Temperature–Dependent Rotational Dynamics of a Non–Polar Probe in n–Alkane Solvents: Insights from Hydrodynamic and Quasi–Hydrodynamic Model

The rotational diffusion behavior of 3-(benzo[d]thiazol-2-yl)-7-(diethylamino)-2H-chromen-2-one (3BT7D2H-one) was investigated in two non-polar solvents, n-tridecane and n-hexadecane, across a range of temperatures. Steady-state and time-resolved fluorescence depolarization techniques were employed to measure the rotational reorientation times (τr) of the fluorescent probe molecule. The results demonstrate a linear dependence of τr on the viscosity-to-temperature ratio (η/T), highlighting that rotational dynamics are closely linked to changes in solvent viscosity. The experimental τr values were compared to predictions made by both the hydrodynamic Stokes-Einstein-Debye (SED) model and quasi-hydrodynamic models, including the Gierer-Wirtz (GW) and Dote-Kivelson-Schwartz (DKS) models. In both solvents, the observed τr values suggest sub-slip behavior, indicating that 3BT7D2H-one rotates with less frictional resistance than expected for a fully hydrodynamic regime. Specifically, the experimental τr values in n-hexadecane were found to be higher than those in n-tridecane, corresponding to the higher viscosity of the former solvent. While the SED model with sub-slip boundary conditions provided a reasonable approximation for the rotational times, both the GW and DKS models failed to quantitatively capture the experimental behavior. These models either underestimated or overestimated the frictional interaction between the solute and solvent, suggesting that additional factors such as solute-solvent size ratio and molecular shape might need to be incorporated for more accurate predictions. This study enhances the understanding of solute-solvent coupling in non-polar environments and underscores the limitations of traditional hydrodynamic models in describing molecular rotational diffusion in complex solvent systems.