(744e) Multiscale Modelling and Model Predictive Control of CsPbBr3 Quantum Dots Production: A Step Towards on-Demand Smart-Nanomanufacturing

Solution-processed inorganic lead halide perovskite quantum dots (QDs) have recently garnered a lot of attention as a promising semiconducting material for applications in next-generation solar cells, displays, and photocatalysis.¹ Particularly, cesium lead bromide (CsPbBr₃) QDs, due to its near-unity photoluminescence quantum yield (PLQY), has received significant attention. The optoelectronic properties of CsPbBr₃ QDs are majorly dictated by their bandgap energy (related to their size) and PLQY (related to surface passivation and defects). Thus, it is of paramount importance to fine-tune the size and surface passivation of CsPbBr₃ QDs for the targeted optoelectronic devices. Furthermore, device-level applications demand a fast and continuous production of application-ready QDs. However, most of the published work on perovskite QDs are pertaining to the conventional flask-based synthesis techniques.² Despite the ease of assembly and operation, the batch synthesis strategies are not a viable solution for mass production of such high-priority semiconducting materials because of (a) batch-to-batch variation, (b) scale-up challenges due to irreproducible and uncontrollable mixing and mass transfer characteristics, and (c) the fast formation kinetics of perovskite QDs (typically in the order of seconds). Hence, a continuous synthesis platform with precise size-tuning and prediction abilities for large-scale QD production is highly coveted in the materials community.

Recently, an automated microfluidic platform for continuous production and mass transfer-controlled size-tuning of CsPbBr₃ QDs was demonstrated.³ A continuous size-tuning of CsPbBr₃ QDs in the range of 7-11 nm was achieved by manipulating the precursors mixing rate that was controlled by the average flow velocity in the microreactor. Interestingly, increasing the flow velocity (i.e., faster mixing rates) resulted in a blue shift (i.e., smaller CsPBr₃ QDs). Furthermore, it was observed that the concentration of the surface ligands (oleic acid) played a vital role in CsPbBr₃ synthesis by forming a loosely bound ligand shell around the QD surface.⁴ The results of our previous studies also suggest that the CsPbBr₃ QDs do not follow classical crystallization models and need a more comprehensive modeling effort.⁵ Such fundamental understanding will be a crucial factor for large-scale on-demand nanomanufacturing of CsPbBr₃ QDs with designer optoelectronic properties.

The goal of this work is to address the above-mentioned knowledge gap in the perovskite QD research field by proposing a multiscale model for plug-flow crystallizer (PFC). Specifically, the macroscopic phase of PFC was modelled to describe the dynamic spatio-temporal evolution of concentration and QD size using differential mass and energy balance equations (MEBEs). The discretized MEBEs were integrated with the proposed kinetic Monte Carlo simulation (KMC) to formulate a high-fidelity multiscale model; the KMC, based upon solid-on-solid crystal model, describes the physics behind QD synthesis (viz., attachment and mass-transfer of ligand and desorption of the ligand) and depends on the local environment and location of the crystal. Furthermore, for model validation, precise time-series QD size data for different precursor mixing rate scenarios are generated.³ The model predictions are in excellent agreement with the experimental results. Lastly, a model predictive controller (MPC) was designed to produce QDs of the desired size in the presence of disturbances. To this end, precursors flowrate and concentration were used as manipulated inputs to the PFC system. Overall, this work will be major leap towards on-demand continuous smart-nano-manufacturing.