Thin films with advanced technical specifications have many uses, including within lithium-ion batteries1,2solar panels3 Polymer Electrolyte Membrane Fuel Cells4,5. Roll-to-roll slot die coating is a widely used technology for industrial-scale manufacturing of thin films, which involves pumping fluids through slots in metal blocks into moving substrates.4,6. High line speed, high material utilization, and the ability to pre-select the coating thickness are factors that contributed to the coating of roll-to-roll slot dies.7.
Slot die coatings have many adjustable process parameters that affect the formed coating. As shown in Figure 1, these parameters include substrate rate, coating gap, shim thickness, and coating solution composition.4,8. Slot die coating foams defect-free coating using a set of parameters within the working window4. Outside this window, the coating process is susceptible to serious defects such as ribs, drip and air confinement. However, different sets of coating parameters provide different coating properties, even when they stay within the operation window9,10. For example, the thickness of the wet coating may vary within the operating window, depending on the ratio of pump speed to substrate speed.4. However, more subtle features such as coating uniformity and edge quality also depend on the process conditions used.10,11. Schmitt et al. The area within the operation window has high coating uniformity, quality window10.
Schematic diagram of a side view of a slot die labeled with the slot die coating process parameters.
Many theoretical models can predict the working window of slot die coatings like Ruschak12Higgins and Scriven13 And Yamamura14. However, to the author's knowledge, there is no efficient theoretical understanding or analytical model of how process parameters affect coating characteristics. Inside Operation window. This is noteworthy because coating properties such as unexpected coating thickness deviations and coating uniformity have a significant impact on the performance of subsequent devices.15. For example, high coating uniformity is essential for lithium-ion battery electrodes. Minimizes removal rates and has a major impact on the electrochemical performance of the electrodes.1,16. A concrete example of this is et al. The heterogeneous lithium-ion NMC electrode coating showed low speeds and low Coulomb efficiency, particularly at high rates.17. Coating uniformity is also an important coating function for organic photovoltaic devices, and higher uniformity improves device performance.18.
Despite the dogma that slot die coating provides complete thickness control, in practice, small changes in coating width can occur depending on the process parameters used, which will change the coating thickness19. This effect is due to the non-Newtonian behavior of the polymer coating solution.20. The thickness of the coating determines the energy density of the lyrion battery, and thinner than expected electrodes give a lower cell energy densitytwenty one. Furthermore, thicker than expected electrodes can lead to limiting the charging/emission rate. These differences in coating thickness are particularly important for industrial operators in applications that utilize stripe coatings or strict thickness requirements.
Lack of theoretical modeling and understanding of how input parameters influence these basic coating properties of slot die coatings.4 This means that operators now optimize production through iterative, trial and error adjustments1,11. The output competing with a large number of process parameters exacerbates the complexity of this optimization and is unlikely to be truly optimized for the coating process. This has cost implications as waste produced during this laborious process and production time were lost. Furthermore, this type of optimization will not yet be determined to improve the performance of potential devices.
Despite computer-aided optimization, it has been implemented in various manufacturing processes in other sectors, such as additive manufacturing22,23 Pharmaceutical manufacturingtwenty fourIt is not routinely applied to industrial roll-to-roll slot die coating lines. Computer-aided optimization in this context allows you to unlock the significant cost and performance benefits of a wide range of devices. Furthermore, such an approach may provide valuable insight into the relationship between key coating parameters and the resulting properties of the coating.
The literature documented several instances of computer-aided optimization for roll-to-roll slot die coating16,25,26. However, no reports link basic process parameters to important coating properties, highlighting a major gap in understanding slot die coating within the working window. Furthermore, there was no use of machine learning models to provide experimental improvements to coating functionality. This cut highlights the difference between theoretical modeling and practical applications, and raises concerns about the effectiveness or applicability of previously reported methods.
Machine learning-based surrogate optimization is suitable for slot die coating due to the complexity of the process and numerous interacting inputs and outputs. Variant modeling involves building computationally efficient approximations of approximate complex, computationally expensive, or time-based simulations using experimental data, and is well known for capturing complex nonlinear relationships.16,27. Surrogate models are particularly effective when the analytical models are not available.
There are analytical approaches and multivariate modeling tools that can be used to model industrial processes. For example, multiple linear regression (MLR), polynomial regression (PR)28Principal Component Analysis (PCA), Latent Variable Model (LVM), Orthogonal Partial Least Squares (OPLS)29Gaussian Process (GP), and Artificial Neural Networks (ANN)30. Of these, radial basis function neural networks (RBFNNS) are prominent machine learning modeling methods due to their ability to accurately describe complex nonlinear relationships while maintaining computational efficiency. It has its universal approximation capabilities31,RBFNNS is excellent at modeling complex systems with high accuracy, efficiently capturing local variations of data.
However, alternative alternative modeling methods also need to be considered. For example, Gaussian process regression is widely recognized for its flexibility and ability to provide estimates of uncertainty, making quantifying predictive confidence a strong candidate for a key issue. Similarly, support vector regression, which adapts support vector machine methodology to regression tasks, is known for its robustness in high-dimensional spaces, and often achieves good generalizations on relatively small data sets.32. Comparative studies show that RBFNNs usually provide rapid training and effective local modeling, but Gaussian process models may be superior to them in terms of predictive errors in particular situations, particularly when quantification of small data sets or uncertainties is required. Furthermore, recent studies have shown that SVR can provide competitive performance, but its accuracy may be increased under several conditions, such as the detection of compound laminate peeling.33. Therefore, incorporating these surrogate modeling techniques and comparative analyses further strengthen the strengths and appropriate use cases of RBFNNs, highlighting the need for model selection based on the specific characteristics of the data and modeling goals.
Gradient-based optimization techniques can effectively explore solution spaces, but have inherent limitations, such as generalization challenges and lack of performance guarantees. The surrogate-assisted evolutionary calculation addresses these problems by estimating the fitness functions of evolutionary algorithms using computationally efficient models. This approach is especially valuable for complex optimization problems with computationally expensive objective functions. By adopting a proxy model like RBFNNS, this approach significantly reduces the need for costly experimental assessments and accelerates both the exploration and exploitation of the parameter space. Furthermore, acquisition is a further balance between research and exploitation, and this method is particularly effective for high-dimensional optimization tasks.
Reference Vector Guided Evolution Algorithm (RVEA), a flexible and scalable metaheuristic evolution optimization method34suitable for complex processes. Traditional multi-objective problem algorithms struggle in terms of performance and diversity maintenance35. RVEA utilizes uniform distribution Reference Vector – Input parameter space orientation – Guides you to find the best solution. This method ensures a diverse set of solutions that extend to the front of Pareto. This represents the optimal set of trade-offs between competing goals. Furthermore, the adaptive angle penalty mechanism of RVEA dynamically adjusts the selection pressure, maintains a balance of convergence and diversity, making it suitable for complex, high-dimensional problems.
This article presents an experimentally validated optimization approach for roll-to-roll slot die coatings combining the RBFNN surrogate model with RVEA. The coating composition used is similar to many industrially related coatings, such as lithium-ion batteries and solar cell slurries.1,36gains applicable insights across a wide range of fields. The purpose of this article is to facilitate the broad implementation of machine learning-based optimization in roll-to-roll slot die coatings, providing potential improvements in cost, performance and process understanding.
