Interactions between amphoteric surfaces with strongly overlapping double layers.

The entropic repulsion between strongly overlapping electrical double-layers from two parallel amphoteric plates is described via the Donnan equilibrium in the limit of zero electric field. The plates feature charge-regulation and the inter-plate solution is in equilibrium with a reservoir of a monovalent electrolyte solution. A finite electric potential and disjoining pressure is found at contact between the plates, due to a complete discharging of the plates. For low potentials, the decay of potential and pressure is fully governed by a characteristic length scale and the contact potential. Additionally, for large separations we find a universal inverse square decay of disjoining pressure, irrespective of the contact potential. The results of the Donnan theory show quantitative agreement with self-consistent field computations that solve the full Poisson equation.

Algebraic repulsions between charged planes with strongly overlapping electrical double layers.

Langmuir's disjoining pressure between two flat, charged planes was calculated analytically for strongly overlapping double layers in the limit of zero electric field between the planes. The resulting repulsion has a long-range algebraic decay that stems from the thermodynamic equilibrium between homogeneously distributed interplate ions and ions in the surrounding electrolyte reservoir. Together with the van der Waals attraction, the repulsion forms the zero-field pendant of the exponentially screened DLVO potential, a pendant that is always repulsive at large plate-plate distances. The experimental occurrence of algebraic repulsions can be simply predicted from surface charge density and ionic strength.

A thermodynamic gauge for mobile counter-ions from colloids and nanoparticles.

A thermodynamic equilibrium sensor is proposed that measures the ratio of the number of elementary charges z to the mass m of charged solutes such as charged colloids and nanoparticles. The sensor comprises a small, membrane-encapsulated salt solution volume that absorbs neutral salt molecules in response to the release of mobile counter-ions by charge carriers in the surrounding suspension. The sensor state emerges as a limiting case of the equilibrium salt imbalance, and the ensuing osmotic pressure difference, between arbitrary salt and suspension volumes. A weight concentration of charge carriers c is predicted to significantly increase the sensor's salt number density from its initial value ρs,0 to ρRs, according to the relation (ρRs/ρs,0)(2)-1=zc/mρs,0, under the assumption that the mobile ions involved in the thermodynamic sensor-suspension equilibrium are ideal and homogeneously distributed.