Donnan potential of dilute colloidal dispersions: Monte Carlo simulations

Donnan equilibrium between a salt-free colloidal dispersion and an electrolyte solution has been investigated by Monte Carlo simulations. The Donnan potential is directly calculated by considering two compartments separated by a semipermeable membrane. In order to understand the role played by colloid–ion interactions, the influences of colloidal characteristics, including particle size R, intrinsic particle charge Z  , counterion valency zczc, and concentration cpcp, on Donnan potential ΨDΨD and effective charge ZeffZeff are examined. Our simulations show that the electroneutrality condition is not followed in both compartments and the Donnan potential arises due to the net charge density. The Donnan potential grows by increasing cpcp and ZeffZeff and by decreasing dielectric constant εrεr, i.e., ΨD∼Zeffcp/εrΨD∼Zeffcp/εr approximately. Note that the effective charge varies with R,Z,cp,εrR,Z,cp,εr and zczc as well. When the salt concentration is increased, the net charge density is lowered and thus the Donnan potential decays accordingly. The validity of the classical theory based on the Nernst equation and the electroneutrality assumption is also examined. In general, the simulation results at high-salt condition can be well represented by such mean-field theory.

Graphical abstractSchematics of a chamber at Donnan equilibrium. The ion-selective membrane is permeable to small ions and impermeable to charged colloids, the exchange of small ions results in an uneven distribution of ionic solute concentration in the two sides of the membrane.Figure optionsDownload full-size imageDownload as PowerPoint slide