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

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 $t^{-\frac{3}{2}}$ 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-μm diameter suspended in pure water. Results of the experimental determination of the coefficient $p_{\frac{1}{2}}$ at three different temperatures were 0.397±0.035 ${\mathrm{s}}^{-1/2\mathrm{}}$ at 32.8°C, 0.326±0.029 ${\mathrm{s}}^{-1/2\mathrm{}}$ at 28.0°C, and 0.267±0.027 ${\mathrm{s}}^{-1/2\mathrm{}}$ at 23.5°C, the corresponding theoretical values being 0.409, 0.346, and 0.293 ${\mathrm{s}}^{-1/2\mathrm{}}$, respectively. Thus there is good agreement between the experimental values and the theoretical predictions.