Dynamic light scattering from thin rigid rods: Anisotropy of translational diffusion of tobacco mosaic virus

An Exact theoretical expression for the apparent diffusion coefficient D app ( K ) of a thin rigid rod with arbitrary anisotropy of its translational diffusion diffusion coefficient is derived from the first cumulant of its dynamic structure factor. D app ( K ) is predicted to reach a limiting plateau value at extermely large values of KL , where K is the scattering vector and L the rod length. Howerver, that limiting plateau value is approached only very slowly along a quasi‐plateau with a very gradual slope. Dynamic light‐scattering studies have been performed on tobacco mosaic virus from K 2 = (0.4–20) × 10 10 cm −2 using 632‐8‐nm laser radiation. The present data yield D 0 = (4.19 ± 0.10) × 10 −8 cm 2 /s (corrected to 20, w conditions) and, with literature data to establish L = 2980 Å and the rotational diffusion coefficient D R = 318s −1 , yield also Δ ≡ D ∥ − D ⊥ = (1.79 ± 0.38) × 10 −8 cm 2 /s. The experimental data closely follow the curve of D app ( K ) vs K 2 calcuated for these parameters. The present value of D 0 substantially exceeds all previous dynamic light‐scattering values, but is in good aggreement with previous sedimentation data, which were confirmed for the presemt sample. The anisotropy ratio Δ/ D 0 = 0.43 ± 0.09 is in accord with theoretical predictions based on the modified Kirkwood algorithm, despite the fact the D 0 lies significantly below its corresponding theoretical value. The present data largely predlude the possibility that both D 0 and Δ/ D 0 could simultaneously match their theoretical predictions. We present a detailed comparison of the experimental data with the calculations of Tirado and Garcia de la Torre based on the modified Kirkwood algorithm and with the Broersma formulas.