Molecular dynamics study of the translation and rotation of amphiphilic Janus nanoparticles at a vapor-liquid surface

We study the effects of heterogeneity on interfacial pinning and hydrodynamic drag using molecular dynamics (MD) simulations of Janus nanospheres at a liquid-vapor interface. We construct the free-energy landscape for this system, both in the continuum approximation using surface tensions and the flat-interface approximation, and atomistically using MD and thermodynamic integration. The results of the two methods differ in detail due to interfacial distortion and finite width, as well as thermal fluctuations, and only the MD landscape is consistent with simulations of a nanosphere approaching the interface from the liquid or vapor side. When dragged along an interface, these Janus particles exhibit a velocity-dependent tilt accompanied by a weak variation in drag force, but never an enhancement of the drag force beyond the value when fully immersed. This velocity dependence arises when the interface is pinned at heterogeneities and prevents the particle from rotating, and similar behavior is observed for homogeneous but nonspherical particles. The occurrence of different particle orientations having different drag coefficients may lead to an apparent violation of the Stokes-Einstein relation.

Figure 1

Computational cell showing the tetrameric liquid (“1”), the fcc lattice base (“4”), and the Janus nanoparticle consisting of “2” and “3” at the fluid interface.

Figure 2

(a) Liquid density profile and (b) variation in liquid density near an interfacial homeogeneous nanoparticle with $c_{12}=0.9$ [47].

Figure 3

Continuum calculation of the free-energy landscape of a Janus particle as a function of orientation $\theta$ and position $z_p$ from the solid free energies of the Janus faces, assuming a flat fluid interface. (a) Geometry of the calculation; (b) free-energy surface for a 1.2/0.7 Janus particle.

Figure 4

Continuum and MD landscape at the fixed orientations along $\theta =0$ and $\theta ={180}^{\circ }$ for the 1.2/0.7 and 1.2/0.8 Janus particles.

Figure 5

Molecular free-energy surface and numerical experiments for a 1.2/0.7 Janus particle. (a) Free-energy surface, computed from thermodynamic integration. (b) Particle released at $0^{\circ }$ in vapor and not allowed to rotate, at times 0, 500, 1000, 2500, and $5000\tau$. (c) Particle released at $0^{\circ }$ in liquid and not allowed to rotate, at times 0, 500, 1000, and $5000\tau$. The last frame shows the configuration at the same final time when the particle is free to rotate. (d) Particle released at $0^{\circ }$ in vapor with rotation allowed, at times 500, 700, 800, 900, and $2500\tau$. (e) Particle released at ${180}^{\circ }$ in vapor and allowed to rotate, at times 0, 300, 600, 1000, and $5000\tau$.

Figure 6

Deformations of the liquid-vapor interface in the presence of a 1.2/0.7 Janus particle. Intermediate states during thermodynamic integration at (a) $z_p=46.1\sigma$ and $\theta ={180}^{\circ }$, (b) $z_p=31\sigma$ and $\theta ={180}^{\circ }$, and (c) $z_p=38\sigma$ and $\theta ={120}^{\circ }$.

Figure 7

Molecular free-energy surface and numerical experiments for a 1.2/0.8 Janus particle. (a) Free-energy surface computed from thermodynamic integration. (b) Particle released at $0^{\circ }$ in vapor and not allowed to rotate, at times 300, 500, 800, 1000, and 5000 $\tau$.

Figure 8

A three-banded particle with a small central wettability.

Figure 9

Top: Snapshots of Janus spheres pulled from right to left along an interface at speeds (left to right) 0.01, 0.025, 0.5, 0.075, and $0.1\sigma /\tau$.

Figure 10

Top: Probability distribution of particle orientation when pulled right to left along an interface at speeds 0.01 (magenta), 0.025 (cyan), 0.5 (blue), 0.075 (green), and $0.1\sigma /\tau$ (red).

Figure 11

Average mean-square displacement in the plane of the interface for a 1.2/0.8 Janus particle.

Figure 12

Hourglass-shaped homogeneous particle with atoms interacting with liquid with a single interaction $c_{12}=0.8$.