Relaxation in Polymers

R. Granek. Stress relaxation in polymer melts and solutions Bridging between the breathing and reptation regimes. Macromolecules 2<5 5370-5371, 1995. 

D. Moses, A.J. Heegcr, in Relaxation in Polymers (Ed. T. Kobayashi), World Scientific, Singapore 1993. 

To account for the variation of the dynamics with pressure, the free volume is allowed to compress with P, but differently than the total compressibility of the material [22]. One consequent problem is that fitting data can lead to the unphysical result that the free volume is less compressible than the occupied volume [42]. The CG model has been modified with an additional parameter to describe t(P) [34,35] however, the resulting expression does not accurately fit data obtained at high pressure [41,43,44]. Beyond describing experimental results, the CG fit parameters yield free volumes that are inconsistent with the unoccupied volume deduced from cell models [41]. More generally, a free-volume approach to dynamics is at odds with the experimental result that relaxation in polymers is to a significant degree a thermally activated process [14,15,45]. 

The two main sources for slow relaxation in polymers are entanglement effects and the glass transition. The first is entropic in origin, whereas the second—at least in chemically realistic polymer models—is primarily enthalpic. We write the largest relaxation time in the melt as... 

We can therefore conclude that differences in the structural relaxation between bead-spring and chemically realistic models can be attributed to either the differences in packing that we discussed above or the presence of barriers in the dihedral potential in atomistic models. To quantify the role of dihedral barriers in polymer melt dynamics, we now examine high-temperature relaxation in polymer melts. 

Since none of the lattice models is now clearly superior, the choice for interpretation of spin relaxation in polymers is arbitrary. Familiarity leads us to select the Jones and Stockmayer model so we will now consider application of this model to several well studied polymer systems in order to compare dynamics from polymer to polymer. Also the equations required to consider anisotropic Internal rotation of substituent groups and overall molecular tumbling as independent motions in addition to backbone rearrangements caused by the three-bond jump are available for the Jones and Stockmayer model (13). 

Note 5 The relaxation spectrum (spectrum of relaxation times) describing stress relaxation in polymers may be considered as arising from a group of Maxwell elements in parallel. 

S. Matsuoka, Relaxation in Polymers Hanser Publishers, New York, 1992. 7a is sometimes denoted as T. ... 

The dynamic mechanical thermal analyzer (DMTA) is an important tool for studying the structure-property relationships in polymer nanocomposites. DMTA essentially probes the relaxations in polymers, thereby providing a method to understand the mechanical behavior and the molecular structure of these materials under various conditions of stress and temperature. The dynamics of polymer chain relaxation or molecular mobility of polymer main chains and side chains is one of the factors that determine the viscoelastic properties of polymeric macromolecules. The temperature dependence of molecular mobility is characterized by different transitions in which a certain mode of chain motion occurs. A reduction of the tan 8 peak height, a shift of the peak position to higher temperatures, an extra hump or peak in the tan 8 curve above the glass transition temperature (Tg), and a relatively high value of the storage modulus often are reported in support of the dispersion process of the layered silicate. 

The electrostriction effect, beside its effect on the piezoelectricity, gives a new insight onto relaxations in polymers when the electrostriction constant is obtained over a wide frequency range. It provides us with a knowledge of the strain dependence of relaxation time. 

Frosini, V. Mechanical relaxation in polymer mesophases. Proc. 28th Macromol. Symp. IUPAC, U. Mass., Amherst, MA, p. 806, 1982... 

Since 13C relaxation of polymers has already been reviewed (Schaefer, 1974) we can restrict ourselves here to a few general remarks and to more recent papers in this field. Although i3C relaxation in polymers is generally dominated by dipolar relaxation, the NOE factors do not reach the maximum of tj = 2 commonly observed for small molecules. This is due to the fact that polymers usually do not satisfy the extreme narrowing limit only for which this NOE maximum is valid. In this case it is helpful to compare H relaxation data (Cutnell and Glasel, 1977). 

Fujita, H., and Kishimoto, A. J. (1958). Diffusion-controlled stress relaxation in polymers. II. stress relaxation in swollen polymers, /. Polym. Sci. 28, 547-567. 

Although molecular mobility is severely restricted below the glass transition temperature, the dynamic glass transition temperature (main transition or, conventionally -relaxation) in polymers as it have been described above, is usually accompanied by subglass secondary relaxations labeled as p, y, S, relaxations. The glass transition at low temperatures is assumed to be caused by the cooperative motion of many particles, while the secondary relaxations have a more localized molecular... 

F. Boue, J. Bastide, M. Buzier, A. Lapp, J. Herz and T.A. Vilgis, Strain induced large fluctuations during stress relaxation in polymer melts observed by small-angle neutron scattering. Lozenges , butterflies , and related theory, Coll. Polym. Sci., 269, 195 (1991). 

Gao J, Weiner JH (1994) Monomer-level description of stress and birefringence relaxation in polymer melts. Macromolecules 27(5) 1201-1209 Gardiner CW (1983) Handbook of stochastic methods for physics, chemistry, and the natural sciences. Springer, Berlin... 

DSC has been amply demonstrated in the pat to be a useful instrument to follow the kinetics of enthalpy relaxation in polymers 41,42,74>. Figure 21 shows the DSC... 

Most studies of magnetic relaxation in polymers have dealt with solid or melted polymers (73)] however, Odajima (20) has studied proton relaxation in solutions of polystyrene and polyisobutylene. It is desirable to extend and refine such measurements. In concentrated solution, some insight into the motional effects of polymer-solvent interactions should be obtainable and if, despite low sensitivity, reliable 7 values can be obtained for polymers in dilute solutions, valuable information concerning the detailed motional behavior of isolated polymer molecules may be provided. 

Boyer RF (Ed), "Transitions and Relaxations in Polymers", Interscience, New York, 1967. 

Relaxations observed in polymers show broader dispersion curves and lower loss maxima than those predicted by the Debye model, and the (s" s ) curve falls inside the semicircle. This led Cole and Cole (1941) to suggest the following semi-empirical equation for dielectric relaxations in polymers ... 

More recently, it has been suggested that a departure from the assumed exponential form of the approach to equilibrium may be responsible for the breadth of dipolar relaxation in polymers. A decay function that describes a wide range of slow relaxation processes is the so-called stretched exponential ... 

Another way of describing experimentally observed dielectric relaxation in polymers is based on an empirical function formulated by Havriliak and Negami (1967) for the frequency domain ... 

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