Giant Colloidal Single Crystals of Polystyrene and Silica Spheres in

in diameter (d) are studied mainly with close-up color photographs in the diluted and ... Two kinds of single crystals, (1) block-like crystals grown ...
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Langmuir 1994,10, 1695-1702

1695

Giant Colloidal Single Crystals of Polystyrene and Silica Spheres in Deionized Suspension T . Okubo Department of Polymer Chemistry, Kyoto University, Kyoto 606-01, Japan Received August 8, 1993. I n Final Form: January 3, 1994@ Shape and size of colloidal single crystals of polystyrene and silica spheres ranging from 81 to 212 nm in diameter ( d ) are studied mainly with close-up color photographs in the diluted and exhaustively deionized suspensions with ion-exchange resins. Two kinds of single crystals, (1)block-like crystals grown up from the homogeneous nucleation mechanism in the bulk phase far from the cell wall and (2) pillar-like ones from the heterogeneous nucleation along the cell wall, are observed clearly. Size of the colloidal single crystals is very large (3-8 mm) at the sphere concentration slightly higher than the critical concentration of melting (&). &Values are around 0.0002 in volume fraction irrespective of sphere diameter ranging from 90 to 210 nm, and much higher for the spheres smaller than 90 nm, e.g., 0.0036 and 0.0014 for colloidal silica (CS-61,d = 81 nm) and polystyrene spheres (DlC25, 85 nm), respectively. Crystal size decreases very sharply as sphere concentration increases, since the number of nuclei increases substantially with sphere concentration. Colloidal suspensions display extraordinary structures in particle distributions, such as gas-like, liquid-like, and crystal-like structures, especially in deionized suspension~.’-’~Suspensions showing crystal-like structures are named as colloidal crystals and are ideal for model studies of metals and protein crystals, since the colloidal structures are able to be analyzed much conveniently with optical techniques and even with the naked eye. Furthermore, “phase transition” phenomena such as crystallization and melting occur sharply. A study of the colloidal crystals is also helpful in understanding the fundamental properties of states of substances and electrostatic interactions of macroionic systems. Two essentially important factors causing the colloidal crystals are an electrostatic intersphere repulsion and an expanded electrical double layers around the spheres in the deionized state. Many researchers have studied colloidal crystals both experimentally and theoretically. Structural investigation has been made from transmission and reflection spectroscopy, light-, X-ray-, and neutron-scattering techniques, and microscopic observation. Keen attention has been paid also to the structural change with an external field, such as ac and dc electric fields. Furthermore, the phase diagram and rheological and elastic properties have been studied. The iridescent colors and single crystals are most

* Abstract published in Advance ACS Abstracts, May 15, 1994. (1)Luck, W.; Klier, M.; Wesslau, H. Ber. Bunsenges. Phys. Chem.

1963, 67, 15; 84.

(2) Vanderhoff, W.; van de Hul, H. J.; Tausk, R. J. M.; Overbeek, J. Th. G. Clean Surfaces: Their Preparation and Characterization for Interfacial Studies; Goldfinger, G., Ed.; Dekker: New York, 1970. (3) Hiltner, P. A,; Papir, Y. S.; Krieger, I. M. J.Phys. Chem. 1971, 75, 1881. (4) Koae, A,; Ozaki, M.; Takano, K.; Kobayashi, Y.; Hachisu, S. J. Colloid Interface Sci. 1973, 44, 330. (5) Crandall, R. S.; Williams, R. Science 1977, 198, 293. (6)Mitaku, S.;Otsuki, T.; Okano, K. Jpn. J.Appl. Phys. 1978,17,305. (7) Clark, N. A,; Hurd, A. J.; Ackerson, B. J. Nature 1979, 281, 57. (8) Lindsay, H. M.;Chaikin, P. M. J. Chem. Phys. 1982, 76, 3774. (9) Tomita, M.; Takano, K.; van de Ven, T. G. M. J. Colloid Interface Sci. 1983, 92, 367. (10) Pieranski, P. Contemp. Phys. 1983, 24, 25. (11)Pusey, P.N.; van Megen, W. Nature 1986, 320, 340. (12) Okubo, T. Acc. Chem. Res. 1988,21, 281. (13) Ottewill, R. H. Langmuir 1989,5, 4. (14) Russel, W. B.; Saville, D. A.; Schowalter, W. R. Colloidal Dispersions; Cambridge University Press: Cambridge, 1989. (15) Okubo, T.Prog. Polym. Sci. 1993, 18, 481. (16) Okubo, T. Naturwissenschaften 1992, 79, 317.

0743-7463/94/2410-1695$04.50/0

beautiful and attractive to the naked eye. Colloidal crystals are surrounded by grain boundaries and are quite similar to metals. The iridescent colors are ascribed to the Bragg diffraction of visible light by the lattice planes of the colloidal crystals. Lattice spacing of the colloidal crystals is a factor of several thousands larger than that of metals and is in the range of light wavelengths. Very little work has been reported on the morphology (shape and size) of the colloidal single crystals, because the size of the crystals was very small,in the order of severalhundred micrometers even for the largest ones. The main reason for the scarcity of the work is the fact that it has been difficult to obtain completely deionized suspensions, which contain the charges from the particles, their counterions, and H+and OH- from the dissociation of water. The deionized suspension is believed to contain no contaminant ions from air, glass, etc. In order to obtain the completely deionized suspension, highly effective mixed beds of cation- and anion-exchange resins such as Bio-Rad resins have to coexist in suspension for a long time, more than 3 weeks. From our experiences, the deionization process of suspension with resins is unexpectedly slow. This may be due to the fact that the deionization reaction takes place between solid (colloidal particles)-solid (resins) phases via liquid medium. It is interesting to note that the colloidalcrystallization takes place at the very low particle concentrations for the deionized suspension. Deionized suspensions are able to be obtained in nonaqueous media, and colloidal crystals can be formed-ll However, critical concentrations of melting are high compared with those in aqueous systems, and single crystals formed in nonaqueous media are very small in most cases. Quite recently, we observed very large single crystals, 2-8 mm in size in a test tube of 13 mm in outside diameter.16J7 The diluted suspension (ca. 0.0002in volume fraction) was deionized with Bio-Rad ion-exchange resins [type AG501-X8(D), 20-50 mesh] more than 3 weeks. In this report, the shape and size of the colloidal single crystals are studied as systematically as possible. Fifteen kinds of monodispersed colloidal spheres of polystyrene and silica having different sizes and charge densities have been used in this work. (17) Okubo, T. Colloid Polym. Sci. 1993, 271, 190.

0 1994 American Chemical Society

1696 Langmuir, Vol. 10, No. 6, 1994

Okubo

Table 1. Characteristics of Colloidal Spheres Used sphere DlC25 DlC27 DlB76 DlP30 NlOO . DlK88 DlB72 VNlOOl DlB28 CS-61 CS-81 cs-91 cs-121

cs-22

CS-161

d (nm)

8 (nm)

b/d

85 91 109 109 120 137 173 192 212 81.2 103 110 136 178 184

6 6 3 27.8 7 16 7 6 3 11.5 13.2 4.5 10.9 9 18.6

0.07 0.066 0.028 0.26 0.06 0.12 0.04 0.03 0.014 0.14 0.13 0.041 0.08 0.05 0.10

charge densitv (rrC/cm2) strong acid weak acid 1.5 1.0 1.4 2.0 2.1 0.71 0.32 0.62 1.2 6.8 0.60 0.58 1.0 0.50 0.36 1.29 4.90 0.60 0.38 0.48 0.40 44.0 0.52 0.47

Table 2. Change in Critical Concentration of Melting in Deionized Suspension of Polystyrene Spheres

0.001

I

I

I

100

150

200

A

0.00:

a"

0.002

0 0.001

dh

sphere DlC25 DlC27 DlB76 DlB72

A" 0.005 0.002 0.005 0.025

Bb 0.002 0.001 0.001 0.0015

CC 0.0014 0.0003 0.00016 0.00038

(A) Without resins. (B) With resins for 1 hour. With resins for more than 3 weeks (this work). a

0

Figure 1. Plots of

d (nm) against d. 0: polystyrene spheres, A:

silica spheres.

Table 3. Change in in t h e Course of Deionization with Resins Coexisting with Spheres sphere DlC25 DlC27 cs-91 cs-22

A" 0.0023 0.001 0.0011 0.0015

Bb 0.0015 0.0004 0.00096 0.0008

CC 0.0014 0.0003 0.0004 0.00028

(A) Five hours after suspension preparation. (B) Three days. (C) More than 3 weeks.

Experimental Section Materials. DlC25, DlC27, DlB76, DlP30, DlK88, DlB72, and DlB28 were polystyrene spheres purchased from Dow Chemical Co. NlOO polystyrene spheres were a product of Sekisui Chemical Co. (Osaka). VNlOOl was monodisperse polystyrene spheres kindly donated by Nippon Zeon Co. (Tokyo). Colloidal silica spheres of CS-61, CS-81, CS-91, CS-121, and CS-161 were gifts from Catalyst & Chemicals Ind. Co. (Tokyo). CS-22 was the silica spheres prepared by us previously.ls Diameter ( d ) , standard deviation (6) from the mean diameter, and polydispersity index (bld) are listed in Table 1. These values were determined from an electron microscope. The charge densities of the spheres were determined by conductometric titration with a Wayne-Kerr autobalance precision bridge, model B331, mark I1 (Bogner Regis, Sussex), or a Horiba conductivity meter, model DS-14 (Kyoto). Strongly acidic and weakly acidic groups coexisted. All these spheres were carefully purified several times using an ultrafiltration cell (model 202, membrane: Diaflo-XM300, Amicon Co.). Then 7 mL of the samples were treated on ca. 1mL of a mixed bed of cation- and anion-exchange resins [Bio-Rad, AG501-X8(D), 2C-50 mesh] for a t least 1 month. Amount of resins added was always much in excess compared with the ionic impurities in suspension. Absorption of the colloidal particles on the resins was safely neglected by the repeated mixing of the suspension. Water used for the purification and for suspension preparation was deionized by using cation- and anion-exchange resins [PuricR, type G10, Organo Co. (Tokyo)] and purified further by a Milli-Q reagent grade system (Millipore Co., Bedford, MA). Colloidal suspension was prepared in test tubes of type A (18)Okubo, T. Ber. Bunsenges. Phys. Chem. 1992, 96,61.

0

1

2

3

0, (pm) Figure 2. Comparison of den and D,. 0:polystyrene spheres, A: silica spheres.

(disposable culture tube, borosilicate glass, Corning Glass Works, Corning, NY, 11 and 13 mm, inside and outside diameters) shielded tightly with Parafilm (American Can Co., Greenwich, CT). Test tubes of type B were 13 and 15 mm of inside and outside diameters and with stoppers. T h e sample suspensions were treated with a small amount of Bio-Rad resins more than 3 weeks in the cell with up-and-down mixing several times a day. Close-Up P h o t o g r a p h i n g a n d Video Films. Photographing of colloidal crystals in a test tube was done with a Canon EOSlO camera, macro-lens (EF50 mm, f = 2.5) and life-size converter EF. Velvia film (Fujichrome, RVP135, IS0 = 50) was used for color transparencies. Close-up video films were taken with a video camera recorder (CCD-VSOO, Sony). Color photographs were reproduced from the video films with a color printer (NVMP1, Panasonic). The light source was a pocket-type flashlight (BF-775, Xenon 4, National).

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Langmuir, Vol. 10, No. 6, 1994 1697

Figure 3. Close-up pictures of DlC25 suspension with resins. Type A cells were used. 4 = 0.00234, 3 weeks after suspension preparation. Pictures were taken 3 hours after up-and-down mixing. Exposure time = 1 s, iris = 22.

Results and Discussion Preparation of the Completely Deionized Suspension of Colloidal Spheres, Quite recently, we have reported that very large single crystals of colloidal spheres are observed for the exhaustively deionized and diluted suspensions.16 Table 2 compiles the critical concentration of melting (&) for aqueous suspensions of polystyrene spheres,which have been deionizedwith the Bio-Rad resins more than 3 weeks (data C). A and B are our previous data of & for the suspensions treated in the observation cells without resinslg and with resins shortly for 1hour,2o respectively. Clearly, the &-values decreased substantially, one by a factor of 65, when experiments A and C for DlB72 sample are compared,for example. This finding is rather surprising because the concentrations of the diffusiblesimple ions are not so different from each other, ranging from to 10-6 mol/dm3. Table 3 also shows that it takes more than 3 weeks before the colloidal suspensions are deionized completely. Specific conductivities of the completely deionized suspensions, which have coexisted with Bio-Rad resins more than 3 weeks, were always smaller than 0.1 pS. The measurements have been made with a cell of 1.3 cm-l in its cell constant and the observed values scattered rather significantly for each samples. In some cases the specific conductivities of the exhaustively deionized suspensions were similar to or even smaller than that of the fresh and deionized water used for suspension preparation. Thus, it is concluded that the deionization reaction is very slow unexpectedly, and the most reliable data of $c in the completezy deionized suspensions are obtained after the resin treatment more than 3 weeks. This author believes that the limit of the completeness in the deionization process was reached already in this work and our attain(19) Okubo, T. J. Chem. SOC.Faraday Trans. 1990,86,2871. (20) Okubo, T. J. Chem. Phys. 1991,95,3690.

Figure 4. Close-up pictures of DlC27 suspension with resins. Type A cells were used three weeks after suspensionpreparation. From the left, = 0.000359, 0.000419,0.000479, and 0.000539. Pictureswere taken 30 min after up-and-downmixing. Exposure = 1 s, iris = 27. Length of the bar is 6 mm.

ment of the completeness will not be overcome for a long time in future. We note further that the melting temperature also shifted substantially toward very high values as the deionization proceeded.21 It should be mentioned further that the ionic character of colloidal spheres will be clarified nicely by the fingerprinting technique, which has been developed by Rowell et al.22923However, this method is not applied so easily for our completely deionized (21) Okubo, T. Colloid Polym. Sci. 1993,271, 190. (22) Marlow, B. J.; Rowell, R. L. Langmuir 1991, 7,2970.

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1698 Langmuir, Vol. 10, No. 6,1994

Figure 5. Close-uppictures of DlP30 suspensions. Type A cells were used three weeks after suspension preparation. From the left, = 0.000551, 0.000771, and 0.000881. Pictures were taken after 1 h, 30 min, and 20 min after uD-and-down mixing, respectively. Exposure = 2 s, iris = 22. @

suspensionsystem,since the conductivityof the suspension is quite low. Figure 1shows the most reliable values of 9,obtained in this work for the completely deionized suspensions of monodisperse polystyrene spheres and colloidal silica spheres ranging from 81 to 212 nm in diameter. It is interesting to note that the &-values locate around 0.0002 irrespective of the sphere diameter in the range of 100 to 200 nm. Sharp increase in $, for the spheres smaller than 100 nm is ascribed to the enhanced thermal movement of the spheres and the partial instability of the electrical double layers around the small spheres. These circumstances will be due to the fact that the colloidal spheres are not definitely large enough compared with hydronium ions which form the electrical double layers. Importance of the Expanded Electrical Double Layers in the Formation of Colloidal Crystals. Ionic groups on the colloidal surfaces leave their counterions in the suspension, and these excess charges accumulate near the surface forming an electrical double layer. The double layer consists of two regions, an inner region composed of adsorbed counterions (the Stern layer) and a diffuse region containingthe remainder of the excess counterions (GouyChapman layer). The counterions in the diffuse region are distributed according to a balance between their thermal motion and the forces of electrical attraction with the colloidal spheres. The thickness of the diffuse double (23) Rowell,R. L.; Shiau, S. J.; Marlow,B. J. Particle Size Distribution 11. Assessment and Characterization; Provder, T., Ed.; ACS Symposium Series 472, American Chemical Society: Washington, DC, 1991;Chapter

I Figure 6. Close-up pictures of DlK88 and DlB72 suspensions with resins. Type A cells were used three weeks after suspension

preparation. Left picture: DlK88,@= 0.000529. Right: DlB72,

4 = 0.000509.

layer is approximated by the Debye-screening length, D1.

D,= ( 4 ~ e ~ n / ~ k , T ) - ' / ~ where e is the electronic charge, E is the dielectric constant of the solvent, kg is the Boltzmann constant, and n is the concentrationof free-state cationsand anions in suspension and given by n = n, + n, + no,where n, is the concentration (number of ions per cm3) of diffusible counterions, n, is the concentration of foreign salt, sodium chloride, for example, and no is the concentration of both H+and OHfrom the dissociation of water. In order to estimate n,,

Colloidal Single Crystals of Polystyrene and Silica Spheres

Langmuir, Vol. 10, No. 6,1994 1699

Figure 7. Close-up pictures of CS-61 suspensions with resins. Type A cells were used 17 days after suspension preparation. 4 = 0.0044. Width of the pictures is 13 mm, i.e., outer diameter of the test tube. Pictures were taken, from the left, 140 min, 5 h, and 20 h after up-and-down mixing, respectively. Exposure = 2 s, iris = 22.

the fraction of free-state counterions (p) must be known, since the counterion binding is important for the colloidal spheres like linear-type macroions. Note that the maximum value of D1 observed hitherto was ca. 1pm in water. The similar value of D1,i.e., 1.2 pm,is also estimated from eq 1by taking no = 2 X (mol/dm3) X N A X ~m-~, where N Ais Avogadro’s number. It should be mentioned here that 6-values are very small for typical colloidal particles,2,2P26and the n-values calculated using the stoichiometric charge number (2) on a colloidal surface is always overestimated. We must use the effective charge number, @Zinstead of 2. According to the effective hard-sphere m0de1,~733which is a simple but very convenient assumption for the deionized colloidal suspension, crystal-like ordering is formed when the effective diameter (deff)of the spheres containing Debye-screeninglength is close to or larger than the intersphere distance (D),i.e., deff [diameter (d) + 2 X 011 > D. Figure 2 shows comparison of the deff values estimated using eq 1and the mean intersphere distance a t the critical concentration of melting (&). The agreement between deffandD,is excellent,though the deviation cannot be neglected when Dc is larger than 2 pm. This agreement supports the validity of the effective hardsphere model. Systematic comparison of deffand D values has supported the validity of the effective hard-sphere (24) Alexander, S.; Chaikin, P. M.; Grant, P.; Mordes, G. J.; Pincus, P.; Hone, D. J. Chem. Phys. 1984,80,5776. (25) Okubo, T. Ber. Bunsenges. Phys. Chem. 1987,91, 1064. (26) Okubo, T. J. Colloid Interface Sci. 1988,125, 380. (27) Baker, J. A.; Henderson, D. J. Chem. Phys. 1967,47, 2856. (28) Wadachi, M.; Toda, M. J. Phys. SOC.Jpn. 1972,32, 1147. (29) Hachisu, S.; Kobayashi, Y.; Kose,A. J.Colloid InterfaceSci. 1973, 42, 342.

(30) Brenner, S. L. J. Phys. Chem. 1976,80, 1473. (31) Takano, K.; Hachisu, S. J. Chem. Phys. 1977, 67, 2604. (32) Barnes, C. J.; Chan, D. Y.; Everett, D. H.; Yates, D. E. J. Chem. SOC.Faraday Trans. 2 1978, 74,136. (33) Voeglli, L. P.; Zukoski, IV, C. F. J. Colloid Interface Sci. 1991, 141, 79.

Figure 8. A close-up picture of CS-81 suspension with resins. Type A cells were used 11 days after suspension preparation. 4 = 0.00144. Picture was taken 10 h after up-and-down mixing.

Exposure = 2 s, iris = 22.

model strongly.12J5 The Debye-screeninglength is, therefore, essentially the important factor for the formation of colloidal crystals, especially in deionized suspension.

Okubo

1700 Langmuir, Vol. 10,No.6,1994 I

Figure 9. Examples of the colloidal single crystals observed for CS-81suspension with resins. Type A cells were used. = 0.00144. Pictureswere taken 11daysafter suspensionpreparation and more than 10 h after up-and-down mixing. Exposure = 2 a, iris = 22.

I I

Figure 10. Examples of the colloidal single crystals observed for CS-81 suspension with resins. 4 = 0.00144. Pictures were taken 11days after suspension preparation and more than 10 h after up-and-down mixing. Exposure = 2 a, iris = 22.

Shape of Colloidal Single Crystals of Polystyrene Spheres. Nine kinds of polystyrene spheres of various diameters, monodispersities, and charge densities were used. Their stock suspensions have been completely deionized for more than 1month with the Bio-Rad ionexchange resins, coexisting after purification processes of ultrafiltration. Large size of single crystals (or crystallites) appeared for the very diluted suspensions, ranging 0.0001 to 0.004 in volume fraction when the suspensions were completely deionized with the Bio-Rad resins more than 3 weeks after suspension preparation in the observation cells (test tubes). It is clear that the deionization reaction of suspensions with the resins is very slow. Figure 3 shows the close-up color pictures taken by rotating the test tube differently for the same DlC25 (d = 85 nm, Q = 0.00234) sample. The three pictures differ greatly to each other, which is due to the appearance of the single crystals at the different location. The width of these pictures corresponds to the outer diameter of the test tube, Le., 13 mm. Most of the single crytals look like the associatesof small blocks (association-type). Some of them were lozenge-shaped (rhombic) crystals as is circled with black ink in the picture. The lozenge-shaped crystals have been observed also for DlC25 suspension at $I. =

Figure 11. A close-up picture of CS-91 suspension with resins. TypeB cellswere used. 4 = 0.000682. Picture was taken 23 days after suspension preparation and 70 min after up-and-down mixing. Exposure = 1 s, iris = 22.

0.00195, though the picture showing this was omitted. Further, note that the shape of single crystals of DlC25 suspensions at the concentrations higher than Q = 0.0039 was quite different from the association-type and had smooth crystal planes, similar to Figures 5 and 6 given later. The reason for the formation of the associationtype single crystals is not clear yet. It should be noted that the very similar shape has been observed also for the small size of colloidal silica spheres of CS-61 (81 nm in diameter) as will be described below. Note further here that most of the single crystals seen in the Figure 3 are formed after the homogeneous nucleation mechanism in the bulk phase far from the cell wall. However, pillar-like and rather small single crystals can be also observed in a line at the surface of the cell wall. These crystals may form from the heterogeneous nucleation mechanism a t the cell wall. Figure 4 shows typical examples of single crystals appeared for DlC27 suspensions. Shape of the single crystals were block-like. The association-type crystals, which have been observed for DlC25 suspension, were not recognized at all in the whole range of sphere concentrations exhibitingsingle crystals. The suspensions exhibiting single crystals were rather transparent. In this figure a background is very dark, but the suspension must be full of single crystals surrounded with grain boundaries. With a slow rotation of the test tube, bright patterns of single crystals changed rapidly. Change in colors from bluish to reddish is due to the change in the incident angles of light through the curved wall of the test tube. The shape of the single crystals for DlB76 (d = 109 nm, 6/d = 0.028) suspensionswas very similar to those of DlC27 suspensions, and the pictures showing this were omitted. Figure 5 shows the close-up pictures of deionized suspensions of DlP30 spheres; their diameter is the same as

Langmuir, Vol. 10, No. 6, 1994 1701

Colloidal Single Crystals of Polystyrene and Silica Spheres

~

A

Figure 13. A close-up video picture of CS-22 suspension with resins. Type A cell was used. 4 = 0.000366. Picture was taken 21 days after suspension preparation and 40 min after up-and-

down mixing.

I

4 -

Figure 12. Close-uppictures of CS-91suspensionswith resins.

Type B cells were used. Pictures were taken 23 days after suspensionpreparation. From the top: 4 = 0.000682 and 70 min after up-and-down mixing, 0.000833 and 20 min, and 0.00114 and 12 min, respectively.

DlB76 but highly polydispersed (6/d= 0.26). Surprisingly, very large single crystals have appeared even for the highly polydispersed spheres, though the suspensionswere rather milky turbid compared with those of DlB76 spheres. At the extremely diluted suspensions, the effective diameter of spheres including Debye length becomes 10- to 20-fold larger than the real diameter. Thus, the effective polydispersity index given by Gld,ffshouldbe l / l o to l/20 smaller than the 6/d value. Such a small value in the effective polydispersity index may safely permit the formation of the crystal-like distribution even for the highly polydisperse spheres of DlP30. Figure 6 shows large single crystals for the deionized anddiluted suspensionsof DlK88 (d = 137nm) and DlB72 (173nm). Suspensionsof comparatively large spheres were highly turbid even in the state of the crystal-likestructure. Furthermore, large single crystals have appeared only in the very narrow range of sphere concentration slightly higher than the critical concentration of melting. Single crystals of DlB28 (d = 212 nm) were recognized with the naked eye for the suspensions with 4 = 0.00038-0.0005! Shape of Colloidal Single Crystals of Silica Spheres. Three pictures in the course of crystal growth of CS-61 (d = 81 nm, 6 = 12 nm) suspensions are shown in Figure 7,140 min, 5 h, and 20 h after inverted mixing

-

E

A

I

I

1

3

E

0

Y

0

A X F

2 Q)

A X

.-N cn 1

Bax x x

-

0

0 0.0001

0.001

0.01

I - Bc Figure 14. Plots of size of colloidal single crystals of DlC25 (O), DlC27 (X), DlB76 (A),DlP30 ( O ) , DlK88 (O), DlB72 (A),and DlB28 (1) against 4 - &.

of the sample, which were deionized completely before the measurements. Association-typeand lozenge-shaped single crystals formed, which is very similar to the observation for DlC25 spheres. &-Values of DlC25 and CS-61 are 0.0014 and 0.0036, respectively. These values areca. 10-fold larger than those of the other larger spheres. Association-typesingle crystals must be related deeply to the small size of colloidal spheres and also large &values.

Okubo

1702 Langmuir, Vol. 10, No. 6, 1994

‘F-

I

I

,“,.A A

I

I

0

X

AA

I

0

-

I

X

0

’A

1

0

2 Y

A 0 0 0

1

o.ooo1

000 X

A

a m AI

Ax A

0.001

xopo

n

0.01

0.0007,0.0008,0.001 in volume fraction. Size of the single crystals decreased sharply as sphere concentration increased, though their size was highly dispersed. Figure 13shows a close-upcolor video picture of colloidal single crystals observed for CS-22 (d = 178 nm, 6 = 9 nm) suspension. The suspension was very turbid, but very brilliant crystals appeared when the cell was rotated very slowly. Size of Colloidal Single Crystals. Figures 14 and 15 demonstrate clearly that first, size of single crystals from the homogeneous nucleation mechanism decreases very sharply, either for polystyrene or silica spheres, as 4 - q5c increases. Furthermore, very large crystals are formed at the sphere concentrations slightly higher than the critical concentration of melting (d).Third, decrease in size with increasing $I is very sharp, especially for the large spheres. For example, for DlB28 (d = 212 nm) spheres, very large crystallites are observable only in the condition of - I $ ~ 50.0001 as is shown in Figure 14! Thus, it is not easy to determine the C#J~ value and giant crystals experimentally. For the small size of spheres, on the other hand, such as DlC25 (d = 85 nm) and CS-61 (d = 81 nm), large crystals appear in the comparatively wide range of sphere concentrations (@- & I 0.01). The nucleation rate (4for the homogeneous nucleation is given by eq 2 C#J

b - 9, Figure 15. Plots of size of colloidal single crystals of CS-61(01, CS-81 (X), CS-91 (A),cs-121(o),CS-22 (O), and CS-161 (A) against 4 - &. However, this author does not have any appropriate explanation for this yet. Figure 8 shows a close-up picture of CS-81 (d = 103nm, 6 = 13 nm) suspension. Crystal planes are recognized for some crystals clearly. Two kinds of single crystals, blocklike in the bulk phase and pillar-like along the cell wall, are observed. Color change from bluish to reddish is again due to the change in the incident angle of light through the curved cell wall. Figures 9 and 10show the typical shapes of single crystals that appeared for the same suspension sample as is shown in Figure 8. Size is between 1.5and 3 mm. It is interesting to note that the fundamental feature of the colloidal single crystals does not depend on the kind of spheres studied, either polystyrene or silica spheres. This is quite understandable if we take into account the fact that formation of the colloidal single crystals is due to the long-ranged electrostatic repulsion, not to attraction. Figure 11 shows the colloidal single crystals in the deionized suspensions of CS-91 silica spheres (d = 110 nm, 6 = 4.5 nm). Very big and beautiful single crystals are observed for the very diluted suspensions, 0.00068 in volume fraction. Figure 12 shows the colloidal single crystals of CS-91 spheres at different sphere concentrations, from the top:

J = K exp(-AGlkBT)

(2)

where K is the kinetic coefficient and AG is the critical activation free energy for nucleation. AG is given by eq 3.34 AG

0:

(In r)-’

(3)

where r is @I&[or (4 - &)/& + 11. Combination of eqs 2 and 3 supports the observation, i.e., the size of single crystals decreases as C#J - @c increases, since the size should increase with decreasing nucleation rate and with decreasing number of nuclei.

Acknowledgment. This work was supported by grantsin-aid from Iketani Science and Technology Foundation and Japanese Ministry of Education, Science and Culture. Nippon Zeon Co. and Catalyst & Chemicals Ind. Co. are sincerely acknowledged for their kindness in providing polystyrene and silica spheres, respectively. (34) Boistelle, R.;Astier, J. P.J . Cryst. Growth 1988, 90,14.