Intermediate length-scales

A polymer coil does not only possess a structure on the atomistic scale of a few A, corresponding to the length of covalent bonds and interatomic distances characteristic of macromolecules are coils that more or less, obey Gaussian statistics and have a diameter of the order of hundreds of A (Fig. 1.2) [17]. Structures of intermediate length scales also occur e. g., characterized by the persistence length. For a simulation of a polymer melt, one should consider a box that contains many such chains that interpenetrate each other, i. e., a box with a linear dimension of several hundred A or more, in order to ensure that no artefacts occur attributable to the finite size of the simulation box or the periodic boundary conditions at the surfaces of the box. This ne-... 

Chapter 5 considers the connection between the universal large scale dynamics discussed first and the local specific dynamics discussed in the second step. The dynamics at intermediate length scales bridges the two and we will address the leading mechanism limiting the universal dynamics in flexible polymers. 

The above expressions provide a universal description of the dynamics of a Gaussian chain and are valid for real linear polymer chains on intermediate length scales. The specific (chemical) properties of a polymer enter only in terms of two parameters N =Rl and The friction parameter is gov-... 

Up to date the only published work on the dynamic structure factor of a glass forming system at intermediate length scales is a study on PIB [147]. The NSE measurements explored the Q-range 0.20[Pg.136]

K and 390 K (Tg=205 K). As can be seen in Fig. 4.32a, the dynamics were accessed from the intermediate length scales region to the valley between the first and the second peaks of across Qmax Figure 5.13 shows some of the... 

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. 

IV. Extended Hydrodynamics Dynamics at Intermediate Length Scale... 

IV. EXTENDED HYDRODYNAMICS DYNAMICS AT INTERMEDIATE LENGTH SCALE... 

An analysis of the relevant integrals shows that the dominant contribution of the density mode to the viscosity and the friction comes from intermediate length scale (8 > qa > 3). That is, more than 90% of the contribution comes from a region surrounding the sharp first peak of the static structure factor— that is, around qa = 2n. At these values of the wavenumber, the dynamic structure factor is well-determined by the following simple mean field expression ... 

Domains having different degrees of fluidity may appear as a consequence of density fluctuations at intermediate length scales. Note that in an ergodic system the probability of fluctuation of the wavenumber-dependent density, pv is given by the following well-known expression ... 

---