Diffusion Coefficients of Several Rhodamine Derivatives as Determined by Pulsed Field Gradient–Nuclear Magnetic Resonance and Fluorescence Correlation Spectroscopy

Rhodamine derivatives are popular, photostable fluorophores that are used in a number of fluorescent based techniques, including fluorescence correlation spectroscopy (FCS). Indeed, in FCS, both rhodamine 6G (R6G) and rhodamine 110 (R110) are used as calibration standards to determine the dimensions of the instrument confocal volume. In spite of a requirement for precise values of the diffusion coefficients, literature values are scarce and vary over an order of magnitude. In this paper, the diffusion coefficients of four rhodamine fluorophores (rhodamine 6G (R6G), rhodamine B (RB), rhodamine 123 (R123), rhodamine 110 (R110)) were determined by pulsed field gradient nuclear magnetic resonance (PFG-NMR) spectrometry and then validated by comparison with fluorescence correlation spectroscopy. With the objective of validating the FCS calibration, diffusion coefficients of several dextrans and a polystyrene nanoparticle were also determined and compared with literature values or theoretical values that were based upon the Stoke–Einstein equation. The work presented here lead us to conclude that the diffusion coefficients for R6G and R110 have generally been underestimated in the literature. We propose revised values of 4.4 × 10−10 m2 s−1 for R110 and 4.0 × 10−10 m2 s−1 for R6G. Using the revised D value for R110 to calibrate the FCS instrument, diffusion coefficients have then been systematically determined for different conditions of pH, ionic strength and concentration. To correct for differences due to solvent effects (D2O vs. H2O), an isotopic correction factor, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{D_{{\text{D}}_2 {\text{O}}} } \mathord{\left/ {\vphantom {{D_{{\text{D}}_2 {\text{O}}} } {D_{{\text{H}}_2 {\text{O}}} }}} \right. \kern-\nulldelimiterspace} {D_{{\text{H}}_2 {\text{O}}} }}$$\end{document} of 1.23, was determined from both FCS and from the solvent auto-diffusion coefficients obtained by NMR.