Simulating Polydisperse Polymer Adsorption onto Porous Substrates

Simulated adsorption isotherms that describe the irreversible binding of cationic polydisperse polymers onto anionic porous wood pulp fibers were used to relate the physicochemical properties of the polymers and fibers to five attributes of both simulated and experimental isotherms. The analysis is complicated because the lower molecular weight fractions of the adsorbing polymer access more fiber surface area compared to the larger chains. A key assumption is that Γ = λ·ssa = CP·D, where Γ (mg/g) is the amount of adsorbed polymer, λ (mg/m²) is the coverage, ssa (m²/g) is the accessible specific surface area, CP is the cumulative polymer chain length probability, and D is the corresponding polymer dose. The polymers are assumed to have a log–normal chain length distribution characterized by a mean, n_m, and a coefficient of variation, cv. The final polymer property is the Mark–Houwink exponent β. The fiber’s accessible specific surface area, ssa, was assumed to be a power-law function of the adsorbing polymer chain length. This power law is described by three properties: the slope, the ssa of the exterior fiber surfaces, and the corresponding polymer chain length. Simulated isotherms exhibited the general features of published isotherms. The simulations indicated the links between five isotherm attributes and six simulated isotherm physical properties. Comparisons with published adsorption data supported this approach.