Statistical properties of a polymer chain in the environment with low concentration of nanoparticles

We have investigated the statistical properties of polymer in the environment with low concentration of nanoparticles by using large-scale molecular dynamics simulations. The scaling law for the mean square radius of gyration was examined and simulation results for the polymer lengths 64≤N≤144 yielding a reasonably accurate value of the Flory exponent ν=0.58 at weak polymer-nanoparticle interaction ε_{PN}. Within the same range of N, the mean asphericity of the chain is independent of N. We found that the polymer behaves like a self-avoiding walk chain at small ε_{PN} and a compact sphere at large ε_{PN}. The results are attributed to the increase in the contact between polymer and nanoparticles with increasing ε_{PN}. Normal diffusions of polymer are always observed at whatever ε_{PN} and size and concentration of nanoparticles. Our result shows that the normal diffusion behavior of polymer is independent of polymer's state even though there is a phase transition from a desorbed polymer phase at small ε_{PN} to an adsorbed polymer phase at large ε_{PN}.