Relaxation free volume

There are a number of important concepts which emerge in our discussion of viscosity. Most of these will come up again in subsequent chapters as we discuss other mechanical states of polymers. The important concepts include free volume, relaxation time, spectrum of relaxation times, entanglement, the friction factor, and reptation. Special attention should be paid to these terms as they are introduced. 

A modulus value increase upon storage under ambient conditions is also reported for other semi-crystalline polymers like, for instance, polypropylene. Struik [11] measured for PP a continuously increasing dynamic stiffness at 20°C in combination with a decrease of the intensity of the glass-rubber (S) transition of PP (the temperature location of the S-transition did not change). Struik called this phenomenon an amorphous phase ageing effect a densification process of the amorphous PP phase due to a free volume relaxation effect. 

Volume relaxation is considered to be determined by free-volume relaxation. The agents of this process, segmental conformational changes, are therefore to be coupled to local free-volume states. These states are therefore to be viewed as mobility measures. Thus, we have the connections of mobility rate free volume/= h. (The... 

The time-temperature superpositioning principle was applied f to the maximum in dielectric loss factors measured on poly(vinyl acetate). Data collected at different temperatures were shifted to match at Tg = 28 C. The shift factors for the frequency (in hertz) at the maximum were found to obey the WLF equation in the following form log co + 6.9 = [ 19.6(T -28)]/[42 (T - 28)]. Estimate the fractional free volume at Tg and a. for the free volume from these data. Recalling from Chap. 3 that the loss factor for the mechanical properties occurs at cor = 1, estimate the relaxation time for poly(vinyl acetate) at 40 and 28.5 C. 

It has been found, too, that the relaxation times are eompatible with an Arrhenius-hke variation with density cj) (Fig. 19). This suggests that free volume eoneepts [42] might be useful for the understanding of the dynamies of dense polymerie films. 

The problem-solving approach that ties the processing variables to products properties includes considering melt orientation, polymer degradation, free volume/molecular packing and relaxation, cooling stresses, and other such factors. The most influential of these four conditions is melt orientation, which can be related to molded-in stress or strain. 

Stimulation of the conformational relaxation movements of the polymeric chains (by repulsion between the nascent positive charges), with the generation of free volume. Local nuclei or general and simultaneous relaxation occur, depending on the initial compaction of the polymer film. 

The action of a muscle is a consequence of electrochemically stimulated conformational relaxation processes that occur along every electroactive chain inside a polymeric film. A free-volume model dependent on the... 

Experimental data on nitrogen obtained from spin-lattice relaxation time (Ti) in [71] also show that tj is monotonically reduced with condensation. Furthermore, when a gas turns into a liquid or when a liquid changes to the solid state, no breaks occur (Fig. 1.17). The change in density within the temperature interval under analysis is also shown in Fig. 1.17 for comparison. It cannot be ruled out that condensation of the medium results in increase in rotational relaxation rate primarily due to decrease in free volume. In the rigid sphere model used in [72] for nitrogen, this phenomenon is taken into account by introducing the factor g(ri) into the angular momentum relaxation rate... 

A more rigorous free-volume treatment is due to Cohen and Grest (CG) [34,35], according to which the material is comprised of liquid and solid-like cells. The former have free volume, but mobility requires continuity of the local empty space. The temperature dependence of the relaxation times according to the CG model is... 

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]. 

Steady-state behavior and lifetime dynamics can be expected to be different because molecular rotors normally exhibit multiexponential decay dynamics, and the quantum yield that determines steady-state intensity reflects the average decay. Vogel and Rettig [73] found decay dynamics of triphenylamine molecular rotors that fitted a double-exponential model and explained the two different decay times by contributions from Stokes diffusion and free volume diffusion where the orientational relaxation rate kOI is determined by two Arrhenius-type terms ... 

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