Non-Forster distance and orientation dependence of energy transfer and applications of fluorescence resonance energy transfer to polymers and nanoparticles: How accurate is the spectroscopic ruler with $1/R^6$ rule?

摘要

Fluorescence resonance energy transfer (FRET) is a popular tool to study equilibrium and dynamical properties of polymers and biopolymers in condensed phases and is now being widely used in conjunction with single molecule spectroscopy. The rate of FRET is usually assumed to be given by the Förster expression: $ k_F = k_{rad}(rac {R_F} {R} )^6$ where $k_{rad}$ is the radiative rate (typically less than $10^9 s^{-1}$) and $R_F$ is the well-known Förster radius which is given by the spectral overlap between the fluorescence spectrum of the donor and the absorption spectrum of the acceptor. We first present a critical analysis of the derivation of the above expression and argue why this expression can be of limited validity in many cases. We demonstrate this by explicitly considering a donor–acceptor system, polyfluorene $(PF_6)$ tetraphenylporphyrin (TPP), where their sizes are comparable to the distance separating them. In such cases, one may expect much weaker distance (as $1/R^2$ or even weaker) dependence. Another limitation is that optically dark states can make significant contribution to the energy transfer rate – these contributions are neglected in the Förster expression. Yet another limitation is that Förster, being based on Fermi Golden Rule, neglects vibrational energy relaxation which can be a serious limitation when the rate is in the few picoseconds regime. We have also considered the case of energy transfer from a dye to a nanoparticle. Here we show that the distance dependence can be completely different from Förster and can give rise to $1/R^4$ distance dependence at large separations. We also discuss recent applications of FRET to study biopolymer conformational dynamics and an interesting breakdown of the famous Wilemski–Fixman theory.