Optimization\nof Reactive\nInk Formulation for Controlled\nAdditive Manufacturing of Copolymer Membrane Functionalization

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