Layering Theory of Liquids at Solid Interfaces: Interfacial Layering Oscillator Model

TL;DR

The paper tackles interfacial density layering in liquids near solid walls by introducing the Interfacial Layering Oscillator Model (ILOM), a concise second-order ODE that behaves like a damped harmonic oscillator to reproduce oscillatory density profiles with exponential decay. Grounded in a reduced YBG framework and calibrated against MD data for water on hydrophilic and hydrophobic surfaces, ILOM provides parameters that describe amplitude, decay, and wavelength with high computational efficiency and transferability to methanol and LJ-like liquids. The work demonstrates robust agreement with MD across graphene, hBN, and LJ interfaces, establishes scaling relations linking oscillator parameters to wall strength and temperature, and outlines a path to rapid, physics-based predictions of nanoscale interfacial transport properties. By bridging classical statistical mechanics with a tractable continuum description, ILOM offers a versatile tool for nanoscale fluid mechanics, materials design, and interfacial engineering. Key contributions include a damped-oscillator formulation of interfacial density, parameterizations that encode wall-fluid interactions, and validated applicability to multiple liquids and surface chemistries, enabling efficient exploration of interfacial phenomena in nanoconfined environments.

Abstract

The structural organization of liquids near solid interfaces profoundly influences phenomena such as wettability, nanofluidic transport, and interfacial heat transfer. This study introduces the Interfacial Layering Oscillator Model (ILOM), a concise, semi-phenomenological framework that accurately captures the oscillatory density profiles of liquids adjacent to planar solid surfaces. By deriving a second-order differential equation rooted in classical statistical mechanics and calibrated with molecular dynamics simulations, ILOM predicts the amplitude, decay rate, and wavelength of interfacial density layering with exceptional computational efficiency. This versatile model applies to both hydrophilic and hydrophobic surfaces and extends to liquids beyond water, including methanol, providing valuable insights into critical interfacial properties that advance nanoscale fluid mechanics and material design.

Figures (5)

• Figure 1: Illustration of the MD model configurations for water over graphene and hexagonal boron nitride (hBN) surface.
• Figure 2: Density profiles of water near graphene (a) and hBN (b) surfaces, each exhibiting three distinct layers. Blue square dots represent the SHO model Eq.\ref{['eq:5']}, green triangular dots the SHO1 model, and red circle dots MD simulation data for comparison. The color bar indicates the density distribution across the channel, measured from the graphene wall.
• Figure 3: Density plot of the density variation according to the SHO solution Eq.\ref{['eq:5']} for (a) $\gamma_0 = 0.80 \, \text{Å}^{-1}$, $\phi = 1.356\pi$, and $h_s = 0.97$, with $\omega_d$ ranging from 1.5 to 4.5 $\text{Å}^{-1}$ and $z - z_0$ from 0 to 8 $\text{Å}$; and (b) $\omega_d = 3.5 \, \text{Å}^{-1}$, $\phi = 1.356\pi$, and $h_s = 0.97$, with $\gamma_0$ ranging from 0.4 to 1.5 $\text{Å}^{-1}$ and $z - z_0$ from 0 to 8 $\text{Å}$. Panel (c) shows the effects of $\phi$ for $\gamma_0 = 0.80 \, \text{Å}^{-1}$, $h_s = 0.97$, and $\omega_d = 3.5 \, \text{Å}^{-1}$. The bottom panels (d) and (e) present the front view of (a) and (b) for a narrower range of $\omega_d$ and $\gamma_0$ respectively.
• Figure 4: (a) Illustration of the molecular dynamics (MD) model configurations for methanol over graphene. (b) Density profiles of methanol near graphene surfaces. Blue square dots represent the SHO model Eq.\ref{['eq:5']}, green triangular dots the SHO1 model, and red circle dots MD simulation data for comparison. The color bar indicates the density distribution across the channel, measured from the graphene wall.
• Figure 5: Normalized density profiles for a LJ liquid over graphene. Blue square dots represent the SHO1 model Eq.\ref{['eq:9']}, green triangular dots the SHO2 model , and red circle dots MD simulation data for comparison. Optimized parameters from table \ref{['tab:params_LJ']} align well with the first two peaks.