(399c) Molecules to Systems Design of Advanced Membrane Materials and Technologies

The synthesis of many advanced materials in the past three decades have failed to produce a corresponding revolution in sustainable separation applications.^[1] For example, new technologies for carbon capture can take up to 30 years to progress from a laboratory to commercial deployment.^[2] To accelerate technology development, there is a critical need to move away from classical Edisonian iterative methods of materials discovery. Principled and data-driven frameworks will overcome the gaps in knowledge which inhibit the translation of new materials and devices from laboratory scale to sustainable separation technologies. In this talk, we describe our work using superstructure optimization at the systems scale and nonlinear parameter estimation at the materials scale in designing next generation membrane technologies and materials. We highlight how the current work lays the foundation for a holistic molecules-to-infrastructure computational design framework for the development of sustainable separation technologies.^[3]

Relative to conventional technologies, membrane separations have demonstrated significant advantages in sustainability and energy efficiency.^[4] For example, chemically selective separations enabled by polymer membranes have the potential to replace hazardous and toxic solvents used in conventional lithium-ion battery (LIB) recycling technology. However, there is no clear understanding of the interfacial and thermodynamic phenomena underlying the chemically-selective transport mechanisms needed to separate molecules with comparable sizes such as lithium (Li) and cobalt (Co) which hinders the development of membrane materials for this task.^[5] Another challenge is the recovery of high purity products from a membrane separations unit. The formation of salt precipitate layers at the membrane interface when the feed side solution approaches the solubility limit prevents the extraction of high purity products, which also prevents the direct staging of these units.

In the first part of this talk, we demonstrate how a continuous, membrane based diafiltration cascade^[6] enables the recovery of high purity Li and Co rich solutions for a LIB recycling case study at purities comparable with existing technologies. In diafiltration, the effects of salt precipitation encountered while staging membrane units are offset by adding a pure or dilute solvent, known as the dialysate to the feed side of the membrane filtration process. We show how the unique configuration of our system enables the utilization of the retentate side product, which is dilute in Li, to be recycled as dialysate to preceding stages of the process. We highlight how superstructure optimization searches multiple, complex process configurations postulated by the modeler to identify promising applications for emerging materials. We treat flow and concentration of all streams as decision variables in our nonlinear optimization model. We then characterize the Pareto set using an epsilon-constrained method to understand the tradeoffs between purity and recovery objectives for the diafiltration cascade. We observe interesting regions of the Pareto set with unique flow and concentration profiles but having similar recycle strategies. We use this information to discern physical insights into the phenomena governing the underlying process and demonstrate the top-down capabilities of this framework to identify property targets for emerging membrane materials for LIB recycling.

The superstructure optimization framework developed so far uses lumped parameter models in optimizing the diafiltration cascade. In the second part of this talk, we apply parameter estimation and design of experiments formalisms to analyze novel dynamic diafiltration. We use timeseries data to characterize membranes by estimating model parameters governing interfacial and transport phenomena across membranes. We argue that analyzing timeseries data from dynamic experiments will allow for faster characterization of membranes and capture non-equilibrium effects characteristic of the process. Moreover, dynamic modeling and parameter estimation will provide first pass insights into realizing model predictive control for diafiltration systems. We formulate a multiobjective parameter estimation problem, to characterize the trade-offs between minimizing errors for three different experimentally measured quantities (permeate concentration, retentate concentration and timeseries filtration cell mass). We perform localized and Monte Carlo analysis to identify the uncertainty in fitted parameters. Finally, we discuss how to optimize sequential experimental campaigns to elucidate transport and thermodynamic mechanisms that govern multicomponent separations via diafiltration.

We conclude this two-part talk by demonstrating how superstructure optimization and advanced data analytics form the pillars for comprehensive molecules-to-infrastructures computational design framework. We hypothesize that embedding detailed membrane models into the superstructure optimization framework will reveal optimum process network configurations that enable the identification of operating parameters and control strategies that influence the behavior of the diafiltration cascade (bottom-up design). Detailed membrane models will also inform how to engineer materials with desirable properties for specific application requirements (top-down design). Uncertainty information quantified in the statistical learning framework will allow the optimal design of future experiments using techniques such as model-based design of experiments. Finally, we provide brief comments on materials informatics and the ubiquitous role of uncertainty quantification which make up the rest of our holistic framework.

References

[1] Luo, J. & Crittenden, J. C. Nanomaterial Adsorbent Design: From Bench Scale Tests to Engineering Design. Environmental Science & Technology 53, 10537 - 10538 (2019). 10.1021/acs.est.9b04371.

[2] Miller, D. C., Syamlal, M., Mebane, D. S., Storlie, C., Bhattacharyya, D., Sahinidis, N. V., Agarwal, D., Tong, C., Zitney, S. E., Sarkar, A., Sun, X., Sundaresan, S., Ryan, E., Engel, D. & Dale, C. Carbon Capture Simulation Initiative: A Case Study in Multiscale Modeling and New Challenges. Annual Review of Chemical and Biomolecular Engineering 5, 301-323 (2014). 10.1146/annurev-chembioeng-060713-040321.

[3] Eugene, E. A., Phillip, W. A. & Dowling, A. W. Data science-enabled molecular-to-systems engineering for sustainable water treatment. Current Opinion in Chemical Engineering 26, 122-130 (2019). 10.1016/j.coche.2019.10.002.

[4] Phillip, W. A., & Elimelech, M. The Future of Seawater Desalination: Energy, Technology, and the Environment. Science, 333, 6043, 712–717 (2011). 10.1126/science.1200488.

[5] Park HB, Kamcev J, Robeson LM, Elimelech M, Freeman BD. Maximizing the right stuff: the trade-off between membrane permeability and selectivity. Science 356, 1-10 (2017). 10.1126/science.aab0530.

[6] Eugene, E., Phillip, W. & Dowling, A. Material Property Goals to Enable Continuous Diafiltration Membrane Cascades for Lithium-ion Battery Recycling. In Computer Aided Chemical Engineering 47, 469-474 (2019). 10.1016/B978-0-12-818597-1.50075-8.