Controlled Assembly of Micrometer-Sized Spheres: Theory and

Langmuir 2007, 23, 7859-7873

7859

Controlled Assembly of Micrometer-Sized Spheres: Theory and Application Elizabeth J. Tull, Philip N. Bartlett,* and Kate R. Ryan School of Chemistry, UniVersity of Southampton, Highfield, Southampton, Hampshire S017 1BJ, U.K. ReceiVed January 12, 2007. In Final Form: March 15, 2007 Site-selective assembly of 5 µm amine-functionalized glass spheres from aqueous suspensions onto gold surfaces patterned with carboxylic acid and methyl-terminated thiols has been achieved through the introduction of a variable tilt flow cell. In situ microscope imaging has been employed to study the four phases of assembly independently, and the relative roles of electrostatic attraction and capillary emersion have been explored. In contradiction to the commonly recognized electrostatic assembly model, detailed theoretical analysis and experimental evidence are presented to support a mechanism where patterning occurs at the point of meniscus contact. Control of pattern quality is demonstrated through the comparison of results obtained from a variety of experiments, and the best conditions for the assembly of monolayer features are identified. Finally, evidence for the extension of this assembly method to the production of singlet sphere arrays is discussed.

Introduction Resonant cavities are key components in photonic circuits providing feedback, wavelength selectivity, and energy storage to allow dispersion control and enhanced nonlinearity1 resonant filtering,2,3 waveguiding with low bend radius,4,5 and ultralow threshold lasing.6-8 Glass microspheres and microcylinders with diameters ranging from a few micrometers to a hundred micrometers have been shown to exhibit high-quality factors of the order of 109 when an appropriate whispering gallery mode is excited and lend themselves to evanescent coupling to optical waveguides, making assemblies of glass spheres on planar waveguide substrates ideal candidates for the construction of a new class of integrated optical devices. The ability to assemble spheres at specific locations on a planar optical circuit would allow the configuration of optical circuit function after photolithographic definition of the basic optical circuit in conventional waveguide technology. Furthermore, the assembly of several types of spheres would yield the potential for integration of different materials, tailored for the function required, such as rare earth-doped spheres for oscillation (lasing) and spheres with high χ(3) (third-order optical nonlinearity) for switching and bistability. Ideally, all spheres would assemble on the surface in one step, avoiding time-consuming and expensive sphere-bysphere assembly. The success of this approach depends upon the precision repeatability and robustness of sphere positioning. The efficiency of coupling between a waveguide and sphere varies with sphere size and both lateral and vertical spherewaveguide spacing. To eliminate significant optical losses, circuits must be constructed from spheres with diameters in excess of 5 µm (radius, a > 2.5 µm) positioned relative to the waveguide with nanometer precision. The presence of additional spheres, * Corresponding author. E-mail: [email protected]. (1) Heebner, J. E.; Boyd, R. W.; Park, Q. H. J. Opt. So. Am. B 2002, 19, 722. (2) Laine, J. P.; Little, B. E.; Lim, D. R.; Tapalian, H. C.; Kimerling, I. C.; Haus, H. A. Opt. Lett. 2000, 25, 1636. (3) Little, B. E.; Chu, S. T.; Hryniewicz, J. V.; Absil, P. P. Opt. Lett. 2000, 25, 344. (4) Yariv, A.; Xu, Y.; Lee, R. K.; Scherer, A. Opt. Lett. 1999, 24, 711. (5) Xu, Y.; Lee, R. K.; Yariv, A. J. Opt. Soc. Am. B 2000, 17, 387. (6) Spillane, S. M.; Kippenberg, T. J.; Vahala, K. J. Nature 2002, 415, 621. (7) Fujiwara, H.; Sasaki, K. J. Appl. Phys. 1999, 86, 2385. (8) Cai, M.; Vahala, K. Opt. Lett. 2001, 26, 884.

in random positions on the waveguide, will result in interference effects. At present, this sort of positioning has been reported using only optical tweezers9 or AFM10 -based processes, which are expensive and difficult to scale up. The assembly of polystyrene microspheres11-18 or glass nanospheres16-21 from aqueous solution or using mercury,6,9 into monolayer films or patterned arrays, is well documented in the literature. Chemically11,14,16,19 and topographically13,17,21 patterned substrates are exposed to drying droplets,16 gradually receding flows,13 or suspensions of spheres that are subjected to electric fields12 or selectively removed by spin21 or washing procedures.14 Efficient optoelectronic devices can be manufactured only by positioning glass microspheres (a > 2.5 µm) on clean flat substrates in the absence of nonuniform heavy metal or dense organic deposits. Accordingly, assembly from an aqueous solution or a volatile organic solvent is required. Under these conditions, the glass microspheres do not form a stable sol, even over a short period of time. Consequently, capillary and electrostatic forces are competing with sedimentation, and many of the conventional assembly methods result in nonspecific gravity-driven deposition. Brozell et al.22 and Masuda et al.23 have demonstrated methods for the assembly of large microspheres into arrays with a high (9) Moothoo, D. N.; Arlt, J.; Conroy, R. S.; Akerboom, F.; Voit, A.; Dholakia, K. Am. J. Phys. 2001, 69, 271. (10) Yang, D. Q.; Sacher, E. Appl. Surf. Sci. 2003, 210, 158. (11) Aizenberg, J.; Braun, P. V.; Wiltzius, P. Phys. ReV. Lett. 2000, 84, 2997. (12) Suzuki, M.; Yasukawa, T.; Mase, Y.; Oyamatsu, D.; Shiku, H.; Matsue, T. Langmuir 2004, 20, 11005. (13) Lu, Y.; Yin, Y. D.; Xia, Y. N. AdV. Mater. 2001, 13, 34. (14) Chen, K. M.; Jiang, X. P.; Kimerling, L. C.; Hammond, P. T. Langmuir 2000, 16, 7825. (15) Dimitrov, A. S.; Dushkin, C. D.; Yoshimura, H.; Nagayama, K. Langmuir 1994, 10, 432. (16) Maury, P.; Peter, M.; Mahalingam, V.; Reinhoudt, D. N.; Huskens, J. AdV. Funct. Mater. 2005, 15, 451. (17) Schaak, R. E.; Cable, R. E.; Leonard, B. M.; Norris, B. C. Langmuir 2004, 20, 7293. (18) Nagayama, K. Colloids Surf., A 1996, 109, 363. (19) Mahalingam, V.; Onclin, S.; Peter, M.; Ravoo, B. J.; Huskens, J.; Reinhoudt, D. N. Langmuir 2004, 20, 11756. (20) Hoogenboom, J. P.; Retif, C.; de Bres, E.; de Boer, M. V.; van LangenSuurling, A. K.; Romijn, J.; van Blaaderen, A. Nano Lett. 2004, 4, 205. (21) Ozin, G. A.; Yang, S. M. AdV. Funct. Mater. 2001, 11, 95. (22) Brozell, A. M.; Muha, M. A.; Parikh, A. N. Langmuir 2005, 21, 11588. (23) Masuda, Y.; Itoh, T.; Koumoto, K. Langmuir 2005, 21, 4478.

10.1021/la0700974 CCC: $37.00 © 2007 American Chemical Society Published on Web 06/07/2007

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Figure 1. Schematic illustration of the forces acting on a sphere as it passes through different stages of assembly onto a solid substrate on the base of a thin-layer flow cell, supported at an angle θT to the horizontal, after injection of a dilute suspension of spheres into the cell, from which solution is being removed at a controlled rate with a syringe.

density of pattern sites. Thus, Brozell et al. produced 100 µm patches of 5.66 µm spheres using an inverted sandwich method, and Masuda et al. produced small clusters (2-57 µm) of 1 µm microspheres by evaporation of a bicomponent solvent mixture. However, we are unaware of any literature describing the assembly of spheres into individual isolated patches on large planar substrates of the type required to prepare functional photonic circuits. Assembly effects are commonly attributed to the relationship between electrostatic and capillary forces within each colloidal system. Theoretical rationalization of capillary forces in assembling films was provided in a series of papers by Nagayama and Kralchevsky24,25 and Paunov26 and later used by Aizenburg et al.11 in a simple model comparing the role of electrostatic and capillary forces in the assembly of spheres on a chemically patterned slide. However, when glass microspheres are assembled from an aqueous solution, sedimentation leaves the upper liquid volume empty, forcing assembly to take place at the base of the container where gravitational forces locate spheres inside the double layer. As such, the linear superposition approximation27 used by Aizenburg et al. to calculate electrostatic interactions becomes invalid, and capillary interactions are altered. A new method of assembly and a new model tailored to accommodate the effects of sedimentation are required. In the present study, chemically patterned slides were exposed to various ionic solutions containing glass microspheres in a variable-tilt, double-injection flow cell. Gold substrates, patterned with octadecane thiol (ODT) and mercaptopropionic acid (MPA) to provide large hydrophobic methyl-terminated areas and small hydrophilic carboxyl-terminated patches with dimensions on the order of 35 µm, were placed into a thin-layer flow cell. An aqueous suspension of glass spheres, functionalized with [3-(2(24) Denkov, N. D.; Velev, O. D.; Kralchevsky, P. A.; Ivanov, I. B.; Yoshimura, H.; Nagayama, K. Langmuir 1992, 8, 3183. (25) Kralchevsky, P. A.; Nagayama, K. Langmuir 1994, 10, 23. (26) Paunov, V. N. Langmuir 1998, 14, 5088. (27) Bell, G. M.; Levine, S.; McCartne, L. N. J. Colloid Interface Sci. 1970, 33, 335.

aminoethylamino)propyl]trimethoxysilane (AAPTMS), was injected into the cell. The fluid was then withdrawn from the cell at a controlled rate, drawing the solution meniscus across the patterned substrate. In such a system, sphere assembly occurs in four distinct stages: delivery of spheres to the substrate via sedimentation, immobilization of spheres on the substrate in a moving flow, initial interaction of spheres with a receding meniscus, and simultaneous interaction with the meniscus and the substrate (Figure 1). The presence of these four distinct stages permits an interrogation of the individual contributions of gravitational, electrostatic, viscous drag, lift, and capillary emersion force in the assembly of spheres on patterned substrates. This article is organized as follows. In the next section, the theoretical basis for each of the four stages of assembly is discussed, and where possible, theoretical models describing the forces acting on the spheres at each stage of assembly are provided. This is followed by a description of all of the experiments conducted and a summary of the results obtained. Theoretical and experimental results are then compared, and the effects of flow rate, tilt angle, pH, ionic strength, and chemical functionality on sphere assembly are discussed. The article concludes with a summary of the proposed assembly mechanism and a comparison of the relative merits of two possible assembly methods.

Theoretical Basis The theoretical considerations underlying the assembly of micrometer-sized glass spheres in a thin flow cell can be examined in the same four stages: delivery of spheres to the substrate via sedimentation, immobilization of spheres on the substrate in a moving flow, initial interaction of spheres with a receding meniscus, and simultaneous interaction of spheres with the meniscus and the substrate. The nomenclature utilized in this section is listed in Table 1. Stage 1: Delivery of Spheres to the Substrate Surface via Sedimentation. In a flow cell where the width is much greater than the depth (2h), laminar flow is established for central flow

Controlled Assembly of Micrometer-Sized Spheres

Langmuir, Vol. 23, No. 14, 2007 7861 Table 1. Definition of Symbols

symbol a A ai B c∞ c∞i cpi

definition

symbol

definition

P R Re T U u0 ua

Di

radius of sphere area radius of ion hard sphere parameter concentration of ions of one type in the bulk concentration of ions of type i in the bulk concentration of ions of type i on the sphere surface diffusivity of counterion

e

charge on one electron

uL+a

EP F

potential energy Faraday’s constant

urelative usurface

FG

force due to gravity

uy

FB FChannel FD

force due to buoyancy force with flow force due to Stokes drag

x y z

FE FHS FS FSubstrate FNormal FT FT Channel FT Substrate g ∆GPlate h k L Lmeniscus

force due to electrostatic attraction force due to hard sphere repulsion frictional force due to surface roughness force toward the substrate force normal to the substrate force due to meniscus surface tension force due to meniscus with flow force due to meniscus normal to the substrate acceleration due to gravity energy between two plates half the depth of the flow cell Boltzman constant sphere-substrate spacing sphere substrate spacing when the sphere has been drawn into the meniscus equilibrium sphere substrate spacing entry length Avogadro number

zi β r 0 ηkH2O ηH2O κ FH2O Fp σp σs θA θT θp

radius of the sphere contact line universal gas constant Reynolds number temperature translational velocity of sphere w.r.t. substrate central fluid velocity in flow cell velocity of the fluid at a distance a from the substrate surface relative velocity between sphere and fluid in the direction of flow velocity of the fluid at a distance L + a from the substrate surface relative velocity between the sphere and the fluid relative velocity between the sphere and the fluid normal to the surface velocity of the fluid at a distance y from the center of the channel unit in the direction normal to the substrate distance from the center of the channel depth of sphere segment protruding outside of the solution charge on ion type i slip length relative permittivity of water permittivity of free space kinematic viscosity of water viscosity of water inverse Debye length density of water density of sphere surface potential of the sphere surface potential of the substrate surface angle subtended by the arc of the meniscus tilt angle of flow cell receding contact angle on the sphere surface

θs φp

receding contact angle on the substrate surface surface charge density on sphere

Lequilibrium le NA

uflow

velocities, u0, provided that Reynolds number, Re, is less than 2000,28 where

Re )

u0h ηk H2O

(1)

Under these conditions, a plug of solution entering a wide, shallow channel experiences friction at the walls, which slows down the flow in this region, creating a parabolic flow velocity profile called Poiseuille flow29 after an entry length le into the flow cell, where

le ) 0.1hRe

(2)

The flow velocity uy then varies with the distance y (normal to the substrate) from the midplane of the cell,29,30 where the parameter β describes the amount of slip at the surface.

[( ) ]

u y ) u0 1 -

y2 β +2 2 h h

(3)

Consequently, in addition to gravitational FG, buoyancy FB, and drag FD forces, spheres in a suspension introduced into the flow cell will experience classical lift forces as a result of the differential velocities across their surface and electrokinetic lift FEH and electroviscous drag FEV forces as a result of the charged nature of their surfaces.31,32 According to Staben et al.,33 the velocity profile present in the flow cell is unlikely to induce significant classical lift in low viscosity fluids such as water, and according to Tabatabaei et al.,32 the electroviscous drag and electrokinetic lift will also be small in this medium (Supporting Information). Accordingly, spheres of a density greater than that of water, placed in the flow cell, will sediment to the base of the channel where they experience a small fraction of the central flow velocity. Provided that the relative velocity urelative of a sphere of radius a with respect to the flow is sufficiently low that the flow around the sphere is laminar (i.e., the sphere Reynolds number, ReS ) FH2Ourelativea/ηH2O , is less than 0.234), then the drag force on the sphere is given by the Stokes equation28

FD ) 6πηH2Oaurelative

For a hydrophilic surface where there is no slip, β ) 0, and for a hydrophobic surface where there is slip, β > 0.

(4)

(31) Dukhin, A. S.; Vandeven, T. G. M. J. Colloid Interface Sci. 1993, 158, 85.

(28) Douglas, J. F.; Gasiorek, J. M.; Swaffield, J. A. Mechanics, 4th ed.; Prentice Hall: Upper Saddle River, NJ, 2000. (29) New Techniques for the Study of Electrodes and Their Reactions; Compton, R. G., Hamnett A., Eds.; Elsevier: Amsterdam, 1989; Vol. 29, p 181. (30) Tretheway, D. C.; Meinhart, C. D. Phys. Fluids 2002, 14, L9.

(32) Tabatabaei, S. M.; van de Ven, T. G. M.; Rey, A. D. J. Colloid Interface Sci. 2006, 301, 291. (33) Staben, M. E.; Davis, R. H. Int. J. Multiphase Flow 2005, 31, 529. (34) Bike, S. G.; Lazarro, L.; Prieve, D. C. J. Colloid Interface Sci. 1995, 175, 411.

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Considering forces parallel to the substrate (Figure 1, stage 1), the following expression can be derived:

FG sin θT ) (FD + FB)sin θT

(5)

Substituting for the gravitational force

4 FG ) πa3FPg 3

(6)

4 FB ) πa3FH2Og 3

(7)

and the buoyancy

together with the drag from eq 4 yields an expression for the relative velocity of the sphere parallel to the substrate:

[

]

2 1 4(FP - FH2O)ga sin(θT) uflow ) 6ηH2O 3

(8)

Similarly considering the forces on the sphere normal to the substrate, substituting in from eqs 4-7 yields the expression for the relative velocity normal to the substrate:

[

a charged sphere and a flat plane, which is valid for surfaces of like charge, in 1:1 electrolytes with low surface potentials or separations outside of the double layer. Because SAM-functionalized substrates exhibit high surface potentials in most electrolytes35,40 and the surfaces in this study are both oppositely charged and are forced into close contact (less than the thickness of the double layer) by the mass of the sphere, neither model is appropriate. However, Ben-tal41 observed that on close approach of oppositely charged surfaces in buffer, osmotic and dielectric pressure effects, arising from the exchange of solvated ions for charged spheres, result in repulsive interactions. In 1999, Jo¨nsson42 extended this idea, deriving an expression for the electrostatic interaction between two highly charged, planar surfaces of opposite charge located close to their most attractive separation in a 1:1 electrolyte with overlapping double layers. Jo¨nsson also demonstrated the extension of this theory to the description of sphere-plane interactions through application of the Derjaguin approximation. According to Jo¨nsson,42

]

2 1 4(FP - FH2O)ga cos(θT) usurface ) 6ηH2O 3

∆Gplane(L) ) A -

(

(

))

φP2 2 (1 - e-κL) 2e-2κL + R ln 0r κR2 (1 - e-2κL) (1 + e-κL)

(10)

where

(9)

As the sphere approaches the substrate, it will also experience additional opposition to translation across the substrate surface from frictional forces that can be attributed to surface roughness. The prediction of sphere trajectories is outside the scope of this study, but it is obvious that when the density of the sphere is significantly greater than that of the fluid, sedimentation will occur, bringing spheres close to the substrate surface. Additionally, we can infer that flow rate and tilt angle will alter the sedimentation characteristics observed in the flow cell and hence may be employed to control the density of deposits made on the substrate before the meniscus recedes across the substrate surface. Stage 2: Immobilization of Spheres on the Substrate in a Moving Flow. Stationary spheres close to a substrate surface in fluid flow experience a combination of electrostatic FE, hard sphere FHS, gravitational FG, buoyancy FB, drag FD, and surface roughness-related frictional FS forces as illustrated in Figure 1, stage 2. The ratio of these forces determines whether the spheres will adhere to the substrate upon deposition or simply move across the substrate surface under the influence of the fluid flow. Electrostatic forces vary according to the substrate-sphere spacing and the shear potential at the substrate that, in turn, varies with ionic strength,35 choice of electrolyte, and solution pH. The electrostatic interaction between two charged planar surfaces is generally evaluated using the linear superposition approximation36 or the constant surface potential model.37 Modification of these results according to the Derjaguin approximation,38 or for a more accurate analysis, the Zypman model,39 produces a detailed expression for the forces between (35) Schweiss, R.; Welzel, P. B.; Werner, C.; Knoll, W. Langmuir 2001, 17, 4304. (36) Gregory, J. J. Colloid Interface Sci. 1975, 51, 44. (37) Hogg, R.; Healy, T. W.; Fuerstenau, D. W. Trans. Faraday Soc. 1966, 62, 1638. (38) Intermolecular and Surface Forces: With Applications to Colloidal and Biological Systems, 2nd ed.; Israelachvili, J. N., Ed.; Academic Press Inc., 1991, pp 161. (39) Zypman, F. R. Journal of Physics-Condensed Matter 2006, 18, 2795.

R)

φPF 20rRTκ

(11)

and φP is the charge density on the surface of the particle, which can be obtained by combining the Boltzmann

cPi ) c∞ie-zieσP/kT

(12)

and the Grahame equations38

φp2

∑i cpi ) ∑i c∞i + 2 kT

(13)

0 r

to give

∑i c∞ie

-zieσp/kT

)

φp2

∑i c∞i + 2 kT

(14)

0 r

For a 1:1 electrolyte, this reduces to

c ∞e

-eσP/kT

+ c ∞e

+eσP/kT

φP2 ) 2c∞ + 20rkT

(15)

and consequently

φP )

x[ ( ) ] sinh

eσP - 2 (20rkTc∞) kT

(16)

If Zypman’s method39 for extracting the surface interaction force from a knowledge of the energy separation function between two planes is applied to eq 12, then the following result, for the sum of the electrostatic and hard sphere forces exerted by a charged surface (|σs|> 50 mV), on a charged sphere with smaller (40) Shyue, J. J.; De Guire, M. R. Langmuir 2004, 20, 8693. (41) Bental, N. J. Phys. Chem. 1995, 99, 9642. (42) Jonsson, B.; Stahlberg, J. Colloids Surf., B 1999, 14, 67.


Langmuir, Vol. 23, No. 14, 2007 7863

surface charge density close to their most attractive separation is obtained:

FHS(L) + FE(L) ) 2πa

(

[

∆Gplane(L) ∆Gplane(L + 2a) + + A A

)] [ (

1 B 1 + 72π L8 (L + 2a)8

+ 2π

)

1 B 1 + 504π (L + 2a)7 L7 L+2a ∆Gplane(L) (17) L A

]

∫

Accordingly, the total force acting normal to the surface of the substrate in the flow cell can be written as follows:

FNormal ) FHS + FE - (FG - FB)cos θT

(18)

Equations 10-18 demonstrate that the choice of electrolyte (σp, κ), the radius (a), and the surface chemistry (σp, κ) of the spheres determine the strength of the electrostatic interaction between spheres and surfaces with |σs| > 50 mV. Because spheres will settle at an equilibrium sphere-substrate spacing Lequilibrium, where the net force normal to the substrate is zero, these factors also determine the location of stationary spheres in the fluid with respect to the substrate. Surface roughness-related frictional forces increase with decreasing sphere-substrate spacing. Accordingly, the comparative strength of the electrostatic, hard sphere, gravitational, and buoyancy forces additionally determine the magnitude of the surface roughness-related frictional force evident on spheres after sedimentation and hence the flow rate and tilt angle required to induce movement of the spheres parallel the substrate. Equating the forces parallel to the substrate for stage 2, the surface roughness-related frictional force can be described by

FS ) FD + (FG - FB)sin θT

(19)

Assuming that Stokes’ law applies, this can be written as

FS ) 6πηH2OauL+a +

4π(Fp - FH2O)a3 3

g sin θT

(20)

The effects of differing surface modification will be reflected both in the frictional force arising as a consequence of the spheresubstrate spacing and in the drag component of eqs 19 and 20 (i.e., through differences in uL+a caused by slip at the substrate surface). Increased frictional forces will be required to maintain spheres at increased separation from the substrate above surfaces where the velocity of flow is higher,30 but these differences may not be strong enough to induce patterning of the substrate surface on their own. Stage 3: Initial Interaction of Spheres with a Receding Meniscus. Capillary forces result from pressure differences and surface tension effects that arise when spheres interrupt the shape of the vapor-liquid phase boundary.43 The basic rules set out by Laplace43 to describe the pressure acting across a curved surface can be applied to many different situations. In rationalizing improved packing observed on drying chemically patterned substrates after electrostatic localization of polystyrene spheres, Aizenburg et al.11 made use of the work of Nagayama et al.24-26 Nagayama demonstrated that when a suspension of spheres stable to coagulation is brought into contact with a substrate, a pressure difference draws spheres to the air-water boundary and across (43) Intermolecular and Surface Forces: With Applications to Colloidal and Biological Systems, 2nd ed.; Israelachvili, J. N., Ed.; Academic Press: New York, 1991; p 331.

Figure 2. Schematic of the capillary emersion forces acting on a sphere trapped between the substrate surface and the receding meniscus in a flow cell.

the meniscus surface toward the substrate. Once they are confined to a water layer thinner than their diameter, emersion capillary forces exert lateral and vertical forces on the spheres, acting in the case of small spheres (a < 1 µm) to draw spheres together and, in the case of larger spheres, to immobilize the spheres on the substrate surface. Alternatively, describing the interaction between an AFM tip and a wettable substrate, de Lazzer43 states that the total force acting on a single sphere in the direction normal to a nearby flat substrate when a liquid film shallower than the radius of the sphere is present is given by the sum of the capillary adhesion due to the pressure difference across the free surface and the surface tension forces acting tangentially to the interface along the contact line. This article is concerned with a system of spheres maintained on the base of a 1-mm-deep flow cell by gravitational forces. In this instance, the initial point of impact for the receding flow is at a height, exceeding the radius of the sphere, above the substrate surface. Because all fluid in the meniscus remains in contact with the bulk of the receding flow when impact occurs at this height, capillary pressures acting to draw the sphere toward the substrate will be negligible, and it is unlikely that the sphere will sustain any pressure inequalities of the type described by de Lazzer. Accordingly, it is valid to assume that initially the sphere meets an almost linear meniscus, influenced only by the forces associated with surface tension, FT, acting tangentially to the contact line. A schematic illustrating the action of surface tension on the sphere is given in Figure 2. The component of force across the surface of the meniscus is balanced in all directions, but there is a net force normal to the meniscus, determined by the receding contact angle of the sphere, θp, and the substrate surface, θs, over which the meniscus is passing. The resultant forces experienced by the sphere in the direction of flow (FT Channel) and toward the substrate (FT Substrate) are described by

(

π - θΑ sin(θS) (21) 2

(

π - θΑ cos(θS) (22) 2

FT Channel ) 2πFT sin(θΑ) cos θP +

)

and

FT Substrate ) 2πaFT sin(θΑ) cos θP +

)

where

θA ) arccos

(a -a z)

(23)

and FT is determined by the nature of the fluid and its environment. For an air/water boundary, FT is equal to 72.75 mJ m-2.44 The capillary forces are strongly influenced by the nature of the (44) Atkins, P. W. Physical Chemistry, 5th ed.; Oxford University Press: Oxford, U.K., 1994.

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Figure 4. Schematic of sphere-sphere impulses occurring as the meniscus recedes over hydrophobic and hydrophilic areas of the substrate in the thin-layer flow cell. Figure 3. Graph of the capillary emersion force acting, in the direction of flow (-) (eq 21) and directed toward the substrate (...) (eq 22), on a sphere (a ) 2.5 µm) with receding contact angles of (a) θp ) 20° and (b) θp ) 40° situated over a surface with receding contact angles of θs ) 20° (-) and θs ) 60° ()) as the meniscus recedes over its surface, assuming that FT ) 72.75 mJ m-2.48

sphere’s surface, falling into one of two categories: strongly hydrophilic or weakly hydrophilic. If strongly hydrophilic spheres (θP < 20°) are present on the substrate surface, then capillary emersion forces of the order of 10-7 N (Figure 3a) direct the sphere toward the substrate and down the channel from the moment of meniscus impact, as illustrated in Figure 1, stage 4. Irrespective of chemical patterning, sphere-substrate spacing is reduced, and surface friction increases. The additional force experienced by all spheres in the direction of flow is enhanced over the hydrophobic areas of the substrate (θS > 45°) with respect to hydrophilic areas of the substrate (θS < 45°). Coupled with the reduction in flow rate experienced in hydrophilic areas, where the capillary tail of the meniscus is pinned to the substrate, this increases the probability of sphere removal from hydrophobic areas and sphere attachment to hydrophilic areas. If spheres of a weakly hydrophilic (20° < qP < 40°) nature are employed to accommodate the required surface contact angle, then capillary emersion forces (Figure 3b) initially draw spheres away from the substrate and into an equilibrium position in the meniscus as illustrated in Figure 1, stage 3. The forces acting on the weakly hydrophilic sphere while it is in its equilibrium position, stationary with respect to the meniscus line, are detailed in Figure 1, stage 3. Although drag forces may arise from the movement of the sphere, these will be negligible with respect to other forces present, and the total force acting to draw the particle toward the substrate (FSubstrate) and resisting its motion down the flow channel (FChannel) can be expressed as

FSubstrate ) (FG - FB)cos θ - (FHS + FE + FEV) (24) FChannel ) (FS + FEH) - (FG - FB)sin θ

(25)

Strong capillary emersion forces oppose the movement of the weakly hydrophilic sphere away from the equilibrium meniscus position in either direction. Thus, as long as there is a net force with potential energy in excess of kT acting towards the substrate, initially the sphere will simply slide down the retreating meniscus surface until it resumes its equilibrium sphere-substrate spacing, Lequilibrium. At this point, surface roughness-related frictional forces act to oppose the movement of the sphere across the substrate surface. As long as the frictional force is in excess of kT, spheres will be drawn beyond their equilibrium position in the meniscus, and capillary forces will act to restore equilibrium, forcing the weakly hydrophilic spheres into an identical situation to that described previously for the strongly hydrophilic spheres (Figure 1, stage 4).

Sphere-Sphere Collisions in Advance of the Meniscus. Under conditions of sphere removal, sphere-sphere impact in advance of the meniscus contributes significantly to the patterning process. Spheres in front of the meniscus experience the translational capillary force via a hard sphere impact, without experiencing any of the accompanying vertical constraints. In addition, because free spheres sit further above the substrate than those trapped in a nonequilibrium position in the meniscus, this impact will direct them away from the substrate into the flow. After their release, in the absence of surface roughnessbased frictional forces, variations in tilt angle can be employed to determine the extent to which spheres accelerate in advance of the flow as illustrated in Figure 4a. When the meniscus arrives at a region of lower contact angle, its shape relaxes, trapping not only the spheres on the substrate surface but also any others previously released from hydrophobic areas, as illustrated in Figure 4b. The meniscus then passes, trapping these spheres in the thin film of water that is retained on the hydrophilic areas. The shape of the film, and hence the maximum size of spheres that can be retained, is defined by the contact angles of the two patterned regions.45 Although the concentration of spheres will therefore be highest along the leading edge of the hydrophilic area, spheres within the water film will repel each other because of their like charge and, as long as the depth of the confined film exceeds 2a, will move under the influence of gravitational forces to redistribute themselves within the thin water layer before the emersion capillary forces described by de Lazzer46 act to fix the spheres on the surface as the water evaporates. Experimental Details Chemicals. All solvents were of HPLC grade and were purchased from Rathburn. Deionized water (18 MΩ cm) was obtained from a Whatman Still Plus system. SU8-5 was purchased from Chesteck, 5 µm borosilicate glass spheres were purchased from Brookhaven Instruments Ltd, and polydimethylsiloxane (PDMS) was purchased from Farnell as a Sylgard silicone elastomer 184 kit. 3-Aminopropyltrimethoxysilane (APTMS), [3-(2-aminoethylamino)propyl]trimethoxysilane (AAPTMS) (Aldrich 06668), propylene glycol methyl ether acetate (PGMEA) (Aldrich 537543), trichloro(1H,1H,2H,2H-perfluorooctyl)silane (TPFS) (Aldrich 448931), octadecanethiol (ODT) (Aldrich 0-185-8), mercaptopropionic acid (MPA) (Aldrich M5 80-1), MES, MOPS, TAPS, and CAPSO acids and salts were purchased from Sigma-Aldrich. PDMS Stamp Production. A piece of silicon wafer was primed by a 15 min immersion in piranha mixture at 70 °C (Caution! Piranha solution is corrosiVe.), a 20 min immersion in 5 M KOH, and overnight immersion in a solution of APTMS (10% by volume in HPLC-grade EtOH). After spin coating with a 10 µm depth of SU8-5 photoresist, the wafer was exposed to a soft bake of 2 min at 65 °C and 5 min at 95 °C before the photoresist was patterned using a 364 nm Enterprise laser and a confocal microscope. The sample was (45) Leopoldes, J.; Bucknall, D. G. J. Phys. Chem. B 2005, 109, 8973. (46) de Lazzer, A.; Dreyer, M.; Rath, H. J. Langmuir 1999, 15, 4551.


Figure 5. SEM image of a patterned slide after the deposition of 5 µm amine-functionalized spheres (a ) 2.5 µm) from a pH 6, ionic strength 1 × 10-5 M, 0.08% by volume suspension of spheres passing through a flow cell at a tilt angle of 45° with a flow rate of 0.52 mm3 s-1 (ua ) 0.38-0.53 µm s-1) where the shape and relative location of the deposition areas formed an accurate replica of the features on the PDMS stamp. The inset shows a close-up view of one of the features. postbaked for 1 min at 65 °C and 2 min at 95 °C before developing for 2 min in PGMEA. The silicon/SU8 master was coated in a monolayer of TPFS by immersion in 0.02 volume % TPFS in EtOH for 30 min before drying for 30 min at 120 °C, casting in PDMS, and baking at 80 °C for 3 h. Substrate Preparation. Glass slides coated with 20 nm Cr and 300 nm Au by chemical vapor deposition were rinsed in a Soxhlet for at least 3 h in HPLC-grade 2-propanol. Samples were patterned using a PDMS stamp and solutions of 2 mM octadecanethiol and 2 mM mercaptopropionic acid in HPLC-grade EtOH. For the majority of experiments conducted, the stamp contained four distinct features spaced at 1 mm intervals diagonally with respect to the oncoming flow. Each feature was formed of 35-µm-wide strips in the form of an arrow or an arc and occupied an area of approximately 150 × 200 µm2 on the stamp (Figure 5), Sphere Preparation. Borosilicate glass spheres (5 µm; a ) 2.5 µm, FP ) 2.5 g cm-3) were functionalized through overnight immersion in a 10% by volume solution of AAPTMS in HPLCgrade EtOH and stored, after extraction in EtOH and water, as an aqueous solution. Solutions were buffered with organic buffers prepared fresh from 0.01 M stock solutions of salt and acid, and their pH was checked on a Corning 145 pH meter. Contact Angle. Contact angle titrations were performed with 15 and 30 µL droplets of buffer solution on gold slides patterned with hydrophobic and hydrophilic SAMs and equilibrated in buffer for 4 min prior to measurement on a Kruss DSA100 goniometer with tilting stage. MES, MOPS, TAPS, and CAPSO buffers were employed to provide a 1:1 system of consistent ionic strength over the pH range of 5.5 to 9.5. Surface Potential and Topography Measurements. Sphere surface potentials were measured directly via light-scattering experiments47 in fresh solutions of MES, MOPS, TAPS, and CAPSO buffers on a Brookhaven particle size analyzer (at the University of Bristol) using a Smoluchowski model (κa > 1). AFM images were recorded on a Topometrix AFM Explorer in contact mode at a scan rate of 10 µm s-1. Flow Cell Experiments. Fresh solutions were prepared by dilution, with buffer solution and 18 MΩ cm deionized water, of a 0.8% by volume stock sphere solution. Most experiments were performed with 0.08% by volume sphere solutions. Patterned samples (10 × 12 × 1 mm3) were located in the main compartment of a two-part flow cell (Figure 6) with a cross-sectional area of 12 × 2 mm2. The cell was connected to a glass syringe (piston diameter 11.5 mm) controlled by a piezoelectric worm (Burleigh Q5203205) and tilted (47) Vold R. D., V. M. J. Colloid and Interface Chemistry; Addison-Wesley: San Diego, CA, 1983. (48) Atkins, P. W. Physical Chemistry, 5th ed.; Oxford University Press: Oxford, U.K., 1994.

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Figure 6. Schematic of the flow cell apparatus employed for sphere assembly. The inset shows the design of the flow cell, with a small opening at B and channels for the insertion of syringe needles at A, C, and D. The operation of the flow cell is explained in the Experimental Section. to the required angle as illustrated in Figure 6. Sample suspensions were injected rapidly at C, and a Burleigh 600ULN controller was employed to regulate the rate of fluid removal through opening D. Flow rates of 0.52-20.8 mm3 s-1 were achieved with piston withdrawal rates of 5-200 µm s-1. For experiments requiring longer “in-fluid” observation times, the second chamber acted as a buffer reservoir that could be emptied by closing the tap at A. Taking the kinematic viscosity of water at 25 °C, ηkH2O, as 0.891 × 10-6 m2 s-1 48, for a cell of depth 2 mm containing a sample of depth 1 mm in aqueous solution (h ) 1 mm), laminar flow exists for all reasonable experimental velocities. Meinhart and Tretheway30 report a slip distance of 1 µm for octadecylsilane-functionalized surfaces. Accordingly, the effective surface flow velocity (2.5 µm from the base of the cell) according to eq 3 will be 1.4% of the central flow rate over hydrophobic areas and 1% of the flow rate over hydrophilic areas; therefore, a flow rate of 0.52 mm3 s-1 corresponds to effective surface flow rates (ua) of 0.375 µm s-1 over hydrophilic areas and 0.525 µm s-1 over hydrophilic areas. For the purposes of modeling, it was assumed that uL+a ≈ ua. Image Analysis. Samples were imaged in situ and immediately after assembly using an Olympus BX41M microscope with a CC12 soft imaging system. SEM (scanning electron microscopy) conducted on a Philips XL30 ESEM confirmed that dark areas in the microscope images are representative of multilayer structures or, in some cases small, fragments of the gold/chrome layer that was released in the flow cell. Individual images of the four separate features assembled on each sample were recorded on the optical microscope and collected for data analysis.

Results The experimental results are considered in two stages. Initially, results obtained from surface potential measurements, AFM, and contact angle analysis are discussed and compared with the wealth of information available in the literature in order to evaluate the relevant parameters (θS, θP, Ψ0S Ψ0P, β, and surface roughness) of our system. Subsequently, these parameters are employed, in conjunction with the equations presented in the Theoretical Section of this article, to determine the magnitude of the various forces acting on the spheres throughout each stage of the assembly process. Calculated data are then compared with results obtained from patterning experiments, and evidence for the proposed mechanism of assembly is discussed. Sphere Surface Potential Measurements. Surface potential measurements on amine-functionalized glass spheres (Figure 7) yielded a classic ionization curve40 with a pKa of approximately 7.5 in buffer solutions of 10-5 M ionic strength. The results suggest that amine groups on the surface of the spheres are fully ionized below pH 6-6.5, exhibiting increased surface potential

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Tull et al.

Figure 9. Graph of the force acting normal to the substrate, FNormal (eq 18), on a 5 µm amine-functionalized sphere (a ) 2.5 µm) at rest at 298 K above a negatively charged SAM surface (|σs| > 50 mV) in a flowing stream of pH 6 MES buffer of ionic strengths 1 × 10-5 M (...), 2 × 10-5 M (-), and 1 × 10-4 M ()) versus spheresubstrate separation L (σP ) 50, 72, and 78 mV, 0 ) 8.85 × 10-12 F m-1, r ) 78.36,53FH2O ) 1 g cm-3, FP ) 2.5 g cm-3, g ) 9.8 m s-1, and B ) 10-72 J m-2 38). (Gravitational forces are small compared to electrostatic forces, and hence the effect of the tilt angle is negligible.) Figure 7. Graphs of the sphere surface potential (σP) recorded from 5 µm amine-functionalized glass spheres (a ) 2.5 µm) in 0.08% by volume aqueous suspensions versus (a) ionic strength at pH 5.5 (0) and pH 6 (9) and (b) pH in MES (9), MOPS (0), TAPS (b), and CAPSO (O) buffers of ionic strength × 10-5 M.

Figure 8. Graphs of receding contact angles of 15 µL droplets of MES, MOPS, TAPS, and CAPSO buffers of ionic strength 10-5 M on (a) MPA and (b) ODT SAMs on gold-coated glass slides equilibrated in MES (9), MOPS (0), TAPS (b), and CAPSO (O) buffers prior to measurement.

with decreasing ionic strength as the number of counterions available for adsorption decreases. Contact Angle Analysis. Contact angle analysis confirmed that the surface pKa of the carboxylic acid-terminated areas was consistent with that recorded by Schweiss et al.35 (Figure 8a), indicating that the surface potentials of the SAM-coated Au substrate lie below -50 mV at pH >6 in buffer solutions of e10-4 M employed in this study. Contact angles recorded from the hydrophobic areas (Figure 8b) confirmed that the pKa of the hydrophobic layer was shifted to higher pH with a loss

Table 2. Nature of Interactive Forces under Different Environmental Conditions for Sphere Assembly surface SAM

sphere SAM

pH

interaction

ODT/MPA ODT/MPA ODT/MPA

AAPTMS AAPTMS SiOH

6 10 10

attractive weakly attractive repulsive

of definition commensurate with that expected from a mixed chain length CH3/COOH-terminated layer with a large percentage of CH3 chains, where unequal ion adsorption dominates the surface potential.49,50 Previous studies49,50 indicate that in solutions of low ionic strength (6. Because the electrostatic force observed is independent of surface potential when its magnitude exceeds 50 mV,42 these results imply that both hydrophilic and hydrophobic areas of the patterned substrates employed in this study will exert the same magnitude of electrostatic force on the positively charged spheres in pH 6 aqueous solution. If true, then this would explain why, in the work of Aizenburg et al.,11 the assembly of positively charged spheres onto substrates suspended upside down in solution was less selective on neutral/negative patterned substrates than on positive/negative patterned substrates. The behavior of nonfunctionalized silica is well documented,40 with surfaces adopting a negative charge at pH >4. Accordingly, three regions of assembly can be defined as detailed in Table 2. AFM and Calculation of Forces Prior to the Arrival of the Meniscus (Stage 2). Most assembly experiments were conducted at pH 6 where the positively charged spheres are attracted to the negatively charged surface. Taking B as 1 × 10-72 J m-2,51 calculation of the forces acting on a sphere during stage 2 of the assembly process predicts sphere-substrate spacings on the order of 20-70 nm in solutions of various ionic strength, as shown (49) Bain, C. D.; Whitesides, G. M. Langmuir 1989, 5, 1370. (50) Whitesides, G. M.; Laibinis, P. E. Langmuir 1990, 6, 87. (51) Israelachvili, J. N. Intermolecular and Surface Forces: With Applications to Colloidal and Biological Systems, 2nd ed.; Academic Press: New York, 1991.


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Figure 11. Graph of the surface sphere density observed on the substrate surface before the advent of the meniscus in experiments employing 0.08 volume % suspensions of spheres (a ) 2.5 µm) (a) versus ionic strength at 85° tilt with a flow rate of 2.08 mm3 s-1 (ua ) 1.50-2.10 µm s-1) and a buffer wash on MPA (0) and ODT(9) patterned areas and (b) at pH 6 and 10 with amine-functionalized and unmodified glass spheres at 85° tilt with flow rates of 0.52 mm3 s-1 (ua ) 0.38-0.53 µm s-1) (9) and 2.08 mm3 s-1 (ua ) 1.50-2.10 µm s-1) (0) in the absence of a buffer wash. Figure 10. Graph of the force required parallel to the substrate, FS, (eq 20) in opposition to the direction of flow to maintain an aminefunctionalized 5 µm sphere (a ) 2.5 µm) at rest over (a) a hydrophilic patch (uL+a ) 1.0% uflow) and (b) a hydrophobic patch (uL+a ) 1.4% uflow) on the substrate in moving flow, prior to arrival of the meniscus, at different flow rates and tilt angles where FΗ2Ο ) 1 g cm-3, FΗ2Ο ) 2.5 g cm-3, g ) 9.8 m s-1, and ηΗ2Ο ) 8.91 × 10-4 kg m-1 s-1.53 Table 3. Equilibrium Sphere-Substrate Separation (Calculated from Equation 19) and the Corresponding Debye Lengths in Solutions of Varying Ionic Strength (Calculated from Equation 35) buffer concentration/ mol dm-3

equilibrium substrate-sphere spacing/nm

Debye length/nm

1 × 10-4 2 × 10-5 1 × 10-5

22 48 68

30.2 67.4 95.4

in Figure 9. A comparison of these values with the double-layer thickness, as estimated by the Debye length52 (Table 3)

κ -1 )

(

r0kT

)

2e2c∞NAzi2

1/2

(26)

demonstrates that surfaces are located close enough for double layers to overlap. AFM analysis of the gold-coated substrates yielded surface roughness values on the order of 30 nm, indicating that, assuming spheres exhibit a surface roughness of similar or increased magnitude to that of the gold surface, surface roughness-related frictional forces will act on spheres after sedimentation from all suspensions under investigation here. Theoretical models predicting the forces between surfaces of like charge inside the (52) Shaw, D. J. Introduction to Colloid and Surface Chemistry, 2nd ed.; Butterworths: London, 1970. (53) CRC Handbook of Chemistry and Physics, 58th ed.; Weast, R. C., Ed.; CRC Press: Cleveland, OH, 1977.

double layer are not currently available, but negatively charged spheres will experience stronger repulsive forces and hence would be expected to settle further from the substrate surface, where friction due to surface roughness will be reduced and consequently spheres should be easier to remove. The net force acting to oppose surface friction was calculated from eq 21 for the range of flow rates and tilt angles available (Figure 10). Making adequate provision for the parabolic flow velocity and the hydrophilic or hydrophobic nature of the substrate surface through application of eq 3 and the slip factor given by Tretheway et al.,30 it was demonstrated that the force applied over hydrophobic areas was enhanced by only 10% with respect to hydrophilic areas and that the best conditions for removal were those of high tilt angle. A flow cell containing 0.5 mL of buffer solution to lengthen the period of time between sedimentation and the arrival of the meniscus was used to evaluate sphere-surface interactions experimentally. A suspension of spheres (0.35 mL of a 0.08% by volume solution) was injected into the cell, which was maintained at 85° and a fast flow rate of 2.08 mm3 s-1 (ua ) 1.5 µm s-1 over hydrophilic areas and 2.1 µm s-1 over hydrophobic areas) was employed to apply a reasonable force (∼10-12 N) to the spheres present. Using an appropriately aligned microscope, images of spheres at rest on the substrate were recorded through the flowing aqueous phase, and the sphere densities retained on different regions of the substrate under different environmental conditions were recorded. Sphere densities were comparable for both hydrophobic and hydrophilic areas over a large range of ionic strengths (10-110-5 M) when the experiments were conducted with aminefunctionalized glass spheres at pH 6 (Figure 11a). Thus, the results indicate that, for all reasonable experimental conditions, these positively charged spheres adhere to the surface of both regions equally well. In experiments conducted with nonfunctionalized or amine-functionalized spheres at pH 10, spheres were observed to roll slowly down the substrate surface after sedimentation, indicating that when the substrate and the sphere exhibit like charges, frictional forces (kT is required to return them to their equilibrium sphere-substrate spacing (Lequilibrium). At all separations greater than Lequilibrium, the net force acting to draw the sphere toward the substrate (Figure 1, stage 3) as calculated from eq 24 (Figure 15) is attractive, angle-independent, and on the order of 7 × 10-10 N. This restoring force corresponds to a potential energy on the order of 10-17-10-16 J, where

EP )

∫LL

meniscus

equilibrium

F dx ≈ F(Lmeniscus)Lmeniscus

(27)

Because this value greatly exceeds kT (at 298 K, kT ≈ 4.1 × 10-21 J), it is reasonable to assume that spheres are drawn back along the meniscus surface toward the substrate until their equilibrium sphere-substrate spacing is obtained.


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Figure 16. Graph of the component of gravitational force acting in the direction of flow versus tilt angle for a 5 µm (a ) 2.5 µm) amine-functionalized sphere maintained in the meniscus surface of a solution of pH 6 MES buffer of ionic strength 10-5 M at 298 K (σP ) 78 mV, σw ) -50 mV, 0 ) 8.85 × 10-12 F m-1, r ) 78.36,53 FΗ2Ο ) 1 g cm-3, FP ) 2.5 g cm-3, g ) 9.8 m s-1).

Figure 14. Graph of the capillary emersion force acting in the direction of flow (-) (eq 21) and directed toward the substrate (...) (eq 22) on an amine-functionalized 5 µm sphere (a ) 2.5 µm) characteristic of an amine-functionalized glass slide, situated over MPA (-) and ODT ()) surfaces as the meniscus recedes over the sphere at (a) pH 6 (θP ) 12°, θS MPA ) 11°, θS ODT ) 46°) and (b) pH 10 (θP ) 10°, θS MPA ) 20°, θS ODT ) 54°) assuming that FT ) 72.75 mJ m-2.48

Figure 15. Graph of the net electrostatic, hard sphere, and gravitational force, FSubstrate, (eq 24) with respect to sphere-substrate spacing, L, for a 5 µm (a ) 2.5 µm) amine-functionalized sphere maintained in the meniscus surface of a solution of pH 6 MES buffer of ionic strength 10-5 M at 298 K (σP ) 78 mV, σw ) -50 mV, 0 ) 8.85 × 10-12 F m-1, r ) 78.36,53 FΗ2Ο ) 1 g cm-3, FP ) 2.5 g cm-3, g ) 9.8 m s-1, and B ) 10-72 J m-2).38 (Gravitational forces are small compared to electrostatic forces, and hence, the effect of the tilt angle is negligible.)

Despite the fact that during transit spheres are maintained slightly in advance of their equilibrium position in the meniscus by the balance of gravitational, FChannel, (eq 25) and capillary emersion, FT Channel, forces (eqs 21-23), once the equilibrium sphere-substrate separation is regained surface frictional forces exceeding 10-12 N act on the sphere (Figure 10a,b, eq 20), and FChannel acquires a negative value of .kT. Spheres are drawn out of the fluid beyond their equilibrium position in the meniscus, and a positive capillary emersion force directs spheres toward the substrate and down the flow channel. If, alternatively, it is assumed that the contact angles for the glass spheres employed in this study are similar to those recorded from glass slides coated in AAPTMS, then application of eqs 21-23 yields the values of FT Channel and FT Substrate presented in Figure 14a,b. The absence of negative values in Figure 14a,b indicates that interactions are representative of the very hydrophilic case. From the moment of contact, spheres are directed toward the substrate and down the flow channel.

Figure 17. Graph comparing the net force, FNormal, acting (eq 18) between a 5 µm amine functionalized sphere (a ) 2.5 µm) and the substrate at distances of close approach (-) in a buffer solution of ionic strength 10-5 M at any angle of tilt, with the maximum (zmax Si ) 3.3 µm, zmax Glass ) 2.7 µm) capillary restoring force acting on the sphere normal to the substrate, FT Substrate, (eq 22) over areas of ODT ()) and MPA (-) SAMs at pH 6 (...) and 10 (-) calculated for silicon (gray) and glass (black) sphere surfaces (using the contact angles presented in Table 4) and assuming a surface tension of FT ) 72.75 mJ m-2.48

Accordingly, whether the spheres are weakly or strongly hydrophilic they will experience the same ratio of capilliary emersion forces FT Channel and FT Substrate over hydrophobic and hydrophilic areas of the substrate, and patterning according to capillary selection is possible in either case. Effect of the Meniscus and the Surface (Stage 4). The maximum value of FT Substrate available in all cases is sufficient to reduce the sphere-substrate spacing to the order of 10 Å (Figures 13, 14, and 17), so friction due to surface roughness is increased to a consistent value in all areas. The increase in FT Channel predicted in all areas at pH 10 (Figures 13 and 14) implies that conditions for assembly should be more favorable at pH 6 where the force available to remove spheres from hydrophilic areas (thin solid line) is reduced but that conditions for removal should be more favorable at pH 10 where the force available to remove spheres from hydrophobic areas is increased (thick solid line). Similarly, the increase in FT Channel predicted in all areas for strongly hydrophilic spheres (Figures 13 and 14) indicates that conditions for assembly should be more favorable with weakly hydrophilic spheres (Figure 13) where the force available to remove spheres from hydrophilic areas (thin solid line) is reduced but that conditions for removal should be more favorable for strongly hydrophilic spheres where the force available to remove spheres from hydrophobic areas is increased (Figure 14).

7870 Langmuir, Vol. 23, No. 14, 2007

Figure 18. Composite of optical microscope images of features obtained from flowing 0.08 volume % suspensions of 5 µm amine functionalized and unmodified glass spheres (a ) 2.5 µm), buffered to pH 6 or pH 10 with 1 × 10-5 M MES or CAPSO buffer, across patterned samples, in a flow cell maintained at 85°, at a flow rate of 0.52 mm3 s-1 (ua ) 0.38-0.53 µm s-1).

To obtain evidence to support the method of assembly by capilliary selection, sequences of microscope images were recorded as the meniscus of a 0.08% by volume pH 6 suspension of amine-functionalized spheres of ionic strength 10-5 M was withdrawn at a flow rate of 2.08 mm3 s-1 (ua) 1.50-2.10 µm s-1) from gold-coated glass slides, patterned with ODT/MPA features. Images recorded from two slides maintained at a tilt angle of 85° are provided in Figures 23 and 24 of Supporting Information. As predicted, spheres maintained in an even distribution over the surface prior to the arrival of the meniscus are removed from the surface in hydrophobic areas and swept along in a brushing action, dislodging other spheres that move out into the main bulk of the flow. When the meniscus reaches an area patterned with a hydrophilic SAM, its shape changes (Figure 23, image 2 in Supporting Information), trapping spheres close to the meniscus, along with those already at rest on the surface, in a water droplet that remains behind after the main body of fluid has retreated. Microscope images acquired prior to the arrival of the meniscus show spheres, removed from hydrophobic areas in the top portion of the flow cell, accelerating down the channel over lower parts of the substrate, in advance of the retreating meniscus (Supporting Information, Figure 25). Controllability. One of the main advantages of the flow cell process is that sphere assembly is subject to a number of variable parameters: flow rate, tilt angle, pH, and suspension concentration. Earlier in the Results section, the ability to use these parameters to define the surface sphere density encountered by the receding meniscus was demonstrated. In the section that follows, their implications for capillary selection are examined. The quality of patterning achieved under various conditions was assessed using a stamp with four distinct features spaced at 1 mm intervals diagonally with respect to the oncoming flow (Figure 5). Each feature was formed of 35-µm-wide strips in the form of an arrow or an arc and occupied an area of approximately 150 × 200 µm2 on the stamp. In Figures 18-21, separate images of

Tull et al.

Figure 19. Composite of optical microscope images of features obtained from flowing 0.032, 0.080, and 0.400 volume % suspensions of 5 µm amine-functionalized glass spheres (a ) 2.5 µm), buffered to pH 6 with 1 × 10-5 M MES buffer across patterned samples, in a flow cell maintained at 85° at a flow rate of 0.52 mm3 s-1 (ua ) 0.38-0.53 µm s-1).

spheres assembled on each of the features are presented with the direction of flow acting directly down the page. Effects of pH. By employing bare and amine-functionalized borosilicate glass spheres in solutions of 10-5 M ionic strength at pH 6 and 10 under conditions of efficient sphere removal (85°, 0.52 mm3 s-1 (ua) 0.375-0.530 µm s-1)), the effect of pH on substrate pattering was investigated. Patterning was observed in all cases as illustrated in Figure 18, indicating that the ratio of FT Channel/FT Substrate was sufficient to induce patterning at pH 6 or 10; consequently, FChannel must exceed 3.8 × 10-7 N when L is reduced to 10 Å (Figures 13 and 14). In accordance with the proposed mechanism, the population of spheres in the features obtained was representative only of the sphere density recorded prior to the arrival of the meniscus, demonstrating no other pHrelated effects. Sphere Density. The effects of solution sphere concentration were more thoroughly investigated in situations of efficient sphere removal. Images recorded from experiments conducted with sphere suspensions of 0.032, 0.080, and 0.400 volume % at 85° and 0.52 mm3 s-1 (ua ) 0.375-0.530 µm s-1) are presented in Figure 19. Patterning is observed in all cases, with the population of shapes reflecting the concentration of the sphere solution employed and hence the sphere density maintained on the substrate prior to the arrival of the meniscus. The multilayer deposition observed at high sphere concentration indicates that, in accordance with the mechanism proposed, the quality of patterning reflects the population not just of the surface over which it is passing but also of the region of fluid just behind the meniscus. Even under high tilt angle conditions that promote the efficient removal of spheres from the meniscus, spheres from this region are trapped when the meniscus recedes over a hydrophilic area. Efficiency of Removal. To investigate the combined effects of varying the density of spheres encountered by the receding meniscus and the efficiency of sphere removal, patterning quality was investigated over a range of flow rates and tilt angles. By employing amine-functionalized borosilicate glass spheres in


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Figure 20. Composite of optical microscope images of features obtained from flowing 0.08 volume % suspensions of 5 µm aminefunctionalized glass spheres (a ) 2.5 µm buffered to pH 6 with 1 × 10-5 M MES buffer) across 12 patterned slides in a flow cell maintained at various tilt angles at flow rates of 0.52 mm3 s-1 (ua ) 0.38-0.53 µm s-1), 1.04 mm3 s-1 (ua ) 0.75-1.05 µm s-1), and 2.08 mm3 s-1 (ua ) 1.50-2.10 µm s-1).

Figure 21. Composite of optical microscope images of features obtained from flowing 0.08 volume % suspensions of 5 µm aminefunctionalized glass spheres (a ) 2.5 µm) buffered to pH 6 with 1 × 10-5 M MES buffer across patterned samples in a flow cell maintained at 20° initially, during sedimentation, at a flow rate of 0.52 mm3 s-1 (ua ) 0.38-0.53 µm s-1) and subsequently for substrate patterning at an accelerated flow rate of 10.4 mm3 s-1 (ua ) 7.5-10.5 µm s-1) or 20.8 mm3 s-1 (ua ) 15-21 µm s-1).

0.08% by volume suspensions of 10-5 M ionic strength at pH 6 for runs with flow rates of 0.52-2.08 mm3 s-1 (ua ) 0.3752.100 µm s-1) and tilt angles of between 20 and 85°, substrates were patterned and imaged under the optical microscope. As illustrated in Figure 20, increased deposition is observed at lower angles and lower flow rates where the density of spheres on the substrate surface encountered by the receding meniscus is increased and removal from the substrate is less efficient. Dark areas in these images indicate multilayer sphere deposition. Multilayers are concentrated mostly at the base of features in

high tilt angle runs where gravitational rearrangement is most likely to occur and are more evenly spread in lower angle runs where spheres remain in place after deposition, indicating that the aqueous film left on the substrate must exceed 2a in thickness in some areas. To evaluate the effect of the strong drag forces present in situations of vastly increased flow rate, two high-speed experiments were conducted. Spheres were deposited on the substrate at 0.52 mm3 s-1 (ua ) 0.375-0.530 µm s-1), after which the cell was subjected to accelerated flow rates to simulate the effects of enhanced speed at low angle. Results are presented in Figure 21. Shape definition was maintained despite the increased velocity of the meniscus, and the deposition density was not noticeably altered at 10.4 mm3 s-1 (ua ) 7.5-10.5 µm s-1) or 20.8 mm3 s-1 (ua ) 15.0-21.0 µm s-1), indicating that gravitational effects remained dominant and drag forces were still not sufficient to remove spheres at low angles.

Discussion Our theoretical analysis and experimental results demonstrate that two possible methods of assembly exist for large glass spheres in a tilted flow cell environment. Electrostatic Attraction. At 85° and 2.08 mm3 s-1 (ua ) 1.5-2.1 µm s-1), negatively charged spheres are observed to move across a negatively charged substrate under the influence of the solution flow, whereas positively charged spheres adhere. If substrates were patterned with amino and carboxylic acid groups and lengthy buffer washes were employed, then amine-functionalized spheres should adhere selectively to acidic patches at pH 6. Under these conditions, electrostatic forces should locate spheres on specific areas during stage 2 of the assembly process. Spheres should be retained in these specified locations in a thin film of water that covers the whole hydrophilic substrate after

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the meniscus recedes. However, a concentrated solution of spheres would have to be employed to ensure that the moving spheres addressed all areas of the substrate, and the process would require a large buffer reservoir to provide sufficient time for the slow removal of spheres from repulsive areas. In addition, the process would be very sensitive to surface defects because of the fine force balance between movement and adhesion. Finally, subsequent drying processes may disturb the delicate array. For these reasons, this is not an attractive approach for this type of patterning and has not been attempted in this study. Meniscus Selection. Meniscus selection is possible over a range of pH but is most effective for amine-functionalized spheres and a carboxylic acid/methyl-patterned substrate at pH 6. The process can be described in four stages. (1) Sedimentation - Delivery of Spheres to the Substrate. Flow rate, concentration of spheres in suspension, and tilt angle can be varied to control the concentration of spheres on the substrate surface encountered by a receding meniscus. (2) Immobilization of Spheres on the Substrate in a Moving Flow. Gravitational and electrostatic forces determine the equilibrium sphere-substrate spacing, and friction maintains spheres on the substrate surface against the solution flow prior to the arrival of the meniscus. Despite increasing sphere-substrate spacing, decreasing the ionic strength maintains adequate spheresphere separation without reducing the density of spheres on the substrate surface over the range of experimental conditions studied. (3) Initial Contact with the Meniscus. Upon initial contact with the meniscus, spheres are drawn to their equilibrium position within the meniscus where the sum of the capillary forces is zero. Gravitational forces draw the sphere down the meniscus surface to its equilibrium sphere-substrate separation as the meniscus moves over the substrate. (4) Contact with the Meniscus and the Substrate. As the meniscus recedes, frictional forces draw the sphere beyond its equilibrium position in the meniscus, and capillary emersion forces direct spheres toward the substrate and down the flow channel. As a result of enhanced values of FChannel, the meniscus selectively removes spheres from hydrophobic areas, initially drawing a single layer of spheres into the meniscus and transporting them over the substrate surface at reduced substrate-sphere separation. The spheres in the meniscus act like a brush supplying strong impulses to other spheres resting on the substrate surface, sweeping them into the channel and away from the meniscus, where the tilt angle defines the efficiency of their removal from the substrate. Upon the arrival of the meniscus onto a hydrophilic region, the contact angle relaxes, trapping spheres in the region close to the meniscus in a thin film of fluid that remains on the substrate when the meniscus has receded. Subsequent gravitationally driven rearrangement of spheres within this thin film indicates that the height of the film exceeds the sphere diameter 2a and sphere-sphere repulsion encourages free movement within the film prior to solvent evaporation. The four-stage capillary selection process outlined above has been employed successfully in this study to pattern ODT/MPApatterned gold slides with 5 µm amine-functionalized spheres. The tunability of the technique has been clearly demonstrated in Figures 18-21, and well-defined monolayer patterns, as exemplified by images in Figure 20, have been produced from a flow cell maintained at 85° exposed to a flow rate of 0.52 mm3 s-1. In addition to its obvious controllability, the process is preferable to assembly via electrostatic attraction because it is fast, not very sensitive to small differences in sphere charge

Tull et al.

Figure 22. SEM image of features obtained from flowing 0.08 volume % suspensions of 5 µm amine-functionalized glass spheres (a ) 2.5 µm) buffered to pH 6 with 1 × 10-5 M MES buffer across a sample patterned with smaller MPA areas (dimensions of the order of 20 × 15 µm) in a flow cell maintained at 20° at a flow rate of 1.04 mm3 s-1 (ua ) 0.75-1.50 µm s-1). The inset shows a close-up image of one set of features.

density, and provides efficient cleaning of hydrophobic areas with no risk of pattern alteration upon drying. Miniaturization. Initial trials with smaller patterned regions indicate that with the correct density of spheres deposited on the surface sparse patterns of the type required for integrated optical applications with small monolayer features surrounded by large vacant areas can be obtained (Figure 22). For efficient patterning of these smaller features, slower withdrawal of the meniscus may be required to allow time to differentiate between contact angles in smaller areas, and hence reasonably high tilt angles may be required for efficient sphere removal. Comparison with Previous Work. This study has demonstrated that, within the pH range where -COO- and -NH3+ surface groups can coexist, highly charged substrates such as gold coated in ODT and MPA SAMs exhibit comparable electrostatic forces on positively charged spheres. Accordingly, the origin of patterning under these conditions must be attributed to capillary rather than electrostatic interactions. Therefore, we believe that the differential quality in patterning over -CH3/COO- and -NH3+/-COO- surfaces observed by Aizenburg11 must be attributed to the relative efficiencies of capillary selection and electrostatic assembly, not to differing levels of electrostatic repulsion from -CH3 and -NH3+ functionalized areas.

Conclusions The well-documented technique of assembly by chemical patterning, in particular, isolation of amine-functionalized glass particles on substrates patterned with ODT/carboxylic acidterminated thiols, has been adapted for the assembly of spheres from unstable suspensions. Through the introduction of a variable tilt flow cell with in situ microscope imaging, both the effects of sphere substrate interactions and the action of the receding meniscus have been independently examined. Variable flow rates have been employed to examine chemical interactions across the substrate surface and the influence of the water removal rate. Surface potential measurements and contact angle characterization methods have been employed to demonstrate that, as a result of unequal ion adsorption in solutions of 10-4-10-5 M ionic strength at pH 6 where the amine groups acquire a positive charge, both ODT and MPA SAMs on gold substrates exhibit


strong negative potentials, and hence in accordance with Jo¨nsson’s theory39 for highly charged surfaces, the strength of the electrostatic interaction between aminosilane-functionalized glass spheres and a mixed ODT/MPA surface should be independent of the chemical character of the underlying layer. The independent nature of these interactions has been demonstrated by consistent sphere densities, recorded across both ODT and MPA surfaces under the most aggressive removal conditions in this study (5 µm amine-functionalized spheres, pH 6 suspension, ionic strength 10-1-10-5 M, 85°, 2.08 mm3 s-1, lateral force >10-12 N). The strength of these interactions has been calculated according to the theories of Zypman and Jo¨nsson, yielding values on the order of 10-9 N. The subsequently derived equilibrium sphere substrate spacings of 20-70 nm have been used in conjunction with AFM surface roughness measurements to support the proposal that, contrary to assertions made in other studies, in an ODT/COOH system patterning does not occur as a result of differing electrostatic interactions. Prior to the arrival of the meniscus, a uniform coverage of spheres is maintained by frictional forces at a distance of 20-70 nm over all areas of an ODT/MPApatterned substrate. This theory has been further corroborated by the observation of consistent but reduced sphere densities when the spheres and the substrate surface carry like charges, and spheres are observed to move across the substrate under appropriate flow conditions. Optical microscope images depicting the arrival of the receding meniscus have been presented, and a viable mechanism for substrate patterning via the hydrophilic and hydrophobic interactions of the receding meniscus has been proposed. A theoretical model describing the capillary emersion forces acting on a hydrophilic sphere incident over a hydrophilic or hydrophobic surface has been derived and subsequently employed to demonstrate that emersion forces acting on 5 µm glass spheres close to a patterned ODT/MPA surface have values in the range of 10-7 N and should dominate over all other interactions present. The quality of patterning achievable over a wide range of flow rates and tilt conditions has been investigated using patterned substrates supporting four well-separated features with dimensions on the order of 35 µm. Support for the assumption that capillary

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interactions dominate all other forces has been demonstrated by the occurrence of patterning in all cases. Additionly, in accordance with the overall proposed assembly mechanism, it has been clearly illustrated that the quality of patterning obtained reflects the assembly conditions used. The population of features vary in direct contrast with the density of spheres present on the surface prior to the arrival of the meniscus, and the definition of features appears to be enhanced under conditions of high tilt angle, which promote the efficient removal of spheres after their release from the substrate surface. Appropriate conditions for the production of monolayer features have been identified, and the benefits of assembly by capillary selection have been discussed. Finally, by utilizing stamps with smaller features, this assembly technique has been extended to the isolation of small groups of two or three particles in small clusters on otherwise particle-free substrates. This is an important milestone in the processing required for the manufacture of microsphere resonator devices and a key advantage of this technique over other assembly methods that are restricted by scavenging processes to the production of high-density arrays. Acknowledgment. This work was funded by EPSRC grant no. GR/S96500/01. We thank our colleagues James Wilkinson, Dan Hewak, Mikhail Zervas, Senthil Ganapathy, Yuwapat Panitchob, and Greg Elliot in the ORC University of Southampton for useful discussions, the University of Bristol for the use of their particle size analyzer, Sumeet Mahajan, University of Southampton, for AFM, and Dr. Ian Roberts for consultation on fluid dynamics. Supporting Information Available: Microscope images recorded in situ through the glass window of the flow cell as the meniscus withdraws from a gold-coated glass slide. Microscope image depicting spheres that were removed from a gold-coated glass slide. SEM images of each of the features presented in Figures 18-21. Calculation of the electroviscous and electrokinetic forces evident on an amine-functionalized sphere. This material is available free of charge via the Internet at http://pubs.acs.org. LA0700974

Controlled Assembly of Micrometer-Sized Spheres: Theory and

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