Spectra obtained with FOCUS (hPEO) at and the -values indicated. The Fourier transformed data are shown in the inset (lines: KWW fits).
Momentum transfer dependence of the characteristic times obtained from the KWW fit of the Fourier transformed incoherent (, full symbols) and coherent (, empty symbols) scattering functions at the temperatures investigated. Solid lines indicate a -dependence. Inset: ratio between the coherent and incoherent time scales for 375 K. The arrow shows the position of the maximum of the static structure factor.
Spectra obtained with TOFTOF (dPEO) at and the -values indicated. The Fourier transformed data are shown in the inset (lines: KWW fits).
Direct comparison of Fourier transformed TOFTOF data (empty symbols) with NSE results at and two temperatures. The TOFTOF points have been interpolated to the NSE temperatures using the three measured temperatures of 350, 375, and 400 K.
Static structure factor as calculated from MD simulations (line) and from neutron diffraction experiments with polarization analysis (symbols) (Ref. 60).
Direct comparison of the incoherent scattering functions calculated from MD simulations (empty symbols) with Fourier-transformed results from FOCUS measurements (full symbols) at and the -values indicated (units: ).
Incoherent intermediate scattering function, , as calculated from MD simulations for the hydrogen atoms of PEO. The curves correspond to the -values of 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.5, and (top to bottom). KWW fits with are displayed by the solid lines; in their fit, only the full symbols (times longer than ≈1 ps) have been considered.
Momentum transfer dependence of the characteristic times obtained from the KWW fits of the incoherent intermediate scattering function. The empty symbols represent data from MD simulations, while the full symbols show experimental data [FOCUS (PSI), BSS (FZ-Jülich), and IN16 (Grenoble)]. For clarity points for have been multiplied by 0.1 and points for by a factor of 0.01. The solid lines show -laws.
Direct comparison of the normalized dynamic structure factor as calculated from MD simulations (empty symbols) and obtained through Fourier transformation of TOFTOF-measurements (full symbols). The shown scattering vectors are indicated in units of .
Momentum transfer dependence of the ratio between the coherent and incoherent characteristic times (full circles are from the MD simulations and empty squares are from TOFTOF) for 375 K. The line shows the static structure factor for comparison.
Radial probability distribution functions obtained from the self-part of the van Hove correlation functions for PEO hydrogens at the three temperatures investigated (blue: 300 K, green: 375 K, and red: 400 K) at the different times indicated. Gaussian fits for the 400 K data are shown by black lines.
(a) Non-Gaussian parameter and (b) for the hydrogen atoms at the temperatures investigated. The values in (b) have been multiplied by a factor of 10 for and 100 for .
Temperature dependence of the Rouse rates obtained for PEO from different sources: NSE experiments on the single chain dynamics [triangles: high-molecular weight sample (Ref. 58), diamond: low-molecular weight sample (Ref. 58)], backscattering, and FOCUS experiments on fully protonated sample addressing H self-motions (circles) and our MD simulations (squares) (see the text). The solid line is a fit to a Vogel–Fulcher law with the values and given in Ref. 58.
Normalized Rouse correlators for the modes using one monomer as bead. The solid lines show fits by stretched exponential functions.
Mode-wavelength dependence of the fitting parameters obtained for the KWW descriptions of the Rouse-mode correlators at the different temperatures investigated: (a) average time and (b) shape parameter . The mode amplitudes are depicted in panel (c). The line in (b) shows the asymptotic value of the shape parameter, while in (a) and (c) it indicates the mode number dependence predicted by the Rouse model in the low- range.
MSD of the H-atoms (circles), of the blob (monomer) (squares), and of the center of mass of the chain (diamonds) at 400 K. The vertical arrows indicate the Rouse time , the segmental time , and the structural relaxation time .
Mode-wavelength dependence of the characteristic ratio calculated from the coarse grained chain at the three temperatures investigated.
Mode-wavelength dependence of the average characteristic times obtained from KWW fits of the modes (circles) compared with the Rouse (dashed-dotted line) and the ARS (dotted line) predictions. The squares show the effective monomeric friction coefficient deduced (see the text). The horizontal solid line indicates the experimental -value (Ref. 58).
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