Fabrication of Ordered 2D Colloidal Crystals on Flat and Patterned Substrates by Spin Coating.

Spin coating is a simple and rapid method for fabricating ordered monolayer colloidal crystals on flat as well as patterned substrates. In this article, we show how a combination of factors, particularly concentration of the dispensed colloidal solution (C n) and spin-coating speed, influences the ordering process. We have performed systematic experiments on different types of substrates with two types of colloidal particles (polystyrene and silica). We also show that even when perfect ordering is achieved at some locations, there might be a significant spatial variation in the deposit morphology over different areas of the sample. Our experiments reveal that higher C n is required for obtaining perfect arrays, as the diameter of the colloids (d D) increases. Interestingly, a combination of higher C n and rotational speed (expressed as revolutions per minute) is required to achieve perfect ordering on a topographically patterned substrate, as compared to that on a flat surface, because of loss of inertia of the particles during outward flow because of impact on the substrate features. Finally, we also identify the relation between the particle diameter and the height of the pattern features to achieve topography-mediated particle ordering.

Introduction

It is well-known that monodispersed colloidal particles self-assemble into hexagonal close-packed (HCP) structures, under appropriate conditions, which are also known as two-dimensional (2D) colloidal crystals, and find wide applications in fabrication of optical chips,[1] photonic band gap materials and photonic crystals,[2−4] data storage,[5] chromatography,[6] sensors,[7] masks for nanosphere lithography,[8] etc. Various interfacial self-assembly techniques, such as sedimentation,[9] confined convective self-assembly,[10] dip coating,[11] drop casting and evaporative drying,[12] deposition during retraction of liquid meniscus within a microfluidic chamber,[13] electrophoretic deposition,[14,15] self-assembly at the gas–liquid interface,[16,17] Langmuir–Blodgett (LB) technique,[18] inkjet printing,[19] spray coating,[20] spin coating,[21−41] and so forth, have been utilized to fabricate monolayer colloidal crystals with HCP ordering. Almost all methods rely on the convective assembly of particles engendered by lateral capillary forces, which cause an attractive interaction between the particles that push them together, favoring the nucleation of a close-packed ordered monolayer. Surface stabilization of the particles is important to prevent uncontrolled aggregation in the early stage of self-assembly.[11] Methods such as sedimentation or electrophoretic deposition are well suited for three-dimensional assembly, as they easily form multilayers. Although dip coating and LB-based techniques are capable of producing high-quality 2D crystals, they are inherently slow, require large volume of colloidal solution, and are difficult to scale up. It turns out that spin coating, which is widely used for coating polymer thin films over large areas, is also well suited for creating 2D colloidal crystals. Major advantages of spin coating include rapid formation (∼few minutes), high-throughput, extremely low amount of colloidal solution requirement (∼microliter), high degree of reproducibility, scalability, and direct integration with standard microfabrication approaches.

The possibility of creating a 2D monolayer array of latex particles [polystyrene (PS) beads] on a rigid substrate by spin coating was first demonstrated by Deckman and Dunsmuir in early 80s.[21,22] Subsequently, on the basis of this concept, Van Duyne pioneered the concept of nanosphere lithography, which is widely used as a physical mask for subsequent additive deposition of various types of materials.[8,23] Monolayer arrays of many other types of colloids such as silica, titania, core–shell particles, hollow titania spheres, and nanoparticles of gold, silver, cobalt, etc. have been fabricated by spin coating.[24−26] Jiang and McFarland spin-coated a colloidal sol comprising a mixture of a tri-acrylate monomer and a photoinitiator to fabricate a well-ordered nonclose-packed hexagonal array. The monomer, which acts as a spacer, is subsequently photopolymerized to form either a polymer nanocomposite[36] or a macroporous polymer with reverse opal structure (in conjugation with etching),[37] spanning over large areas.[38] However, it is important to point out that as the spin-coating process is radially symmetric about the center of rotation, it is not possible to arrange all the particles in the form of a single defect-free crystal spanning over the entire substrate.[29] It has been shown by Yethiraj and co-workers that under idealized conditions, it becomes possible to obtain crack-free orientationally correlated polycrystal (OCP) structures,[29,31] which comprise defect-free single-crystal domains radially arranged with respect to the center of the film. While each single crystalline domain laterally spans about 10 μm (represented with the correlation length, lR), their orientation undergoes continuous macroscopic rotation on length scales much larger than the diameter of the colloidal particles.[31] Application of an external magnetic field has been shown to be a promising approach that enhances the uniformity of the deposited colloidal particles, provided the colloids are magnetic in nature.[39−41]

Apart from monolayer arrays with HCP ordering, colloidal particles arranged in a nonhexagonal manner also find applications in many exotic areas such as optics and photonics and as sensing materials.[42,43] Such arrays are typically created by depositing the colloids on a chemically or a topographically patterned substrate, which acts as a template. The possible formation of a topography-directed non-HCP colloidal array was first reported by van Blaaderen et al. based on gravity settling of silica particles, which was referred to as colloidal epitaxy.[44,45] Subsequently, several other techniques such as micromoulding,[46,47] electrostatic assembly,[48] flow inside the microfluidic cell,[49] dip coating,[50] LB technique,[51] spin coating,[52−57] and so forth have been used to obtain pattern-directed particle arrays with a nonhexagonal geometry. A spin-coated pattern-directed particle array was first demonstrated by Ozin and Yang where they obtained non-HCP arrays of silica microspheres into anisotropically etched square pyramid pits,[52] based on a combination of gravity-driven sedimentation and evaporation-induced capillary forces, which lead to rapid settling, self-assembly, and crystallization within the pits. Brueck and co-workers reported the self-assembled array formation of sub-100 nm silica particles inside line gratings and circular holes. They highlighted the critical role of pH of the casting solution and showed that good ordering was possible only when pH was 7.[53] The same group showed the possible fabrication of aligned multilayer particle arrays inside deeper trenches, where the layer thickness could be controlled by multiple spin-coating steps. Varghese et al. obtained size selective array of particles within the pattern grooves from a mixture of particles of different sizes.[56]

From the above discussion, it is clear that spin coating is a simple method, which can be used to fabricate monolayer colloidal crystals with both HCP and non-HCP ordering on flat and patterned substrates, respectively. However, in spin coating, particle array formation depends on a combination of capillary, gravitational, centrifugal, and electrostatic forces. The situation gets further complicated on a topographically patterned substrate where the solution layer undergoes topography-mediated rupture during spin coating.[57−59] Further, because of symmetry issues discussed already,[29] as well as nonplanarization of colloidal suspensions during spin coating from a volatile medium,[40] it becomes impossible to achieve perfect ordering with the particles over a large area, and at best crack-free OCP structures can be obtained.[31] Colson et al. approached this complex parameter optimization problem from the concept of Experimental Design and predicted the optimum condition for obtaining a defect-free array over SA ≈ 200 μm2 area.[60] Most experimental papers only report the optimized condition that offers a near perfect array, and there are not too many systematic experimental studies that show how the morphology varies with change in various input parameters. Lack of such a study often renders it difficult to identify the conditions for perfect ordering, particularly over large areas.

In this article, we show the conditions under which perfect colloidal arrays can form on flat as well as patterned surfaces of a variety of materials based on systematic experimental investigations. Our results show that a uniform array is formed within a narrow parameter window spanning over large areas. The best structures we obtained exhibit correlation length lR ≈ 15 ± 2.5 μm and SA ≈ 210 ± 12 μm2 in each single crystalline domain comprising HCP monolayer arrays of the colloidal particles, with no crack between adjacent domains over the entire sample surface (15 mm × 15 mm). Such a structure will be referred to as “perfectly ordered structure” in the subsequent section of the paper. We show that such perfect ordering is achieved within a very narrow parameter window that depends strongly on the diameter of the colloidal particles (dD). We also show that there can be a significant spatial variation in the morphology of the structures and extent of ordering primarily because of nonplanarization of the colloidal suspension,[30] and therefore, care must be taken to examine the structure at different locations of the sample. We hope the reported results will act as a guide, particularly for beginners to identify the actual optimized condition based on a first trial that may lead to nonuniform deposition. Further, on a patterned surface comprising grating geometry, we show how the morphology of the ordered particles within the grooves depend on relative commensuration between the particle diameter (dD) and the groove width (lP), in addition to the concentration of the particles in the colloidal solution (Cn). Finally, by coating the colloidal solution on grating patterned substrates with the same periodicity (λP) and lP, but a different groove depth (hP), we identify the minimum height of the features necessary to successfully align the particles.

Results and Discussion

Self-Assembly of PS Colloids on the Sylgard 184 Substrate

As discussed in the Introduction section, the objective of the work is to identify the condition at which perfect monolayer arrays of colloidal particles can be achieved. We performed systematic experiments for each size and types of colloids on different substrates by casting the sols with different colloidal concentrations (Cn) at different revolutions per minute (rpm), to find out the condition that leads to perfect ordering. Figure highlights one such optimization attempt, showing various degrees of ordering with PS colloids having dD = 600 nm, as a function of Cn and rpm on the UVO-exposed Sylgard 184 substrate. A UVO-exposed poly(dimethyl siloxane) (PDMS) substrate is deliberately chosen as it is hydrophobic in nature (θE-W ≈ 109.5°). We show that it becomes possible to create a perfect array even on a hydrophobic surface using methanol as the solvent. However, it must be highlighted that because of UVO exposure, the PDMS surface becomes almost completely wetted by methanol, and therefore, ordered array formation gets favored.

Figure 1

Morphology of the colloidal deposit at different Cn–rpm combinations, when PS colloids with dD = 600 nm are spin-coated on a flat UVO-exposed PDMS substrate. The location is 4 mm away from the center of the substrate.

It may be noted that in all cases, the surfactant used is sodium dodecyl sulfate (SDS) and its concentration is 0.025 wt %. The presence of surfactant molecules in the colloidal suspension in appropriate quantity is essential for achieving perfect ordering, as they get adsorbed on the particle surface and control the interaction between the particles and surrounding. Self-assembly of colloidal particles into monolayer colloidal crystals require repulsive interactions between the particles, as strong attraction leads to the formation of highly disordered structures.[61] Though a detailed analysis on how ordering is influenced by the surfactant concentration is beyond the scope of the present study (and will be taken up separately), we observed that disordered structures form both when the surfactant concentration is very low (or absent) or higher than 0.1 wt %, when micelles start to form. Apart from SDS, we could also obtain perfect ordering using a nonionic surfactant (Triton-X). However, no ordering could be achieved when a cationic surfactant [hexadecyltrimethylammonium bromide (HTAB)] was used. This is attributed to the Coulombic binding of the positively charged head group of HTAB onto PS and silica particles, both of which have negative surface charge, as verified by dynamic light scattering measurements (data shown in Figure S1 of online Supporting Information). As the head group of the cationic surfactant molecules adsorbs on the particle surface, their hydrophobic tail orients outward and adjacent surfactant-covered particles experience strong attraction in the presence of alcohol because of hydration pressure. This leads to agglomeration and consequent suppression of ordered crystal formation.

Before presenting the experimental results, we feel it will be appropriate to highlight the key theoretical results related to spin coating,[62−64] particularly some of the recent theoretical papers which are specific to spin coating of colloidal dispersions.[39−41] This will help us in qualitatively explaining some of the experimental findings reported in this paper. It is well-known that in the initial stage of spin coating, the dispensed solution flows radially outward because of centripetal forces and the advancing solution meniscus reaches the edge of the sample. The excess solution (including the particles) is subsequently thrown out, which is known as splash drainage. Spin coating of simple fluids has been modeled based on lubrication approximation ever since the pioneering work of Emslie et al.,[62] where the primary focus was to find out how film thickness (h) varies as a function of spinning time (t) and radial distance from the center of spinning (r). However, the model neglected the role of evaporation, and thinning was considered only because of centrifugal forces. Meyerhofer subsequently improved the model by incorporating the effect of evaporation by considering spin coating to be a two-step process comprising two different stages: (a) initial phase dominated by the radially outward flow and (b) evaporation-dominated later stage where there is virtually no flow. The model considered rate of evaporation (e) to depend on rpm as e ∝ (rpm)1/2.[63] Subsequent improvement on spin-coating modeling was proposed by Cregan and O’Brien,[64] based on the argument that solvent evaporation starts almost instantaneously with deposition of the solution and therefore cannot be neglected even in the initial phase. Although the model is based on lubrication approximation and utilizes matched asymptotic expansion techniques, it considers a constant rate of evaporation and predicts the deposited layer thickness of the solute (not colloids) h∞(s) rather accurately and is given as[64]where C0 is the initial solute concentration, γ is the kinetic viscosity, ω is the angular velocity, and E is the rate of evaporation of the solvent. Equation can be simplified aswhere is constant for a specific experimental condition and β = 2/3.

The Cregan model was extended specifically for colloids by González-Viñas and co-workers, who argued that for a particulate system the film thickness h∞(s) should be replaced by a term “compact-equivalent height”, which depends on the kind of deposited structure and can be calculated as the product of packing fraction and Vornoi cell volume.[65] Aslam et al. proposed that the term h∞(s) in eq for a simple solute should be replaced by compact-equivalent height (CEH) for colloidal deposition, which giveswhere the contact 1 can be obtained by simply replacing the solute concentration C0 with the initial colloid concentration (Cn) in the expression of mentioned above. Further, for the submonolayer deposit with a hexagonal structure, the expression of CEH is given as[41]where ϵ2 is the local occupation factor, which is defined as the area occupied by the colloidal clusters relative to the total area. In this paper, the term fractional surface coverage (Fs) can be considered identical to the occupation factor (ϵ2) used by Pichumani and González-Viñas.[39] It may also be noted that we have written eq in terms of dD, the diameter of the colloidal particles, rather than the particle radius as in refs (40) and (41).

Figure shows the morphology of the colloidal deposit obtained for various Cn–rpm combinations. At low rpm, the centripetal force remains weak and therefore fails to spread the particles uniformly. Thus, the evolution is dominated by viscous shear forces, which in turn results in the particles getting arranged in a disordered fashion (series A, Figure ). As the rpm increases, the centripetal force becomes stronger, resulting in uniform spreading. This also enhances the evaporation rate up to a point where the forces acting on the colloidal particles get balanced. Under this condition, the particles move on the substrate surface easily and self-assemble into a monolayer with HCP ordering that spans over a large area (frames B22, C33, and D44 of Figure ). It also becomes clear that the balance between the shear force and the drying rate can only be maintained when Cn is increased along with an increase in rpm. However, increase of Cn to much higher values leads to a sharp enhancement in the viscosity of the remnant colloidal suspension during the late stage of spinning. This hinders the mobility of the particles on the substrate surface, and HCP ordering gets suppressed in favor of random disorganized structures (frames B25 and C35, Figure ). When the speed of rotation is increased further, the radial outflow of the particles increases and consequently, a larger amount of particles are thrown out of the substrate because of splash drainage. Consequently, the remnant suspension rotating on the substrate becomes very dilute. Consequently, the remaining PS particles fail to form monolayer coverage on the substrate, though they may show localized HCP ordering (series E, Figure ).

The gradual morphology transition along each column and row of Figure highlights the influence of enhanced rpm and Cn on the ordering process, respectively. It can be clearly seen that the fractional coverage of the surface (Fs) reduces with an increase of rpm, for a given Cn, as the proportion of splash drainage increases at higher rpm. On the other hand, Fs gradually increases with an increase in Cn for a constant rpm, as more number of particles are initially dispensed on the substrate. In fact, in most cases, the morphology gradually transforms from monolayer with partial coverage to scattered multilayers with an increase in Cn, where the drying front fails to drag the particles over the initially assembled particles.

Important observation in Figure is the formation of a perfectly ordered monolayer with HCP ordering in frames B22, C33, and D44 (Fs ≈ 1.0). This means that a perfect monolayer coverage is possible for different combinations of Cn and rpm. At this point, it is worth highlighting that all the images in Figure are captured at a location which is approximately 4 mm away from the center of the substrate. However, in order to claim that a specific coating condition is optimum for achieving perfect crystalline ordering, it is important to check the structure uniformity over the entire sample substrate. We checked this by performing careful atomic force microscopy (AFM) scan of the samples at different radial distances (rD) from the center of the sample at 1 mm intervals. The samples chosen for this study include the ones which are seen to give perfect ordering in Figure . In addition, few samples corresponding to different Cn–rpm combinations were also explored, the details of which are mentioned in the legend of Figure A. We note that at an rpm of 200 as well as at a higher rpm (=2500), perfect ordering is not achieved anywhere on the sample surface. For the low rpm case, the morphology comprises a scattered multilayer over major portion of the substrate (rD > 2 mm), indicating weak action of the centripetal force, which fails to drag the particles. On the other hand, at higher rpm, the centripetal force is much higher than the shear force and a large amount of particles are lost because of splashing. Consequently, Fs never exceeds 50% over the entire substrate. For the sample with Cn = 0.52% rotated at 400 rpm, we observe a slight undercoverage till rD ≈ 2 mm but a very high degree of multilayer formation beyond rD > 5 mm. An opposite trend is observed in the sample with Cn ≈ 1.2%, rotated at rpm = 1000. Here, a near perfect array with Fs ≈ 1.0 is obtained in the outer section of the sample (rD ≥ 4 mm). However, the areas close to the center show a significant undercoverage (Fs down to ≈0.75%). As can be seen in Figure A, the most uniform coverage is observed in the sample with Cn = 0.67%, rotated at rpm = 600. Thus, for PS colloids with dD ≈ 600 nm, we identify a combination of Cn = 0.67% and rpm = 600 to be optimum.

Figure 2

Variation of fractional coverage Fs as a function of distance from center (rD) for different Cn–rpm combinations. AFM images in insets (A1–A3) show perfectly ordered HCP morphology at rD = 2, 5, and 7 mm. In all cases, PS colloids with dD = 600 nm have been used.

The trend in Figure A highlights the critical role of solvent evaporation time on the array formation. Unlike water, which has a vapor pressure = 3.17 kPa, methanol has a much higher vapor pressure (13.02 kPa), which means methanol evaporates much faster. Therefore, particle spreading can take place only till the adequate amount of solvent is present. This means at low rpm (200 and 400), even before major part of the particles can reach the sample periphery, the solution starts to dry up, which is also associated with the enhancement of viscosity, and therefore, multilayers are formed toward the outer areas of the sample. Thus, for an organic solvent, the balance of shear force and centripetal force must be established within a very narrow time window, before major part of the solvent evaporates away. This in turn allows perfect array formation at Cn which is typically much lower than that reported in the literature with an aqueous colloidal sol, which also implies much reduced splash drainage of the colloidal particles. Further, Figures and 2 clearly highlight the success of our work in obtaining a neat and perfect array on a hydrophobic surface (θE-W ≈ 109°) of the cross-linked PDMS substrate, UVO-exposed for 30 min (Table ). In fact, Choi et al. have clearly mentioned that it is nearly impossible to obtain a perfect array on a hydrophobic surface.[32] We show that this limitation can be circumvented by using methanol as the solvent. The only requirement is methanol must wet the surface, which is achieved by 30 min UVO exposure, despite the substrate remaining hydrophobic.

Table 1

Details of the Flat Substrates Used

sl. no.	substrate	RMS roughness (nm)	water contact angle (θE-W°)	methanol contact angle (θE-M°)	surface energy (mJ/m2)
1	glass	0.429 ± 0.043	17.3	8.2	56.4
2	silicon wafer	0.305 ± 0.039	11.1	2.3	59.17
3	PS film coated on glass	0.486 ± 0.044	91.5	5.1	38.3
4	PMMA film coated on glass	0.493 ± 0.038	73.2	3.2	41.8
5	cross-linked PDMS film on glass	0.505 ± 0.042	114.5	35.8	24.2
5A	UVO-exposed PDMS film on glass	0.514 ± 0.023	109.5	2.4	28.3

Self-Assembly of PS and Silica Colloids on Different Substrates

In Table , we show the optimized conditions for obtaining HCP arrays on different substrates with colloids of different sizes and of different materials. The optimized Cn–rpm combination is obtained by performing experiments in line with Figures and 2 for particles of each diameter on each type of substrate. The corresponding images of the ordered arrays are shown in Figures S2–S5 of online Supporting Information

Table 2

Optimized Conditions for Perfect Ordering on Flat Substrates

material of particle	dD (nm)	substrate	Cn (wt/vol %)	rpm	figure number in online Supporting Information
PS	300	glass	0.25 wt %	1000 rpm, 120 s	S2A
		silicon wafer	0.2 wt %	1000 rpm, 120 s	S2B
		PS film	0.3 wt %	800 rpm, 120 s	S2C
		PMMA film	0.25 wt %	800 rpm, 120 s	S2D
		UVO-exposed PDMS film	0.4 wt %	800 rpm, 120 s	S2E
PS	600	glass	0.5 wt %	800 rpm, 120 s	S3A
		silicon wafer	0.4 wt %	800 rpm, 120 s	S3B
		PS film	0.6 wt %	600 rpm, 120 s	S3C
		PMMA film	0.5 wt %	600 rpm, 120 s	S3D
		UVO-exposed PDMS film	0.67 wt %	600 rpm, 120 s	S3E
PS	800	glass	0.8 wt %	600 rpm, 120 s	S4A
		silicon wafer	0.75 wt %	800 rpm, 120 s	S4B
		PS film	0.85 wt %	500 rpm, 120 s	S4C
		PMMA film	0.8 wt %	500 rpm, 120 s	S4D
		UVO-exposed PDMS film	0.9 wt %	500 rpm, 120 s	S4E
silica	350	glass	0.4 wt %	800 rpm, 120 s	S5A
		silicon wafer	0.3 wt %	1000 rpm, 120 s	S5B
		PS film	0.47 wt %	600 rpm, 120 s	S5C
		PMMA film	0.4 wt %	600 rpm, 120 s	S5D
		UVO-exposed PDMS film	0.5 wt %	600 rpm, 120 s	S5E

In order to highlight the dependence of the optimum condition on simultaneous variation of several parameters, we construct morphology phase diagrams. Two types of morphology phase diagram can be constructed, which are shown in Figure . The phase diagram shown in Figure A can be constructed for each particle with a specific dD—substrate combination to identify the optimum condition. The diagram shown in Figure B is obtained by plotting each of the optimum points obtained for different dD—substrate combinations. To generate a plot like the one shown in Figure A, which is specific to PS particles with dD = 600 nm on UVO-exposed PDMS substrates at a location that is 4 mm away from the center of the substrate, we classify the morphology obtained at different Cn–rpm combinations into three subcategories, which are perfectly ordered, underfilled, and overfilled, as has been discussed in the context of Figure . The three distinct morphologies are represented with different symbols. The information in Figure is further used to identify the Cn = 0.67% and rpm = 600 as the optimum condition which is marked with a square. It can further be seen that the Cn at which transition from underfilled to overfilled structures take places varies linearly with rpm.

Figure 3

Morphology phase diagram (A) for PS colloids having dD = 600 nm on a UVO-exposed flat PDMS substrate and (B) for colloids of different sizes on different types of flat substrates. While each color represents colloid of a specific type and dD, each symbol represents a type of substrate, as per legend provided in the figure.

Figure B represents the global morphology phase diagram which is constructed by using the data reported in Table , each one of which has been obtained by constructing a particle and substrate specific morphology phase diagram similar to that shown in Figure A. Representing data with simultaneous variation of four parameters (Cn, rpm, dD, and substrate type) on a single plot was itself challenging, and therefore, the logic adopted for representation needs to be mentioned. In the plot, a particular color of the symbols represents particles of a specific dD. In contrast, different types of substrates have been represented with different shapes of the symbols. The figure highlights that for a particular type of particle, perfect ordering is achieved on three polymeric substrates [PS, polymethylmethacrylate (PMMA), and UVO-exposed PDMS] at nearly identical conditions. In contrast, it emerges out from Figure B that a higher rpm is required to obtain perfect ordering on glass and silicon substrates. This probably is a signature of slippage of the solvent on a polymeric substrate and needs to be explored in greater detail. Also, it becomes evident from both Figure B and Table that for obtaining perfect ordering, Cn increases with an increase in dD, a trend that is counterintuitive, as lesser number of larger particles are required to cover the same surface area, when dD is larger. It may however be explained rather easily from eq , which suggests that to achieve constant surface coverage (Fs) or occupation factor (ϵ2), is proportional to dD.[41] As Cn is very dilute, one may further argue that 1 – Cn ≈ 1, and hence, Cn exhibits direct proportionality with dD.

Figure 4

Morphology of the colloidal deposit at different Cn–rpm combinations, when PS colloids with dD = 600 nm are spin coated on the patterned UVO-exposed PDMS substrate with type 2 geometry (λP = 1.5 μm).

Table also reveals that for a particular dD, the optimum Cn increases slightly, with lowering of the substrate surface energy. This can be attributed to the reduced strength of the particle–substrate interaction with lowering of γ. However, how exactly the surfactant molecules adsorb on the substrate and thus influence the ordering process is not fully clear and will be analyzed separately. It can be seen that there is no monotonic correlation of Cn and rpm with the substrate surface energy for the formation of a perfect array, though the parameters are quite close on various substrates. This observation is an indirect evidence that the surface has a much lower role on the assembly, apart from its wettability. We argue this happens because of the presence of the surfactant molecules, which favor wetting of solution on the substrate, which is the necessary condition for achieving ordering.

Template-Directed Assembly of Colloids

Particle Diameter Approximately Equal to Pattern Line Width (dD ≈ lP)

It is well-known that physical confinement provided by the patterned substrate effectively traps the colloidal particles during spin coating.[51] The grooves act as the preferred location for the deposition of the particles, as the solvent layer ruptures over the substrate pattern protrusions.[57] Consequently, the remaining liquid flows in the grooves, localizing the colloids there. Subsequently, the lateral capillary forces between the particles drive them to form closely packed structures aligned along the grooves. It has also been recently shown by Aslam et al. that a patterned substrate also eliminates axial symmetry by spin coating and therefore suppresses the formation of OCP structures.[57]

In this section, we show how the morphology of the particle deposit varies as a combination of Cn and rpm. As a test case, we examine the ordering of dD = 600 nm PS particles on the type 2 grating patterned substrate of the UVO-exposed cross-linked PDMS. For a type 2 substrate, the groove width is lP ≈ 750 nm, the groove depth is hP ≈ 250 nm, and the periodicity is λP ≈ 1.5 μm. Using a substrate of the same material as that in Figure allows direct comparison between the conditions that leads to a perfect ordering on a flat substrate and a patterned substrate. As dD and lP are comparable, we consider that the particle and the patterned substrate are commensurate.

Figure shows various deposition morphologies of dD = 600 nm PS particles on type 2 substrate, obtained at different Cn–rpm combinations. The trend is similar to that observed on a flat surface; for a particular Cn, Fs-P (surface coverage or fill fraction on a patterned substrate) gradually reduces with an increase in rpm because of higher splash drainage. On the other hand, increase of Cn at a constant rpm leads to the deposition of more particles, leading to disorder, as particles get deposited on top of the stripes, after filling the grooves (frames A14, A15, B24, and B25 of Figure ). Among all the frames of Figure , perfect ordering is observed in frame B23 for a parameter combination of Cn = 0.75% and rpm = 1000. It is interesting to note that perfect ordering on a patterned substrate requires higher Cn as well as higher rpm for particles with the same dD as compared to the flat substrate of the same material. This means that on a patterned substrate, more number of particles are required for perfect ordering. This is counterintuitive as perfect ordering on a grating patterned substrate implies that particles align only inside the grooves, and therefore, only about 50% of the number of particles is required to achieve the same, in comparison to a perfect HCP structure on a flat surface (Fs ≈ 1.0). The observation can be explained well with the help of eq (modified Cregan model).[41] As Fs (or ϵ2) is almost half on a grating patterned substrate, as compared to that on a flat substrate, CEH on a patterned substrate is also approximately half than that on a flat substrate. From eq , we note that CEH = 1ω–β. Figure shows that Cn = 0.75% for perfect ordering on a patterned substrate, which is compared to a value of Cn = 0.67% on a flat surface (Figure ). As the values of Cn are rather close to each other, the values of are also rather close on a flat and a patterned substrate. Thus, from eq , lower CEH becomes possible on a patterned substrate only when ω is higher as compared to that on a flat substrate.

We summarize the optimized conditions for obtaining perfectly ordered structures (Fs-P ≈ 1.0) on type 1 and type 2 substrates of different materials, with both silica and PS colloids of different sizes, as presented in Table , by performing experiments in line with Figure for particles of each dD on each type of patterned substrate. Figure A shows the perfectly ordered structure obtained with silica colloids having dD = 350 nm on a patterned type 1 PMMA substrate, under conditions mentioned in Table . Interestingly, on patterned substrates, we find that the rpm at which perfect ordering is obtained for a particular colloid is independent of the substrate material, though Cn differs slightly from substrate to substrate. This clearly highlights the critical role of colloidal spreading on the formation of perfect structures, rather than the particle–substrate interaction, which seems to influence the ordering process weakly. The results imply that the evolution during spinning up to the stage of topography-mediated rupture of the solvent layer is not much influenced by the substrate. Also, as already discussed, in all cases higher rpm is required for obtaining a perfect array, as compared to that on a flat substrate of the same material.

Table 3

Optimized Conditions for Perfect Ordering on Patterned Substrates

material of particle	dD (nm)	substrate	substrate type	Cn (wt %)	rpm
PS	300	patterned PS film	type 1	0.45	1400 rpm, 120 s
		patterned PMMA film	type 1	0.45	1400 rpm, 120 s
		UVO-exposed patterned PDMS film	type 1	0.5	1400 rpm, 120 s
PS	600	patterned PS film	type 2	0.67	1000 rpm, 120 s
		patterned PMMA film	type 2	0.65	1000 rpm, 120 s
		UVO-exposed patterned PDMS film	type 2	0.75	1000 rpm, 120 s
silica	350	patterned PS film	type 1	0.55	1200 rpm, 120 s
		patterned PMMA film	type 1	0.5	1200 rpm, 120 s
		UVO-exposed patterned PDMS film	type 1	0.6	1200 rpm, 120 s

Figure 5

(A) Perfectly ordered structure with Fs-P ≈ 1.0 obtained by spin coating silica colloids having dD = 350 nm on type 1 patterned PMMA substrate. (B) Unique ordered structures with PS colloids having dD = 600 nm on type 2 patterned PMMA substrate, where the particles fully cover the patterned substrate. Inset (B1) shows the cross-sectional AFM line profile and (B2) represents a schematic highlighting the particle arrangement. The overall pattern is HCP, but particles rest at two different elevations.

Until this point, we have considered a perfectly ordered structure to be one where only the grooves are completely filled up by the colloids in an uninterrupted threadlike manner (Fs-P ≈ 1.0). However, Figure B shows another interesting morphology where the entire patterned substrate is covered in a near HCP manner by PS colloids (dD = 600 nm). The section B1—B1 in the inset of Figure B shows that some particles are at a lower level as compared to others. This happens when Cn is adequately high and they start depositing covering the entire patterned substrate. The particles which lead to within the grooves arrange themselves in a zigzag threadlike manner. The remaining particles, which deposit over the substrate stripes, align themselves in an interesting arrangement of alternate single and double particles along the length of the stripes, alongside the particle thread formed within the groove. The arrangement is schematically shown in inset (B2) of Figure B. This structure forms when Cn ≈ 2.5% and rpm = 1000. Because lP is higher than dD, the particles align in a zigzag fashion inside the grooves, allowing more particles to pack themselves side by side over the stripes. As larger number of particles are dispensed (Cn for optimum coverage = 0.75%, as per Table ) on the surface, the applied centripetal force fails to splash out significant fraction of the excess particles that are available after filling of the grooves. The morphology is novel and highlights that the hexagonal arrangement still leads to minimum energy configuration even if the particles remain at multiple levels.

Effect of Template Height on Pattern-Directed Assembly

In this section, we show how the feature height (hP) of the substrate patterns influences the pattern-directed ordering. For this purpose, type 2 substrates of different hP were used. The experiments were performed with dD = 600 nm PS colloids so that the dD and λP remain commensurate. The initial Cn–rpm combination chosen was the same as that which is seen to give perfect ordering in Figure , frame B23. It can be seen that perfect pattern-directed ordering is obtained till hP ≈ 150 nm, when the Cn–rpm combination was kept unaltered. It can be seen in Figure B that the ordering is lost when hP ≈ 125 nm. The uniqueness of Figure B can be understood by comparing it with frames A13–A15 and B24–B25 of Figure which also shows distorted arrays on patterned substrates. However, in all those frames of Figure , the grooves are totally filled and the excess particles are seen to get localized over the stripes, resulting in disorder. In contrast, in Figure B, the particles are seen to accumulate over the stripe tops, despite some grooves remaining vacant. This means that during the radial outward flow, the hP of the features is too low to intercept the flow and guide the particles within the grooves. When we performed similar experiments with dD = 300 nm on type 1 substrates of different hP, we observed that ordering gets lost below hP ≈ 75 nm. The trend, including the critical hP below which topography-guided ordering is lost, is nearly similar for all substrates having identical pattern topography. It can be seen that the limiting value of hP/dD lies between 0.2 and 0.25 below which the topography of the substrate patterns fails to provide confinement to the particle organization process. On the basis of the first results reported in this article, a detailed investigation on this problem will be taken up separately. Similar transition from order to disordered structures with gradual reduction of hP has been observed earlier in the context of pattern-directed dewetting of thin polymer films.[66] A detailed investigation on this topic is underway. It will be particularly interesting to explore if there is a critical hP around which there will be a transition from OCP structures to purely template-guided ordered structures, which is likely to depend on dD of the colloids as well.

Figure 6

Morphological variation in template-guided assembly of PS colloids (dD = 600 nm) on type 2 gratings of height (A) 150 and (B) 125 nm.

Particle Diameter Smaller Than Pattern Line Width (dD < lP)

In Figure , we show how the morphology of the deposit depends when dD is much smaller than the groove width of the patterned substrate. Unlike all the earlier cases, where perfect ordering means a single thread of particles aligned along the substrate groove, more complex ordering is possible when dD and lP are noncommensurate. We produce one such example with dD = 300 nm PS particles coated on type 2 PMMA substrate, which has lP = 750 nm. While we obtained a variety of morphologies depending on the combination of Cn and rpm, we report the morphology which can be considered as the perfectly ordered structure and can be considered analogous to Figure , frame B23. In Figure , the laterally coexisting particles are seen to arrange in a hexagonal manner, though they are aligned along the groove.

Figure 7

Particle doublet obtained with PS colloids having dD = 300 nm on type 1 substrate, obtained with Cn = 05% and rpm = 1000.

Conclusions

In this article, we have systematically demonstrated the conditions under which perfect arrays of monodispersed colloids can be obtained on both defect-free flat and topographically patterned substrates of different materials, using spin coating. On the flat surface, we obtained structures that exhibit correlation length lR ≈ 15 ± 2.5 μm and SA ≈ 210 ± 12 μm2 in each single crystalline domain comprising HCP monolayer array of the colloidal particles, with no crack between adjacent domains over the entire sample surface (15 mm × 15 mm). We have shown in details the optimization process, and the role of individual parameters, particularly Cn and rpm on the extent of ordering process and constructed a morphology phase diagram to highlight the collective role of Cn and rpm on perfect ordering with particles of different sizes on different surfaces. We have also highlighted the need to check the spatial variation of the as-cast morphology, as there can be a significant variation in the extent of ordering and Fs over the surface. Our results also highlight the critical role of surfactants added on the formation of uniform particle arrays, which might eventually open up a new route to overcome the nonplanarization effect in spin coating, particularly from a volatile organic solvent. Our intention is that the report will significantly help beginners in the area to quickly optimize the parameters by identifying the nature of the defect in the structure and appropriately modulating either rpm or Cn. To facilitate this, we have highlighted the likely types of defects that may result when Cn and/or rpm is low or high. We also show that higher Cn is required for obtaining perfect arrays with larger dD particles, which is in line with the recent theoretical predictions on the spin coating of colloidal particles by Aslam et al.[41]

On a patterned surface, we note that both higher rpm and Cn are required for obtaining perfect ordering, which can be attributed to lower Fs as compared to that on a flat surface and has been explained well from the theory. We also explored how the ratio of dD and hP can influence the ordering process. If the features are shallower than 20% of the particle diameter, then the patterns fail to confine the particles. Or in other words, a grating much shallower than the particle diameter is sufficient for confining the particles. We also report the formation of novel multielevation structures under certain conditions when the topographically patterned substrate is fully covered with particles at high Cn, as well as interesting structure comprising an array of particle doublets when dD is nearly 50% of lP.

As a final summary, we understand that 2D monolayer colloidal array formation on both flat and patterned substrates by spin coating is a complex problem because of its multiparameter nature. While we have carefully examined the dependence of Cn and rpm on the ordering process, various other parameters such as effect of surfactant type and concentration, relative commensuration between particle size and pattern geometry, and so forth also influence the ordering process, which needs detailed investigation.

Materials and Methods

Substrates

Glass slides, silicon wafer, films of cross-linked PDMS, PS (molecular weight: 280 kDa, Sigma-Aldrich USA), and PMMA (molecular weight: 120 kDa, Sigma-Aldrich USA) were used as different substrates. The size of the substrates was 15 mm × 15 mm. The glass and silicon substrates were cut from glass slides and silicon wafer (test grade, Wafer World Inc.) respectively. They were subsequently cleaned following a standard procedure. All polymer films were spin-coated on cleaned glass pieces. The thickness of the PDMS film was ∼10 μm, which was obtained by spin-coating a degassed mixture of part A to part B (1:10 wt/wt) of Sylgard 184 (a thermo curable, PDMS-based elastomer, Dow Corning, USA) in n-hexane (SRL, India) at 2500 rpm for 1 min. The coated film was cured at 120 °C for 12 h in an air oven for complete cross-linking. The thickness of the PS and PMMA films was ∼500 nm, which was obtained by coating dilute solutions [10% (w/v) PS and PMMA] in toluene on the glass slides at 2500 rpm for 1 min. After coating, the PS and PMA films were annealed at 60 °C for 3 h in a vacuum oven to remove the remnant solvent. All the flat substrates were characterized using an atomic force microscope. Contact angle goniometry (ramé-hart Instrument Co.) was used to measure the water and methanol contact angle on each of the substrates, which along with the substrates surface energy are listed in Table .

All the substrates were used as it is, except cross-linked PDMS substrates which were not wetted by the solvent (methanol). To make it wettable, the cross-linked PDMS substrates were exposed to UVO (PSD Pro UV–O, NovaScan, USA). UV irradiation at 185 nm wavelength leads to the production of ozone from atmospheric oxygen. The ozone molecules, in turn, dissociate into oxygen at 254 nm irradiation.[67] The reactive oxygen radicals, thus created, attack the methyl groups present in Sylgard 184 (Si–CH3) and replace them with silanol groups (Si–O–H), hence generating a superficial oxide layer of higher surface energy and leads to enhanced wetting of the samples. The drastic drop in methanol contact angle on the UVO-cured PDMS substrate can be observed in Table .

Patterned Substrates

Some PS, PMMA, and PDMS films were patterned using topographically patterned stamps, which were obtained from peeling the foils of commercially available optical data storage disks such as DVD and CD.[68] The PS and the PMMA films were patterned using capillary force lithography.[69,70] The cross-linked PDMS films were patterned using a UVO-mediated soft embossing technique reported elsewhere.[68] The morphology of all three films patterned using the same stamps was identical, implying the formation of a perfect negative replica of the stamp pattern, which was verified using an atomic force microscope. While the grating patterns obtained with a DVD foil has the periodicity λP ≈ 750 nm, groove width lP ≈ 350 nm, and groove depth hP ≈ 100 nm (Figure S6, online Supporting Information, marked as type 1 patterns), the films patterned with a CD foil has λP ≈ 1.5 μm, groove width lP ≈ 750 nm, and groove depth hP ≈ 250 nm (Figure S7, online Supporting Information, marked as type 2 patterns).

Grating patterns with the same λP but different hP was obtained following stress relaxation-associated imprinting of partially precured PDMS films, which is reported in detail elsewhere.[71,72] In short, PDMS films of different viscoelasticities were created by precuring the films for different durations before embossing. These films, once imprinted with flexible foils, underwent stress relaxation, which resulted in films with different hP. Figure A shows the hP of different PDMS substrates used in our study, created as a function of precuring time (tP) of the PDMS film. Figure B1,B2 shows the cross-sectional line profiles of the type 1 and type 2 patterns having different hP.

Figure 8

(A) Variation of pattern feature height (hP) with precuring time (tP). (B) AFM cross-sectional profile of patterns with different features hP, as a function of tP.

Colloidal Particles

Monodispersed colloids of PS with diameters dD ≈ 300, 600, and 800 nm were purchased from Sigma, UK. Monodisperse silica particles of diameter (dP) ≈ 350 nm were synthesized following Stöber’s method by the hydrolysis of tetraethyl orthosilicate (99.99%, Sigma-Aldrich) in ethanol (99.99%, Sigma-Aldrich) medium in the presence of ammonium hydroxide (28%, Sigma-Aldrich) as a catalyst.[73] The details about the reaction can be found in the online Supporting Information (Section S4.0).

Prior to spin coating, dilute solution of PS and silica colloids in methanol was mixed with 0.025 wt % (unit of Cn is in terms of wt/vol %) solution of SDS (purest grade purchased from Merck, India) in methanol to stabilize the colloidal dispersion and was sonicated in a water bath for 1 h. All the results reported in this paper are with SDS. However, in some cases, a nonionic surfactant (Triton-X) or a cationic surfactant (HTAB) was also used. It is quite clear that the presence of surfactants favors better ordering, and therefore, surfactant concentration is going to be an important factor influencing the morphology of the deposits. A detailed analysis on how the nature and concentration of the surfactant influence the ordering process will be analyzed separately.

Spin-Coated Array Fabrication

For spin coating, the bare substrate (mounted onto the chuck) was first started to rotate and allowed to attain the final rotational velocity. Subsequently, 100 μL of the stabilized colloidal dispersion was dispensed on the rotating substrate using a micropipette. This protocol of dispensing the colloidal suspension was adopted to minimize the effects of acceleration on the sample. Coating over all the samples was performed at a room temperature of 25 °C and a relative humidity of 30%. The rpm and the colloid concentration (Cn) vary from sample to sample and are mentioned in the appropriate sections. The morphology of the colloidal arrays was investigated using an atomic force microscope (Agilent Technologies, AFM 5100) in intermittent contact mode using a silicon nitride cantilever (PPP-NCL, Nanosensors Inc., USA) and a field emission scanning electron microscope (JSM7610F, JEOL, Japan). For every AFM image, the fractional coverage (Fs) was calculated using the “slice” feature of Pico Image Basic (Version 5.1), an integrated AFM imaging and analysis software package. Details about the calculation procedure of Fs can be found in Section S5.0 of the online Supporting Information