Viscoelastic response of amorphous

The viscoelastic response of amorphous polymers at elevated temperatures is governed to a significant extent by the average molecular weight, M , the presence of any long chain branching, and the MWD [100-105]. Even the... 

In addition to the free volume [36,37] and coupling [43] models, the Gibbs-Adams-DiMarzo [39-42], (GAD), entropy model and the Tool-Narayanaswamy-Moynihan [44—47], (TNM), model are used to analyze the history and time-dependent phenomena displayed by glassy supercooled liquids. Havlicek, Ilavsky, and Hrouz have successfully applied the GAD model to fit the concentration dependence of the viscoelastic response of amorphous polymers and the normal depression of Tg by dilution [100]. They have also used the model to describe the compositional variation of the viscoelastic shift factors and Tg of random Copolymers [101]. With Vojta they have calculated the model molecular parameters for 15 different polymers [102]. They furthermore fitted the effect of pressure on kinetic processes with this thermodynamic model [103]. Scherer has also applied the GAD model to the kinetics of structural relaxation of glasses [104], The GAD model is based on the decrease of the crHiformational entropy of polymeric chains with a decrease in temperature. How or why it applies to nonpolymeric systems remains a question. 

Smith, T.L. (1962) Nonlinear viscoelastic response of amorphous elastomers to constant strain rates. Trans. Soc. Rheol., 6,61. 

The situation is somewhat similar in the case of polyvinyl chloride (PVC). PVC has a far lower degree of crystallinity than polyethylene so that the viscoelastic response of PVC might be expected to approximate more closely that of an amorphous polymer than does polyethylene. Figure 4-3 indicates that... 

In spite of these complications, the viscoelastic response of an amorphous polymer to small stresses turns out to be a relatively simple subject because of two helpful features (1) the behavior is linear in the stress, which permits the application of the powerful superposition principle and (2) the behavior often follows a time-temperature equivalence principle, which permits the rapid viscoelastic response at high temperatures and the slow response at low temperatures to be condensed in a single master curve. 

Below the glass temperatin-e, the nonlinear viscoelastic response of polymeric materials has been much less widely studied than has the behavior of melts and solutions. One reason for this is the lack of an adequate theory of behavior. Therefore the discussion about amorphous materials below the glass tem-peratiu e focuses on recent measin-ements of the nonlinear response as well as... 

Colombini and co-workers [42] used DMTA and DETA (Chapter 12) to explore the relaxation processes occurring in amorphous and semi-crystalline polyethylene naphthalene-2,6,-dicarboxylate. The two secondary relaxations P and P, the main a-relaxation and the p-relaxation processes were revealed by both mechanical and electro viscoelastic responses of the polymer. The DMTA results clearly identified the T(a) loss factor peak. 

It was pointed out in an earlier section that the viscoelastic properties are strongly related to the frictional properties of the polymers. Ferry has described some typical examples of viscoelastic responses of various polymers. The factors upon which the response depends are the molecular weight, the structure (amorphous or crystalline), the test temperature in relation to the glass transition temperature and the type and amount of foreign material which is usually added in commercial preparations for obtaining certain additional desirable properties. 

Ductile deformation requires an adequate flexibility of polymer chain segments in order to ensure plastic flow on the molecular level. It has been long known that macromoleculai- chain mobility is a crucial factor decisive for either brittle or ductile behavior of a polymer [93-95]. An increase in the yield stress of a polymer with a decrease of the temperature is caused by the decrease of macromoleculai chain mobility, and vice versa the yield stress can serve as a qualitative measure of macromolecular chain mobility. It was shown that the temperature and strain rate dependencies of the yield stress are described in terms of relaxation processes, similarly as in linear viscoelasticity. Also, the kinetic elements taking pai-t in yielding and in viscoelastic response of a polymer are similar segments of chains, part of crystallites, fragments of amorphous phase. However, in crystalline polymei-s above their glass transition temperature the yield stress is determined by the yield stress required for crystal deformation... 

Nonlinear Viscoelastic Response of Solid-like Polymers. The study of the nonlinear viscoelastic response of solid or solid-like polymers is one that has been relatively neglected. One reason is that there is no real molecular framework for the description of these materials, particularly when they are amorphous. The other reason is that many workers in the field have adopted the framework of metal plasticity and then made modifications to try to adapt it to, for example, the fact that amorphous polymers do not readily admit to treatment with the physics of dislocations. In the case of semicrystalline polymers, the... 

Fig. 3.14. The data is for a very broad range of times and temperatures. The superposition principle is based on the observation that time (rate of change of strain, or strain rate) is inversely proportional to the temperature effect in most polymers. That is, an equivalent viscoelastic response occurs at a high temperature and normal measurement times and at a lower temperature and longer times. The individual responses can be shifted using the WLF equation to produce a modulus-time master curve at a specified temperature, as shown in Fig. 3.15. The WLF equation is as shown by Eq. 3.31 for shifting the viscosity. The method works for semicrystalline polymers. It works for amorphous polymers at temperatures (T) greater than Tg + 100 °C. Shifting the stress relaxation modulus using the shift factor a, works in a similar manner.

With polymers, complications may potentially arise due to the material viscoelastic response. For glassy amorphous polymers tested far below their glass transition temperature, such viscoelastic effects were not found, however, to induce a significant departure from this theoretical prediction of the boundary between partial slip and gross slip conditions [56]. 

The time-temperature equivalence principle makes it possible to predict the viscoelastic properties of an amorphous polymer at one temperature from measurements made at other temperatures. The major effect of a temperature increase is to increase the rates of the various modes of retarded conformational elastic response, that is, to reduce the retarding viscosity values in the spring-dashpot model. This appears as a shift of the creep function along the log t scale to shorter times. A secondary effect of increasing temperature is to increase the elastic moduli slightly because an equilibrium conformational modulus tends to be proportional to the absolute temperature (13). 

Our discussion of the viscoelastic properties of polymers is restricted to the linear viscoelastic behavior of solid polymers. The term linear refers to the mechanical response in whieh the ratio of the overall stress to strain is a function of time only and is independent of the magnitudes of the stress or strain (i.e., independent of stress or strain history). At the onset we concede that linear viscoelastie behavior is observed with polymers only under limited conditions involving homogeneous, isotropie, amorphous samples under small strains and at temperatures close to or above the Tg. In addition, test conditions must preclude those that ean result in specimen rupture. Nevertheless, the theory of linear viseoelastieity, in spite of its limited use in predicting service performance of polymeric articles, provides a useful reference point for many applications. 

The four-parameter model provides a crude quahtative representation of the phenomena generally observed with viscoelastie materials instantaneous elastie strain, retarded elastic strain, viscous flow, instantaneous elastie reeovery, retarded elastie reeovery, and plastic deformation (permanent set). Also, the model parameters ean be assoeiated with various molecular mechanisms responsible for the viscoelastic behavior of linear amorphous polymers under creep conditions. The analogies to the moleeular mechanism can be made as follows. 

This has the same form as Eq. (7.1) the renamed constants are a Young s modulus , and a viscosity 17. It is not possible to directly link these constants to the modulus of the crystalline phase and the viscosity of the amorphous inter-layers in a semi-crystalline polymer. Hence, the Voigt model is an aid to understanding creep, and relating it to other viscoelastic responses, rather than a model of microstructural deformation. 

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