Relaxation mechanisms, viscoelastic study

Direct determination of relaxation time through viscoelastic studies (all mechanical properties involve this important parameter). 

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],... 

In most non-crystalline linear polymers described to date, the relaxation mechanism (in the absence of such extraneous factors as degradation) is the simple molecular flow, or the a mechanism. Exceptions have been found, for instance in the case of the polysulfides (4,54,56,57) or pol5mrethanes (57) in which far above the gla transition temperature a ixmd interchange mechanism was observed. For a number of reasons (which will be described below), it is of interest to study viscoelasticity of polymers which are subject to both mechanisms, i. e., a and (as bond-interchange will be called due to the intrinsically chemical nature of the reaction), particularly if both mechanisms occur with comparable relaxation times. Among the benefits of such a study, particularly in the case of the ionic inorganic polymers would be ... 

It is advisable to review very briefly the preceeding work done on the viscoelastic properties of polymers subject to multiple relaxation mechanisms, as well as previous solution studies of phosphates in the presence of lanthanum on the basis of these studies La" was chosen as the ion most likely to lead to bond interchange. 

This paper has reviewed several studies, particularly those performed on the phosphate polymers, in which ionic forces were imjx>rtant in determining the properties or behavior of the material. Only very few properties were investigate among these were 1) the glass transitions as a function of the molecular we ht, the nature of the terminal group, and the nature of the counterion, 2) the viscoelastic properties as a function of the counterion and 3) the viscoelastic relaxation mechanism, with specific emphasis on the separation of the a and mechanisms. In this treatment, a deliberate attempt was made to present pertinent theories, insofar as they exist, but it seems evident that here as much work remains to be done as on the experimental level, if not more. 

It is clear from fig. 7.14 that measurements made at fixed co over a wide enough temperature range can show the complete viscoelastic behaviour. For instance, measurements made at 100 Hz over the temperature range — 14 to 130°C for this polymer show almost the full range of values of J co, T). It is much easier to vary the temperature of a sample than it is to obtain measurements over the equivalent wide range of frequencies, so measurements as a function of T at fixed cd are often used to study relaxation mechanisms in polymers. Figure 7.15 shows some data of this type obtained for PVC on a commercial apparatus. It is important to note, however, that such data cannot be used to construct curves showing the... 

Theoretical studies of the dynamics of self-assemblies of wormlike surfactant micelles have been reported by a number of investigators, such as Cates and coworkers [Turner and Cates, 1991 Marques et al 1994]. Since they are subject to reversible scission and recombination, they are called living polymers. The continuous breaking and repair of the micellar chains provides more complex solution behavior than do reptating polymer chains that is, their stress relaxation mechanisms are a combination of reptation and breaking followed by reassembly. At low frequencies, linear viscoelastic (Maxwell) behavior is predicted and observed for some surfactant systems. However, non-Maxwell behavior was observed in Cole-Cole plots of a number of cationic surfactant systems [Lu, 1997 Lin, 2000]. 

The objectives of the present research were (i) to develop a solvent transport model accounting for diffusional and relaxational mechanisms, in addition to effects of the viscoelastic properties of the polymer on the dissolution behavior (ii) to perform a molecular analysis of the polymer chain disentanglement mechanism, and study the influence of various molecular parameters like the reptation diffusion coefficient, the disentanglement rate and die gel layer thickness on the phenomenon and (iii) to experimentally characterize the dissolution phenomenon by measuring the temporal evolution of the various fronts in the problem. 

In the preparation and processing of ionomers, plasticizers may be added to reduce viscosity at elevated temperatures and to permit easier processing. These plasticizers have an effect, as well, on the mechanical properties, both in the rubbery state and in the glassy state these effects depend on the composition of the ionomer, the polar or nonpolar nature of the plasticizer and on the concentration. Many studies have been carried out on plasticized ionomers and on the influence of plasticizer on viscoelastic and relaxation behavior and a review of this subject has been given 119]. However, there is still relatively little information on effects of plasticizer type and concentration on specific mechanical properties of ionomers in the glassy state or solid state. 

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 creep of a viscoelastic body or the stress relaxation of an elasacoviscous one is employed in the evaluation of T] and G. In such studies, the long-time behavior of a material at low temperatures resembles the short-time response at high temperatures. A means of superimposing data over a wide range of temperatures has resulted which permits the mechanical behavior of viscoelastic materials to be expressed as a master curve over a reduced time scale covering as much as twenty decades (powers of ten). 

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... 

Studies on the mechanical properties of glassy polymer-solvent or, more generally, polymer-diluent mixtures have been primarily concerned with the deformation behavior at small strains which is governed by the viscoelastic properties of the material. From these studies it is well known that diluents significantly affect relaxation processes in glassy polymers, as clearly evidenced by phenomena such as plasticization and antiplasticization... 

The effect of diluents on the viscoelastic behavior of amorphous polymers is more complex at temperatures below T, i.e., in the range of secondary relaxation processes. Mechanical, dielectric and NMR measurements have been performed to study the molecular mobility of polymer-diluent systems in this temperature range (see e.g. From extensive studies on polymers such as polycarbonate, polysulfone and polyvinylchloride, it is well known that diluents may suppress secondary relaxation processes. Because of the resulting increase in stiffness, these diluents are called antiplasticizers . Jackson and Caldwell have discussed characteristic properties... 

Time constants are related to the relaxation times and can be found in equations based on mechanical models (phenomenological approaches), in constitutive equations (empirical or semiempirical) for viscoelastic fluids that are based on either molecular theories or continuum mechanics. Equations based on mechanical models are covered in later sections, particularly in the treatment of creep-compliance studies while the Bird-Leider relationship is an example of an empirical relationship for viscoelastic fluids. 

In contrast to other Tg methods, dynamic measurements easily detect glassy state relaxations and have been extensively applied to their study. These include dynamic mechanical methods, dielectric relaxation, and nuclear magnetic resonance (NMR). Since we are primarily concerned with viscoelastic response at this point, we shall confine the discussion to the dynamic mechanical technique and delay our consideration of dielectric and NMR methods until Chapter 7. 

Stress relaxation experiments involve the measurement of the force required to maintain the deformation produced initially by an applied stress as a function of time. Stress relaxation tests are not performed as often as creep tests because many investigators believe they are less readily understood. The latter point is debatable, and it may only be that the practical aspects of creep measurements are simpler. As will be shown later, all the mechanical parameters are in theory interchangeable, and so all such measurements will contribute to the understanding of viscoelastic theory. Whereas stress relaxation measurements are useful in a general study of polymeric behavior, they are particularly useful in the evaluation of antioxidants in polymers, especially elastomers, because measurements on such systems are relatively easy to perform and are sensitive to bond rupture in the network. 

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