Intermittently fluorescing single molecule systems are found in many materials, including (1) dyes on crystal or nanoparticle film surfaces and (2) semiconductor quantum dots (QD), among others. Experimental observations include a power law for the intermittency and, in the case of the “on” state of the QD’s, an exponential tail. We interpret the experiments in terms of a diffusion/electron transfer (ET) theory (“spectral” diffusion for the QD’s and particle diffusion for the semiconductor surfaces). The two theories differ in dimensionality, and so differ in their power (-1.5 versus -1.0) dependence. The ET’s are treated as resonant ET’s, and, for the QD’s at high incident light intensities that produce biexcitons, a Fermi Golden Rule ET (particle ejection) is used in treating it. It causes an exponential tail for the “on” state but no change in the power law behavior of the “off” state. The expected change of power at short “on” or ”off” times, due to a building up of a concentration gradient near the “on-off” transition point, is also discussed. Experiment and theory on these many aspects are compared and desirability of additional theory-motivated experimental data is discussed. 

Less studied than QD’s is single molecule dye-photoinjection of electrons or holes into semiconductors or semiconductor films of nanoparticles, of solar cell relevance. Here an injection can in principle be either into a conduction band (valence band in the case of hole injection) or into the band gap. We describe a diffusion/ET theory, leading to different kinetics for band and band gap injections and recombinations. Existing data are discussed. 

Nanoparticles have been a boom for electron transfer enthusiasts, both for single molecule and ensembles studies. An active problem in electrochemistry and battery research has been looking for curvature in Tafel plots. An example using ensembles of nanoparticles is discussed. We had focused for QD’s on single molecule experiments, but illustrate the complementarity of ensemble studies with an example from QD’s.

References: Z. Zhu and R. A. Marcus  “Extension of the Diffusion Controlled Electron Transfer Theory for Intermittent Fluorescence of Quantum Dots: Inclusion of Biexcitons and the Difference of “On” and “Off” Time Distributions” Phys. Chem. Chem. Phys., 10.1039/C4CP01274G (2014). Wei-Chen Chen and R. A. Marcus “Theory of a single dye molecule blinking with a diffusion-based power law distribution” J. Phys. Chem. C, 116, 15782-15789 (2012). P. Bai and Z. Bazant, Charge Transfer Kinetics at the Solid-Solid Interface in Porous Electrodes, Nature Com. 5, 3585 (2014).