Multiscale Modeling of Spray Coating of Perovskite QDs: Understanding the Role of Molecular Interactions in Particle Aggregation.

The US Department of Energy has set high-priority targets to reduce the cost of photovoltaics from ~ 10 cents/kWh to half of that at 5 cents/kWh by 2030. This has fueled a plethora of research in the discovery, optimization, and commercial production of high-efficiency solar cells. Perovskite solar cells (PSCs), especially CsPbBr₃, have received special attention due to their high quantum efficiency and tunable absorption/emission spectra [1]. Often, the perovskite quantum dots (QDs) are synthesized using one of the various batch synthesis routes, and after appropriate post-processing, they are spin-coated and separately cured to make a functional layer for the PSCs [2]. However, the problems of batch-to-batch variation, low-material utilization, and separate curing required in the spin coating process have slowed down and made the commercial production of PSCs difficult. In response, recent studies have demonstrated that spray coating can counter these challenges associated with spin coating by (a) providing a fast-scalable continuous production alternative with better material utilization; (b) offering a large control space for uniform deposition without the need for a separate curing step [3], and (c) integrating it with a continuous crystallizer to result in higher production capacity [4]. That being said, modeling and control of spray coating is a non-trivial task due to a combination of macroscopic phenomena (e.g., transport and thermal), and molecular-level interactions (e.g., dipole-dipole, van der Waals, and steric forces), thereby requiring a multiscale modeling approach.

In spray coating, the colloidal solution from the continuous crystallizer is atomized and sprayed onto a thermally heated silicon substrate through a pressurized nozzle. Consequently, the atomized droplets impinge onto the substrate and form a liquid splat followed by evaporation of the solvent (toluene). In this work, the spray coater is modeled using a system of macroscopic mass and energy balance equations (MEBE), which describe the effect of surface tension, vapor pressure, nozzle velocity, and the size of the impinging droplet on solvent evaporation. Further, during the solvent evaporation, the QD particles undergo particle aggregation due to the presence of various molecular interactions, and can lead to the formation of a non-uniform film, and demonstrate the coffee-ring effect. Thus, a modified form of the discrete element method (DEM), which solves newton’s equation of motion for each QD particle, is utilized to accurately model these microscopic interactions [5]. Specifically, the DEM considers four molecular interactions, viz., steric hindrance, dipole-dipole forces, Brownian motion, and van der Waals forces. This is because, (a) the QD particles have a long-chain ligand-shell around them, which results in steric hindrance (repulsion) if two QD particles come very close to each other during aggregation; (b) experimental observations show a non-zero dipole moment for the QD particles [6]; and (c) the QD particles have a size range of 5-10 nm, which makes them very susceptible to undergo Brownian motion. Finally, the continuum model (MEBE) and the DEM are dynamically coupled to develop a high-fidelity multiscale model of spray coating.

The simulation results generated for different nozzle velocities and QD concentrations demonstrate the typical coffee ring formation as seen in the experiments [7]. The results also elucidate the effect of controllable macroscopic variables (i.e., substrate temperature, nozzle velocity, and QD particle concentration) on microscopic film evolution (i.e., aggregate formation, fractal structure and size). Overall, the proposed multiscale modeling framework provides a mechanistic understanding of the role of molecular interactions in QD particle aggregation and film deposition during temperature-controlled spray coating of QD particles for application in PSCs. Furthermore, this work provides a general platform for multiscale modeling of spray coating of different particle systems and will be incorporated with advanced optimization or process control frameworks to ensure adequate set-point (film thickness and smoothness) tracking in future works.

Literature Cited:

1. Protesescu L, Yakunin S, Bodnarchuk MI, Krieg F, Caputo R, Hendon CH, Yang RX, Walsh A, Kovalenko MV. Nanocrystals of cesium lead halide perovskites (CsPbX₃, X= Cl, Br, and I): novel optoelectronic materials showing bright emission with a wide color gamut. Nano Letters. 2015 Jun 10; 15(6): 3692-6.
2. Chen LC, Tien CH, Tseng ZL, Ruan JH. Enhanced efficiency of MAPbI₃ perovskite solar cells with FAPbX3 perovskite quantum dots. Nanomaterials. 2019 Jan; 9(1): 121.
3. Yuan 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. Sitapure N, Epps R, Abolhasani M, Kwon JS. Multiscale Modeling and Optimal Operation of Millifluidic Synthesis of Perovskite Quantum Dots: Towards Size-Controlled Continuous Manufacturing. Chemical Engineering Journal. 2020 Dec 7: 127905.
5. Peng Z, Doroodchi E, Evans G. DEM simulation of aggregation of suspended nanoparticles. Powder Technology. 2010 Dec 10; 204(1): 91-102.
6. Wang W, Zhang Y, Wu W, Liu X, Ma X, Qian G, Fan J. Quantitative modeling of self-assembly growth of luminescent colloidal CH₃NH₃PbBr₃ The Journal of Physical Chemistry C. 2019 Apr 28;123(20):13110-21.
7. Xu T, Lam ML, Chen TH. Discrete Element Model for Suppression of Coffee-Ring Effect. Scientific Reports. 2017 Feb 20;7(1):1-0.