Calibration of an optical self‐beating spectrometer by polystyrene latex spheres and confirmation of the stokes‐einstein formula

Abstract

Abstract The Rayleigh linewidth Γ of light scattered by dilute aqueous solutions of polystyrene latex spheres has been measured by using time‐dependent photocurrent signal correlation with a precision typically of 0.5–1% over a range of scattering angles θ. With independent measurements of the diffusion coefficient D from D = lim K → 0 (Γ/ K 2 ), the diameter of the sphere d by means of electron microscopy, and the hydrodynamic shear viscosity η, we have confirmed the Stokes‐Einstein relation D = kT /3πη d to within 1% if we take into account the effect of polydispersity on our Rayleigh linewidth data. We also find that d EM = 907 ± 56 Å for sample LS‐1132‐B as reported by the Dow Chemical Company differs from our d SB = 847 (±1.6%) Å ≈ d EM = 851 (±2%) by about 7%, which is outside the limits of error of our experiments. The subscripts EM and SB denote electron microscope and self‐beating, respectively, while K ≡ (4π/λ)sin(θ/2) is the magnitude of the momentum transfer vector.