# Molecular Simulation Study on the Wettability of a Surface Texturized with Hierarchical Pillars

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Results and Discussion

## 3. Simulation Methods

^{−1}and 3.166 Å, respectively. The interactions between carbon and water oxygen atoms were also modeled by using the LJ potential with ${\epsilon}_{ij}$ is 0.4389 kJ mol

^{−1}and ${\sigma}_{ij}$ is 3.190 Å. The long-range Coulomb interactions between point charges were treated with the particle–particle-particle–mesh (PPPM) method [35]. We cut off both the LJ and Coulomb interactions at a distance of 12.0 Å.

^{2}), which constrains D to a target value. The initial 0.2 ns was discarded for equilibration. The PMF profile was extracted using the weighted histogram analysis method [40,42]. Finally, D was converted to the filling fraction F defined as:

_{CB}and D

_{WZ}were Ds corresponding to the CB and WZ states, respectively. By construction, F = 0 and 1 for the CB and WZ states, respectively. The CB and WZ states were defined as those located at the local or global minima of the PMF curve. The PMF calculation method described above was implemented by using the LAMMPS combined with the PLUMED package [42].

_{2}O molecules (14.0 nm in diameter) was equilibrated by running an NVT simulation at 300 K for 2.0 ns. The equilibrated droplet was then positioned 1.0 nm above a pillared or flat surface. A 16.0 ns-long NVT simulation was run for the water droplet. The initial 1.0 ns was discarded for equilibration. The CA was calculated by employing the method of Khalkhali et al. [43]: in this method, a convex hull algorithm was used to approximate the liquid–vapor interface of a droplet as a collection of small interconnected triangles. The CA was further obtained from the surface normal vectors of these triangles. This method obviates construction of the density profile of water by means of the three-dimensional binning of molecules, which can be computationally intensive. Additionally, the shape of a liquid droplet does not have to be assumed in this method. The computational efficiency of this method is much better than that of a conventional method, especially for a big droplet. The present large droplet, made of 47,940 water molecules, prevents the line tension effect, which provides an increased CA with decreasing the size of a droplet [33,44].

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Sample Availability

## References

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**Figure 1.**(

**a**) Periodic simulation cell of the present surface texturized with hierarchical pillars. The height, width, and interpillar spacing of major pillars are represented by H, W, and S, respectively. On top of each major pillar, we constructed multiple minor pillars of h, w, and s in height, width and interpillar spacing, respectively. (

**b**) Schematic diagram for four distinct wetting states possible for a surface texturized hierarchical pillars: CB-CB, WZ-WZ, CB-WZ, and WZ-CB states.

**Figure 2.**Free energy profiles of the CB-to-WZ wetting transitions of the surfaces texturized with nonhierarchical pillars. At the top, the PMF is plotted vs. the filling level F for surfaces with pillars with heights Hs of 8.9, 10.7, 12.5, 14.3, and 19.6 Å. The transition states, defined as the maxima in the PMF curves, are marked as symbols. The density profiles of water at the transition states are shown at the bottom, marked as different symbols in the PMF curves. In each panel, two cross sections of the density profile taken along the XZ and YZ planes are drawn as color maps.

**Figure 3.**Free energy profiles for the wetting transitions of surfaces with the hierarchical pillars. The PMF is plotted vs. the filling level F for minor pillars with relative heights, h*s (h* = h/H), of 0.0, 0.5 and 0.75. The representative snapshots of water at the transition states, marked as different symbols in the PMF curves, are shown at the bottom. In all the cases shown here, s* is fixed to 0.231.

**Figure 4.**Free energy profiles for the wetting transitions of surfaces patterned with hierarchical pillars. The PMF is plotted vs. the filling level F for minor pillars s* = 0.0, 0.23 and 0.69. The representative snapshots of water at the transition states, marked as different symbols (numbers in triangles or squares) in the PMF curves, are shown in the bottom. In all three cases, h* is fixed to 0.25.

**Figure 5.**Variation in the CA of a water droplet with changing the texture of a surface. The CAs are shown for the flat surface and the surfaces patterned with nonhierarchical and hierarchical pillars. We set H = 14.3 Å and S = 23.2Å for the pillared surfaces. In the case of the surface with hierarchical pillars, h* = 0.5 and s* = 0.23.

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**MDPI and ACS Style**

Kim, K.; Choi, S.; Zhang, Z.; Jang, J.
Molecular Simulation Study on the Wettability of a Surface Texturized with Hierarchical Pillars. *Molecules* **2023**, *28*, 4513.
https://doi.org/10.3390/molecules28114513

**AMA Style**

Kim K, Choi S, Zhang Z, Jang J.
Molecular Simulation Study on the Wettability of a Surface Texturized with Hierarchical Pillars. *Molecules*. 2023; 28(11):4513.
https://doi.org/10.3390/molecules28114513

**Chicago/Turabian Style**

Kim, Kiduk, Seyong Choi, Zhengqing Zhang, and Joonkyung Jang.
2023. "Molecular Simulation Study on the Wettability of a Surface Texturized with Hierarchical Pillars" *Molecules* 28, no. 11: 4513.
https://doi.org/10.3390/molecules28114513