Rouse modes temperature

Figure 13 Temperature dependence of the time scales for the first five Rouse modes in the bead-spring model in the vicinity of the MCT Tc. 

Since the junctions are intermolecularly coupled and have significantly large n j, so is the longer length scale modes, i, of the polymer strands anchored on both ends to the junctions, which now have nonzero coupling parameters,, and obviously they cannot be modeled by Rouse modes. The temperature dependences of their relaxation times, t, a are no longer that... 

Moreover according to the CM (Ngai et al., 1997a), in pure PEO the Rouse modes or its friction factor, (T), should have the same temperature dependence as that of the primitive relaxation time, ro(T), related to the segmental a-relaxation time, t (T), by Eq. (5.39). We can verily this prediction by comparing... 

Figure 12 depicts, as a representative example, the initial correlation function, ip(0)> p = 1,..., 9, to test the orthogonality of the Rouse modes. It shows that the modes remain statically uncorrelated down to the lowest studied temperatures. In the normal high temperature state of the melt this result is either assumed due to the good agreement of theoretical predictions, derived from the Rouse modes, with experiments and simulations or verified directly by simulations (65), However, for supercooled melts the orthogonality of the Rouse modes has, to the best of our knowledge, not been observed before. Of course, the lowest temperature of our... 

Figure 12. Test of the orthogonality of the Rouse modes at t = 0 for various temperatures ranging from the normal liquid>like (T = 0.6) to the moderately supercooled regime (T = 0.23). The figure shows a representative example for the correlation of the first Rouse mode with all modes (except p = 0), i.e., ip(O) for p = 1,..., 9. Prom (53).

Figure 13 tests another prediction of the Rouse model, the time-temperature superposition property. Again, a representative example is shown, t.e., the correlation function of the third Rouse mode. As the theory anticipates, it is indeed possible to superimpose the simulation data, obtained at different temperatures, onto a common master curve by rescaling the time axis. The required scaling time, T3, is defined by the condition pp(r3) = 0.4. The choice of this condition is arbitrary. Since the Rouse model predicts that the correlation function satisfies equation (10) for all times, any other value of pp(t) could have been used to define T3. This scaling behavior is in accordance with the theory. However, contrary to the theory, the correlation functions do not decay as a simple exponential, but as... 

Figure 13. Time-temperature superposition property for the Rouse mode correlation function, exemplified by the third mode, 33(f)j temperatures...

Finally, Figure 15 shows the temperature dependence of the inverse relaxation time for the first three Rouse modes. As for the diffusion coefficient and the relaxation time of the end-to-end vector, l/r decreases by about 2 — 3 orders of magnitude in the studied temperature interval and may be fitted by the Vogel-Fulcher equation with a common (but, compared to D and 1/tr, slightly higher)... 

Figure 14. Attempt to scale the Rouse-mode correlation functions for different mode indices, p = 1,..., 6, at a given temperature (here T = 0.23). The decay of the curves is always stretched, and the degree of stretching increases with increasing p. Prom (53).

Figure 15. Temperature dependence of the Rouse-mode relaxation times for the first three Rouse modes, p = 1,2,3, and comparison with the Vogel-Rilcher equation (solid lines). As for D and Tete (see Figure 9), the Vogel-Fulcher activation energy and temperature agree for the three relaxation times reasonably well. FVom (53).

The exponent, 1/(1 - n), is larger than one. Hence has a stronger dependence on V (/) and/or 5 (Sc), and on temperature and pressure, than toa or The softening dispersions of entangled low molecular weight polymers are often modeled by the Rouse modes modified for undiluted polymers [1]. From their very definition only involving the coordinates of a single chain, the Rouse modes are not intermolecularly coupled, and their relaxation times, %, are proportional to the monomeric friction coefficient Co [18], i.e.. 

Experimentally the maximum loss frequency is typically measured for lower temperatures [23, 24] to study the temperature dependence of the structural glass transition or a process. Two sets of experiments in the literature show some discrepancies in an intermediate temperature window but agree with each other and with our simulation data at higher temperatures where we have an overlap temperature window between simulation and experiment. Prom this we can conclude, that also in the experiment one sees no correlations between the dipole moments of different chains. When we furthermore compare the time scale given by the maximum loss frequency with the time scales of the Rouse modes for our chains we can obtain from the simulation, we can say that the dielectric measurements on PB see the relaxation of a chain segment of about 6 backbone carbons, which is exactly the length of a statistical segment of the chains. 

---