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Modeling Drop Shape on Contaminated Surfaces or Surfaces with Physical Structures Sanat Mohanty,*,† Caroline Ylitalo,‡ and Oh Sang Woo‡ Materials Modeling Group, Organic Materials Technology Center, and Receptor Materials Group, Interface Materials Technology Center, 3M Company, 201-2E-23, St Paul, Minnesota 55144-1000 Received June 9, 2003. In Final Form: October 15, 2003 Surface contaminants are commonly found on films. They get transferred to the surface from incompletely cured silicone liners on the films or owing to migration of additives to the surface from within the film. During the process of ink jet printing (a noncontact printing process), surface contamination affects the shape of the drops (causing the formation of fingers and crescents) and hence image quality. This study uses modeling methods to examine how such surface contamination affects the drops shapes. Subsequently, it models the effect of surface structures (pits) on the drop shape. This study explores how image quality can be controlled in the presence of surface contamination and surface structures.
Introduction Ink jet printing is emerging as the digital printing method of choice due to its good resolution, flexibility, high speed, and affordability. Ink jet printers operate by ejecting, onto a receiving substrate, controlled patterns of closely spaced ink droplets. The inks most commonly used in ink jet printers are water-based or solvent-based. Waterbased inks require porous substrates or substrates with swellable coatings that absorb water. On the other hand, solvent-based inks are typically printed directly onto various types of polymeric films such as vinyl, olefin, or urethane. With a growing piezo ink jet industry, problems of piezo printing have attracted significant effort in academic circles as well as industry. One aspect of interest is the behavior of solvent-based ink drops once they are jetted on to the substrate. Variations in surface properties of the polymeric substrate affect the drop spreading and hence the image quality. In conventional contact printing methods, such as screen-printing, a blade forces the ink to advance and wet the receiving substrate. Image defects are typically due to a subsequent recession of the ink from the substrate. In the case of ink jet printing, which is a noncontact printing method, the individual ink drops are merely deposited on the surface. To achieve good image quality, the ink drops need to spread, merge, and form a substantially uniform, leveled coating. This process requires a low advancing contact angle between the ink and the substrate. For good image quality, the drops should remain circular and have an optimal spread. Too little spreading of the drops will result in visible spaces of the uncovered substrate surface, giving rise to low color density and banding defects; excess spreading of the drops will cause mixing between adjacent drops and blurring of the image, which leads to poor resolution. The drop shape is also important. Noncircular drops will result in poor image quality due to mottled appearance and low color density. A number of studies have been done to understand the behavior of drops on surfaces and the influence of physical * Corresponding author. † Materials Modeling Group. ‡ Receptor Materials Group.
and chemical properties of the substrate surface on the drop shape and size.1,2 These studies have looked at drop behavior on substrates with various surface energies,2,3 on porous surfaces,4 and on substrates with surface structure5,6 and roughness.7-9 They have also investigated the effect of different kinds of molecules in the ink10-12 and on spreading properties as well as the effects of temperature.13,14 All of these studies add to the understanding of parameters that can be used to control dot behavior and hence image quality. They are important for the design of inks and printing surfaces. Substrates for printing include paper and polymer films. The processes for manufacture of these substrates are not carried out in clean room facilities. Neither is printing of these surfaces done in controlled environments. There are many ways by which the printing surfaces can get contaminated. The backing or liners of the polymer films often have silicone that may not be completely cured that may be transferred to the printing surface. Polymer films usually have a number of additives and stabilizers to ensure optimal properties that the application may demand. These additives and stabilizers may migrate to the surface owing to changes in temperature that a polymer film goes through in transportation and storage (1) Elyousfi, A. B. A.; Chesters, A. K.; Cazabat, A. M.; Villette, S. J. Colloid Interface Sci. 1998, 207, 30. (2) Mourougou-Candoni, N.; Prunet-Foch, B.; Legay, F.; Vignes-Adler, M.; Wong, K. Langmuir 1999, 15, 6563. (3) Voue, Valignat, M. P.; Oshanin, G. M.; Cazabat, A. M.; De Connick, Langmuir 1998, 14, 5951. (4) Clarke, A.; Blake, T. D.; Carruthers, K.; Woodward, A. Langmuir 2002, 18, 2980. (5) Gerdes, S.; Cazabat, A. M.; Strom, G. Langmuir 1997, 13, 7258. (6) Ulman, A. Thin Solid Films 1996, 273, 48. (7) Schwartz, L. W. Langmuir 1998, 14, 3440. (8) Schwartz, L. W.; Eley, R. R. J. Colloid Interface Sci. 1998, 202, 173. (9) Voue, M.; Rollivard, S.; De Connick, J.; Valignat, M. P.; Cazabat, A. M. Langmuir 2000, 16, 1428. (10) Garnier, G.; Wright, L.; Godbout, L.; Yu, L. Colloids Surf. A: Physicochem. Eng. Aspects 1998, 145, 153. (11) Perez, E.; Schaffer, E.; Steiner, U. J. Colloid Interface Sci. 2001, 234, 178. (12) Lahtinen, J. M.; Hjelt, T.; Ala-Nissila, T. Surf. Sci. 2000, 454456, 598. (13) Zhang, H. Int. J. Heat Mass Transfer 1999, 42, 2499. (14) Hwang, C.; Lee, S.; Hsieh, J.; Huang, S. J. Phys. Soc. Jpn. 1999, 68, 3742.
10.1021/la035008b CCC: $27.50 © 2004 American Chemical Society Published on Web 01/31/2004
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Figure 1. Shapes of 70 pL drops of Scotchcal piezo ink jet ink deposited by ink jet onto contaminated polymer film. Note the poor ink flow and wetting.
between manufacturing and printing. The surface of the substrate may be contaminated due to handling. Thus, these printing surfaces are often not clean at a molecular level. These contaminants that are found on the surface can change the chemical and physical properties and thus affect the drop behavior and image quality of piezo ink jet prints. The purpose of this study is to understand the effect of such surface contamination on drop shape, to quantify how they may affect the image quality, and to explore ways to control the shape. Image quality is affected by the extent of drop spread once the drop has hit the surface as well as by the shape of the drop. It has been observed that image quality is good when the shape of the dot is circular. Image quality also depends on the color density, which is a function of the extent of drop spread. These are necessary but not sufficient conditions; other aspects also affect the image quality. In this study, we will focus on how surface contaminants that affect wetting of the liquid on the surface affect the roundness of the drop (which is the ability of the drop to spread uniformly in all directions). It is also known that physical structuressgrooves, channels, posts, etc.saffect the shape and size of the spreading drop.5,6 This study will scope the effect of such surface structure on drop shape and explore the possibility of using physical structures on the surface to counter the influence of contaminated surfaces on image quality.
Monte Carlo simulations were used to study the effect of contaminants on the shape of the spreading drop. Monte Carlo simulation is the tool of choice for the modeling of a large number of equilibrium systems. It is also capable of predicting some dynamic systems. More details about Monte Carlo methods can be found elsewhere.15,16 In this case, the surface is modeled as a lattice. Each square on a lattice is assumed to be the smallest unit of interest and all regions within that square are assumed to have the same properties. When a part of the surface has a contaminant that hinders wetting, the fluid will wet other contiguous regions more easily than it wets the contaminated surface. In the lattice model, this is defined by a probability of wetting. During a time step, any given dry square that has liquid in a neighboring square has a certain probability of being wetted. If the square is uncontaminated, it has a higher probability of being wetted than if it is contaminated. In this study, we are only interested in the drop shape, not on the dynamics or the time trajectory of the drop. In all such problems of image quality, it is the maximum drop size that matters. Thus, aspects such as hysteresis of the jetted drop as it spreads are not important, nor is it important to model the recession of the drop. Thus, time or trajectories of the drop are not important for the purpose of this study. While surface energy and contact angles are important for any drop spreading problem, they are not explicitly significant here for the simple reason that it is impossible to quantify the surface energies in micron-sized regimes where contaminants reside. Further, it is not feasible to control the nature of the contaminants. In such a scenario, more detailed theory17 does not necessarily help provide a keener understanding of the problem. Consequently, the difference in wetting is introduced as a difference in wetting probabilities in a diffusion-like equation. We focus on aspects of the problem that are quantifiable and point to solving this problem: the extent of contamination and the topology of the contaminants lying on the surface. In this study, the focus is not on the size of the spreading drop but only on how the contaminants affect the uniformity of the spreading. Hence, redistribution of the solvent between squares is not critical. Different algorithmssfrom those that are analogous to concentrationbased diffusion to those that equally distribute the fluid between all wet squares (and thus only differentiate between wet and dry squares)shave been tried. In terms of understanding the effect on the drop shape, there is little difference between these algorithms. In this study, the algorithm is diffusion-like. The surface spreading of a drop can be approximated by a diffusive equation
∆(V - Vo) ∆x
J ) -D
Experimental Evidence A black ink (Scotchcal piezo ink jet ink) was jetted onto polymeric substrates whose surface had been contaminated by chemicals that are incompatible with the solvents in the ink, resulting in poor ink spread and nonuniform wetting of the polymer film. Figure 1 presents optical micrographs of drops on the contaminated surfaces. Clearly, the drops are misshapen. One sees bays and coves in these distinctly noncircular drops. When these drops lie next to each other, they will leave uncovered surface, resulting in a faded image.
where V is the volume of liquid in a unit lattice. One assumes that when there is less than a certain amount of liquids (Vo), the lattice unit can be assumed to become too “dry” to spread. ∆x is the size of a unit lattice and has the value L. D is a coefficient of spreading similar to (15) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon Press: Oxford, 1987. (16) Frenkel, D.; Smit, B. Understanding Molecular Simulations: from Algorithms to Applications; Academic Press: San Diego, 1996. (17) Bico., J.; Thiele, U.; Quere, D. Colloids Surf. A: Physicochem. Engi. Aspects 2002, 206, 41.
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diffusivity. The probability of a drop spreading, then, can be defined as
P)
Do∆t L2
where ∆t is the time for iteration. For the purpose of this study, we are not interested in the time over which the drop spreads. The focus is on the drop shape. Thus, we can lump Do∆t as a parameter D. The variable for a contaminated unit lattice (Dc) will be different from that of a clean unit lattice (Do). Thus, the probability of liquid wetting a contaminated unit lattice, Pc, is different from that for a clean unit, Po.
Po )
Do Dc ; Pc ) 2 2 L L
Fluid movement can be defined by the probabilities above. It accounts for fluid flow between wet squares as well as to dry ones based on gradients in amount of fluid. If we are not interested in the rate of drop spread, the parameter of interest is really the ratio in the probabilities of spread for clean and contaminated surfaces. Since the lattice is a square lattice, it is easier to model square drops. Though such drops are not “natural”, they are easier to model and present as accurate a description of uniform drop spreading as a round drop. When the drop spreads uniformly, the “squareness” of the drop is maintained initially, though it becomes circular over time owing to diffusive processes. When the drop spreads nonuniformly, the formation of bays, islands, and peninsulas is evident. The model places the contaminant on the lattice surface based on two parameters: the amount of contaminant and the extent of connectivity. The amount of contaminant defines the extent to which the surface is covered by the dewetting contaminant. The extent of connectivity decides whether the squares that have the dewetting contaminant are connected or not. It is measured by the average number of contaminated lattice units in the neighborhood of a contaminated lattice unit. This defines whether the entire region of contamination is one blob or consists of a number of smaller and more distributed patches. When the extent of contamination is very high, the contaminated squares will become connected. In simulating the contaminated surface, the algorithm keeps picking squares on the lattice surface till an appropriate fraction of the surface is covered by the contaminant. If the connectivity is high, the squares that are contaminated are preferably chosen (by a weighted probability) to be next to already contaminated squares. An example of such a simulated surface is presented in Figure 2. The gray background represents the surface while the black patches represent the contaminated regions. This surface is 20% contaminanted with a moderate connectivity of 1.5 contaminated lattice units in the neighborhood of a contaminated unit. Results When a drop is placed on such a surface and allowed to spread, it moves to neighboring squares. Naturally, it moves more easily to squares that have no dewetting contaminant (that have a greater probability for ink reception) than ones that are contaminated. The effect of contaminant on the square drop shape owing to various levels of contamination at connectivity of 1.5 is presented in Figure 3.
Figure 2. Simulated surface with 20% contamination with connectivity of 1.5.
In Figure 3, it is clear that at low levels of contamination, and at moderate connectivity between these contaminants, spreading is uniform and the shape of the drop is largely maintained. The ratio of Po to Pc is 5:1. At 30% contaminant coverage, the drop is a square with few defects, pretty close to what it might be for an uncontaminated surface. On increasing the fraction of the surface contaminated, the spreading drop becomes more misshapen, forming fingers, bays, and peninsulas. At 60 or 70% coverage, the drop has taken on a very different shape. This is because at high coverage, the contaminated squares begin to connect and hence the spreading is allowed in certain directions only. It is also noticeable that the extent of spread has also decreased in the same time period; the dewetting contaminants make it difficult for the drop to spread. At low densities, contaminants that hinder wetting do not affect the drop spread. However with increasing densities (or with higher connectivity between contaminants), certain “paths” are blocked off and the drop spreads with fingers that may interconnect, which finally give rise to bays and peninsulas. The fingers and the unusual shapes in Figure 3 are very similar to the pictures presented in Figure 1. The model explains the physical phenomena. The connectivity, in real systems, can be related to the processes that cause the contamination. If the contaminant is based on migration of additives to the surface of the film or is owing to patchy uncured silicone in the liner, it is possible that the connectivity will be low. However, if the contaminant is owing to a process errorssuch as a grease streak on the belt or greasy fingerprintssthe connectivity will be high. Figure 4 presents the effect of changing connectivity on the spreading of the drop (compared to drop spread in the absence of any contaminant). The y-axis represents the ratio of the average drop size on the surface of interest to the drop size on an uncontaminated surface. When the amount of contaminant on the surface is either low or high, the drop spread is not significantly affected by the extent of contaminant connectivity. Figure 5 presents the effect of changing the ratio of Po to Pc. The y-axis represents the ratio of the average drop size on the surface of interest to the drop size on an uncontaminated surface. Increased dewetting of the contaminated surface restricts the drop from spreading. For this study, a lower average drop spread also corresponds to a more misshapen drop. Changing the lattice size did not affect the results (for small changes). If the lattice is made too large, the simulation becomes too coarse with respect to the drop. If it is made too small, the simulation takes much longer with no significant change in results.
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Figure 3. Effect of surface contamination on drop shape.
Figure 4. Effect of contaminant connectivity on average drop spread.
Effect of Physical Structures The results from this model provide an understanding of the effect of contaminants on the surface. We can see that the extent of contamination and the nature of the contaminants significantly distort the drops, affecting image quality. At the same time, a number of studies have shown that physical structures on the surfacesposts, wells, channels, etc.scan be used to control fluid flow as well. The next part of this study focuses on the effect of physical structures at the surface of the film on the shape of the spreading drop. In this study, two kinds of structures were chosen: random pits and a regular array of pits. In the case of random pits, the size of the pits was changed and its effect on the drop shapes was analyzed.
Figure 5. Effect of wettability on drop spread.
The lattice units are smaller than if not the same size as the pits. In reality, drops may preferentially occupy the edges of the pit rather than the center. However, for the purpose of this study, it is assumed that fluid occupies a pit uniformly. Thus, when fluid enters a pit all lattice squares that are parts of the pit fill up immediately. Behavior of drop spreading over a pitted surface is modeled by changing the probability of drop spreading to or from a pit relative to the drop spreading over a clean surface. The pits work by offsetting some of the effects of the random contaminants. By acting as partial barriers where fluids collect before further spreading, they increase the probability of causing interconnects between fingers. However, the results of these random pits are not very encouraging and are presented in Figure 6. The gray patch
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Figure 6. Effect of random pits on a contaminated surface.
shows the initial drop. In both cases, the pits are twice as susceptible for the drop to spread into than the background surface. The figure on the left has a surface that is 30% covered by pits; the figure on the right has 50% pit coverage. The one on the right is less distorted, but not by much. Further increases in the density of the pits do not help either. Increasing the size of the pits also causes coalescence and reduction in the resolution of the image. When there are multiple colors, blurring will also be observed. Thus, random pits do little to solve the problem of misshapen drops. The simulations for a surface with a regular array of pits are similar to those used for the random pits. The regular pits in parts a and b of Figure 7 cover 60% and 80% of the surface, respectively. As long as the pit size is about an order of magnitude smaller than the drop, the size of the pit is not a significant factor. The drops move into a pit based on a relative probability as discussed earlier. Once in, they fill all squares that lie in the pit. In this simulation, the probability of a drop spreading into a pit is twice as great as a drop spreading into the rest of the surface (same as in the case of pits). The effect of these pits is shown in Figure 7a,b. The distortion of the drop is significantly smaller. The fingers are all interconnected and the spread is uniform. The pits slow a moving front. In the case of random pits, the slowing down occurs at random and exacerbates the distortion of the drops. In regularly pitted surfaces, the slow in the drop spread allows for the compensation of slow wetting of certain regions compared to others, thus reducing distortion in the drop. The model shows that it is possible to use such a regular array of pits to mask the effect of dewetting contaminants on the drop shape. Other structures on the surface could also control fluid spreading in a way to ensure optimal drop shape. It must be noted, however, that such surface structures will affect the extent of drop spread and the surface tension of the ink must be chosen to account for that. Conclusions This model is useful in identifying the effect of surface contamination (especially those that cause dewetting) on the shape of the drop. Given that the drop shape is one of the simplest indicators of image quality, understanding the effect of ink-substrate interactions on drop spreading and its shape is important. This study advances our
Figure 7. (a) Effect of an array of pits covering 60% of the surface on a spreading drop. (b) Effect of an array of pits covering 80% of the surface on a spreading drop.
understanding of drop behavior in the presence of surface contamination. This study shows that drops will be largely unaffected by low levels of contaminant, but higher concentrations of surface inhomogeneties will distort the drop shape. Such distortion can be countered by embossing the surface with structures, a regular array of pits being preferred. They help to control the drop shape significantl; however, they may cause other problems, such as a reduction of dot gain, which can lead to low image densities. More work needs to be done to optimize the dimensions of these structures, though such optimization will need to be specific to the substrate and ink material of interest. Acknowledgment. We are grateful to Dr. Joe McGrath and Dr. Buren Ree for useful pointers and informative discussions. LA035008B
