Isotherm model for moisture-controlled CO₂ sorption

Moisture-controlled sorption of CO₂, the basis for moisture-swing CO₂ capture from air, is a novel phenomenon observed in strong-base anion exchange materials. Prior research has shown that Langmuir isotherms provide an approximate fit to moisture-controlled CO₂ sorption isotherm data. However, this fit still lacks a governing equation derived from an analytic model. In this paper, we derive an analytic form for an isotherm equation from a bottom-up approach, starting with a fundamental theory for an alkali liquid. In the range of interest relevant to CO₂ capture from air, an isotherm equation for an alkali liquid reduces to a simple analytic form with a single parameter, K_eq. In the limit K_eq ≫ 1, a 2nd order approximation simplifies to a Langmuir isotherm that, however, deviates from experimental data. The isotherm theory for an alkali liquid has been generalized to a strong-base anion exchange material. In a strong-base anion exchange material, water concentration inside a sorbent, [H₂O], is not large enough to be regarded as constant, which allows us to extend K_eq to K_eq(AEM)eff = K_eq(AEM) × [H₂O]⁻ⁿ according to the law of mass action. The final isotherm formula has been validated by experimental data from the literature. For a moisture-controlled CO₂ sorbent, K_eq(AEM)eff varies significantly with moisture content of the sorbent. Depending on moisture level, the observed K_eq(AEM)eff in a specific sorbent ranges from a few times to a few thousand times the value of K_eq of a 2 mol L⁻¹ alkali liquid.