9044
J. Phys. Chem. B 2000, 104, 9044-9047
Evolution of a Steady State Island Size Distribution during Self-Assembled Monolayer Dissolution Ivo Doudevski and Daniel K. Schwartz* Department of Chemistry, Tulane UniVersity, New Orleans, Louisiana 70118 ReceiVed: May 2, 2000; In Final Form: July 21, 2000
We have observed the dissolution of a self-assembled monolayer of octadecylphosphonic acid from a mica surface in real time using atomic force microscopy. Holes in the monolayer are observed to nucleate and grow with time, eventually percolating across the sample. The rate of dissolution is increased by flowing solvent through the cell compared to stagnant solvent. If the monolayer is brought into contact with a small enough volume of stagnant solvent, the surface coverage stabilizes at some point due to the buildup of adsorbate molecules in solution. Under these conditions of steady state surface coverage, the local dynamical processes of island shrinkage, growth, and nucleation continue, eventually leading to a distinctive island size distribution characteristic of the system. The final distribution is in good agreement with a decaying exponential form, consistent with a “point island” model of island shrinkage and growth.
Introduction Adsorbed monolayers of many amphiphilic molecules form spontaneously at the interface between a solid surface and a dilute solution of the adsorbate.1 When one end (the “headgroup”) of the adsorbate molecule has a specific attractive interaction with the solid substrate, the monolayers are known as self-assembled monolayers (SAMs) and have been extensively studied in recent years due to potential applications in surface modification.2,3 A common theme in the growth process of all known SAM systems is the clustering of adsorbate molecules into densely packed two-dimensional (2D) islands which grow, coalesce, and eventually cover the surface.4-11 In most cases (a notable exception being trichlorosilane-based SAMs capable of covalent cross-linking4,5) there is reason to believe that the molecules in islands are in dynamic exchange with a dilute, disordered phase of molecules adsorbed on the regions of surface between islands and possibly with adsorbate molecules in the adjacent solution phase. However, these issues are difficult to probe with experiments where a partial monolayer remains in contact with solution used for SAM growth, since only the net growth process can be observed. In this paper, we report in situ atomic force microscopy (AFM) observations of the dissolution/desorption of SAMs into pure solvent and very dilute solution. If adsorbate concentration is allowed to build up in stagnant solution, a dynamical steady state is established, leading to a distinctive island size distribution that provides information regarding the competition between island nucleation, growth, and shrinkage. Also, it may be possible to take advantage of these processes to tailor the cluster size distribution. For example, since the steady-state island size distribution is peaked in the region of small islands, these observations suggest a simple method by which molecular “dots” can be formed on a surface, starting with any initial conditions. A similar dissolution procedure might also be used to “sharpen” the island size distribution formed during growth, for example.12 Such a strategy would be related to methods used * To whom correspondence should be addressed. Tel: 504/862-3562. Fax: 504/865-5596. E-mail:
[email protected].
successfully to form monodisperse size distributions of nanocrystals that involve manipulating growth rates by adjusting the solution concentration during growth.13 Experimental Details AFM images were obtained with a Nanoscope III MMAFM (Digital Instruments, Santa Barbara, CA) in contact mode. To avoid surface contamination during in situ imaging, the deposition solution came into contact with only glass, PTFE Teflon, and a fluoropolymer Kalrez O-ring (Dupont). Initially, the liquid cell was filled with clean tetrahydrofuran (THF) and images were obtained of the clean mica substrate. Then a solution containing approximately 0.5 mM octadecylphosphonic acid (OPA), CH3(CH2)17PO(OH)2, dissolved in THF, was allowed to flow into the liquid cell. After the monolayer was nearly complete, the deposition solution was replaced by pure THF and the monolayer proceeded to dissolve into the solvent. The dissolution was performed using either a fixed volume of stagnant THF or by flowing clean THF continuously through the cell. The dissolution was monitored in situ by AFM. Typically, images were obtained over a 2 µm × 2 µm area. At several stages during monolayer growth and dissolution, the scanned area was increased to 5 µm × 5 µm to check that the smaller initial scanning area contained no evidence of damage due to scanning. Images of dissolution were obtained at regular time intervals. Between image acquisitions the scanning was stopped and the tip moved about 50 µm away from the surface in order to minimize the effect of convection (stirring) due to tip scanning. Image analysis was performed using NIH Image software on images that were 2 µm × 2 µm in area. Methods for determining surface coverage and island size distributions were discussed in detail previously.9,12 Results Figure 1 shows a sequence of AFM images typical of SAM dissolution into flowing solvent (the flow rate was about 0.1 mL/min). The first image shows the surface topology a few minutes after exposing the nearly complete monolayer to pure
10.1021/jp001651k CCC: $19.00 © 2000 American Chemical Society Published on Web 09/01/2000
Island Distribution during SAM Dissolution
J. Phys. Chem. B, Vol. 104, No. 38, 2000 9045
Figure 1. In situ AFM images (400 nm × 400 nm) showing the surface topology of an OPA monolayer during dissolution into THF that is flowed continuously through the cell at about 0.1 mL/min. The images were obtained 4, 7, 25, 93, 110, 122, and 138 min, respectively (left to right), after the dissolution process started.
Figure 2. In situ AFM images (400 nm × 400 nm) showing the surface topology of an OPA monolayer during dissolution into a small volume of stagnant THF (about 30 µL). The images were obtained 2, 47, 90, 180, 212, 249, and 288 min, respectively (left to right), after the dissolution process started.
solvent. Holes about 2 nm deep develop in the monolayer and gradually grow and coalesce. The magnitude of the height difference suggests that the high areas are regions of densely packed adsorbate molecules standing on end and the low areas are either bare substrate or a low-density phase of adsorbed molecules. These are analogous to images observed during monolayer formation, where “islands” of molecules are observed to nucleate and grow.9 By the time approximately half of the monolayer has been removed, continuous paths of bare substrate traverse the image from side to side. Eventually, only isolated islands of molecules remain and these are gradually etched away, leaving a bare surface. The fact that the holes that form are observed to grow with time can be taken as qualitative evidence that molecules at island edges are removed preferentially compared with molecules in the island interior. The AFM images in Figure 2 show the process of SAM dissolution into stagnant solvent/solution. The initial part of the dissolution is qualitatively similar to that in Figure 1 (flowing solvent). However, after about 3 h, the surface coverage stops decreasing (fourth image). Presumably, the molecules desorbed from the surface into the stagnant solution raise the concentration enough to reach a steady state between dissolution and redeposition. The approximate concentration of the solution in this regime is 5 × 10-6 M. After this point, although the coverage is stable, the surface morphology continues to evolve. Large patches and islands are observed to shrink and are “replaced” by nucleation of tiny islands. The evolution of the island size distribution will be discussed in more detail below. Figure 3 shows the coverage kinetics for the dissolution experiments illustrated in Figure 1 (flowing solvent, open circles) and Figure 2 (stagnant solvent, filled circles). Clearly, solvent flow results in faster dissolution; the monolayer is completely dissolved after about 150 min. When the solvent is not replaced by flow, the solution concentration gradually increases and the coverage reaches a minimum of about 0.5 after about 190 min. The concentration of OPA molecules in solution at this point is about 5 µM. After this time, the coverage remains approximately constant with occasional fluctuations. The data points marked by the numbers 1-4 on Figure 3 refer to the last four images in Figure 2. The island size distributions corresponding to these time points are shown in Figure 4. The island density was scaled by the approximate molecular cross sectional area (0.25 nm2) in order to make it dimensionless. Island areas were converted to the number of molecules using the same factor. After 180 min dissolution into stagnant solvent (point 1, filled circles), the island size distribution is fairly flat, except for a small rise for small island size. After 212 min (point 2, open circles), the distribution has increased in the small island
Figure 3. Time dependence of the surface coverage during dissolution experiments in continuously flowing solvent (open circles) and stagnant solvent/solution (filled circles). The points marked 1-4 correspond to the final four images shown in Figure 2 and to the island size distributions shown in Figure 4.
region. The island size distributions after 249 min (point 3, filled triangles) and 288 min (point 4, open triangles) are indistinguishable from each other and rise dramatically for small island sizes. The fact that the distribution does not change after 249 min suggests that a steady state has been reached. This evolution of the island size distribution is consistent with the proliferation of small islands at later times shown in Figure 2. Although the distributions at 249 and 288 min appear to correspond to larger coverage than the earlier times since they have larger values over the range of island sizes shown (up to 5000 molecules), in fact the coverage has not changed, as shown in Figure 3. This is due to the fact that small numbers of relatively large islands (larger than 5000 molecules) contribute significantly to the coverage at earlier times. Since the number of islands in each histogram bin in this region is small, the distributions are noisy and overlap closely. Therefore, it is not particularly helpful to display this section of the distributions at the expense of clarity in the small island region. The poor statistics in individual histogram bins does not translate to large uncertainties in the total coverage calculation based on the sum of all island areas. Analysis and Discussion A kinetic approach using coupled rate equations to describe
9046 J. Phys. Chem. B, Vol. 104, No. 38, 2000
Doudevski and Schwartz containing s molecules (for s > 2) is
dNs ) DN1(σs-1Ns-1 - σsNs) + r(σs+1Ns+1 - σsNs) dt We do not include any island-size dependence of the removal rate r such as would lead to Ostwald ripening. This is motivated directly by the observation that the steady-state size distribution is peaked at small island sizes. Coarsening phenomena, such as Ostwald ripening, involve growth of large clusters at the expense of small clusters and would lead to a distribution skewed toward large island sizes. The size distribution previously observed during the aggregation regime of SAM growth also did not suggest the influence of Ostwald ripening.12 The coupled differential equations have a steady-state solution that gives dNs/dt ) 0 for all s if consecutive island densities meet the condition
DN1σs-1 Ns ) Ns-1 r σs If we demand continuity of the distribution function in the limit s ) 1, we find
Ns ) Figure 4. Island size distributions during the late stages of dissolution into stagnant solution when the surface coverage is approximately constant. The number density of islands containing s molecules per “site” (estimated at 0.25 nm2) is plotted versus s for images obtained 180, 212, 249, and 288 min after the start of dissolution as reflected in the inset. The solid line is the best fit of the point island model (decaying exponential function) to the distributions at 249 and 288 min. The dashed line corresponds to a model where the capture cross section is assumed to be proportional to the island perimeter.
two-dimensional cluster nucleation and growth has been quite successful at reproducing certain aspects of SAM growth9 as well as vapor phase thin film deposition.14-16 This type of model can be modified to describe the processes of island nucleation, growth, and shrinkage that take place in dissolution experiments. In particular, we are interested in describing the situation for stagnant solvent in the regime of constant coverage at long times. We assume that, due to rapid exchange with the solution phase, the density of mobile adsorbate molecules (monomers), N1, on the regions of surface between islands is constant in time. We write a Smoluchowski-type rate equation for the number density of islands containing s molecules, Ns. For example, the rate equation for dimers is written
dN2 ) DN12 - DN1σ2N2 + r(σ3N3 - σ2N2) dt where D is the 2D diffusion constant, r is a removal rate from an island, and σs is a capture cross section factor for an island with s molecules. The first term on the right is the nucleation rate assuming a critical nucleus of two molecules, consistent with our previous observations.9,12 The second term reflects the reduction in the number of dimers due to growth into trimers. The last two terms on the right correspond to a trimer losing a molecule to become a dimer and the dissociation of a dimer, respectively. Since our aim is not to calculate actual values of the dynamic parameter, e.g., r and D, we have not concerned ourselves with incorporating exact geometrical factors of order unity. The general rate equation for the density of islands
( )
rσ1 DN1 s 1 D r σs
Two commonly used forms for the capture cross section are σs ) xs (proportional to the island perimeter), or σs ) 1 (point island model). Although the first form seems intuitively reasonable, our previous analysis of island nucleation and growth kinetics was consistent with the point island assumption.9 The forms of the island size distribution for these two models are
( ) ( )
Perimeter model: Ns ) Point island model: Ns )
r DN1 s 1 D r xs
r DN1 s ) N1e-(s-1)/ξ D r
Note that the point island model can also be expressed as an exponential distribution function that decays with a characteristic island size of ξ molecules, where ξ ) -[ln(DN1/r)]-1. The parameter DN1/r represents the ratio of the island growth rate to the island shrinkage rate. It is to be expected that this parameter should have a value near (but less than) unity under steady-state conditions. The lines on Figure 4 represent the best fit of the steadystate distributions to these two models. The point island model (decaying exponential function) is consistent with the data. The best fit corresponds to DN1/r ) 0.99943 ( 0.00001 or a decay length of ξ ) 1750 molecules. However, the model using the island perimeter as the capture cross section deviates systematically from the data. This suggests that the growth and shrinkage rates of an island are essentially independent of the island size. Under rapid growth conditions, where 2D diffusion is fully developed around each island, the point island approximation for island growth is often appropriate. The justification for this is that the expression for the diffusive flux to a mass sink has only logarithmic dependence on the sink radius in 2D.9 However, the scenario during the steady-state dissolution regime is one of rapid exchange between molecules at the boundary of an island and adsorbed molecules on the region adjacent to the island. Under such circumstances, one would not expect to find a concentration gradient around an island related to 2D diffusion
Island Distribution during SAM Dissolution and the rate of collisions between monomers and an island should be proportional to the island perimeter. One might intuitively expect the rate of desorption from an island also to be proportional to the perimeter. The observed island size distribution is, therefore, somewhat unexpected and we cannot offer a definitive mechanistic explanation. One possibility to consider is that, for each island, a small number of boundary sites dominates the adsorption and desorption kinetics and that the number of these sites depends only weakly on the island area. The classic model for such a notion involves a cluster of molecules on a lattice where the desorption probability, for example, of a molecule on the boundary is strongly dependent on the number of nearest neighbors. For a square cluster on a square lattice, as a simple example, the molecules in the four corners have only two nearest neighbors whereas a molecule on a side of the square has three neighbors. For such islands, therefore, the desorption rate might be dominated by the number of “corner” molecules, which depends only weakly on the island area. The application of this concept for this particular system is purely speculative, however, and there are doubtless a number of alternative explanations. Regardless of the mechanism that leads to the observed island size distribution, the simple fact that such a steady-state distribution exists, and that it rises monotonically for small island sizes, suggests that one could tailor the growth conditions to bias the details of the surface morphology. We have previously shown, for this SAM system, that the island size distribution in the aggregation regime of growth scales with a single characteristic length that evolves with time.12 The underlying dimensionless size distribution is an asymmetric peak with a long “tail” for large island sizes. By subjecting a monolayer to growth and dissolution cycles, one could attempt to engineer a particular island size distribution, in particular, a narrow range of island sizes. Similar strategies have been used by the Alivisatos group to manipulate the growth rate of growing nanocrystals by varying the concentration of solution during growth.13 Such “focusing” strategies can significantly narrow the size distribution. Conclusions The dissolution of octadecylphosphonic acid SAMs from mica have been observed using in situ AFM. The desorption/
J. Phys. Chem. B, Vol. 104, No. 38, 2000 9047 dissolution proceeds by nucleation, growth, etc. of holes in the monolayer. When clean solvent is continually flowed through the cell, the monolayer eventually dissolves completely. However, when only a small volume of stagnant solvent is brought in contact with a monolayer, the concentration of adsorbate gradually increases as molecules desorb from the monolayer. The monolayer coverage eventually stabilizes when the solution concentration reaches a level of about 5 µM. Under these conditions of steady state surface coverage, the local dynamical processes of island shrinkage, growth, and nucleation continue, eventually leading to a distinctive island size distribution characteristic of the system. The final distribution is in good agreement with a decaying exponential form, consistent with a “point island” model of island shrinkage and growth. The fact that the distribution is monotonically decreasing suggests that Ostwald ripening is not an significant factor, i.e., the rate at which molecules are removed from islands does not decrease with island size. Acknowledgment. This work was supported by the National Science Foundation (grant number CHE-9980250) and the Camille Dreyfus Teacher-Scholar Awards Program. References and Notes (1) Adamson, A. W.; Gast, A. P. Physical Chemistry of Surfaces, 6th ed.; Wiley: New York, 1997. (2) Ulman, A. Chem. ReV. 1996, 96, 1533. (3) Poirier, G. E. Chem. ReV. 1997, 97, 1117. (4) Schwartz, D. K.; Steinberg, S.; Israelachvili, J.; Zasadzinski, J. A. N. Phys. ReV. Lett. 1992, 69, 3354. (5) Bierbaum, K.; Grunze, M.; Baski, A. A.; Chi, L. F.; et al. Langmuir 1995, 11, 2143. (6) Poirier, G. E.; Pylant, E. D. Science 1996, 272, 1145. (7) Yamada, R.; Uosaki, K. Langmuir 1997, 13, 5218. (8) Eberhardt, A.; Fenter, P.; Eisenberger, P. Surf. Sci. 1998, 397, L285. (9) Doudevski, I.; Hayes, W. A.; Schwartz, D. K. Phys. ReV. Lett. 1998, 81, 4927. (10) Hayes, W. A.; Schwartz, D. K. Langmuir 1998, 14, 5913. (11) Richter, A. G.; Durbin, M. K.; Yu, C.-J.; Dutta, P. Langmuir 1998, 14, 5980. (12) Doudevski, I.; Schwartz, D. K. Phys. ReV. B 1999, 60, 14. (13) Peng, X.; Wickham, J.; Alivisatos, A. P. J. Am. Chem. Soc. 1998, 120, 5343. (14) Bartelt, M. C.; Evans, J. W. Phys. ReV. B 1992, 46, 12675. (15) Tang, L. H. J. Phys. I 1993, 3, 935. (16) Amar, J. G.; Family, F.; Lam, P. M. Phys. ReV. B 1994, 50, 8781.
