Structural relaxation length scale

As described in Sect. 1, the relevant length scales and time scales are a serious problem for any simulation of polymer melts [12,16-20] and, as discussed, a polymer coil has structures on different distance scales (Fig. 1.2) [17] and relaxations on different time scales. A brute force approach, consisting of a simulation of fully atomistic models of a sufficiently large system over time scales for which thermal equilibration could be reached at practically relevant temperatures, is totally impossible. Useful progress requires a different approach. 

How can one hope to extract the contributions of the different normal modes from the relaxation behavior of the dynamic structure factor The capability of neutron scattering to directly observe molecular motions on their natural time and length scale enables the determination of the mode contributions to the relaxation of S(Q, t). Different relaxation modes influence the scattering function in different Q-ranges. Since the dynamic structure factor is not simply broken down into a sum or product of more contributions, the Q-dependence is not easy to represent. In order to make the effects more transparent, we consider the maximum possible contribution of a given mode p to the relaxation of the dynamic structure factor. This maximum contribution is reached when the correlator in Eq. (32) has fallen to zero. For simplicity, we retain all the other relaxation modes = 1 for s p. 

With respect to the dynamics of such systems, there is a strong correlation between the structure factor and the initial decay of relaxation on microscopic length scales... 

In the discussion on the dynamics in the bead-spring model, we have observed that the position of the amorphous halo marks the relevant local length scale in the melt structure, and it is also central to the MCT treatment of the dynamics. The structural relaxation time in the super-cooled melt is best defined as the time it takes density correlations of this wave number (i.e., the coherent intermediate scattering function) to decay. In simulations one typically uses the time it takes S(q, t) to decay to a value of 0.3 (or 0.1 for larger (/-values). The temperature dependence of this relaxation time scale, which is shown in Figure 20, provides us with a first assessment of the glass transition... 

Recently a very detailed study on the single chain dynamic structure factor of short chain PIB (M =3870) melts was undertaken with the aim to identify the leading effects limiting the applicability of the Rouse model toward short length scales [217]. This study was later followed by experiments on PDMS (M =6460), a polymer that has very low rotational barriers [219]. Finally, in order to access directly the intrachain relaxation mechanism experiments comparing PDMS and PIB in solution were also carried out [186]. The structural parameters for both chains were virtually identical, Rg=19.2 (21.3 A). Also their characteristic ratios C =6.73 (6.19) are very similar, i.e. the polymers have nearly equal contour length L and identical persistence lengths, thus their conformation are the same. The rotational barriers on the other hand are 3-3.5 kcal/mol for PIB and about 0.1 kcal/mol for PDMS. We first describe in some detail the study on the PIB melt compared with the PDMS melt and then discuss the results. 

Further results on PI and PVE also point to different thermal behaviours for the structural relaxation and the dynamics at intermediate length scales [228,229]. 

Q-dependence of Tp ir at the lowest temperature investigated, it fails to describe the temperature behaviour of the PIB collective response at intermediate length scales, at least in the temperature range investigated. MCT predicts universality of timescales. This prediction is incompatible with the observation of two different temperature dependencies for the structural and the stress relaxation. 

Reaction-induced phase separation is certainly also the reason for which an inhomogeneous structure is observed for photocured polyurethane acrylate networks based on polypropylene oxide (Barbeau et al., 1999). TEM analysis demonstrates the presence of inhomogeneities on the length scale of 10-200 nm, mostly constituted by clusters of small hard units (the diacrylated diisocyanate) connected by polyacrylate chains. In addition, a suborganization of the reacted diisocyanate hard segments inside the polyurethane acrylate matrix is revealed by SAXS measurements. Post-reaction increases the crosslink density inside the hard domains. The bimodal shape of the dynamic mechanical relaxation spectra corroborates the presence of a two-phase structure. 

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