Surface Clusters of Colloid Particles Produced by Deposition on Sites

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Surface Clusters of Colloid Particles Produced by Deposition on Sites Zbigniew Adamczyk,* Katarzyna Jaszczo´łt, Barbara Siwek, and Paweł Weron´ski Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences, 30-239 Krako´ w, Niezapominajek 8, Poland Received March 21, 2005. In Final Form: June 17, 2005 The possibility of producing surface clusters of well-defined structure formed by colloid particles was analyzed theoretically and experimentally. Theoretical results were derived by performing Monte Carlotype simulations according to the generalized random sequential adsorption (RSA) mechanism. In these simulations, the jamming coverage of particles adsorbing irreversibly on spherical sites was determined as a function of the particle-to-site size ratio λ. It was revealed that, by properly choosing λ, a targeted site coordination can be achieved; for example, there can be one, two, three, and so forth particles attached to one site. The structure of the heterogeneous clusters produced in this way was described in terms of the pair correlation function. It was predicted that the extent of ordering within surface clusters was diminished as the concentration of sites increased. These theoretical predictions were checked by performing deposition experiments of negatively charged polystyrene latex particles (average diameter 0.9 µm) under the diffusion-controlled transport regime. Mica sheets precovered by positively charged polystyrene latex (average diameters 0.45 and 0.95 µm) were used as the substrate surface in these experiments. Positive latex (site) deposition was also carried out under diffusion-controlled transport conditions. The concentration of the sites and the adsorbed particles was determined by direct particle counting using optical microscopy. It was found, in quantitative agreement with theoretical simulations, that the structure of surface clusters produced in this way exhibits a significant degree of short-range ordering. It also was proven experimentally that clusters containing a targeted number of colloid particles (e.g., 2 and 4) could be produced by the deposition procedure.

I. Introduction The adsorption and deposition (irreversible adsorption) of proteins and other biomaterials on solid/liquid interfaces is of great significance in many practical and natural processes, such as filtration, chromatography, separation of viruses, bacteria, pathological cells, thrombosis, biofouling, biomineralization, and so forth. The effectiveness of these processes is often enhanced by the use of coupling agents bound to interfaces (often called precursor films; e.g., polyelectrolytes).1-8 Analogously, by using the alternative layer-by-layer deposition method involving polyelectrolytes, multilayer particle films of a targeted architecture can be produced.9-13 In biomedical applications, special proteins (antibodies) attached to the surface are applied for the selective binding of desired ligands from protein mixtures, as is the case in affinity chroma* To whom correspondence should be addressed: E-mail: [email protected]. (1) Boluk, M. Y.; van de Ven, T. G. M. Colloids Surf. 1990, 46, 157. (2) Lvov, Y.; Ariga, K.; Ichinose, I.; Kunitake, T. J. Am. Chem. Soc. 1995, 117, 6120. (3) Serizawa, T.; Takashita, H.; Akashi, M. Langmuir 1998, 14, 4088. (4) Serizawa, T.; Kamimura, S.; Akashi, M. Colloids Surf. 2000, 164, 237. (5) Schmitt, J.; Machtle, P.; Eck, D.; Mohwald, H.; Helm, C. A. Langmuir 1999, 15, 3256. (6) Chen, K. M.; Jiang, X.; Kimmerling, L. C.; Hammond, P. T. Langmuir 2000, 16, 7825. (7) Ngankam, A. P.; Mao, G.; Van Tassel, P. R. Langmuir 2004, 20, 3362. (8) Lvov, Y.; Ariga, K.; Onda, M.; Ichinose, I.; Kunitake, T. Langmuir 1997, 13, 6195. (9) Jiang, C.; Markutsya, S.; Tsukruk, V. V. Langmuir 2004, 20, 882. (10) Sun, C. Y.; Hao, E.; Zhang, X.; Yang, B.; Gao, M.; Shen, J.; Chi, L.; Fuchs, H. Langmuir 1997, 13, 5168. (11) Kotov, N. A.; Dekany, I.; Fendler, J. H. J. Phys. Chem. 1995, 99, 13065. (12) Chase, H. A. Chem. Eng. Sci. 1984, 39, 1099. (13) Willner, I.; Lion-Dagan, M.; Marx-Tibbon, S.; Katz, E. J. Am. Chem. Soc. 1995, 117, 6581.

tography,12 recognition processes (biosensors),13-14 immunological assays,15,16 and so forth. A characteristic feature of all of these processes is that solute (ion, particle, or protein) adsorption occurs at heterogeneous surfaces bearing isolated adsorption sites. Despite the significance of particle adsorption at sites and heterogeneous surfaces leading to multilayer formation, few have studied this subject experimentally and in a systematic manner. The existing results were obtained for polystyrene latex adsorbing at mica under the convection-dominated transport conditions in the impinging-jet cells.17,18 On the other hand, preliminary results concerning the diffusion-controlled adsorption of colloid particles at surfaces precovered by sites have been reported in refs 19 and 20. It was found in these studies that, for a particleto-site ratio less than four, more than one particle was attached to one site. This site multiplicity effect profoundly influenced the structure of the adsorbed particle layer and the jamming limit. It can be expected that, by exploiting this effect, a general procedure can be developed for producing heterogeneous surface clusters of desired composition. One can expect that a controlled number of particles (colloids or proteins) can be attached to the site by physisorption. Subsequently, other particles with the opposite surface (14) Katz, E.; Buckmann, A. E.; Willner, I. J. Am. Chem. Soc. 2001, 123, 10752. (15) Inerowicz, H. D.; Howell, S.; Reniger, F. E.; Reifenberger, R. Langmuir 2002, 18, 2563. (16) Howell, S. W.; Inerowicz, H. D.; Reifenberger, R. Langmuir 2003, 19, 436. (17) Adamczyk, Z.; Siwek, B.; Musiał, E. Langmuir 2001, 17, 4529. (18) Adamczyk, Z.; Siwek, B.; Weron´ski, P.; Musiał, E. Appl. Surf. Sci. 2002, 196, 250. (19) Adamczyk, Z.; Siwek, B.; Weron´ski, P.; Jaszczo´łt, K. Colloids Surf., A 2003, 222, 15. (20) Adamczyk, Z.; Jaszczo´łt, K.; Siwek, B.; Weron´ski, P. J. Chem. Phys. 2004, 120, 11155.

10.1021/la058008f CCC: $30.25 © 2005 American Chemical Society Published on Web 08/11/2005

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Figure 1. A schematic view of particle adsorption at heterogeneous surfaces bearing spherically shaped adsorption sites.

charge can be attached and so forth. This can potentially be exploited in many processes of practical significance, not to mention producing replicas of surface features too small to be observed under an optical microscope. Hence, the aim of this work was to study both the theoretical and the experimental aspects of the process of generating surface clusters that contain a desired number of particles attached to sites preadsorbed on a substrate surface. II. The Theoretical Model A theoretical modeling of the irreversible adsorption of particles on surfaces that exhibit a continuous distribution of adsorption sites has extensively been carried out in terms of the random sequential adsorption (RSA) model.21-28 To examine a more realistic situation of the discrete distribution of adsorption sites, Jin et al.29,30 developed a more general RSA approach, referred to as the random site surfaces model (RSS). In this model, a finite number of sites (surface heterogeneities) were assumed to be in the pointlike form. A correspondence (mapping function) between the adsorption process at the RSS surfaces and the widely studied continuous surface RSA model was found. Later, more elaborate models were developed that considered the finite dimensions of the sites, having the form of either hard disks31 or hard spheres attached to the surface32,33 (see Figure 1). The configuration of these sites was produced by performing the continuous RSA simulations. Adsorption kinetics, particle configurations, (21) Widom, B. J. Chem. Phys. 1966, 44, 3888. (22) Hinrichsen, E. L.; Feder, J.; Jossang, T. J. Stat. Phys. 1986, 44, 793. (23) Schaaf, P.; Talbot, J. J. Chem. Phys. 1989, 91, 4401. (24) Adamczyk, Z.; Siwek, B.; Zembala, M.; Weron´ski, P. J. Colloid Interface Sci. 1990, 140, 123. (25) Evans, J. W. Rev. Mod. Phys. 1993, 65, 1281. (26) Adamczyk, Z.; Senger, B.; Voegel, J. C.; Schaaf, P. J. Chem. Phys. 1999, 110, 3118. (27) Senger, B.; Voegel, J. C.; Schaaf, P. Colloids Surf., A. 2000, 165, 255. (28) Adamczyk, Z. Irreversible Adsorption of Particles. In Adsorption Theory, Modeling and Analysis; Toth, J., Ed.; Marcel-Dekker: New York 2002; pp 251-374. (29) Jin, X.; Wang, N. H. L.; Tarjus, G.; Talbot, J. J. Phys. Chem. 1993, 97, 4256. (30) Jin, X.; Talbot, J.; Wang, N. H. L. AIChE J. 1994, 40, 1685. (31) Adamczyk, Z.; Weron´ski, P.; Musiał, E. J. Chem. Phys. 2002, 116, 4665. (32) Adamczyk, Z.; Weron´ski, P.; Musiał, E. J. Colloid Interface Sci. 2002, 248, 67. (33) Adamczyk, Z.; Siwek, B.; Weron´ski, P.; Musiał, E. Appl. Surf. Sci. 2002, 196, 250.

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and the jamming coverage were determined via Monte Carlo-type simulations as a function of the particle-tosite size ratio λ ) ap/as (in which 2as is the site diameter, and 2ap is the adsorbing particle diameter) and the site coverage Θs. The basic assumption of this model is that the colloid particle (of a spherical shape) can only be adsorbed upon touching the site (see Figure 1). Otherwise, at bare interface, the particle will not adsorb. Physically, this corresponds to the situation in which particles are irreversibly bound to sites because of short-range attractive interactions of an electrostatic or chemical nature. Furthermore, particle adsorption was assumed to be irreversible and localized, which meant that all particle positions remained fixed during the entire simulation run. In this work, we used, in principle, the same algorithm of simulations that was described in refs 31 and 32. The simulation loop consisted of the following major steps: (i) A homogeneous substrate having surface area ∆S (see Figure 1) was precovered by sites according to the classical RSA model.24-27 The number of spherically shaped sites was Nos, and its dimensionless surface concentration (coverage) was Θs ) πas2Nos. As proven in previous numerical simulations,23,24 the distribution of sites generated in the RSA processes for Θs < 0.1 remained quasi-random. (ii) An adsorbing (virtual) particle of diameter 2ap was generated at random within the simulation area. If it did not touch any of sites, the particle was rejected, and another virtual particle was produced (the number of attempts, Natt, was increased by one). (iii) If the particle touched any of the sites, the overlapping test was performed according to the usual RSA rules; that is, the sample was checked for the presence of any previously adsorbed particles within the exclusion volume. If overlapping was detected, the simulation loop was repeated (the number of attempts was increased by one). (iv) If no overlapping occurred, the virtual particle was assumed to be irreversibly adsorbed at the given position, its coordinates were stored, and the number of adsorbed particles, Np, was increased by one. Similar to the classical RSA simulations, adsorbed particle coverage at heterogeneous surfaces was expressed as Θp ) πap2Np. On the other hand, the structure of the particle monolayer that was adsorbed on the sites was quantitatively characterized in terms of the pair correlation function g(r) [often referred to as the radial distribution function (RDF)],which is defined as27,28

〈

〉

πap2 ∆Np g(r) ) Θp 2πr∆r

(1)

in which 〈 〉 means the ensemble average, and Np is the number of particles adsorbed within the ring 2πr∆r drawn around a central particle. The function can be interpreted as an average probability of finding a particle (site) at a distance r from another particle (with the center located at r ) 0) normalized to the uniform probability at large distances. For the sake of convenience, the distance r is usually normalized by using the particle radius ap as a scaling variable. It is also worth mentioning that particle adsorption at spherically shaped sites is truly a threedimensional (3D) process, in contrast to particle adsorption at disk-shaped sites.31 Accordingly, by calculating the pair correlation function from eq 1, the distance r was measured between the projections of the adsorbed particle centers on the adsorption plane. To obtain a satisfactory accuracy

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Figure 2. The dependence of the jamming coverage of particles (Θ∞p ) on the λ2Θs parameter. The points denote the results of numerical simulations performed for (1) λ ) 1, (2) λ ) 1.1, (3) λ ) 1.7, (4) λ ) 2, (5) λ ) 2.37, (6) λ ) 3, and (7) λ ) 4; the solid lines represent the linear regression.

Figure 3. The dependence of the site coordination number (ns) on λ (particle-to-site size ratio). The solid line represents the hyperbolic fitting function ns ) 5.967/λ - 0.517.

of g(r), particle populations reaching 105 are usually considered. The main task of the simulations performed in this work was to determine the site coordination number ns as a function of the site coverage Θs and the particle-to-site size quotient λ. The coordination number can be determined most directly by plotting the dependence Θ∞p versus λ2Θs. For low jamming coverage of the particles, when the volume exclusion effects are negligible, this should produce a straight line with the slope ns.20 Examples of such calculations performed for λ that varied between 1 and 4 are shown in Figure 2. As determined from linear regression fits, for λ ) 1, the site coordination number ns was 5.5; for λ ) 2, ns ) 2.4; and for λ ) 4, ns ) 1. The latter case is in accordance with simple geometrical considerations that indicate that, for λ g 4, one site can accommodate no more than one adsorbing particle.20 The theoretical dependence of ns on λ is plotted in Figure 3. It is well-fitted by the simple interpolating function

ns ) 5.967/λ - 0.517

(2)

As shown in Figure 3, ns increases abruptly when the size of the particle approaches the site dimension, that is, for

λ f 1. From the results shown in Figures 2 and 3, one can deduce that when Θs is not too large, the jamming coverage of particles is given by the expression Θ∞p ) nsλ2Θs, with ns being calculated from eq 2. The results shown in Figure 3 also suggest that particle clusters of targeted composition, that is, those containing between two and six particles coordinated at one site, can be produced by exploiting the particle deposition process. For example, on the basis of Figure 3, the following predictions can be made: ns ) 2 for λ ) 2.37, ns ) 3 for λ ) 1.7, ns ) 4 for λ ) 1.4, and ns ) 5 for λ ) 1.1. These predictions were confirmed by the simulations of particle monolayers shown in Figure 4 for λ ) 2.37, 1.7, and 1.1. The site coverage in these calculations was kept constant at Θs ) 0.005, and the corresponding particle coverage Θp was 0.053, 0.0428, and 0.0294, respectively. This provided the actual values of ns ) 1.9 for λ ) 2.37, ns ) 3 for λ ) 1.7, and ns ) 4.9 for λ )1.1. Note that the number of particles attached to one site, for most of the simulated clusters, was close to the above coordination numbers. The structure of the particles forming the surface clusters is reflected by the pair correlation function, which is also shown in this series of figures. Note that, in all cases, a maximum of considerable height appears at the distance between the particles of ∼2ap that varies from 22 (for λ ) 2.37) to ∼35 (for λ ) 1.1). Interestingly, for λ ) 1.1 there appears to be a secondary peak at the distance r ) 3.5 that was never predicted or observed in adsorption on homogeneous surfaces. The position of the peak reflects particles located on opposite sides of the cluster. Another series of monolayers was generated in the simulations with the aim of illustrating the effect of vanishing order within the clusters with increased coverage of particles. This can most directly be seen by comparing the pair correlation functions in Figure 5 obtained for λ ) 1.1 and Θs increasing progressively from 0.01 to 0.1 (the pair correlation function was calculated for the jamming state of the particles, i.e., for particle coverage Θp ) 0.058, 0.1128, 0.255, and 0.437). Note that the primary peak height decreased from 18 to ∼3 when Θp increased from 0.058 to 0.437. This indicates that the ordering of the particles largely vanished because of the overlapping of the adjacent clusters. The theoretical results presented above suggest quite unequivocally that surface clusters of desired composition can be produced in the process of particle adsorption on sites, the coverage of which should be kept very low, on the order of 0.01 or less. III. Experimental Procedures A. The Experimental Cell. Particle deposition experiments were carried out using the direct microscope observation method in the diffusion cell described previously.19-20 The main part of the cell was a Teflon container with dimensions 1.5 × 2.5 × 8 cm (height) and with a 2 × 6-cm rectangular window made of a mica sheet, which was used as the substrate for particle adsorption. The cell was fixed to the optical microscope stage (Nikon) that was attached to a special metal table, which could be inclined (rotated) up to a 90° angle. The microscope was oriented horizontally, with the objective perpendicular to the substrate surface. In this arrangement, gravity was directed parallel to the mica surface, which effectively eliminated the particle sedimentation effect. To eliminate the natural convection effects, the temperature of both the cell and the room was set to 25 °C. The deposition kinetics and particle distribution over the substrate were followed in situ using the Nikon microscope equipped with a long-distance objective coupled with a CCD camera (Hamamatsu C-3077) and an image analyzing system. B. Materials and Methods. Three samples of polystyrene latex were used as model colloid systems in this study of particle

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Figure 4. Monolayers of the particles adsorbed at heterogeneous surfaces with the corresponding pair correlation function derived from numerical simulations (Θs ) 0.005). (a) λ ) 2.37, Θp ) 0.053; (b) λ ) 1.7, Θp ) 0.0428; (c) λ ) 1.1, Θp ) 0.0294. deposition. These latex particles of submicrometer size are known to possess perfectly spherical shape and low polidispersity. The negatively charged latex suspension was synthesized according to the polymerization procedure using a persulfate initiator. The concentrated stock suspension obtained from the polymerization was purified by a steam distillation and a prolonged membrane filtration according to the procedure described in ref 34. The particle concentrations of the dilute samples used in the experiments were determined by a Coulter-Counter. Particle size distribution was determined by laser diffractometry (BeckmanCoulter Laser Diffraction Particle Size Analyzer LS 13 320) and by photon correlation spectroscopy (PCS) using a Malvern NanoZS. The average size (2a) of the negative latex used in the deposition experiments was 0.9 µm with a standard deviation of 0.06 µm. The positively charged latex suspension (used for modeling adsorption sites) was produced and cleaned according to a similar procedure in which an azonitrile initiator was used in place of the persulfate initiator. Two samples of positive latices were used, having average diameters of 2as ) 0.45 µm, with a standard deviation of 0.04 µm, and 0.95 µm, with a standard deviation of 0.09 µm. Hence, the particle size ratio, being an important parameter and being denoted by λ, was equal to 2 and 0.95 in our case. The ζ potential of the latex samples was determined by a Malvern Zetasizer. For samples with an ionic strength I of 10-3 M, which was adjusted by KCl addition, and pH ) 5.5 prevailing in experiments, the ζ potential of the negative latex was -89 mV, whereas the potentials for the positive latices were 56 and 62 mV for smaller and larger particles, respectively. The adsorbing (substrate) surfaces were prepared from mica sheets provided by Dean Transted Ltd., England. The ζ potential of this mica was determined by the streaming potential method in the plane-parallel channel cell.35 For the above experimental conditions, the ζ potential on the mica was -80 mV. The experiment proceeded as follows: a mica plate cut to the appropriate size was freshly cleaved and mounted into the cell’s window without using any adhesive. Then, the positive latex suspension was carefully poured into the cell. Particle deposition was carried out for a desired time (typically 15-60 min at bulk particle concentration, changing in the range of 109 -1010 cm-3) until the prescribed surface concentration of particles was attained. The surface concentration was determined by direct (34) Goodwin, J. W.; Hearn, J.; Ho, C. C.; Ottewill, R. H. Colloid Polym. Sci. 1974, 252, 464. (35) Zembala, M.; Adamczyk, Z. Langmuir 2000, 16, 1593.

microscope counting in statistically chosen areas. The total number of particles counted was ∼1000, which ensured a relative precision of coverage determination of better than 3%. For the sake of convenience, the surface concentration of the particles was expressed as the dimensionless coverage Θs ) πas2〈Ns〉 (in which 〈Ns〉 is the average surface concentration of the adsorbed smaller particles). After the heterogeneous substrate (mica covered by adsorption sites) was prepared, the positive latex suspension was replaced by a 10-3 M KCl solution and then by the negative latex suspension, and the particle deposition run was performed. The bulk suspension concentration of the negative latex nb was typically (2-5) × 109 cm-3 in these experiments. Images of adsorbed particles were collected in a wet state of the monolayer at selected coverages of particles. Coordinates of typically 1000-2000 particles were collected and processed by special software to obtain the pair correlation function. It was also proven in separate experiments that the particle adsorption of both latices was perfectly irreversible and localized. No lateral motion or particle desorption was observed when the particle monolayers were rinsed in situ with an electrolyte, 10-3 M KCl, for a prolonged period of time.

IV. Results and Discussion Because of the relatively large size of both the negative and the positive latex particles used in our experiments, these particles could be observed under an optical microscope, which allowed one to determine not only surface concentration but also the relative positions (coordinates) of the particles. Moreover, because of the larger size ratio, both the uncovered sites and the adsorbed particles could be easily distinguished from one another, which considerably enhanced the reliability of the experimental data discussed below. In the first series of experiments, the kinetics of the positive latex adsorption was determined to select appropriate conditions for the controlled preparation of substrate surfaces bearing a desired coverage of sites. A typical kinetic run observed for bulk suspension concentration nb ) 2 × 109 cm-3 is shown in Figure 6. Here, it can be seen that the site coverage Θs increased linearly with the square root of the deposition time t, in accordance

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Figure 5. Monolayers of the particles at the jamming state and the corresponding pair correlation function (derived from numerical simulations for λ ) 1.1). (a) Θs ) 0.01, Θp ) 0.058; (b) Θs ) 0.02, Θp ) 0.113; (c) Θs ) 0.05, Θp ) 0.255; (d) Θs ) 0.10, Θp ) 0.437.

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Figure 6. Initial deposition kinetics of positive latex (averaged diameter 0.45 µm) at bare mica. I ) 10-3 M, and nb ) 2.0 × 109 cm-3 (points). The solid line denotes the theoretical results calculated from eq 3.

Figure 8. The pair correlation function g(r/ap) and micrographs of negative latex particles (averaged diameter 0.9 µm) adsorbed on sites. Θs ) 0.014, Θp) 0.075, λ ) 2, and I ) 10-3 M. The solid line denotes the theoretical pair correlation function derived from the extended RSA model.

Figure 7. Micrographs showing site distributions (positive latex particles adsorbed on mica), with the corresponding pair correlation function g(r/as). Θs ) 0.05, and I ) 10-3 M. The dashed line shows the pair correlation function derived from the Boltzmann distribution.

with diffusion-controlled transport to a plane surface, which is described by the formula

x

Θs ) 2πas2

Dst n π b

(3)

in which Ds ) kT/6πηas is the diffusion coefficient of the particle in the bulk (k is the Boltzmann constant, T is the absolute temperature, and η is the dynamic viscosity of the suspension). Equation 3 was used to predict the adsorption time needed to obtain a desired surface concentration (coverage) of sites. However, the real coverage in every run was determined, as mentioned above, by directly counting the number of adsorbed particles. The uniformity of the site distributions that were produced according to the above procedure was also examined. This was done by a thorough variance analysis28 carried out for various areas of the mica substrate that were covered by sites. It was found that the site distributions were statistically uniform with no tendency toward clustering. This can be qualitatively observed in Figure 7 in which a micrograph of the sites (positive latex particles 0.95 µm in size) is shown for Θs ) 0.05 and I ) 10-3 M.

A quantitative characteristic of the site distribution in terms of the pair correlation function is also shown. Note that for such low surface coverage, particle distribution closely resembles the Boltzmann distribution that is calculated by taking into account the repulsive doublelayer interactions between particles only.24,28 The slight deviation of the pair correlation function from zero observed for r/as values less than 2 can be attributed to the latex suspension polidispersity. After the conditions of producing well-defined site distributions of desired coverage were established, systematic studies of larger particles deposition were performed, with the aim of checking the possibility of producing particle clusters of various structure. Examples of large particle configurations within the clusters obtained in these experiments are shown in Figures 8 and 9. In Figure 8, the results obtained for λ ) 2, Θs ) 0.014, and Θp ) 0.075 are presented. Hence, the average coordination number ns ) Θp/Θsλ2 ) 1.4. As shown in the micrograph, most of the clusters obtained under these conditions are in the form of two larger particles attached to one site. This interesting observation apparently represents the first indication of the site multiplicity effect that occurs in the colloid adsorption processes. Because of the larger particle size, the distributions shown in Figure 8 can be quantitatively analyzed in terms of the pair correlation function g(r/ap) defined by eq 1. A characteristic feature of the g(r/ap) function shown in Figure 8 is that it exhibits a well-pronounced peak (the height of which reaches ∼5) at the distance r/ap ≈ 2. Another interesting fact is that the pair correlation function did not vanish at a distance of r/ap < 2 but rather vanished at rmin/ap ≈ 1.7. As discussed in ref 20, this represents direct experimental proof of the fact that particle adsorption occurred in various planes (quasi-3D) as a result of the finite size of the adsorption sites. It is worth mentioning that all the

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Figure 9. The pair correlation function g(r/ap) and micrographs of negative latex particles (averaged diameter 0.9 µm) adsorbed on sites. λ ) 0.95, and I ) 10-3 M. (a) Θs ) 0.015, Θp) 0.06. (b) Θs ) 0.023, Θp) 0.09. (c) Θs ) 0.040, Θp) 0.16. The points denote the experimental results, and the solid lines denote the theoretical pair correlation function derived from the extended RSA model.

characteristic features of the correlation function shown in Figure 8 are well-reflected by the theoretical simulations derived from the generalized RSA model described above. As predicted theoretically (see Figure 3), site coordination numbers higher than those obtained for λ ) 2 can be achieved if the size of the adsorbing particle becomes comparable to the size of the site. This hypothesis was confirmed by further experiments performed for λ ) 0.95. As mentioned, in this case, sites were produced by the adsorption of positive latex particles that were 0.95 µm in size. The micrographs of the particle clusters produced in this case are shown in Figure 9. The site coverage Θs varied between 0.015 and 0.04, and the particle coverage Θp varied between 0.06 and 0.16. The average site coordination number was therefore 4.4 in these experiments. As shown in the micrographs, most of the clusters that were obtained under these conditions were composed of four or five particles coordinated near one adsorption site, forming “flower-like” structures. The particles within the cluster are well-structured, which is reflected by the large peak height of the pair correlation function reaching

10 for Θp ) 0.06. A secondary peak also appeared at the distance 3.5ap, which is in accordance with theoretical predictions. It is interesting to note that the effect of the 3D adsorption of the particles is even more pronounced than it was in the previous case of λ ) 2 because, in this case, the pair correlation function assumes values larger than zero for r/ap > 1, rather than r/ap > 1.7. However, the ordering degree of the particles within the clusters decreased significantly with the coverage Θp, which is evident from the pair correlation function shown in Figure 9b,c. This occurred because the particles from neighboring clusters started to overlap with each other. It can be deduced from the above results that colloid particle adsorption on sites can be used not only for producing surface clusters of a desired coordination number but also for enhancing the image of the site. For example, in the latter case of λ ) 0.95, the volume of the cluster exceeds approximately five times the volume of the site. Because light scattering in the Rayleigh’s regime depends on the square of the particle volume, a considerable enhancement of the scattered light intensity can be

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achieved. In this way, sites invisible under an optical microscope can be made visible. V. Conclusions The possibility of producing surface clusters of welldefined structure was demonstrated both theoretically by performing Monte Carlo-type simulations and experimentally by using direct microscope observation. It was also revealed that by properly choosing the particle-tosite size ratio λ, a targeted site coordination can be achieved; for example, there can be one, two, three, and so forth particles attached to one site. For λ values that are close to unity, flower-like structures of particle

clusters can be produced experimentally. The degree of ordering within the surface clusters produced by particle adsorption was diminished as the concentration of the sites and adsorbed particles increased. It can be predicted that the method presented in this work can be used not only to generate surface clusters of desired architecture but also to make replicas of surface features (sites) that are invisible under an optical microscope. Acknowledgment. This work was supported by the KBN Grant 4T09A 076 25. LA058008F