(363k) Multiscale Modeling and Control of Spray Coating of Quantum Dots

Over the past few years, quantum dots (QDs) have received significant attention due to their high quantum efficiency, tunable photoluminescence characteristics, and a newly developed array of continuous manufacturing techniques [1-3]. This has resulted in increased market demand for QD-based applications like solar cells and high-resolution displays [4]. Interestingly, these applications require the deposition of a thin film with desirable characteristics (i.e., film thickness and roughness) [5]. This has necessitated the development of scalable manufacturing frameworks for spray coating of QD thin films for meeting market demand. Unfortunately, existing conventional continuum level spray coating models do not consider the surface-level QD-specific interactions that are present during the spray coating of QD solution, and thus, do not provide an accurate description of this phenomenon [6]. Specifically, at the microscopic scale, the QD particles show evaporative aggregation and demonstrate the characteristic ‘coffee-ring effect (CRE)’, which contributes to the roughness of the thin films. Thus, alongside considering the macroscopic dynamics of spray coating, incorporation of surface-level QD interactions is important.

To address this knowledge gap, we have adopted a multiscale modeling approach, wherein macroscopic dynamics key to the spray coating process are integrated with a detailed microscopic model for modeling spray coating of QD solutions. First, a spray nozzle with variable liquid and airflow rates is considered, which can atomize the QD solution using pressurized air. Here, the size distribution of the atomized droplets is included to mimic droplet-to-droplet heterogeneity, and the conical spread of impinging droplets on the substrate surface is modeled using a gaussian distribution. Second, the evaporation dynamics of individual droplets after impinging the substrate surface are described using appropriate heat and mass balance equations. Third, a discrete-element method (DEM)-based microscopic model is developed to consider the CRE of QD particles in individual droplets to provide a detailed surface-level description of the spray coating process. Subsequently, the above equations are integrated to develop a detailed film-deposition model for spray coating of QDs. As a result, the effect of deposition rate, the height of the spray nozzle, and other process parameters on the film characteristics (i.e., film thickness and roughness) is investigated.

Furthermore, since for high-performing QD-based thin-film applications, a specified film thickness () with minimizing roughness () is required, a model predictive controller (MPC) framework is formulated to regulate and . Specifically, a reduced-order model (ROM) is developed to understand the relationship between air and liquid flow rates ( and ), and the height of the spray nozzle () and and . Then, the ROM is integrated with the MPC framework to calculate the optimal inputs, which are then used to simulate the high-fidelity film deposition model (which acts as a virtual experiment) and use as feedback for the MPC. Overall, the developed film-deposition model in conjunction with the MPC framework showcases effective control of film characteristics (i.e., desired film thickness and minimum roughness).

References:

1. Sitapure, Niranjan, et al. "Multiscale modeling and optimal operation of millifluidic synthesis of perovskite quantum dots: Towards size-controlled continuous manufacturing." Chemical Engineering Journal 413 (2021): 127905.
2. Sitapure, Niranjan, et al. "CFD-based computational studies of quantum dot size control in slug flow crystallizers: Handling slug-to-slug variation." Industrial & Engineering Chemistry Research 60.13 (2021): 4930-4941.
3. Protesescu, Loredana, et al. "Nanocrystals of cesium lead halide perovskites (CsPbX3, X= Cl, Br, and I): novel optoelectronic materials showing bright emission with wide color gamut." Nano letters 15.6 (2015): 3692-3696.
4. Zhang, Ting, et al. "Halide perovskite based light-emitting diodes: a scaling up perspective." Journal of Materials Chemistry C 9.24 (2021): 7532-7538.
5. Park, Nam-Gyu, and Kai Zhu. "Scalable fabrication and coating methods for perovskite solar cells and solar modules." Nature Reviews Materials 5.5 (2020): 333-350.
6. Eslamian, Morteza. "A mathematical model for the design and fabrication of polymer solar cells by spray coating." Drying technology 31.4 (2013): 405-413.