Casimir effect with dielectric matter in salted water and implications at the cell scale

TL;DR

This work shows that in salted water the Casimir interaction between dielectric objects acquires a large, universal contribution arising from transverse electromagnetic fluctuations and the zero Matsubara frequency, yielding a purely entropic energy governed by geometry: $\\mathcal{F}_{\\mathrm{univ}}^{\\mathrm{bulk}} = - \\frac{A H}{12\\pi d^2}$ with $H = \\frac{3\\zeta(3)}{4} k_B T$. Using scattering theory, the authors separate this universal term from the nonuniversal, frequency-dependent parts and demonstrate that longitudinal (Debye-screened) contributions decay as $e^{-2d/\\lambda_D}$, leaving the universal term unscreened. Experimental validation via optical tweezers with silica spheres shows the universal contribution dominates above ~200 nm and agrees with theory without free parameters. The analysis extends to two-sphere and two-cylinder geometries, providing universal expressions in terms of dimensionless geometries and showing that nonuniversal terms are negligible in biologically relevant conditions. Applying these results to actin filaments suggests the universal Casimir attraction can yield several $k_B T$ of binding energy at cell-relevant spacings, potentially influencing cytoskeletal self-assembly and cohesion at the cellular scale.

Abstract

The Casimir interaction in salted water contains a universal contribution of electromagnetic fluctuations that makes it of a longer range than previously thought. The universal contribution dominates non universal ones at the distances relevant for actin fibers inside the cell. We discuss universal and non-universal contributions with a model mimicking biological matter. We also show that the universal Casimir effect should have important implications at the cell scale.

Figures (9)

• Figure 1: Sketch view of the two-bulks configuration, with $d$ the distance between the two parallel interfaces, $\varepsilon_1$ and $\varepsilon_2$ the dielectric functions for water and immersed matter.
• Figure 2: Principle of the experiment reported in Ref. Pires2021: a silica microsphere (radius $R_1$) is held by a tightly focused laser beam close to a larger silica microsphere (radius $R_2$) which is attached to the glass slide at the bottom of the sample chamber. The distance $D$ between the larger microsphere and the laser axis is controlled by using a piezoelectric nano-positioning system. The Brownian fluctuations of the trapped microsphere are measured for different values of $D$. The distance of closest approach of the two spheres is denoted $d$ and the height of the small sphere above the glass slide $h$.
• Figure 3: Variation of the Casimir interaction energy (in units of the thermal energy $k_\mathrm{B} T$) with the distance $d$ between two dielectric microspheres in salted water for the setup depicted in Fig. \ref{['fig:experimentscheme']}. Experimental points are shown with their error bars (blue). The old approach relying on overlooking the universal contribution (red) leads to much too small values to be compatible with the experimental data. New theory (black), with the universal contribution included, agrees fairly well with experiments (with no fitting). Adapted from Pires et al. Pires2021 under the terms of the Creative Commons Attribution 4.0 International license.
• Figure 4: Geometry for two spheres (a) or two cylinders (b) immersed in salted water. $R_1$ and $R_2$ are the radii of spheres or cylinders, and $d$ the distance of closest approach ($\varepsilon_1$ and $\varepsilon_2$ defined as for Fig.\ref{['fig:twobulks']}).
• Figure 5: Universal functions (solid black curves) showing the variations of the universal free energy versus $x=d/R_\mathrm{eff}$: (a) function $f$ calculated for two spheres with equal radii; (b) function $\phi$ calculated for two cylinders with equal radii. In both plots, red dotted and blue dashed lines represent the proximity force and small size approximations giving the asymptotic behaviors at $x\ll1$ and $x\gg1$ respectively.