A process model for slot coating of narrow stripes
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Selective deposition of patterned films, without masks or subtractive postprocessing steps, can potentially be achieved by extending the capabilities of traditional slot coating. Realization of a fully additive-only approach of this nature will elevate the viability of slot coating for numerous emerging technologies such as flexible optoelectronic devices, sensors, and wearables. In this study, we develop a process model for slot coating of variable-width narrow stripes, as a fundamental and representative pattern feature for patterned slot coating. Our process model addresses the sensitivity of stripe output to fluid deposition rate, substrate speed, and coating gap for a given coating material. To explain the observed process behavior, we distinguish between separate configurations of contact line pinning of the liquid bridge at the coating tool surface and show experimentally how these configurations relate to regimes in the process model that must be characterized separately. We also demonstrate how the geometry of the liquid bridge and range of intermediate contact angles along its contact line correspond to observed hysteresis of the coated stripe width.
KeywordsSlot die coating Pattern printing Narrow-stripe coating Polyvinyl alcohol Process modeling
List of symbols
- Lu, Ld
Length of upstream and downstream portion of die lip, respectively
Wet film thickness
Width of slot die slot
Width of coating bead and coated narrow stripe
- wa, wr
Width of narrow stripe in advancing and receding configurations, respectively
Offset distance between centers of coating bead and slot die outlet
Width/length ratio of the coating bead
- θa, θr
Advancing and receding contact angle, respectively
Dimensionless coating gap
- wa*, wr*
Dimensionless stripe width in advancing and receding configurations, respectively
Average flow velocity at slot die outlet
In recent years, slot die coating of stripe-patterned films has been applied across a range of emerging printed device technologies. These technologies include thin-film solar cells,1, 2, 3, 4 transistors,5,6 batteries,7 and display devices.8, 9, 10 Slot die coating has drawn attention within this ecosystem of applications because it offers a variety of advantages related to manufacturing scale-up. Slot coating offers precise metering of wet thickness, excellent film uniformity, adaptability to new coating materials, low-waste deposition, and wide-area coverage. Slot die coating is therefore a dependable option for high-throughput roll-to-roll (R2R) manufacturing.
For slot die coating of stripe patterns, outflow of coating fluid can be directed using grooves machined into the coating tool or meniscus guides.11 This approach is typically used to deposit continuous stripes at a fixed width. However, the research community has expressed interest in extending the slot coating approach to more ambitious patterning capabilities. Vak et al.4 have developed a 3D printer-based slot die capable of printing curved stripes and patches at fixed width. Lin et al.12 have demonstrated the capability of a narrow slot die to produce a range of stripe widths by varying substrate speed and flow rate. Parsekian and Harris have reported on a slot die coater with on-demand patterning capability comprising independent flow control across local outflow regions.13 These efforts underscore the potential of slot die as an archetype for mask-free, additive-only deposition of sophisticated patterns.
Narrow-stripe deposition, using both conventional slot coating and its various pattern-capable iterations, requires an understanding of pattern morphology with respect to process inputs such as volumetric flow rate (Q), substrate velocity (U), and coating gap (H). Since film thickness (h) and stripe width (w) both depend on similar process conditions, the need arises for sufficient characterization to specify both independently. Physically, process behavior is tied to the mechanics of the coating bead, the liquid bridge between the substrate and slot die outlet. Here, the coating bead cannot be approximated as a two-dimensional phenomenon as is customary for conventional slot die coating.14, 15, 16 Furthermore, the body of literature on liquid bridges focuses primarily elsewhere, on axisymmetric cases under extension and compression,17, 18, 19, 20, 21 although there are relevant insights available regarding shearing,22,23 contact line hysteresis,24, 25, 26 and contact line confinement.27 Thus, direct modeling of the narrow coating bead presents a considerable challenge and would require accurate, extensive characterization of wetting and rheological properties.
In this paper, we develop a process characterization methodology for slot coating of variable-width narrow stripes. These efforts incorporate classification of several key liquid bridge phenomena, each observed in previous studies, as they relate to the slot die coating process. To circumvent extensive characterization of fluid wetting and rheology, the model relies on direct measurement of process output and general knowledge of liquid bridge mechanics. The resulting empirical relationships are validated across a range of coating fluid viscosity, deposition rate, and coating gap. The modeling methodology is then evaluated in terms of the requisite experimental characterizations required to characterize a selected tool geometry, substrate, and coating fluid.
Materials and Methods
Physical properties of coating fluids at 25°C
Process parameters are illustrated schematically in Fig. 1a. The coating gap (H) is adjusted manually using a linear positioner, flow rate (Q) is set by a syringe pump, and substrate velocity (U) is set by a PID-controlled motor. These process inputs are recorded in software automatically with each captured image, while the remaining geometric parameters are kept fixed at G = 76 µm, w0 = 0.78 mm, Lu = 1.2 mm, and Ld = 1.1 mm for all experiments. Image data such as that shown in Fig. 1b are analyzed ex situ using the MATLAB image processing toolbox to extract pattern morphology (w), and average film thickness (h) is calculated as h = Q/(U·w). For each measurement, the coating bead is qualified as either advancing or receding, and any pinning of the contact line at the coating tool surface is noted.
Empirical modeling approach
We seek a model relating process conditions (U, Q, H) to pattern morphology (w). Previous studies have explored the influence of individual parameters. Lin et al. noted that stripe width correlates positively with Q and negatively with U, as would be expected from continuity.12 In addition, a negative correlation between w and H has been observed in previous studies,12,13 as might be expected from the relationship between gap height and contact radius of a liquid bridge between two plates.25,26 However, a precise explanation for the combined influence of Q, U, and H has been less straightforward. Experimentally, it has been demonstrated that (1) increasing H facilitates the onset of breakup defects in a narrow-stripe pattern at high U and low Q12; (2) the shape of the coating bead relates directly to the final width of the narrow stripe13; (3) the coating bead shape is subject to significant confinement effects at corners and edges of the coating tool12,27; and (4) the proportion of coating bead volume transferred to the substrate is dependent on wettability of the substrate and coating tool, as well as the rate of strain in the bead.20, 21, 22, 23 Together, these published results suggest that the narrow-stripe coating process can be more clearly understood in the context of liquid bridge phenomena. The model constructed for this study incorporates knowledge of these phenomena to improve upon results of previous empirical modeling efforts.
The empirical process model also assumes hysteresis of the coating bead contact line, a physical consequence of the contact angle hysteresis at the substrate and slot die lip. This effect has been previously noted and studied extensively in liquid bridges of fixed volume subject to tensile and compressive strain.24, 25, 26 The range of intermediate contact angles between θa and θr implies a range of physically permissible liquid bridge volume for a particular stable contact line width. Analogously, in narrow-stripe slot die coating, the coating bead exhibits the hysteresis behavior illustrated in Figs. 2d and 2e. Here, however, the liquid bridge is subject to shear as well as a mass flux condition at two boundaries. The model proposed in this work relies on direct measurement of stripe width for both advancing (wa) and receding (wr) contact line configurations. These correspond to the cases where coating bead size is incrementally increasing or decreasing, respectively, under a quasi-static condition. Separate empirical relationships are constructed for wa and wr, which constitute an upper and lower bound on possible stripe width for a given set of processing parameters.
The transitions between pinning regimes are influenced by the geometry of the die lip (Lu, Ld, and G), the center offset between the coating bead and die slot (ℓ), and the length/width ratio of the coating bead (α). The transition between I and II occurs within (Lu/2) ≤ αw ≤ (Lu + Ld + G), and the transition between II and III occurs at αw ≥ (Lu + Ld + G). While parameters ℓ and α can be measured directly using the R2RIS in Fig. 1a, it may be impractical to do so on typical R2R systems. Therefore, the process model presented here places the regime pinning transitions based on an initial guess and a data-driven correction.
Previous analysis of the physical quantities relevant to deposition flow suggests several dimensionless groups for formulation of an empirical model.12,13 These consist of a dimensionless length H* ≡ H/(Lu + Ld + G), which expresses the ratio between the coating gap and die lip length; capillary number, Ca ≡ µU/σ, which expresses the ratio of viscous to interfacial forces; Reynolds number, Re ≡ ρu avg 2 /(µU/H), which expresses the ratio of inertial to viscous forces; and a dimensionless stripe width, w* ≡ w/w0, which expresses output pattern morphology. The empirical relationships developed for this process model are based on these dimensionless groups. Here, uavg ≡ Q/(w0·G), the average flow velocity at the slot die outlet, is taken as the velocity scale for inertial forces, while U is used for viscous forces. To distinguish between the advancing and receding contact line configurations, wa* ≡ wa/w0 and wr* ≡ wr/w0 are considered separately in the model formulation.
Results and discussion
As expected, an abrupt feature is present at the boundary between regimes II and III. However, no corresponding feature at the boundary between regimes I and II is easily identifiable. This may be explained by the type of influence that each confinement regime exerts on the liquid bridge, whereas regime II primarily confines the location of the liquid bridge and regime III influences both its location and shape. Thus, in Fig. 3, the presented linear regression fit results have been performed separately over regime III and over the remaining data. It is interesting to note that in all cases, stripe width is significantly less sensitive to other processing parameters within confinement regimes I and II, relative to regime III. This result illustrates the effect of the die lip edge on process sensitivity and suggests that by decreasing the length of the die lip (Lu, Ld), one would be able to achieve a greater range of stripe widths for a given film thickness at the cost of decreased process robustness. It is also notable that pattern output is least sensitive to Q, U, and H near the minimum feature size produced.
Empirical model formulation
To evaluate the influence of viscosity on contact line hysteresis, it may be noted that the results in Fig. 4 exhibit a marginal decrease in model slope for wa, concurrent with a marginal decrease in model slope for wr, for the higher-viscosity solution. From the trends in Fig. 3, hysteresis of the coating bead width becomes more pronounced due to a change in process inputs when wa decreases by a greater amount than wr, or equivalently, when wr increases by a greater amount than wa. Thus, the effect of increased viscosity is to mitigate the severity of contact line hysteresis for relatively wide stripes, near pinning regime III. Intuitively, this may be anticipated from the observation that coating bead hysteresis is an interfacial phenomenon and thus less significant where viscous forces dominate over interfacial ones.
Methodology and demonstration
Narrow-stripe width (w) is sampled across a range of process input parameters (Q, U, H). Each sample point is associated with either advancing or receding coating bead width, based on the history of the sample run (e.g., increasing U from its previous value implies advancing bead width, and vice versa).
Since wII−III* is not known explicitly, wII−III* ≈ (Lu + Ld + G)/w0 is used as an initial estimate.
Data are binned into two subsets based on the measurements of w*. One bin contains data where 0 < w* ≤ wII−III*, and the other bin contains data where w* > wII−III*.
Binning and regression analysis are updated in order to ensure that the transition between liquid bridge confinement regimes is reflected appropriately, while maintaining continuity of the piecewise model.
Uncertainty analysis is performed on model components Ba, Br, Da, and Dr to construct bounds for each piecewise model segment.
The uncertainty level where the bounds for the two model segments intersect at wII−III* is determined.
The binning process is repeated about Πa(wII−III*) and Πr(wII−III*).
Regression analysis and determination of wII−III* are repeated using the updated binning scheme.
In a physical sense, the empirical model provides a range of possible w for each specific combination of U, Q, and H. The piecewise curve fits for wa and wr constitute a stripe width minimum and maximum, respectively. Interestingly, since the models for wa and wr each depend on a different dimensionless group, it follows that process parameters can be chosen to produce a range of wa with wr held constant, and vice versa. This underscores the high degree of variability in stripe width exhibited by the slot coating process. The empirical model provides a clear physical interpretation of this variability where pure correlations between U, Q, H, and w cannot.
Our experimental investigation has highlighted how narrow-stripe slot die coating under steady-state conditions can be described by simple single-input model. Wetting hysteresis and contact line confinement have been illustrated as influential mechanisms in the narrow-stripe slot die coating process, and sharp transitions in observed experimental trends have been related to boundaries between regimes of wetting behavior. The primary outcome of this work has been the development of an empirical modeling methodology for the narrow-stripe slot coating process, validated for a sample aqueous polymer solution. It is of practical significance that the methodology can be applied to other materials without extensive knowledge of their physical properties. Straightforward measurements of pattern morphology and standard R2R process inputs are sufficient for its use.
For future investigations on narrow-stripe slot coating, it will be valuable to consider a wider range of coating material properties to further validate and extend the empirical model. Highly non-Newtonian polymeric fluids, for example, will require the addition of one or more model parameters in order to account for the shear rate dependence of viscosity. Similarly, the viscoelastic effects should be examined. Furthermore, it may be worthwhile to compare results for a non-Newtonian fluid with results from Newtonian fluids over the same viscosity range. In addition to further experimental work, the development of analytical or computational descriptions of the narrow-stripe coating bead will likely provide valuable insights and points of comparison with respect to the empirical model presented here. Such a description could also be used to extend the results of this study to non-steady flow rate conditions and other slot die materials and geometry.
In each of these efforts, the experimental modeling approach developed through this study will be a valuable tool to help isolate the influence of individual process inputs. Even for significantly different tool geometries and material systems, the liquid bridge hysteresis and confinement effects explored in this paper will remain influential and can be considered using the framework developed here.
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