Viscoelasticity amorphous polymers

Contents Chain Configuration in Amorphous Polymer Systems. Material Properties of Viscoelastic Liquids. Molecular Models in Polymer Rheology. Experimental Results on Linear Viscoelastic Behavior. Molecular Entan-lement Theories of Linear iscoelastic Behavior. Entanglement in Cross-linked Systems. Non-linear Viscoelastic-Properties. 

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.

According to the more widely used Williams, Landel, and Ferry (WLF) equations, all linear, amorphous polymers have similar viscoelastic properties at Tg and at specific temperatures above Tg, such as Tg + 25 K, and the constants Ci and C2 related to holes or free volume, the following relationship holds ... 

The challenges involved in the material properties of PPC relate to its thermal features, i.e., its thermal decomposition, and the glass transition temperature (Tg) of about body temperature of the otherwise amorphous polymer. These have implications for processing and application of the material. This review will discuss consecutively the thermal, viscoelastic, and mechanical properties of PPC and the experiences in processing PPC and its composites. The properties of solutions of PPC will also be presented, and the biodegradabUity and biocompatibility discussed. Spectroscopic properties will not be discussed. Further information on NMR data can be found in the following references [2, 10-12]. A t3 pical spectrum is shown in Fig. 2 [13]. 

In conclusion, we may state that viscoelastic data presented in this paper further reaffirm the contention that polyvinyl chloride has a network structure with microcrystallites acting as cross-links. Incorporation of plasticizer affected PVC in a way similar to amorphous polymers mainly by lowering Tg of the amo-rophous regions. Microcrystallites appear to be stable even in the presence of... 

Some examples of viscoelastic materials include amorphous polymers, semicrystalline polymers, biopolymers, and metals at very high temperatures. Cracking occurs when the strain is applied quickly and outside of the elastic limit [8],... 

Linear amorphous polymers can behave as either Hookian elastic (glassy) materials, or highly elastic (rubbery) substances or as viscous melts according to prevailing temperature and time scale of experiments. The different transitions as shown schematically in Figure 5.1 are manifestations of viscoelastic deformations, which are time dependent [1]. 

Nakada, O. Theory of viscoelasticity of amorphous polymers. III. Dispersion of dynamic bulk modulus. J. Polymer Sci 43, 149—165 (1960). 

This relaxation has been discovered in some non-vulcanized amorphous polymers and copolymers. It tends to fall at approximately 1.2Tg. Because it appears to be connected with the change from the viscoelastic to the normal viscous state it will also depend on the molecular weight and accordingly increases with Mw. 

The small-strain viscoelastic behaviour of all amorphous polymers is similar, so that in a limited region it can be described by a single universal formula... 

The theory is not limited in its application to the transient properties of amorphous polymers it can be used to make molecular interpretation and prediction of the dynamic viscoelastic properties of crosslinked polymers [24] as well. According to the Fourier-Laplace transformation, the complex tensile modulus can be separated into the real and imaginary parts... 

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 constitutive model makes use of the decomposition of the rate of deformation D into an elastic, De, and a plastic part, Dp, as D = De + Dp. Prior to yielding, no plasticity takes place and Dp = 0. In this regime, most amorphous polymers exhibit viscoelastic effects, but these are neglected here since we are primarily interested in those of the bulk plasticity. Assuming the elastic strains and the temperature differences (relative to a reference temperature T0) remain small, the thermoelastic part of the response is expressed by the hypoelastic law... 

We expect that the modification creates the free volume (Vf) in wood substance from the similarity of the effect of and n on viscoelasticity. The discussion for wood, however, is impossible on the basis of a concept of the free volume, although the flexibility of molecular motion for synthetic amorphous polymers is discussed. Unfortunately, we can not directly know the created free volume because the time-temperature superposition principle is not valid for wood [19]. The principle is related to WLF equation by which the free volume is calculated. The free volume, however, relates to volumetric swelling as follows. 

Let s start our discussion of the range of viscoelastic properties of amorphous polymers by considering the modulus of an amorphous polymer measured as a function of temperature. We know that any measurement of stress, hence modulus, we make is going to vary with time (see Equation 13-71), so to compare values at different temperatures we make all our measurement... 

Sketch a plot of the modulus of an amorphous polymer as a function of temperature, labeling the different regions of viscoelastic behavior. Briefly describe the types of relaxation behavior that occur in each region. 

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... 

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