Molecular dynamics studies on spatial scale of low energy excitation in a simple polymer system

A molecular dynamics simulation is performed to investigate spatial scale of low energy excitation (LEE) in a single linear chain of united atoms. The self part of the dynamic structure function, $S_mathrm{S}(q,omega)$, is obtained in a wide range in frequency space ($omega$) and reciprocal space ($q$). A broad peak corresponding to the LEE is detected at $omega/2pi=2.5 times 10^{11} mathrm{s^{-1}}$ ($equiv omega_{mathrm{LEE}}/2pi$) on the contour maps of $S_mathrm{S}(q,omega)$, near and below the glass transition temperature ($T_{mathrm{g}}$=230 K). The $S_mathrm{S}(q,omega_{mathrm{LEE}})$ is symmetric around a maximum along the logarithm of $q$. The inverse of $q_{mathrm{max}}$, giving the maximum position of $S_mathrm{S}(q,omega_{mathrm{LEE}})$, depends on temperature as $2pi/q_{mathrm{max}}sim T^{0.52}$ for $60 mathrm{K}<T<T_{mathrm{g}}$ and $2pi/q_{mathrm{max}}sim T^{0.97}$ for $T_{mathrm{g}}<T<600 mathrm{K}$, which is the spatial scale of the motion corresponding to the LEE at low temperatures. Based on a Gaussian approximation for the displacements of monomer groups which give rise to the motion relevant to the LEE, it is found that the number of monomers contained in a group is about 6.