Liquid-vapor interfaces of patchy colloids

We investigate the liquid-vapor interface of a model of patchy colloids. This model consists of hard spheres decorated with short-ranged attractive sites (“patches”) of different types on their surfaces. We focus on a one-component fluid with two patches of type $A$ and nine patches of type $B$ $(2A9B$ colloids), which has been found to exhibit reentrant liquid-vapor coexistence curves and very low-density liquid phases. We have used the density-functional theory form of Wertheim's first-order perturbation theory of association, as implemented by Yu and Wu [J. Chem. Phys. 116, 7094 (2002)], to calculate the surface tension, and the density and degree of association profiles, at the liquid-vapor interface of our model. In reentrant systems, where $AB$ bonds dominate, an unusual thickening of the interface is observed at low temperatures. Furthermore, the surface tension versus temperature curve reaches a maximum, in agreement with Bernardino and Telo da Gama's mesoscopic Landau-Safran theory [Phys. Rev. Lett. 109, 116103 (2012)]. If $BB$ attractions are also present, competition between $AB$ and $BB$ bonds gradually restores the monotonic temperature dependence of the surface tension. Lastly, the interface is “hairy,” i.e., it contains a region where the average chain length is close to that in the bulk liquid, but where the density is that of the vapor. Sufficiently strong $BB$ attractions remove these features, and the system reverts to the behavior seen in atomic fluids.

Figure 1

(a) X junction $({\epsilon }_{AA}\ne 0$, ${\epsilon }_{BB}\ne 0$, and ${\epsilon }_{AB}=0)$ and (b) Y junction $({\epsilon }_{AA}\ne 0$, ${\epsilon }_{BB}=0$, and ${\epsilon }_{AB}\ne 0)$ formed by patchy colloids with two patches of type $A$ (colored yellow, located at the poles) and nine patches of type $B$ (colored green, located along the equator), which we denote $2A9B$. For simplicity, only one $B$ patch per particle is shown. (Picture courtesy of D. de las Heras.)

Figure 2

Liquid-vapor phase diagram of $2A9B$ patchy colloids for ${\epsilon }_{BB}=0$ and varying $r={\epsilon }_{AB}/{\epsilon }_{AA}$: Here only Y junctions occur. Lines with open symbols correspond to our DFT calculations, and lines with solid symbols to Monte Carlo simulations [16].

Figure 3

DFT liquid-vapor phase diagrams of $2A9B$ patchy colloids for ${\epsilon }_{AB}=0.35{\epsilon }_{AA}$ and several strengths of the $BB$ attraction ${\epsilon }_{BB}$. The presence of X junctions disrupts the reentrance, which for sufficiently large ${\epsilon }_{BB}$ disappears altogether.

Figure 4

DFT liquid-vapor surface tension vs reduced temperature $T/T_c$ for $2A9B$ patchy colloids without $BB$ attraction, ${\epsilon }_{BB}=0$, and varying strengths of the $AB$ attraction ${\epsilon }_{AB}$.

Figure 5

DFT density profiles across the liquid-vapor interface of $2A9B$ patchy colloids without $BB$ attraction, ${\epsilon }_{BB}=0$, and ${\epsilon }_{AB}=0.40{\epsilon }_{AA}$, at four temperatures. Note the interface thickening at low $T$.

Figure 6

DFT $10–90$ liquid-vapor interfacial thickness vs reduced temperature $T/T_c$ for $2A9B$ patchy colloids without $BB$ attraction, ${\epsilon }_{BB}=0$, and varying strengths of the $AB$ attraction ${\epsilon }_{AB}$.

Figure 7

DFT liquid-vapor surface tension vs reduced temperature $T/T_c$ for $2A9B$ patchy colloids with ${\epsilon }_{AB}=0.35{\epsilon }_{AA}$ and varying strengths of the $BB$ attraction ${\epsilon }_{BB}$.

Figure 8

DFT density profiles across the liquid-vapor interface of a fluid of $2A9B$ patchy colloids with ${\epsilon }_{BB}=0.30{\epsilon }_{AA}$ and ${\epsilon }_{AB}=0.35{\epsilon }_{AA}$.

Figure 9

DFT $10–90$ liquid-vapor interfacial thickness vs reduced temperature $T/T_c$ for $2A9B$ patchy colloids with ${\epsilon }_{BB}=0.35{\epsilon }_{AA}$ and varying strengths of the $BB$ attraction ${\epsilon }_{BB}$.

Figure 10

Distance (in units of $\sigma$) between the midpoints of the DFT density profile and $X_A\left(z\right)$ profile for $2A9B$ patchy colloids. For all systems pictured ${\epsilon }_{BB}=0$.