Yield in polymers

The stresses and strains of practical importance for polymers at T Tg or are often relatively large, and, unlike the small strains referred to in the preliminary discussion of the glassy state in Section 14.1.1, they may result in significant plastic deformation, in that the associated changes in specimen morphology are not recovered after stress release over laboratory time scales. A plastically deformed polymer with sufficiently high M is nevertheless able to return to its initial shape 

Ao is the initial cross-sectional area of the specimen, so that Eq. (57) holds. 

In an amorphous glassy polymer, work hardening is considered to correspond to stretching of the entanglement network invoked to account for the rubbery plateau above Tg (see Section 14.3.3). This explains the recoverability of the deformation above Tg (in the absence of an applied force, the network retracts to its equilibrium conformation) and it is borne out by the observed correlation between the value of X in the neck and the maximum extensibility of the network, X ax In semicrystalline polymers, the evolution of the crystalline texture may also contribute to work hardening, because the resolved shear stress on activated slip systems tends to decrease as deformation proceeds at constant stress, as will be discussed further (see Section 14.4.3). 

The large strain response in the glassy or semicrystalline state is that of a nonlinear viscoelastic solid. However, both engineering and theoretical approaches to plasticity in polymers have largely developed as an independent discipline, in which (Ty plays a central role, in spite of its somewhat arbitrary definition (indeed it is not always possible to associate cty with a maximum in the force-deformation curve [5]). This is because in practice the yield point, rather than the ultimate strength, is usually considered to be the failure criterion for ductile materials. 

For yield to occur at all, the global stress state must contain a deviatory component, so that pure hydrostatic stress states do not result in plasticity in a uniform specimen. Indeed, in many types of material, including metals, yield is usually well described by the Von Mises criterion, in which it is considered to be independent of the hydrostatic pressure, p = (jxx + ryy + Tzz)/3. With an appropriate frame of reference, any multiaxial stress state may be expressed as Eq. (58), where (7i,ct2, and ctj are the principal stresses (compare Section 14.2.1). 

During elastic deformation the cross-sectional area of the specimen decreases uniformally as length increases, but an important change occurs at the yield point. The cross-sectional area starts to decrease more rapidly 

The true stress a is defined as the load L divided by the instantaneous cross-sectional area A and so 

It may be assumed that deformation takes place at approximately constant volume and so A can be related to the original cross-sectional area Aq through the equation 

Combining Equations (5.148) to (5.151) gives the relationship between the nominal and true stress as 

This means that for finite tensile strains a will always be greater than or . 

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However, a study of a few dyes of higher fluorescence quantum yield in polymer microparticles did not show any change in the fluorescence lifetime even though the modification of the fluorescence spectra was observed [4]. In this work, a new molecule (9-amino acridine hydrochloride hydrate, 9AAHH) is reported in which we have observed the effect of MDR in both, the steady state spectra and the fluorescence lifetimes. The dephasing time of 9AAHH in polymer matrix at room temperature have been determined from this study. 

A brief description of mechanical tests that can be performed to obtain information on yielding in polymer materials is given below. Figure 14.5 shows some diagrams that reproduce the conditions of each type of experiment. 

Figure 14.5 Scheme of tests used for determining yield in polymers (a) Tension (b) uniaxial compression (c) plane strain compression (d) simple shear. 

In practice, the crack tip yielding in polymers is often not of a circular zone type as described above, but is a co-linear extension of the crack. The deformed material within the zone often forms a porous structure with ligaments restraining the zone faces, as illustrated in Fig. 13. This porous material, usually termed the craze, can be regarded as providing cohesive forces over the zone length. The zone can then be... 

Shear yielding in polymers has much in common with ductility in metals. In polymers, the yielding may be localised into shear bands, which are regions of high shear strain less than 1 m in thickness or the yield zones may be much more diffuse " Under a general state of stress, defined by the three principal stresses Gi, 02 and 03, the condition for yielding is given by a modified von Mises crite-rion l ... 

Rothe C, King S, A1 Attar HA, Monkman AP (2006) Direct measurement of the singlet generation yield in polymer light emitting diodes. Phys Rev Lett 97 076602... 

It is clear that there are still many important experiments to be done in order to rationalise, select from and to reconcile aspects of these many and varied ideas regarding the molecular aspects of yield in polymers. 

Figure 3.2 Composition of reaction medium as a function of conversion. In chain polymerisation (hatched), the reaction medium contains monomers and high-molecular-weight polymer even at low conversion. Increasing conversion increases yield in polymer, not molecular weight. In step polymerisation (dotted), the reaction medium contains monomers and oligomers at low conversion. Increasing conversion increases polymer molecular weight...

Yielding in polymer blends is a very complicated event and is usually composed of several micromechanisms that are activated at various stages of deformation depending on the deformation rate, the temperature, deformation mode, and blend morphology. 

The changes and yields in polymer irradiation are often similar to those found with lower-molecular-weight compounds with similar structural features. The radiolysis of linear polyethylene is similar to that of the -alkanes, polystyrene resembles the alkylbenzenes, and polymethyl methacrylate behaves like a branched chain ester. Lower-molecular-weight compounds are often used to model processes taking place in polymer irradiation. 

Table 2. Some Typical Monomer Yields in Polymer Pyrolysis...

While the true stress-true strain response is qualitatively similar in both compression and tension, the resulting deformation states are very different. Tensile loading leads to uniaxial molecular orientation along the loading axis. Compression on the other hand results in a biaxial orientation state in a plane perpendicular to the loading direction and so it is expected that quantitatively different stress-strain curves are seen. In addition, as discussed below, the hydrostatic pressure difference between tension and compression leads to differences in yield strength because yield in polymers is pressure dependent. 

Strain-Induced Dilatation. An alternative view of yield in polymers comes from the fact that a tensile strain induces a hydrostatic tension in the material and a corresponding increase in the sample volume. This in turn translates to an increase in the free volume, which increases the polymer mobility and effectively lowers the glass-transition temperature (Tg) of the polymer (alternatively it can be looked upon as increasing the free volume to the value it would have at the normal measured Tg). The increased mobility results in a lowering of the yield stress. Rnauss and Emri (35) used an integral representation of nonlinear viscoelasticity with a state-dependent variable related to free volume to model the yield behavior, with the free volume a function of temperature, time, and stress history. This model uses the concept of reduced time (see VISCOELASTICITY), where application of a tensile stress causes a volume dilatation and consequently causes the material time scale to change by a shift factor related to the magnitude of the applied stress. Yield occurs because the free-volume shift factor causes the molecular mobility to increase in such a way that yield can occur. 

Equation 30 shows that the yield stress is both rate and temperature dependent, hence it captures some important features of yield in polymers. For example, Figure 10 (44) shows a plot of ax/T (or aJT in the notation of Reference (44)) as a function of log strain rate and, as predicted by equation 30, a linear relationship is seen at each temperature. It is worth noting that the Eyring equation (typically in the form of two activated processes acting in parallel) has been successfiilly applied not only to the yield behavior of polsrmers but also to the creep rupture behavior of isotropic and oriented polymers (45- 8). 

As we observed at the end of the previous chapter, the non-linear behaviour of polymers, as represented by the Eyring model, gives rise to a phenomenon resembling yield. The observed maximum stress can be treated as a yield stress, although Equation (10.40) shows that this yield stress depends on the rate of strain. Wineman and Waldron [1] have pointed out that there appear to be two approaches to the modelling of yield in polymers the use of non-linear viscoelasticity and the direct application of metal plasticity. The use of the Eyring model is one example of the former approach. Relatively simple theories of plasticity, where there is no rate dependence, are available from the metals field. These theories, which embody the classical concepts of plasticity, still may be applied usefully to polymers, for instance in cases where changes in strain rate are small. 

Poor yields in polymer as well as low polymerization rates were observed due to the steric hindrance of carbohydrate moieties and because of the electronic effects on the C=C bonds. More efficient polymerization was achieved by optimizing monomer concentration and/or by selecting proper comonomer combinations, particularly with respects to mutual polarity effects. ... 

Table 10-2. Some typical monomer yields in polymer pyrolysis.

The important feature is the formation of polyene sequences by successive eliminations. These absorb visible light, causing the polymer initially to become yellow and eventually black. Similar reactions can occur with many polymers, e.g. poly(vinyl alcohol), poly(vinyl acetate) and cellulose and its esters. If the elimination reactions are allowed to go to high conversions, the polymer is typically transformed into a carbonaceous char, which may be quite thermally stable. Much of fire retardant chemistry is aimed at increasing char yields in polymer thermolysis. 

As it has been shown above using position spectroscopy methods [22], the yielding in polymers is realized in densely packed regions of their structure. Theoretical analysis within the frameworks of the plasticity fractal concept [35] demonstrates that the Poisson s ratio value in the yielding point, can be estimated as follows ... 

Proceeding from the said above and also with appreciation of the known fact, that rubbers do not have to some extent clearly expressed yielding point the authors of Ref [73] proposed hypothesis, that glassy polymer structural state changed from multifiactal up to regular fiactal, that is, criterion (4.44) fulfillment, was the condition of its yielding state achievement. In other words, yielding in polymers is realized only in the case, if their structure is multifi actal, that is, if it submits to the inequality Eq. (4.45). 

The polymer had primarily trans configuration and contained the cyclohexane ring in the boat form. On the other side, polymerization of 5-methyl-substituted bicyclo[2.2.2]octene has been carried out with cationic and Ziegler-Natta systems [146] leading to low yields in polymers, probably of mainly vinylic structures. 

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