Complex Stain Morphologies - Industrial & Engineering Chemistry

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Complex Stain Morphologies Pavlo Takhistov and Hsueh-Chia Chang* Department of Chemical Engineering, University of Notre Dame, Notre Dame, Indiana 46556

We examine the morphology of crystal, precipitate, and colloidal aggregate stains left by microliter drops evaporated on hydrophilic or hydrophobic surfaces. An understanding of such morphologies is important in the design of high-density stain libraries for high-throughput drug screening. Unlike classical homogeneous crystallization patterns, we find that the film and solutal flux dynamics of such small drops at their contact lines can induce macroscopic concentration segregation and produce distinct large-scale stain patterns such as concentric rings on hydrophilic surfaces and latticed crystals on hydrophobic ones. Coupling between these bulk segregation instabilities and the classical Mullins-Sekerka crystallization instability results in a large variety of crystal patterns with interwoven complex structures of two length scales. Furthermore, lowdensity crystals can occupy a larger area than the initial drop, and gravitational drainage on inclined substrates can change the larger length scale. The most symmetric stains with the smallest stain or drop areas are produced on hydrophobic or partially hydrophobic surfaces either above or below two critical concentrations. 1. Introduction Current high-throughput drug screening (HTS) technology is based on a compound matrix library of miniature solution wells containing drugs or target samples. Automated micropipet arrays then inject the other reagent, and the reaction yield is recorded by several characterization techniques, including radiometric, fluorometric, and luminescent assays. Chemiinformatic and bioinformatic software processes millions of pieces of data to minimize screening errors with a minimum of screening steps. Technological advances have been very rapid. Compound libraries for genomicsderived novel targets have, for example, advanced from the 96-well plate format to 384- and now 1536-well formats within 5 years. The current benchmark is 100 000 compounds a day with ultra-HTS. HTS biotechnology companies now number close to 100 and have a market approaching $1 billion. Pharmaceutical companies also spend roughly $6 billion annually on drug development and are increasingly relying on HTS before animal and clinical tests. These expenses and market shares are expected to increase in the near future as genomic and proteomic advances continue. However, a new technology must be developed to fundamentally improve the efficacy of HTS. The synthesis and screening of large numbers of drug candidates are most cost-effective at minute scales. The wet microwell library is near its miniature size limit of microliters. Batch screening with individual wells is also inefficient compared to multitasking miniature biochips that can transport and mix microvolumes of specimens with a multitude of reagents. Paramount to this future multitasking HTS technology is the replacement of wet well plates for storage and testing. Recently, our contacts in the pharmaceutical industry have suggested that protein solutions can be evaporated into small stains on slides that are easier to store and handle. In fact, protein is often more stable dry than in solution. To be superior to the 1536-well matrix, however, the stain area must be below 1 mm. Moreover, because such * Corresponding author: H.-C. Chang at [email protected].

stains will be dissolved and retrieved by micropipets, they should ideally be perfectly centered at predetermined locations. They should also be axisymmetric and uniform, as individual crystals tend to promote rivulet spreading by capillary action when the solvent is deposited onto the stain. The stain morphology is obviously related to the classical homogeneous or surface nucleation and crystallization patterns produced by supersaturated solutions without evaporation, such as the ubiquitous fractal snow crystal. Nucleation is triggered by certain imperfections on the solid or seeds in the solution. The nucleation rate and density are strong functions of temperature and concentration. More highly supersaturated solutions tend to create larger crystals. The macroscopic crystal geometry reflects how the molecules or ions are packed at the atomic and molecular levels. However, the facets tend to grow more slowly than the corners because of the diffusive Mullins-Sekerka instability.1 The Mullins-Sekerka instability is unique to solidification and crystallization processes. Any protrusion from a solid plane would experience a higher flux of solute from solution if the process were diffusioncontrolled and would accelerate the growth of the protrusion. The same geometric factors accelerate the growth of corners relative to facets. This diffusive instability occurs at the cusps or wedges of the crystal at all scales and generates fractal dendrites. The actual complex fractal structure of a snow crystal, for example, depends on the local degree of supersaturation created by the concentration and temperature history of the crystal as it falls from the sky. Although colloidal aggregation occurs at a much lower rate with larger units, they too form well-packed crystal-like aggregates and often produce dendrite arms. As the colloidal concentration is difficult to vary in time and as its aggregation kinetics is relatively insensitive to temperature, aggregate dendrites tend to have similar fractal geometries. However, precipitation, crystallization, or aggregation from a small evaporating drop suffers from additional pattern formation dynamics. Bulk flow and nonuniform

10.1021/ie010788+ CCC: $22.00 © 2002 American Chemical Society Published on Web 04/02/2002

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evaporation rates can produce concentration gradients across the drop. Thus, the degree of supersaturation can vary across the drop. As the drop evaporates, the solute concentration also increases in time. Hence, we expect such spatio-temporal variations to create an even richer variety of crystal patterns than is found in snow crystals. The well-known coffee stain experiments of the Chicago group2 have shown that the higher evaporation rate at the contact line of a drop can induce an outward flow that results in a ring of coffee grinds as the final stain morphology. Because coffee stains do not form ordered aggregates, their precipitates do not suffer from the Mullins-Sekerka instability, and we do not expect more complex patterns. The same can be said of largescale patterns generated by natural convection in volatile drops.3 The ceramic helices that form when colloidal solutions evaporate in a small test tube4 are probably also due to bulk hydrodynamic flow. Probably the most important flow-induced aggregations during evaporation are two-dimensional colloidal crystals in thin evaporating films.5 Uniform-sized latex spheres with submicron diameters are packed by the flow into a localized patch of thin film with a thickness slightly smaller than the particle diameter. Thus, the particles pierce the film to generate a patch of two-dimensional hexagonal arrays. Although this system does not have the same geometry as an evaporating drop, the presence of a particle-carrying convective flow toward a thinner film connects the two phenomena. The flow is generated by wetting forces that drive the liquid over the top portion of the spheres above the film. A micron-sized meniscus appears at the contact line around each sphere. The inward flow into the thin-film patch then packs the spheres into unbroken two-dimensional hexagonal arrays. This type of flow is now being used to create protein arrays. Ring patterns have also recent been observed during colloid aggregation from evaporating drops.2,3,6 Particles at the edge of the precursor film (contact-line boundary) pin the contact line and do not flow toward the receding contact line. They then become the aggregation centers for well-packed layers of colloidal particles at the contact-line edge. The transport of new colloidal particles toward the aggregates is due to an evaporatively driven convective flow. Because of the enhanced evaporation at the contact line and over the layer of packed colloids, the contact line actually slips over the packed colloid and continues to recede within the first ring. It repins when it encounters another fixed particle. The packing and slipping mechanism then continues to generate concentric rings of colloid aggregates. For this mechanism, the contact-line slip velocity must be faster than the packing of aggregates, and the contact line must land on the substrate before repinning again; this is the stripe segregation mechanism from evaporating drops of colloidal solution. In this manuscript, we report an entire library of crystal stain morphologies from evaporating drops (Figure 1). Coupling among the Mullins-Sekerka instability, enhanced evaporation at contact lines, and a new bulk concentration segregation instability produces a complex variety of patterns with two length scales, including a distinct and new concentric ring pattern (second and third frames of Figure 1). Unlike the colloidal rings of Shmuylovich et al.,6 our crystal rings appear only at high concentrations when the crystals are taller than the film at the contact line. Also, the

crystals are obviously wettable by the solution and are, in fact, preferred over the substrate. Consequently, our contact line cannot recede beyond the first ring and onto the substrate, as is the case for colloids, but must repin at the inside face of the crystal. Hence, it is not the receding contact line on the substrate that generates concentric rings. Instead, a unique interfacial dimple ring forms on the inside of the last crystal ring precisely because of the latter’s size and wettability. The next generation of rings then forms at this dimple because of the higher concentration beneath it. This new mechanism is sensitively dependent on the wettability of the solid substrate and the solute concentration of the original drop. It is minimized on hydrophobic substrates but can still create latticed crystals from salt solutions (eighth frame in Figure 1). This pattern formation mechanism also disappears on hydrophilic surfaces if the drop dimension is smaller than the capillary radius of about 2 mm. It is also distinct from both the contactline coffee stains of Deegan et al.2 and the freeconvection patterns of Cuk et al.3 It shares some features with the hexagonal colloidal arrays of Dushkin et al.,5 but the crystal patterns in this case are disjoint and have much longer length scales. For NaCl and albumin protein solutions, extremely small and symmetric stains are obtained on hydrophobic surfaces without imperfections (fourth and ninth frames of Figure 1). This strategy and the use of patterned hydrophilic centers to pin the centers of the drops are the keys to designing high-density compound stain libraries for HTS. 2. General Experimental Procedure Evaporation experiments were carried out with a variety of aqueous solutions, including NaCl, bovine serum albumin, citric acid, urea, copper sulfate, sugar, and 10-nm gold colloids. With the exception of the gold colloid solution, which was evaporated on a silica disk, all drops were evaporated on commercial microscopic slides. The slides were cleaned with methyl alcohol and water sequentially and repeatedly to remove small particles that might act as crystal seeds. Rinsing with methyl alcohol was intended to remove chemical impurities from the slide, but it often introduced new particles. These particles were removed during the water rinsing cycle. The cleaned slides wereexamined under the microscope to ensure that they were particle free. The degree of hydrophobicity of each slide is altered with ethyl alcohol and castor oil. The static contact angles of water drops on the cleaned slides was measured to be 3°; hence, these slides are hydrophilic. Covering a slide with ethyl alcohol and letting the latter evaporate produced a partially hydrophobic surface with a water static angle of about 45°. Completely hydrophobic surfaces were achieved by coating the slide with a film of castor oil. The static contact angle of a water drop on such slides was measured to be 105°. The solutions were prepared with concentrations spanning as much as four decades of molarity. They were metered by microsyringes of varying size and deposited on the slides as a single drop. To standardize our experiments, we chose to use one single drop volume of 0.2 cm3. On a hydrophobic surface, this drop covers a cross-sectional area with a radius of 0.4 cm. This size was chosen so that the drop dimension was comparable to the capillary length of water at about 3 mm. The

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Figure 1. Library of stain morphologies. The frames from left to right and top to bottom are from 20-µL drops of (1) albumin solution on partially hydrophobic glass substrate at 0.2 M concentration, (2) albumin solution on hydrophilic glass substrate at 0.1 M concentration, (3) NaCl stains on hydrophilic glass substrate at 10-4 M concentration, (4) NaCl solution on precleaned hydrophobic glass substrate at 2 M concentration, (5) NaCl solution on partially hydrophobic glass substrate at 0.1 M concentration, (6) NaCl solution on hydrophilic glass substrate at 0.5 M concentration, (7) urea solution on hydrophilic glass substrate at 0.5 M concentration, (8) NaCl solution on partially hydrophobic glass substrate at 1 M concentration, and (9) albumin solution on partially hydrophobic substrate at 1 M concentration.

extent of drop spreading on hydrophilic surfaces changes dramatically when the drop dimension is below the capillary length. The slides with the evaporating drops were placed in a glovebox with controlled humidity and convection. The drops typically evaporated within 30 min to 2 h, depending on the concentration, and left behind stain patterns. The evaporation rate of identical drops was found to be significantly faster (by a factor of 1.5-2) if the drops evaporated outside the glovebox. This enhanced evaporation rate was a result of forced convection being absent in the box. The evaporation rate was recorded by placing the slide on a Sartorius MC-1 analytical balance with an accuracy of 10-4 g. Some evaporations were carried out on slanted slides, and the contact lines were observed to translate in the direction of gravity. The evaporation rate of NaCl was found to be depend weakly on the salt concentration, with a

factor of 3 reduction resulting from a 4-order-ofmagnitude increase in concentration, as shown in Figure 2. A high-resolution digital camera was used to record the Newton interference rings to estimate the local film thickness of the drop. The reflected light intensity from a constant light source was also recorded by the same camera and used to estimate the film thickness. Both methods are highly unreliable, as the crystal and solution have widely different reflective and refractive indices that are also strong functions of concentration. Near the contact line, where crystallization typically begins, a slurry phase with even more complex indices was expected. Nevertheless, these measurements offered a qualitative depiction of the film near the contact line that could be used to determine whether a minimum (a dimple) in the film existed. Despite the multitude of solutions used, the macroscopic patterns due to bulk hydrodynamics were quite

Ind. Eng. Chem. Res., Vol. 41, No. 25, 2002 6259 Table 1. Crystal Stain Morphologies for Different Substrates and Solution Concentrations

stripe patterns appeared at both temperatures with very similar dimensions, but the fractal dendrites only occurred at the lower temperature. Hence, the larger scale patterns were quite similar for all solutions, but the smaller ones could differ. In Table 1, we depict a general classification of the large-scale patterns according to the surface hydrophobicity and solute concentration. These patterns at larger scales are also weakly concentration dependent, as indicated. Different morphologies occur over large windows of concentration over decades of molarity. 3. Stains from Hydrophilic Slides

Figure 2. Average evaporation rate of NaCl drops on hydrophilic slides for different concentrations.

similar but distinct for the hydrophobic and hydrophilic surfaces. In contrast, the dendrite patterns from the Mullins-Sekerka instability were highly sensitive to temperature, concentration, and solute diffusivity. For example, we depict in Figure 3 two concentric NaCl ring stains on hydrophilic slides at 22 and 35 °C. The larger

Except for the most concentrated NaCl drops, with concentrations above 1 mol/L, drops on untreated hydrophilic slides spread extensively until they exceed a radius of 0.4 cm for the 20-µL standard drop. However, the spreading does not continue indefinitely and stops at a critical radius with a contact angle larger than the static contact angle of 3° for pure water. The images presented in Figure 4 show that a ring of crystals forms at the contact line at this point. This initial crystal ring pins the contact line and prevents further spreading. The faceted crystals within this first ring are interconnected. Concentrated NaCl drops exceeding 1 M in concentration do not spread and form a large isolated crystal in the relatively short time of 30 min (see Table

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Figure 3. Crystal patterns of 0.1 M NaCl drops on hydrophilic slides at 22 and 35 °C.

Figure 4. Formation of the first peripheral crystal ring for a 1 M NaCl drop on a hydrophilic slide. Note the pancake shape of the drop.

1). Such isolated crystals from concentrated drops are independent of the substrate and resemble the fourth frame of Figure 1. The pinned drops at lower concentrations resemble thin pancakes with thicknesses of several hundred microns (see Figure 4). As they continue to evaporate, their radii remain constant, but their thicknesses decrease linearly. This is reflected in the evaporation rate measurements of Figure 5. Over the first hour, the evaporation rate remains constant as the drop thins layer-by-layer. This constant evaporation rate occurs because the cross-sectional area of the drop remains the same as the drop thickness decreases from 30 to ∼10

µm. For NaCl drops between 0.1 and 1 M and for very dilute solutions below 10-3 M, this constant evaporation continues indefinitely. The peripheral crystal ring then continues to grow and forms an annular stain of interconnected but faceted crystals at the end (Table 1 and fifth and sixth frames of Figure 1). The resulting crystal band is very high and narrow at high concentrations but thin and wide at low concentrations. As a result, the annular band actually increases in width with decreasing concentration, as shown in Figure 6. For the other extreme of very dilute concentrations less than 0.001 M, a thin slurry film appears within the peripheral ring, and fractal crystals emanate from the


Figure 5. Instantaneous evaporation rate of a 0.01 M NaCl drop on a hydrophilic surface.

Figure 6. Annulus window and fractional coverage by the annular band. Because of the crystal size dependence on the concentration, the band width decreases with increasing concentration. The radii R0 and R are the outer and inner radii, respectively, of the annular band of stain.

perimeter, as seen in the third frame of Figure 1. Particles in the peripheral ring acts as crystal seeds for the crystal dendrites. The classical fractal patterns from the Mullins-Sekerka instability, including fingers, spirals, and fractal branches, are all present. These short fractal patterns appear if crystallization only begins within very thin slurry films at the end of the drop evaporation process. This is expected as the Mullins-Sekerka instability is driven by diffusion and occurs if the crystallization process is mass-transportlimited. This condition is met for thin slurries of lowconcentration drops where bulk hydrodynamic convection is impossible as a transport mechanism. Hence, we expect fractals to appear at low concentrations on hydrophilic surfaces, which create thin films. The most interesting concentration window is for NaCl concentrations between 0.001 and 0.1 M. At about 80 min, the initially pinned drop begins to shrink and decrease its cross-sectional area. This process can be observed visually and is reflected in a decrease in the evaporation rate, which correlates with the crosssectional area. The contact line recedes in stages with sequential depinning and pinning steps. It leaves behind concentric bands of interconnected crystals as seen in

Figures 7-9. The separation between these rings does not change significantly as the contact line recedes. The band separation, the band width, and the individual crystal size, however, all increase with increasing concentration, as seen in Figure 10. The size of crystals from supersaturated solutions is known to increase with increasing concentration, and hence, the size-concentration correlation is expected. However, there is a strong correlation between the crystal size and the band separation, as documented in Figure 11, with a proportionality constant of about 2. At the lower half of this concentration window, concentric rings appear with the fractal dendrites, as seen in Figure 9. The dendrites emanate from the first peripheral crystal band and form concentric bands of complex fractals. These concentric ring patterns seem to be generic to most drops evaporating on hydrophilic slides. However, the boundaries of the corresponding concentration window are difficult to characterize for the other solutions. An albumin stain, shown in the second frame of Figure 1 and in Figure 12, produces the same concentric patterns but with continuous and smooth bands rather than bands of interconnected individual faceted crystals. The crystal stains sometimes inherit the dendritic structures of the Mullins-Sekerka instability,1 but they are still partitioned into distinctive bands. The only exceptions occur for gold colloids and urea. Gold aggregates tend to form only annular stains with dendrites appearing within the thin film inside the annulus. However, unlike the NaCl fractals in a different concentration window, these fractal dendrites grow not from the peripheral ring but from internal seeds. One particular structure is shown in Figure 13, where each branch has a typical radius of 30 µm with hundreds of 10-nm colloids in any given cross section. The lowdensity urea crystals explode from the first ring and prevent the formation of additional bands, as seen in the seventh frame of Figure 1. If a large volume (∼0.5 cm3) of gold colloid solution is spread by a ruler on a hydrophilic substrate to create straight rivulets with straight contact lines, micron-size gold wires (30-40 µm in diameter) result when the rivulets evaporate (Figure 14). As mentioned earlier, drops much smaller than 2-4 µL do not spread at all, even on hydrophilic surfaces. Instead, they settle into hemispherical capillary shapes and produce just a single crystal, as in larger drops that are highly concentrated. 4. Stains from Hydrophobic and Partially Hydrophobic Slides Drops do not spread on the hydrophobic slides, but instead, they ball up into a sphere-like geometry with contact angles larger 90°. The contact line recedes continuously at all times, and the evaporation rate decreases monotonically, in contrast to the behavior seen in Figure 5 for hydrophilic surfaces. At high concentrations, C > 1 M in Table 1, a peripheral crystal ring never forms, and the final crystal is always a single isolated crystal with a minimum of covered area (see Figure 1d). There is some residue stain around the lone crystal. Both the crystal size and the stain area decrease with increasing solute concentration. Hence, highconcentration stains are identical for both hydrophobic and hydrophilic surfaces: they form isolated single crystals. This corresponds to the most favorable stain morphology for high-density stain libraries. The initial

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Figure 7. Concentric rings from a 0.1 M NaCl drop on a hydrophilic surface. Newton interference rings inside the smallest ring show a thicker film at the ring.

spreading is excessively large on a hydrophilic surface, however. On the other hand, the overhanging sphere on a hydrophobic surface is quite unstable during evaporation, and it often rotates away from its original location. This instability can be eliminated by anchoring the drop to a hydrophilic spot on the hydrophobic surface or to a small hydrophilic protrusion. A matrix of such patterned spots would produce high-density and regular stain libraries. As shown in Table 1, lower concentration values (C < 10-1 M) also produce single crystals on hydrophobic surfaces, in direct contrast to the peripheral ring pattern they form on hydrophilic surfaces. It is in the intermediate concentration range, 10-1 M < C < 1 M, that a peripheral ring forms. This ring sometimes grows to resemble a doughnut, as in the albumin stain in the ninth frame of Figure 1. For salt solutions, doughnut stains are observed in the higher concentration range of this window, but a ring of 10 symmetric crystals is observed in place of the doughnut, as seen in the eighth frame of Figure 1. Only one ring is observed in this intermediate concentration window on a hydrophobic substrate. Drops on partially hydrophobic slides spread, but not as far as they do on hydrophilic slides. The concentration windows for hydrophilic surfaces with different stain morphologies still exist and have roughly the same bounds as the hydrophobic surface (see Table 1). The morphologies in this case are different, however. For albumin, shown in the first frame of Figure 1, rings now form within the intermediate concentration window, but the periphery is more irregular than it is on a hydrophilic surface (Figure 12). For NaCl solutions, the single ring of 10 symmetric crystals on a hydrophobic substrate is now replaced by several rings of latticed crystals. These crystals, however, are elongated in the azimuthal direction. Hence, they are intermediate between individual symmetric crystals on a hydrophobic surface and bands of interconnected crystals on a hydrophilic one.

This effect of surface hydrophobicity on the crystal morphology of the crystal bands is summarized in Figure 15. 4. Gravitational Film Drainage When NaCl drops are evaporated on an inclined plane with an inclination angle R with respect to the horizon above 10° and below 70°, the hydrophobicity of the surface becomes irrelevant. A pendant drop is formed initially with a steepened ridge. This ridge advances in the direction of gravity until it stops at a specific point. As the stationary drop evaporates after this initial spreading, only the back contact line recedes, and for concentrations below 1 M, the recession occurs in steps and leaves behind a stripe of stain for each step, as seen in Figure 16. In the final stage of evaporation, the drop becomes circular, and the stain begins to shrink horizontally as a ring as well. Unlike concentric ring formation on horizontal hydrophilic slides, the ring separation is clearly due to gravity drainage and can be quantified precisely. It is gravitational drainage that advances the back edge of a ring. Because the gravitational drainage velocity for a constant thickness film scales as sin R, the stain spacing in the direction of gravity, y, along the plane should be constant for a given inclination angle R and should scale as sin R. Hence, one can map the y coordinate of each generation of stain, yn, to a universal value for all inclination angles by the scaling yn/n sin R, where n ) 1 is chosen to be the last circular ring before the drop completely evaporates (see Figure 17). The origin of the y coordinate is also the limiting point where the drop disappears at the front edge shared by all of the ring stains. The width of the rings is constant for each value R but varies with inclination angle. More inclined substrates (higher R) produce narrower rings, as the initial drop spreading in y is more


Figure 8. Concentric rings for NaCl concentrations from 1 to 0.1 M with a concentration decrement of about 0.17 M from left to right and top to bottom.

severe. Because the spreading speed again scales as sin R, the width then scales as 1/(sin R) if we assume that the area of the drop remains constant during the initial spreading and that the time required for the drop spreading process to cease is identical for all R. Hence, the scaling x sin R should collapse the horizontal position of all stains, where x is measured from the same limiting point origin as y. Therefore, one can map different stain rings for all drops on various inclined surfaces into a universal stain image by these scalings. In Figure 17, we collapse the stain rings from different drops at different inclination angles with the gravitational scalings. Gravity drainage tends to create thick drops at the end of the evaporation process, even on hydrophilic surfaces. As a result, the short fractal patterns are absent. 5. Feasible Mechanisms We begin with the curious observation that the evaporation rate is a decreasing function of concentration that is significantly beyond thermodynamic corrections. One feasible explanation is the Marangoni effect.

A curious property of electrolytes is that their surface tension increases with electrolyte concentration. Hence, it is possible that convection to the contact line is driven by a solutal Marangoni effect arising from the higher concentration at the contact line. The convection velocity resulting from this effect would be

uM )

1 ∂γ ∆ch η ∂c l

( )

where h ≈ 10-4 cm is the film thickness at the contact line and l ≈ 1 mm is the width of the film. Our drops typically have a concentration difference of ∆c ) 5 mol/L across the film and a solutional Marangoni number of ∂γ/∂c ≈ 0.4 dyn/(mol L) for an electrolyte. For these values, uM is roughly 0.04 cm/s, and the Marangoni numberrthat

M)

c0 ∂γ γ0 ∂c

( )

is 0.03. This velocity is comparable to our observed receding speed. Consequently, the convection of fluid to

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Figure 9. Concentric rings of fractal patterns at the lower-concentration half of the window. The concentrations range from 0.1 to 0.001 M with a concentration ratio of about 4:1 for each successive frame.

Figure 10. Average ring separation as a function of initial NaCl concentration for the patterns in Figures 8 and 9.

the contact line with high evaporation rate can be significantly enhanced by this solutal Marangoni effect.

Figure 11. Linear correlation between crystal size and ring separation for the concentration range of Figure 9.

At higher concentration, ∆c is lower, and less fluid is convected to the contact line. As a result, the overall evaporation rate is lower.


Figure 14. Micron-sized gold wires constructed by the manual spreading of a large volume of solution with a long ruler.

Figure 12. Concentric crystal band of a 0.1 M bovine serum albumin drop.

Figure 13. Gold fractal aggregates in the center of an annular stain. The solution is a 10-4 volume fraction of a 10-nm gold colloid solution. Each branch of the fractal is about 30 µm.

The most dramatic macroscopic stain formation mechanism is the one responsible for the rings in Figures 7-9, 12, and 15. It clearly involves a bulk concentration segregation phenomenon. Because the evaporation rate is low, as seen in Figure 2, we estimate the temperature difference across the drop to be no more than 3-4 °C. More importantly, the drop thickness is a mere 10 µm. This yields a minuscule Rayleigh number, which scales as the cube of the thickness, of Ra ≈ 5 × 10-5, much

less than the critical value of 1708 necessary for the onset of free convection. Thus, this segregation mechanism is not due to the Rayleigh-Benard convection rolls observed by Cuk et al. for volatile drops.3 The thermal Marangoni instability, with a critical Marangoni number that scales linearly with the drop thickness, is more likely. However, our small drop thickness on hydrophilic surfaces also excludes this possibility. It is also difficult to see how the enhanced evaporation rate at the contact line, responsible for the coffee stain rings studied by Deegan,2 and enhanced convection by solutal Marangoni convection can produce segregated stripes. Fast recession of contact lines over a slower-packing aggregate, responsible for colloidal stripes,6 is was also not observed during our concentric crystal ring formation. A new hydrodynamic mechanism must therefore be in play. A light intensity recording of the film near the peripheral crystal ring of a NaCl drop on a hydrophilic substrate is shown in Figure 18. Because the crystal and the solution have drastically different reflective indexes, the relative heights of the crystal and the film clearly cannot be quantified using this technique. However, the relative thickness of the film away from the crystal should still be able to be captured. It is clear from the first frame that a minimum in the film thickness exists about 200 µm inside the first peripheral crystal ring. More interestingly, the next crystal ring appears at this shallow dimple, and the process repeats itself to generate higher-generation rings. This shallow dimple is also apparent from the Newton interference rings in Figure 7. Such a dimple has a thickness of roughly 10 µm and a lateral length scale of 200 µm. We also visually examined this long macroscopic film at the outer edge of the drop. At about 10 µm, it is much thicker than the usual precursor film of a wetting water drop without the peripheral crystal ring, which is typically 10-100 nm thick (see, for example, Jones and Wilson7 or Kalliadasis and Chang8).The peripheral ring is observed to pin the contact line and prevent further spreading. In doing so, it also thickens the film to macroscopic dimensions. However, the ring still retains a long flat geometry with a radius of curvature much larger than the capillary length (3 mm) of a gravity-capillary meniscus. Its 10-µm thickness is therefore still much smaller than the thickness of the pancake-shaped main drop, which is close to the capillary length. Molecular forces that thin the precursor film of a wetting drop to a 10-nm

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Figure 15. Stains left behind by 10-3 M salt solution in a 20-µL drop for (a) hydrophilic, (b) partially hydrophobic, and (c) hydrophobic surfaces.

Figure 16. Stains left behind by a 20-µL drop of 0.1 M albumin solution on a hydrophilic slide inclined at 20 and 40°.

Figure 17. Raw nth ring of a drop on a slide inclined at angle R and collapsed universal ring pattern for all generation numbers n and all inclination angles. First frame: Five generations of rings for R ) 20°. Second frame: fourth ring for five inclination angles. Third frame: Collapsed ring after scaling.

thickness clearly cannot be a factor in this 10-µm macroscopic film. Instead, this thin film must be sustained by evaporation or contact with the peripheral crystal ring. As each successive ring pierces the film at the dimple, the film is observed to recede over the new ring and to pin its new contact line on the inside face of the ring. It forms a meniscus at the crystal and a dimple further inward during this receding process. This is

consistent with the light intensity images of Figure 18. Submicron menisci have been observed on submicron latex spheres that pierce a film surface,5 but the dimples have never been observed before. The shallow dimple must be responsible for the ring formation. Its lower thickness means that, at uniform evaporation rate, the solute concentration is highest at the dimple. This segregated zone reaches supersatura-


Figure 18. Light intensity recording of the film near the peripheral ring over an interval during which two higher-generation rings have formed. Note the minimum in the interfacial height at a few hundred microns inside each successive ring. The next ring appears at this shallow dimple.

tion conditions before other parts of the film. As a result, the next ring nucleates below this dimple. The film on the outside of the dimple resembles a microscopic meniscus in contact with the crystal ring. Thus, the dimple location relative to the ring position is roughly the crystal height. Because the new ring appears at the dimple, the ring separation must be roughly the same as the crystal size within each ring. This is confirmed in Figure 11 for NaCl rings over two decades of solute concentration. The crystal size changes by a factor of 10 over this window, as the degree of supersaturation increases with concentration. Nevertheless, the ring spacing scales linearly with the crystal size over the entire window and, in fact, remains within a factor of 2. This strongly supports the observation that the dimple is responsible for the bulk solute segregation that leads to concentric ring formation. Two physical mechanisms work against this segregation phenomenon, namely, diffusion and convection, and try to homogenize the film concentration to the bulk value. Because the film is hundreds of microns long, we estimate the ion diffusion time across the film to be excess of 15 min, much longer than the time interval for ring formation, which is on the order of 1 min. Hence, diffusion cannot homogenize the bulk concentration segregation under the dimple. Convection, however, can be significant. The film on the inside of the dimple is, in contrast, a long sloping one that connects to the main drop. This large interfacial curvature difference across the dimple creates a large capillary pressure gradient that can drive fluid across the dimple to the outside.

Such capillary drainage is common for capillary dimples,7 but capillary dimples typically have larger capillary dimensions of 3 mm. This capillary drainage could convect the more dilute solution from the bulk and homogenize the segregated zone under the dimple. However, the strength of this capillary drainage is determined by the curvature of the capillary meniscus film outside the dimple which, in turn, should be inversely proportional to the crystal size. With decreasing concentration, the crystals become smaller, and hence capillary, convection should become larger. The resulting homogenization should suppress ring or even annulus formation. In contrast, the patterns summarized in Table 1 show the opposite trend, with annuli and rings being favored at low concentration. This observation seems to rule out capillary convection as the mechanism behind ring formation. There is another feasible mechanism for the formation of annuli, rings, and dimples. The solutal Marangoni convection resulting from the higher surface tension of the denser electrolyte at the contact line might dominate over that due to enhanced the evaporation rate at the contact line. Consequently, this effect might be chiefly responsible for the transport of fresh solvent toward the contact line. Once the first ring of crystal forms at the contact line, the solution carried by this convection then accumulates at the inside of the ring to form the dimple. Depending on the thickness of the film, this convection of the bulk concentration can then reduce the concentration at the dimple sufficiently to prevent the next ring from forming. Instead, the first ring will continue to grow. On hydrophobic substrates, the film near the contact line is extremely thick, and Marangoni convection is strong. It will therefore reduce the concentration gradient between the bulk and the contact line. At low concentrations, this homogenization can even prevent the concentration at the contact line from reaching saturation values. Consequently, even the first ring does not form on hydrophobic surfaces at low concentrations. At higher concentrations on hydrophobic surfaces, the first ring is able to form, but the homogenization process resulting from Marangoni convection prevents additional rings from forming. As a result, the first ring grows into a doughnut or a full drop at high concentration (see Table 1). Although this proposed mechanism obviously requires quantitative scrutiny, it seems to be qualitatively consistent with all of our observed morphologies. Another observation concerns the striking circular symmetry of the rings. The thin film below the dimple also limits diffusion transport in the transverse azimuthal direction. The crystal rings thus tend to form from solute that transports radially outward from their insides. This explains why the crystal rings are so strikingly circular. At lower concentrations on hydrophobic surfaces, insufficient ions are available to form a full doughnut. Moreover, without the dimple on such surfaces, ions can transport in both the radial and azimuthal directions to the peripheral annulus. The azimuthal direction, which has a higher concentration because of enhanced evaporation, is favored. As a result, a ring of latticed crystals replaces the doughnut annulus on hydrophobic substrates at low concentrations (Figure 15). The equal spacing between crystals suggests that there are many crystal seeds of high concentration within the annular patch. All of them compete for the same ions. As a

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Figure 19. Schematics contrasting the mechanism for colloidal stripe formation with that for crystal ring formation with a dimple.

result, two seeds within a certain diffusion length cannot both grow into crystals. This competitive selection mechanism then specifies a cutoff length that determines the number of crystals within each ring, which is almost always 10. On more hydrophilic surfaces, the film thins, and radial transport begins to be favored over azimuthal transport. This explains the increasing connectedness of the crystal band with decreasing hydrophobicity in Figure 15. Once the first doughnut, annulus, or latticed crystal ring forms, it creates a wetting patch, and the ring formation mechanism with dimples can now take place even for hydrophobic surfaces. This explains the internal rings of latticed crystals. They do not necessary form continuous circular rings if the film confined by the first ring is still relatively thick and allows azimuthal solute transport. The large crystals in the doughnuts and annuli of high-concentration drops would also consume too many ions to produce any internal rings of latticed crystals. All of these observations confirm the existence and importance of the dimple during the pattern formation dynamics. In Figure 19, schematics are offered to contrast this dimple mechanism for concentric crystal rings to the receding-contact-line mechanism for colloidal stripe formation.6

the presence of a distinct dimple. This new mechanism generates successive concentric crystal and stain rings. The short diffusive fractal patterns then couple with these striped hydrodynamic patterns to create most of the stain morphologies we observed for a large class of stains. Additional effects such as viscoelasticity and gravitational drainage on inclined planes create more features, but the basic template for stain patterns comprises these two basic mechanisms. Several outstanding issues concerning these basic mechanisms remain, however. It is still unclear why the receding contact line creates a microscopic dimple on the inside face of the crystal ring. Whereas submicron menisci have been observed around latex spheres that pierce through a thinner film,5 dimples of similar dimension have never been observed near these menisci. Liquid flow from the drop can, in principle, flatten the dimple and even cover the crystal ring. Evaporation from the film and the contact mechanism with the crystal, as well as our proposed convective flux due to the concentration gradient, could determine why such an energetically unfavorable interfacial shape is created. The conjectured homogenization mechanism should be analyzed and verified theoretically by producing a quantitative estimate of the upper concentration boundary for the concentric ring window. The complex stain morphologies are obviously undesirable for high-density stain libraries in high-throughput screening. Our study suggests using low-concentration drops (less than 0.1 M) on hydrophobic or partially hydrophobic substrates to eliminate ring or crystal lattice formation and to minimize the stain and crystal dimensions. If high concentrations are necessary, concentrations above 1 M for 20-µL drops should always form single crystals on any substrate (Tables 1 and fourth and ninth frames of Figure 1). However, hydrophobic substrates are preferred because initial drop spreading is minimized. As mentioned earlier, patterned hydrophilic centers can also anchor the tall spherical drops that appear on the hydrophobic surface. Another important design consideration for the high-density format is that small-volume drops with dimensions smaller than the capillary length tend to create more compact stains. These drops, however, are submicroliter in volume and are difficult to meter, handle, and retrieve rapidly in large numbers with micropipets. Acknowledgment

5. Summary and Discussion We have shown that the stain morphology from evaporating drops can be quite complex, and yet the pattern generation mechanisms are quite generic for many salt, protein, and colloid solutions. These mechanisms involve the coupling between short-length-scale diffusive Mullin-Sekerka diffusion instabilities for thin films, where there is no bulk hydrodynamic convection, and the longer segregation mechanisms arising from bulk flow in thicker films. The former results in the distinctive classical fractal crystal patterns. The latter can result from natural convection for volatile drops or heated substrates. It can also occur as a result of convection generated by enhanced evaporation rate at the contact line, which creates peripheral stains and crystal rings. The new bulk segregation mechanism reported here is likely due to a new flow occurring in

This work was supported by an NSF XYZ-on-a-Chip grant. We are grateful to Eric Sherer and Justin Burt for performing some of the experiments. We also thank Howard Stone for pointing out the unique solutal Marangoni effect of electrolytes. Literature Cited (1) Mullins, W.; Sekerka, R. F. Morphological stability of a particle growing by diffusion or heat flow. J. Appl. Phys. 1963, 34, 323. (2) Deegan, R. D.; Bakajin, O.; Dupont, T. F. Capillary flow as the cause of ring stains from dried liquid drops. Nature 1997, 389, 827. (3) Cuk, T.; Troian, S. M.; Hong, C.-M.; Wagner, S. Using convective flow splitting for the direct printing of fine copper lines. Appl. Phys. Lett. 2000, 77, 2063. (4) Giraldo, O.; Brock, S. L.; Marquez, M. Spontaneous formation of inorganic helices. Nature 2000, 405, 38.

Ind. Eng. Chem. Res., Vol. 41, No. 25, 2002 6269 (5) Dushkin, C. D.; Yoshimura, H.; Nagayama, K. Nucleation and growth of two-dimensional colloidal crystals. Chem. Phys. Lett. 1993, 204, 455. (6) Shmuylovich, L.; Shen, A. Q.; Stone, H. A. Surface morphology of drying latex films: Multiple ring formation. Langmuir, manuscript submitted. (7) Jones, A. F.; Wilson, S. D. R. The film drainage problem in droplet coalescence. J. Fluid Mech. 1978, 87, 263.

(8) Kalliadasis, S.; Chang, H.-C. Apparent dynamic contact angle of an advancing gas-liquid interface. Phys. Fluids 1994, 6, 12.

Received for review September 24, 2001 Revised manuscript received February 21, 2002 Accepted February 26, 2002 IE010788+

Complex Stain Morphologies - Industrial & Engineering Chemistry

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