Rotational Dynamics of Excited Probes: Analysis of Rate Constants Based on the Predictions of Hydrodynamic Theory

Abstract

The rotational diffusion of benzo(rst)pentaphene (RST) in n‐hexadecane solvent has been investigated using time‐resolved linear dichroism spectroscopy. Theoretical models of rotational diffusion predict biexponential decays of the observed dichroism for this planar polycyclic aromatic probe in solution. Consistent with theory, two time constants of τ₁=12 ±5 and τ₂=180±10 ps are observed in the loss of dichroism for RST. The ratio of these two time constants is τ₂/τ₁≈15 and they occur with approximately equal weights within the decay. Hydrodynamic theory, using either slip or stick boundary conditions, would suggest a ratio of only ca. 2–4. Detailed analysis of the preexponential factors for the decay components according to current hydrodynamic theory reveals that there are no physically allowed conditions that would result in a ratio of time constants that exceed ca. 4 while simultaneously allowing the two exponentials to be observed with nearly equal weights within the decay. Based on this finding, it is unlikely that both observed decay components can be due to random diffusional motion.

Keywords:

• Debye–Stokes–Einstein diffusion theory
• fluorescence anisotropy
• hydrodynamic theory
• polarized spectroscopy
• slip boundary
• stick boundary

Acknowledgments

Support for this work by the University of Maryland, Baltimore County, and NSF (CHE‐9985299) is gratefully acknowledged. D.L. also acknowledges NIH for support through a Chemistry‐Biology Interface Training Grant (T37 GM066706).

Notes

¹The tabulated diffusion coefficients from ref. 28 were plotted and the data interpolated to estimate the values at the axial ratios of RST.

²It is important to consider the magnitudes of the quantities D – D _L and Δ as the isotropic limit is approached. Near the isotropic limit, D – D _L must approach zero faster than does Δ if Eq. (17) is valid. Thus, for isotropic diffusion, the ratio of time constants approaches unity and both Δ and α must approach zero.