Continuous Convective Assembling of Fine Particles into Two-Dimensional Arrays on Solid Surfaces
by Lidiya Mishchenko
Antony S. Dimitrov and Kuniaki Nagayama, Langmuir 1996, 12, 1303-1311
Convective assembly, colloid, disjoining pressure, force balance, hyrdostatic pressure, dynamic equilibrium
"Forming regular textures of an arbitrary size on smooth solid surfaces is the challenge of future technology to produce new types of optical gratings, optical filters, antireflective surface coatings, selective solar absorbers, data storage, and microelectronics. Here we present a novel approach to form such sophisticated textures: controlling the growth of particle arrays on smooth and wettable solid surfaces. The obtained centimeter-size polycrystalline monolayer films consist of closely packed fine particles. Coloring of the monolayer which arises from the light diffraction, interference, and scattering exclusively inherent in textured films shows the size of the differently oriented crystal domains building the film. The results show that the higher the particle monodispersity, the lower the particle volume fraction, and the higher the environmental humidity, the larger the size of the forming domains."
Soft Matter Example
The theory in this paper serves as a seminal work for understanding convective colloidal assembly. The basic principle is that if a wetting vertical substrate is withdrawn from a solution of colloidal crystals at a particular rate (as calculated in the paper), one may be able to deposit a monolayer of colloids on the substrate (with deposition at the meniscus).
No later paper seems to contradict the basic principle behind this assembly. There have been papers, however, that go into more detail about the fluid flow responsible for the convective formation of colloidal crystals and how this flow results in fcc packing. Also, some papers did not use the withdrawal method employed here to create monolayers, but instead left the substrate in the suspension, and created multilayer colloidal crystals (through pure evaporative assembly).
The basic theory behind this convective flow of colloids to the meniscus involves a simple force balance.
If the system (meniscus) is in equilibrium with the surrounding air (i.e. the surrounding air is saturated with water), then the forces within the thin wetted film shown in Figure 1 balance.
where Pi is the sum of van der Waals and electrostatic disjoining pressures that the colloids/thin film experince (as they interact with the substrate), Pcp is the capillary pressure due to the curvature of the liquid surface between neighboring colloids in the film (see the inset in Figure 1, this incorporates the concept of surface tension into the equation), Pc is a reference capillary pressure (0 if compared to the horizontal surface of the bulk suspension), Ph is the hydrostatic pressure, hc is the height relative to horizontal water surface, delta-rho is the density difference between the suspension and the surrounding gas atmosphere, and g is gravity. So hydrostatic pressure is trying to pull the film down, and the surface tension is keeping the film up (as we've seen before).
As evaporation begins, the right side of the equation remains relatively constant (since evaporation from the bulk has much less impact than evaporation from a thin film, so hc remains constant). The left side of the equation changes, however, due to the increase of capillary foces between neighboring colloids as the water evaporates. Due to the thinning of the film, disjoining forces also increase (since this is a stable, wetting film, i.e. the derivative of pressure with respect to thickness is negative). Thus, away from equilibrium (when the air around the meniscus is not saturated with water), there is a pressure gradient from the suspension to the wetting film due to water evaporation:
The argument is right, though maybe the language is a little sloppy. The "increase" in capillary and disjoining pressures actually mean an increase of a negative pressure. The menisci formation actually creates lower pressure in the film, and the increasing disjoining/repulse force simply means that the film wants to be a certain thickness (not less). Thus, an inflow of water from the bulk would result in a less "strained" system.
The paper then goes on (with the use of balancing of fluxes) to figure out the rate of deposition of the colloids and how fast one has to withdraw the substrate from the suspension to deposit a monolayer film.