc) lattices (lobs,f and lobs,b) is given by eq 1.

lobs,f ) lobs,b ) 0.6124(λp/ns)

(1)

where λp denotes the wavelength of the primary reflection peak and ns indicates the refractive index of the sample suspension. In this work, ns was taken as 1.333 at 25 °C which is the value of water, since the measurements were made at relatively low sphere concentrations. From our experiences, the lattice structure of the colloidal crystals

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Figure 3. Change in the intersphere spacing of the mixtures of CS-82 and gel spheres as a function of temperature. φ ) 0.016. O, w ) 0 g/mL; ×, w ) 0.0003 g/mL; 4, w ) 0.003 g/mL; 0, w ) 0.007 g/mL; b, w ) 0.010 g/mL; 2, w ) 0.020 g/mL.

Figure 4. Change in the intersphere spacing of the mixtures of CS-82 and gel spheres as a function of temperature. φ ) 0.032. O, w ) 0 g/mL; ×, w ) 0.004 g/mL; 4, w ) 0.008 g/mL; 0, w ) 0.010 g/mL; b, w ) 0.017 g/mL; 2, w ) 0.020 g/mL.

of silica spheres in the absence of the gel spheres is assumed to be fcc, since the sphere concentration 0.032 is high enough for the formation of fcc lattices. Much work has reported that the fcc lattices are more stable than bcc, though the critical concentration of melting13,19 is quite sensitive to the degree of deionization of the suspension. The lattice spacing calculated for a simple cubic lattice, l0, is given by eq 2.

l0 ) 0.904d0φ-1/3

(2)

where d0 and φ are the diameter (in nm) and concentration (in volume fraction) of the colloidal silica spheres. Figure 3 shows the nearest-neighbor intersphere distances, lobs, as a function of suspension temperature at φ ) 0.016. In the absence of gel spheres, lobs increased very slightly from 387 to 389 nm as the temperature was raised, values which are close to the calculated value of 370 nm. In the presence of gel spheres at concentrations (w) higher than 0.003 g/mL, the lobs values also decreased transitionally at ca. 35 °C, when the suspension temperature was raised. When the concentration of the gel spheres (φ) increased up to 0.02 g/mL, the reflection peak disappeared at temperatures higher than 35 °C as is shown by the solid triangles in Figure 3. These thermosensitive responses in the lobs values were much clear when the sphere concentration increased twice, φ ) 0.032 (see Figure 4). The lobs and l0 values at w ) 0 g/mL were 303 and 293 nm, respectively. The agreement

Figure 5. Plots of ∆lobs/lobs against w for the CS-82 and gel spheres at 25 °C: O, φ ) 0.016; ×, φ ) 0.032.

Figure 6. ζ-Potential and effective diameter of the mixtures of CS-82 and gel spheres as a function of gel sphere concentration at 25 °C. φ ) 3.2 × 10-4.

was satisfactory. When the concentrations of the gel spheres were higher than 0.008 g/mL, the transitional change in lobs was observed. The differences between the lobs values at temperatures lower than and higher than the critical temperature (35 °C), ∆lobs, are shown in Figure 5. Clearly, the ratio of ∆lobs against lobs decreased substantially as w increased. Mechanism of the Thermosensitive Expansion and Contraction in the Crystal Lattices. The reversible expansion and contraction in the lattice spacing with temperature supports the idea that the weak adsorption of gel spheres occurs with the neighboring colloidal silica spheres. To ascertain this idea, electrophoretic lightscattering measurements were made for the mixtures of CS-82 and gel spheres. The results are shown in Figure 6. Clearly, the ζ-potential of the silica spheres increased from -50 mV to a saturated value, ca. -20 mV, as the gel concentration increased. This observation is consistent with the weak adsorption between the gel and silica spheres, since the gel sphere layer coated on the silica surfaces must result in the increase in the ζ-potential by the shielding of the charges of silica spheres. The effective diameter of silica spheres, deff, estimated from the electrophoretic light-scattering measurements increased significantly from 115 to 200 nm when the gel concentration increased, which also supports weak adsorption of the gels on the silica surfaces. The observed deff value, ca. 115 nm, without gels was larger than the real diameter of silica spheres, 103 nm, by 10%. This may be due to the contribution of the extended electrical double layers in the absence of the foreign salt and also to the difference in the method of measurement.

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Figure 8. Change in the intensity and the peak wavelength of the reflection spectra in the course of crystallization for the mixtures of CS-82 and gel spheres at 45 °C. φ ) 0.032. w ) 0.004 g/mL.

Figure 7. Schematic representation of colloidal crystals of the mixtures of CS-82 and gel spheres: (a) without gel spheres, (b) with gel spheres at low temperatures, and (c) with gel spheres at high temperatures.

A schematic picture of the thermosensitive colloidal crystals in this work is shown in Figure 7. In the absence of gel spheres (see Figure 7a), the crystal structure of silica spheres forms by the intersphere repulsion interactions intermediated by the electrical double layers surrounding the silica spheres.13-18 In the presence of gel spheres, the gel spheres locate between the neighboring silica spheres and bind weakly with the surfaces. The gel spheres are quite soft and vague in the outer boundary as is shown in Figure 7b,c. Thus, the expansion and/or contraction of the gel spheres with temperature results in the expansion and/or contraction in the lattice spacing of the crystal structure of silica spheres. Kinetics Analyses of the Thermosensitive Colloidal Crystallization. The size of the colloidal single crystals from the homogeneous nucleation, L, is estimated from the peak intensity (I) in the reflection spectra,33,34

I ∝ NcrystL3 ∝ L3

(3)

where Ncryst is the number of single crystals in the reflecting volume, which is directly proportional to the number concentration of crystals in the final stages of the crystallization process, being equal to the total number of nuclei formed in the whole course of crystallization. Figure 8 shows the typical traces of the peak intensity and the peak wavelength for the mixture of CS-82 and NIPAAm gel spheres in the course of crystallization. The intensity increased as time increased and saturated to a constant value. The wavelength, on the other hand, decreased with time and reached a certain value. These results support the idea that the observed changes in the peak intensity and the peak wavelength correspond to the secondary crystallization step, where the metastable and loose crystals formed in the first crystallization step become stable and compact ones.34 (33) Dhont, J. K. G.; Smits, C.; Lekkerkerker, H. N. W. J. Colloid Interface Sci. 1992, 152, 386. (34) Okubo, T.; Ishiki, H. J. Colloid Interface Sci. 2000, 228, 151.

Figure 9. Apparent crystallization rate for the mixtures of CS-82 and gel spheres as a function of gel sphere concentration: (a) φ ) 0.016; (b) φ ) 0.032. O, 25 °C; ×, 35 °C; 4, 45 °C; 0, 55 °C.

The apparent growth rates, k, were estimated in Figure 9 from the initial slope in the peak intensity versus time curves. k decreased as w increased irrespective of the temperature. This supports the idea that the bulky gel spheres disturb the secondary crystallization process mainly by the distortion of the crystal structure formed in the primary step. Interestingly, k without the gel decreased as the suspension temperature decreased whereas k increased with the gel spheres as is clear in the figure. Rigidity of the Thermosensitive Colloidal Crystals. Figure 10 shows the time dependencies in the reflection peak wavelength without and with NIPAAm gel spheres. Without gel, the peak wavelength reached a constant value within 10 days after the sample was set in the cell. On the other hand, with gel spheres (at w ) 0.008 g/mL, for example), the peak wavelengths changed very slowly and the sedimentation equilibrium was achieved after 2 months or even more after the suspensions were set.

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Langmuir, Vol. 18, No. 18, 2002 6787 Table 1. Several Parameters for the Thermosensitive Colloidal Crystals at 25 °C. w (g/mL)

Figure 10. Change in the reflection peak wavelength for the mixtures of CS-82 and gel spheres in the course of sedimentation equilibrium at 25 °C. φ ) 0.032. (a) w ) 0 g/mL; (b) w ) 0.008 g/mL. Height: O, 1.35 cm; ×, 2.15 cm; 4, 2.65 cm; 0, 3.65 cm; b, 5.65 cm; 2, 6.35 cm; 9, 6.85 cm.

Np (1/cm3)

Ng (1/cm3)

Np + Ng (1/cm3) G (Pa)

g

0 0.0003 0.0010 0.0020 0.0030 0.0050 0.0070 0.0100 0.0200

φ ) 0.016 2.80 × 1013 2.80 × 1013 0 13 2.80 × 10 0.15 × 1013 2.95 × 1013 2.80 × 1013 0.51 × 1013 3.31 × 1013 2.80 × 1013 1.03 × 1013 3.83 × 1013 2.80 × 1013 1.54 × 1013 4.34 × 1013 2.80 × 1013 2.56 × 1013 5.36 × 1013 2.80 × 1013 3.59 × 1013 6.39 × 1013 2.80 × 1013 5.13 × 1013 7.93 × 1013 2.80 × 1013 10.3 × 1013 13.1 × 1013

190 177 135 141 145 171 223 554 1830

0.025 0.026 0.032 0.033 0.034 0.036 0.034 0.024 0.017

0 0.0025 0.0042 0.0083 0.0100 0.0170

5.59 × 1013 5.59 × 1013 5.59 × 1013 5.59 × 1013 5.59 × 1013 5.59 × 1013

φ ) 0.032 0 5.59 × 1013 1.28 × 1013 6.87 × 1013 2.15 × 1013 7.74 × 1013 4.26 × 1013 9.85 × 1013 5.13 × 1013 10.7 × 1013 8.72 × 1013 14.3 × 1013

264 254 286 353 407 1970

0.030 0.033 0.033 0.034 0.033 0.017

of the gel spheres was added, G increased drastically. By the addition of gel spheres, the elastic modulus must increase by the increased contribution from the rigidity of the gel spheres themselves. The latter is, of course, much harder than the former when the gel sphere concentration increases. Generally speaking, the order of magnitude of G of the colloidal crystal is written in terms of the magnitude of the thermal fluctuation, δ, of a sphere as20,36

G ∼ f/l ∼ (kBT/〈δ2〉)/l

(5)

Here, f and l are the force constant between colloidal spheres and the nearest-neighbor intersphere distance in the colloidal crystals, δ is the thermal fluctuation of a sphere in the effective potential valley, kB is the Boltzmann constant, and T is the suspension temperature. Introducing a nondimensional parameter g for 〈δ2〉1/2/l, the modulus is obtained as a linear function of the number density of spheres, N,

G ∼ NkBT/g2

Figure 11. Plots of the reflection peak wavelength against height for the mixtures of CS-82 and gel spheres in the sedimentation equilibrium at 25 °C. φ ) 0.032. O, w ) 0 g/mL; ×, w ) 0.008 g/mL; 4, w ) 0.017 g/mL.

In the sedimentation equilibrium, eq 4 holds.35

λp - λp,m ) (Feffg0λ p,mφm/G)(h - hm)

(4)

Here λp,m and φm indicate the lattice spacing and the sphere concentration at the midplane of the cell, hm, respectively. φm is, therefore, equal to the initial concentration of silica spheres. Feff is the effective density given by the specific gravity of the spheres minus that of the solvent, and g0 is the gravitational constant. h is the height from the bottom of the cell. G is Young’s elastic modulus for the colloidal crystals and is obtained from the slopes of λp versus h as is shown in Figure 11, for example. The linearity between λp and h was satisfactory. Table 1 shows the elastic modulus, G, thus obtained. At the gel sphere concentrations lower than 0.01 g/mL, G values kept constant around 250 Pa. When a large amount (35) Crandall, R. S.; Williams, R. Science 1997, 198, 293.

(6)

When g ) 1, eq 6 gives the elastic modulus of an ideal liquid having the same sphere concentration. Lindemann’s law of crystal melting tells us that g < 0.1 holds for a stable crystal. The g values cited in Table 1 were between 0.017 and 0.036 and increased as the gel concentration increased and then decreased passing the maximum. These results support the fact that the addition of the gel spheres distorts the crystal structure of silica spheres and even transforms the crystals into the amorphous-solid-like structure (not liquidlike). The number densities (Np) of silica spheres and gel spheres (Ng) and the sum of them (Np + Ng) are also compiled in Table 1. The drastic increase in G at w ) 0.02 and 0.017 for φ ) 0.016 and 0.032, respectively, will support the formation of the network of gel and silica spheres. Conclusion In this work, thermosensitive colloidal crystals have been prepared, for the first time, simply by the mixing of colloidal crystals and NIPAAm gel spheres in an aqueous suspension state. (36) Mitaku, S.; Ohtsuki, T.; Kishimoto, A.; Okano, K. Biophys. Chem. 1980, 11, 411.

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Acknowledgment. Financial support from the Ministry of Education, Science, Sports and Culture, Japan is gratefully acknowledged for Grants-in-Aid for Scientific Research on Priority Area (A) (11167241) and for Scientific Research (B) (11450367). The silica sample was a gift from

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Catalyst & Chemicals Ind. Co. (Tokyo). T.O. thanks deeply the late Professor Emeritus Sei Hachisu for his encouragement on our work on colloidal crystals. LA020315N