Optimization of Reactive Ink Formulation for Controlled Additive Manufacturing of Copolymer Membrane Functionalization

Multifunctional, nanostructured membranes hold immense promise for overcoming permeability-selectivity trade-offs and enhancing membrane durability in challenging molecule separations. Following the fabrication of copolymer membranes, additive manufacturing technologies can introduce reactive inks onto substrates to modify pore wall chemistries. However, large-scale implementation is hindered by a lack of systematic optimization. This study addresses this challenge by elucidating the membrane functionalization mechanisms and optimal manufacturing conditions using a copper(I)-catalyzed azide-alkyne cycloaddition (CuAAC) "click" reaction. Leveraging a data science toolkit (e.g., nonlinear regression, uncertainty quantification, identifiability analyses, model selection, and design of experiments), we developed two mathematical models: (1) algebraic equations to predict equilibrium concentrations after preparing reactive inks by mixing copper sulfate, ascorbic acid (AA), and an alkynyl-terminated reactant; and (2) reaction-diffusion partial differential equations (PDEs) to describe the functionalization process. The ink preparation chemistry with side reactions was validated through pH and UV-vis measurements, while the diffusion and kinetic parameters in the PDE model were calibrated using time-series conversion of the azide moieties inferred from Fourier-transform infrared spectroscopy. This modeling framework avoids redundant experimental efforts and offers a functionalization protocol for scaling up designs. Ink optimization problems were proposed to reduce the use of expensive and environmentally insulting ink materials, i.e., Cu(II), while ensuring the desired chemical distributions. With optimal ink formulation Cu(II)/AA/alkyne = 1:1:2 identified, we uncovered trade-offs between Cu(II) usage and functionalization time; for example, in continuous roll-to-roll manufacturing with a conserved functionalization bath setup, our optimal operational conditions to achieve ≥90% functionalization enable at least a 20% reduction in total copper investment compared to previous experimental results. The data science-enabled ink optimization framework is extendable for on-demand multifunctional membranes in numerous future applications such as metal recovery from wastewater and brine.