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Published: February 09, 2011 r 2011 American Chemical Society 5838 dx.doi.org/10.1021/jp1099877 |J. Phys. Chem. A 2011, 115, 58385846
 

Summary: Published: February 09, 2011
r 2011 American Chemical Society 5838 dx.doi.org/10.1021/jp1099877 |J. Phys. Chem. A 2011, 115, 58385846
ARTICLE
pubs.acs.org/JPCA
Single Molecule Diffusion and the Solution of the Spherically
Symmetric Residence Time Equation
Noam Agmon*
The Fritz Haber Research Center, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
ABSTRACT: The residence time of a single dye molecule diffusing within a laser spot is propotional
to the total number of photons emitted by it. With this application in mind, we solve the spherically
symmetric "residence time equation" (RTE) to obtain the solution for the Laplace transform of the mean
residence time (MRT) within a d-dimensional ball, as a function of the initial location of the particle and
the observation time. The solutions for initial conditions of potential experimental interest, starting in the
center, on the surface or uniformly within the ball, are explicitly presented. Special cases for dimensions 1,
2, and 3 are obtained, which can be Laplace inverted analytically for d = 1 and 3. In addition, the analytic
short- and long-timeasymptotic behaviors ofthe MRT arederived and comparedwith the exact solutions
for d = 1, 2, and 3. As a demonstration ofthe simplificationafforded by the RTE, the Appendix obtains the
residence time distribution by solving the Feynman-Kac equation, from which the MRT is obtained by
differentiation. Single-molecule diffusion experiments could be devised to test the results for the MRT presented in this work.
' INTRODUCTION

  

Source: Agmon, Noam - Institute of Chemistry, Hebrew University of Jerusalem

 

Collections: Chemistry