(363aa) Modeling and Predictive Control of the Coffee-Ring Effect in Coalescing QD-Droplets

There is an ever-increasing need for the production of better display technologies in our modern world. One of the latest techniques is using quantum dots (QDs) in LED screens attributed to the exceptional photoluminescence properties of these QDs [1]. In this pursuit, spray coating and inkjet printing of QDs have come into the limelight for manufacturing of QD-based thin-films for Perovskite Solar Cells (PSCs), and QD-based LEDs [2]. Inkjet printing is a type of computer printing that recreates a digital image by propelling droplets of ink onto paper and plastic substrates. The literature review shows that these QD-based thin-film applications' performance depends on the film characteristics (i.e., film thickness and roughness). Specifically, it has been shown that having smooth thin films with minimum roughness is critical to the performance, and uneven deposition is detrimental to the electron-hole transport within these devices’ thin film [3,4]. Unfortunately, during thin-film deposition of QDs, there is an uneven deposition of QDs due to the presence of the coffee-ring effect (CRE). CRE happens when a drop of liquid dries on a solid surface, and its suspended particulate matter is deposited in a ring-like fashion [5]. Thus, understanding the various factors affecting the CRE, and the mechanism for its formation is critical for developing better thin films for QD applications.

There has been a plethora of studies on the formation of coffee rings in various systems. For example, Kumar and co-workers developed an analytical solution for CRE [6]. In another study, the authors utilized kinetic Monte Carlo simulations to describe CRE [7]. However, most of these previous works focus on the formation of coffee rings in a single evaporating drop without considering the effect of coalescence of droplets, which is very frequent during thin-film deposition. Thus, there is a requirement of developing accurate models to describe the CRE in coalescing droplets and their effect on uneven thin-film deposition.

To address this knowledge gap, we developed a high-fidelity microscopic model that describes the evaporation of coalescence and its effect on the formation of the coffee ring. First, we considered four different types of coalescence configurations (i.e., two droplets overlapping to a varying degree). These configurations were sampled from a Gaussian probability distribution. Second, we developed a Discrete Element Method (DEM)-based model to describe the spatiotemporal variation of QD particles within the droplet, thus, enabling the demonstration of CRE in coalescing droplets. DEM provides the solution to the Newton’s law of motion for each particle, and is an effective method for computing the motion and effect of many small particles [8]. In addition to this, we constructed a model predictive controller (MPC) to regulate the CRE patterns in coalescing droplets in various configurations. Specifically, we considered three manipulated input variables (i.e., droplet size, droplet temperature, and deposition rate), and the extent of the CRE as an output in the developed MPC. Simulation results indicate that small droplet size and higher temperature results in weaker CRE and lead to an even deposition. Overall, the proposed high-fidelity model provides a mechanistic understanding of the patterns of coffee rings formed in coalescing evaporating and acts as a foundational model for developing a framework for thin-film deposition.

Literature cited:

1. Yun-Fei Li, Jing Feng and Hong-Bo Sun. Perovskite quantum dots for light-emitting devices. Nanoscale, 2019, 11, 19119
2. Gao A, Yan J, Wang Z, Liu P, Wu D, Tang X, Fang F, Ding S, Li X, Sun J, et al. Printable CsPbBr3 perovskite quantum dot ink for coffee ring-free fluorescent microarrays using inkjet printing. Nanoscale. 2020;12(4):2569–2577.
3. Bag A, Radhakrishnan R, Nekovei R, Jeyakumar R. Effect of absorber layer, hole transport layer thicknesses, and its doping density on the performance of perovskite solar cells by device simulation. Solar Energy. 2020; 196:177–182Yuan J, Bi C, Wang S, Guo R, Shen T, Zhang L, Tian J. Spray‐Coated Colloidal Perovskite Quantum Dot Films for Highly Efficient Solar Cells. Advanced Functional Materials. 2019 Dec; 29(49): 1906615.
4. Nukunudompanich M, Budiutama G, Suzuki K, Hasegawa K, Ihara M. Dominant effect of the grain size of the MAPbI 3 perovskite controlled by the surface roughness of TiO 2 on the performance of perovskite solar cells. CrystEngComm. 2020;22(16):2718–2727.
5. Peter J. Yunker1, Tim Still1,2, Matthew A. Lohr1 & A. G. Yodh. Suppression of the coffee-ring effect by shape-dependent capillary interactions. doi:10.1038/nature10344
6. Kara L. Maki†, § and Satish Kumar*‡. Fast Evaporation of Spreading Droplets of Colloidal Suspensions. dx.doi.org/10.1021/la202088s |Langmuir 2011, 27, 11347–11363
7. Crivoi A, Duan F. Three-dimensional Monte Carlo model of the coffee-ring effect in evaporating colloidal droplets. Scientific Reports. 2014;4(1):1–6.
8. Blais B, Vidal D, Bertrand F, Patience GS, Chaouki J. Experimental methods in chemical engineering: Discrete element method—DEM. The Canadian Journal of Chemical Engineering. 2019;97(7):1964–1973.