Photon correlation spectroscopy of the non-Markovian Brownian motion of spherical particles

Abstract

The non-Markovian Brownian motion was studied by photon correlation spectroscopy on spherical particles suspended in viscous fluid. The non-Markovian property has been expected to give rise to a long-time tail proportional to ${t}^{\ensuremath{-}\frac{3}{2}}$ in the velocity correlation function and, correspondingly, a term of the form ${p}_{\frac{1}{2}}{t}^{\frac{1}{2}}$ in the argument of the exponential function of the photon correlation spectroscopy. Measurements were done on polystyrene latex spheres of 0.804-\ensuremath{\mu}m diameter suspended in pure water. Results of the experimental determination of the coefficient ${p}_{\frac{1}{2}}$ at three different temperatures were 0.397\ifmmode\pm\else\textpm\fi{}0.035 ${\mathrm{s}}^{\ensuremath{-}1/2}$ at 32.8\ifmmode^\circ\else\textdegree\fi{}C, 0.326\ifmmode\pm\else\textpm\fi{}0.029 ${\mathrm{s}}^{\ensuremath{-}1/2}$ at 28.0\ifmmode^\circ\else\textdegree\fi{}C, and 0.267\ifmmode\pm\else\textpm\fi{}0.027 ${\mathrm{s}}^{\ensuremath{-}1/2}$ at 23.5\ifmmode^\circ\else\textdegree\fi{}C, the corresponding theoretical values being 0.409, 0.346, and 0.293 ${\mathrm{s}}^{\ensuremath{-}1/2}$, respectively. Thus there is good agreement between the experimental values and the theoretical predictions.