Intermediate dynamic length, dependence

Phillies, et a/. (69) present results confirming Streletzky and Phillies s(64) prior interpretation that HPC solutions have a dominant, concentration-independent characteristic dynamic length scale, namely the radius of a polymer chain, which for this species is i 50 nm. In particular (i) There are distinct small-probe and large-probe phenomenologies, with the division between small and large probes being about 50 nm, the same at all polymer concentrations, (ii) For small probes, the relative amplitude of the sharp and broad modes depends markedly on scattering vector q with a crossover near q 70 nm. (iii) The mean relaxation rate of the small-probe broad mode increases markedly near 50 nm. (iv) The probe intermedi-... 

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... 

In conclusion of Section 6.3 we wish to stress that the elastic attraction of similar defects (reactants) leads to their dynamic aggregation which, in turn, reduces considerably the reaction rate. This effect is mostly pronounced for the intermediate times (dependent on the initial defect concentration and spatial distribution), when the effective radius of the interaction re = - JTX exceeds greatly the diffusion length = y/Dt. In this case the reaction kinetics is governed by the elastic interaction of both similar and dissimilar particles. A comparative study shows that for equal elastic constants A the elastic attraction of similar particles has greater impact on the kinetics than interaction of dissimilar particles. 

The intermediate length (tube diameter) 2 can be estimated from the modulus with the aid of the above equations. Comparison of values of the intermediate length found from dynamic modulus and from neutron-scattering experiments was presented by Ewen and Richter (1995). They found the values to be close to each other, though there is a difference in the temperature dependence of the values of intermediate length found by different methods. 

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