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Particle Growth Kinetics in Zirconium Sulfate Aqueous Solutions Followed by Dynamic Light Scattering and Analytical Ultracentrifugation: Implications for Thin Film Deposition H. Co¨lfen and H. Schnablegger† Max Planck Institute of Colloids and Interfaces, Colloid Chemistry, Am Mu¨ hlenberg, D-14476 Golm, Germany
A. Fischer, F. C. Jentoft,* G. Weinberg, and R. Schlo¨gl Department of Inorganic Chemistry, Fritz Haber Institute of the Max Planck Society, Faradayweg 4-6, D-14195 Berlin, Germany Received November 2, 2001. In Final Form: January 28, 2002 Acidic aqueous solutions of Zr(SO4)2‚4H2O can be used to deposit nanocrystalline zirconium oxide films on functionalized surfaces. Because zirconium hydrolyzes easily, such solutions are potentially unstable toward colloid formation and precipitation. Particle growth (conditions: 2 or 4 mM Zr(SO4)2, 0.4 or 0.6 N HCl, T ) 323, 328, 333, or 343 K) was investigated using dynamic light scattering (DLS, in situ) and analytical ultracentrifugation (AUC, ex situ after quenching to 77 K and rethawing to 298 K). The AUC measurements revealed three stages of growth (all dimensions given are hydrodynamic radii): (1) coexistence of several discrete polynuclear complexes with rh ) 0.43-2.29 nm; (2) particle size distribution with a single sharp maximum; (3) above rh ≈ 260 nm rapid transition to polydisperse medium with particles up to 100 µm. The DLS measurements revealed a linear increase of the hydrodynamic radii (z-average of particle population) from 5 nm to 1000-2500 nm with rates of 0.01-0.6 nm‚s-1. The rates were proportional to the Zr(SO4)2 concentration, while the increase of the HCl concentration slowed or even inhibited growth. The apparent activation energy for this step was 136 kJ‚mol-1. From the induction period before detection of first particles, initial growth rates (rh < 5 nm) were calculated to be ≈1 × 10-4 to 5 × 10-3 nm‚s-1. Independent of the conditions, the two reaction rates were always proportional to each other, indicating linked rate laws. A 4 mM Zr(SO4)2 in 0.4 N HCl solution exhibited no particle growth at 323 K, but complexes of a constant radius (after 6, 12, and 24 h) of 1.16 nm were detected (AUC). Under these conditions, films were deposited and their thickness increased linearly with time, specifically by 2.1 × 10-4 nm‚s-1. This rate corresponds to the initial growth rate in solution. In contrast to films grown from media with significant particle growth, these films showed surfaces free of attached particles, cracks, and holes.
I. Introduction Thin films of zirconium dioxide play an important role as thermal barrier coatings and are potentially useful for optical, electrical, or sensor applications, or as solid electrolyte in fuel cells. Thus, there is a demand for zirconia thin films that are structurally uniform, dense, and adherent to the substrate. One recently developed method1,2 to make such ceramic layers uses aqueous zirconium sulfate dispersions to deposit zirconia nanocrystals on functionalized surfaces. Specifically, the surface of a silicon single crystal (wafer) is oxidized and coated with a self-assembled monolayer (SAM), an array of ordered long-chain (C16) hydrocarbon molecules. Bifunctional surfactant molecules3 are used to form this array, whereby trichlorosilyl groups (-SiCl3) help attach the hydrocarbon molecules to the oxidized silicon surface, and sulfonic acid (-SO3H, introduced after the formation of the SAM on the Si surface) groups provide a hydrophilic function at the monolayer-air interface.4,5 Such pretreated * Corresponding author. E-mail:
[email protected]. † Present address: Institute of Physical Chemistry, University of Hamburg, Bundesstrasse 45, 20146 Hamburg, Germany. (1) Agarwal, M.; De Guire, M. R.; Heuer, A. H. J. Am. Ceram. Soc. 1997, 80, 2967. (2) Shin, H.; Agarwal, M.; De Guire, M. R.; Heuer, A. H. J. Am. Ceram. Soc. 1996, 79, 1975. (3) Netzer, L.; Sagiv, J. J. Am. Chem. Soc. 1983, 105, 674.
wafers are immersed into acidic aqueous zirconium sulfate solutions, and a layer of zirconia nanocrystals with admixtures of basic zirconium sulfate is deposited within several hours.1 The films are dense and adherent and can be converted into purely tetragonal zirconia by calcination at 773 K for 2 h.1,2 As an example, immersion into a 10 mM Zr(SO4)2 solution in 0.6 N HCl for 24 h at 343 K gives a ca. 125 nm thick zirconia layer.1 Under these conditions, though, the deposition medium is not stable, and colloids or even precipitates are formed in the liquid phase while the wafer is immersed. Previous investigations showed that micrometer-sized colloids from the deposition medium are embedded in and attached to the nanocrystalline film, leaving unwanted holes behind when removed in a washing step.6 A gradient was found in the size of the grains forming the film, with the grains being 10 nm closest to the interface with the substrate and 2-3 nm at the zirconia film surface.1 It would be desirable to tune film properties such as thickness and zirconia crystallite size, and the question arises of whether this is possible by modifying the (4) Collins, R.; Sukenik, C. N. Langmuir 1995, 11, 2322. (5) Balachander, N.; Sukenik, C. N. Langmuir 1990, 6, 1621. (6) Fischer, A.; Jentoft, F. C.; Weinberg, G.; Schlo¨gl, R.; Niesen, T. P.; Bill, J.; Aldinger, F.; De Guire, M. R.; Ru¨hle, M. J. Mater. Res. 1999, 14, 3725.
10.1021/la0116286 CCC: $22.00 © 2002 American Chemical Society Published on Web 04/03/2002
Particle Growth Kinetics in Zr(SO4)2 Solutions
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deposition conditions. In this context, it would be helpful to understand the mechanism of film formation. Two pathways have been described for other systems:7-9 (i) ion-by-ion growth, i.e., heterogeneous nucleation occurs at the polar terminating groups of the SAM; (ii) cluster growth, i.e., first homogeneous nucleation occurs in the liquid phase and then small particles adsorb on the polar terminating group of the SAM. Understanding the colloidal chemistry of the deposition media is thus of great interest. Because zirconium salt solutions have a number of industrial uses,10 e.g., in the production of metal oxide powders, textile finishing, paper coating, polishes, cosmetics, emulsion paints, or antiperspirants, zirconium salt solution chemistry has been studied extensively.11-31 In general, zirconium(IV) cations have a strong tendency to hydrolyze in aqueous medium, and solutions typically turn cloudy and a precipitate is formed. Attempts have been made to identify the complexes that are formed in the hydrolysis reaction as well as the species that are formed in subsequent reactions. The research has focused on solutions containing anions such as chloride, nitrate, and perchlorate which are neither strongly complexing nor bridging. First proposals on the species in solution were made by Clearfield and Vaughan,12 who studied the crystal structure of ZrOCl2‚8H2O and ZrOBr2‚8H2O by X-ray diffraction. The authors described the zirconyl ion as a discrete tetrameric complex, [Zr4(OH)8(H2O)16]8+, and suggested that similar species may be present in solutions. Muha and Vaughan13 performed X-ray scattering experiments with 2 m ZrOCl2 solutions that had been aged for at least 18 h and confirmed the existence of the postulated complex. Their fit of the data could be improved by addition of eight chloride ions to give a neutral complex, consistent with the results obtained by Lister and McDonald,14 who observed little electromigration of zirconium species in hydrochloric acid. The existence of the tetrameric complex in zirconium oxychloride solutions was confirmed by Hannane et al.15 using NMR and Raman spectroscopies and by Singhal et al.16 and Hu et al.18 using small-angle X-ray scattering (SAXS), likewise in zirconium perchlorate solutions by Åberg and Glaser19 using NMR, and in zirconium nitrate solutions by Toth at al.20 using SAXS. A number of studies with different techniques such as titration,21,22 equilibrium ultracentrifugation,23,24 measurement of the diffusion coefficients,25 and light scattering26 gave slightly varying
polymerization degrees of 2-6 (with variations in conditions). The size (radius of gyration) of the tetramer as determined by SAXS was found between 3.8 and 5 Å,16,18,20 and it is the stable species over a wide range of conditions. Upon increase of temperature or pH, the tetramer oligomerizes, presumably in the first step to give an octamer15,27 of the constitution16 [Zr8(OH)20(H2O)24Cl12] and then to higher oligomers that will finally aggregate and precipitate. At 373 K, primary particles were 3-7 nm;28 secondary particles (aggregates of primary particles) reached 175-250 nm.29,30 The particle growth rate was decreased through the addition of HCl.18 The chemistry of zirconium sulfate solutions is different because sulfate not only strongly complexes with zirconium32,33 but is a potential bridging ligand and promotes polymerization.34,35 While cationic or neutral complexes prevail in chloride, nitrate, and perchlorate solutions, anionic14,36,37 mixed hydroxo sulfato complexes,35 also of polynuclear type, are formed in sulfate solutions. Hence, hydrous zirconia is not precipitated from these solutions but sulfates are, and the large number of possible sulfates,38 particularly basic sulfates,39-41 of different constitutions would suggest that many complexes of different constitutions may exist in solution. Consistently, no particular species have been reported as being stable over a range of conditions in zirconium sulfate solutions. Rather, the chemistry may be ruled by complicated equilibria,35 and the time frame for changes in these solutions40 indicates that equilibration is slow: Hauser42 observed precipitation in 0.5 M Zr(SO4)2 solutions only after 2 weeks, and Matijevic34 managed to delay the precipitation in 0.2 mM Zr(SO4)2 by 10 h, 2 days, or 4 days in the presence of 1, 2, or 4 mM HNO3, respectively. Heating promoted hydrolysis.43 The goal of this paper was to investigate the zirconium solutions used for the zirconia film deposition on SAMmodified substrates, specifically to study particle sizes as a function of zirconium concentration (2-4 mM), acid concentration (0.4-0.6 N), temperature (323-343 K), and time (up to 24 h). We used dynamic light scattering (DLS) as in situ technique to follow the growth of particles with a hydrodynamic radius larger than 5 nm (detection limit). Analytical ultracentrifugation (AUC) is an excellent tool to investigate particles with radii 97% purity, Alfa Chemicals, Karlsruhe, Germany) and aqueous hydrochloric acid (Merck, Darmstadt, Germany). Doubly distilled tap water was used for all preparation steps. Three aqueous stock solutions were freshly prepared by magnetic stirring of the respective components at room temperature: experiments I and IV-VII, 4 mM Zr(SO4)2 solution in 0.4 N HCl; experiment II, 4 mM Zr(SO4)2 solution in 0.6 N HCl; and experiment III, 2 mM Zr(SO4)2 solution in 0.4 N HCl. 2.Dynamic Light Scattering (Expts I-III in Table 1). The experiments were performed with a laboratory-built goniometer with temperature-controlled ((0.05 K) cuvette holders, an attached single-photon detector ALV/SO-SIPD, and a multiple tau digital correlator ALV 5000/FAST from ALV (Langen, Germany). The light source was an INNOVA 300 argon ion laser operated at λ ) 488.0 nm in single-frequency mode and powered at approximately 800 mW. Quartz cuvettes (Hellma, Mu¨lheim, Germany) were charged with the freshly prepared stock solutions by directly filtering them through ANOTOP filters (Merck, Germany) with 20 nm pore size. Placement of the cuvettes in the heatable holders is defined as t ) 0. The set (reaction) temperature was reached after about 1 min. Correlation functions were recorded every 30 s for approximately 800 min. 3. Analytical Ultracentrifugation (Expts IV-VI in Table 1). From the freshly prepared stock solution, 50 mL was transferred into a 100 mL glass vial (no stirring bar). The sealed vial was placed in a room-temperature silicon oil bath, which was then heated. “Reaction temperature” refers to the set temperature of the oil bath. The beginning of the heating is defined as t ) 0. Variations in the time span for the observation of the first milkiness (30-40 min) under seemingly identical conditions (expts IV and V) are explained by variations in heat transfer due to different bath volumes. After the desired reaction times, 2 mL of reaction medium was transferred into plastic vials with a Pasteur pipet. To prevent further particle growth after removal from the reaction medium, each vial was immersed in liquid nitrogen until the sample liquid was frozen. After thawing to room temperature, the sample liquid was injected with a syringe into acid-resistant titanium cells (in-house design). The cells were filled completely with ≈300 µL of the sample liquid. Supplement AUC experiments showed that the quenching was successful; i.e., no particle growth was observed after the thawed samples were kept at room temperature for at least 24 h. The experiments were designed to collect information before (expt IV) and during (expt V) colloid formation in the reaction medium at 343 K and to search for colloidal species in the visibly
data for T ) 328 K not shown
data for T ) 328 K not shown
reaction medium milky after 30 min; Si wafer removed after t ) 17 h
clear reaction medium at 323 K (expt VI). Two sets of samples were generated in expt VI, one set in the absence and one in the presence of a SAM-coated silicon wafer in the reaction medium, the latter to see if zirconia films can be deposited under these conditions, and, vice versa, to ensure that the presence of the wafers does not initiate nucleation. The SAM-coated silicon wafer was immersed into the reaction medium shortly before the start of the heating. Experiments IV and VI. A Beckman Optima XL-I analytical ultracentrifuge (Beckman-Coulter, Palo Alto, CA) equipped with on-line Rayleigh interference optics and UV/vis scanning absorption optics (200-800 nm) was used in order to detect nanometer-sized particles in the early stages of particle growth. All experiments were performed at 298 K and 60 000 rpm applying the Rayleigh interference optics for the detection of the sedimenting colloids and self-made titanium 12 mm 2.5° double sector centerpieces. Experiment V. An Optima XL-80K preparative ultracentrifuge (Beckman-Coulter, Palo Alto, CA) equipped with self-made turbidity optics similar to those described by Ma¨chtle47 and Mu¨ller48 was applied to detect particles in the range of 20 nm100 µm. For these experiments at 298 K, a linear acceleration profile of 60 rpm‚s-1 was applied for speeds from 0 to 40 000 rpm enabling the detection of even most polydisperse species. In contrast to all commercial analytical ultracentrifuges, the signal is recorded as a function of time at one position and not as a function of position. Self-made 12 mm titanium 1.5° monosector centerpieces were applied in the measuring cells. 4. Dynamic Light Scattering Data Analysis. The intensity autocorrelation functions g2(t), as obtained from the multiple tau digital correlator, were transformed into the corresponding amplitude autocorrelation functions g1(t) using Siegert’s relation49 (eq 1):
g1(t) ) sign[g2(t) - 1]x|g2(t) - 1|
(1)
The resulting g1(t) functions were converted into the corresponding distributions rh di(rh) of the apparent hydrodynamic radius rh (particle size) with a specialized version of an inverse Laplace transform program50 (eq 2): (47) Ma¨chtle, W. Analysis of Polymer Dispersions with an Eight CellAUC Multiplexer: High Resolution Particle Size Distribution and Density Gradient Techniques. In Analytical Ultracentrifugation in Biochemistry and Polymer Science; Harding, S. E., Rowe, A. J., Horton, J. C., Eds.; The Royal Society of Chemistry: Cambridge, 1992; pp 147175. (48) Mu¨ller, H. G.; Herrmann, F. Prog. Colloid Polym. Sci. 1995, 99, 114. (49) Berne, B. J.; Pecora, R. Dynamic Light Scattering; John Wiley & Sons: New York, 1976. (50) Schnablegger, H.; Glatter, O. Appl. Opt. 1991, 30, 4889.
Particle Growth Kinetics in Zr(SO4)2 Solutions g1(t) )
∫
∞
t)0
rh di(rh) exp(-Dq2t) d ln(rh)
Langmuir, Vol. 18, No. 9, 2002 3503 (2)
where D ) kT/(6πηrh), q ) 4πn/λ0 sin(θ/2), k ) Boltzmann’s constant, T ) absolute temperature, η ) solvent viscosity (at 0.4 N HCl and 323 K, 0.556 91 cP; at 0.4 N HCl and 343 K, 0.411 65 cP), rh ) hydrodynamic radius, λ0 ) wavelength of the laser (488.0 nm), and n ) refractive index of the solvent at the laser wavelength. The hydrodynamic radii (z-average) at the maxima of the size distributions were collected and plotted to determine their dependency on temperature, pH, and concentration. 5. Analytical Ultracentrifugation Data Analysis. The radial interferometric traces from the XL-I ultracentrifuge as well as the time-dependent turbidity signals from the Optima XL-80K ultracentrifuge were transformed into the sedimentation coefficient distributions via the definition of the sedimentation coefficient (eq 3):
s)
ln(rb/rm) ω2t
(3)
Figure 1. Particle size as measured by DLS vs time with temperature and zirconium sulfate concentration as parameters. Zr(SO4)2 concentration 2 or 4 mM; reaction temperature 323, 333, or 343 K; HCl concentration 0.4 N (expts I and III).
where rb ) the position of the laser detection beam, rm ) the position of the meniscus, ω ) angular velocity of the rotor, and t ) time. The turbidity signals had to be corrected for Mie scattering.51 Because the refractive index of the particles was not known, a quantitative correction was not possible and the resulting particle concentrations are thus only apparent. The sedimentation coefficient distributions were not corrected for the effects of diffusion. Hence, these distributions have apparent character with respect to polydispersity, and the polydispersity can be overestimated. However, these effects are considered to be negligible for the very large particles and comparable for the small ones so that comparisons between the particle size distributions for the early growth stages are possible. Finally, the sedimentation coefficient distributions were transformed into a particle size distribution using eq 4:
d)
x
18ηs Fp - Fs
(4)
where η ) solvent viscosity (at 0.4 N HCl and 298 K, 0.906 83 cP), Fs ) density of the solvent (at 0.4 N HCl and 298 K, 1.004 19 g‚mL-1), Fp ) density of the particles, and d ) the hydrodynamic particle diameter. The density of the particles had to be estimated, and as complexes of different constitution may be formed during hydrolysis, it can only be presumed that the average density is between the density of monoclinic ZrO2, F ) 5.66 g‚cm-3, and that of Zr(SO4)2, F ) 3.22 g‚cm-3. 6. Zirconia Thin Film Preparation and Characterization (Expts VI and VII in Table 1). The preparation of the zirconia thin films has been described by Fischer et al. in detail.6 The self-assembled monolayer was formed by immersing oxidized pieces of 2 cm2 single-crystal silicon wafer 〈100〉 (700 µm thickness, p-type, double polished) in a dilute solution of the surfactant, Cl3Si(CH2)16SCOCH3, in bicyclohexyl. The terminating thioacetate groups (-SCOCH3) at the monolayer-air interface were then oxidized using an aqueous solution of KHSO4‚KHSO5‚K2SO4 to give a sulfonic acid terminated (-SO3H) monolayer. The SAM-coated wafers were immediately transferred into a vial with 50 mL of the deposition medium, i.e., a 4 mM Zr(SO4)2 solution in 0.4 N HCl. The closed vial was then heated in an oil bath as described above. Deposition was performed in a clear medium (expt VI) or in a medium with precipitate formation (expt VII). After removal from the deposition medium, the specimens were rinsed thoroughly with water and dried under ambient conditions. The surface morphology and composition of the siliconsupported zirconia thin films were compared using scanning electron microscopy and energy-dispersive X-ray analysis (SEMEDX). SEM investigations were performed with a Hitachi S-4000(51) Cantow, H. J. Makromol. Chem. 1964, 70, 130.
Figure 2. Particle size as measured by DLS vs time with temperature and HCl concentration as parameters. HCl concentration 0.4 or 0.6 N; reaction temperature 328, 333, or 343 K; Zr(SO4)2 concentration 4 mM (expts I and II). FEG/EDAX DX 4 using 5 kV acceleration voltage and secondary electron mode.
III. Results 1. Dynamic Light Scattering Measurements. The results of the dynamic light scattering measurements on different zirconium sulfate dispersions (expts I-III) are presented in Figures 1 and 2, and the evolution of particle size with time is represented by the change in the apparent hydrodynamic radius (rh). Figure 1 shows the plots obtained when keeping 2 or 4 mM Zr(SO4)2 solutions in 0.4 N HCl at three different temperatures, namely 343, 333, or 323 K, over a period of up to 700 min. Figure 2 shows how the particle growth is affected by variations of the HCl concentration (0.4 and 0.6 N) and of the temperature (328, 333, 343 K). All curves start with a horizontal region in which the particle size is below the detection limit of the DLS technique, i.e., rh < 5 nm. The length of this induction period (tind) before particle growth varied. At identical reaction temperatures, the length of the induction period increased with decreasing zirconium concentration (Figure 1). For example, the first indication of particle growth at 343 K of the 4 mM Zr(SO4)2 solution was observed after 16 min in comparison to 29 min for the less concentrated solution measured at the same temperature. The same tendency was observed for the solution heated to 333 K; namely, the first signal observation was at 57 min for 4 mM Zr(SO4)2 solution and at 149 min for the less
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Table 2. Calculated Hydrodynamic (rh) and Average Weighted (rw) Particle Radii from Analytical Ultracentrifugation Measurementsa rh and rw expt
F ) 3.22 g‚cm-3 (Zr(SO4)2)
F ) 5.66 g‚cm-3 (ZrO2)
reaction conditions
apparatus
IV
4 mM Zr(SO4)2; 0.4 N HCl; T ) 343 K
AUC (XL-I) [0-20 nm]
rh ) 0.43, 0.87 nm; rw ) 0.62 nm (t ) 35 min) rh ) 0.78, 1.51 nm; rw ) 1.30 nm (t ) 37 min) rh ) 1.61, 2.29 nm; rw ) 2.06 nm (t ) 39 min)
rh ) 0.30, 0.60 nm; rw ) 0.43 nm (t ) 35 min) rh ) 0.54, 1.04 nm; rw ) 0.90 nm (t ) 37 min) rh ) 1.11, 1.58 nm; rw ) 1.42 nm (t ) 39 min)
V
4 mM Zr(SO4)2; 0.4 N HCl; T ) 343 K
AUC (XL-80K) [20 nm-100 µm]
rw ) 0.26 µm (t ) 28 min) rw ) 0.51 µm (t ) 30 min) rw ) 0.72 µm (t ) 36 min)
rw ) 0.18 µm (t ) 28 min) rw ) 0.35 µm (t ) 30 min) rw ) 0.50 µm (t ) 36 min)
VI
4 mM Zr(SO4)2; 0.4 N HCl; T ) 323 K
AUC (XL-I) [0-20 nm]
rh ) 1.16 nm; rw ) 1.04 nm (t ) 6, 12, 24 h)
rh ) 0.80 nm; rw ) 0.72 nm (t ) 6, 12, 24 h)
a
Conditions: 4 mM Zr(SO4)2, 0.4 N HCl; T ) 323 or 343 K.
concentrated solution containing 2 mM Zr(SO4)2. Once particle growth became observable, rh increased linearly with reaction time. The slopes (drh/dt) of the growth curves were related to the induction time; the earlier the growth started, the steeper were the growth curves. A plateau in the particle growth was reached at a final particle radius of approximately 3200 nm in the case of the 4 mM Zr(SO4)2 solution heated to 343 K. This can be attributed to the increasing sedimentation of the large particles out of the scattering volume. During the observation time, no particle formation was observed for both solutions heated to 323 K (plot for the 2 mM Zr(SO4)2 not shown). An increase in the HCl concentration resulted in a prolonged induction period (Figure 2). The first particles were detected after 236 min for a 0.6 N HCl/4 mM Zr(SO4)2 solution heated to 343 K, in comparison to a first signal observation after 16 min for the less acidic 0.4 N HCl solution. After the induction period, the particle size increased linearly with increasing reaction time. The particles grew faster in the less acidic medium (0.4 N HCl). No particle formation was observed for solutions measured at 333 and 328 K (Figure 2). A general linear trend of the hydrodynamic radius with time was obtained for all curves in Figures 1 and 2 that indicated growth. There was also an increased deviation of the signals from the linear extrapolation and an increased noise of the signal with reaction time. Both observations can be explained with the presence of a few larger particles in the developing polydisperse reaction medium. These lead to strongly nonergodic conditions (particle number fluctuations) and thus to a gradually increasing breakdown of the assumptions inherent to the equations used for the data evaluation. 2. Analytical Ultracentrifugation Measurements. Particle size distributions are given in Figures 3-5, and they are presented as plots of mass-weighted frequency versus the hydrodynamic radius. All numbers given in the figures and the text were obtained by assuming a particle density of F ) 3.22 g‚cm-3 for Zr(SO4)2; the smaller values obtained with the density of F ) 5.66 g‚cm-3 for monoclinic zirconia are given in braces. Particle sizes are summarized in Table 2. Figure 3 shows the particle size distributions of the sedimenting particles for three different samples from a reaction medium that was activated at 343 K (expt V). The reaction times of 28, 30, and 36 min were chosen to encompass the time period in which the reaction medium turns cloudy; the first precipitate was visible after 30 min in this experiment. The peak of the distribution for the sample taken from the reaction medium at 28 min was
Figure 3. Evolution of particle size distribution with time as measured by AUC with turbidity detection, representative of the transition from clear to cloudy medium. Particle size calculated with F ) 3.22 g‚cm-3, values obtained with F ) 5.66 g‚cm-3 in braces. Conditions: 4 mM Zr(SO4)2, 0.4 N HCl, T ) 343 K (expt V). The particle concentrations, i.e., the massweighted frequencies, are only apparent, as correction for Mie scattering was not quantitatively possible as a result of the unknown particle refractive index.
located at rh ) 0.23 {0.16} µm with a full width at halfmaximum (fwhm) of ≈0.30 {0.21} µm. Further processing of the particle size distribution data yielded a weighted average particle radius rw of 0.26 {0.18} µm. It, however, has to be mentioned that these weighted average particle radii are apparent because they are derived using the particle concentrations, which are only apparent due to nonquantitative correction for Mie scattering. The fast growth of particles and the heterogeneity of the particle sizes in solution were indicated through the curves corresponding to the samples taken at 30 and 36 min. In comparison to the 28 min sample with its relatively narrow size distribution, the curves were broadened. The apparent weighted average particle radius, rw, of the detected particles from the samples taken at 30 and 36 min was 0.51 {0.35} µm and 0.72 {0.50} µm, respectively. Particles with sizes up to 100 µm were detected at longer reaction times (data not shown). Early stages of particle growth of an experiment with the same concentrations and the same set temperature (expt IV, 343 K) as in Figure 3 are presented in Figure 4. However, due to differences in heat transfer, the reaction times were not comparable and precipitation was observed only after about 40 min. The first sample was taken after
Particle Growth Kinetics in Zr(SO4)2 Solutions
Figure 4. Evolution of particle size distribution with time as measured by AUC with Rayleigh interference detection, early stages of particle formation. Particle size calculated with F ) 3.22 g‚cm-3, values obtained with F ) 5.66 g‚cm-3 in braces. Conditions: 4 mM Zr(SO4)2, 0.4 N HCl, T ) 343 K (expt IV). The thin lines represent the results of multiple Gauss fits to the experimentally obtained distributions.
35 min, and the main peak of the size distribution was located at rh ) 0.87 {0.60} nm with a fwhm of approximately 0.49 {0.34} nm. This particle size distribution was bimodal and showed a second species at 0.43 {0.30} nm (fwhm ) 0.39 {0.27} nm). Therefore, the experimental distribution was fit with two Gaussian curves, and it resulted that the smaller species populated 23% of the total concentration. The second sample was taken after 37 min and larger particles were observed; the main peak was shifted to 1.51 {1.04} nm with a fwhm of 0.33 {0.23} nm. The peak did not reach the baseline toward larger radii due to poor data quality in the raw scans for this particular region. A peak at 0.78 {0.54} nm (fwhm ) 0.54 {0.37} nm, 28% of the total concentration) was still evident, yielding an overall bimodal distribution. After 39 min, the particle size distribution became broader with rw ) 2.06 {1.42} nm vs 0.62 {0.43} and 1.30 {0.90} nm after 35 and 37 min. The distribution appeared not as distinctly bimodal as during the earlier stages because the individual peaks were much broader. The main peak corresponded to rh ) 2.29 {1.58} nm (fwhm ) 0.83 {0.57} nm, 83% of the total concentration), the minor one to rh ) 1.61 {1.11} nm (fwhm ) 0.80 {0.55} nm). From the sequence of AUC measurements it follows that the growth of particles proceeds through distinct stages with the following radii: (1) rh ) 0.43 {0.30} nm; (2) rh ) 0.80-0.87 {0.550.60} nm; (3) rh ) 1.51-1.61 {1.04-1.11} nm; (4) rh ) 2.29 {1.58} nm. The smaller particles disappear with longer reaction times, indicating that these species are consumed. Investigations of a 4 mM Zr(SO4)2 solution in 0.4 N HCl at 323 K by the DLS technique indicated that under these conditions no particles larger than rh ∼ 5 nm were formed, consistent with the clear appearance of the medium. We immersed SAM-coated silicon wafers in such clear media for 24 h to deposit zirconia films. Figure 5 shows the size distribution of the hydrodynamic radii (AUC) of the sedimenting particles from a sample that was removed from the reaction medium after 24 h of deposition procedure. The curve is identical with the curves obtained from samples removed at 6 or 12 h, indicating that the particle size distribution remains constant over this period of time. Three samples taken at 6, 12, and 24 h from a reaction medium that was not in contact with a Si wafer gave the same results, indicating that the Si wafer has no
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Figure 5. Evolution of particle size distribution after 24 h as measured by AUC with Rayleigh interference detection, representative of clear medium. Particle size calculated with F ) 3.22 g‚cm-3, values obtained with F ) 5.66 g‚cm-3 in braces. Conditions: 4 mM Zr(SO4)2, 0.4 N HCl, T ) 323 K (expt VI).
Figure 6. Scanning electron micrographs of rinsed freshly deposited zirconia thin films. (a) Conditions: 4 mM Zr(SO4)2, 0.4 N HCl, T ) 343 K, deposition time 17 h. Selected area shows film (gray background) and large agglomerates of colloidal particles on top of the film surface. (b) Conditions: 4 mM Zr(SO4)2, 0.4 N HCl, T ) 323 K, deposition time 24 h.
influence on the particle growth behavior in the deposition medium. The breadth of the signal in Figure 5, i.e., fwhm ) 1.01 {0.70} nm, suggests that there is some heterogeneity in the size of the species formed. The maximum of the distribution is located at rh ) 1.16 {0.80} nm, consistent with the existence of large complexes. 3. Scanning Electron Microscopy Investigations of Zirconia Films. Figure 6a shows the surface of a film prepared in a deposition at 343 K lasting 17 h, using 4
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mM Zr(SO4)2 in 0.4 N HCl (expt VII). Under these conditions, a precipitate is formed in the reaction medium after 30-40 min, so that colloids are present in the liquid phase during most of the deposition. We observed particles adhering to the zirconia film surface and others embedded in the film. These particles consisted of almost spherical particles with a typical diameter of approximately 300500 nm. Agglomerates of such subunits were found with sizes between 800 nm and a few micrometers. The film surface and the particles consist of zirconium, oxygen, and sulfur, as shown previously by EDX analysis.6 The film surface was characterized by the presence of fissures, which were up to 500 nm long. Figure 6b shows the surface of a film deposited within 24 h at 323 K, also using 4 mM Zr(SO4)2 in 0.4 N HCl (expt VI). The reaction medium stayed clear to the eye throughout the deposition. The wafer was covered with a film consisting of zirconium, oxygen, and sulfur (EDX). The surface exhibited a decidedly different appearance compared to the sample shown in Figure 6a in that it was mostly defect-free. The adsorbed particles and fissures that are characteristic for the sample shown in Figure 6a were not observed, only occasionally some contaminants. IV. Discussion 1. Complex Formation in Zirconium Sulfate Solutions. While the chemistry in zirconium solutions with anions that are neither strongly complexing nor bridging, such as chloride, perchlorate, and nitrate, leads to the formation of a tetrameric zirconium complex over a wide range of conditions, the chemistry in sulfate solutions appears much more complicated and these solutions exhibit decidedly different properties. Initial reactions include hydrolysis, schematically described by
Zr4+ + H2O f Zr(OH)3+ + H+
(5)
The number of protons freed in this reaction is negligible in our case because the HCl concentration is 2 orders of magnitude larger than the Zr(SO4)2 concentration. More important is the complexation of zirconium with sulfate according to
Zr4+ + HSO4- f H+ + [Zr(SO4)]2+
(6)
The equilibrium constant for this reaction has been determined depending on the ionic strength to be K ) 460 33 (at 298 K) or K ) 700 (at 293 K),32 suggesting strong affinity between zirconium and sulfate. The equilibrium constant for the formation of a disulfato zirconium complex is about 1 order of magnitude smaller than that of the monosulfato complex.32,33 Zirconium complexes in sulfatecontaining solutions were found to be anionic14,36 by investigation of their migration in an electric field, and are thus presumed to be mixed hydroxo-sulfato complexes37 of the type Zr(OH)n(SO4)mx-. Polynuclear complexes can form through different bridging mechanisms, i.e., hydroxo bridges (formed in an “olation” reaction), oxo bridges (“oxolation”), and sulfato bridges. Clearfield35 proposed sulfate-bridged complexes of the constitution [Zrn(OH)n+1(SO4)2n](n+1)- and Ciesla et al.52 complexes of the type [Zr(OH)2(SO4)x(OH2)y]nn(2x-2)-, which include water as a ligand. Our solutions contain a high concentration of chloride, which could function as another ligand in complex formation. Particularly, if cationic complexes were formed, (52) Ciesla, U.; Fro¨ba, M.; Stucky, G.; Schu¨th, F. Chem. Mater. 1999, 11, 227.
chloride could attach to those complexes.13,16 However, we never detected chlorine in the films or in the colloids attached to the film surface (Figure 6a), neither with EDX nor with photoelectron spectroscopy. All colloids contained sulfur (EDX), i.e., sulfate must be incorporated as expected from the equilibrium constants. It is thus a fair assumption that anionic complexes with structures similar to those suggested by Clearfield or Ciesla are formed. 2. Stages of Growth. For one set of conditions, i.e., a starting solution of 4 mM Zr(SO4)2 in 0.4 N HCl and a reaction temperature of 343 K, all stages of growth until formation of a solid precipitate were followed using AUC (size ranges rh < 5 nm in Figure 4 and rh > 100 nm in Figure 3) and DLS measurements (rh ) 5-4000 nm, Figures 1 and 2). AUC, which gives information of particle size distributions of particles with sizes well below 1 nm with a resolution in the angstrom range,44 was used to monitor the initial stages of growth. For several minutes (Figure 4), a bimodal particle size distribution was observed, which shifted toward a larger weighted average radius. Specifically, the small species disappeared, the larger species of the previous measurement became the smaller species in the actual measurement, and a new large species formed, whereby the radius difference between small and large increased and the contribution of the smaller species decreased. Assuming spherical morphology and a density of Zr(SO4)2 or ZrO2, radii can be calculated from the maxima in the particle size distribution. Spherical morphology was chosen on the basis of literature reports53 and of electron microscopic images of colloids, which always showed spherical particles and aggregates thereof (Figure 6a). The calculated radii are given in Table 2. With the constitution proposed by Clearfield35 and thus the density of Zr(SO4)2, distinct complexes can be identified. The smallest species with a radius of 0.43 nm corresponds to a complex with the n in Clearfield’s formula being 2, and the next size with a radius of 0.78-0.87 nm fits complexes with n ) 14-18. For larger sized particles, the assignment becomes less clear; i.e., the species with a radius of from 1.50 to 1.61 nm can be described with n ) 91-114, and rh ) 2.29 nm already yields n ≈ 325. The absolute numbers for r and n may deviate from reality because neither morphology, nor density, nor constitution of the complexes is known and may change depending on the size of the complexes, but certain sizes (similar to magic numbers) appear preferentially. This behavior is comparable to that of ZrOCl2 solutions in which a 0.4 nm sized (radius) tetrameric complex of the constitution [Zr4(OH)8(H2O)16Cl6]2+ is in equilibrium with a 0.6 nm sized octameric complex [Zr8(OH)20(H2O)24Cl12]. However, the sulfate complexes are not stable but clearly transients under the chosen conditions, where it remains to be resolved if the smaller particles dissolve (Ostwald ripening), or oligomerize to give the larger ones. The particle size distribution develops toward a single but broad maximum at the end of this first stage (Figure 4), i.e., at a size of 2.29 {1.58} nm. It appears that a certain uniformity of size is maintained at least until rw ) 260 {180} nm; a transition to a polydisperse medium occurs within a few minutes before rw ) 510 {350} nm (Figure 3). Consistent with these AUC results is the nature of the particles that were found to adhere to a zirconia film (Figure 6a). The individual particles of the dominant species in the SEM image are of spherical shape with a radius of about 250 nm. These particles were agglomerated or sometimes intergrown (Figure 6a) to give larger (53) Shi, J. L.; Gao, J. H. J. Mater. Sci. 1995, 30, 793.
Particle Growth Kinetics in Zr(SO4)2 Solutions
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Table 3. Kinetic Data from DLS Measurements c(Zr), mmol‚L-1
c(HCl), mmol‚L-1
temp, K
radius increase rate, nm‚s-1
induction time , s (min)
first-order rate const, L‚mol-1‚s‚nm-1
2.0 2.0 2.0 4.0 4.0 4.0 4.0
0.4 0.4 0.4 0.4 0.4 0.4 0.6
328 333 343 328 333 343 343
0.033 0.068 0.330 0.011 0.172 0.575 0.067
26 5572 (443) 8 927 (149) 1 737 (29) 15 163 (253) 3 457 (57) 961 (16) 14 152 (236)
17 34 165 3 43 144 17
structures, suggesting that, at this stage, flocculation and coalescence take place. The various sizes of these agglomerates are reflected in the 30 and 36 min curves in Figure 3. After longer reaction times, the particle size distributions spanned a range from below rh ) 1 µm to about 100 µm or even wider. Look et al.54 studied colloidal interactions during the precipitation of particles formed through the hydrolysis of metal alkoxides and found that narrow particle size distributions result when the rate of aggregation is faster than the rate of formation of primary particles. Aggregates are then allowed to rearrange into denser aggregates and particle uniformity is maintained. Following this interpretation, the relatively narrow particle size distribution up to 260 {180} nm < rw < 510 {350} nm and the disappearance of small species suggest an aggregation rate faster than the particle formation rate. The particle sizes obtained from DLS measurements are on the same order of magnitude as the sizes determined with AUC. Because of the small cuvettes used for DLS, the set temperature was reached faster, and particle growth occurred somewhat earlier. With the same concentrations and the same temperature as used for the AUC experiments in Figures 3 and 4, the particles reached rh ) 250 nm already after about 22 min. Interestingly, the linear net increase in radius in the DLS curves proceeds to radii as large as 800-3000 nm. The DLS curves represent only the population maxima of the particle size distribution and thus do not account for polydispersity. The plateaus at the end of the curves indicate sedimentation of the large particles out of the analyzed volume. Particle growth in acidic zirconium sulfate solutions can thus be divided into three stages: (1) coexistence of differently sized discrete complexes in the range rh ) 0.432.29 {0.30-1.58} nm; (2) relatively narrow particle size distribution up to rw ) 260-510 {180-350} nm; (3) polydisperse medium, flocculation. 3. Growth Kinetics. DLS was conducted in situ, and hence the dynamics of the growth process and the influence of the reaction conditions on the dynamics could be studied. Temperature, acid (HCl) concentration, and zirconium sulfate concentration were varied. The general trends were as follows: increase in zirconium concentration and/or increase in temperature produced an increase in growth rate, while increase of the acid concentration slowed or even prevented particle growth. The influence of the zirconium sulfate concentration on the growth rate of particles that consist of these species is expected and trivial as is the positive influence of the temperature on a reaction rate; the negative influence of the acid concentration can be derived from eqs 5 and 6. Qualitatively, these results are similar to those obtained in earlier investigations of other zirconium salt solutions.16,18,23,27 Quantitatively, the colloid formation rate in sulfate solutions is much higher than that in zirconyl chloride solutions, as can be seen in comparison to the findings of Hu et al.,27 who detected (54) Look, J.-L.; Bogush, H.; Zukoski, C. F. Faraday Discuss. Chem. Soc. 1990, 90, 345.
Figure 7. Arrhenius plot derived from DLS data. Conditions: 0.4 N HCl, 2 or 4 mM Zr(SO4)2, T ) 328, 333, 343 K. Rate constant calculated by assuming first order in Zr(SO4)2, see Table 3.
particles with a radius of ≈60 nm after heating a mixture of 0.05 M ZrOCl2 in 0.2 N HCl to 373 K for 42 h. The counterion of zirconium in the salt thus plays an important role in the polymerization process, and the complexation ability of sulfate may be the significant factor promoting the growth. Consistent with Hu’s results27 on zirconyl chloride solutions is the increase in growth rate with increasing zirconium salt concentration. The linear increase of the radius is consistent with addition (adsorption) of ions (complexes) to an existing particle at a constant rate per unit surface area according to eq 7, if the change in radius per unit surface area is directly proportional to the number of ions (complexes) reacted:
dr/dt ) fA-1 dn/dt
(7)
where dr/dt ) change in radius (nm‚s-1), f ) proportionality factor, A ) unit surface area (au), and dn/dt ) number of moles of complex/ions reacted (mol‚s-1). Under the assumption that the reaction is first order with respect to the reactants, a rate constant can be calculated, whose temperature dependence would allow the calculation of an apparent activation energy. Because the zirconium-to-sulfate ratio is fixed, simply the zirconium sulfate concentration has been used for the calculation; using the individual concentrations of zirconium and/ or sulfate would give a different rate constant but would not affect its temperature dependence. A summary of rate data is given in Table 3. The influence of the HCl concentration is not known; only data obtained with the same HCl concentration can thus be compared. The temperature dependence of the rate constant is shown in an Arrhenius plot in Figure 7. The linear correlation justifies the above assumptions about the rate equation, and the resulting apparent activation energy amounts to 136 kJ‚mol-1. The so far assumed rate equation is only valid in a certain growth stage, because the extrapolation of the DLS
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Figure 8. Correlation of the particle growth rate as directly observed by DLS for particles >5 nm with the initial particle growth rate as estimated from detection limit and induction time.
curves in Figures 1 and 2 to t ) 0 gives a negative value for the starting radius. A mechanism characterized by a slower rate must be in operation initially. If the change in rate occurs at or close to the detection limit (smallest detectable radius rdet ≈ 5 nm) of the method, then the induction time reflects this rate; i.e., the rate is given by rdet divided by the induction time. A plot of the rate directly observed by DLS vs the calculated initial rate is shown in Figure 8, demonstrating a linear correlation between the two rates and a difference of about 2 orders of magnitude. The two rate equations must be analogous with respect to their temperature dependence to give this proportionality, but they must differ by a quantity that explains the proportionality factor. The factor is at least 112 as can be seen from Figure 8; if the change in mechanism occurred prior to the detection of particles, a higher factor would result. For the conditions 0.4 N HCl, 4 mM Zr(SO4)2, and 343 K, a rate of 5.6 × 10-3 nm‚s-1 is estimated for the slow initial reaction. The AUC data for this set of conditions (Figure 4) also allow the calculation of an approximate initial rate by comparing rw at 35 and 39 min (Table 2). Depending on the density used, the rate is 6.8 × 10-3 nm‚s-1 (Zr(SO4)2) or 4.7 × 10-3 nm‚s-1 (ZrO2), and these values nicely bracket the predicted rate for this initial growth stage, showing the consistency of the experimental data. 4. No Growth within Observation Span. Knowing the rates and their temperature dependence, it is possible to predict the growth rate for a 4 mM Zr(SO4)2 solution in 0.4 N HCl at different temperatures. At 323 K, the rate of the “fast” mechanism is appreciable and should lead to a growth of more than 100 nm‚h-1, and even the “slow” mechanism would produce about 1 nm‚h-1. However, it has been found by DLS that no particles with a radius >5 nm were formed within 13 h, and the medium remained visibly clear for 96 h. Interestingly, lowering the temperature from 328 to 323 K, i.e., by a mere 5 K, was sufficient to suppress growth. It could be speculated that oligomerization is frozen at a particular size, and thus the particle size distribution in this seemingly stable dispersion was of interest. Indeed it was found that after 6, 12, and 24 h reaction time, no changes occurred in the particle size distribution (Figure 5). Furthermore, the particles are small with an average radius rw ) 1.04 {0.72} nm (Table 2). Although the polydispersity seems to be rather significant, it must be kept in mind that these particles are very small and thus diffusion effects are likely
Co¨ lfen et al.
Figure 9. Film thickness vs deposition time as determined by cross-section transmission electron microscopy. Deposition medium: 4 mM Zr(SO4)2, 0.4 N HCl. Data at 343 K taken from Agarwal et al.,1 data at 323 K taken from Roddatis et al.59,60
to be significant. As no diffusion correction was applied to the particle size distributions, the polydispersity will be overestimated. Nevertheless, it is clear that, under these reaction conditions, very small, rather uniform, and stable particles are formed. The particle radius corresponds to a complex with n ≈ 30 when using the constitution proposed by Clearfield. If these species were precursors for the films, then their availability would be ensured for at least 24 h, which might be advantageous for controlled deposition. However, the medium still needs to be considered metastable because precipitation in zirconium sulfate solutions was observed after time spans as long as 2 weeks.42 5. Implications for Film Deposition and Film Growth Mechanism. Thin “zirconia” films can be deposited on SAM-functionalized Si wafers by immersing them in acidic zirconium sulfate solutions at temperatures of 323-343 K.1,55 The method can also be employed to grow films of other oxides such as titanium56 or yttrium oxide,57 and various models for the growth mechanism of such films have been proposed.9,58 Of particular interest is the question whether supersaturation, leading to homogeneous precipitation in the liquid phase, is a prerequisite for film formation. Moreover, our experiments might answer the question of a relationship between particle growth in solution and film growth on the substrate surface. On the basis of AUC and DLS experiments it was possible to identify conditions of rapid particle growth as were also used in the literature,1 and conditions without any growth. The solution concentrations were 4 mM Zr(SO4)2 and 0.4 N HCl, and the temperature was 343 or 323 K. Average film growth rates were compiled from the literature1 or measured by cross-section transmission electron microscopy (TEM).59,60 The results are presented in Figure 9, which shows the film thickness vs the (55) Jentoft, F. C.; Fischer, A.; Weinberg, G.; Wild, U.; Schlo¨gl, R. Stud. Surf. Sci. Catal. 2000, 130, 209. (56) Shin, H.; Collins, R. J.; De Guire, M. R.; Heuer, A. H.; Sukenik, C. N. J. Mater. Res. 1995, 10, 692. (57) Agarwal, M.; De Guire, M. R.; Heuer, A. H. Appl. Phys. Lett. 1997, 71, 891. (58) Shin, H.; Agarwal, M.; De Guire, M. R.; Heuer, A. H. Acta Mater. 1998, 46, 801. (59) Roddatis, V. V.; Su, D. S.; Beckmann, E.; Jentoft, F. C.; Braun, U.; Kro¨hnert, J.; Schlo¨gl, R. Surf. Coat. Technol. 2002, 151-152, 63. (60) Roddatis, V. V.; Su, D. S.; Jentoft, F. C.; Schlo¨gl, R. Submitted for publication in Philos. Mag. A.
Particle Growth Kinetics in Zr(SO4)2 Solutions
deposition time. Film and particle growth can both be envisioned as addition of material from solution to an already existing surface, and as we express the according rates in equivalent units, which are thickness and radius increase per time, respectively, they become easily comparable. The growth rate of the films is on the order of magnitude of 10-4-10-3 nm‚s-1 and thus in the same order as the rate of the initial growth stage in the liquid phase. Additionally, the grains in the freshly deposited films were found to be 5-10 nm,1,61 also pointing toward the initial growth stage and excluding the role of any of the larger colloidal species that are present in the liquid phase at longer reaction times. Again, using the ratio between the rates and the temperature dependence of the rates, the initial stage growth rates can be estimated for the conditions that were used to grow the films analyzed in Figure 9. The rate is estimated to be 5.6 × 10-3 nm‚s-1 at 343 K and to be 2.9 × 10-4 nm‚s-1 at 323 K. At 343 K, the growth rate levels off soon when a single deposition is performed (Figure 9), which is most likely related to depletion of small zirconium complexes in the liquid phase because of particle growth and precipitation. The observed film growth rates are thus smaller than predicted. Evidence for the depletion hypothesis is the more rapid growth that was achieved when repeated depositions were performed on the same substrate with fresh solutions than when a single deposition was performed with the same overall deposition time (Figure 9). In this case the actual growth rate was 4.2 × 10-3 nm‚s-1 and close to the predicted rate, although the individual deposition steps were too long to avoid precipitation and depletion entirely. At 323 K, the thickness increases linearly with time giving a more reliable rate of 2.1 × 10-4 nm‚s-1 which is somewhat less than the predicted growth rate of 2.9 × 10-4 nm‚s-1. Oligomerization of the complexes in liquid phase under these conditions is obviously not possible, but the complexes must attach to the terminal groups of the SAM or the already grown film surface. Some of the attached species must still have the freedom to rearrange as they do in solution, which would explain the typical film structure, i.e., round features in a surrounding matrix.60 The film growth rate is constant over 96 h; for the first 24 h it was proven that small zirconium complexes are available (AUC, Figure 5) and in turn the continuation at the same growth rate beyond 24 h proves that such complexes are present for many hours more. It follows that films can also be grown from media that do not show significant particle growth in the liquid phase during the deposition. Large, polynuclear zirconium complexes are most likely responsible for the film formation, and it is difficult to categorize the growth mechanism into either “ion-by-ion growth/heterogeneous nucleation” or “cluster growth/homogeneous nucleation”. If the “ionby-ion” growth mechanism is envisioned as the attachment of mononuclear zirconium species to the substrate, then it does not reflect the events. Nevertheless, there is no growth in the liquid phase and the film growth is “hetero”initiated by the SAM surface. It was previously proposed58 that the sulfonic acid group of the SAM is deprotonated and thus negatively charged, and that positively charged small zirconium oxide particles would attach through electrostatic and van der Waals forces. In light of our results and of literature reports on negatively charged complexes in sulfate solutions,14,36 we propose an alternative attachment scenario. By way of ligand exchange, i.e., the sulfonic acid groups of the SAM replace (61) Polli, A. D.; Wagner, T.; Fischer, A.; Weinberg, G.; Jentoft, F. C.; Schlo¨gl, R.; Ru¨hle, M. Thin Solid Films 2000, 379, 122.
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sulfates in the complexes, a chemical bond could be formed, which would additionally explain why the films adhere so strongly. Earlier investigations have shown that the formation of particles in the liquid phase is disadvantageous because the particles adhere to the film and create holes when being detached.6 Additionally, the film surface appeared to be prone to cracks in proximity to holes.6 Figure 6a shows a representative section of the surface of such a film with adhering particles; the film was deposited over 17 h in a 4 mM Zr(SO4)2 solution in 0.4 N HCl at 343 K. Figure 6b on the other hand shows a film obtained at 323 K over 24 h, employing the same solution composition. The corresponding AUC measurements are presented in Figure 5, demonstrating that the species in liquid phase are stable throughout many hours. Deposition under such stable conditions yields surfaces free of adsorbed particles, holes, and cracks. Studying the solution chemistry thus proved extremely valuable for fine-tuning the deposition conditions to obtain the best products. V. Conclusions The combination of ex situ AUC and in situ DLS measurements proved to be very powerful in revealing the particle growth kinetics in acidic Zr(SO4)2 solutions over a wide range of particle sizes, i.e., in a radius range of
