# Statics and Dynamics of Polymeric Droplets on Chemically Homogeneous and Heterogeneous Substrates

## TL;DR

This study uses molecular dynamics simulations to analyze how polymer droplets behave on striped surfaces, revealing how surface heterogeneity affects equilibrium contact angles, slip length, and droplet motion under force.

## Contribution

It provides a detailed molecular-level understanding of droplet statics and dynamics on chemically heterogeneous substrates, including the effects of stripe width on contact angle and motion.

## Key findings

- Cassie-Baxter equation approximates equilibrium contact angle for small stripes.
- Damping increases with stripe width, reaching a plateau.
- Droplet velocity under force depends on stripe size, viscosity, and slip length.

## Abstract

We present a molecular dynamics study of the motion of cylindrical polymer droplets on striped surfaces. We first consider the equilibrium properties of droplets on different surfaces, we show that for small stripes the Cassie-Baxter equation gives a good approximation of the equilibrium contact angle. As the stripe width becomes non-negligible compared to the dimension of the droplets, the droplet has to deform significantly to minimize its free energy, this results in a smaller value of the contact angle than the continuum model predicts. We then evaluate the slip length, and thus the damping coefficient as a function of the stripe width. For very small stripes, the heterogeneous surface behaves as an effective surface, with the same damping as an homogeneous surface with the same contact angle. However, as the stripe width increases, damping at the surface increases until reaching a plateau. Afterwards, we study the dynamics of droplets under a bulk force. We show that if the stripes are large enough the droplets are pinned until a critical acceleration. The critical acceleration increases linearly with stripe width. For large enough accelerations, the average velocity increases linearly with the acceleration, we show that it can then be predicted by a model depending only the size of droplet, viscosity and slip length. We show that the velocity of the droplet varies sinusoidally as a function of its position on the substrate. On the other hand, for accelerations just above the depinning acceleration we observe a characteristic stick-slip motion, with successive pinnings and depinnings.