Nonlinear modeling of equilibrium sorption of selected anionic adsorbates from aqueous solutions on cellulosic substrates. Part 1: model development

A new nonlinear isothermal sorption model, incorporating Donnan equilibrium and electrical neutrality in the classical sorption model of direct dyes onto cellulosic substrates, as model adsorbates, is proposed. The nonlinear isothermal model was used to simulate equilibrium sorption of adsorbates containing ionic charges (z) of −2 to −4 on cellulose adsorbents at various temperature (T) and sodium chloride concentrations ([NaCl]). A detailed analysis of simulation results demonstrates that results based on the nonlinear sorption model highly agree with those based on the log-linear sorption model when the deviation in the concentration of sodium ions in the aqueous solution ([Na⁺] _S ) relative to [NaCl] used in the sorption system is restricted to <5.0%. Compared to the log-linear model, the nonlinear model avoids using graphical techniques that are relatively insensitive for determining important sorption parameters such as the internal accessible volume (V) and the standard affinity associated with sorption (−Δμ°). The nonlinear sorption model was used to examine the correlation of fit for previously reported sorption data. The model parameters V and −Δμ° based on curve fits were used to estimate V for cellulose as well as −Δμ°. The values were found to match those based on the conventional log-linear model when deviations of [Na⁺] _S relative to \( \overline{{[{\text{Na}}^{ + } ]_{S} }} \) were below 5%. The nonlinear model therefore provides a convenient and accurate technique to interpret the sorption of a range of anionic adsorbates on cellulosic substrates.