Kinetic Analyses of Colloidal Crystallization in Alcoholic Organic Solvents and Their Aqueous Mixtures As Studied by Reflection Spectroscopy

JOURNAL OF COLLOID AND INTERFACE SCIENCE ARTICLE NO.

204, 198 –204 (1998)

CS985598

Kinetic Analyses of Colloidal Crystallization in Alcoholic Organic Solvents and Their Aqueous Mixtures As Studied by Reflection Spectroscopy Tsuneo Okubo1 and Shinji Okada Department of Applied Chemistry, Faculty of Engineering, Gifu University, Yanagido 1-1, Gifu 501-1193, Japan Received February 12, 1998; accepted April 17, 1998

Reflection spectroscopy is used for the kinetic analyses of the nucleation and growth process of colloidal crystals of silica spheres (110 nm in diameter) in exhaustively deionized suspensions of purely alcoholic organic solvents (methyl alcohol, ethyl alcohol, and ethylene glycol) and aqueous mixtures with alcohols (methyl, ethyl, n-propyl, and n-butyl alcohols and ethylene glycol). Sphere concentrations studied range from 0.001 to 0.01 in volume fraction, rather high compared with those in water. Induction periods are from 5 to 2000 s and are prolonged with decreasing sphere concentration. Nucleation rates are 1023 to 103 mm23 s21 and increase sharply as sphere concentration increases. The crystal growth rates, v have been determined from the increase of intensity in the sharpened reflection peaks. Values of v range from 1 to 27 mm/s and decrease linearly as the reciprocal sphere concentration increases. Nucleation and crystallization rates decrease sharply as the fraction of the organic solvents increases in the mixtures with water. The importance of the electrostatic intersphere repulsion through the electrical double layers and the cooperative and synchronized fluctuation of colloidal spheres in the crystallization processes is supported. © 1998 Academic Press Key Words: colloidal crystal; crystal growth kinetics; reflection spectrum; nucleation; silica spheres.

1. INTRODUCTION

Recently, keen attention has been paid to the structural and dynamic properties of colloidal crystals (1–13). Suspensions showing crystal-like structures are ideal for model studies of crystals. Furthermore, the phase transition phenomena of crystallization or melting occur sharply. The mechanism of the colloidal crystallization has been studied by several researchers hitherto for two groups of colloidal crystals: (a) diluted and deionized aqueous suspensions (14 –23) and (b) concentrated suspensions in the refractive index matched organic solvents (24 –38). The formers are very convenient models for both the soft and hard sphere systems depending on the ionic concentrations of suspension, i.e., soft crystals in the completely deionized state and 1

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0021-9797/98 $25.00 Copyright © 1998 by Academic Press All rights of reproduction in any form reserved.

hard crystals in the presence of rather large amounts of sodium chloride, for example. It is now widely accepted that the phase transition, kinetics of crystallization, structure, and physico-chemical properties of the soft colloidal crystals are explained by the extended electrical double layers and the interparticle repulsive coulomb potential (39). We have studied the crystallization processes in the exhaustively deionized and highly diluted aqueous suspensions from the sharpening of the reflection peak in the reflection spectroscopy (15, 19, 40, 41). The crystallization process was unexpectedly fast. In previous papers (40, 41), nucleation rates in aqueous media increased drastically as sphere concentration increased. Crystal growth rates also increased substantially as the sphere concentration increased. Furthermore, nucleation and crystallization rates were very sensitive to the degree of deionization of the aqueous suspensions. We must pay our utmost attention to attain the complete deionization of the suspensions. The critical sphere concentration of melting, fc, is quite sensitive to the degree of deionization and increases sharply for the suspensions contaminated with ionic impurities. When the sample suspensions in the mixtures of alcohol and water were deionized with resins most carefully for more than four weeks, the fc value became quite low, 0.02 for 100% ethyl alcohol, for example (42), though the fc values in the mixtures are always high compared with those in pure water, i.e., in the range from 0.0001 to 0.0003 as we have reported recently. In this paper, we investigated the kinetics of the colloidal crystallization processes in alcohol organic solvents and their aqueous mixtures, in which the former solvents were dehydrated completely with molecular sieves and further deionized with the mixed beds of cation- and anion-exchange resins exhaustively and the latter were deionized with the resins completely. Several researchers have studied the colloidal crystals in the organic solvents such as 1,4-dioxane, benzene, and bromoform (42– 45). However, kinetic studies on colloidal crystallization have never been reported as far as the authors know.

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2. MATERIALS AND METHOD

2.1. Materials Colloidal silica spheres of CS-91 was a gift from Catalyst & Chemicals Ind. Co. (Tokyo). The diameter (do), standard deviation (d) from the mean diameter, and polydispersity index (d/do) were 110 nm, 4.5 nm, and 0.041, respectively. The values of do and d were determined with an electron microscope. The charge density of the spheres was determined to be 0.48 mC/cm2 for strongly acidic groups by conductometric titration with a Horiba model DS-14 conductivity meter. The sphere sample was carefully purified several times using an ultrafiltration cell (model 202, membrane: Diaflo-XM300, Amicon Co.), and then the sample was treated on a mixed bed of cation- and anion-exchange resins [Bio-Rad, AG501-X8(D), 20 –50 mesh] for more than two years before use, as newly produced silica spheres always release a considerable amount of alkali ions from the sphere surfaces for a long time. 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). Organic solvents were methyl alcohol (MeOH), ethyl alcohol (EtOH), n-propyl alcohol (PrOH), n-butyl alcohol (BuOH), and ethylene glycol (EG), which were the highest purity grade reagents commercially available and which were used after dehydration treatment and further deionization with molecular sieves (type 3A-1/6, Wako Pure Chemicals, Osaka) and BioRad resins for more than a month, respectively. The sample suspension was prepared in a test tube with a stopper (type B), with 13 and 15 mm inside and outside diameters. The suspensions were further treated with a small amount of Bio-Rad resins in a test tube for more than four weeks with inverted mixing several times a day. For preparation of the 100% MeOH, EtOH, and EG suspensions, molecular sieves were also used in addition to the Bio-Rad resins in order to eliminate the tiny amount of water contamination as completely as possible.

FIG. 1. Reflection spectra in the course of crystallization of CS-91 spheres in 100% EtOH at 23°C. f 5 0.0379, 33 days after suspension preparation with the resins. Curve 1, 0 s after mixing; 2, 15 s; 3, 30 s; 4, 60 s; 5, 120 s; 6, 180 s; 7, 300 s; 8, 1500 s; 9, 15 h.

reflection volume. However, it is difficult to maintain this assumption for colloidal crystals, since the most dense planes of the colloidal single crystals are apt to orient parallel to the cell plane. On the other hand, the peak intensity, I, of the reflection spectra is approximated by (48) I } N cryst L 3 } L 3 ,

[2]

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 crystallization process and is equal to the total number of nuclei formed in the whole course of crystallization. 3. RESULTS AND DISCUSSION

2.2. Reflection Spectroscopy

3.1. Reflection Spectra

The reflection spectra at an incident angle of 90° were recorded on a multichannel photodetector, MCPD-110B (Otsuka Electronics, Hirakata, Osaka), connected to a Y-type optical fiber cable. The size of the colloidal single crystals from the homogeneous nucleation, L, is estimated by Scherrer’s equation from the half-width of the reflection spectra (46 – 48):

Typical reflection spectra in the course of crystallization are shown in Fig. 1 at f 5 0.0379 in 100% EtOH. The spectra were taken every 15 s. The reflection peak became sharp with time in the course of crystallization, which corresponds to the increase in crystal size. The background intensity decreased very slightly in the course of crystallization, though this is not so clear in the figure. This decrease is ascribed to the diminution in the multiple scattering of the suspension in the course of crystallization. Figure 2 shows the typical examples of the shift of the reflection peaks, lp, in the course of crystallization in 100% EtOH. Clearly the lp values decreased with time especially in the beginning of the crystallization, which is the same behavior as in pure water systems. This peak shift reflects the fact that the loose and extended crystals are formed first and that they

L } nDq 21 ,

[1]

where n is the number of the order in the Bragg equation, q is the scattering vector, and Dq denotes ql 2 qs, with ql and qs referring the largest and smallest wavelengths corresponding to the half-width of the reflection peak. It should be noted here that Eq. [1] is derivable by assuming a powder-like random distribution of a large number of colloidal crystals in the

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FIG. 2. Shift of the reflection peaks in the course of crystallization of CS-91 spheres in 100% EtOH at 23°C. (E) f 5 0.0379; (3) lp observed 1 20 nm, f 5 0.0417; (‚) 150 nm, f 5 0.0454.

come to be stable and compact ones. In most cases the transition between the subphases of face-centered cubic (fcc) and body-centered cubic (bcc) lattices did not occur for the suspensions containing the organic solvents. Figure 3 shows the time dependencies of the crystal size estimated from the half-widths of the reflection peaks using Eq. [1] for 100% EtOH suspension. Size vs time curves show the S-shaped characteristics especially at the low sphere concentrations. The induction period (ti) before the crystallization was observed at low concentrations of spheres and determined from the intersection of the slope line and the time axis. ti increased sharply as sphere concentration decreased. This parameter will be discussed later in Section 3.2. The crystal growth rate was evaluated from the slope in the size vs time curves and is discussed in Section 3.3. In these calculations, the final mean sizes (L) of colloidal crystals formed were estimated with video camera. The L values in the EtOH 1 water mixtures are shown in Fig. 4. The size decreased sharply as sphere concentration increased, irrespective of the fraction of alcohol in the mixtures, though the critical sphere concentration of melting, fc, increased drastically as the fraction of the alcohol increased.

FIG. 4. Mean size of single crystals formed for CS-91 spheres in EtOH– H2O mixtures at 23°C. (E) H2O (previous work); (3) 20% EtOH; (‚) 40%; (h) 60%; (F) 80%; (Œ) 100%.

3.2. Induction Period and Nucleation Process Most kinetic measurements on the colloidal crystallization including this work have observed the induction periods, after which the crystal growth started especially in the diluted suspensions. This observation supports the kinetics of colloidal crystallization as explained by the classical diffusive crystallization theory including nucleation and crystal growth processes. According to the classical nucleation theory, the nucleation rate, vn, is given by (49) v n 5 v no exp@2DG* /k B T # ,

[3]

where kB is Boltzmann’s constant and DG* is the nucleation barrier related to the macroscopic surface tension, g, and the chemical potential difference, Dm, between the crystal and liquid phases given by Eqs. [4] and [5]. DG* 5 16 pg 3 a 2 /3~D m ! 2 , D m /k B T 5 ln~ f / f c ! > s ,

[4] [5]

where s is the relative supersaturation given by (f 2 fc)/fc and a is the volume of the growing unit in the crystal phase. The number of nuclei that germinate per unit time, the nucleation rate, vn, is approximated by v n 5 N n /t i ,

FIG. 3. Change of crystal size in the course of crystallization of CS-91 spheres in 100% EtOH at 23°C. (E) f 5 0.0379; (3) 0.0417; (‚) 0.0454.

[6]

where Nn is the total number of nuclei formed during the nucleation process and ti is the induction period. Here, we assume that the number of nuclei equals the number of single crystals formed. The number of sphere particles per mean size of single crystal, Nc, will be given for the cubic lattice by

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3.3. Crystal Growth Process According to Wilson (51) and Frenkel (52), the crystal growth rate of a crystal, v, is given by v 5 v ` @1 2 exp~2D m /k B T !# .

[10]

Here, Dm is the chemical potential difference between the crystal and liquid phases appeared in Eq. [4] and is given by D m 5 m cryst 2 m liq .

[11]

Dm . 0 means that crystallization will proceed. From Eqs. [5] and [10], Eq. [12] is derived (53): FIG. 5. Induction period for CS-91 spheres in EtOH–H2O mixtures at 23°C. (E) H2O (previous work); (3) 20% EtOH; (‚) 40%; (h) 60%; (F) 80%; (Œ) 100%.

v 5 v ` @1 2 exp~2s !# .

[12]

Equation [12] is further simplified as N c 5 Ï 2L /l , 3

3

[7]

where L and l are the mean size of single crystals formed and the closest intersphere distance, respectively. The total number of colloidal spheres (NT) in a unit volume is f/[(4/3)p(do/2)3]. Then vn is given by v n 5 N T /N c t i 5 f l 3 /@~4 Î 2/3! p ~d o / 2! 3 L 3 t i # .

[8]

The ti values in the aqueous mixtures of EtOH and in 100% ethanol are shown in Fig. 5. Clearly, ti decreases as the sphere concentration increases. vn values in the EtOH–water mixtures using Eq. [8] thus estimated are shown in Fig. 6. The l values in Eq. [8] are given by l 5 0.904d o f 21/3 ,

v 5 v` 2 v` fc /f .

[13]

Figures 7–11 show the v vs 1/f plots thus evaluated for the aqueous mixtures with MeOH, EtOH, PrOH, BuOH, and EG. The data are rather scattered, but linearity is good irrespective of the fraction of the alcohols. Figure 12 shows the v` values in the aqueous mixtures with the alcohols. Surprisingly, v` values in the mixtures were higher than those in pure water and increased as the alcohol fractions increased, except 100% EG. v` and fc in pure water were 15.3 mm/s and 0.0014, respectively (41). Clearly, the degree of deionization of the suspension in this work is lower than that of previous work, i.e., fc 5 0.00055 (40), where measurements were made about two weeks after suspension preparation with ion-exchange resins. Kinetic parameters of the colloidal crystallization are highly

[9]

where do is the real diameter of the colloidal spheres. The nucleation rates increased sharply as sphere concentration increased in all the mixtures. However, the slopes in the vn vs f plots decreased as the fraction of EtOH increased as is clear in the figure. The graphs showing the vn values in the other alcohol–water mixtures are omitted in this work. It should be mentioned here that the size of single crystals is highly polydisperse as has been observed hitherto (50). Therefore, the clear-cut separation of the nucleation step from the crystallization process will be difficult, and the nucleation reaction may remain in part even in the crystal growth period. Furthermore, the Ostwald ripening of the crystals, i.e., further growth of large crystals and disappearance of small ones, has not been observed at all for our colloidal crystallization systems.

FIG. 6. Nucleation rates for CS-91 spheres in EtOH-H2O mixtures at 23°C. (E) H2O (previous work); (3) 20% EtOH; (‚) 40%; (h) 60%; (F) 80%; (Œ) 100%.

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FIG. 7. Crystal growth rate as a function of reciprocal sphere concentration for CS-91 spheres in MeOH–H2O mixtures at 23°C. (E) H2O (previous work); (3) 20% MeOH; (‚) 40%; (h) 60%; (F) 80%; (Œ) 100%.

FIG. 9. Crystal growth rate as a function of reciprocal sphere concentration for CS-91 spheres in PrOH–H2O mixtures at 23°C. (E) H2O (previous work); (3) 20% PrOH; (‚) 40%; (h) 60%.

sensitive to the degree of deionization of suspensions. We assume here that Eq. [13] is applicable for the colloidal system and that the maximum growth rate, v` is determined by the diffusion of single spheres near the crystal surface. Then Eq. [14] holds.

must move in a cooperative manner by the electrostatic repulsive forces. In this sense, the colloidal crystal systems are quite similar to the fused metal systems. Slight movement of the effectively enlarged spheres including electrical double layers will be enough to allow the crystallization. Thus, the agreement of v` between the calculation and the observation will be explained by balancing the two factors in the decreases of Do and j. As is clear in Fig. 12, the v` values in the mixtures increased as x increased. Furthermore, v` increased in the order of Eq. [15] when they were compared at the same x value:

v ` 5 4D o / j .

[14]

Here, j is the mean diffusion length (path) and Do is the diffusion coefficient of spheres in the crystallization suspension. When j and Do were assumed to be the mean intersphere distance (l, 1.18 mm in pure water), the diffusion coefficient of spheres in the gas-like distribution calculated by the Stokes– Einstein equation (4.36 3 10212 m2/s) (41). Then v` was calculated to be 14.8 mm/s in pure water, which agrees surprisingly with the observation, 15.3 mm/s. We should note here that the Do should be the diffusion coefficient in the supersaturated liquids, for example, 1 3 10212 m2/s in the previous work of dynamic light scattering (40). Furthermore, the mean diffusion length (j) was clearly overestimated when j > l was taken, since the colloidal spheres in the supersaturated liquids

FIG. 8. Crystal growth rate as a function of reciprocal sphere concentration for CS-91 spheres in EtOH–H2O mixtures at 23°C. (E) H2O (previous work); (3) 20% EtOH; (‚) 40%; (h) 60%; (F) 80%; (Œ) 100%.

EG % H2 O , MeOH % EtOH % PrOH , BuOH.

[15]

The parameter j in Eq. [14] is approximated roughly by do and is quite insensitive to the fraction of the organic solvents, x (40). Thus, Eq. [16] holds: v ` } D o } 1/~ h d eff ! } h 21 ~a 1 b e 1/ 2 ! 21 .

[16]

Here, deff is the effective diameter of colloidal spheres includ-

FIG. 10. Crystal growth rate as a function of reciprocal sphere concentration for CS-91 spheres in BuOH–H2O mixtures at 23°C. (E) H2O (previous work); (3) 5% BuOH.

KINETICS OF COLLOIDAL CRYSTALLIZATION

203

ing the electrical double layers (deff 5 do 1 2Dl), Dl is the Debye screening length given by (4pe2n/ekBT)21/2, n is the sum of the concentrations of the diffusible ions (free-state counterions, foreign salt, and both H1 and OH2 from the dissociation of water) in suspension, and v` should change proportionally to the reciprocal values of h and a 1 be1/2 when Eq. [16] holds properly for our systems. According to the reference values, the dielectric constants, e, of the organic solvents decrease in the order H2 O~ e 5 79 at 25°C! . EG~38! . MeOH(32) . EtOH(24) . PrOH(20) . BuOH(18).

[17]

The viscosities, h, on the other hand, decrease in the order EG~ h 5 13.6 mPa s at 30°C! .. BuOH~2.3 at 30°C! . PrOH~1.9 at 25°C! . EtOH~1.0 at 30°C! . H2 O~0.8 at 30°C, 0.9 at 25°C! . MeOH~0.5 at 30°C!.

[18]

The observed order of v` shown in Eq. [15] is quite similar to that given by Eq. [17]. The order shown in Eq. [18] is not consistent with the order of v` observed except EG. Thus, the v` values observed can be explained by the differences in the dielectric constant and viscosity of solvents, especially the former. 3.4. Importance of the Inter-Sphere Repulsion and the Synchronous Fluctuation of Colloidal Spheres in Crystallization The critical concentration of melting (fc) of the colloidal crystals in the exhaustively deionized aqueous suspension is very low, around 0.0002 in volume fraction in most cases as described in the Introduction. However, the effective concentration of spheres including the expanded electrical double

FIG. 12. Maximum crystal growth rate as a function of fraction of organic solvent in the organic solvent–water mixtures at 23°C. (E) MeOH; (3) EtOH; (‚) PrOH; (h) BuOH; (F) EG at 23°C; (#) pure water.

layers is substantially high, even close to 0.74 in volume fraction corresponding to the close packing. The spheres in the colloidal crystals interact with each other very strongly and further in a cooperative manner through the electrical double layers by the electrostatic repulsion. Recently, Schatzel and Ackerson (30) proposed the importance of the dynamic phase transition by the density fluctuation for the colloidal crystallization. It should be noted that the synchronous fluctuation of colloidal spheres in the crystal cages plays an important role for the colloidal crystallization. The importance of the dynamic phase transition has been reported for other crystals such as metals (54) and polymers (55). Many researchers including Hachisu et al. have clarified the importance of the electrostatic repulsive forces between the spheres in the colloidal crystallization hitherto (56, 57). The inter-sphere repulsion should also exist during the course of crystallization, including nucleation and growth. The electric double layers for the colloidal crystals are more expanded compared with those of colloidal liquids (58, 59). This situation means that the microscopic intersphere repulsion forces in the colloidal crystals is weak, though very slightly, compared with that of colloidal liquids. Therefore, there should exist an apparent inter-sphere attraction in the course of nucleation and growth processes in the phase transition from liquids to crystals. In other words, the slight difference in the repulsive forces in the crystals and the liquids leads to the apparent attraction between the spheres in the nucleus regions. This apparent attraction in the colloidal crystallization processes must be one of the main reasons why the kinetic and molphological properties of colloidal crystals are so similar to those of other crystal systems such as metals, protein crystals and minerals. Among the many crystal systems, crystallization of fused metals may be one of the best systems to mimic the colloidal crystals. ACKNOWLEDGMENTS

FIG. 11. Crystal growth rate as a function of reciprocal sphere concentration for CS-91 spheres in EG–H2O mixtures at 23°C. (E) H2O (previous work); (3) 100% EG.

Drs. M. Komatsu and M. Hirai of Catalysts & Chemicals Ind. Co. (Tokyo and Kitakyusyu) are deeply thanked for their providing the silica samples.

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Professor Akira Tsuchida of Gifu University is acknowledged for his valuable comments.

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