Molecular dynamics studies on spatial scale of low energy excitation in a simple polymer system
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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, $S_\mathrm{S}(q,ω)$, is obtained in a wide range in frequency space ($ω$) and reciprocal space ($q$). A broad peak corresponding to the LEE is detected at $ω/2π=2.5 \times 10^{11} \mathrm{s^{-1}}$ ($\equiv ω_{\mathrm{LEE}}/2π$) on the contour maps of $S_\mathrm{S}(q,ω)$, near and below the glass transition temperature ($T_{\mathrm{g}}$=230 K). The $S_\mathrm{S}(q,ω_{\mathrm{LEE}})$ is symmetric around a maximum along the logarithm of $q$. The inverse of $q_{\mathrm{max}}$, giving the maximum position of $S_\mathrm{S}(q,ω_{\mathrm{LEE}})$, depends on temperature as $2π/q_{\mathrm{max}}\sim T^{0.52}$ for $60 \mathrm{K}<T<T_{\mathrm{g}}$ and $2π/q_{\mathrm{max}}\sim T^{0.97}$ 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.
4 pages, 3 figure; Figure 3 replced; Abstract replced
4 pages, 3 figure; Figure 3 replced; Abstract replced