Equilibrium adsorption and self-assembly of patchy colloids in microchannels

A theory is developed to describe the equilibrium adsorption and self-assembly of patchy colloids in microchannels. The adsorption theory is developed in classical density functional theory, with the adsorbed phase and fluid phase chemical potentials modeled using thermodynamic perturbation theory. Adsorption of nonpatchy colloids in microchannels is typically achieved through nonequilibrium routes such as spin coating and evaporation. These methods are required due to the entropic penalty of adsorption. In this work we propose that the introduction of patches on the colloids greatly enhances the temperature dependent and reversible adsorption of colloids in microchannels. It is shown how bulk fluid density, temperature, patch size, and channel diameter can be manipulated to achieve the adsorption and self-assembly of patchy colloids in microchannels.

Figure 1

Representation of two patchy colloids interacting with the potential equations (1, 2, 3, 4).

Figure 2

Patchy colloids interacting in a 1D channel. Short arrows represent orientation vector and long arrow represents $z$ axis. Colloids are allowed to explore all Euler orientation angles (orientation vectors may point into or out of page).

Figure 3

Theory results for patchy colloids with ${\theta }_c={10}^{\circ }$ in a cylindrical channel of diameter $1.5d$, versus fluid phase density. Top: selectivity defined by Eq. (21). Bottom: Solid curves give average adsorbed phase cluster size, while dashed curves give fluid phase associated cluster size.

Figure 4

Adsorbed phase order parameters for same system as Fig. 3.

Figure 5

Theory results for patchy colloids at a reduced association energy ${\varepsilon }^{*}=12$ and bulk fluid phase density ${\rho }_b=0.3d$ [3] versus cylindrical channel diameter at various patch sizes. Top: selectivity defined by Eq. (21). Symbols represent Monte Carlo simulation results for hard spheres [31]. Bottom: Solid curves give average adsorbed phase cluster size, while dashed curves give fluid phase associated cluster size.

Figure 6

Diagram of large patch (top) and small patch (bottom) patchy colloid fluids interacting with a cylindrical channel (parallel lines). Large patch colloids remain depleted in the channel due to strong association in the bulk, while small patch colloids adsorb in the channel due to weak association in the bulk.