[Paper Review] Enhancement of non-contact friction between metal surfaces induced by the electrical double layer

A. I. Volokitin|arXiv (Cornell University)|Jan 7, 2021

Quantum Electrodynamics and Casimir Effect37 references5 citations

TL;DR

This paper proposes that the electrical double layer (EDL) at metal surfaces dramatically enhances non-contact friction—specifically Casimir and electrostatic friction—between gold plates or a gold tip and plate in the extreme near-field (d < 10 nm). By incorporating the EDL's surface charge density (σs ≈ 0.38 C/m²) into fluctuational electrodynamics, the theory shows friction increases by many orders of magnitude compared to conventional models, enabling detectable Casimir friction with current AFM technology.

ABSTRACT

Casimir and electrostatic non-contact friction between two gold plates, and a gold tip and a gold plate, are calculated taking into account the contribution of the electrical double layer. It is shown that in an extreme-near field ($d<10$nm) the contribution from the electrical double layer leads to the enhancement of non-contact friction by many orders of magnitude in comparison to the result of the conventional theory without this contribution. Casimir and electrostatic friction dominate for short and large separations, respectively. The calculated electrostatic friction is in good agreement with experimental data. The results obtained open the way to detect the Casimir friction using Atomic Force Microscope.

Motivation & Objective

• To investigate the role of the electrical double layer (EDL) in enhancing non-contact friction between metallic surfaces.
• To resolve the long-standing discrepancy between theoretical predictions and experimental observations of Casimir friction.
• To demonstrate that EDL-induced surface charge density significantly modifies electromagnetic response and friction at nanoscale separations.
• To provide a theoretical framework that enables experimental detection of Casimir friction using atomic force microscopy (AFM).

Proposed method

• Incorporated the electrical double layer (EDL) as a surface charge layer with σs ≈ 0.38 C/m², derived from d0 ≈ 0.1 nm and Δϕ ≈ 4.3 eV for gold.
• Modified the p-polarized reflection amplitude using a surface dipole susceptibility αs = σ²sM, accounting for EDL screening effects.
• Used fluctuational electrodynamics to calculate Casimir and electrostatic friction forces between gold plates and tip-plate systems.
• Solved the friction coefficient γrad via the integral expression involving ImR1pImR2p and the reflection amplitude with EDL correction.
• Compared results with conventional Fresnel-based theory to isolate EDL contribution.
• Validated the electrostatic friction model against experimental data, showing good agreement.

Experimental results

Research questions

• RQ1 How does the electrical double layer affect the magnitude of non-contact friction in the extreme near-field (d < 10 nm)?
• RQ2 To what extent does the EDL enhance Casimir and electrostatic friction compared to conventional theories?
• RQ3 Can the EDL-induced enhancement make Casimir friction detectable with current atomic force microscopy (AFM) technology?
• RQ4 What is the quantitative contribution of the EDL to the reflection amplitude and friction coefficient in metallic systems?
• RQ5 How does the inclusion of EDL effects reconcile theoretical predictions with experimental observations of non-contact friction?

Key findings

• The electrical double layer enhances non-contact friction by many orders of magnitude in the extreme near-field (d < 10 nm), particularly for Casimir and electrostatic friction.
• The calculated electrostatic friction shows good quantitative agreement with experimental data, validating the EDL model.
• Casimir friction dominates at short separations (d < 10 nm), while electrostatic friction dominates at larger separations.
• The EDL contribution increases the friction coefficient γrad significantly, making it detectable with state-of-the-art AFM setups.
• The EDL model explains the long-standing discrepancy between theoretical predictions and experimental measurements of non-contact friction.
• The results open a viable pathway for direct mechanical detection of Casimir friction using atomic force microscopy.