Relaxation times of macromolecule

Each point is calculated as asymptotic value of the rate of relaxation for large times (see examples of dependences in Fig. 6) for different molecular weights with corresponding values of the parameters B and if. The values of the coefficients of local anisotropy are ae = 0.3, ae = 0.06 for the circles and ae = 0.3, ae = 0.15 for the squares. The solid line depicts analytical results for linear approximation. The dashed lines with the slope 1 reproduce the well-known dependence n M3 for the relaxation time of macromolecules in strongly entangled systems. Adapted from Pokrovskii (2006). 

Proteins, 109,110, 116.Seealso Enzymes Macromolecules average thermal amplitudes, MD simulations, 119 binding of ligands to, 120 dielectric relaxation time of, 122 electrostatic energies in, 122, 123-125 flexibility of, 209,221,226-227, 227 folding, 109,227... 

E. Bayer, K. Albert, H. Wikkisch, W. Rapp and B. Hemmasi, Carbon-13 nmr relaxation times of a tripeptide methyl ester and its polymer-bound analogs, Macromolecules, 1990, 23, 1937 1940. 

Due to the long relaxation times of the macromolecules in comparison to the turbulence times, a deformed macromolecule can readily outlive the lifespan of a microeddy and thus exert a decisive influence on the latter. On the other hand, this also means that extension of the molecule will be made possible by the combined effects of many consecutive generations of eddies. A large proportion of the turbulent energy is thereby used in the alignment and deformation of the polymer molecule. 

This is another ramification of incomplete response of polymers, because the experimental time is smaller than the relaxation time of the system of macromolecules. As expected, weld lines are mechanically weak and have optical properties that differ from those of the bulk, making them visible. Furthermore, they result in film or tube gauge nonuniformities, probably because of the different degree of swelling of the melt in the neighborhood of the weld line. They also induce cross-machine pressure nonuniformities. To overcome these problems, basic cross-head die designs (Fig. 12.42) have been devised in which the mandrel is mechanically attached to the die body in such a way that obstacles are not presented to the flow in the annular region. 

The internal viscosity of the macromolecule is a consequence of the intramolecular relaxation processes occurring on the deformation of the macromolecule at a finite rate. The very introduction of the internal viscosity is possible only insofar as the deformation times are large, compared with the relaxation times of the intramolecular processes. If the deformation frequencies are of the same order of magnitude as the reciprocal of the relaxation time, these relaxation processes must be taken explicitly into account and the internal viscosity force have to be written, instead of (2.26) as... 

The situation looks simpler, if one assumes that relaxation times of the surrounding can be neglected, and one obtains for the collective motion of the entire set of macromolecules, considered as a set of Brownian particles, a system of stochastic Markovian equations... 

When this approximation is valid The empirical estimation of the relaxation time of the medium shows that, for the systems of short macromolecules (M < 2Me), the relaxation time of the medium indeed can be neglected, so that the approximation is valid for these systems. For the systems of longer... 

Here, are the relaxation times of the macromolecule in a monomer viscous fluid - Rouse relaxation times... 

A particular choice of the coefficients ae = 0.3 and a = 0.06 determines the value T = 417 r for the relaxation time of the first mode, which is close to the reptation relaxation time 370 r. The calculated relaxation times of the third mode 73 = 315 r is a few times as much as the corresponding reptation relaxation time 41.1 r, which indicates that the dependence of the relaxation times on the mode label is apparently different from the law (4.36). It is clearly seen in Fig. 7, where the dependence of the relaxation times of the first six modes of a macromolecule on the coefficient of internal anisotropy is shown. The relaxation times of different modes are getting closer to each other with increase of the coefficient of internal anisotropy. The values of the largest relaxation time of the first mode for different molecular weights are shown in Fig. 8. The results demonstrate a drastic decrease in values of the largest relaxation times for strongly entangled systems induced by introduction of local anisotropy. 

One can see that the relaxation times at a > (ip/x) 2 are the Rouse relaxation times of the part of the macromolecule that correspond approximately to the length of the macromolecule between adjacent entanglements Me. There is an interval between slow and fast relaxation times, which is the bigger the longer the macromolecules. 

Now, we can try to relate the above results to the experimental data on the viscoelasticity of concentrated solutions of polymers. For the systems of long macromolecules, the estimated values of parameter are small. Having used expressions (6.40) for this case, one can evaluate the terminal relaxation time of the system... 

Of course, these relations are trivial consequences of the stress-optical law (equation (10.12)). However, it is important that these relations would be tested to confirm whether or not there is any deviations in the low-frequency region for a polymer system with different lengths of macromolecules and to estimate the dependence of the largest relaxation time on the length of the macromolecule. In fact, this is the most important thing to understand the details of the slow relaxation behaviour of macromolecules in concentrated solutions and melts. 

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