[Paper Review] Interaction between point charges, dipoles and graphene layers

F. Guinea, Niels R. Walet|arXiv (Cornell University)|May 26, 2016

Graphene research and applications3 citations

TL;DR

This paper develops a theoretical model for the interaction between point charges, dipoles, and graphene layers using linear response and Thomas-Fermi approximations. It shows that graphene acts as an imperfect conductor with finite dielectric response, inducing image charges that align molecular dipoles perpendicularly to the layer; for water molecules near graphene, this interaction energy exceeds thermal energy at room temperature, significantly influencing confined systems like water in van der Waals heterostructures.

ABSTRACT

We analyse the interaction between charges and graphene layers. The electric polarisability of graphene induces a force, that can be described by an image charge. The analysis shows that graphene can be described as an imperfect conductor with a finite dielectric constant, $ε_r$, for weak coupling, and it behaves as a metal for strong fields. As a consequence, the interaction between polar molecules and graphene layer(s) tends to align the molecular dipole along the direction normal to the graphene, and quantitative estimates of the energy gain are given The strength of this interaction can be sufficient to overcome thermal effects when the molecule is close to the layer, even at room temperature. Hence, boundary effects play a significant role in determining the structure of systems such as water confined in atomically narrow van der Waals heterostructures.

Motivation & Objective

• To develop an effective model for long-range electrostatic interactions between charges/dipoles and graphene layers, avoiding full DFT complexity.
• To quantify the role of graphene's polarizability in confining polar molecules, especially in van der Waals heterostructures.
• To determine whether image charge forces from graphene can overcome thermal fluctuations and dominate molecular orientation.
• To provide a quantitative estimate of the energy gain from dipole alignment normal to the graphene surface.
• To establish a framework applicable to other dipolar molecules and multilayer graphene systems.

Proposed method

• Uses linear response theory and the Thomas-Fermi approximation to model screening of point charges and dipoles near a graphene layer.
• Derives the induced potential via the polarizability response function, treating graphene as a 2D medium with finite dielectric constant.
• Applies the image charge method in both weak-coupling (ZαG ≪ 1) and strong-coupling (ZαG ≳ 1) regimes, showing graphene behaves as a metal under strong fields.
• Solves coupled equations for bilayer graphene to compute the total screening potential and image charge effects in momentum space.
• Reconstructs the full potential using Fourier transforms and derives expressions for the effective potential in terms of q∥ and z.
• Generalizes results to unequal Fermi velocities in bilayers, e.g., one layer on a substrate, using modified response parameters.

Experimental results

Research questions

• RQ1 How does graphene’s polarizability affect the interaction energy of a point charge or dipole near its surface?
• RQ2 What is the strength and angular dependence of the image charge force on a dipole near a graphene layer?
• RQ3 Can the dipole-graphene interaction energy exceed thermal energy (kT) at room temperature for molecules like water?
• RQ4 How does the interaction change in a bilayer graphene configuration compared to a single layer?
• RQ5 To what extent can image charge effects be captured by an effective dielectric model rather than full ab initio calculations?

Key findings

• Graphene exhibits finite dielectric response (εr) in the weak-coupling regime and behaves like a metal in strong fields, enabling image charge formation.
• The interaction energy for a water molecule near graphene is comparable to or larger than kT at room temperature, making it significant for molecular orientation.
• Dipole alignment normal to the graphene surface is energetically favored, with energy gains sufficient to overcome thermal fluctuations at distances of a few Å.
• For a water molecule in a graphene bilayer, the energy gain from optimal dipole orientation is on the order of several kT, comparable to intermolecular dipole-dipole interactions.
• The image charge model provides a robust approximation for long-range interactions, outperforming simple 3-9 dispersion forces in accuracy.
• The formalism can be extended to charged graphene and systems with asymmetric layers, such as graphene on substrates, by adjusting the Fermi velocity and response parameters.