pubs.acs.org/Langmuir © 2009 American Chemical Society
Particle Deposition onto Charge-Heterogeneous Substrates Tania Rizwan and Subir Bhattacharjee* Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta T6G 2G8, Canada Received December 10, 2008. Revised Manuscript Received February 6, 2009 The deposition of model colloidal particles onto striped charge-heterogeneous surfaces was studied to determine the influence of surface chemical heterogeneity on the deposit morphology. The charge heterogeneity was created employing self-assembled monolayers of carboxyl- and amine-terminated alkanethiols using a soft lithographic technique. Polystyrene sulfate microspheres and fluorescent polystyrene nanoparticles were sequentially deposited onto the patterned substrate under no flow (quiescent) condition. The deposited structures and the micropatterns were imaged using a combination of phase contrast and fluorescence microscopy. The experimental particle deposition behavior was compared to predictions based on random sequential adsorption (RSA) employing a Monte Carlo technique. Comparison of radial distribution obtained from experimental data was made with the theoretical results and found to be in good agreement despite the use of a simple binary probabilistic model in the simulations. The primary conclusion from the study is that particles tend to preferentially deposit at the edges of the favorable stripes. However, the extent of this bias can be controlled by the proximity of consecutive favorable stripes (or width of the intervening unfavorable stripes) as well as the particle size relative to the stripe width. Second, a simple binary probability distribution-based Monte Carlo RSA deposition model adequately predicts the deposit structure, particularly the periodicity of the underlying patterns on the substrate. These observations suggest that the patterns could be encrypted by the deposited particles, which can subsequently be decoded, given the proper “key” or information that is based on analyzing the deposit morphology.
Introduction Naturally occurring deposition substrates generally contain surface charge heterogeneity arising from differences in constituent minerals, chemical imperfections, and surface-bound “impurities” and coatings.1-6 This chemical variability results in uneven or heterogeneous surface charges that are randomly distributed, of arbitrary geometrical shapes, and various length scales. A commonly adopted technique to model surfaces with macroscopic charge heterogeneity is to define at least two types of charge locations on a given collector (for instance, positive and negative), assigning the surface area fraction occupied by one type of charge and using a two-site averaging process generally referred to as the “patchwise heterogeneity model”.7,8 These patches are assumed to be much larger than the depositing colloidal particles, such that the interactions between patch boundaries have a negligible effect on particle deposition. For such surfaces, the overall particle deposition rate is considered to be a linear combination of deposition rates on the various surface patches and regions. While the patchwise heterogeneity models provide an accurate description of macroscopic charge heterogeneity *Corresponding author. Telephone: (780) 492-6712. Fax: (780)4922200. E-mail:
[email protected]. (1) Kihira, H.; Ryde, N.; Matijevic, E. J. Chem. Soc., Faraday Trans. 1992, 88(16), 2379–2386. (2) Vaidyanathan, R.; Tien, C. Chem. Eng. Sci. 1991, 46(4), 967–983. (3) Vreeker, R.; Kuin, A. J.; Denboer, D. C.; Hoekstra, L. L.; Agterof, W. G. M. J. Colloid Interface Sci. 1992, 154(1), 138–145. (4) Ryan, J. N.; Elimelech, M. Colloids Surf., A: Physicochem. Eng. Aspects 1996, 107, 1–56. (5) Loveland, J. P.; Bhattacharjee, S.; Ryan, J. N.; Elimelech, M. J. Contam. Hydrol. 2003, 65(3), 161–182. (6) Khachatourian, A. V. M.; Wistrom, A. O. J. Phys. Chem. B 1998, 102 (14), 2483–2493. (7) Johnson, P. R.; Sun, N.; Elimelech, M. Environ. Sci. Technol. 1996, 30 (11), 3284–3293. (8) Song, L. F.; Johnson, P. R.; Elimelech, M. Environ. Sci. Technol. 1994, 28(6), 1164–1171.
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(i.e., when the patches are much larger than the depositing particles), they may not be well-suited for microscopic chargeheterogeneous patches that have a length scale comparable to the particle size.9-11 For such systems, it was theoretically demonstrated that the initial particle deposition rates on a 50% favorable surface may resemble that of a completely favorable surface.10,11 It is therefore of great importance from both a theoretical and a practical point of view to fundamentally explore the effects of microscale charge heterogeneity on governing mechanisms of the particle deposition process. A systematic experimental study of chemical heterogeneity employing naturally occurring substrates is nontrivial. This is owing to the randomness in the distribution of chemical properties of substrates, and the presence of physical heterogeneity (roughness) in conjunction with chemical heterogeneity. In this context, it would be appropriate to systematically create chemical heterogeneity by chemically patterning smooth model substrates of regular geometries. Studying particle deposition onto such a model substrate, where the heterogeneity is artificially created and its nature is known accurately, can lead to considerable insight into how the deposition behavior is influenced by the presence of surface charge heterogeneity. If the distribution of the heterogeneous patches is known a priori, elucidation of their influence on particle deposition becomes more tractable.12,13 From a theoretical perspective, deposition on such patterned substrates poses interesting challenges by itself, (9) Elimelech, M.; Chen, J. Y.; Kuznar, Z. A. Langmuir 2003, 19(17), 6594–6597. (10) Nazemifard, N.; Masliyah, J. H.; Bhattacharjee, S. Langmuir 2006, 22 (24), 9879–9893. (11) Nazemifard, N.; Masliyah, J. H.; Bhattacharjee, S. J. Colloid Interface Sci. 2006, 293(1), 1–15. (12) Chen, J. Y.; Ko, C. H.; Bhattacharjee, S.; Elimelech, M. Colloids Surf., A: Physicochem. Eng. Aspects 2001, 191, 3–16. (13) Walker, S. L.; Bhattacharjee, S.; Hoek, E. M. V.; Elimelech, M. Langmuir 2002, 18(6), 2193–2198.
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including the identification of the parameters that control the properties of the resulting deposit.10 Such studies employing patterned heterogeneity have mostly been limited to elucidation of the initial deposition rates on a clean surface. To our knowledge, not much attention has been given toward understanding the long-term kinetics of deposition and the ensuing deposit morphologies formed on patterned charge-heterogeneous substrates. Several experimental studies during the past years report deposition of particles on select types of patterned substrates (such as circles, lines, or a checkerboard structure).14-16 Systematic experimental studies employing large periodic arrays of a repeated pattern, where the pattern features are varied relative to particle size, are not available in literature. Experimental quantification of the surface coverage and deposit morphology on large-scale patterned areas of substrates is also lacking. Micrometer-scale patterned charge heterogeneity is created on smooth planar substrates by the modification of their surfaces through chemical patterning; the patterns can be produced by photolithography,17-19 laser ablation,20-22 or by soft lithographic processes.9,14-16,23-30 Soft lithography23 is a widely used technique for ‘‘printing’’ and attaching molecules that are used for surface modification. Control of surface chemistry and corresponding patterns of chemical functional units can be achieved by using self-assembled monolayers (SAMs)31 of organic molecules that have good adhesion to the substrates (for example, thiols to gold,14,24,25,29,31,32 silanes to silica substrates,27,30,31 and polyelectrolytes14,29,31). Of all the soft lithographic techniques, development of charge heterogeneity on substrates employing microcontact printing (μCP) is well-established.28,33 μCP involves the transfer of molecules of a SAM from an elastomeric stamp to a metallic thin film (usually Au). Recently, substrates bearing patterned surface features of (14) Chen, K. M.; Jiang, X. P.; Kimerling, L. C.; Hammond, P. T. Langmuir 2000, 16(20), 7825–7834. (15) Zheng, H. P.; Rubner, M. F.; Hammond, P. T. Langmuir 2002, 18 (11), 4505–4510. (16) Chen, J. Y.; Klemic, J. F.; Elimelech, M. Nano Lett. 2002, 2(4), 393– 396. (17) Clark, P. Biosens. Bioelectron. 1994, 9(9), 657–661. (18) Kruger, C.; Jonas, U. J. Colloid Interface Sci. 2002, 252(2), 331–338. (19) Scotchford, C. A.; Ball, M.; Winkelmann, M.; Voros, J.; Csucs, C. Biomaterials 2003, 24(7), 1147–1158. (20) Wright, J.; Ivanova, E.; Pham, D.; Filipponi, L.; Viezzoli, A.; Suyama, K.; Shirai, M.; Tsunooka, A.; Nicolau, D. V. Langmuir 2003, 19 (2), 446–452. (21) Shadnam, M. R.; Kirkwood, S. E.; Fedosejevs, R.; Amirfazli, A. Langmuir 2004, 20(7), 2667–2676. (22) Rhinow, D.; Hampp, N. A. IEEE Trans. Nanobiosci. 2006, 5(3), 188– 192. (23) Xia, Y. N.; Whitesides, G. M. Annu. Rev. Mater. Sci. 1998, 28, 153– 184. (24) Zheng, H. P.; Berg, M. C.; Rubner, M. F.; Hammond, P. T. Langmuir 2004, 20(17), 7215–7222. (25) Aizenberg, J.; Braun, P. V.; Wiltzius, P. Phys. Rev. Lett. 2000, 84(13), 2997–3000. (26) Fan, F. Q.; Stebe, K. J. Langmuir 2004, 20(8), 3062–3067. (27) Fustin, C. A.; Glasser, G.; Spiess, H. W.; Jonas, U. Langmuir 2004, 20 (21), 9114–9123. (28) Kumar, A.; Biebuyck, H. A.; Whitesides, G. M. Langmuir 1994, 10(5), 1498–1511. (29) Lee, I.; Zheng, H. P.; Rubner, M. F.; Hammond, P. T. Adv. Mater. 2002, 14(8), 572–577. (30) Masuda, Y.; Itoh, T.; Itoh, M.; Koumoto, K. Langmuir 2004, 20(13), 5588–5592. (31) Ulman, A. Chem. Rev. 1996, 96(4), 1533–1554. (32) Tien, J.; Terfort, A.; Whitesides, G. M. Langmuir 1997, 13(20), 5349– 5355. (33) Michel, B.; Bernard, A.; Bietsch, A.; Delamarche, E.; Geissler, M.; Juncker, D.; Kind, H.; Renault, J. P.; Rothuizen, H.; Schmid, H.; SchmidtWinkel, P.; Stutz, R.; Wolf, H. IBM J. Res. Dev. 2001, 45(5), 697–719.
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regular shapes such as circles (dots),15,25,34 squares,16,26 and rectangles (stripes)14,24,35 have been created on homogeneous surfaces by μCP. The aim of this work is to experimentally create welldefined charge-heterogeneous surfaces by employing soft lithographic techniques. We then study the deposition of model colloidal particles onto such substrates under a noflow (or quiescent) condition, mainly focusing on the surface coverage and deposit morphologies obtained after a long time. Furthermore, we present a simple mathematical description of particle deposition on the created rectangular (striped) surface features employing a Monte-Carlo-type simulation technique, the results of which are compared with the experiments.
Mathematical Model Geometry. We consider a smooth planar collector represented as a square lattice of edge, L, as shown schematically in Figure 1. The substrate consists of striped chemical heterogeneity. The width of the favorable (attractive) stripes is w, whereas the width of the unfavorable stripes is b. The structure thereby created is periodic along the x direction, which is aligned perpendicular to the stripes with the periodicity length or pitch, p = w + b. The number of favorable (or unfavorable) stripes on the square lattice is npair= L/p, although their relative contribution to the total surface area will vary depending on the ratio w/p. The total surface area of the favorable stripes is given by Sf= npairwL, and the corresponding favorable area fraction is λ ¼
Sf npair w w ¼ ¼ L p S
where S is the total surface area of the collector. The adsorbing particles are assumed to be spheres (with a disk shaped projected area) of diameter d = 2ap. The ratio of the width of the favorable stripe to the particle diameter is given by γ = w/d. Simulations of Particle Deposition. We applied a simple probabilistic method to derive information on the distribution of particles deposited on the patterned surface. These simulations were conducted according to the random sequential adsorption (RSA) model. 36,37 For these simulations, we define the probability, p(x, y), of a particle attaching to a site, as pðx, yÞ
¼
pf
S
¼
pu
S
∈ Sf , a ∈ ð1 -Sf , a Þ
ð1Þ
When the particle is located on an accessible favorable region of the collector, Sf,a, we assign pf = 1. Elsewhere on the substrate, the probability is assumed to be pu = 0. More complex distribution functions can be proposed, but this study will be primarily based on the above simple representation of the deposition probabilities. The deposition algorithm starts by randomly selecting an (x, y) location on the substrate as a probable attachment point. Following this, the probability of the attachment at (34) 2417. (35) (36) (37)
Karakurt, I.; Leiderer, P.; Boneberg, J. Langmuir 2006, 22(6), 2415– Kokkoli, E.; Zukoski, C. F. Langmuir 2001, 17(2), 369–376. Evans, J. W. Rev. Mod. Phys. 1993, 65(4), 1281–1329. Feder, J. J. Theor. Biol. 1980, 87(2), 237–254.
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where Fi*(x) is the normalized density distribution on the ith stripe pair. Note that eqs 3 and 4 yield identical results in the limit of an infinitely large surface or a large number of samples. For finite sized samples and small surface areas, though, eq 4 provides a smoother density profile over a single stripe pair. The radial distribution (pair correlation) function g(r) is defined as the probability of finding a particle at a radial distance r from another particle (placed at r = 0) normalized with respect to a uniform distribution. We calculate the g(r) for the entire particle populations generated according to the RSA scheme by exploiting the definition:40 gðrÞ ¼ Figure 1. Schematic representation of the modeled surface charge heterogeneity. The square collector of height L consists of rectangular stripes with alternate regions that are favorable (gray) and unfavorable (white) to deposition of having widths w and b, respectively. The total width of a favorable and unfavorable stripe gives the pitch, p. The deposited spherical particles of diameter d = 2ap have their centers constrained to lie within the favorable stripes. this point is determined. If the surface is favorable and vacant, the probability of deposition is 1, and the particle position is accepted (deposition on an accessible favorable site). Otherwise, if the randomly selected position overlaps with the projected area of a previously deposited particle, the probability is chosen to be zero. Finally, if the particle position lies on the unfavorable region, the probability of deposition is again chosen to be zero. Surface Coverage, Particle Density Distribution, and Pair Correlation Function. We consider deposition of spherical particles of diameter d on a square substrate with edge L. Accordingly, the overall and favorable fractional surface coverage of particles are calculated as, respectively, θ ¼
πNp d 2 4L2
θf ¼
and
πNp d 2 4λL2
ð2Þ
where Np is the number of adsorbed particles over the collector, πd2/4 (= Sp) is the projected cross-sectional area of the particle, L2 (= S) is the surface area of the collector, and λ (= Sf/S) is the favorable area fraction of the substrate. The local particle density distribution, F*(x), is defined as the probability of finding a particle at a given location of the substrate relative to a uniform distribution, Fav(= Np/S):38,39 F ðxÞ ¼
FðxÞ ΔNp nbin S ΔNp nbin ¼ ¼ Fav L2 Np Np
ð3Þ
where ΔNp is the particle number in each bin, and nbin is the number of rectangular bins along the x axis. In subsequent sections of this paper, the density distributions are reported over a single heterogeneous stripe pair. We denote this quantity as Fn*(x). Since the entire substrate consists of npair = L/p pairs of stripes, Fn*(x) can be computed by averaging the normalized density distributions over the npair stripe pairs, yielding nP pair
Fn ðxÞ
¼
i ¼1
Fi ðxÞ
ð4Þ
npair
(38) Allen, M. P.; Tildesley, D. J., Computer Simulation of Liquids; Oxford University Press: Oxford, 1987. (39) Kim, A. S.; Bhattacharjee, S.; Elimelech, M. Langmuir 2001, 17(2), 552–561.
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ΔNp 4θ 2πrΔr πd 2
ð5Þ
where ΔNp is the number of particles adsorbed within the annular bin of area 2πrΔr drawn around the central particle. The directional distribution function is calculated following a scheme similar to the radial distribution function; the primary difference is that the radially scanned annular shell used for the g(r) calculation is replaced by a rectangular bin of area LΔx and scanned along the x direction: gðxÞ ¼
ΔNp 4θ LΔx πd 2
ð6Þ
Materials and Experimental Methods Patterned Sample Preparation. The stamps for μCP were fabricated from poly(dimethyl siloxane) (PDMS) (Sylgard 184, Dow Corning) by casting the PDMS against a silicon master containing the complementary pattern. The silicon master used to cast the PDMS stamp was fabricated using standard photolithographic procedures. The cast stamps were peeled and cut into individual pieces with each stamp having a patterned area of 1 mm2. Prior to use, the stamps were cleaned using 100% anhydrous ethanol and dried in a stream of N2. The substrates were prepared from glass slides (Fisher Scientific) coated with 1-3 nm of Cr and 200 nm of Au and diced into 1 mm 1 mm pieces. Each substrate piece was then cleaned in cold Piranha solution for about 10 min followed by a thorough wash using deionized (DI) water and drying in N2. Patterned SAMs were formed on them using μCP, employing standard procedures.23,28,41 The patterned surfaces were made using 11mercaptoundecanoic acid, HS (CH2)10-COOH of 98% purity (Sigma Aldrich), and 11-amino-1-undecanethiol hydrochloride, C11H25NS-HCl of 99% purity (Asemblon), solutions in anhydrous ethanol (Fisher Scientific). PDMS stamps with the imprinted microstructures were inked with a 10-4 M ethanolic solution of HS(CH2)10COOH, brought into contact with the gold surface for about 15 s, and then rinsed with anhydrous ethanol to produce discrete (negatively charged) domains of a carboxylic acid-terminated SAM on the substrate. The substrates were subsequently immersed in a 10-4 M solution of C11H25NS-HCl in ethanol for 1 h to cover the remainder of the substrate surface with the amine-terminated SAM. The zeta potentials of carboxylate SAMs are reported to be near neutral at pH 3-4 and become more negative with increasing pH, consistent with the weak acidity of carboxyl groups.42-44 (40) Pathria, R. K., Statistical Mechanics; Pergamon: New York, 1972; pp 447-448. (41) Wilbur, J. L.; Kumar, A.; Kim, E.; Whitesides, G. M. Adv. Mater. 1994, 6(7-8), 600–604. (42) Zhu, P. X.; Masuda, Y.; Yonezawa, T.; Koumoto, K. J. Am. Ceram. Soc. 2003, 86(5), 782–790. (43) Cheng, S. S.; Scherson, D. A.; Sukenik, C. N. Langmuir 1995, 11(4), 1190–1195. (44) Shyue, J. J.; De Guire, M. R. Langmuir 2004, 20(20), 8693–8698.
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Rizwan and Bhattacharjee Table 1. Relevant Properties of Polystyrene Sulfate Particles Used in the Deposition Experiments
mean diameter , μm standard deviation of diametera, % percent solids in stocka, (gm/100 mL) particle number concentrationa, m-3 surface charge densitya, μC 3 cm-2 zeta potentialb, mV a
a
1 μm model particles
2 μm model particles
100 nm fluorescent Nile Red particles
0.96 9.4 8.4 1.7 1016 -6.4 -83.57 ( 0.50
2 2.6 8.1 1.8 1016 -7.1 -104.80 ( 1.03
0.10 4.1 2.2 3.9 1019 -1.0
As reported by manufacturer. b As measured using a Brookhaven ZetaPals, 10 runs taken in a 0.01 mM KCl solution of pH 5.12.
On the other hand, the amine SAMs exhibit positive zeta potential at low pH, decreasing with increasing pH and becoming negative above pH 7.42,44 On the basis of above information, the pH of the suspension of particles of different volume fractions was kept within the range of 5.1 to 5.2 in order to encourage charging of both the carboxylic acid (negative) and the amine (positive) headgroups on the patterned SAM. Characterization. The stamped patterns contained rectangular stripes ranging from 2 to 4 μm in width, which are not visible optically. To characterize these patterns, the chemical property variations in the pattern features were detected using atomic force microscopy (AFM) in the lateral force microscopy38 (LFM; also known as friction force microscopy, FFM) and scanning surface potential microscopy (SSPM)45 modes in air and under ambient conditions. The measurements were performed on a Bioscope equipped with a Nanoscope IIIa controller and Extender Module (Digital Instruments). FFM was performed using a 200 μm long silicon nitride (DNP) cantilever with a nominal spring constant of 0.12 N/m and a resonant frequency of 20 kHz (Veeco Metrology) in the contact mode. Surface potential (SP) mapping was performed using a two-pass technique (lift mode).45 The technique allows separate measurements of topography and SP data, and has previously been used to characterize SP variations of patterned SAMS.46 Magnetic force etched silicon probes (MESPs, Vecco) coated with a thin conductive layer with a nominal spring constant of 2.8 N/m and resonant frequency of 75 kHz was used for the experiment. The initial conditions used for SP mapping were as follows: interleave drive amplitude: 5 V; frequency: 130 kHz; lift height: 100 nm; and scan rate: 0.5 Hz. Time-of-flight secondary ion mass spectroscopy (TOFSIMS) spectra were acquired using an ION-TOF TOF SIMS IV spectrometer (ION-TOF GmbH) using a 15 keV Ga+ ion source. Spectra were acquired for the negative secondary ions over a mass range of m/z = 0-1000 using an analysis area of 30 30 μm2. Deposition Procedure. As model colloids in the deposition experiments, two different diameters of white polystyrene sulfate (PS) particles (Interfacial Dynamics Co.) were used. The properties of the particles are shown in Table 1. Size and charge data are as reported by the manufacturer. The zeta potential of these particles was determined using a Brookhaven ZetaPals (Brookhaven Instruments Co.). The colloidal suspensions were made using ACS grade KCl (Fisher Scientific) with ionic concentration of 10-4 M, and the pH was held between 5.1 and 5.2 by adding an appropriate amount of 0.01 N HCl solution. The particles are negatively charged at these pH levels. The concentration of the PS particles was typically between 1.7 1013 to 1.8 1014 m-3. Approximately 2 mL of the suspension was placed in a cell consisting of two glass slides of dimension of 2 cm 6 cm separated by a PDMS spacer about 3 mm thick. The patterned substrate was attached to one of the glass slides, and remained immersed in the liquid throughout the experiment. (45) Electric Force Microscopy (EFM). In Support Note No. 230 Rev. A; Digital Instruments: Santa Barbara, CA, 1996. (46) Getty, R. R.; Alvarez, R.; Bonnell, D. A.; Sharp, K. G.; Percec, S.; Hietpas, P. B. In Surface Potential Mapping Of Patterned SAMs By Scanning Probe Microscopy; MRS Symposium Proceedings-Nanostrcutured Interfaces, San Francisco, CA, 2002; pp R11.9.1-R11.9.6.
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Figure 2. Schematic of the closed deposition cell assembly. The glass slides and spacer were enclosed in an aluminum holder provided with a rectangular opening on its top surface for visualization (Figure 2). All experiments were performed at 25C, and deposition was allowed to occur for 24 h under quiescent condition. After deposition, the cell was flushed to remove the excess particles using 10-4 M KCl solution modified to have the same pH as the particle suspension used, thereby preserving the final deposition structure in solution. Microscopy and Analysis. The structures formed by the particles were investigated in situ with an optical microscope. The closed deposition cell was placed under an upright microscope (Zeiss) coupled with a charge-coupled device (CCD) camera (Basler A 311f, Basler Vision Technologies). Images were captured at two magnifications (10 and 25), and the image sizes were 640 by 480 pixels. Post processing of the images was conducted using NI Vision 8.0 (National Instruments) to determine the position of the centers of the deposited particles and count the total number of particles deposited. Fluorescence Microscopy. As noted earlier, the patterns on the substrates are not visible under an optical microscope. In order to capture the patterns optically both before and after deposition of the model particles, we used negatively charged Nile Red fluorescent polystyrene particles of 100 nm diameter (excitation/ emission wavelength of dye: 520 nm/580 nm; Interfacial Dynamics). Other relevant properties of these particles are listed in Table 1. These particles preferentially deposit on the positively charged stripes. The images were captured using a fluorescence microscope (Axiovert 200M, Zeiss) fitted with a fluorescein isothiocyanate (FITC) filter set (FS10, Zeiss) having an excitation band-pass filter of range (450-490 nm) and emission band-pass filter of range (515-565 nm) and coupled with a color CCD camera (Basler A 102 fc, Basler Vision Technologies). Images were captured at 10, 20, and 40 magnifications using the NI Vision 8.0 frame grabber (National Instruments). To capture the image of the bare patterned substrate, 100 μL of the fluorescent particle laden stock suspension was added to Langmuir 2009, 25(9), 4907–4918
Rizwan and Bhattacharjee the closed cell containing the sample immersed in 10-4 M KCl solution. The particles were allowed to deposit over a 24 h period after which the suspension was flushed and replaced again with fresh KCl solution. The captured images reveal the negatively charged patterns as dark colored stripes while the positively charged stripes fluoresce due to the deposition of the 100 nm particles. To image the underlining pattern concomitantly with the deposited structures, first the larger model particles were allowed to deposit (using the deposition procedure mentioned earlier) in the closed cell. At the end of the deposition cycle, the model particle suspension was flushed out, and a second suspension containing the 100 nm fluorescent particles was added. The deposition of the fluorescent particles was allowed to continue for 24 h, after which the second suspension was removed and replaced by fresh KCl solution. Next, the substrates were imaged under a microscope to acquire two types of images under identical magnification, and on the same region of the substrates. The first image was captured in the phase contrast mode (no fluorescence), showing only the deposited structure of the larger model particles. The second image was captured in the fluorescence mode. The fluorescent regions correspond to locations on the substrate which are positively charged and do not contain any large model particle.
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Results and Discussion Characterization of SAM Pattern. The SAM patterns were characterized using AFM and TOF-SIMS spectrometry. Images of the SAM patterns, produced by μCP using a PDMS stamp containing alternate 4 μm (positive or NH2terminated) by 3 μm (negative or COOH-terminated) wide stripes, are shown in Figure 3. In the first topographic image obtained using tapping-mode AFM (Figure 3a), no pattern is evident because the lengths of the NH2- and COOHterminated thiols are similar (both C11), and consequently no perceptible height variations are observed. However, in the friction mode AFM imaging (Figure 3b), the contrast between the two different regions become visible as this technique allows the detection of changes in the lateral forces between the tip and the substrate due to the change in the chemical functionality of the adjacent regions. In Figure 3b, the scanned area of 30 30 μm2 shows the relative variation in the frictional property of the two types of stripes; the bright region (higher friction) of approximately 4 μm width corresponds to the stripe patterned with the NH2-terminated thiol, and the darker region (lower friction) of approximately 3 μm width corresponds to the COOH terminated stripe.
Figure 3. Images showing the results of the various techniques used to characterize the created patterned charge heterogeneous substrate. The substrates shown in all the images have 4 μm (positive) by 3 μm (negative) stripes. (a) AFM tapping-mode image of the topography of the patterned substrate showing no visible physical variation in the topology of the surface due to the similarity in chain length of the two thiols used. (b) FFM image of the same area as scanned in panel a. The image shows the low friction areas (dark), which correspond to the negative charged stripe and the high friction areas (light) corresponding to the positively charged stripes. (c) SSPM image showing the relative SP difference between the adjacent patterned thiol groups. The more positive SP (light) is associated with the NH2-terminated thiol monolayer. (d) TOF-SIMS image of the pattern showing the presence of the amine thiol (bright) as evident by the contrast obtained from the Cl- signal. Langmuir 2009, 25(9), 4907–4918
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Figure 4. Fluorescence microscopy image of a patterned chargeheterogeneous substrate. The patterns are 2 μm (positive) by 2 μm (negative), and the image was taken at a magnification of 10 (scale bar is 10 μm and view area is approximately 251 251 μm2). The negatively charged patterns appear as dark colored stripes, while the positively charged bands fluoresce (red) as a result of the negatively charged 100 nm particles depositing on the oppositely charged stripes.
Figure 3c is the SP map of a section of the same patterned substrate shown in Figure 3a,b. This image shows the relative variation in SP of the two regions obtained in the SSPM mode; the bright region (higher SP) corresponds to the stripe patterned with the NH2-terminated thiol, and the darker region (lower SP) corresponds to the COOH terminated stripe. TOF-SIMS was used to confirm the presence of the thiols in the pattern. In Figure 3d, the contrast obtained from the Cl- signal (for the amine-HCl thiol) clearly shows the stamped 4 μm pattern, but with less definition than that seen in the FFM or SSPM images. In summary, a variety of surface characterization modes were used to indicate that the pattern has been successfully reproduced over the gold substrate. A second set of experiments was used to validate the formation of the patterned SAM over a large area. In this case, the patterned substrate was immersed in a concentrated dispersion of the fluorescent Nile Red 100 nm polystyrene particles. The negatively charged particles deposited on the positive stripes of the substrate. A high concentration of the fluorescent particles was used in the deposition to ensure that the favorable stripes would be almost entirely covered by the particles, thus making them visible for imaging. Figure 4 depicts the fluorescence microscopy image obtained for 2 μm (positive) by 2 μm (negative) patterns on the substrate. The
Figure 5. Fluorescence microscopy images displaying the deposition of 2 μm negatively charged latex particles on a 2 μm (positive) by 2 μm (negative) striped pattern (λ = 0.5, γ = 1). (a) Phase contrast image showing the 2 μm particles deposited in an apparently random fashion on the substrate. (b) Fluorescent image of the exact same area in panel a obtained by depositing 100 nm negatively charged Nile Red particles onto the remaining regions of the positively charged stripe. The model 2 μm sized particles appear as dark circular shapes on the fluorescent positively charged strip, while the negatively charged patterns appear as dark colored stripes. (c) Image of a larger area on the same substrate obtained by superimposing images like those obtained in (a) and in (b), such that the model particles and the underlying pattern are now visible, simultaneously. All images are obtained under liquid. 4912
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negatively charged patterns appear as dark stripes, whereas the positively charged bands fluoresce as a result of the deposited 100 nm particles. This method of imaging the patterns allows us to capture larger view areas (a maximum of 800 600 μm2) on the substrate, which is not possible in the other modes of characterization (AFM or TOF-SIMS) described earlier. This shows the modest uniformity of the SAM patterns over relatively large areas of the substrate. Deposition Experiments. Figure 5 depicts the deposit morphologies obtained after deposition of model 2 μm diameter PS particles on the patterned substrate consisting of alternate negative and positive stripes that are both 2 μm in width (γ = w/d = 1). The favorable area fraction λ of the substrate is 50%. The images were obtained by initially depositing the model 2 μm particles followed by the deposition of the 100 nm fluorescent particles. Figure 5a depicts the phase contrast image where the particles (bright spots)
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appear to be depositing in an apparently random fashion on the substrate; the pattern underneath cannot be discerned readily from this image. In Figure 5b, we see the fluorescence image of the exactly same area shown in Figure 5a. In this image, the positively charged stripes appear as bright colored regions whereas the dark regions are negatively charged. This method provides a unique way of in situ observation of the deposit morphology in conjunction with the underlying substrate pattern without having to dry out the sample. Figure 5c is an image of a larger area on the same substrate obtained by superimposing the images obtained in Figure 5a, b, so that the model particles and the underlying pattern are now visible simultaneously. This imaging method provides insight regarding the deposit morphology on the patterned heterogeneity. It is apparent that the majority of the particles are deposited on the positively charged stripes. There seems to be a propensity of these particles to deposit near the edges
Figure 6. (a) Optical micrographs of polystyrene particles (bright spots) deposited on chemically patterned planar substrates for three different γ values (from left to right) of 1, 2, and 4. View area represents 160 160 μm2 on the substrates. The surface coverage calculated was θ(γ=1) = 0.27, θ(γ=2) = 0.26 and θ(γ=4) = 0.1. (b) Plots of the radial distribution function and (c) x-directional distribution functions obtained for the corresponding deposition images. All distances are scaled with respect to particle diameter. Table 2 contains other information pertinent to the deposition images obtained in part a.
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Rizwan and Bhattacharjee Table 2. Experimental Conditions under Which the Deposition Experiments Were Performed for Figures 5 and 6 γ (= w/d)
1
2
4
mean diameter of model particle, d (μm) width of favorable stripe, w (μm) pitch, p (μm) favorable area fraction, λ(= w/p) particle concentration used in deposition, n (particles/m3) KCl solution molarity (M)/pH
2 2 4 0.5 1.8 1013 10-4 M/ 5.12
0.96 2 4 0.5 1.7 1014 10-4 M/ 5.11
0.96 4 7 0.57 1.7 1014 10-4 M/ 5.13
Figure 7. Single particle distribution histograms for varying width to diameter ratios (a) γ = 0.25, (b) γ = 0.5, (c) γ = 1.0, and (d) γ = 2.0
obtained by depositing particles of diameter d (varying from 0.05 to 0.00625) on a scaled square area of 1.0 with λ = w/p = 0.5 (where, w = b = 0.0125). Each stripe pair (composed of half-favorable and half-unfavorable region) has been divided into 16 bins. The particles (centers) present in each bin are counted, and a distribution of deposited particles is obtained over a single pair of stripe. This is repeated over the entire area, and the particle count is normalized with the average particle number in each bin and averaged for the total number of stripe pairs (in this case 40 pairs).
of the favorable stripes. Finally, we note that the negatively charged stripes are not completely devoid of particles. In Figure 6, the results of the particle deposition experiments on patterned substrates conducted for three different ratios γ (= w/d) are presented. Figure 6a shows the three microscopic images of the deposition structure created on the patterned substrate. In each image, the stripes are vertically oriented. Three combinations of stripe width and particle size were investigated. The images (from left to right) represent the cases of γ ≈ 1 (particle diameter is 2 μm and pitch is 4 μm), γ ≈ 2 (particle diameter is 0.96 μm and pitch is 4 μm), and γ ≈ 4 (particle diameter is 0.96 μm and pitch is 7 μm), respectively. All images show bright specks (the model particles) against a dark background (the substrate). In the first image (γ ≈ 1), at first glance, the particles appear to have deposited randomly with no apparent pattern. For this case, the favorable area fraction of the substrate is λ = 0.5. In the images representing the cases γ = 2 (with λ = 0.5) and γ = 4 (with λ = 0.57), the deposition pattern appears much more ordered. In both these images, the particle size (or diameter) is smaller than the stripe. The 4914
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fractional surface coverages calculated for the images in Figure 6a are θ(γ=1) = 0.27, θ(γ=2) = 0.26 and θ(γ=4) = 0.097. Comparing all three images, it appears that the underlying pattern cannot be discerned readily when γ ≈ 1, particularly if the favorable stripes are very closely spaced. The close spacing of the favorable stripes is ensured when the favorable area fraction, λ g 0.5. This scenario, to our knowledge, has not been explored in previous studies. We analyze the deposit morphologies using the twodimensional (2D) RSA process36,37 and utilizing the pair correlation functions.40 The 2D pair correlation function has been extensively used in deposition studies.37,47-50 (47) Adamczyk, Z.; Zembala, M.; Siwek, B.; Warszynski, P. J. Colloid Interface Sci. 1990, 140(1), 123–137. (48) Hanarp, P.; Sutherland, D. S.; Gold, J.; Kasemo, B. Colloids Surf., A: Physicochem. Eng. Aspects 2003, 214(1-3), 23–36. (49) Johnson, C. A.; Lenhoff, A. M. J. Colloid Interface Sci. 1996, 179(2), 587–599. (50) Lavalle, P.; Schaaf, P.; Ostafin, M.; Voegel; Senger, B. Proc. Natl. Acad. Sci. U.S.A. 1999, 96(20), 11100–11105.
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Figure 6b,c shows plots of the pair correlation functions (radial and directional, respectively) of the corresponding deposition images underneath which they are placed. In Figure 6b, all three radial distribution profiles show a series of well-developed peaks, varying periodically with r. This oscillatory behavior of the plot implies that there is a longrange pattern of alternately enhanced and reduced deposition probability. The periodicity (pitch) of the consecutive peaks for the first two images (γ = 1 and γ = 2) are approximately 4 μm, and about 7 μm for the third image (γ = 4). These are also the pitch values for the underlying stripes in these figures (Table 2). Although the distribution profiles all closely emulate the periodic nature of the underlying heterogeneity, the correlation becomes weaker at large distances. This long-range correlation is not observed for deposition on a homogeneous favorable surface (cf. Figure 7, in Feder et al.37). We will further discuss these radial distribution functions in a later subsection. The graphs in Figure 6c are plots showing the directional pair probability distribution, g(x), in the x direction of the patterned substrate (the patterns align vertically along the y axis). The correlation effect is more pronounced in these plots, remaining quite pronounced even at larger distances. This is due to the constant favorable fraction of each bin area used while calculating the g(x) (eq 6), as opposed to the varying favorable area fraction in the radial distribution calculations (eq 5). The directional probability plots in the y direction (not shown) showed no correlation, implying the patterns are positioned perpendicularly along the x direction. The
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wavelength of the plots is in conformity with the pitch of the underlying pattern (as seen for the radial distribution). Comparison of Theoretical and Experimental Deposit Morphologies. The distribution of particles on the charge patterned surface was computed theoretically, and, in this section, we compare these theoretical results against the experimentally observed deposit morphologies reported in the previous section. As mentioned earlier, the theoretical calculations were performed assuming pf = 1 and pu = 0. With this simple binary deposition probability, the resulting deposit morphologies obtained on the substrate depend on the favorable surface area fraction, λ, and the favorable stripe width-to-particle diameter ratio, γ. Figure 7 depicts the normalized particle density distributions, calculated theoretically using a Monte Carlo approach, for different combinations of γ corresponding to a fixed λ. The distribution is shown over a rectangular region of the substrate having an area of pL. Clearly, all the particle centers are located on the favorable fraction of the surface. When γ = 0.25 and 0.5, i.e., when the particle diameter is 4 and 2 times the favorable stripe width, respectively, the distribution is fairly uniform on the favorable stripe, with the probability density being =2 on every segment of the favorable stripe (Figure 7a,b). When γ = 1, we observe a greater probability of finding the particles at the edges of the favorable stripes (Figure 7c). This behavior is also apparent when γ = 2 in Figure 7d. Therefore, as γ g 1, the particle distribution appears to be considerably biased toward the edges of the favorable stripes.
Figure 8. Particle density distribution charts for varying favorable width to pitch ratios of (a) λ = 0.25, (b) λ = 0.5, (c) λ = 0.8, and (d) λ = 1.0 obtained by depositing particles of diameter d = 0.0125 on a scaled square area of 1.0 with γ = w/d = 1.0 (where, w = 0.0125 and b is varying). Each stripe pair has been divided up into 20 bins. The particles (centers) present in each bin are counted and a distribution of deposited particles is obtained over a single pair of stripe. This is repeated over the entire area, and the particle count is normalized with the average number of particles present in each bin and averaged over the total number of stripes. Langmuir 2009, 25(9), 4907–4918
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Figure 8 depicts the particle density distributions for a fixed value of γ = 1 corresponding to different favorable area fractions, λ ranging between 0.25 and 1.0. In Figure 8a, b, the density distributions depict a considerable bias toward a greater particle density at the edges of the favorable stripes. However, for λ = 0.8 and 1 (Figure 8c,d), the density distribution becomes more uniform over the entire favorable surface. The above parametric studies indicate that there is a considerable variation in the deposit morphology corresponding to different ratios of particle size to favorable stripe width, and the favorable area fraction of the charge heterogeneous substrate. It is particularly interesting that the deposit morphology can be systematically altered by judiciously changing these ratios. In the following, we address how these distributions influence the fractional surface coverage of the deposited particles on the patterned surface and the ensuing blocking effects. It is straightforward to calculate the fractional coverage of these spherical particles on the substrate. Two types of fractional coverages were defined in eq 2. Notably, when λ = 1, θf = θ. In this limiting situation, the maximum surface coverage attained by hard spherical particles is θ¥ ∼ 54.6%.36,37 In all cases, the maximum coverage on homogeneous surfaces after a large number of attempted particle placements approached 54.6%. Although we use a uniform probability, pf = 1, to deposit the particles on the favorable stripe, the particles have a greater tendency to deposit at the stripe boundaries. Recently, this trend was also reported by Adamczyk et al.,51 and has been explained in light of the entropic principle.36,51 In previous studies, however, a single boundary of a favorable stripe was considered. Consequently, the probability of a particle depositing at the edge of a favorable stripe remained unchanged as particle deposition progressed. Our results indicate that this entropic maximization of the deposition probability at the favorable stripe boundary is subject to modification depending on the width of the adjoining unfavorable stripes. In particular, if the width of the unfavorable stripes becomes comparable to (or smaller than) the particle diameter, then the particles deposited on two consecutive favorable stripes can influence the deposition probabilities at the stripe edges. Figure 9 depicts the maximum surface coverage attained on the charge heterogeneous surfaces for different combinations of λ and γ. The primary calculated variable shown in the figures is the maximum surface coverage based on the entire surface area, θmax. The filled symbols are the fractional surface coverage on the favorable area fraction, θf,max = θmax/λ. The maximum coverage was determined approximately after depositing a large number of particles, when 2000 consecutive attempts failed to result in deposition of a new particle on the substrate. In Figure 9a, the variation of the fractional surface coverage with γ is depicted for a fixed favorable area fraction of 0.5 In this case, the fractional surface coverage approaches the hard-sphere jamming limit, i.e. θmax fθ¥ for small values of γ e 0.5. For larger values of γ, the maximum coverage is lower. In all cases, the fractional coverage on the favorable regions is much higher. Clearly, values greater than 1 are unreasonable (the two values of θf,max enclosed in the dotted (51) Adamczyk, Z.; Barbasz, J.; Nattich, M. Langmuir 2008, 24(5), 1756– 1762.
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Figure 9. Near-blocking surface coverage calculated over the total favorable available area (θf,max in 9) and the total collector area (θmax in O) for varying (a) γ values and (b) λ values. box in Figure 9a for γ e 0.5). For γ < 1, even particles depositing at the center of a favorable stripe can block a portion of the neighboring unfavorable stripes. These results show that on heterogeneous surfaces, the deposition on the favorable fraction of the substrate is greatly enhanced. Our results also show that only a 50% favorable surface can act as a homogeneously favorable surface to particle deposition. This interesting observation was pointed out in our earlier studies10,11and shows how the deposit morphology leads to such a behavior. Figure 9b depicts the maximum coverage corresponding to different favorable area fractions for a fixed value of γ = 1 (particle diameter = favorable stripe width). The hardsphere jamming limit is attained (θ¥ = 0.546) when λ = 1 (entire surface is favorable). When λ is reduced, the overall surface coverage, θmax, decreases monotonically, but θf,max, increases. This observation indicates that small favorable patches on an otherwise unfavorable substrate are highly amenable to particle deposition. In Figure 10, we explore the particle distributions obtained on two surfaces: one that is 50% favorable (λ = 0.5) and one that is homogeneously favorable (λ = 1.0) for γ = 0.25. Figure 10a shows the configuration of the deposited particles generated on the 50% favorable surface, while Figure 10b shows the deposited particles on the homogeneous surface. The total fractional coverage (which is near the maximum limit for both) was θ = 0.551 for the striped surface and θ = 0.527 for the homogeneous one. In both distribution maps, it appears as though the particles have adsorbed randomly on the surface of the collectors. From a cursory observation of Langmuir 2009, 25(9), 4907–4918
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Figure 10. (a) Distribution of adsorbed particles generated in the RSA simulation by depositing on a striped surface with a 50% favorable area
(λ = 0.5) by spheres (disks) of diameter that is twice the size of the width of a favorable stripe (γ = 0.5) and coverage is θ = 0.551. (b) Distribution of the same sized particles as in panel a, deposited onto a homogenously favorable collector (λ = 1.0) with θ = 0.527. (c) Radial pair distribution functions and (d) directional distribution functions plotted for the cases shown in panels a and b. Both the plots are shown over a scaled distance of 5 particle diameters, with the dotted line representing the data for the striped surface (λ = 0.5) and the solid line representing the homogeneous surface (λ = 1.0).
the maps, it is difficult to determine which substrate has an underlying pattern. Figure 10c is a comparison of the radial distribution function for the two cases. The g(r) obtained for the homogeneous substrate is typical of those obtained by using the 2D hard sphere RSA model.37 For both the striped (dashed line) and the homogeneous (solid line) surfaces, the primary peak (nearest-neighbor particle probability) occurs at a distance of r = d, and the peak value is only slightly higher for the striped surface. Compared to the striped surface, the oscillations of the g(r) around the uncorrelated value of 1 are more strongly damped for the homogeneous substrate. This implies a long-range order and a periodicity that matches with the pitch of the underlying heterogeneity (pitch, p = d). The salient difference between the two cases is observable in Figure 10d. These are the plots of the directional distribution function for the two cases. There is no correlation observed for the homogeneous surface in the x direction, since the particles have an equal probability of depositing anywhere on the substrate along that direction. This is not the case for the striped surface. Thus we see a strong oscillatory behavior in the directional distribution function (discontinuous line) with an alternation between enhanced (representing the favorable locations) and reduced probability (unfavorable regions) of finding a particle. The favorable particle locations, as seen in the g(r) plot, coincide with the pitch of the pattern. This phenomenon has a probable application in the area of microcryptography. As we have seen so far, the striped pattern is concealed by the deposited particles. One could then essentially “decode” the message Langmuir 2009, 25(9), 4907–4918
Figure 11. Comparison of the radial distribution functions ob-
tained for γ = 1.0 and λ= 0.5 with a total coverage of θ ≈ 0.3; the continuous line shows the numerical results for a 2D hard sphere, and the dots show the experimental results. The inset shows a comparison of the x-directional distribution function. All distances are scaled with respect to the particle diameter.
underneath, given the proper “key” or information that is based on analyzing the deposit structure. Finally, in Figure 11 we compare experimental data with our numerical results for the case of γ = 1.0 and λ = 0.5 and plot the g(r) and x-directional distribution functions (inset). Relevant information regarding the experimental conditions used is cited in Table 2. In Figure 11, we find a fairly good agreement of experimental data (dashed line) and the numerical results (solid line). Both the g(r) and g(x) plots DOI: 10.1021/la804075g
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show that the numerical model predicts the periodicity in the particle distribution functions remarkably well. The position of the peaks of the numerically obtained g(r) and g(x) plots coincide with those of the experiments. There is, however, a discrepancy in the magnitudes of the peaks; the numerical results show consistently larger oscillations compared to the experimental results. In this regard, it is worth mentioning that an important feature which we ignored in our simple RSA model is the effect of colloidal interactions (e.g., electrostatic and van der Waals interactions). We believe that defining the probabilities employing the accurate interaction potentials should improve the quantitative agreement. Alternatively, one can elucidate the interaction potentials through an inverse problem of fitting the experimental pair correlation functions with appropriate models.40
Concluding Remarks Deposition of model colloidal particles onto striped charge heterogeneous planar substrates was studied. The striped patterns were developed using μCP of carboxyl- and amineterminated thiols on a gold substrate. Deposit morphologies were observed using a unique combination of phase contrast and fluorescence microscopy on a bidisperse particle deposit. The experimental results were then compared against predictions based on a simple Monte Carlo simulation for different particle sizes and stripe dimensions. The primary conclusions from the study are as follows: i. Particles tend to preferentially deposit at the edges of the favorable stripes. However, the extent of this bias is controlled by the proximity of consecutive favorable stripes (or width of the intervening unfavorable
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stripes) as well as the particle size relative to the stripe width. ii. Deposit morphologies near jamming limits formed on 50% favorable patterned surfaces can be visually identical to those formed on fully favorable surfaces. Under such circumstances, the underlying patterns cannot be readily discerned, except by investigating subtle differences between particle radial distributions. iii. A simple binary probability distribution-based Monte Carlo RSA deposition model adequately predicts the deposit structure, particularly the periodicity of the underlying patterns on the substrate. Incorporation of the actual particle substrate interactions may provide a more accurate quantitative agreement between the experimental and theoretical distributions. The observations may have application in the area of microcryptography. The patterns could be encrypted by the deposited particles over them, which can be “decoded” given the proper “key” or information that is based on analyzing the deposition structure. This study reports deposition in a quiescent medium. It is expected that deposition on chemically patterned surfaces in the presence of flow can lead to interesting variations of deposit morphologies. Acknowledgment. The authors gratefully acknowledge the financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC), the Canada Research Chairs (CRC) Program, and the Alberta Ingenuity Fund. The assistance of the staff of the University of Alberta Nanofabrication Facility during the microfabrication work is also gratefully acknowledged.
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