1404
J. Phys. Chem. B 1998, 102, 1404-1410
Electrostatically Controlled Diffusion of Carboxylic Acid Derivatized Silver Colloidal Particles in Thermally Evaporated Fatty Amine Films Murali Sastry,* Vijaya Patil, and S. R. Sainkar Materials Chemistry DiVision, National Chemical Laboratory, Pune 411 008, India ReceiVed: June 16, 1997; In Final Form: December 31, 1997
We have recently demonstrated that carboxylic acid derivatized silver colloidal particles can be incorporated in thermally evaporated fatty amine films by immersion of the films in the silver sol and that the process is controlled through electrostatic interactions [Sastry, M.; Patil, V.; Mayya, K. S. Langmuir 1997, 13, 4490]. In this paper, we analyze the influence of colloidal particle concentration, solution pH, and film thickness on the kinetics of cluster incorporation in thermally evaporated fatty amine films obtained from quartz-crystal microgravimetry (QCM) measurements in terms of a one-dimensional (1-D) Fickian-type diffusion model. Although it is found that 1-D diffusion adequately represents the cluster mass uptake kinetics observed using QCM, an interesting film-thickness dependence on the diffusivity was observed. The nature of the clusterdiffusion curves were quite different for amine films annealed prior to immersion in the colloidal solution. In these cases, the 1-D-diffusion model with a single diffusivity fails, indicating the possible occurrence of additional diffusion channels for cluster incorporation. In situ QCM and optical absorption spectroscopy measurements have been made to elucidate the mechanism for cluster diffusion in the thermally evaporated films.
Introduction The organization of nanoparticles to form thin films is an important research problem of today.1 This is motivated primarily by the interesting application potential of these particles in optoelectronics2 and catalysis3 among others. One approach is based on the use of colloid chemistry for the synthesis of the nanoparticles followed by organization in thinfilm form by a variety of methods such as self-assembly of suitably derivatized clusters,4-6 organization at the air-water interface by hydrophobic stabilization of capped clusters,7,8 and electrostatic immobilization of charged clusters under Langmuir monolayers.9,10 We have recently demonstrated that carboxylic acid derivatized silver colloidal particles can be incorporated in thermally evaporated fatty amine films through electrostatic interactions.11 The density of clusters in the amine films could be controlled through variation of colloidal solution pH, which modulates simultaneously the charge on the amine and carboxylic acid groups. Although quartz-crystal microgravimetry (QCM) and optical absorption spectroscopy were used primarily to identify trends in the equilibrium cluster density in the films,11 in this paper we seek to understand further the cluster-incorporation process through an analysis of the kinetics of cluster incorporation based on the QCM measurements in terms of a onedimensional (1-D) Fickian-type diffusion model. Although the 1-D-diffusion model adequately describes the cluster-incorporation kinetics, an interesting dependence of the cluster diffusivity on the film thickness is observed. Optical absorption spectroscopy measurements of cluster-incorporated films in air and in colloidal solution show interesting shifts in the surface-plasmon * Author to whom correspondence should be addressed. Telephone: 0091-212-337044. Fax: 0091-212-337044/330233. E-mail: sastry@ ems.ncl.res.in.
resonance indicative of a water-assisted cluster-diffusion process. However, in situ QCM studies did not reveal significant mass changes due to possible swelling of the immersed amine films. The kinetics of cluster incorporation in the films is found to be altered by annealing of the films, which leads to considerable disorder in the films. As a consequence, additional diffusion channels for cluster incorporation into the thermally evaporated films are created and a simple 1-D model with a single diffusivity is no longer applicable to the mass-uptake data for the annealed films. Presented below are details of the investigation. Experimental Details Silver9 and gold colloidal particles10 were prepared and capped with an aromatic bifunctional molecule, 4-carboxythiophenol (4-CTP), as described elsewhere. Both procedures yielded clear, stable hydrosols at pH ) 10 with the size of silver and gold particles being 73 ( 12 and 130 ( 25 Å, respectively. Thin films of octadecylamine of thickness 150, 500, and 1000 Å were deposited on Si(111) wafers and gold-coated 6 MHz AT-cut quartz crystals by thermal evaporation in an Edwards E 306A coating system equipped with a liquid-nitrogen trap. A 500-Å-thick amine film was also deposited on a quartz substrate for optical absorption spectroscopy measurements. The pressure during film deposition was better than 1 × 10-7 Torr, and the deposition rate was 1 Å/min. The film thickness/deposition rate was monitored in situ using a water-cooled quartz-crystal microbalance (QCM). After deposition of the octadecylamine films, the kinetics of cluster incorporation was followed by immersing the amine-film-coated quartz crystals in the 4-CTPcapped silver hydrosol and measuring the frequency change ex situ after thorough washing and drying of the crystals. All immersions of the amine-coated quartz crystals were in fresh
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Electrostatically Controlled Diffusion colloidal solutions, since it was observed that immersion in the same sol for prolonged periods of time led to flocculation of the silver particles and finally precipitation. We hasten to add here that the sols themselves were stable over many months, and therefore, flocculation was induced by the presence of the amine film. This point will be discussed later in light of simulations based on 1-D diffusion of the clusters. The change in the quartz-crystal resonance frequency was measured using an Edwards FTM5 QCM, which had a frequency resolution and stability of (1 Hz. For the 6-MHz crystal used in this study, this yields a mass resolution of (12 ng/cm2 . Measured frequency changes were converted to a mass loading using the Sauerbrey formula.12 The kinetics of mass uptake in the amine films was determined from QCM for the following experimental conditions: (a) for films of 500-Å thickness immersed in silver sols at pH values of 7, 8.5, and 11.5; (b) for films of 150-, 500-, and 1000-Å thickness immersed in the silver sol at a pH ) 8.5; (c) for films of 500-Å thickness immersed in silver sols with an as-prepared concentration of silver colloidal particles, and cluster concentration reduced by a factor of 2 and 4 (hydrosol pH ) 8.5); (d) for a 500-Å thick film after being annealed at 60 °C for 2 h and then immersed in the silver sol at pH ) 8.5. To better understand changes in the film morphology due to annealing (experiment d) and the consequent influence on the cluster-incorporation kinetics, scanning electron microscopy (SEM) was performed on the 500-Å amine film deposited on Si(111) substrates before and after annealing as well as after cluster incorporation. SEM measurements were done on a Leica Stereoscan S-440 model microscope operated at a voltage of 20 kV and 25 pA electron current. TEM studies were done on a 500-Å-thick amine film deposited on electron-microscope grids that were immersed in the silver sol at pH ) 7, 8.5, and 11.5 in order to compare the particle size distributions (PSD) in the film vis-a`-vis the PSD in the as-prepared sol. The role of cluster size on the diffusion process was studied by repeating experiment b by immersion of a 500-Å-thick amine film in the gold hydrosol (pH adjusted to 8.5).13 The kinetics of cluster incorporation was also studied using optical absorption spectroscopy for a 1000-Å-thick amine film during immersion in the silver hydrosol and in air after drying the film.14 Results and Discussion The kinetics of mass uptake determined using QCM for a 500-Å-thick amine film immersed in silver sols at pH ) 7, 8.5 (curve a), and 11.5 are shown in Figure 1. The solid lines in the figure are based on a 1-D-diffusion-model calculation, which will be described subsequently. Although the salient features of the work have been dealt with earlier, we repeat them for completeness’ sake. It is observed from Figure 1 that the mass uptake, and therefore, the cluster density in the film, is a maximum at pH ) 8.5 and falls at lower and higher pH values. At pH ) 8.5, both the amine molecules and carboxylic acid groups on the cluster are expected to be fully ionized (to -NH3+ and -COO-, respectively), leading to maximum electrostatic interaction. Above pH ) 9, the amine groups become progressively less charged, while below pH ) 8, the carboxylic acid groups follow the same trend.9-11 Thus, by simple alteration of the colloidal solution pH, the density of clusters in the film can be controlled. We have used the same concept of electrostatic interaction with success to alter the cluster density of carboxylic acid derivatized silver clusters at the air-water interface using octadecylamine Langmuir monolayers.9 Figures 2a and 3a show TEM pictures of the clusters incorporated in
J. Phys. Chem. B, Vol. 102, No. 8, 1998 1405
Figure 1. Mass uptake with time measured with QCM for a 500-Åthick amine film immersed in the 4-CTP-capped silver sol at pH ) 11.5 (×3, [), pH ) 8.5 (9, curve asbefore annealing; b, curve bsafter annealing for 2 h at 60 °C), and pH ) 7 (×3, 1).
Figure 2. (A) TEM picture of a 500-Å-thick amine film with silver colloidal particles incorporated at pH ) 8.5. The scale bar indicates 1200 Å. (B) Particle size distribution histogram for the silver colloidal particles shown in part A. The solid line is a Gaussian fit to the histogram.
500-Å amine films after immersion in the silver sol at a pH ) 8.5 and 7, respectively. It can clearly be seen that there is increased cluster density in the film immersed at pH ) 8.5, in agreement with the QCM results of Figure 1. Figures 2b and 3b show the corresponding particle size distributions for the micrographs of Figures 2a (70 ( 33 Å) and 3a (60 ( 25 Å), respectively. It is observed that the average cluster size in both the films is close to that obtained for the as-prepared sol. Thus, within the spread of the PSDs, there appears to be no appreciable size-dependent fractionation effect during the electrostatic immobilization process. The TEM results of the clusters incorporated at pH ) 11.5 were similar to that of cluster incorporation at pH ) 7 and therefore have not been shown. Figure 4 shows the QCM mass uptake with time for films of 150-, 500-, and 1000-Å thickness on immersion in the silver sol at pH ) 8.5 where maximum cluster incorporation has been shown to occur (Figure 1). The mass uptake kinetics data for a 500-Å-thick amine film on immersion in the gold sol (pH )
1406 J. Phys. Chem. B, Vol. 102, No. 8, 1998
Sastry et al. CHART 1: Cartoon (Not to Scale) of Silver-Cluster Incorporation in a Thermally Evaporated Film Amine during Immersion in the Silver Hydrosol
below the mathematical background for the 1-D-diffusion model and, thereafter, its application to the QCM data of this study. One-Dimensional-Diffusion Model
Figure 3. (A) TEM picture of a 500-Å-thick amine film with silver colloidal particles incorporated at pH ) 7. The scale bar indicates 1200 Å. (B) Particle size distribution histogram for the silver colloidal particles shown in part A. The solid line is a Gaussian fit to the histogram.
Figure 4. Mass uptake with time determined from QCM for amine films of thickness 1000 Å (b), 500 Å (2), and 150 Å (9) on immersion in 4-CTP-capped silver hydrosol at pH ) 8.5. The mass uptake with time, QCM data for a 500-Å-thick amine film immersed in 4-CTPcapped gold sol at pH ) 8.5 (cluster size ) 130 Å) is also shown ([). The solid lines are based on fits to the 1-D-diffusion model (eqs 3 and 4).
8.5) is also shown (filled diamonds). The equilibration times (time for maximum cluster incorporation to occur, teq ) are determined from the figure for the silver-cluster films to be ∼80, 50, and 10 h for the 1000-, 500-, and 150-Å-thickness films, respectively. If one assumes a 1-D-diffusion process for the clusters from the colloidal solution into the film, it can be easily shown for the above films that the diffusivity L2/teq (L is the film thickness) is not constant and that it increases as the film thickness increases. However, this in itself does not imply that a 1-D-diffusion model is not representative of silver-cluster incorporation in the amine films. One may need to consider a diffusivity that is dependent on the experimental conditions such as film thickness, and as will be shown subsequently, an electrostatic interaction mechanism for the cluster diffusion indicates that this is not completely unreasonable. We present
Recently, Frances et al.15,16 have studied the process of ion exchange and water transport in Langmuir Blodgett (LB) films of calcium stearate using infrared spectroscopy. An analysis of the ion-diffusion process in terms of a 1-D-diffusion model was done by taking into account a reaction term (due to salt formation), and it was shown that the model did not adequately account for the IR intensity variations observed. A possible explanation put forward was that ion (and water) diffusion could occur through defects such as pores in the film as well as through the hydrophilic lamellar spaces present in the LB films studied, resulting consequently in two simultaneous 1-D-diffusion processes. In the present situation, the thermally evaporated amine films are disordered, as evidenced by the complete lack of Bragg peaks in the XRD patterns, and therefore, a 1-D model may be appropriate. To simplify the calculations, we have omitted the reaction term in the diffusion equation. We feel this is justified given that the electrostatic interaction between the clusters and the amine molecules is weak when compared with the energies involved in salt formation. This is corroborated by the IR measurements of the cluster-incorporated amine film presented in the earlier work where a negligible shift in the NH3 antisymmetric stretch frequency was observed, indicating weak coupling between the negatively charged clusters and positively charged amine molecules.11 The equation for simple 1-D diffusion is written as
∂C(x, t) ∂2C(x, t) )D ∂t ∂x2
(1)
where C(x, t) is the time- and distance-dependent cluster concentration in the film and D is the cluster diffusivity. Chart 1 shows the physical situation in this cluster incorporation study and leads naturally to the following boundary conditions:
C(L, t) ) 0 t < 0 ) C0 t g 0 ∂C(0, t)/∂x ) 0
(2a) (2b)
where C0 is the colloidal particle concentration at the film/ colloidal solution interface (Chart 1, x ) L) and condition 2b is a consequence of the fact that the quartz-crystal substrate is impervious to cluster diffusion (at x ) 0, the film/quartzsubstrate interface, Chart 1). The solution of eq 1, subject to
Electrostatically Controlled Diffusion
J. Phys. Chem. B, Vol. 102, No. 8, 1998 1407
Figure 5. Optical absorption spectra recorded as a function of time for a 1000-Å-thick octadecylamine film during immersion (in situ, solid lines) and corresponding spectra after removal and measurement in air (ex situ, dashed lines). The times of immersion are indicated next to the curves. The inset shows the variation of the surface-plasmon resonance intensity with time (9, ex situ; b, in situ).
the above boundary conditions (eq 2), is given by17
[ [∑ ∞
C(x, t) ) C0 1 + 4
e-D[(2n+1) π /(4L )]t × 2 2
[
n)0
2
]
(2n + 1)πx (-1)n+1
cos
2L
]]
(2n + 1)π
(3)
In QCM studies, one observes a mass uptake over the whole length of the film covering the sensing electrode. The total mass uptake recorded as a function of time, M(t), is therefore
∫0LC(x, t) dx
M(t) ) m0
(4)
where m0 is the mass per cluster. In the calculation of the QCM mass uptake from eq 4, a cluster diameter of 70 Å was taken from the TEM measurement of the PSD in the primary sol, which leads to a mass/cluster value (m0) of 2 × 10-9 ng. However, before proceeding with calculations based on the above 1-D-diffusion model, a physical mechanism for the cluster-diffusion process must be identified. An understanding of this will also shed light on the appropriate boundary conditions that must be applied in the calculation, in particular, the dimensions of the region of diffusion L. The following simple experiments were performed to understand this aspect. Optical absorption spectra of a 1000-Å-thick amine film immersed in the silver sol (pH ) 8.5) recorded as a function of time and the spectra for the corresponding films in air are shown in Figure 5.14 The solid lines refer to the films in solution, while the dashed lines are the spectra from the films in air (the time of immersion is indicated next to the curves). The spectrum of the amine film in the solution measured at time t ) 0 (indicated in Figure 5) has been subtracted from all the spectra recorded for the immersed films to account for absorption from the colloidal particles in the sol. As mentioned earlier, fresh sol was substituted at regular time intervals. This serves to maintain a uniform colloidal particle concentration and thus faithfully reproduces a constant background used in the subtraction procedure outlined above. It is observed from Figure 5 that the surface-plasmon resonance intensity increases steadily
with time for the films in solution and the corresponding films measured in air, the inset of Figure 5 showing the time variation of the resonance intensity. Although this agrees with the QCM results shown in Figure 1, an interesting shift in the surfaceplasmon resonance from 434 nm for the immersed films to 475 nm for the films measured in air is observed. By use of the Mie expression for the absorption coefficient of metal sols, it can be easily shown that the surface-plasmon resonance for silver sols shifts to the blue (i.e., toward shorter wavelengths) when the effective refractive index of the medium in which the clusters are immersed is reduced.18 In air, the medium in which the clusters are embedded is primarily the amine matrix, which has a refractive index close to 1.5.19 If, on immersion, water with a refractive index of 1.33 enters the film, the effective refractive index of the ambient would be lowered from 1.5 and would thus explain the blue shift in the silver-surface-plasmon resonance observed on immersion in the sol.18 The shift in the optical absorption resonance indicates that the clusters diffuse into the film with a fair amount of water. The carboxylic acid derivatized clusters are expected to be highly solvated by water molecules. However, a mechanism based on solvation of the charged amine molecules during immersion in the hydrosol and consequent swelling of the film leading to cluster incorporation in the film would also explain the blue shift of the resonance observed. Such a swelling mechanism has been invoked to explain the spontaneous self-organization of thermally evaporated fatty acid films via cation exchange.20 To further elucidate the water-mediated cluster-diffusion process, we performed an in situ QCM study21 of silver-cluster diffusion in a 150-Å-thick amine film thermally evaporated on the quartz crystal. Accounting for damping of water, it was observed that the in situ mass increase during cluster diffusion was only marginally higher than that expected solely from the mass of clusters incorporated.21 The in situ QCM study thus indicates that substantial swelling due to water solvating the amine groups had not occurred. The extremely slow massuptake times observed (Figure 1) also indicate that swelling of the films due to solvation of the amine molecules may not be responsible for the cluster-diffusion process and that the presence of water in the immersed amine films inferred from optical absorption measurements (Figure 5) is likely to be due to water molecules solvating the diffusing silver colloidal particles. As the clusters diffuse into the amine matrix, expansion of the films is expected to occur due to the large volume occupied by the incorporated clusters. We use the term “expansion” to avoid confusion with the term “swelling” employed earlier, which was used to indicate water incorporation in the films due to amine molecule solvation. Optical interferometry was used for all the films of this study to determine the film thickness after equilibration of the colloidal particle densities had occurred and are given within parentheses in Table 1. The final thickness values thus determined (L) were used in eq 3, and the QCM kinetics results were fitted to eq 4 using a nonlinear least-squares procedure using an application written in Mathcad.22 C0, the concentration of the colloidal particles at the film/colloidal solution interface, and the cluster diffusivity, D, were left free in the fitting routine. The use of the steady-state final thickness in the fits was motivated by the fact that film expansion occurs due to cluster incorporation with more than 60% of the overall mass change occurring within the first 10 h of immersion (Figures 1 and 4). Other than the fact that this approach is physically more meaningful, it would also lead to a more tolerable χ2 error value than if the film initial thickness had been used in the fits.
1408 J. Phys. Chem. B, Vol. 102, No. 8, 1998
Sastry et al.
TABLE 1: Parameters Obtained from Fits to the QCM Mass-Uptake Data of Silver Colloidal Particle Incorporation in Amine Films Based on a 1-D-Diffusion Model Section A expt
thickness (Å)
C0 × 1018 (clusters/cm3)
D × 104 (Å2/h)
silver colloid, pH ) 8.5
150 (300)a 500 (1000)a 1000 (1800)a 500 (1200)a
0.99 1.17 1.06 0.11
0.85 (2.36 × 10-20)b 2.44 (6.78 × 10-20)b 4.17 (11.59 × 10-20)b 1.90 (5.28 × 10-20)b
gold colloid, pH ) 8.5
(B) Colloid pH ) 8.5, Thickness ) 500 Å
b
cluster concn in the silver sol
C0 × 1018 (clusters/cm3)
D × 104 (Å2/h)
as-prepared ) 100% (1000)a 50% (700)a 25% (600)a
1.17 1.13 1.0
2.44 (6.78 × 10-20)b 2.59 (7.2 × 10-20)b 2.61 (7.26 × 10-20)b
a The numbers in the parentheses are the values of the film thickness “L” used in the 1-D-diffusion calculations (eqs 3 and 4). See text for details. The numbers in the parentheses are the cluster diffusivities in units of m2/s.
The QCM mass-uptake data shown in Figure 4 have been fit to eq 4 as detailed above and are shown as solid lines in the figures. In the fit to the mass-uptake data for the amine film immersed in the gold sol, the cluster mass m0 was calculated to be 23 × 10-9 ng for 130-Å-size colloidal particles. We have not attempted to fit the mass-uptake data shown in Figure 1 for colloidal solution pH values of 7 and 11.5 (mass-uptake data scaled up by a factor of 3 for clarity), since the data showed the presence of fairly large “steps” (indicated by arrows, Figure 1). We are unable to account for this behavior at present. This steplike nature of the mass-uptake kinetics is also observed for cluster incorporation at pH ) 8.5 (Figure 1, curve a), but it is much less pronounced, and therefore, the deviation from the predicted mass uptake based on the 1-D model is smaller. From the quality of the fits for the films immersed in the 8.5 pH gold and silver sols, it is inferred that a 1-D-diffusion model is an adequate representation of the cluster-incorporation mechanism in the amine films. The parameters obtained from the fits are listed in Table 1, and we repeat, the actual film thickness values (determined from optical interferometry) used in the fits are indicated within parentheses in the table. From the parameters obtained from fits to the silver colloidal solution data of Figure 4 (Table 1, section A), it is observed that the cluster concentration at the film/colloidal solution interface (C0 ) is fairly constant and independent of the film thickness. However, an interesting increase in the silver-cluster diffusivity with increasing film thickness is observed. We would like to point out that the calculated cluster concentration at the film/silver colloidal solution interface is nearly 5 orders of magnitude larger than that in the bulk of the solution (∼1.1 × 1013/cm3 ) for 70-Å clusters assuming complete reduction of 2 × 10-4 M silver ions in solution. A similar 5 orders enhancement of the gold-cluster density at the film/colloidal solution interface is determined from the calculated value of C0; the concentration of the gold colloidal particles in solution can be shown from a similar calculation to be ca. 25% of the silver-cluster concentration. The enhancement of the cluster concentration at the interface calculated from the fits relative to that in the bulk of the colloidal solution can be understood in terms of an attractive electrostatic interaction between the negatively charged clusters and positively charged amine film. Such large enhancements (about 4-5 orders of magnitude) in divalent counterion concentrations are known to occur at charged Langmuir monolayer surfaces and can be understood in terms of a Poisson-Boltzmann-Stern formalism.23 Although viewing negatively charged silver colloidal particles as “giant anions” with “variable valence” dictated by
the colloidal solution pH is appealing, further work taking into account the large size of the clusters, etc. is required before a complete simulation of the accumulation of the clusters at the film/colloid interface followed by diffusion into the amine films can be done.23b However, the trends in the calculated parameters appear to be physically meaningful. The calculated silver-cluster concentration at the film interface of 1.06 × 1018/cm3 (a typical value taken from Table 1) leads to a volume-packing fraction at the interface of ca. 18%. Thus, the volume-packing fraction of the clusters at the film/solution interface is very close to the equilibrium cluster volume fractions in amine films determined from a rough analysis of the QCM mass uptake determined in our preliminary investigation.11 This indicates that the 1-Ddiffusion model used in the calculation of the parameters of Table 1 is physically meaningful and engenders confidence in the model used. The diffusivity of the gold clusters in the amine matrix is marginally smaller than that calculated for the smaller silver clusters. It appears that the additional electrostatic interaction due to larger surface charge on the gold-particle surface is almost completely nullified by the greater bulk of the particle. This aspect needs further investigation based on varying cluster sizes of a particular metal13 and will be addressed in a forthcoming communication. There is a steady increase in the silver colloidal particle diffusivity from 0.85 × 104 to 4.17 × 104 Å2/h as the amine film thickness is increased from 150 to 1000 Å, as has been pointed out earlier (Table 1). This result is not understood at present but may be related to changes in the film microstructure as a function of film thickness and is being investigated further. The kinetics of cluster incorporation into an amine film of 500-Å thickness immersed in the 4-CTP-capped silver sol at different colloidal particle concentrations determined from QCM is shown in Figure 6. After dilution, care was taken to adjust the colloidal solution pH to 8.5 for direct comparison of the cluster-intake data. In Figure 6, curve a corresponds to the normal cluster concentration measurement while curves b and c correspond to the 50% and 25% cluster concentration cases, respectively. As before, the solid lines are fits based on a 1-Ddiffusion model. In this case as well, the 1-D-diffusion model is a faithful representation of the cluster-incorporation process. The parameters obtained from the fits are shown in Table 1, section B. It is observed that there is very little dependence of both the cluster density, C0, and cluster diffusivity, D, on the cluster concentration in the sol. The fact that the cluster density at the film/solution interface is insensitive to the cluster concentration in the bulk of the colloidal solution (within the
Electrostatically Controlled Diffusion
J. Phys. Chem. B, Vol. 102, No. 8, 1998 1409
Figure 6. Mass uptake with time determined from QCM for a 500Å-thick amine film on immersion in 4-CTP-capped silver hydrosol (pH ) 8.5) at as-prepared particle concentration (100%, curve a), 50% particle concentration (curve b), and 25% particle concentration (curve c). The solid lines are based on fits to the 1-D -diffusion model (eqs 3 and 4).
narrow concentration range studied here) is consistent with a Poisson-Boltzmann model of the “counterion” cluster density near the interface.23 Since there is no change in the electrostatic interaction energy during dilution through variation of the charge on the colloidal particles/amine film, the diffusivities are also not expected to change significantly. To understand the role of film surface morphology and organization in the kinetics of cluster incorporation, QCM studies were carried out on a 500-Å-thick amine film annealed at 60 °C as described in the Experimental Section. Figure 1 shows the kinetics mass QCM mass uptake for the annealed film (curve b, dotted line) and can be compared with the data for the unannealed film (Figure 1, curve a). No change in the film thickness was noted by QCM and ellipsometry measurements after annealing of the films. Therefore, no ambiguity in boundary condition 2b is expected to enter into the diffusioncurve simulation. For the annealed film, it is observed that there is an initial region lasting up to 30 h where the mass uptake increases linearly with time, after which a sudden saturation of the mass is observed. This behavior is quite different from that of the unannealed film where an abrupt change in the mass uptake with time curve did not occur (Figure 1, curve a). This implies that a simple 1-D-diffusion model based on a single diffusivity for the colloidal particles fails to represent cluster incorporation in the annealed film. However, it is to be noted that the equilibrium mass uptake is nearly the same in both cases, indicating an almost identical final-state cluster density in the films, a finding that is consistent with the ellipsometry and QCM measurements, which indicated negligible thickness and mass change in the film after annealing. Interferometry measurements of the annealed film after cluster incorporation yielded a thickness close to that measured for the unannealed film (ca. 1800 Å). Parts a-c of Figure 7 show the SEM micrographs of the amine film on Si(111) substrates before annealing, after annealing, and after cluster diffusion, respectively. A comparison of parts a and b of Figure 7 clearly shows that the uniformity of the film is considerably reduced after annealing with the presence of large gaps occurring on annealing. These gaps can act as channels for the colloidal solution to permeate the film and therefore provide an additional lateral diffusion component to the mass-uptake process. This is a tentative explanation for
Figure 7. SEM picture of (A) an as-prepared 500-Å-thick amine film, (B) the film shown in part A after annealing for 60 °C for 2 h, and (C) annealed film shown in part B after silver colloidal particle incorporation at a solution pH ) 8.5.
the different kinetics of cluster incorporation in the annealed film observed as well as the nonapplicability of a 1-D-diffusion model with a single diffusivity for the mass-uptake kinetics. Frances et al.15,16 observed a similar increase in the ion-exchange kinetics after annealing of calcium stearate films, which was attributed to the generation of pores in the film. Although they did not provide visual evidence, the SEM micrographs of Figure 7 clearly agree with their conclusions. Another interesting point is that Figure 7c shows improved film uniformity after cluster diffusion into the film. From the SEM picture of the unannealed film shown in Figure 7a, it is difficult to comment on whether pores of dimensions larger than the colloidal particle dimensions (70 Å) are responsible for water transport and thus cluster incorporation in the film. In situ QCM studies indicate that water (and cluster) transport through the pores in the film is not the likely mechanism, since little water uptake in the films was observed even after prolonged immersion of the amine films in the colloidal solution. It is clear that further work leading to a better
1410 J. Phys. Chem. B, Vol. 102, No. 8, 1998 understanding of more microscopic details of the cluster “diffusion” process is required and is being pursued. Conclusions To summarize, a 1-D-diffusion model satisfactorily explains the cluster-incorporation kinetics observed using ex situ QCM on immersion of thermally evaporated octadecylamine films in carboxylic acid derivatized silver colloidal solution. The noninclusion of a reaction term in the diffusion equation is rationalized in terms of weak coupling between the amine molecules and carboxylic acid derivatized silver clusters. The applicability of this model to thermally evaporated films leads to physically meaningful cluster-concentration enhancements at the film-colloidal solution interface as well as cluster diffusivities. A simple 1-D-diffusion model using a single diffusivity cannot be applied to cluster diffusion into annealed octadecylamine films possibly because of additional channels becoming available for cluster diffusion. Acknowledgment. V.P. is thankful to the Council of Scientific and Industrial Research (CSIR), Government of India, for a research fellowship. Illuminating suggestions of the reviewers are gratefully acknowledged. The authors thank Dr. P. Ganguly, Head, Physical and Materials Chemistry Division and Dr. B. D. Kulkarni, Head, Chemical Engineering Division, NCL Pune, for useful discussions. References and Notes (1) Alivisatos, A. P. Science 1996, 271, 933. (2) Colvin, V. L.; Schlamp, M. C.; Alivisatos, A. P. Nature 1994, 370, 354. (3) Hoffman, A. J.; Mills, G.; Yee, H.; Hoffman, M. R. J. Phys. Chem. 1992, 96, 5546. (4) Colvin, V. L.; Goldstein, A. N.; Alivisatos, A. P. J. Am. Chem. Soc. 1992, 114, 5221. (5) Doron, A.; Katz, E.; Willner, I. Langmuir 1995, 11, 1313. (6) Freeman, R. G.; Hommer, M. B.; Grabar, K. C.; Jackson, M. A.; Natan, M. J. J. Phys. Chem. 1996, 100, 718. (7) Meldrum, F. C.; Kotov, N. A.; Fendler, J. H. J. Phys. Chem. 1994, 98, 4506.
Sastry et al. (8) Kotov, N. A.; Meldrum, F. C.; Wu, C.; Fendler, J. H. J. Phys. Chem. 1994, 98, 2735. (9) Sastry, M.; Mayya, K. S.; Patil, V.; Paranjape, D. V.; Hegde, S. G. J. Phys. Chem. B. 1997, 101, 4954. (10) Mayya, K. S.; Patil, V.; Sastry, M. Langmuir 1997, 13, 2575. (11) Sastry, M.; Patil, V.; Mayya, K. S. Langmuir 1997, 13, 4490. (12) Sauerbrey, G. Z. Phys. (Munich) 1959, 155, 206. (13) The role of cluster size on the diffusion process was studied using 130-Å gold colloidal particles and not silver, since we are yet to standardize an experimental procedure for reproducibly obtaining larger/smaller-sized silver colloidal particles. (14) Optical absorption spectroscopy measurements were carried out on a Hewlett-Packard 8452 diode-array spectrophotometer operated at 2-nm resolution. The quartz substrate for optical absorption measurements was cut in such a way as to fit in a snug, vertical position in the spectrophotometer quartz cuvette. Spectra of the film were recorded during immersion in the hydrosol and in air after evacuating the cuvette and thoroughly washing and drying the film prior to measurement. (15) Marshbanks, T. L.; Ahn, D. J.; Frances, E. I. Langmuir 1994, 10, 276. (16) Marshbanks, T. L.; Frances, E. I. J. Phys. Chem. 1994, 98, 2166. (17) Carslaw, H. S.; Jaeger, J. C. Conduction of Heat in Solids; Clarendon Press: Oxford, 1960; p 101. (18) Henglein, A. J. Phys. Chem. 1993, 97, 5457. Mulvaney, P. Langmuir 1996, 12, 788. (19) If one neglects the optical anisotropy in long-chain fatty amine molecules, a reasonable assumption given that the thermally evaporated amine molecules are expected to be fairly disordered, the refractive index of the amine film would be close to 1.5. See, for example, the following. Paudler, M.; Ruths, J.; Riegler, H. Langmuir 1992, 8, 184. Honig, E. P.; De Konig, B. R. Surf. Sci. 1976, 56, 454. (20) Ganguly, P.; Pal, S.; Sastry, M.; Shashikala, M. N. Langmuir 1995, 11, 1078. (21) In situ QCM measurements were made on a 150-Å-thick thermally evaporated amine film on a 10-MHz quartz crystal. Measurements were made as a function of time of immersion of the amine film in a silver hydrosol at pH ) 8.5 using an Elchema model 702 electrochemical quartzcrystal nanobalance. The damping of the resonance frequency due to water was calculated to be 1750 Hz (Wang, J.; Frostman, L. M.; Ward, M. D. J. Phys. Chem. 1992, 96, 5224) and was subtracted from the measured in situ frequency. This difference was then converted to a mass loading using the Sauerbrey formula (ref 12). The mass uptake due to cluster incorporation was estimated from the change in weight of the dry cystals after removal from the silver sol. (22) Mathcad is a commercial mathematical software package for the PC available from Mathsoft Inc., Cambridge, Ma 02142. (23) (a) Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: New York, 1985; Chapter 12. (b) Borukhov, I.; Andelman, D.; Orland, H. Phys. ReV. Lett. 1997, 79, 435.
