Relaxation Behaviour of Polymers

The reversible extensibility of a polymer is usually characterised by the measurement of the compression set. Because this measurement is a long-term relaxation experiment, which is usually performed at higher temperature, it summarises the effects of physical and chemical relaxation processes and is therefore not appropriate for the characterisation of the reversible extensibility and the stress relaxation of articles under dynamic service conditions. Wrana and Pask [141] introduced a method for the dynamic characterisation of the reversible extensibility and the stress relaxation. 

The results of the measurements can be used for a quantitative test of the appropriateness of polymers in articles used dynamically as well as for the determination of the molecular mechanism, which generate the stress relaxation and the permanent deformation in polymers. This method can be used for a quantitative evaluation of polymers in articles used dynamically such as timing belts, engine moimts or seals. 

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The stress-relaxation behaviour of polymers is extremely temperature-dependent, especially in the region of the glass temperature. 

Gotlib, Yu. Ya. Some relationships of relaxation behaviour of polymer solutions. In Relaksatsyonnye yavleniya v polimerakh (Relaxation phenomena in polymers). Bartenev,... 

Induced stress is always a factor in structural applications and can result from processing conditions, thermal history, phase transitions, surface degradation, and variations in the expansion coefficient of components in a composite. Since the modulus of a material is not only temperature dependent but time dependent as well, the stress relaxation behaviour of polymers and composites is of great importance to the structural engineer. Stress relaxation is also important to the polymer chemist developing new engineering plastics because relaxation times and moduli are affected by polymer structures and transition temperatures. Therefore, it is essential that polymeric materials that will be subjected to loading stress be characterised for stress relaxation and creep behaviour. 

It must be emphasised that the site model is applicable only to relaxation processes showing a constant activation energy, examples being those associated with localised motions in the crystalline regions of semi-crystalline polymers. The temperature dependence of the glass transition relaxation behaviour of polymers does not fit a constant activation energy model, and where this has appeared to be true it is probably a consequence of the limited range of experimental frequencies that were available. 

Before discussing tire complex mechanical behaviour of polymers, consider a simple system whose mechanical response is characterized by a single relaxation time x, due to tire transition between two states. For such a system, tire dynamical shear compliance is [42]... 

Hardy, L., Stevenson, I., Boiteux, G., Seytre, G., and Schonhals, A. (2001). Dielectric and dynamic mechanical relaxation behaviour of poly(ethylene 2,6 naphthalene dicarboxyl-ate). I. Amorphous films. Polymer 42(13), 5679-5687. 

To describe the behaviour of a macromolecule in an entangled system, we have introduced the ratio of the relaxation times x and two parameters B and E connected with the external and the internal resistance, respectively. These parameters play a fundamental role in the description of the dynamical behaviour of polymer systems, so that it is worthwhile to discuss them once more and to consider their dependencies on the concentration of polymer in 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. 

The monograph contains the fundamentals of the theory and reflects the modern situation in understanding the relaxation behaviour of a polymer solutions and melts. The contents of the monograph can be related to the fields of molecular physics, fluid mechanics, polymer physics and materials science. I have tried to present topics in a self-contained way that makes the monograph a suitable reference book for professional researchers. I hope that the book will also prove to be useful to graduate students of above mentioned specialities who have some background in physics and mathematics. It would provide material for a one or two semester graduate-level course in polymer dynamics. 

All together relaxation time measurements are a powerful tool to study the dynamic behaviour of polymers in the solid state. 

Although the Maxwell-Wiechert model and the extended Burgers element exhibit the chief characteristics of the viscoelastic behaviour of polymers and lead to a spectrum of relaxation and retardation times, they are nevertheless of restricted value it is valid for very small deformations only. In a qualitative way the models are useful. The flow of a polymer is in general non-Newtonian and its elastic response non-Hookean. 

This chapter discusses the dynamic mechanical properties of polystyrene, styrene copolymers, rubber-modified polystyrene and rubber-modified styrene copolymers. In polystyrene, the experimental relaxation spectrum and its probable molecular origins are reviewed further the effects on the relaxations caused by polymer structure (e.g. tacticity, molecular weight, substituents and crosslinking) and additives (e.g. plasticizers, antioxidants, UV stabilizers, flame retardants and colorants) are assessed. The main relaxation behaviour of styrene copolymers is presented and some of the effects of random copolymerization on secondary mechanical relaxation processes are illustrated on styrene-co-acrylonitrile and styrene-co-methacrylic acid. Finally, in rubber-modified polystyrene and styrene copolymers, it is shown how dynamic mechanical spectroscopy can help in the characterization of rubber phase morphology through the analysis of its main relaxation loss peak. 

The above phenomenological description of the viscoelastic behaviour of polymer melts and concentrated solutions leads to the following important conclusions if one focuses on the behavioiu- in the terminal region of relaxation, what is usually done for temperature (time-temperature equivalence) may also be done for the concentration effects and the effects of chain length one may define a "time-chain length equivalence" and "time-concentration equivalence"[4]. For monodisperse species, the various shifts along the vertical (modulus) axis and horizontal (time or frequency axis) are contained in two reducing parameters the... 

Stracke, A., Bayer, A., Zimmermaim, S., Wendorff, J. H., Wirges, W., Bauer-Gogonea, S., Bauer, S., and Gerhard-Multhaupt, R. Relaxation behaviour of electrically induced polar orientation and of optically induced non-polar orientation in an azo-chromophore side group polymer. J. Phys. D-Appl. Phys. 1999, 32, pp. 2996-3003. 

In addition, luminescence intensity and lifetime data obtained not only from the labelled polymer but also.from emission of dispersed naphthalene, acenaphthene and 1,1-dinaphthyl-l,3-propane (DNP) are briefly discussed. These measurements have provided information not only of relevance to the relaxation behaviour of the polymer matrix but also to the photophysies which occur therein and intramolecularly within the DNP. 

E may be aetirmined from the intersection of this asymptote with the C -axis. In addition, the relaxation time T can be estimated as illustrated in Figure 9 Although the deformation model shown in Figure 9 is extremely simplified and neglects some important factors (e.g. the fact, that instead of a single relaxation time a complicated relaxation spectrum may be valid), the model may serve as a basis for the discussion of the contact deformation behaviour of polymers. 

Becker, G. W., Schreuer, E. "Deformation Mechanics and Relaxation Behaviour", in "Structure and Physical Behaviour of Polymers" (in German) Nitsche,... 

Hohn, W. Jungnickel, B.-J. "Structure and Relaxation Behaviour of Compressed Polyoxymethylene" (in German), Colloid and Polym. Sci. 260 (1982) 1093. 

Many polymers may partially crystallise, and the presence of a crystalline component will greatly influence the physical properties of the material. Boyd has analyzed the different aspects related to the presence of crystallinity in the relaxational behaviour of different polymers [159]. Two major effects may be genetically distinguished the first effect is detected in polymers with low- or medium- degrees of crystallinity (see Section 3.5.1) and e second effect is typically observed in highly-crystalline systems (Section 3.5.2). 

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. 

In its original form the model sought to derive the temperature dependence of the relaxation behaviour of a composite amorphous polymer having two distinct phases in terms of the properties of the individual components. The resultant response would depend on whether the components were in parallel or series (Fig. 5). For the parallel model the complex modulus is given by ... 

From these results, no relaxation at lower frequencies is perceptible. However, Ross-Murphy and Higgs [8,9] measured the creep behaviour of gelatin gels (2.4-15 wt%) at room temperature. The gels show a typical creep behaviour of polymer solutions with equilibrium compliances, J, of the order of 10 -10 m /N and with rather high viscosities of the order of 10 Ns/m. For a 4 wt% solution at room temperature a retardation time of approximately... 

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