J. Phys. Chem. B 2001, 105, 5383-5390
5383
Heterogeneous versus Homogeneous Nucleation and Growth of Zeolite A Tejinder Brar, Paul France, and Panagiotis G. Smirniotis* Chemical Engineering Department, UniVersity of Cincinnati, Cincinnati, Ohio 45221-0171 ReceiVed: August 22, 2000; In Final Form: February 15, 2001
The effectiveness of the addition of nanoparticles of various materials to act as substrates for zeolite A nucleation and growth was investigated in an attempt to obtain submicron zeolite A crystals. It was found that the important parameters influencing nucleation and growth rates of zeolite A crystals over the substrates were (1) the surface energies of the substrates, zeolite A and the synthesis medium, and (2) the size of the substrate. Nucleation rates of zeolite A over substrates was found to be significantly lower as compared to nucleation rates for homogeneously nucleated zeolite A, even though the energy barrier for nucleation was found to be significantly lower in the former case. This could be attributed to the steric factors associated with the substrate. Indeed, we proved mathematically this to be the case. It was found that the nucleation becomes progressively easier on substrates as the contact angle between the zeolite A embryo and the substrate goes from π to 0. It was interesting to note that synthesis using two Titanias (Hombikat and Hombifine) as substrates gave very promising results in obtaining submicron zeolite A crystals and crystals in the size range of about 0.3 µm on the surface on these substrates were obtained. No zeolite A crystals were found to undergo heterogeneous nucleation and thus grow on other substrates like Fe2O3, TiO2 (Ishihara), Ce2O3, SnO2, ZnO, TiO2 (Nanotek), CuO, TiO2 (Kemira), TiO2 (Degussa). For most of them, the contact angle between the substrate and the zeolite A embryo does not fall between 0 and π/2, which is the range required for heterogeneous nucleation and growth. It was found that the Zeta potential of only TiO2 Hombikat and TiO2 Hombifine goes to zero at pH ≈ 12.6. This leads to an increase in their mean particle sizes thus increasing the ratio of the size of the substrate to the critical zeolite A embryo size, a factor that was found to be crucial for heterogeneous nucleation. X-ray Diffraction (XRD), Laser scattering particle size analyzer, Scanning Electron Microscopy (SEM), EDAX, and Energy dispersive XRF have been used to characterize the zeolites synthesized.
1. Introduction Nucleation, the creation of a new crystal phase in the body of the mother phase, is one of the most fundamental aspects of phase transition in general and crystal growth in particular.1-2 This process can be either homogeneous or heterogeneous depending upon the role of foreign bodies. It is still controversial as to if it is even possible to obtain genuine homogeneous nucleation as in most cases, it is almost impossible to remove completely from the nucleating systems foreign bodies. These foreign bodies may range anywhere from solid or liquid particles, macromolecules or even walls of the crystallization vessel. In homogeneous nucleation, the potential barrier that must be overcome for a new phase to crystallize is a function of the interfacial energy between the crystal and the mother phase and the thermodynamic driving force. Foreign bodies may influence this barrier and the consequent nucleation and crystal growth rates as well as the size distribution of crystals. The classical theories of nucleation as proposed by Volmer3, Becker and Doring,4 Frenckel,5 and Zeldovich6 have dealt with the homogeneous rate of nucleation. Analogous assumptions to that of nucleation of liquids from vapors have been made by in various studies to deal with the general problem of nucleation of solid phases in liquids and aqueous solutions.7-11 For heterogeneous nucleation, the concept of epitaxy and lattice mismatch is useful for vapor phase depositions such as molecular beam epitaxy.12 However, for solution phase nucleation, such rules are still being formulated. In the present work, the concept of interfacial surface energies measured using Van Oss-Chaudhury-Good (VCG) theory of wettability13 has been * To whom correspondence should be addressed.
successfully used to determine the surface energies of the substrates and zeolite A. In our study, an attempt has been made to correlate the surface energies to the concept of heterogeneous nucleation on substrate particles. It was found that though the free energy change for heterogeneous nucleation was less than for homogeneous nucleation, steric factors lead to a lower growth rate. Heterogeneous nucleation and growth of zeolite on substrates was found to be a function of the substrate size as well as the surface energies of the embryo, substrate and the synthesis medium. 2. Experimental Section Synthesis. For the heterogeneous nucleation experiments, 0.4 gs of each substrate (listed in Table 2) was individually dispersed in 40 mL of water and ultrasonicated for half an hour. Afterward, 0.01 mol of NaOH were dissolved in this solution and it was distributed equally in two 150-ml polypropylene bottles. 0.02 mol of sodium aluminum oxide (Na2O.Al2O3, technical grade, Alfa Aesar) were added to one bottle and 0.04 mol of sodium metasilicate (Na2O.SiO2, SiO2 44-47%, Aldrich) to the other. The bottles were capped and shaken until homogenization. Subsequently, the sodium metasilicate solution was poured in the sodium aluminum oxide solution. A thick gel was formed immediately, which was again shaken until homogenized. Thereafter, the gel was heated at a temperature of 80 °C for 4 h.14 The products were washed with distilled water until the pH was below 9. After that, the crystals were filtered using 0.1 µm mixed cellulose ester membrane filters (Cole Parmer) and dried at 110 °C overnight. To double-check the results from the synthesis point of view, all the experiments were repeated and, instead of filtering, the
10.1021/jp003012f CCC: $20.00 © 2001 American Chemical Society Published on Web 06/07/2001
5384 J. Phys. Chem. B, Vol. 105, No. 23, 2001 particles were separated using centrifugation. The rest of the procedure was exactly the same as listed above. Characterization. X-ray Diffraction (XRD). X-ray diffraction on a Siemens model D 500 diffractometer (CuKR radiation) was employed for the identification of the synthesized zeolite after the sample had been dried overnight. The phase identification was done by comparing with the diffraction pattern of commercially available zeolite A. For the substrates, Scintag DMSNT ver.132 software15 was used to quantify the crystallinity of the zeolite samples synthesized. Laser Scattering Particle Size Analysis. The particle size distribution was determined with LASER scattering particle size distribution analyzer (Horiba LA 910). For this purpose, wet method of particle size distribution analysis was used and distilled water was used as the medium to disperse the zeolite. The solution was ultrasonicated for 30 min in order to break down the flocculates before the run was made. The instrument is accurate to within 10% of the median value. All samples were run twice to ensure accuracy of measurement. Variations were never more than 5% of the median value. Scanning Electron Microscopy (SEM/EDAX). Scanning Electron Microscopy (SEM) pictures were taken using Hitachi 2700 Scanning Electron microscope. Samples for SEM analysis were prepared by dispersing the zeolite sample on a carbon coated sample holder followed by gold sputtering at 45µA for 70 s. All samples were analyzed using an accelerating voltage of 5 kV. EDAX was used to characterize the constituent element of the crystals for selected samples. For EDAX, an accelerating voltage of 20 kV was used. Contact Angle Measurement. Contact angles of the substrates with various probe liquids were measured using a goniometer. The contact angles of zeolite A with probe liquids were measured indirectly using the column wicking method.13 Experimental details have been given in section 3.4 of this study. Zeta Potential Measurement. The zeta potential was measured using acoustic and electroacoustic spectrometer (DT-1200, Dispersion Technolgy). The calibration was done with a 20% weight of silica sol in deionized water. This standard is used because the size and charge properties of silica sols are very well-characterized. This instrument was also used to measure the particle sizes of various substrates used in heterogeneous nucleation. TEM. Transmission Electron Micrographs (TEM) of substrates were done using Philips CM200 microscope at 200 kV with a LaB6 filament. The samples were dispersed in ethanol and ultrasonicated for 15 min. Subsequently, the dispersed solution was dropped on a copper grid coated with carbon filament. Several observations were performed for each sample to obtain a representative picture of the properties of the samples under consideration. BET Surface Area Measurements. The substrates were characterized using nitrogen adsorption at 77 K using an accelerated surface area and porosity apparatus (ASAP 2010, Micromeritics). The samples were degassed at 150 °C for 2 h in a helium atmosphere. The adsorption isotherms of nitrogen were collected at 77 K using approximately 7-8 values of relative pressure ranging from 0.05 to 0.99. 3. Results and Discussion The particle size distributions (PSDs) of zeolite A using CeO2 and TiO2 Ishihara as substrates have been shown for comparison along with that for TiO2 Hombifine and TiO2 Hombikat in Figure 1A and 1B, respectively. It can be seen that particle size distributions using TiO2 Ishihara and CeO2 are very similar to
Brar et al.
Figure 1. Particle size distributions (number frequency) of zeolite A synthesized utilizing during synthesis: (A) Titania Hombifine and Cerium Oxide; (B) Titania Hombikat and Titania Ishihara.
Figure 2. Particle size distributions (number frequency) for zeolite A synthesized using various nanoparticle substrates.
each other. The same was the case for all zeolite A batches synthesized using oxides other than TiO2 Hombikat and TiO2 Hombifine. PSDs for zeolite A batches synthesized using other oxides as substrates have been shown in the Figure 2 for the sake of clarity. It can be seen that all of them have a large number of crystals above 1 µm and their PSD profiles are quite similar. From Figure 1A and 1B, it is obvious that the submicron particles in the case of TiO2 Hombikat and TiO2 Hombifine seeding vastly outnumber the particles with dimension greater than 1 µm. This is not the case for other seeding systems. This finding is worthy of further investigation and is the subject of the present study. To understand this phenomenon, it is important to find the free energy change for both the homogeneous and heterogeneous systems and to investigate the relevant properties of substrates. A mathematical model has been presented for homogeneous and heterogeneous nucleation and growth and the dependence of the latter on the properties of the substrate.
Heterogeneous versus Homogeneous Nucleation
J. Phys. Chem. B, Vol. 105, No. 23, 2001 5385
Homogeneous Nucleation and Growth. The energy of formation of a particle of radius r is given by the free energy (∆G) gained upon formation of the bulk phase as well as the energy associated with surface of the new phase due to the surface tension of the solid-liquid interface.16 This can be mathematically expressed by the following relation
4 ∆G ) φ 4πr2γle + β πr3∆GV 3
(1)
Here, ∆GV is the specific free energy change associated with the liquid-solid phase change per unit volume, φ and β are the shape factors, and γle is the interfacial tension between the embryo and the solution. Here, caution needs to be exercised to distinguish between the interfacial tension (embryo-liquid interface) and the surface tension of the embryo (embryo-vapor interface). However, there is one term that has not been taken into account for the calculation of free energy change when we deal with solid liquid systems and that is the free energy due to the electrical double layer.17 When a colloidal particle is brought in contact with an aqueous electrolyte environment, the orientation of water molecules at the solid solution interface induces electrical charging. Mechanisms for this process may include dissociation or ionization of surface sites, specific ion adsorption, or differential dissolution of surface based ions. The presence of the charged surface promotes redistribution of ions in the surrounding solution with counterions preferentially attracted toward and co-ions repelled from the surface. This configuration serves to further decrease the energy of the system. The resultant change in Gibbs energy can thus be described as the electrical field energy near the surface due to the distribution of ions and mathematically expressed as17
∆Gdl )
∫φ ∫Ψ ) 0
Ψ ) final
σdΨdφ
(2)
where Ψ is the potential at the surface and is also known as the zeta potential of the surface, σ is the surface charge density and φ is the surface area. Assuming a spherical embryo of radius r, this equation reduces to17
∆Gdl ) -
or 2
(l + κr)Ψo2
or 4 (l + κr)Ψo2 (4) ∆G ) φ 4πr2γle + β πr3∆GV 3 2 The critical embryo radius can thus be determined by taking the derivative of the free energy change with respect to radius and setting it equal to zero. This gives the maximum energy barrier an embryo needs to cross to survive. The solution gives the critical embryo radius, i.e.
-a + bc ( x(a - bc)2 + 4bd 2d
From eqs 4 and 5, we obtain
∆Ghom ) (a - bc) (rc)2/2 - brc - d/3 (rc)3
∆G ) Ve ∆GV + γle Sel + (γse - γsl) Sse
(7)
Here, V refers to the volume, S to the surface area, and the subscripts l, e, and s stand for the liquid solution, embryo and the substrate over which the nucleation takes place, respectively. γij refers to the interfacial tension between phases i and j and Sij is the surface area between phases i and j. θ is the contact angle between the zeolite A embryo and the substrate and is a measure of their interaction energy. One should note that as this angle decreases, the “wettability” of the substrate by the embryo increases. The usual definition of contact angle is
m ) cos θ ) (γse - γsl)/γle
(8)
Also, by referring to the Figure 3, we find that
Sse ) 2π (Rs)2 (1 - cos χ), Sle ) 2π r2 (1 - cos ζ) (9a) and
1 Ve ) πr3 (2 - 3 cos ζ + cos 3 ζ) 3 1 πR 3(2 - 3 cos χ + cos 3 χ) (9b) 3 s and
(5)
where a ) 8πφγle, b ) oΨo2/2, c ) 2κ and d ) 4π∆GVβ.
(6)
Equation 6 gives the critical Gibbs energy for a nucleus to survive in a homogeneous solution. Heterogeneous Nucleation and Growth. We assume that the substrate over which the nucleation takes place is spherical since in the size range where shape effects enter, many particles tend to be spherical (Figure 3). We present our analysis in a form analogous to that proposed by Fletcher.18 The free energy of formation of the embryo can be mathematically expressed as the energy change that takes place as a result of the emergence of the embryo and consequent change in surface energies between the phases and is given by
(3)
where o is the dielectric constant of the medium and 1/κ is the thickness of the double diffuse layer. Thus, the total Gibbs free energy can be written as
rc )
Figure 3. Schematic diagram of a zeolite A embryo nucleating on a substrate.
cos χ ) (Rs - r m)/l
(9c)
cos ζ ) (Rsm - r)/l
(9d)
l ) [(Rs)2 + r2 - 2 Rs r m]1/2
(9e)
and
5386 J. Phys. Chem. B, Vol. 105, No. 23, 2001
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Thus, the only unknown variables are r and θ provided the size of the substrate is known. However, not all embryos survive and one needs to find the radius of curvature of critical size embryos, which will survive. We assume that there is a homogeneous distribution of these substrates in the vessel. The free energy maximum can be found by finding the derivative with respect to radius
)0 (d∆G dr ) However, the analytical solution for this equation is bulky and can’t be used directly. We assume that the growth of zeolite A in heterogeneous systems occurs the same way as in homogeneous nucleation systems. Thus, as a simplification, we shall use the critical nucleus for homogeneous nucleation. The magnitude of error in estimating the critical radius size that this assumption would lead to will depend on the contact angle of the zeolite A with a particular substrate and the magnitude of difference between the embryo-substrate interfacial tension and the liquid-substrate interfacial tension as compared to liquidembryo surface tension. Exact numbers will vary for each specific case but the error would be well within 20% for our case. Also, the variable b in eq 5 lies in the range from 10-13 to 10-14. Thus, the energy term due to the double layer contributes less than 1% toward the final free energy change and can thus be neglected. This leads to rc ) 0 and rc ) - (a/d). Apparently, the former is a trivial solution and hence
rc ) - (a/d) ) -2 γle/∆GV
(10)
Using eq 10 in eq 7 and substituting x ) Rs/rc, the critical energy of embryo formation comes out to be
∆G* )
16π(γle)3 3(∆GV)2
f(m,x)
(11)
depends strongly on both functions, the relative size of the substrate and critical nucleus and the contact angle which is a measure of interfacial energy between the embryo and the substrate. f(m,x) is a strong function of X for values up to 50 after which it almost becomes constant for a given value of contact angle.. However, there is a continuous decrease of f(m,x) with decrease in contact angle and it becomes progressively easier for the zeolite crystal to nucleate on the surface of the substrate for X > 50 as the contact angle varies from π to 0. For the extreme case of contact angle being π (i.e., no wetting), it is obvious that free energy change in both cases (heterogeneous versus homogeneous) is the same. However, though in heterogeneous nucleation the height of the energy barrier is lowered, the effective surface area of the embryo where crystal growth can take place is decreased. The rate of nucleation in a heterogeneous system is
(
(
Qhetro ) K1 Sle rc No exp -f(m,x)
(
{ (
)
[
(
) (
(
)] )}
and
g ) (1 + x2 -2mx)1/2
16π(γle)3 a3 ) 6d2 3(∆GV)2
(14)
3(∆GV)2kT
))
(
(
Sle rc No exp - f(m,x)
(
16π(γle)3
))
3(∆GV)2kT 16π(γle)3
3(∆GV)2kT
)
(16)
Using eqs 9a and 16, one gets
(
)
∆Ghom 2πrs2 rc N0 (1 - cos ζ) exp -f(m, x) Qhetero kT ) ∆G Qhomo hom 4πr3cN0 exp kT
Qhetero ) Qhomo
(
1-
( ) ) ) ( ( )
∆Ghom (mx - 1) exp -f(m, x) g kT ∆Ghom 2exp kT
(17)
∆Ghom corresponds to the free energy change at nucleation point. This is equal to
∆Ghom ) kT(ln R′)
Consequently
∆G* ) ∆Ghom f(m,x)
16π(γle)3
Hence, the ratio of heterogeneous to homogeneous nucleation rate is
(13)
When eq 10 is used in eq 6 with the assumption b ) 0 as the third term on LHS in eq 3 is much smaller than the other two, one gets
∆Ghom )
(
Qhomo ) K1 4πrc2 No rc exp -
(4rc2) rc No exp -
1 1 - mx 3 x-m x -m 3 1+ + x3 2 - 3 + + 2 g g g x-m 3mx2 - 1 (12) g
3(∆GV)2kT
where No is the density of the critical sized embryos, and K1 is a constant. The term (Sle rc No) has been introduced as heterogeneous nucleation can take place only in the region of thickness equal to critical radius around the substrate. For homogeneous nucleation the same expression would be
where
f (m,x) )
))
16π(γle)3
(15)
Thus, this expression for heterogeneous nucleation agrees exactly with that for homogeneous nucleation for x ) 0 i.e., when no substrate is present. Comparison of Heterogeneous and Homogeneous Nucleation and Growth Rates. The variation of f(m,x) as a function of X and m has been shown in Figure 4. It is apparent that f(m,x)
where R′ is the relative supersaturation at nucleation point. Getting the values of R′ from available literature 19 for zeolite A, we get
∆Ghom /kT ≈ 1 Putting this value in eq 17, we can determine the heterogeneous to homogeneous nucleation ratio in terms of two independent variables, X and m. Solution of eq 17 has been shown
Heterogeneous versus Homogeneous Nucleation
J. Phys. Chem. B, Vol. 105, No. 23, 2001 5387 Hence eq 18a can be rewritten as
γi ) γiLW + 2 xγi+γi-
(18b)
The interfacial free energy between the two phases i and j can also be expressed as the sum of LW and AB forces. Each term can be modeled as a function of the individual surface energy terms using the combining relationships. Thus, γij can be written as
γij ) γijLW + γijAB or Figure 4. Variation of ratio of heterogeneous to homogeneous free energy change associated with nucleation (f(m, x)) with contact angle (m) and ratio of substrate to critical nucleus size (x).
γij ) γi + γj -2 xγiLWγjLW - 2 [xγi+γj- + xγi-γj+]
(19a)
Using eqs 18b and 19, one gets
γij ) [xγiLW - xγjLW]2 + 2[xγi+ - xγj+][xγi- - xγj-] (19b) Thus, it can be seen that phases with complementary properties interact strongly with each other to reduce the magnitude of γij. It is evident that when one of the phases is either strongly acidic or basic, the AB component of the interfacial tension will be negative. When two phases are brought into contact, the work of adhesion is given by13
WA ) γi (1 + cos θ) ) γi + γj - γij
(20)
Using eqs 19a and 20 Figure 5. Variation of ratio of heterogeneous to homogeneous nucleation rates with contact angle (m) and ratio of substrate to critical nucleus size (x).
graphically in Figure 5 and it is obvious that the nucleation rate of crystal in heterogeneous system will always be less than that in a homogeneous solution except for the special case of contact angle being zero. The case of m ) -1 corresponds to θ ) π, i.e., no wetting and hence means that there would be no nucleation on the substrate surface as can be seen from the figure. It also needs to be noticed that for values of X below 50 even at low contact angle, the nucleation rate is almost zero. Thus, at this stage of the study, we need to find the interfacial surface energies of the substrates, zeolite A embryo and the synthesis media. Interfacial Tension Measurements. One of the big unknowns in all the above equations has been the interfacial energies, γij between two phases i and j. In the Van OssChaudhury-Good (VCG) theory of wettability,13 it was shown that the surface tension, or more accurately, the surface free energy is composed of Lifshitz-van der Waals (LW) and Lewis acid/ base (AB) forces
γi ) γiLW + γiAB
(18a)
van der Waals, dispersion and London forces resulting from dipole and induced dipole interactions contribute to the LW forces, whereas forces like hydrogen bonding, π bond and ligand formation comprise the short-range Lewis acid/ base forces. The AB forces can be further broken down into separate Lewis acid γi+ and Lewis base γi- terms.13 The resultant γiAB can be written as the geometric mean of the above two terms as
γiAB ) 2 xγi+γi-
(19)
γi (1 + cos θ) ) 2 xγiLWγjLW + 2 [xγi+γj- + xγi-γj+]
(21)
The three unknowns for phase j would thus be γjLW, γj+, and γj- provided the surface tension components for phase i are known. Thus, to completely specify the three surface tension components of a phase, its contact angles with three probe liquids of known γiLW, γi+, and γi- need to be measured and then simultaneously solve the three linear equations given by eq 21. The advantage of VCG approach is the ability to measure individual surface energy components and then relate them to through appropriate “mixing” rules to find the interfacial free energies between two phases. This is especially true in cases where direct measurement of the interfacial energy between two phases is difficult. Surface Energy Measurements. We use VCG theory explained above to calculate the surface energies of the substrates and zeolite A. For that, it is obvious from eq 21 that contact angles between the object of interest and three probe liquids of known γiLW, γi+ and γi- need to be measured. Two methods were used for the determination of contact angles that can be categorized as direct method and the column wicking method. (a) Direct Method. The substrates for which the contact angles were to be measured were all nano particle materials and are listed in column 1 in Table 2. Thin wafers (height ) 2 mm, diameter ) 1 cm) of the materials were made by compressing the materials in a die press to a pressure of 5000 psi for 2 min. The wafers were then sintered at a temperature of 750 °C for 24 h. It was possible to sinter the particles at such relatively low temperature due to their small grain size.20 A drop of the probe liquid was then placed on the wafer (Figure 6). The angle was visually measured using a goniometer.
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Figure 6. Schematic of a liquid drop on a solid with their interfacial energies shown.
TABLE 1: Properties of Various Probe Molecules Used for Contact Angle Measurements liquid
γi
γiLW
γi+
γi-
η
hexane ethylene glycol formamide glycerol water
16.05 48.0 58.0 64.0 72.8
0 29.0 39.0 34.0 21.8
0 1.92 2.28 3.92 25.5
0 47.0 39.6 57.4 25.5
0. 000 326 0. 0199 0.004 55 1.490 0. 001
This experiment was repeated three times with three different liquids namely, deionized water, Glycerol (Aldrich, 99.5%) and Formamide (Fischer Scientific, 99.7%). (b) Column Wicking Method. It is apparent that the direct method of contact angle measurement cannot be applied for zeolites as sintering would probably lead to the destruction of the cage structure of the zeolite and reduce it to amorphous powder. Hence, an indirect method, i.e., capillary wicking method for measuring contact angle was used. Wicking is the measurement of the contact angle which liquids make with particulate solids, by determining the rate of capillary rise of these liquids in packed beds of such solids. For that use was made of Washburn’s equation21
h2 )
trRpr γ1cosθ 2η
(22)
where h is the height to which liquid has risen to in time tr, Rpr is the effective interstitial pore radius between the packed particles, η is the viscosity of the liquid, γl is the surface tension of the liquid, and θ is the contact angle. One fundamental difficulty of this approach is that one uses two unknowns in one equation, namely Rpr and θ. This difficulty has been circumvented22-24 using a liquid which is expected to spread over the solid material under study, in which case it is known that cos θ ) 1, so that eq 22 can be solved for Rpr. In our case, hexane was used for this purpose. Once Rpr is known, contact angle measurements with the other 3 liquids, namely deionized water, Ethylene Glycol (Fischer Scientific, 99.5%) and Formamaide (Fischer Scientific, 99.5%) was done using the above equation. The properties of the used liquids have been given in Table 1. The units of surface tension components are mJ/m2 and that of viscosity (η) is Ns/m2 at 20 °C. Glass capillaries (Kimax-51, 90 mm long, diameter 1.5-1.8 mm, Kimble products) were filled with zeolite A particles. The glass capillaries were plugged at the bottom with a small wad of cotton wool. The capillaries were filled with the zeolite A particles and were then onward kept in a vertical position to allow the particles to settle. After settling and preliminary wicking with hexane, to promote further settling, the capillaries were placed in an oven at 110 °C overnight, to remove hexane. The experiments were repeated twice to ensure the accuracy of measurements.The variation of h2 vs t has been shown in Figure 7. Using eq 22 and data in Table 1 gives the contact angles for zeolite A which lead to the following values for surface tension
Figure 7. Plot for h2 (height of capillary fluid rise) vs tr (time).
components for the aforementioned material
γzeolLW ) 49.9 mJ/ m 2, γzeol+ ) 1.76 × 10-4 mJ/ m 2, γzeol- ) 10 mJ/ m 2 (23) Using eq 18b, we find that total surface tension for zeolite A is 49.95 mJ/ m 2, which compares well with the value of 42 mJ/ m2 given in the literature.24 The contact angle of various substrates with probe molecules and their surface energies are shown in Table 2. The angles given are in degrees and the unit of surface energy components is J/m2. θs-water,θs-glycerol and θs-formamide refer to contact angles between the substrate and water, glycerol and formamide, respectively. The contact angle between the substrate and the zeolite A have been calculated using eq 19b and the results have tabulated in Table 3. Also, the respective BET areas of the substrates have been included. Using eqs (19 b), (23), and data given in Table 1, we can easily find out that γzeol-water is 12.4 mJ/m 2. Because the standard free energy was difficult to calculate directly, Kelvin’s equation25 was used to determine the critical radius of the zeolite A crystal
rc )
4 Vs γzeol-water RT(ln R′)
(24)
where Vs is the molar volume of the unit cell (93.9 cm3/mol), and R′ is the relative supersaturation at nucleation point and is available from printed literature.19 This gives the critical radius of 2.3 nm, which is very close to the unit cell dimension. However, this would yield X to be somewhere between 5 and 20, which is still too low to be of any significance as regards heterogeneous nucleation and growth of particles. This would suggest that there might be a change in substrate size when they are added to the water solution at high pH. This is possible only if the substrate particles agglomerate. Physically, two main forces that influence the particle agglomeration in a solution are as follows: ( A strongly attractive but short range van der Waals force that however exhibits an energy well and at a distance of a few nanometers turns to a strongly repulsive force. ( A repulsive term of electrostatic origin which decreases exponentially and is strongly dependent on the ionic strength of the medium.
Heterogeneous versus Homogeneous Nucleation
J. Phys. Chem. B, Vol. 105, No. 23, 2001 5389
TABLE 2: Surface Energy Components of Various Substrates Obtained through Direct Contact Angle Measurement substrate
θs-water
θs-glycerol
θs-formamide
xγiLW
xγi+
xγi-
Fe2O3 (gamma) CuO SnO2 CeO2 ZnO TiO2 Nanotek TiO2 Hombikat TiO2 Hombifine TiO2 Ishihara TiO2 Kemira TiO2 Degussa P25
25 45 22 36 65 27 60 55 50 47 40
32 50 16 25 28 17 45 50 40 40 35
20 47 12 45 44 14 20 19 15 17 25
0.183 0.134 0.14 0.00079 0.0076 0.137 0.253 0.235 0.24 0.233 0.065
0.049 0.063 0.0987 0.189 0.219 0.103 0.007 0.019 0.016 0.0169 0.15
0.0514 0.201 0.211 0.244 0.097 0.202 0.1 0.12 0.137 0.150 0.187
TABLE 3: Contact Angle and BET Areas for Various Substrates substrate
m
BET surface area (m2/g)
Fe2O3 (gamma) CuO SnO2 CeO2 ZnO TiO2 Nanotek TiO2 Hombikat TiO2 Hombifine TiO2 Ishihara TiO2 Kemira TiO2 Degussa P25
-0.48 0.89 0.84 -2.133 -1.25 -0.8 0.77 0.81 0.58 0.38 -0.275
47.64 24.6 61.47 62.36 9.5 32.93 360.8 401.3 70.14 52.12 56.16
This is true in the case of small particles since then the gravitational effects may be neglected. For two identical spheres of radius r, the van der Waals force is given by26
FA )
-rAH 12H 2
Figure 8. Variation of energy for two identical spheres with distance.
(25)
where H is the interparticle distance, and AH is the so-called Hamakar constant, dependent on the dielectric permittivites and refractive indices of the particulate and the continuous media. The repulsive forces can be understood in terms of the Zeta potential of the suspension. One useful expression provided for repulsive forces between two particles of identical size and Zeta potential (Ψo) is26
FR )
2πoκΨo2 1 + eκH
(26)
where κ is the Debye-Huckel parameter depending upon the ionic strength and the dielectric constant (o) of the liquid as well as the temperature. The net force acting on a particle is given by
F T ) F A + FR
(27)
These two dictate the thermodynamic equilibrium. If there are particles that are separated by distances that are greater than SMAX, they must cross an energy barrier greater than EMAX, before they will be able to come together and agglomerate (Figure 8). If the particles do not possess this energy (either kinetic or thermal), they will not be able to able to come together and the system will in fact be metastable. Although the van der Waal forces are almost insensitive to the ionic strength of the suspension liquid, repulsive forces depend strongly on the zeta potential. Zeta potential itself is a strong function of the pH as well as the ionic strength and remains a key parameter in understanding the repulsive forces.
Figure 9. Variation of Zeta potential with pH for various substrates.
Increasing the zeta potential of the particles remains an effective way to prevent them from agglomeration. This may be done using chemical modification of the particles or by simply changing the physical conditions of the surroundings. Synthesis of zeolite A takes place in a highly basic environment with pH close to 12.5-13. From Figure 9, it can be seen that Titania Hombifine and Titania Hombikat are the only two substrates used which have their Zeta potentials go to zero or have them in close vicinity to zero at pH conditions where synthesis of zeolite A takes place. Thus, strong agglomeration of these two substrates takes place at such pH conditions. This was also confirmed by direct measurements of particle sizes of substrates using Acoustic and Electroacoustic instrument (DT-1200 Dispersion Technology, NY) at a pH of 13. There,
5390 J. Phys. Chem. B, Vol. 105, No. 23, 2001 the mean particle sizes of all substrates other than Titania Hombikat and Hombifine were found to be less than 50 nm, showing that practically none of these substrates had agglomerated at a pH of 13. However, the mean particle sizes of Titanias Hombikat and Hombifine was found to be close to 180 nm which implies a value for x (Rs /rc) close to 80. Using X ) 80 and m ) 0.8 it is obvious from Figures 4 and 5 that Titanias Hombikat and Hombifine can be the only two substrates on which heterogeneous nucleation of zeolite A particles can take place. This was indeed the case and is reflected in their particle size distribution (Figure 1) and was also observed in the micrographs (not shown) taken at 3 h in the synthesis process. EDAX analysis of these samples showed that Ti, Si, and Al were present at relatively high concentrations indicating the growth of zeolite A film on the substrate. In contrast, for all other substrates SEMs showed well-formed cubes of zeolite A crystals, whereas EDAX showed no trace of any substrate. This proves clearly that the seed particles were completely covered by the zeolite crystals. 4. Conclusions It was found that the contact angle between the substrate, liquid, and zeolite A along with ratio of the size of the substrate to that of the critical nucleus plays an important role in determining nucleation and growth rates of zeolite A over the substrates. Titania Hombikat and Titania Hombifine were found to be the only substrates that allowed for the nucleation and subsequent growth of zeolite A crystals over them. It was found that the zeta potential of these substrates goes to zero at the pH conditions at which synthesis takes place. This leads to their agglomeration and, consequently, a large mean radius. This in turn increases the ratio of the size of the substrate to the critical zeolite A nucleus, which was found to be critical in heterogeneous nucleation. Also, these substrates have a low contact angle with the zeolite A embryo. These two factors coupled together facilitate the nucleation and growth of zeolite A on these substrates. However, it was also found that though the heterogeneous nucleation energy barrier was considerably lower than homogeneous nucleation energy barrier in the case of these substrates, the heterogeneous nucleation rate of zeolite A was still lesser than that of that of homogeneous nucleation rate. Acknowledgment. The authors are grateful to Professor James Boerio and his students at the Department of Materials Science and Engineering in University of Cincinnati for their help in measuring contact angles. Nomenclature AH ) Hamaker constant (kg.m2/s2) H ) interparticle distance (m) Rpr ) effective interstitial pore radius between the particles in a packed bed RS ) radius of the substrate (m) Sij ) interfacial surface area between phases i and j (m2) Vi ) volume of species i (m3) f(m,x) ) ratio of free energy change for heterogeneous nucleation to homogeneous nucleation gr ) ratio of heterogeneous to homogeneous nucleation rates h ) height of liquid rise (m) m ) cosine of contact angle
Brar et al. Q ) nucleation rate r ) radius of the particle/embryo (m) rc ) critical radius (m) x ) ratio of substrate size to the critical embryo size ∆G ) total free energy change (kg.m2/s2) ∆G* ) free energy change for heterogeneous nucleation (kg.m2/s2) ∆Ghom ) free energy change for homogeneous nucleation (kg.m2/s2) ∆GV ) specific free energy change associated with the liquid-solid phase change per unit volume (kg/m.s2) Greek Symbols κ ) Debye-Huckel parameter (m-1) o ) dielectric constant of the medium (kg m2/(volt.s)2) Ψo ) zeta potential (volts) γij ) surface tension between phases i and j (J/m2) φ ) surface area shape factor β ) volume shape factor η ) viscosity of the liquid (kg/m.s) ω ) angular velocity of the spiral (s-1) γiLW ) Lifshitz-van der Waals surface tension component (J/m2) γiAB ) Lewis acid/base surface tension component (J/m2) γi+ ) Lewis acid component of surface tension (J/m2) γi- ) Lewis base component of surface tension (J/m2) θ ) contact angle between two different materials References and Notes (1) Chernov, A. A. Modern Crystallography III-Crystal Growth; Springer-Verlag: Berlin, 1984. (2) Mutaftschiev, B. In Handbook on Crystal Growth; Hurle, D. T. J., Ed.; North-Holland: Amsterdam, 1993; p 187. (3) Volmer, M. Kinetik der Phasenbildung; Steinkopff: Dresden/ Leipzig, 1939. (4) Becker, V. R.; Doring, W. Ann. Physics 1935, 24, 719. (5) Frenckel, J. In Kinetic Theroy of Liquids; Oxford University Press: New York, 1946; p 366. (6) Zeldovich, Y. B. J. Exp. Theor. Phys (Russ.) 1942, 12, 525. (7) Hillig, W. B. In Growth and Perfection of Crystals; Dormeus, R. H., Roberts, B. W., Turnbell, D., Eds.; Wiley: New York, 1958; p 350. (8) Wood, G. R.; Walton., A. G. J. Appl. Phys. 1970, 41, 3027. (9) Coriell, S. R.; Hardy, S. C. J. Cryst. Growth 1971, 11, 53. (10) Jones, D. R. H. Philos. Mag. 1973, 27, 569. (11) Hardy, S. C. Philos. Mag. 1977, 35, 471. (12) Tsao, J. Y. Material Fundamentals of Molecular Beam Epitaxy; Academic Press: San Diego, 1993. (13) Van Oss, C. J.; Chaudhury, M. K.; Good, R. J. Chem. ReV. 1988, 88(6), 929. (14) Reed, T.; Breck, D. W. J. Am. Chem. Soc. 1956, 78, 5972. (15) Available on the Web at “http://www.thermoarl.com/dmsnt.htm”. (16) Wu, W.; Nancollas, G. H. J. Colloid Interface Sci. 1996, 182, 365. (17) Overbeek, J. T. G. In Colloid Science; Kyuyt, H. R., Ed.; Elsevier: Amsterdam, 1952. (18) Fletcher, N. H. J. Chem. Phys. 1958, 29, 572. (19) Chen, W. H.; Hu, H. S.; Lee, T. Y. Chem. Eng. Sci. 1993, 48(21), 3683. (20) Siegel, R. W.; Ramaswamy, S.; Hahn, H.; Zongquan, Li; Ting, Lu J. Mater. Res 1988, 3(6), 1367. (21) Washburn, E. W.; Phys. ReV. 1921, 17, 273. (22) Ku, C. A.; Henry, J. D.; Siriwardane, R.; Roberts, L. J. Colloid Interface Sci. 1985, 106, 377. (23) Giese, R. F.; Costanzo, P. M.; an Oss, C. J. Phys. Chem. Minerals 1991, 17, 611. (24) Wu, W.; Nnacollas, G. H. Colloid, J.; Interface Sci. 1998, 199, 206. (25) McCabe, W. L.; Smith, J. C. Unit Operations of Chemical Engineering; McGraw-Hill: New York, 1976. (26) Hunter, R. J. Foundations of Colloid Science; Clarendon Press: Oxford, 1987; Vol. 1.
