Dynamic Light Scattering of Rigid Rods – A Universal Relationship on the Apparent Diffusion Coefficient as Revealed by Numerical Studies and Its Use for Rod Length Determination

Numerical simulations are performed to study the diffusion behaviors of rigid rods examined by dynamic light scattering (DLS). It was identified that the apparent diffusion coefficient, D p , determined by DLS obeys a universal relationship D p / D G = f( qL ) = 1.1804 + 0.1764 × tanh [11.799× tan −1 ( qL ) ‐17.169], where D G , L , and q are the mass‐of‐center diffusion coefficient, length of the rod, and scattering vector, respectively. This relationship delineates the DLS experiments into weak ( qL < 4.0), intermediate (4.0 < qL < 20.0), and strong translation–rotation coupling regime ( qL > 20.0). In weak (strong) coupling regime, D p is a measure of D G (D // ‐ longitudinal diffusion coefficient) of the rods. In addition, if DLS is performed in the intermediate coupling regime, the rod length can be determined by solving D p / D G = f( qL ).