Feynman-Enderlein Path Integral for Single-Molecule Nanofluidics

Single-molecule motions in the nanofluidic domain are extremely difficult to characterise because of various complex physical and physicochemical interactions. We present a method for quasi-one-dimensional sub-diffraction-limited nanofluidic motions of fluorescent single molecules using the Feynman-Enderlein path integral approach. This theory was validated using the Monte Carlo simulation to provide fundamental understandings of single-molecule nanofluidic flow and diffusion in liquid. The distribution of single-molecule burst size can be precise enough to detect molecular interaction. The realisation of this theoretical study considers several fundamental aspects of single-molecule nanofluidics, such as electrodynamics, photophysics, and multi-molecular events/molecular shot noise. We study {molecules within (an order of magnitude of) realistic lengthscale for organic molecules, biomolecules, and nanoparticles where 1.127~nm and 11.27~nm hydrodynamic radii of molecules were driven by a wide range of flow velocities ranging from $0.01~\mu$m/s to $10~\mu$m/s. It is the first study to report distinctly different velocity-dependent nanofluidic regimes.