J. Phys. Chem. 1995, 99, 5639-5644
5639
Growth of Nanometric Gold Particles in Solution Phase Ram Seshadri? G. N. Subbanna,’ V. Vijayakrishnan2 G. U. Kulkami? G. Ananthakrishna,’ and C. N. R. Rao*9?9* Solid State and Structural Chemistry Unit, CSIR Center of Excellence in Chemistry, and Materials Research Center, Indian Institute of Science, Bangalore 560 012, India Received: January 26, 1995@
The time evolution of colloidal gold particles in the nanometric regime has been investigated by employing electron microscopy and electronic absorption spectroscopy. The particle size distributions are essentially Gaussian and show the same time dependence for both the mean and the standard deviation, enabling us to obtain a time-independent universal curve for the particle size. Temperature dependent studies show the growth to be an activated process with a bamer of about 18 kJ mol-’. We present a phenomenological equation for the evolution of particle size and suggest that the growth process is stochastic.
In the present study, we have used chiefly transmission electron microscopy since only microscopy allows us to obtain Interest in colloidal metal particles exemplified by aqueous the complete particle size histograms. Scanning tunneling gold sols dates back at least to the time of Michael Faraday, microscopy (STM) of gold sols spotted on graphite substrates who coined the term “finely divided metals” and recognized yield similar PSDs and this served as a check on the reliability that the different colors of gold sols could be indicative of of PSDs obtained from electron microscopy. The mean radii different sizes or states of aggregation of the particles. In the of the gold particles can be obtained from other techniques such state of matter comprising particles of a few tens to a few as ultracentrifugation, light scattering, electrophoresis, and thousand atoms, the behavior is known to be distinct from the absorption spectroscopy, but none of these techniques yields bulk as well as from individual atoms. In recent years, there the histogram of particles in the size range.of interest to us. has been a resurgence of interest in this intermediate state of We have however employed electronic absorption spectroscopy matter from several points of view. There is considerable to extend the results obtained by electron microscopy. interest in nanoparticles as a distinct state of matter, with We have followed the evolution of the PSDs as a function particular reference to their structure and reactivity.’ A question of time and of temperature for nanometer-sized gold particles that has attracted attention is whether there is a transformation dispersed in an aqueous sol phase. Surprisingly, we find that from the metallic to the nonmetallic state with decrease in cluster the PSDs are well represented by Gaussians with the mean ~ i z e . ~Secondly, ,~ aggregation of such particles into fractaldiameter (4 and the standard deviation (T showing the same like structures has been the focus of some studies in the past time dependence, thus allowing us to represent the entire time decade or An aspect of some importance in the context evolution data by a universal curve. We have investigated this of metal particles is the phenomenon of nucleation and growth aspect in some detail, and we propose a phenomenological in the nanometer regime, which can be effectively investigated equation governing the evolution of the PSDs. Despite the fact today by employing techniques such as high-resolution electron that the temperature dependence of the growth could be studied microscopy and scanning tunneling microscopy. The subject over a small range due to experimental limitations intrinsic to of nucleation and growth of particles of micrometer dimensions the system, it has enabled us to confirm that the growth process in condensed phases has been the focus of much a t t e n t i ~ n . ~ . ~ is activated. To our knowledge, there have been very few such studies in
Introduction
the nanometer regime. We have chosen an aqueous gold sol for such a study in the belief that it is eminently preferred over traditional condensed phase systems in terms of control and manipulation. Subnanometer gold sols have been the focus of some recent in~estigation.~,’ Another aspect that provoked our interest to examine the distribution of particle sizes at this length scale is whereas aggregates of metal particles exhibit a scaling regime over the length scale of 100-10000 nm with a characteristic fractal dimension, the individual particles appear not to be in contact. There is thus a breakdown of the scaling regime at smaller length scales. The present study is significantly different from that of Turkevich et al.,8who studied bulk growth kinetics of gold sols in terms of volume fractions, rather than following the time evolution of the particle size distributions (PSDs) as we have done here. +Solid State and Structural Chemistry Unit. Materials Research Center. 5 CSIR Center of Excellence in Chemistry. * To whom correspondence should be addressed. Abstract published in Advance ACS Abstracts, March 15, 1995.
*
@
0022-365419512099-5639$09.00/0
Experimental Section Gold sols were prepared, following the method of Duff et a1.: using alkaline solutions of tetrakis(hydroxymethy1)phosphonium chloride (THPC from Fluka) to reduce dark-aged solutions of chloroauric acid (HAuC4, Loba-Chemie). The solutions were aged for at least a month. This ensures that hydrolysis is arrested and improves reproducibility between experiments. Typically, to 50 mL of aqueous 6.6 mh4 NaOH in a stoppered flask, 1 mL of THPC solution (1.2 mL of 80% THPC diluted to 100 mL) was added. After 2 min, 2 mL of 25 mM aged, aqueous chloroauric acid was added rapidly while shaking the flask. We avoided the use of Teflon stir bars as these scratch easily and are prone to contamination. The sols thus produced are typically very dilute, making the study of their growth a more tractable problem. The volume fraction of the particles was of the order of 10-4-10-5. The glassware (new and unscratched) was scrupulously washed with aqua regia followed by detergent-hydrofluoric acid mixtures before each experiment. Water used for the experiments and for making 0 1995 American Chemical Society
5640 J. Phys. Chem., Vol. 99, No. 15, 1995
stock solutions was distilled once in metal or glass and then distilled twice in a quartz apparatus. For the electronic absorption spectroscopy experiments, a sol with larger particles was also prepared, using 3 times the quantity of chloroauric acid. With passage of time, taking the addition of the chloroauric acid as zero time, the sol changes color from orange-brown eventually to dark red. After intervals of time, a drop of the sol was spotted on a carbon-coated copper grid for transmission electron microscopic investigations using a JEOL JEM 200CX. The uncertainty in time during the spotting was on the order of 2-3 min. The high dilution of the sol is necessary to ensure that the particles do not aggregate during drying. For recording UV/vis spectra, a 2-3 mL aliquot of the sol was periodically removed and its absorption spectra recorded in 1 cm cuvettes, following which the aliquot was discarded. The cuvettes were washed in aqua regia before and between measurements. The uncertainty in time was larger in these experiments, on the order of 5 min. STM measurements (as a check on electron microscopy) were carried out by spotting the gold sols on a highly ordered pyrolytic graphite (HOPG) substrate (a gift of Dr. A. Moore, Union Carbide), using a NanoscopeII. The images were acquired in the constant current mode. The disadvantage of this technique over electron microscopy is that fewer particles can be imaged and therefore one obtains poorer statistics for the PSDs. Further details are given in ref 3. The particle size distributions were obtained by considering the diameter of equivalent circles in the electron micrographs. In some cases, this was done using vernier calipers and magnifiers. Typically 100- 180 well-separated particles from one or two micrographs were considered. The variable temperature experiments were carried out by preparing the sol in a double-walled vessel with alcohol circulation at constant temperature. A Julabo thermostat, with the alcohol temperature maintained at better than 0.1 K was used for this purpose. Only a limited temperature range could be probed, since at higher temperatures, there are problems of solvent evaporation and coagulation of the particles.
Results and Discussion Structure and Morphology of the Gold Particles. A typical low-magnification transmission electron micrograph of the gold particles is shown in Figure la. At coarse magnification, the particles appear aggregated, and indeed, the structure resembles that studied by Weitz et al.9 We have not attempted to obtain a fractal dimension for this aggregate, since our interest is more to do with distributions of particle size. Contrary to what one would expect from Figure la, the individual particles are seen to be distinctly separate from one another at higher magnification (Figure lb), allowing us to determine their sizes. Such a crossover of the scaling regimes has been reported for silver particles in the literature.1° At small times (diameters around 2-5 nm) the particles seem to be spherical. Reasons for this could include the possible fluid nature of the smaller particles,' Le., the surface energies are not significant when the areas of the faces are very small. At larger times however (diameters x 20 nm, corresponding to the tails of the PSDs) faceting is clearly observed. The projected morphologies include vertextruncated triangles and squares similar to what is documented in the literature.l2 Particle Size Distribution and Time Evolution of the Particle Size. Since most of the particles were spherical, we were able to obtain reliable distributions of the particle diameters from electron microscopy and other techniques. In Figure 2,
Seshadri et al.
Figure 1. (a) Transmission electron micrograph of a gold sol grown for 60 min at 298 K shown at relatively low magnification. (b) The same particles at higher magnification showing well-separated individual particles.
we show the PSDs obtained from (a) electron microscopy and from (b) STM for a THPC reduced gold sol with particles in the subnanometer range. The similarity in the PSDs serves as a check on the reliability of the data. Electronic absorption spectroscopy is not suited for use in these small size ranges. In Figure 3, we show the electronic absorption spectrum in the visible region of a gold sol prepared by the THPC route at 0, 30, and 60 min the uncertainty in time being 2 5 min. For sols of very small particles, there are no distinct absorption maxima as can be seen in Figure 3 and the traditional Mie13 theory cannot be used to interpret the spectra. Color has been a traditional characterization tool for gold sols, but usually in a slightly larger size range. The colors are largely due to surface plasmon excitations. In Figure 4, we show the absorption spectrum of a sol with a mean diameter of 11.4 nm along with the first term of the Mie12 fit for small gold particles. The spectrum corresponds to particles shown in the electron micrograph in Figure 5, where the measured PSD with a Gaussian fit is shown as an inset. Although the Mie theory is not effective in this size regime as pointed out by Kreibig,14Doremus,15and others, we have obtained an average particle diameter from the ratio of the maximum absorbance to the absorbance at 440 nm, using the empirical correlation of Kreibig and Genzel,14and obtained a mean diameter of 10 nm. This size does indeed compare favorably with the value obtained from electron microscopy (1 1.4 nm). Since the absorption spectrum is well defined for larger particles, we have followed the time evolution of the spectra of a gold sol prepared using a greater initial concentration of gold
J. Phys. Chem., Vol. 99, No. 15, 1995 5641
Nanometric Gold Particles in Solution Phase
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(the initial chloroauric acid concentration was 75 mM, the other conditions being the same). Figure 6 shows representative spectra obtained at different times. The growth is initially very rapid and the uncertainty in time somewhat larger in these experiments. From the plot of the wavelength corresponding to the absorption maxima against the particle diameter as obtained from the Mie theory by Milligan and Morris16 and Chow and Z~kowski,'~ we have obtained the average particle diameters. We have plotted particle diameters against time plotted as an inset in Figure 6. We shall return to this inset later on in our discussion. The bulk of our results is based on the PSD data obtained from electron microscopy. The particle size distributions
Figure 5. Transmission electron micrograph correspondingto the sol whose absorption spectrum is shown in Figure 4. The inset is a histogram of the particle size distribution. The smooth curve is a Gaussian fit.
obtained by us at different times are shown in Figure 7a. At small times of about 30 min, the particles have a mean diameter of around 2 nm. The growth is initially quick, slowing down at longer times. After 240 min, the average particle diameter is about 12 nm. The distributions are nearly symmetric, suggesting that they can be fitted by Gaussians. Indeed, we find on doing so, that Gaussian distributions describe the PSDs very well. Attempts to use other distributions, for example, log-normal, were not as successful. We verified this by plotting the cumulative frequencies against the diameter, and against the logarithm of the diameter on a probability graph paper. This
Seshadri et al.
5642 J. Phys. Chem., Vol. 99,No. 15, I995
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2 30 50 80 98 99.99 Cumulative Frequency% Figure 7. (a) Particle size distributions of the gold sol at different times obtained from electron microscopy. The curves are the fitted Gaussians distributions. The areas under the curve have been normalized to unity. (b) Plot of the diameter and the log diameter against cumulative frequency, on probability graph paper for a typical growth time of 60 min. The lines are guides to the eye.
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is shown in Figure 7b for a typical time of 60 min. Small deviations from a straight line are seen in the plots of diameter against cumulative probability only at larger diameters. However, our large diameter statistics are less reliable because of the difficulty in resolving the larger particles due to overlapping images. The deviations in plots of the logarithm of the diameter against cumulative frequency (Figure 7b) may appear to be
small, but they are actually larger due to the logarithmic scale. A plot of the mean diameter, (4,as a function of t1I3 gives a nearly straight line (Itfit = 0.91) which is the expected time dependence for Ostwald ripening. However, we prefer not to attempt such a power law fit since the data do not run over many decades. Indeed, that the process is not Ostwald ripening is clearly borne out by the fact that the PSDs do not display the sharp cutoff on the size-axis expected from the LifshitzSlyozov-Wagner (LSW) theory of Ostwald ripening.'* A symmetric distribution from LSW theory is possible, but only at high volume fractions.'* In our studies, the volume fraction is so this does not apply. Since a Gaussian process essentially means that the underlying process is that of a sum of independent random events, the suggested growth process is stochastic. Plotting (4 as a function of the standard deviation, cr, for different times, we find that the mean and the u show the same time dependence (Figure 8a). This suggests that it should be possible to represent the PSDs by means of a variable scaled by the mean diameter. A plot of the normalized frequency (normalized by the area under the PSD curve) as a function of d/(d) for all times collapses onto a single curve, as shown in Figure 8b. To the best of our knowledge, this is the fiist growth kinetics which exhibits the same time dependence for both the mean and u. Any theoretical model for the growth should therefore incorporate these unusual features. Conventionally, growth kinetics are often described by partial differential equations for the distribution of particles. Such equations can be derived from a Master equation which in some way represents cluster-cluster aggregation where at most a few elementary clusters are m ~ b i l e In . ~the ~ present ~ ~ ~ situation, the growth kinetics is well described by a Fokker-Planck type equation, having the following form:
Nanometric Gold Particles in Solution Phase
J. Phys. Chem., Vol. 99, No. 15, 1995 5643
where and p(d) are the probability of growth and shrinkage per unit time, and the overbars - denote - the averages over the distribution. Often D = a(d) -t p(d) is used. This can be related to the mobility of the diffusing - monomers. - Since the growth process is new, identifying a(d)and p(S, requires a clear understanding of the basic growth process which is lacking at present. We therefore proceed to guess the form ofa(d), p(d) and D to obtain the desired rate law. We identify a(d)= d d ( t ) and D(d) = 2 D f r ) f ( t ) ,where the primedenotes the derivative with respect to time. Normally, a(& B(d) and D(d) are used as functions of d. However, for convenience of comparison, we have taken them to be functions oft. This gives
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where do is the initial diameter of the particle which grows with a functional fomflr) and can be identified as the growth of the mean particle diameter. The PSD that one obtains from the solution of the above equation is
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where d, is the mean diameter at infinite time and y is some rate. For the fit in Figure 9, we have used do = 1 nm, d, = 12 nm, and y = 0.035 min-’. We may regard do as the upper bound for the critical size of a stable nucleus. We now return to the inset in Figure 6. This inset shows the average particle diameter (from electronic absorption spectroscopy) as a function of time for experiments involving larger particles of gold, starting with a higher initial concentration of chloroauric acid. We obtain a reasonable fit of these data to the sigmoidal growth law given by equation 4. For this fit, we have used the parameters y = 0.125 min.-’, do = 1 nm, and d, = 43 nm. The larger value of y is indicative of the more rapid growth, due to the higher initial gold concentration. (We have maintained the same value of do = 1 nm because this might be some critical nucleus size.) The absorption data do not fit the growth law as well as the PSDs from electron microscopy, probably more due to the intrinsic errors in time as well as in average diameters obtained from absorption spectroscopy. However the fit in the inset of Figure 6 provides additional support to the model proposed in the text. It must be emphasized that the phenomenological growth law presented here is new although we are unable to present a better physical basis for it at the present time. We would expect that at small times, the particles are close to the minimum stable cluster size. For this reason, the particles with sizes beyond the critical size have fairly large inflow due to the large nucleation rates initially. In contrast, further growth of the particles (propagation step) is not likely to be equally fast since
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2 Figure 10. (a) PSDs of gold particles grown for 60 min at different temperatures. The curves are the fitted Gaussian distributions. (b) Data at different temperatures have been collapsed on to a universal curve, by using z = (d - (d))/u~ exp(-E/kBT).
it requires diffusion of monomers. This would explain why the deviations from Gaussian behavior are seen for smaller times. At larger times, one would expect the nucleation rate to have slowed down sufficiently to give rise to more symmetric distributions. Effect of Temperature on the PSD. We have studied the effect of temperature over the limited range 288-308 K, at a fixed time of 60 min, and obtained the respective PSDs (shown in Figure loa) along with (d) and B. We find that In B varies linearly with l / k ~ Timplying , the activated nature of this process within this temperature range. The activation energy works out to be of the order of 17.5 kJ mol-’. Using the a obtained from such a temperature dependence, we are the able to scale the independent Gaussian variable and collapse the PSDs at fixed time and different temperatures on to one curve as shown in Figure lob.
Conclusions The observations of a Gaussian distribution of particle sizes, having the same time dependence for both (d) and 0, suggest
5644 J. Phys. Chem., Vol. 99, No. 15, 1995
Seshadri et al. its time dependence is new and requires further investigation. The observed Gaussian distribution is not only consistant with the process being stochastic, but may also imply that the rates of nucleation and growth are well separated. An aspect worthy of mention is the nature of the structures formed on allowing the gold sol particles to occlude at long times, for example, by evaporating the sol on a glass slide. Figure 11 shows a scanning electron micrograph of a typical branched fractal-like structure so formed. The measured fractal (capacity) dimension of this structure obtained by the boxcounting method was 1.7. Such structures are to be contrasted with the micrographs in Figures 1 and 5, where the particles are well separated and do not seem to form ramified assemblies. Under different evaporation conditions, we are also able to obtain dendrites, usually with four arms and a smaller fractal dimension. The crossover from the fractal to the dendritic regime is of some interest and is presently being pursued by us.
References and Notes
Figure 11. Scanning electron micrograph of a fractal structure formed by evaporating a gold sol on a glass slide. This structure had a fractal dimension of 1.7.
that the basic processes contributing to the growth process at such small nanometric length scales are distinct from those at larger length scales, following traditional growth models such as Ostwald ripening. Earlier studies of evolutions of particle size distributions have chosen to assume Gaussian distributions and then follow their time dependence. Log-normal distributions are ubiquitous in situations such as growth from the vapor phase. As such, these unique features of growth of the nanometric gold particles could be characteristic of growth in solution phase, occurring over a relatively small temperature range. The temperature dependence implies that the process is activated. The small barrier is possibly associated with the typical length scales involved in these systems. The growth law provided to fit the observed particle size distribution and
(1) See for example: Faraday Discuss. Chem. Soc. 1991,92. Henglein, A. J. Phys. Chem. 1993, 97, 5457. (2) Halperin, W. P. Rev. Mod. Phys. 1986, 58, 533. Kubo, R.; Kawabata, A.; Kobayashi, S. Annu. Rev. Mater. Sci. 1984, 14, 49. (3) (a) Rao, C. N. R.; Vijayakrishnan, V.; Aiyer, H. N.; Kulkami, G. U.; Subbanna, G. N. J. Phys. Chem. 1993,97, 11157. (b) Kulkarni, G. U.; Aiyer, H. N.; Vijayakrishnan, V.; Arunarkavalli, T.; Rao, C. N. R. J. Chem. Soc., Chem. Commun. 1993, 1545. (4) Vicsek, T. Fractal Growth Phenomena, 2nd ed.; World Scientific: Singapore, 1992. (5) Gunton, J. D.; Miguel, M. S.; Sahni, P. S. In Phase Transitions and Critical Phenomena; Domb, C., Lebowitz, J. L., Eds.; Academic: New York, 1983; pp 267-482 and references therein. (6) Nielson, A. E. Kinetics of Precipitation; Pergamon: Oxford, 1964. (7) (a) Duff, D. G.; Baiker, A.; Edwards, P. P. J. Chem. SOC.,Chem. Commun. 1993,96. (b) Duff, D. G.; Baiker, A.; Edwards, P. P. Lungmuir 1993, 9, 2301. (8) Turkevich, J.; Stevenson, P. C.; Hillier, J. Discuss. Faraday SOC. 1951, 11, 55. (9) (a) Weitz, D. A.; Oliviera, M. Phys. Rev. Lett. 1984,52, 1433. (b) Weitz, D. A.; Huang, J. S.; Lin, M. Y.; Sung, J. Phys. Rev. Lett. 1985, 54, 1416. (10) Mukherjee,M.; Saha, S. K.; Chakravorty,D. Appl. Phys. Lett. 1993, 63, 42. (11) Iijima, S.; Ichihashi, T. Phys. Rev. Lett. 1986, 56, 616. (12) Kirkland, A. I.; Edwards, P. P.; Jefferson, D. A.; Duff, D. G. Annual Reports C ; The Royal Society of Chemistry: Cambridge, 1988; pp 247304. (13) Mie, G. Ann. Phys. 1908, 25, 377. (14) Kreibig, U.; Genzel, L. Su$ Sci. 1985, 156, 679. (15) Doremus, R. H. J. Chem. Phys. 1964,40, 2389. (16) Milligan, W. 0.;Morris, R. H. J. Am. Chem. SOC.1964,86,3461. (17) Chow, M. K.; Zukowski, C. F. J. Colloid Interface Sci. 1994,165, 97. (18) Jayanth, C. S.; Nash, P. J. Mater. Sci. 1989, 24, 3041. (19) van Kampen, N. G. Stochasiic Processes in Physics and Chemistry; North-Holland: Amsterdam, 1981. (20) Ananthakrishna, G. Pramana J. Phys. 1979, 12, 565.
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