Single molecule optical-probes measured power law distribution of polymer dynamics

The optical signals of single molecules provide information about structures and dynamic behaviors of their nanoscale environments, and eliminations of space and time averaging effect. These are particularly useful whenever complex structures or dynamic behaviors are present, especially in polymers. The single molecules absorbed onto polymer chains rotate with rotational relaxation of polymer chains. Thus, we can measure the dynamic properties of polymer thin films by measuring the rotational properties of single molecules. Here, we use single Nile Red（NR) dye molecules as nano-probes to measure polymer dynamic behaviors of poly（methyl acrylate)（PMA) polymer film. The polymer films are prepared on cleaned glass coverslips by spin-coating 1.0 wt.%solution of PMA containing ~10-9 mol/L NR molecules in toluene. Defocused wide-field fluorescence microscopy is used to measure the three-dimensional molecular rotational diffusion of single NR molecules in PMA polymer thin film. The local environmental change driven by heterogeneous dynamics of the polymer can be probed by parallel imaging of several molecules. It is found that at Tg+19 K, rotations of NR single molecules in different nano-areas are in two different ways, i.e., rotational way（rotational molecules account for ~83%) and non-rotaional way（non-rotational molecules occupy~17%). The rotational molecules include the single molecules of intermittent rotation with a short time and a long time. The different rotational patterns indicate that there is still a spatial and temporal heterogeneity of dynamics in PMA polymer film at a temperature of Tg+19 K. The autocorrelation function C(t) of angular change of dipole orientation of NR single molecules is calculated to reveal the property of polymer dynamics. The decay of C(t) can be fitted by Kohlrausch-Williams-Watt stretched exponential function. The averaged timescale of rotational diffusion c for 183 rotational NR single molecules indicates that the timescale of polymer dynamics at 300 K is~3 s. In order to investigate the temporal heterogeneity of PMA polymer dynamics, we define a threshold to separate the single molecular rotation into two parts:rotational state and non-rotational state. According to the statistics of duration time of rotational state and non-rotational state, we can obtain the probability densities of duration time of rotational states and non-rotational states of the single molecules. The probability densities obey a truncated power law, which indicates that there are still the behaviors of trapping and self-trapping in PMA polymer chains at Tg+19 K. The researches of spatial and temporal heterogeneity of dynamics of PMA polymers in nano-environment have great significance for preparing the high performance materials.