A mathematical analysis of carbon fixing materials that grow, reinforce, and self-heal from atmospheric carbon dioxide

Abstract

Carbon fixing materials are a new class of self-healing, self-reinforcing materials we have introduced that utilize ambient CO₂ to chemically add to an ever extending carbon backbone. This class of materials can utilize biological or non-biological photocatalysts and support a wide range of potential backbone chemistries. However, there is no analysis to date that describes their fundamental limits in terms of chemical kinetics and mass transfer. In this computational study, we employ a reaction engineering, and materials science analysis to answer basic questions about the maximum growth rate, photocatalytic requirements and limits of applicable materials. Our proposed mathematical framework envelops three main functions required for carbon fixing materials: (1) adsorption of CO₂ from air, (2) photocatalytic reduction of CO₂ into selected monomers, and (3) polymerization of CO₂-derived monomers. First, by performing a Damköhler number analysis, we derive criteria for the cross over from kinetic control to mass transfer limited growth, setting upper limits on performance of a potential photocatalyst. Next, we analyze photocatalytic reduction of CO₂ to single carbon products, using known catalytic pathways and kinetic data. We identify formaldehyde as a C1 intermediate having unique potential for incorporation into the material backbone of carbon fixing materials. As an example, we find that a diamond-shaped reaction network graph for CO₂ reduction, passing through CO and HCOOH intermediates, accurately describes kinetic data for cobalt-promoted TiO₂ nanoparticles at room temperature and 1 atm CO₂. Finally, as an applied case study, we consider and analyze the example of a carbon fixing poly(oxymethylene) system with embedded catalyst promoting the photocatalytic reduction of CO₂ to formaldehyde. The latter then trimerizes to a trioxane monomer which subsequently polymerizes to polyoxymethylene. This reaction engineering analysis introduces benchmarks for carbon fixing materials with respect to achievable rates of photocatalysis, adsorption, and polymerization. These results should prove valuable for the design, evaluation, and benchmarking of this emergent and new class of environmentally sustainable materials.