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The authors model the driven diffusive transport of charged, rod-like particles through 3D channels with varying circular and elliptical cross-sections by projecting the high-dimensional dynamics onto an effective 1D landscape via the Fick-Jacobs approximation. Strikingly, the mean first passage times of these anisotropic rods collapse onto the exact same universal master curve as point-like and spherical particles when scaled by the effective free energy barrier. This dimensional collapse eliminates the need to resolve computationally prohibitive rotational and spatial degrees of freedom when predicting transport dynamics across geometric bottlenecks.
Anisotropic charged rods diffuse through 3D constrictions along the exact same universal curve as simple point particles, proving that complex rotational confinement can be compressed into a single scalar free-energy barrier.
We analyze the transport of rod-like particles by diffusion and drift in a three-dimensional channel with varying circular or elliptic cross section. Applying the Fick-Jacobs approximation to the transport equation of the particles'probability distribution, we derive an effective one-dimensional substitute model and the associated free energy profile. Our results show that the data for the mean first passage time of rods, once expressed as a function of the effective free energy barrier, collapse onto the same master curve as obtained for point or spherical particles. The observed universality provides a simple framework for predicting transport times of anisotropic particles in confined geometries without resolving the full multidimensional dynamics.