Investigating the time dynamics of photon sequences scattered by tracer particles immersed in a polymeric gel

By dynamic light scattering, we study the effects of spatial confinement of tracer colloidal particles immersed in polyacrylamide networks on the time dynamics of sequences of elapsed times of scattered photons. We vary the degree of particles spatial confinement by changing the concentration of crosslinker in solution, from 0 to 2% in monomer mass fraction, which allows us to change the elasticity of the polymer gel. By calculating the Allan factor of the point processes of scattered photons arrival times, we are able to characterize the statistical properties of the scattering process. For all the samples we find that: i) the statistics of the photon arrival times is not Poissonian but clusterized in a certain counting time interval; ii) the time dynamics of the photon sequences is fractal in an ample range of counting times, from ∼10−3 to ∼10−1 s, with scaling exponents ranging between ∼1.7 and ∼1.0; iii) the crosslinking density of the polymer network, and thus, the system elasticity is correlated with the value of the fractal exponent. The value of the fractal exponent decreases as the system elasticity, or tracer's spatial confinement, increases.