The VFT fits to the deuteron NMR segmental relaxation times for pure PEO (bold blue solid line) and in blends with PMMA containing from 3% up to 30% PEO (upper thin lines from top to bottom) reported by Lutz et al., 14 the actual data are not shown to avoid crowding. Shown by the blue dashed-dotted line at the bottom is the primitive relaxation time τ 0(T) of neat PEO calculated using n = 0.50. The small size symbols on top are the most probable relaxation times calculated for the 3% (‐), 10% (□), and 30% (▲) PEO blends with = 0.76, 0.75, and 0.715, respectively. 17 The large open and closed symbols are the relaxation times of the slow and fast processes, respectively, found by QENS experiments 69,70 at Q = 1.3 Å−1. Dark blue circles for 10%, green triangles for 20%, red squares for 30%, and + and * for 100% PEO. The upper inset shows by solid symbols the QENS relaxation times, τ QENS,f , of the fast process of PEO at Q = 1.3 Å−1 as a function of 1000/T: (●) 10%, (▲) 20%, (■) 30%, and (×) 100%. Empty symbols correspond to the deuteron NMR segmental relaxation times: (○) 10%, (▵) 20%, and (□) 30%. The lower inset shows log (τ QENS,s ) for the slow process (■) and log (τ QENS,f ) the fast process (●) of PEO in the 20% blend from QENS at Q = 1.3 Å−1 plotted against 1000/T. The units of the x axis and y axis in both insets are K−1 and ps, respectively.
In the main figure, open red circles and open black circles are deuteron NMR data and fit, respectively, of segmental α-relaxation time of the PEO component from Lutz et al. 14 in 20% PEO–80% PMMA blend (see Fig. 4 in Ref. 14 ). The vertical black arrow locates the position of T g = 356 K for the PMMA component in the blend. The magenta, black, and green lines are VFT fits obtained by fitting NMR data of the PEO component in 20% PEO–80% PMMA blend and for it to reach T g with the three possible values of, respectively, T g = 245 K, T g = 237 K, and 229 K (see text). The red closed circles are the relaxation times of the fast process obtained from QENS by Sakai et al., 70 and identified as τ 0. The black and red dotted lines are fits to τ 0 by two possible VFT temperature dependencies, VFT1 and VFT2 (see text). The magenta, black, and green symbols are obtained from the CM equation (1) by substituting VFT1 for τ 0 and applying the n parameter represented by the symbols in Fig. 3 . The inset is an enlargement of data and fits over the short timescale. In addition to the same symbols and lines of the main figure, it shows QENS data for PEO in the 25/75 blend from QENS at Q = 1.02 Å−1 78 (asterisks). Also from QENS data at Q = 1.02 Å−1 70 are open black squares indicating the slow relaxation, and the closed black squares the fast relaxation for the PEO component in 20% PEO–80% PMMA blend (black squares). The red closed and open triangles are the same for the 30% PEO–70% PMMA blend. The blue line is the primitive relaxation time of PEO obtained from NMR data of pure PEO.
The coupling parameters n(T) as obtained from CM equation (1) from the separation between τ 0 and τ α : τ 0 has been extrapolated according to VFT1 and VFT2 fits in Fig. 2 ; τ α are from fitting together the data of Lutz et al. 14 and three different possibilities for the T g of PEO component in 20% PEO–80% PMMA blend as obtained from DSC experiments. The solid symbols are obtained by choosing VFT1 for τ 0, the open ones by choosing VFT2 for τ 0. Magenta, black, and green symbols are for n(T) with T gi = 245 K, 237 K, and 229 K, respectively. The lines are guides for the eye.
The normal mode (NM) relaxation time (open symbols) and the segmental α-relaxation time τ αf (closed symbols) of PI27 in pure PI27 (blue circles), in 35% PI27 blend (green circles), and in 20% PI27 blend (red diamonds) with PtBS1300. Data from Refs. 22 and 39 , and replotted as a new figure. The red × symbols represent the characteristic times obtained from isochronal representation of the data for 20% PI blends. The location of the 1000/T g of the two components for the two blends are indicated by the arrows accompanied by value of T g .
The normal mode (NM) relaxation time (open symbols) and the segmental α-relaxation time τ αf (closed symbols) of PI27 in pure PI27 (red squares), 35% PI27 blend (green circles), and 20% PI27 blend (blue diamonds) with PtBS2300. Data from Refs. 22 and 39 , and replotted as a new figure. The blue × symbols represent the characteristic times obtained from isochronal representation of the data for 20% PI blends. The horizontal dotted line indicates log ( /s) ≈ −0.5, corresponding to log (f NM/Hz) = 0.7. The three vertical thin dashed lines indicate increasing separation between log ( /s) and log (τ αf /s), at constant log ( /s) ≈ −0.5, on decreasing PI27 content. The location of the 1000/T g of the two components for the two blends are indicated by the arrows accompanied by value of T g . The tips of the arrows located slightly to the right of 1000/260 K−1 = 3.85 K−1 are the calculated values of log ( /s) and log (τ αf /s) by the CM (see text).
Plot of the characteristic relaxation time, τ max , of the JG β-relaxation (called α′-relaxation in Ref. 40(a) ) for the PVME component in three blends x% PVME/(1 − x)% PS as functions of temperature obtained by Lorthioir et al. 40(a) Inverted triangles for x = 30, diamonds for x = 20, and squares for x = 10. The purple arrow indicates the reciprocal of the TSDC glass transition temperature T g, TSDC = 293 K for the 20% PVME blend. The lower inset is taken from Fig. 6 in Ref. 40(a) , showing the isothermal spectra of the JG β- or α′-relaxation in the 20% PVME blend. The dielectric strength increases with temperature, which is characteristic of secondary relaxation. Some of the τ max in the main figure was determined from the peak frequencies, f max , in the spectra in the lower inset. The shortest τ max in the figure corresponds to f max at 328 K indicated by the arrow in the lower inset. The upper inset shows the isochronal loss data at 1 Hz of Lorthioir et al. 40(a) for x = 20 (inverted triangles) and x = 30 (open squares). The arrow near 220 K indicates the α′- or JG β-relaxation for x = 20 and 30 corresponding to the in the Arrhenius regime of the relaxation map in the main figure. The arrow near 280 K indicates the α-relaxation of the x = 30 blend.
Logarithm of the relaxation time τ JG vs inverse temperature at different pressures (from bottom to top: P = 0.1, 50, 100, 150, 200, 250, and 300 MPa) for PVME in PS (25/75). Data from Schwartz et al. 52 in which they interpret the observed as α-relaxation with VFT dependence and crossover to Arrhenius dependence due to confinement by the PS matrix. Solid curved lines represent the VFT fits of the experimental data at higher temperatures. The vertical dashed black and the thinner black continuous arrows indicate at ambient pressure the locations of 1000/T g ,TSDC, with T g, TSDC ≈ 289 K of the PVME component and 1000/T g, DSC, with T g ,DSC ≈ 321 K of the blend as a whole obtained by DSC. Results obtained by interpolation of TSDC and DSC data from Leroy et al. 41 The colored vertical arrows mark the positions where the system (likely the slow majority component PS) enters into the glassy state, as determined by PVT data. 97 Note the approximate agreement between this location and 1000/T g ,DSC at ambient pressure. The horizontal black dashed line marks the τ JG(P, T) ≈ 10−4.8 s. The dotted-dashed color lines are polynomial fits drawn to suggest the crossover of temperature dependence of τ JG(P, T) at T X (P) where τ JG(P, T X (P)) ≈ 10−4.8 s independent of P. The open symbols mark the change of concavity at the crossover, which also occurs at the same values of τ JG(P, T X (P)) for all T X (P). Inset shows the master-curve obtained by plotting τ JG(P, T) versus T X (P)/T.
The parameters of the VFT equation, log10(τ α ) = A+B/(T − T 0), used to interpolate τ αf of the PEO in blends from deuteron NMR and any one of the three DSC measurements.
Summary of anomalous properties of the fast component in highly asymmetric polymer blends. Not included is one item, and that is some of the opposite behavior found in the slow component.
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