Viscoelastic relaxation dynamic

PTT has three dynamic mechanical viscoelastic relaxations [61, 62], a, (j and Y (Figure 11.9). The 70°C a-relaxation is the glass transition. In a study on the effect of methylene sequence length on aromatic polyester viscoelastic properties, Farrow et al. [63] reported a PTT a-relaxation as high as 95 °C. They also found that Tg of this series of aromatic polyesters did not show any odd-even effects, which was later confirmed by Smith et al. [64],... 

One conclusion from this study is that although the hard-sphere fluid has been very successful as a reference fluid, for example, in developing analytical equations of state, it is unrealistic in representing the dynamical relaxation processes in real systems, even with very steeply repulsive potentials. Owing to the discontinuity in the hard-sphere potential, this fluid, in fact, is not a good reference fluid for the short time (fast or j9 ) viscoelastic relaxation aspects of rheology. 

While the difference in the upwards and downwards solvent responses presented in Figure 3 is striking, this is not the first time that variations in solvation dynamics for the same solvent have been observed. Experimental studies have shown differences in solvation response for different probe molecules in the same solvent. This is a direct indication that probe molecules which have different excited state charge distributions and different mechanical interactions with the solvent produce differing relaxation dynamics. Computer simulations have also observed differing solvation dynamics for the forward and reverse transitions of the sudden appearance of charge, indicative of a solute-dependent solvent response. Moreover, theoretical work has shown that dielectric solvation dynamics is sensitive to the shape of a solute, and that solute size is intimately connected to viscoelastic relaxation. It is these effects which are manifest in the... 

The Takayanagi model was developed to account for the viscoelastic relaxation behaviour of two phase polymers, as recorded by dynamic mechanical testing. " It was then extended to treat both isotropic and oriented semi-crystalline polymers. The model does not deal with the development of mechanical anisotropy on drawing, but attempts to account for the viscoelastic behaviour of either an isotropic or a highly oriented polymer in terms of the response of components representing the crystalline and amorphous phases. Hopefully, comparisons between the predictions of the model and experimental results may throw light on the molecular processes occurring. 

Interpretation of mechanical measurements in terms of molecular structure was until fairly recently confined essentially to identification of the temperatures of the major viscoelastic relaxations through extensional or torsional dynamic mechanical studies. Now, however, investigations of the elastic constants and their temperature dependence—allied with dynamic mechanical, creep and both wide and small angle X-ray diffraction— are yielding fairly detailed pictures of the interrelation of the crystalline and less well ordered regions of some oriented solid polymers. 

The onset of deformation mechanisms at particular temperatures indicated that it was appropriate to investigate viscoelastic relaxation processes by dynamic mechanical methods. Some preliminary studies were made in 1956 and 1957 by Hellwege et who demonstrated... 

Now, we turn our attention to the dielectric relaxation. The decrease of dynamic dielectric constant Ae and the dielectric loss e" have the mode distribution (cf. Equation 3.18) formally identical to the viscoelastic mode distribution, and the above explanation for the viscoelastic relaxation applies also to the dielectric relaxation For the simplest case, the relaxation times and nonnormalized intensities of fhe dielectric modes exhibit the same change with T irrespective of the mode index q as... 

Nevertheless, we should remember that the viscoelastic relaxation captures just one aspect of the polymer dynamics— that is, the relaxation of... 

If particle motion were observed over times shorter than the viscoelastic relaxation times Particle displacements in successive moments would be correlated. Equation 12 would not be correct. log[g (q, r)]/ would not be proportional to the mean-square particle displacement during r. With respect to polymer dynamics, the interest in eqs 9-12 has been the short time regime in which viscoelastic effects are apparent in D(r), but in the short time regime eq 12 does not describe probe motion in solution. 

Fig. 19.5. Relationship between the activation energies for viscoelastic relaxation (ilHuA/i ) measured by dynamic mechanical relaxation spectra and those for molecular transport (ilEg) in crystallization for poly(ethylene tetrephthalate) (PET) / poly(l-4-cyclohexylene dimethylene terephthalate) (PCT) copoljmers [48]. Copolymer compositions (PCT/PICT) = 1 100/0, 2 80/20, 3 66/34, 4 5/95, 5 0/100...

Viscoelasticity. When in addition, the flnid or the material stores some capacitive energy, an elastic property comes in snpplement to the dynamic and kinematic viscosities for featuring the system. The storage and the transport of capacitive energy is then supported by a combined property of viscoelasticity, analogous to a kinetic constant in physical chemistry (see case study All Reactive Chemical Species in Chapter 4 and case stndy 116 Viscoelastic Relaxation in Chapter 11). 

The second system constitutive property involved in viscoelastic relaxation is the dynamic viscosity defined as the operator linking the lineic density of velocity to the stress... 

Two manifestations of linear viscoelasticity are creep and stress relaxation-, the respective two testing methods are known as transient tests. One can also apply sinusoidal load, an increasingly more used method of study of viscoelasticity by dynamic mechanical analysis (qv) (DMA). We shall now briefly discuss each of these three approaches. 

Dynamic Mechanical Properties. The PTT dynamic mechanical relaxation spectrum shows three viscoelastic relaxations (41). a-Relaxation occurs at -70°C and is the glass-transition temperature. Tg obtained by dynamic mechanical methods is usually higher than that from a dsc, and is frequency dependent. 

This square-root dependence on tw is a fundamental featme of linear chains in the Rouse model. The shear modulus at intermediate frequencies is a signature of the internal, intra-chain dynamics, which is determined by the topology of the GGS. As stressed before, the viscoelastic relaxation forms can be expressed through the relaxation spectrum H r), see Eq. 27. Here one finds [3] ... 

An interesting example of such coupling is observed in polymer solutions between the relaxation of the critical concentration fluctuations and viscoelastic relaxation. This coupling leads to a crossover between the dilfusive critical dynamics in the critical regime and relaxation dynamics of an infinite polymer chain in the theta-pomt. regime. 

Nicolai, T. Randrianantoandro, H. Prochazka, F. Durand, D. (1997) Viscoelastic relaxation of polyurethane at different stages of the gel formation. 2. Sol-gel transition dynamics. Macromolecules, 30(19), 5897-5904. 

The situation schematically described in Fig. 4, can be realized experimentally by choosing a sample having a viscoelastic relaxation time such that qt is in the range of the q investigated. The results are reported in Fig. 9. For q < q f the profile of the dynamical structure factor is exponential, the characteristic decay time varies as q . For q > qt the profile is not exponential and extends from x (q -dependent)... 

In contrast, the dynamic properties such as viscosity, viscoelastic relaxation time, gel diffusion coefficient, which depend on the entanglements and thus on the length f, do not scale with C/C. ... 

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