Langmuir 1986, 2, 251-255
251
Nucleation and Growth of Monosized Ti02 Powders from Alcohol Solution J. H. Jean and T. A. Ring* Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 Received J u n e 25, 1985. I n Final Form: September 30, 1985 The nucleation and growth phenomena in the generation of monodisperse TiOz powders by the hydrolysis of Ti(OC2H5),in ethanol solution have been investigated. Induction time was measured by noting the time of an abrupt change in the turbidity of the reacting solution. Shorter induction times were observed with higher reactant concentrations. The growth rate was measured in situ by photon correlation spectroscopy and compared with transmission electron microscopy. The rate-limitingstep during growth is the liquid-phase diffusion of polymeric species to the surface of the particles.
Introduction There are three regimes in the generation of monodisperse particles for use as pigments and ceramic powders.' The first is induction time, during which the reaction slowly generates molecules of the solid. The concentration in solution builds up until a critical supersaturation is reached, when nucleation occurs. A relatively short nucleation period produces a narrow size distribution of nuclei and relieves the supersaturation to below the critical value, preventing further nucleation. After nucleation, growth proceeds until the reaction stops due to equilibration. Depending on the rate-limiting step during growth, the particle size distribution may become narrower or remain constant as growth proceeds. Several types of monodisperse powders (e.g., Ti02,2 SO2: BaTiO,,, Zn0,4 Zr024)have been generated by the hydrolysis of metal alkoxides in alcohol solutions. However, the principles of nucleation and growth that govern the formation of monodisperse powders are poorly understood. This study describes experiments that investigate nucleation and growth phenomena for the TiOz system. A measurement of the induction time was obtained by noting the time when an abrupt change in turbidity occurred in the reacting solution. Growth rates were measured by both in situ photon correlation spectroscopy (PCS) and electron microscopy of dried samples in which the reaction had been stopped by dilution in propanol. Experimental Section Experiments were performed using the hydrolysis of titanium tetraethoxide in alcohol solution. The reaction proceeds by a stepwise hydrolysis5
C&@H
Ti(OC2H5)4+ 4H20 Ti(OH)4+ 4C2H50H to produce Ti(OH)4.This undergoes condensation, eliminating water to give
cfi@H
Ti(OH)4 TiO2.XHzO(solid)+ (2-X)H20 The precipitation product is controlled by the ratio of the initial concentration of H20and Ti(OC2H5)4.6JWhen the ratio is less than 2.5, a variety of polymers are formed. TiOz particles are precipitated out when the ratio is greater than 2.5. Materials. All glassware was cleaned by soaking in chromic acid followed by repeated rinsing in deionized water, after which (1) Lamer, V. K.;Dinegar, R. H. J. Am. Chem. SOC.1950, 72, 4847. (2) Barringer, C. A.;Bowen, H. K. J.Am. Ceram. SOC.1982,65,12C-
---.
100
(3) Stober, W.; Fink, A. J . Colloid Interface Sci. 1968, 26, 62. (4) Tormey, E. S.; Pober, R. L.; Bowen, H. K.; Calvert, P . D. 'Advances in Ceramics";Manges, J. A., et al., Eds.; American Ceramics Society Press: Columbus, OH, 1984; Vol. 9, p 140. (5) Ishino, T.;Minami, S. Tech. Rep. Osaka Uniu. 1953, 3, 357. (6) Winter, G.J. Oil Color Chem. Assoc. 1953, 36, 689, 695. (7)Boyd, T.J. Polym. Sci. 1951, 7 , 591.
it wasdried in air at 110 "C overnight. The deionized water used had a specific resistance of lo6 R cm. Absolute reagent grade ethanol (200 proof) was used as a solvent and titanium(1V) ethoxide was obtained from Alfa Products, Danvers, MA. Both were used without further purification. All solutions were filtered with a 0.22-pm Millipore filter. All experiments were performed at 25 i 2 O C in a glovebox under nitrogen atmosphere.
Induction Time The induction time for the reaction was measured at various reactant concentrations by using a Spectronic 21 at a wavelength of 690 nm. The reactants dissolved in equal volumes of 200-proof ethanol were quickly injected into a tee mixing section and then into the optical cell (5 cm3) of the Spectronic 21 by using a pair of hypodermic syringes operated by a single plunger. Mixing occurred in less than 0.5 s. A strip chart recorder monitored the optical density as a function of time. The time when the optical density increased abruptly was referred to as the induction time. Typical curves for the change of turbidity with time are shown in Figure 1. The turbidity remains constant until particle size and particle number density are large enough to scatter sufficient light to be detected by the instrument. Induction time decreases with increasing concentration of either H20 or Ti(OC2H,),. A plot of the induction time data is shown in Figure 2. Analyzing the slopes, we find that induction time, I in seconds, can be given by the following equation based on the molar concentration of reactants.
I = 0.33[Ti(OC2H5)4]-2[HzO]-4 (1) Following the induction period, turbidity increases continuously. The slope of the turbidity curve increases with the concentration of either chemical reactant. With the addition of 20 mL of [Ti(OC,H,),] = 0.075M and [H20] = 0.4M mixed with a magnetic stirrer, the induction time was 3650 s. One hour after the induction time ended, the mean particle size was 0.3725 pm and the standard deviation was 16.25%. This compares with an induction time of 3780 s, a mean particle size of 0.385 pm, and a standard deviation of 13.8% for rapid mixing. Therefore, mixing rate does not significantly affect induction time for long induction times. Turbidity as measured by the Spectronic 2 1 changes only when the particle size is greater than one-tenth of the wavelength of incident light.8 The wavelength of incident light was 6900 A, one-tenth of which is still far larger than the size of nuclei calculated from classical nucleation theory: i.e., -20 A. Thus, the induction time investigated (8) Maron, S.H,; Pierce, P. E.; Ulevitch, I. N. J . Colloid Sci. 1963,470.
0743-7463/86/2402-0251$01.50/0 0 1986 American Chemical Society
Jean and Ring
252 Langmuir, Val. 2, No. 2, 1986
I
Table I. Particle Size, Number Density, and Yield vs. Reactant Concentration 1 h after Induction particle Ti(OC2H,),, H,O, particle yield, no. density, M M size, um % 10’O cm-3 0.4 0.43 0.075 0.385 6.6 0.5 0.51 0.425 10.3 0.99 0.460 26.1 0.6 1.21 0.7 0.490 38.8 1.31 0.524 51.3 0.8 1.91 0.485 59.2 0.9 68.1 1.0 2.58 0.460
H 2 0 (M) 0 ’ 0 ‘09 ‘07
306 105
i ti
0.1
0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.366 0.449 0.452 0.478 0.456 0.454 0.460
8.4 24.5 33.9 43.2 54.0 60.4 65.6
0.85 1.32 1.83 1.94 2.80 3.13 3.25
0.125
0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.480 0.477 0.477 0.472 0.447 0.435 0.428
18.0 24.7 36.8 42.1 51.3 60.8 66.9
1.00 1.40 2.08 2.45 3.53 4.53 5.25
0.15
0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.462 0.487 0.488 0.494 0.450 0.440 0.420
19.8 36.6 48.6 60.0 68.1 72.2 78.0
1.23 2.34 3.00 3.68 5.50 6.25 8.35
0.2
0.6 0.7 0.8 0.9 1.0
0.490 0.496 0.465 0.428 0.428
72.3 77.0 81.0 83.3 87.7
6.00 6.18 7.90 10.44 11.00
Figure 1. Turbidity vs. reaction time, 0.125 M Ti(OC2H5)4.
i
TI (OGH,),
t
0
0.075 0.1
5
(M)
H20 (M)
7
0
04
0
0.5
I HzO(M) T I (OCZH& (M) CONCENTRATION
Figure 2. Induction time vs. reactant concentration.
by the change of turbidity is a combination of the induction time for nucleation, the time of the nucleation period, and the time for growth up to a size that could be detected by the instrument. When the particles are spherical and monodisperse, turbidity, To, is a function of particle number density and size, as given belows where N is the particle number density, K , is the Mie scattering coefficient, and r is the particle radius. The turbidity for a system with a low particle number density must have a large particle size. Hence, growth must play a more important role in the induction period for systems with lower particle number densities. Therefore, the particle size measured at the time when turbidity changes abruptly is smaller at higher particle number densities. For this reason, caution should be exercised in interpreting the chemical reaction kinetics from these induction time results. Growth Rate The variation of mean particle size with time was measured in situ using a Malvern photon correlation spectrometer (PCS) operating at an angle of 90” and a wavelength of 638 nm. The solutions were prepared in the
same way as those in the induction time experiments and injected into the sample cell of the PCS unit. Size measurements were made every 30 s by using sample times between 50 and 100 ps and an experimental duration of lo7ps. Generally, the shorter sample time was used at the higher concentration of either H 2 0 or Ti(OC,H,),. Multiple scattering was minimized by low reactant and particle concentrations. The growth rate was confirmed by transmission electron microscopy (TEM) using a Philips Model 300C instrument. T o stop growth, an aliquot of the solution was removed and diluted fourfold with 2-propanol. It was at once put into a tube containing a copper grid coated with a carbon film and centrifuged at 3000 rpm for 2 min. The grid was removed from the tube and rapidly dried with filter paper. The particle size distribution was not altered by aging in 2-propanol for up to 15 min. The particle size distribution was obtained from analysis of electron micrographs using an image analyzer. Generally, 200-300 particles were sized for each sample which gives a size distribution with an expected accuracy of 1%.15 The yield was determined by atomic adsorption analysis (9) Walton, A. G. “The Formation and Properties of Precipitates“; Wiley Interscience: New York, 1967. (IO) Munro, D.; Goodall, A. R.; Wilkinson, M. C.; Randle, K.; Hearn, J. J . Colloid Interface Sci. 1979, 68, 1. (11) Mates, T., M. S.Thesis, MIT, 1985. (12) Overbeek, T. Th. G. Adu. Colloid Interface Sci. 1982, f5, 251. (13) Firsch, H. L.; Collins, F. C. J . Chem. Phys. 1952, 20, 1797. (14) Nielsen, A. E.; “Kinetics of Precipitation”;Pergamon Press: Oxford, 1964. (15) Stockham, J. D., Fochtman, E. G., Eds. “Particle Size Analysis”; Pergamon Press: Oxford, 1977.
Langmuir, Vol. 2, No. 2, 1986 253
Nucleation and Growth of TiO,Powders Table 11. Growth Rate. K,by PCS and TEM for Various Reactant Concentrations conm. M erowth rate
T 3 pcS li(OC&4 A D
v o
0.4 0.4 0.4 0.5
0.15 0.1 0.075 0.075
8.3 3.0 2.29 5.0
A
v
H20
-
0.15M0.4M O.IM 0.4M 0.075M 0 . 4 M 0.075M 0 . 5 M
1.39 1.1 0.89 1.5
(AA) of the supernatants. The particle number density was calculated from the mean particle size and yield, assuming that only singlets were present and using 3.1 g/ cm3 for the particle density. The powder sizes and yields (given in Table I) were measured 1b after the end of the induction time for those conditions. The mean particle sue obtained is dependent on (a) particle number density and (b) growth rate. There is no significant relation between particle size and the concentration of either reactant shown by the results in Table I. Particle number density is determined by the nucleation rate and the length of the nucleation period. It increases with the concentration of either y20or Ti(OC,H,), according to the results given in Table I. The yield also increases with the concentration of either reactant. The yields given in Table I can be used to calculate the equilibrium constant, Kq
ICes= [Ti(OC2H5)r]~'[H201~Z
Figure 3. Mean size v8. reaction time.
(3)
for the overall reaction Ti(OC,H,),
-
+ 4H20C&OH TiOn(s) + 2H20 + 4C2H50H
*
(4)
The value of the equilibrium constant was 400 100 M" for the conditions listed in Table I. The range in values is explained by the fact that the low concentration reactions require more than 1h for completion, giving rise to spurious equilibrium constants for those conditions. Typical plots of the mean particle size measured by PCS vs. time are shown in Figure 3. Each plot is composed of four regions. In the first region, insufficient data were obtained for PCS analysis. These induction times as measured by PCS are almost the same as those measured by the Spectronic 21. In the second region particle ske increases linearly with time; in the third, reduced growth rates are observed. In the fourth region, insufficient data are obtained, where particle size is too great to be detected by the simple Rayleigb scattering themylo applied in conventional PCS analysis. The average slope (KPcs)in the second region varies from 2.29 X lo4 to 8.3 X lo4 pm/s and increases with increasing concentration of either reactant, as shown in Table 11. Parts A-F of Figure 4 are typical TEM pictures of the particle size distributions generated at various times after the induction time. Table I11 shows the image analyzer results (mean size and standard deviation) for various times after the induction time. The mean size data from Table I11 are plotted in Figure 3 for comparison with the
Figure 4. T E M photos of product, 0.15 M Ti(OC,H,),/0.4 M H,O. Time after induction: (A) 180 min; (B) ,120 min; ( C ) 90 min; (D)60 mis; (E) 30 min; (F) 15 min (bar = 5 rm).
PCS results. The TEM mean size shows the same four regions observed with the PCS results; however, the TEM sizes are always smaller than the PCS sizes. The average slope (KmM) in the second region varies from 0.89 to 1.5 x lo4 pm f s and increases with increasing concentration of either reactant as shown in Table 11. Figure 5 is a plot of the standard deviation divided by the mean size as growth proceeds. For all conditions the
Table 111. TEM Mean Size and Standard Deviation VU. Reaction Time time. min H 2 0 Ti(0C2HS), 2 5 10 15 20 30 45 0.3145 0.3553 0.2773 0.4143 0.4523 0.4 0.1996 0.2159 i, pm 0.15 o/i,% 27.92 25.89 21.11 20.11 18.13 15.17 14.20 0.4 0.1 P. um 0.1355 0.2593 0.2066 0.2291 0.1498 0.2930 0.3396 .~ 16.33 18.17 17.30 23.02 16.20 13.80 c/i,% 24.70 0.2412 0.2650 0.1542 0.1931 0.3360 0.2776 0.4 i, pm 0.1426 0.075 19.57 18.56 17.43 16.80 20.32 21.13 c/i,70 23.60 0.2OW 0.2545 0.3030 0.1296 0.1795 0.3130 0.4000 0.5 i,p m 0.075 14.35 12.59 13.17 11.18 18.50 16.50 c/i,% 19.50 m ncn M -------, --
..
60
90
120
0.4623 13.20 0.3667 12.50 0.3850 13.80 0.4250 10.51
0.5387 13.40 0.4218 12.60 0.4150 14.14 0.5000 10.20
0.6040 12.80 0.4670 11.60 0.4370 14.10 0.4860 10.00
Jean and Ring
254 Langmuir, Vol. 2. No. 2, 1986
r
T
a
.
.
.
t
50
.
.
.
*
~
100
. . . . i . . * T
50
I50
100
Figure 5. Standard deviation vs. reaction time.
I50
TIME(min1
TIME lminl
Figure 7. Reciprocal standard deviation vs. reaction time. Table IV. Diffusion Coefficisnte fmm ChmnomPI Analysis mncn. M mncn. M H20 Ti(OC2Hd, D. c"/s H20 Ti(OC2H.), D,cm2/s 0.4 0.5
0.075 0.075
3.6 X IO* 2.9 X IO*
0.4 0.4
0.1 0.15
1.35 X 10' 0.7 X 10'
the suspension 200 min after mixing. Very large aggregates are observed in equilibrium with smaller particles. If a sterically hindering surfactant, hydroxypropylcellulose (HPC), is used during nucleation and growth to prevent agglomeration, a pattern like that in Figure 6A is seen. Photon correlation spectroscopycannot distinguish single particles from aggregates and thus gives the aggregate size, which is much larger than the TEM size and has a steep slope at long times, when the reaction should be completed. For this reason the TEM data are expected to be the more accurate of the two measurements. The decrease in standard deviation of the particle size distribution with growth time, as shown in Figure 5, is charaeteristic of diffusion-limited g10wth.l~'~A linear plot of (u/r)-I vs. time'* as shown in Figure 7 is another test of diffusion control. This plot has two linear sections. The fimt section, occurring at short times, is of interest because this is where most of the growth occurs. The average slope of the first linear section ranges from 7.8 x lo4 to 25.2 x 10-4 S-1. Chronomal analysis" was applied to the TEM data in Figure 3 to find the rate-limiting stepduring the growth of particles from solution. Constant particle number density, uniform particle shape, and narrow particle size distribution during growth are required for this analysis. The TEM photos in Figure 4A-F show that this system fulfills those requirements reasonably well. If the diffusion of TiO, molecules is the rate-limiting step, the growth rate can be expressed as d r / d t = (uD(C - S,))/r (5) Figure 6. Opticnl micrograph of product (A) with HPC (bar = 20 rm) and (B)without HPC (bar = 50 rm).
width of the particle size distribution decreases with time, ending in an asymptotic section in which the widths of the particle size distributions are essentially constant at -10% to 14%.
Discussion The growth data shown in Figure 3 suggest that either the PCS data or the TEM data are incorrect. The PCS data were taken in situ and might be expected to be better than the TEM data, which were taken on particles that had been subjected to high vacuum and electron beam heating. Indeed, Mates" has shown that a 30% shrinkage occurs upon drying a t 80 'C in air; however, more than a 30% difference in PCS size and in TEM size are observed for long times. This large size discrepancy is due to aggregation. Figure 6B is an in situ optical micrograph of
where u is the molar volume of TiO,, D is the diffusion coefficient, r is the radius, C is the concentration, and So is the solubility of precipitate. Because it is difficult to monitor the change of TiOrxH,O concentration in solution with time, a new variable, a d , the degree of reaction, is introduced as ad
= (CO - o/(cO- SO)
(6)
where C is the total concentration of precipitate generated by the reaction, and Co Socan be obtained by the multiplication of the initial concentration C, with the yield as shown in Table 1. For this system a good approximation for the dependence of the degree of chemical reaction on time is
-
ad
= (r(O/rds
(7)
where ro is the equilibrium radius. Practically, ro was selected when the particle size reached a limiting value, in this ease -120 min after the end of induction time. By
Langmuir, Vol. 2, No. 2, 1986 255
Nucleation and Growth of TiOz Powders
TIME(min)
Figure 8. Chronomal for diffusion vs. reaction time.
combination of eq 5-7 an equation that is a function of a d is obtained
t = KdId(ad)
(8)
where Id(ad), the chronomal of this reaction, is given by Id(CYd)
1 2
- h [I - a d / ( l
=
J u d X-lI3
(1- X - ' ) dx
+ (ud'/3)3]- 3 tan-'
[3/(1
(9)
+ 2ad-1/3)] (10)
and where Kd is Kd = ro2/3UD[Co - SO]
(11)
and is obtained from the slope of the Id vs. t line. Several plots of I d vs. t are given in Figure 8, based on previous analysis. It is found that the curves of I d vs. t are always linear and that their correlation coefficients (P) are greater than 0.98. This suggests that diffusion in solution is the rate-limiting step. Chronomal analysis for interface control on an order of 2-4 was also performed. In each case the plots were nonlinear, indicating that this
was not the rate-controlling step. The diffusion coefficients obtained from the slope of the chronomal analysis are listed in Table IV. These diffusion coefficients are several orders of magnitude lower than molecular diffusion in ethanol. One possible reason for these low diffusion coefficients is that the diffusing species is a high molecular weight polymer. However, the polymer would have to be larger than the product particles for this to be the case. Another possible reason is that the diffusing species is not in a stagnant liquid but diffusing against a counter-flux of condensationproducts (i.e., H20),leaving the particle. The decrease of diffusion coefficient with increased reactant concentration observed in Table IV may result from an increase in the counter-flux of water with increased reactant concentration. This counter-flux of water may continue for a long time, since the particles continue to grow for up to 16 h for very low reactant concentrations. This counter-flux of water may be responsible for the finite but small growth rates observed in Figure 3 at long times.
Conclusions To produce monosized particles with the system studied, the nucleation event must produce between 4 X lo9 and 11 X 10'O particles/cm3 and the growth rate (KTEM) must be between 0.9 X and 1.5 X lo-* pm/s. Diffusionlimited growth is necessary to produce these monosized particles, since the nucleus size distribution becomes narrower during growth by this mechanism. The diffusion coefficient measured by chronomal analysis is much smaller than that for molecular diffusion in ethanol. A possible reason is that a counter-flux of water leaving the particle slows the diffusion of the precipitation product. Acknowledgment. We acknowledge the constructive criticisms of Prof. T. Th. G. Overbeek. Funding for this study has been provided by the National Science Foundation under Grant MEA-8310530. Registry No. TiOz, 13463-67-7;Ti(OC,H,),, 3087-36-3.
