Coating Process Regimes in Particulate Film Production by Forced

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Coating Process Regimes in Particulate Film Production by Forced-Convection-Assisted Drag-Out Damien D. Brewer,† Takumi Shibuta,‡ Lorraine Francis,† Satish Kumar,† and Michael Tsapatsis*,† † ‡

Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States Process & Production Technology Center, Sumitomo Chemical Co., Ltd., 2-1 Kitasode, Sodegaura, Chiba 299-0295, Japan

bS Supporting Information ABSTRACT: Operating conditions for the deposition of monolayer and bilayer particulate coatings from aqueous 20-nm-diameter silica dispersions are identified in the context of a drag-out operation assisted by forced convection. The dry film thickness, uniformity, and morphology are assessed within an operating window parametrized by the capillary number and silica dispersion weight fraction. Three film deposition regimes with respect to the capillary number are observed: convective film deposition at low process rates, film entrainment at moderate process rates, and a thin-film transition regime at intermediate process rates. Locally ordered particulate films of variable layering thickness, including (i) a discontinuous submonolayer or (ii) a mixed submonolayer and monolayer, (iii) a mixed monolayer and bilayer, and (iv) multilayers, are dominant under convective deposition conditions. A map of morphologies is presented within the capillary number
weight fraction operating window, where monolayer and mixed monolayer
bilayer films are demonstrated in the thin-film transition regime at an intermediate dispersion weight fraction. A complementary map of the morphologies formed by the drag-out of 110 nm silica dispersions reveals a broader applicability to this type of operability diagram. These operating maps are constructed using model silica dispersions and are therefore relevant to particulate coatings of other inorganic materials.

1. INTRODUCTION Particulate coatings serve a diverse set of functions, including surface finishes, paints, adhesives, and transparent conductors from latex,1,2 the encapsulation of biological transplantation agents,3 templates for porous materials,4 antireflective films,5 and crystalline nanostructures for lithographic templating, electron transport, separation, and catalysis.6,7 Though current uses are extensive, many of these functional thin-film applications represent emerging technologies that depend on particulate coatings, or films, as either intermediates for further processing or functional components in and of themselves. Given the breadth of processes and devices in which particulate films are employed, the demands placed on properties such as film thickness, uniformity, microstructure, and morphology are similarly diverse.8 Hence the processing strategy, which determines the processing speed, attainable uniformity, and stable operating window, bears careful consideration. Therefore, the breadth of emerging technologies based on particulate materials such as thin semiconductors, transparent conductors, and micro- to mesoporous films presents a clear need for understanding particulate coating fundamentals. Although conventional premetered coating operations such as slot die and gravure roll are robust avenues for particulate film production on flexible planar webs, they are less suitable for operation on discrete nonplanar substrates such as porous cylindrical supports.9 For these reasons, we investigate the use of the drag-out operation as a means of producing thin inorganic particulate films using a model silica nanoparticle dispersion.10
12 Described r 2011 American Chemical Society

theoretically first by Landau and Levich13 and then by White and Tallmadge14 and others,15 we refer to drag-out as the immersion of a solid surface, be it a roll, flexible web, or discrete porous support, followed by its withdrawal under controlled conditions so as to entrain or otherwise deposit a thin film of material on the surface. The material may be a homogeneous liquid mixture, a particulate-laden suspension with binders or other polymeric additives, or a partially dry particle film with varying degrees of solvent saturation.16 Among variants of the drag-out operation, vertical withdrawal at low velocity (also termed convective assembly)17 and dip coating (also termed film entrainment)13
15 are well suited to particulate film processing. Colloidal stability,18 rheology,19 and the drying of entrained films20 formed by dip coating from particle dispersions are known to influence the dry film microstructure and morphology. Since the work of Dimitrov and Nagayama on drag-out at low velocity,17 the governing mechanisms involving lateral capillary forces,21 convective particle transport,22 and electrostatic forces23 have been documented. Drag-out at low velocity and its simpler precursor, solvent evaporation, are now widely employed as relatively simple, inexpensive processing methods by which monolayer and multilayer films are obtained.24
28 Orientationally ordered crystalline arrays were first demonstrated by Colvin and co-workers24 using Received: May 31, 2011 Revised: August 4, 2011 Published: August 08, 2011 11660

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Langmuir solvent evaporation, and optical diffraction and reflectivity measurements have since shown that crystalline microsphere arrays are attainable over the square millimeter to square centimeter scale.25,29 Variations on temperature and humidity control have been proposed,30 and the use of substrate templating to direct the particulate film microstructure showed promise despite the added expense of lithography.22,31 A number of studies feature anisotropic particles such as plates,32 dumbbells,33 and rods.27 Meniscus confinement and evaporation assistance using forced convection showed promise as well.34 Each of these studies enlarged the literature on particulate coatings by drag-out but emphasized microsphere coatings or micrometer-scale films from nanometer-scale particles, except for the work of Lee.26,35 In the latter investigation, a facile coating technique was reported and was shown to enable near-monolayer coatings of nanoscale silica particulate coatings, yet the occasional defects are problematic in membrane and related separation applications. This article extends the concepts and techniques developed by Lee26,32,35 and others36,37 toward a better understanding of particulate coating process stability in drag-out operations. Specifically, we investigate the particulate film thickness, uniformity, and morphology within an operating domain parametrized by the capillary number, Ca, and the suspension solids weight fraction, c. The capillary number is a measure of the relative strength of the viscous stresses generated in the region where the film is deposited as compared against the capillary pressure difference established between the film deposition region and the undisturbed liquid far away. The capillary number Ca is defined as Ca = μU/σ, where μ is the solvent viscosity, U is the linear coating speed, and σ is the solvent surface tension. The solvent viscosity and surface tension are kept constant, and for this reason, the drag-out velocity, process rate, and capillary number are referred to interchangeably. These investigations lead to concise heuristic principles for achieving the desired thickness, uniformity, and morphology of particulate films using spherical nanoparticles. Specifically, we identify an operability window for forced-convection-assisted drag-out wherein continuous sub-40-nm films are reproducibly achieved. Moreover, the macroscopic continuity of these films is demonstrated and contrasted with the occasional defects generated by the convective assembly of the nanoparticles. This new operability window is attributed to a capillary
viscous transition phenomenon characterized by the onset of film entrainment, and we posit that the meniscus instabilities responsible for occasional defect formation are effectively damped by the action of enhanced viscous stresses upon the onset of film entrainment. The article is organized as follows. In section 2, we describe the model silica dispersion properties, experimental coating procedures, and film characterization techniques. In section 3.1, we present a coating process regime map with lysine
silica (20-nmdiameter) films and identify operating states for monolayer and bilayer nanoparticle coatings. We explore the applicability of the coating process regime map to larger silica particles and present an analogous coating process regime map for NS
silica (110-nmdiameter) films in section 3.2. The continuity of monolayer and mixed bilayer
monolayer films is demonstrated further in section 3.3. We rationalize these operating regimes in section 3.4 by a transition between the capillary-dominant convective assembly and viscous-dominant film entrainment regimes. In section 3.5, we propose a simple mechanism, akin to a combination of thinfilm entrainment and Langmuir
Blodgett deposition, to explain the formation of macroscopically continuous near-monolayer,

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monolayer, and mixed bilayer
monolayer silica particle coatings by forced-convection-assisted drag-out.

2. MATERIALS AND METHODS 2.1. Silica Particle Synthesis and Characterization. Silica particles were synthesized following a low-temperature solution procedure described by Yokoi et al.10 and Davis et al.12 Specifically, silica particles (referred to here as lysine
silica particles) were synthesized via the hydrolysis of tetraethylorthosilicate (TEOS, 98%, Sigma-Aldrich) in the presence of amino acid L-lysine (Sigma-Aldrich). The synthesis solution was prepared by the addition of TEOS to an aqueous solution of lysine to obtain a molar composition of 60:1.19:9500:240 SiO2/lysine/ H2O/EtOH.12 The synthesis solution was held at 90 °C with stirring at 500 rpm for at least 24 h. Because the stir rate influences the hydrolysis rate via the interfacial mixing of the TEOS and aqueous phases, the synthesis vessel and stir bar also influence the particle size. The seeded growth of larger silica particles (referred to here as meso-silica particles), following previous procedures,38 is described in the Supporting Information. Lysine
silica particle dimensions were characterized with transmission electron microscopy (TEM), small-angle X-ray scattering (SAXS), and zeta potential measurements. TEM micrographs were collected on a FEI Tecnai T12 instrument equipped with a charge-coupled device (CCD) and operated at 300 kV. Zeta potential measurements were collected on a Brookhaven ZetaPALS/ZetaSizer 90 Plus. SAXS patterns were taken at room temperature (20 °C) with a SAXSess (Anton Paar GmbH) employing Cu KR radiation. Lysine
silica particle diameters were measured to be 22 ( 2 nm by TEM and 23 nm by SAXS (Figure S1). The zeta potential was measured to be
40 mV for a lysine
silica suspension at pH 9.3, which is the L-lysine buffer pH. All suspensions are stabilized by electrostatic repulsion. 2.2. Preparation of Coating Suspensions and Substrates. All lysine
silica and meso-silica suspensions were filtered with a 0.2 μm syringe filter (Acrodisk GHP), followed by solids concentration estimation by solvent evaporation. Suspensions were also prepared from silica spheres provided by Nippon Shokubai Co., Ltd. (Seahostar KE-W10) as a water-borne suspension of silica particles with an average diameter of 110 nm and a solids concentration of 15.6 wt % at pH 6.7 (referred to here as NS
silica). The suspensions were then diluted with 18 MΩ cm
1 Milli-Q water (Millipore Corp.) to the desired solids weight fraction. All substrates coated with lysine
silica and meso-silica were silicon wafers cleaned by immersion in piranha solution (30:70 H2O2/H2SO4) at 120 °C for at least 10 min, resulting in oxide surfaces with a static contact angle of less than 5°. (Caution! Personal protective equipment must be worn while processing substrates in piranha solution. Proper containment and secondary containment within a ventilated enclosure should be observed at all times.) Substrates were stored in ultrapure Milli-Q water prior to coating, and each substrate was rinsed thoroughly with water to minimize contamination and dust. Substrates were then dried using a stream of ultra-high-purity (UHP) N2 gas immediately before use. Substrates coated with NS
silica (110 nm particles) were glass slides prepared by repeated immersion in 0.1 M sodium hydroxide solution for 15 min and rinsing in water. 2.3. Particle Film Coating by Drag-Out. We employ a custom coating assembly similar to the apparatus of Lee.26,35 The concept is to perform drag-out while retaining independent control of the material (particle) deposition rate. As described by Dimitrov and Nagayama,17 the evaporation of solvent near the meniscus region drives film assembly at low drag-out velocities and can be tuned by the forced convection of gas. Here, UHP N2 is delivered perpendicular to the substrate as a laminar stream to enhance the liquid
vapor mass transfer. Figure 1 illustrates the gas-delivery apparatus in relation to the actuated substrate. Specifically, the dry N2 is fed into a distribution chamber, which forces gas into a channel with an adjustable gap height. Dry gas is issued onto 11661

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Figure 1. (a) Schematic diagram of the drag-out operation modified by forced convection35 and (b) photograph of the equipment (without suspension), including the gas delivery apparatus shown in part a and a substrate guide employed to control the substrate surface relative to gas delivery during withdrawal. The suspension level is kept 7 mm below the lower gas delivery die lip to avoid meniscus invasion of the channel. the substrate above the film deposition region. This film deposition region is where the meniscus approaches its entrained film thickness or contact line. Film deposition is sensitive to a wide array of process parameters. All of the apparatus dimensions influence the effective liquid
vapor mass transfer, or evaporation, rate. A precise, nearly uniform cross-web gap height enables a nearly uniform-velocity gas stream to be issued directly onto the substrate (Figure 1a). Additionally, the gas delivery channel to the substrate gap is fixed using spacer plates at the lateral substrate edges (Figure 1b). A similar design was described by Kim et al.34 The imposition of forced convection drastically increases the material deposition rate relative to the base case of stagnant gas. The deposited film thickness increases with the volumetric gas delivery rate, though a comprehensive investigation of this effect is beyond the scope of this work. Because the effective mass transfer coefficient in the meniscus region is also a function of the humidity, temperature, and containment geometry, these factors are controlled by operation in an enclosed environment. Measured ranges of the ambient humidity and temperature are respectively 8
15% RH and 20
22 °C. Substrates are attached to a linear translation stage and actuated at drag-out velocities of between 5.0  104 and 1.0  104 μm/s. At the lowest velocities, a stepper motor is coupled to a gearbox and a worm-driven linear stage, and at higher velocities, a dc servo-motor-driven linear stage is employed. The coating suspension level relative to the gas delivery apparatus was maintained at a set point by replenishing the bath with makeup suspension. Thick entrained films of lysine
silica were dried by placing the substrate horizontally in an oven at 80 °C immediately following liquid application. Thick entrained films of NS
silica (110 nm, section 2.2) were dried at room temperature.

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2.4. Particle Film Characterization. Top and cross-sectional views of particle films were obtained after sputtering with Pt (ca. 5 nm) via scanning electron microscopy (SEM) on a field emission JEOL 6700 at 5.0 kV and a Hitachi S-900 instrument at 5.0 kV, respectively. The film morphology and roughness were also characterized ex situ by scanning probe microscopy (SPM) in tapping mode on a humidity-controlled (e5% RH) Agilent 5500 instrument with an ∼100 μm (x
y range) scanner operated in an open loop. A silicon tip integrated with a rectangular, uncoated silicon cantilever (Applied Nanostructures, 10
5), leading to a whole class of morphologies and microstructures dependent largely upon the drying conditions20 (Figure S7). SM films exhibit an even more pronounced variety of morphologies, including banding, sparse disordered, and network structures, as the capillary number increases (Figure S8). Of these, banding has been reported most prominently because it occurs near the narrow operating window in which continuous near-monolayer or monolayer films are attained at very low solids concentration37,40 (Figure 2).

3.2. Monolayer and Near-Monolayer Coatings of Mesoscale Particles. We now address the applicability of a coating

process regime map based on “nanoscale” 20 nm lysine
silica coatings to larger “mesoscale” coatings from 50 and 110 nm silica dispersions. Because the monolayer thickness scales linearly with particle size, the solids concentration of the coating process regime map (Figure 2) should scale in roughly the same way. The operating state (Ca ≈ 3  10
6, c = 0.5 wt %), identified here as leading to a near-monolayer morphology of 20 nm lysine
silica particles, would map approximately to the operating state (Ca ≈ 3  10
6, c = 1 wt %) for 40 nm silica particles. We test this heuristic approach by operating in the capillary
viscous transition regime (U ≈ 160
250 μm/s, Ca ≈ (2
3)  10
6) with meso-silica (ca. 50 nm diameter) at elevated solids 11664

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Figure 4. Stylus probe profilometry scans of lysine
silica films prepared at c = 0.5 wt % and (a) Ca = 1.0  10
6 (U = 70 μm/s), (b) Ca = 1.4  10
6 (U = 100 μm/s), (c) Ca = 2.3  10
6 (U = 160 μm/s), (d) Ca = 3.6  10
6 (U = 250 μm/s), and (e) Ca = 7.1  10
6 (U = 500 μm/s). In each case, the mean film thickness is set to 0 on the accompanying scale bar. Units are in nm. The long axis (1 mm) of each scan is in the coating direction, and the short axis (0.1 mm) is in the cross-web direction.

concentration (c ≈ 1.5 wt %) and reduced gas delivery rates (G ≈ 0.5 LPM, explained in section 3.5). Macroscopically uniform films of near-monolayer morphology are demonstrated in Figures S9 and S10. The predominant morphology is the closepacked monolayer, though occasional particle-scale void spaces appear (Figure S9c). Similar films are achieved with intermediate-diameter silica particles (35
40 nm) at their corresponding concentrations (c ≈ 0.8
1 wt %). We conclude that the process regime map is readily applicable to thin particulate film production from stable, aqueous silica dispersions. We further examine the applicability of these heuristic principles by constructing a coating process regime map for NS
silica films coated by drag-out. Shown in the center of Figure 3, this NS
silica regime map spans a range of capillary numbers (Ca ≈ 10
6
10
4) that is similar to that in the lysine
silica map of Figure 2. Although a quantitative analysis of the effects of particle size is beyond the scope of this work, a qualitative mapping of analogous operating states between the coating process regime maps prepared with lysine
silica and NS
silica is possible by scaling the solids concentration with the particle diameter (Figure S11). Four operating regimes are identified according to the same definitions given previously for lysine
silica films: SM, NM, VMS, and ML. NM and ML coatings are demonstrated on the 0.1 mm scale in Figure S12. For certain applications, the film continuity and thickness are at least as central to the functionality as the packing orientation.41
43 We therefore emphasize the enhanced continuity of monolayer and bilayer nanoparticle films relative to those processed via drag-out at low capillary numbers. The key finding of the regime maps in Figures 2 and 3 is the importance of the solids concentration to the attainability of such monolayer and bilayer coatings. The film thickness increases as expected with the process rate for all solids concentrations, yet the regime map indicates that monolayer, near-monolayer, and

Figure 5. SEM micrographs of lysine
silica films processed in the lowCa assembly regime. Drag-out velocities and solids concentrations are (a) Ca = 2.9  10
7 (U = 20 μm/s), c = 0.3 wt %; (b) Ca = 4.7  10
7 (U = 33 μm/s), c = 0.3 wt %; (c) Ca = 6.0  10
7 (U = 42 μm/s), c = 0.1 wt %; and (d) Ca = 3.6  10
7 (U = 25 μm/s), c = 0.1 wt %.

bilayer
monolayer coatings are formed only at intermediate solids concentration (lysine
silica at 0.3
0.5 wt % and NS
silica at 6
12 wt %) and intermediate capillary number (Ca ≈ (2
7)  10
6, U = 160
500 μm/s). Conversely, an excessive wet coating thickness (above 2 μm) is associated only with SM, VMS, and ML coatings. We return to a discussion of the mechanistic causes of these observations in sections 3.4 and 3.5. The topography of thin NM and BM lysine
silica films is further characterized in the next section to demonstrate continuity and uniformity. 3.3. Continuous Monolayer and Bilayer Lysine
Silica Coatings. A further investigation of macroscopic NM and BM film continuity and uniformity is performed with stylus probe profilometry. We thereby obtain coarse surface topography such as the density of the film thickness transitions (section 2.4). The resulting topography maps are shown in Figures 4 and S13 for a series of BM and NM films prepared from 0.3 and 0.5 wt % suspensions. Layering thickness transitions are prominent at drag-out velocities of 70 and 100 μm/s (Figures 4a,b and S13a,b) but are absent at the higher processing rates of 160, 250, and 500 μm/s (Figures 4c
e and S13c
e). Similarly, fine profile scans (not shown) and optical microscopy measurements indicate an absence of thickness transitions at the higher processing rates of 160, 250, and 500 μm/s. The characteristic wavelengths 11665

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Figure 6. Optical micrographs of a representative (a) variable-thickness multilayer (VM) film coated at Ca = 1.4  10
7 (U = 10 μm/s) and c = 0.1 wt % and a representative (b) bilayer
monolayer (BM) film coated at Ca = 7.1  10
7 (U = 50 μm/s) and c = 0.3 wt %. Axes refer to the cross-web (x) and upstream
downstream (y) directions.

between step heights appear to be ca. 200 and 60 μm at U = 70 and 100 μm/s (Ca = 1.0  10
6 and 1.4  10
6), respectively. Step heights are measured as approximately 16 to 18 nm, roughly 10 to 20% less than the particle diameter. This result is explained by a geometric reduction due to particle packing. More importantly, these topography maps support the claim that uniform monolayer films are generated at intermediate solids concentrations and capillary numbers in the drag-out operation. 3.4. Origin of Coating Process Regimes in the Drag-Out Operation. We emphasize the term drag-out because this operation allows for a spectrum of particle deposition regimes. At low capillary numbers (Ca < 10
6), often termed convective assembly, the isotropic stresses imposed by capillary action outweigh the shearing viscous stresses generated by relative substrate and free surface motion. The material deposition rate is weakly coupled to the drag-out velocity, and as shown by Nagayama and co-workers and others,17,25 the film thickness consequently diminishes as the drag-out velocity increases within this regime. Representative cross-sectional images of isolated monolayer, bilayer, and multilayer films coated by convective assembly are shown in Figure 5. These are close-packed lysine
silica films of tunable mean thickness and low surface roughness (Figure S14, Table S1). The mean thickness progressively decreases from continuous VMS (Figure 5a,b) to NM and BM (Figure 5c,d) as the drag-out velocity increases from 20 to 40 μm/s (Ca = (3
6)  10
7) and the solids concentration decreases from 0.3 to 0.1 wt %. Imaging of the fractured internal surfaces also reveals isolated facets with regular square and hexagonal symmetry (Figure 5a). A strong interparticle adhesive tendency is evident as in Figure 5b, and interparticle bridging contacts viewed in TEM are further evidence of such an adhesive tendency (Figure S1). Interparticle adhesion could be due to the presence of lysine; similar clusters were not observed in micrographs of films prepared from dialyzed silica suspensions. The chief motivation for the convective assembly process at low capillary number is the periodicity of the crystalline particle packing,24
26,28,32 yet the prospect of macroscopic crystalline domains with monodisperse silica nanoparticles has yet to be shown. Our crystalline domains are limited to the micrometer scale with lysine
silica (data not shown), but we cannot comment on the prospects for longer-ranged domains because these particles are not perfectly monodisperse (Figure S1).

Though nanoparticle monolayers (Figure 5c) are possible under a narrow “corridor” of conditions usually termed the natural assembly mode,25 shown as a thin wedge in the lower part of the regime map in Figure 2, nanoparticle monolayer continuity is difficult to achieve via convective assembly (Figure S8a,b).25,26 In fact, nanoparticle monolayers prepared at low capillary numbers almost invariably contain discontinuities on the macroscopic scale, however capable of monolayer assembly the process may be for the case of microspheres. Consequently, the most general result is a variable-thickness film (VMS or BM) as shown in Figure 6. Moreover, topographical variations in both the cross-web and coating directions are commonplace in convectively assembled films (Figures S2
S4). At moderate capillary numbers (10
6 < Ca < 10
2), however, a thin film is entrained with the withdrawing substrate because of the action of viscous stresses as metered by the adverse capillary pressure gradient established in the film deposition region. This analysis by Landau and Levich13 predicts an increase in the mean film thickness with drag-out velocity, and in the absence of suspended particulates, it is asymptotically valid as the capillary number approaches zero.15 These capillary- and viscous-dominant regimes imply a transition over part of the capillary-number domain. This capillary
viscous transition is responsible for the significant operability window for NM and BM films at intermediate capillary number (Ca ≈ 2
7  10
6) and solids concentration (0.3
0.5 wt % lysine
silica; 6
12 wt % NS
silica). However, the transition is also interesting in that it represents an upper bound for the processing speeds at which crystalline particle films are linearly assembled in the absence of external (e.g., electric and magnetic) fields and likewise a lower bound for the process rate at which macroscopically uniform films are generally attained (Figures 2 and 3). Stated explicitly, we can interpret the capillary
viscous transition as the onset of film entrainment: the particle deposition mechanism crosses from convective assembly to thin-film entrainment over a critical range of drag-out velocities. The onset of entrainment due to viscous action is thus an apparent prerequisite to macroscopic (cm2 or larger) uniformity of nearmonolayer films from nanoparticles. The assembly
entrainment transition is clearly evident as the plateau in a plot of mean film thickness versus capillary number shown in Figure 7a. These measurements correspond to operating states shown as dark filled symbols in Figure 2. The plateau 11666

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of the generality of the assembly
entrainment crossover reported here. To illustrate better the process regime transition from convective assembly to film entrainment, we quantify the mean deposition rates associated with the process conditions of Figure 7a. The nondimensional mean deposition rate is defined as r ¼ ð1
fv Þ

Figure 7. Dependence of the dry film thickness and relative deposition rate on the processing rate Ca and solids concentration. (a) Dry film thickness plotted vs capillary number for solid concentrations of (0) 0.1, (]) 0.5, (Δ) 1, and (r) 3 wt %. Error bars represent the standard deviation from the mean. (b) Relative film deposition rate plotted vs the capillary number for the same set of coatings shown in part a. (c) Mean film thickness plotted vs the solids concentration for drag-out velocities of (0) 10 μm/s (Ca = 1.4  10
7), (]) 25 μm/s (Ca = 3.6  10
7), (Δ) 50 μm/s (Ca = 7.1  10
7), and (r) 100 μm/s (Ca = 1.4  10
6). Lines are fitted to the data at each velocity over the range for which linear regression yields an intercept near the origin.

occurs over one decade in the capillary number corresponding to drag-out velocities of roughly 160 to 1000 μm/s (Ca ≈ 2  10
6 to 1.4  10
5). The minimum occurs at Ca ≈ 3.6  10
6 (U ≈ 250 μm/s), in agreement with an analogous measurement of the transition for phospholipid films processed via horizontal dragout.44 A similar study by Mittal et al.27 also suggests a transition at comparable linear translation rates, which is a further indication

t U a U

ð3Þ

where t is the mean film thickness in Figure 7a and r is the mean deposition rate in units of mass per unit length per time. The mass scale is chosen as the individual particle mass M = FPVP, where FP and VP are respectively the particle density and volume. The length scale is L = 2a, where a is the particle radius. The time scale is T = (2a)/U*, where U* = 250 μm/s is the transition velocity. The film void fraction fv is estimated via the procedure described in section 2.4. The mean film deposition rates for drag-out from suspensions of 0.1, 0.5, 1, and 3 wt % are estimated with eq 3 using the mean film thickness data (t vs Ca) shown in Figure 7a. These values from eq 3 are replotted in Figure 7b (r vs Ca). Divergent rates of film deposition by capillary and viscous action as the capillary number is varied are apparent. At the onset of entrainment, the film deposition rate begins to increase sharply and maintains an increasing profile that scales as r µ Ca1.2. Hence, the film entrainment regime features an increasing film thickness that scales as t µ u0.2. The dry film thickness increases linearly with the solids concentration as expected (Figure 7c), though the scaling relationship of t with U is weaker than the 2/3 power law predicted by Landau and Levich.13 This discrepancy is likely due to a combination of metering by forced convection and wet film drainage. At low capillary numbers, the scaling relationship between the film thickness and process rate roughly follows the dependence t µ 1/(u1.4), and this result is also slightly unexpected but can be rationalized by recognizing that the wetted domain length may actually decrease as the capillary number increases. This argument is consistent with coarse-grained material and momentum balances over the wet particle film (Supporting Information). Hence the assembly
entrainment crossover can be characterized as a minimum in the volumetric silica deposition rate associated with the onset of film entrainment. 3.5. Principle of Monolayer Formation by Forced-Convection-Assisted Drag-Out. That the critical capillary number is on the order of 10
6 follows from its definition as Ca = μU/σ, according to convention in the coating literature. Implicit in this definition is the concept that the length scales over which the capillary and viscous forces act are comparable, even if they are of two distinct origins. In the drag-out operation, the natural capillary length scale is (σ/Fg)1/2, or the radius of meniscus curvature from the suspension to the substrate,39 and the viscous length scale is the local wet film thickness. These lengths are comparable where the free surface curves to form a meniscus. By this definition, the capillary number provides an indication as to whether the shape of the entire meniscus is governed by capillary or viscous forces. With respect to the capillary
viscous transition addressed here, however, the relevant phenomenon is contact line motion relative to the substrate. The contact line motion (at low Ca) is governed by competing viscous and capillary forces acting over the microscopic region where the solvent, air, and solid meet. These forces can be traced to films on the 10 to 100 nm scale in which disjoining pressure and other material-dependent effects 11667

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Figure 8. Conceptual schematic of the capillary
viscous crossover mechanism concurrent with the onset of thin-film entrainment. Charge-stabilized particles are convected with the entrained liquid and become concentrated into a laterally distributed surface phase by a combination of electrostatic particle
particle and particle
wall repulsion, evaporative confinement toward the liquid
vapor interface, and attractive capillary forces between particles concentrated at the liquid
vapor interface.

contribute to the local stress.45 The local evaporation rate may also affect the macroscopic wetting behavior and contact line motion.46 For this reason, the capillary number as defined is not the appropriate scaling parameter for an order-unity transition. Correlations of extensive data pertaining to the related problem of interfacial contact line motion relative to the pores of a porous medium, for example, reveal critical capillary numbers on the order of 10
4 to 10
6 (ref 47). These critical capillary numbers indicate thresholds beyond which viscous forces, proportional to the pressure drop in confined pore passages, induce the motion of the curved menisci between two phases. The relevance of porous media flows to film assembly at low Ca is examined in the Supporting Information. The mechanism by which monolayer and bilayer silica nanoparticle films deposit as continuous coatings likely resembles an intermediate state between wet film entrainment and Langmuir
Blodgett-type interfacial “rafting”. The concept is illustrated in Figure 8. Particles become confined by solvent evaporation into a thin film where convective
diffusive particle motion takes place. Nothing unique to the drag-out operation is represented here; indeed, the particle-laden wet film is a ubiquitous processing state, but we emphasize here the scale of the wet film thickness, which by the Landau
Levich analysis would be on the order of 500 nm or less. This wet film thickness is one order of magnitude larger than the ca. 10
50 nm particle dimension that motivated this study, in contrast to the two or three orders of magnitude difference achieved by conventional roll-to-roll and spraycoating techniques.16 Furthermore, as forced-convection-assisted evaporation takes place, the aggregation of particle and substrate surfaces is precluded by double-layer repulsion. Consequently, the primary particles laterally distribute themselves into the liquid
vapor interface as the free surface approaches the substrate. To demonstrate the concept of Figure 8, we imaged the distribution of silica particles near the free surface of an applied wet film. Cryo-SEM cross-sectional imaging reveals that silica particles indeed tend to organize at the liquid
vapor interface of the particle-laden wet film. Figure 9 is a fracture cross-section of

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Figure 9. Cryo-SEM fracture cross-section micrograph of a thick (12.7 μm initial wet thickness) sample after 2 min of drying. Imaging reveals interfacial raft formation as the mechanism of silica particle organization during drying.

such a wet film containing NS
silica particles (ca. 110 nm diameter). Prepared at an estimated initial wet thickness of 12.7 μm and a solids concentration of 6 wt %, the cryo-SEM image represents the film microstructure after 2 min of drying. Closepacked particle networks and isolated rafts are clearly evident at the interface, as are individual particles. Partial sublimation of the water also reveals an apparently uniform spatial distribution of particles within the wet film. Furthermore, the continuity of monolayer and bilayer coatings appears to be due to particle confinement caused by rapid forcedconvection-assisted evaporation. The alternative is the entrapment of multiple layers beneath rafts formed at a low solids loading and an elevated initial wet film thickness (Figure S15). These entrapment events could be caused by local gradients in the lateral particle density at low solids concentration. On this basis, we distinguish between the operating regimes identified as near-monolayer to bilayer
monolayer (NM to BM) and variable-thickness multisubmonolayer (VMS) in Figure 3. In this regard, colloidal stability and electrostatics are critical. Figure 8 illustrates the effect of repulsive double-layer forces between silica surfaces, shown as dashed lines that extend their effective excluded volumes. Double-layer interactions are expected to contribute to the confinement effect whereby the particles are distributed in the plane of the substrate as the thin wetted film evaporates. Double-layer exclusion also seems likely to play a role in expanding the coating window in which the NM film formation is observed in Figures 2 and 3. In other words, entrainment as the sole material deposition mechanism would imply a narrow corridor of operating states under which the appropriate volume of material was entrained to deposit a monolayer (Supporting Information). Empirical observations to the contrary also lead to the proposed rafting and entrainment mechanism, which is similar to a Langmuir
Blodgett process.48 In principle, hexagonally close-packed crystalline domains can form via interfacial rafting in the crossover regime. Evaporation and lateral capillary forces are the principal driving forces.20,21,48 These crystalline domains are observed locally where the surface density is high enough to constitute the close-packed phase (Figure S9b). In contrast to assembled films, however, crystalline domains of lysine
silica and meso-silica particles were not observed homogeneously throughout the coating under the conditions examined here. If long-range crystalline structures are not readily generated in the crossover regime, then the crystalline microstructure and macroscopic uniformity may constitute the main trade-offs encountered in the drag-out operation. 11668

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Langmuir We should emphasize that the absence of detected defects (section 3.3) represents an improvement in uniformity as compared with those reported by Snyder et al.26 and Lee49 for films prepared at 17 μm/s and a 0.04 wt % solids concentration. We conclude that nanoparticle film uniformity in the drag-out operation is achieved by avoiding process instabilities exhibited by the low capillary number (Ca < 10
6) operation. In accord with previous studies,25,27 the film thickness is tuned over a range of processing speeds by independently varying the material deposition rate via the solids concentration and forced convection. The findings presented here suggest that improved process stability is to be achieved by increasing the capillary number, irrespective of the material deposition rate, until viscous action begins to eliminate the meniscus-related instabilities inherent in the capillary-dominant process.26,28,29,32,37,40,45,49
51 We thus identify a critical capillary number, termed here the capillary
viscous transition, at which the onset of this capillary-dominant instability is avoided. A few additional comments on the limitations of drag-out for nano- and mesoscale particle films are also warranted. Aside from the obvious limitation in processing rates well below meters per minute, the operating regimes described here for thin film production are not stable under all mechanical disturbances: enclosure and vibration damping are important components of the operation. Thin films that are used to coat the capillary
viscous crossover regime are susceptible to perturbations caused by excessive forced convection near the film deposition region, for instance. This tendency is avoided by metering the gas delivery rate G. However, the dynamics of such instabilities are found to vary with particle diameter, solids loading, and solvent content. In addition, high-ethanol-content (up to 20 wt %) suspensions are found to yield lower coverage and minimal hexagonal close-packing, and these differences are likely due to the variations in the solution surface tension and viscosity. The presence of lysine also appears to play a role in improving the colloidal stability through electrostatic repulsion mediated by pH buffering.52 In summary, our findings affirm the utility of liquid-borne coatings in achieving sub-micrometer-scale particulate films, particularly with the forced-convection-assisted drag-out operation. These results are significant in that relatively little work on the deposition of nanometer scale films by low-cost, scaleable approaches has been reported thus far.

4. CONCLUSIONS Particulate coatings were processed via a forced-convectionassisted drag-out operation from aqueous suspensions containing stable 20 nm silica particles in order to identify strategies for preparing thin, continuous films. The meniscus instability near a pinned contact line was identified as a constraint on the uniformity and continuity of coatings processed at capillary-dominant (Ca < 10
6) drag-out velocities, whereas higher velocities enabled markedly improved uniformity and continuity. The improved process stability and uniformity were attributed to the onset of film entrainment, where a transition between the capillarydominant and viscous-dominant operating modes is realized. This capillary-viscous crossover was presented for the first time as a strategy for thin, particulate film processing, and its broader applicability was suggested by the observation of near-monolayer and monolayer films from 50 nm silica dispersions. Parametric experiments in the capillary number
solids concentration

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operating window revealed several trends in film morphology, including a tendency toward near-monolayer, monolayer, and mixed bilayer
monolayer films within the transition regime at moderate solids concentrations. Analogous drag-out experiments with 110 nm silica dispersions also identified the solids concentration as a critical parameter in uniform monolayer attainment. On the basis of these parametric experiments, we prepared coating process regime maps containing the operability windows for submonolayer, monolayer, and multilayer coatings of varying uniformity over a range (20
110 nm) of silica particle diameters. Conceptual and heuristic principles were proposed to extend the applicability of these regime maps to other colloidal systems. A systematic investigation of particle film coating by drag-out, including the convective assembly and film entrainment operating states, was presented. Although a great deal of previous work has focused on microsphere particulate coatings, this study is the most thorough investigation to date on nanoparticle coatings by drag-out. We emphasize the applicability of these findings to continuous nanoscale coatings, in contrast to the micrometerscale films in most prior work. Moreover, the silica colloid is a strong model system for other aluminosilicate and siliceous particles, and for this reason, we expect the coating process regime maps of Figures 2 and 3 to be valid for other particle compositions and sizes provided that they are stable in aqueous suspensions.

’ ASSOCIATED CONTENT

bS

Supporting Information. Synthesis of 50 nm lysine
silica particles. Film-formation mechanism at low-capillary-number convective assembly. Estimated drag-out conditions based on the Landau
Levich analysis. This material is available free of charge via the Internet at http://pubs.acs.org.

’ ACKNOWLEDGMENT D.D.B. gratefully acknowledges support from the NSF Graduate Fellowship Program and a University of Minnesota doctoral dissertation fellowship. Capital equipment was funded by industrial sponsors of the Coating Process Fundamentals Program of the Industrial Partnership for Research in Interfacial and Materials Engineering. Wafer processing, film imaging, and characterization were performed at the University of Minnesota Characterization Facility and Nanofabrication Center, both of which receive partial support from the NSF through the NNIN program. We thank Sandeep Kumar for assistance with TEM imaging. ’ REFERENCES (1) Takamura, K; Kroschwitz, J. I.; Seidel, A. Kirk Othmer Encyclopedia of Chemical Technology, 5th ed.; Wiley-Interscience: Hoboken, NJ, 2004; Vol. 20, p 372. (2) Sun, J.; Gerberich, W. W.; Francis, L. F. Prog. Org. Coat. 2007, 59, 115–121. (3) Chaney, L. K.; Jacobson, B. S. J. Biol. Chem. 1983, 258, 62–72. (4) Stein, A. Microporous Mesoporous Mater. 2001, 44, 227–239. (5) Hattori, H. Adv. Mater. 2001, 13, 51–54. (6) Deckman, H. W.; Dunsmuir, J. H. Appl. Phys. Lett. 1982, 41, 377–379. (7) Baxter, J. B.; Aydil, E. S. Appl. Phys. Lett. 2005, 86, 053114. (8) Velev, O. D.; Gupta, S. Adv. Mater. 2009, 21, 1897–1905. 11669

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