Towards an understanding of dipole-dipole interactions in nonlocal media

TL;DR

This work investigates how nonlocal media, notably salt solutions, modify resonance (excited‑state) dipole–dipole interactions between two atoms. Using a semi‑classical electrodynamics framework with Green’s‑function susceptibility and Matsubara frequency summation, it derives salt‑modified resonance energies, highlighting a Debye screening term and distinctive zero‑ and finite‑temperature asymptotics. At zero temperature, the short‑range retarded interaction scales as $U(\rho) \sim 1/\rho^4$ and crosses to $U(\rho) \sim 1/\rho^7$ at large separations, while at finite temperature a leading Debye‑screened term $U(\rho) \propto -k_B T \alpha(0)^* \kappa_D^2 e^{-\kappa_D\rho}/(\rho \epsilon_w(0))$ dominates the long‑range behavior. The results suggest that nonlocal electrolyte effects can compete with van der Waals forces in biological fluids and may influence processes such as pheromone energy transfer, motivating further theoretical development of nonlocal dispersion in media.

Abstract

We commence our study with review of dispersion interactions in electrolytes. We then reflect on how background media change atom-atom excited-state systems. To highlight the impact of nonlocal media, such as salt solutions, we predict that a new contribution to the resonance interaction energy emerges in a form $\propto e^{-κ_{\rm D} ρ}/ρ$. Here $κ_{\rm D}$ is the Debye length and $ρ$ is the distance between the atoms. This contribution vanishes at zero temperature, where a new term proportional to $1/ρ^4$ (similar to free space) occurs. This new term is dampened by the electrolyte at large distances, causing it to decrease much faster, proportional to $1/ρ^7$. The long-range electrolyte-induced resonance interaction at finite temperature may, in addition to the dominating van der Waals attraction (which goes as $1/ρ^6$), take part in the molecular formation of biological fluids.

Figures (1)

• Figure 1: Color online: Schematic figure for two atoms in an excited state, a distance $\rho$ apart, in a nonlocal media.