Surface Pressure Isotherm for a Monolayer of Charged Colloidal Particles at a Water/Nonpolar-Fluid Interface: Experiment and Theoretical Model

Abstract

Monolayers from electrically charged micrometer-sized silica particles, spread on the air/water interface, are investigated. Because of the electrostatic repulsion, the distances between the particles are considerably greater than their diameters, i.e., we are dealing with nondensely packed interfacial layers. The electrostatic repulsion between the particles occurs through the air phase. Surface pressure vs area isotherms were measured by Langmuir trough, and the monolayers' morphology was monitored by microscope. The mean area per particle is determined by Delaunay triangulation and Voronoi diagrams. In terms of mean area, the surface pressure for monolayers from polydisperse and monodisperse particles obeys the same law. The experiments show that Π ∝ L(-3) at large L, where Π is the surface pressure and L is the mean interparticle distance. A theoretical cell model is developed, which predicts not only the aforementioned asymptotic law but also the whole Π(L) dependence. The model presumes a periodic distribution of the surface charge density, which induces a corresponding electric field in the air phase. Then, the Maxwell pressure tensor of the electric field in the air phase is calculated and integrated according to the Bakker's formula to determine the surface pressure. Thus, all collective effects from the electrostatic interparticle interactions are taken into account as well as the effects from the particle finite size. By evaporation of water, the particle monolayers are deposited on a solid substrate placed on the bottom of the trough. The electrostatic interparticle repulsion is strong enough to withstand the attractive lateral capillary immersion forces that are operative during the drying of the monolayer on the substrate. The obtained experimental results and the developed theoretical model can be useful for prediction and control of the properties of nondensely packed interfacial monolayers from charged particles that find applications for producing micropatterned surfaces.