Dynamics terminal relaxation time

The difference in the molecular-weight dependence of the terminal relaxation time can be attributed to the change of the mechanisms (diffusive and repta-tion, correspondingly) of conformational relaxation in these systems. Further on in this section, we shall calculate dynamic modulus and discuss characteristic quantities both for weakly and strongly entangled systems. 

While all relaxation times depend on temperature and pressure, only the global motions (viscosity, terminal relaxation time, steady state recoverable compliance) are functions of Mw (and to a lesser extent MWD). An example of the various dynamics of 1,4-polyisoprene are illustrated in Fig. 10. At frequencies beyond the local segmental relaxation, or at temperatures below Tg, secondary relaxation processes can be observed, especially in dielectric spectra. In polymers, many of these secondary processes involve motion of pendant groups. However, the slowest secondary relaxation, referred to as the Johari-Goldstein process, involves all atoms in the repeat unit (or the entire molecule for low M materials). This Johari-Goldstein relaxation serves as the precursor to the prominent glass transition. 

The modulus recovery experiments allowed measuring the terminal relaxation time of reptation motion of bulk and surface immobilized chains, supporting the hypothesis that theie is no interphase per se when nano-scale is considered. In order to bridge the gap between the continuum interphase on the microscale and the discrete molecular structure of the matrix consisting of freely reptating chains in the bulk and retarded reptatiug chains in contact with the inclusions, higher order elasticity combined with a suitable molecular dynamics model could be utilized [151-155]. 

To describe the change in reptation dynamics of the chains as a function of nanoparticle volume fraction, a percolation model was used. At the percolation threshold, a physical network formed by interconnection of immobilized chains on individual nanoparticles penetrates the entire sample volume. In this case, only physical cross-links are considered and the terminal relaxation time reaches the value characteristic for the life time of the physical filler-polymer bond. Thus, the relaxation time near the percolation threshold is expressed in the form [44] ... 

First, we note that in order to predict a phase diagram as a function of shear rate, we must account for the variation with temperature of the molecular dynamics. It is well established that the terminal relaxation time changes rapidly with temperature, due to changes in the monomeric friction coefficient, and a suitable description of the behaviour is provided by the phenomenological WLF formula [68],... 

Stockmayer and Kennedy (1975) conducted a seminal smdy on the chain dynamics of Rouse chains of AB-type diblock or ABA-type triblock copolymers by modifying the bead—spring model of Rouse for linear flexible homopofymers (see Chapter 4). They calculated the spectrum of relaxation times ftp biodc) block copolymer in terms of the terminal relaxation times for the Rouse chains for the A and B blocks. Once the values of are determined, one can calculate linear dynamic viscoelastic... 

The Rouse model describes the dynamical properties of melts of macromolecules of a relatively small number of Kuhn segments, Ncritical number Nc is the number of Kuhn segments for the critical molecular mass Me- Flexible polymers have critical Kuhn segment numbers typically in the range Mc=40- 60 [1, 42-44, 52]. On the other hand, chain dynamics in concentrated systems of polymers with N Nc is much slower than expected on the basis of the Rouse model. Alluding to chain entanglements that are considered to become relevant in this case, one speaks of entangled dynamics. For example, experimental terminal relaxation times and center-of-mass self-diffusion coefficients scale as and... 

Since T/ does not or only weakly depend on the chain length, the molecular weight dependence of the effective correlation time for entangled dynamics results in Tc oc [35, 139, 144], whereas the terminal relaxation time of rheology scales as Ti oc [52]. The effect of the crossover from unentangled to entangled dynamics on spin-lattice relaxation will be discussed later (see Fig. 31b). 

Some terminal viscoelastic parameters have also been evaluated at 160°C using a Cole-Cole expression for the dynamic viscosity. Table Ic shows the zero shear viscosity (t]o)> the characteristic relaxation time (ko, corresponding to the... 

The simple reptation model does not properly account for all the relaxation modes of a chain confined in a tube. This manifests itself in all measures of terminal dynamics, as the longest relaxation time, diffusion coefficient and viscosity all have stronger molar mass dependences than the reptation model predicts. Tn Sections 9.4.5 and 9.6.2, more accurate ana-... 

The reptation time of the P-mer is Tep(P) and the constraint release time Tube given in Eq. (9.85). The faster of the two types of motion controls the diffusion of the P-mer. For constraint release to significantly affect terminal dynamics, the Rouse relaxation time of the confining tube Ttube must be shorter than the reptation time of the P-mer Tep( ) ... 

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