SEM micrographs of the surface (a) and cross section (b) of the AAO templates.
(a) Ratio between coherent and incoherent contributions to the intensity scattered by the AAO templates; empty circles correspond to 45° and full circles to 135° orientation (see insert in Fig. 6). (b) Intensity scattered by PEO in the pores (full symbols) and by the templates and empty cell (empty symbols). The incoherent contribution from PEO hydrogens is shown by the line. The sample was oriented at 135° with respect to the incident beam. All results are for room temperature.
(a) ToF spectra obtained at 375 K and 135° orientation and the different -values indicated (in ). (b) Fourier transformed ToF spectra at the same temperature and orientation. Lines correspond to fits by KWW function [Eq. (3)] with fixed to 0.5.
Fourier transformed ToF spectra obtained at and 45° orientation of the sample and different temperatures. Lines correspond to fits by KWW function [Eq. (3)] with fixed to 0.5.
BS results corresponding to 350 K at 135° and different -values (symbols). The dashed lines show the resolution function. The solid lines are descriptions with the Fourier transformation of Eq. (3) with and the timescale fixed as obtained from the ToF analysis (see the text).
Comparison between the intermediate scattering functions obtained for the two orientations investigated at different temperatures. The selected -value corresponding to a scattering angle of about 90° relates to directed along the pores for 45° orientation of the sample and perpendicular to the pore axis for 135° orientation (see insert).
-dependence of the characteristic times at 400, 375, and 350 K. Data for bulk PEO are presented by open diamonds (FOCUS), open squares (PI), and open stars (IN16). TOFTOF data at the 45° and 135° sample orientations are shown by open and filled cycles, respectively. SPHERES data at the 45° and 135° sample orientations are presented by open and filled triangles, respectively. The solid lines show a dependence (Rouse behavior).
Intermediate scattering function of PEO hydrogens (circles) in the AAO templates oriented at 135° and that deduced for bulk PEO (solid line) (Ref. 31) at 375 K and . The dashed line presents a fit by a sum of 87% of the fast component with like in a bulk and 13% slow component with . The slower component is shown by dotted line.
Temperature dependence of the local friction coefficient of PEO in the pores and in the bulk compared with results of the literature. The symbols correspond to the different molecular weight samples: squares, [NSE (Ref. 15)]; circles, [backscattering (Ref. 32)]; triangles up, [rheology (Ref. 15)]; triangle down, [rheology (Ref. 15)]; star, [rheology (Ref. 15)]; hexagon, [NSE (Ref. 15)]. TOFTOF results are presented for 45° and 135° orientations by open and filled diamonds, respectively. SPHERES data are shown by open and filled left triangles for 45° and 135° orientations, respectively. The VTF law [Eq. (12)] is shown by the solid line.
Mean-squared displacement obtained by neutron scattering (ToF), MD simulations (Ref. 31), fringe field gradient NMR, and field-cycling NMR relaxometry (circles) (Refs. 36 and 37). Neutron scattering data were calculated from ToF spectra of PEO in AAO pores for , 0.3, and at 350 K using the relation . Both NMR experiments have been performed for bulk PEO at 355 K and molecular weight . The vertical arrows indicate dynamical limits of reptation theory that correspond to (I) unrestricted Rouse motion , (II) local reptation , (III) collective motion of the polymer chains along the tube contour , and (IV) normal diffusion of polymer chain for the molecular weight . The characteristic times have been calculated in accordance with reptation/tube model: entanglement time , Rouse relaxation time , and terminal relaxation time taking into account constraint release (CR) events (see Sec. II) . MD simulations results of bulk PEO at 350 K are presented by a solid line.
Mean-squared displacement obtained from neutron scattering (ToF) and MD simulations (Ref. 31) at 350, 375, and 400 K. MD simulations of bulk PEO are presented by solid lines. ToF results for PEO of molecular weight in AAO pores for , 0.3, and are shown by squares, circles, and triangles, respectively. Segmental relaxation time is 0.028 ns at 350 K, 0.022 ns at 375 K, and 0.011 ns at 400 K.
Comparison of ToF data for PEO in AAO pores (both sample orientations) and bulk PEO at 375 K with reptation model predictions [Eq. (13)] calculated for tube diameter of 0.5, 1, and 1.5 nm relating to entanglement time of 0.012, 0.19, and 0.98 ns, respectively. The function is represented by a dashed line above (i.e., in the applicability region) and by a dash-dotted line below . Rouse self-correlation function is presented by the solid line.
Characteristic timescales determined by the fitting of the ToF spectra presented in the Fig. 6 for different temperatures and sample orientations (see insert in Fig. 6).
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