Dynamics of concentration fluctuations in polymer solutions with spatiotemporal correlated noise

Abstract

We study the problem of concentration fluctuations in polymer solutions under the influence of spatiotemporal correlated noise. We find that in contrast to the case of white noise, where the dynamic structure function is characterized by a single decay rate ${\mathrm{\Gamma }}_{\mathit{k}}$ which is given in terms of the static structure function g(k) in the colored noise case, the decay rate takes a different form depending on a characteristic wave vector κ, given by the solution of the equation 1+${\xi }^2$ ${\mathrm{\kappa }}^2$-τ${\mathrm{\Gamma }}_{\mathrm{\kappa }}$=0, with ξ being the correlation length of the polymers and τ being the correlation time of the colored noise. For the wave vector k≪κ, the decay rate is ${\mathrm{\Gamma }}_{\mathit{k}}$, just as in the white noise case. For k=κ, the decay rate is ${\mathrm{\Gamma }}_{\mathrm{\kappa }}$, but the decay is modified by an extra factor (1+${\mathrm{\Gamma }}_{\mathrm{\kappa }}$t) where t is the time. For k≫κ, the decay rate is (1+${\xi }^2$ ${\mathit{k}}^2$)/τ. Since our result should hold as long as the correlation time τ is not exactly zero, it should lead to experimentally verifiable consequences in dynamic light scattering in polymer solutions in short time scales.