Five Regions of Viscoelastic Behavior

The quantities E and G refer to quasistatic measurements. When cyclical or repetitive motions of stress and strain are involved, it is more convenient to talk about dynamic mechanical moduli. The complex Young s modulus has the formal definition 

Viscoelastic materials simultaneously exhibit a combination of elastic and viscous behavior. While all substances are viscoelastic to some degree, this behavior is especially prominent in polymers. Generally, viscoelasticity refers to both the time and temperature dependence of mechanical behavior. 

The states of matter of low-molecular-weight compounds are well known crystalline, liquid, and gaseous. The first-order transitions that separate these states are equally well known melting and boiling. Another well-known 

By contrast, no high-molecular-weight polymer vaporizes to a gaseous state all decompose before the boiUng point. In addition no high-molecular-weight polymer attains a totally crystalline structure, except in the single-crystal state (see Section 6.4.2). 

In fact many important polymers do not crystallize at all but form glasses at low temperatures. At higher temperatures they form viscous liquids. The transition that separates the glassy state from the viscous state is known as the glass-rubber transition. According to theories to be developed later, this transition attains the properties of a second-order transition at very slow rates of heating or cooling. 

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Fig. 4. The five regions of viscoelastic behavior. All polymers exhibit these five regions, but crosslinking, crystallinity, and varying molecular weight alter the appearance of this generalized curve. The loss modulus Tg peak appears just after the storage modulus enters the glass transition region.

Figure 2.24 Five regions of viscoelastic behavior for a linear, amorphous polymer I (a to b), II (b to c), III (c to d), IV (d to e), and V ( e to f). Also illustrated are effects of crystallinity (dotted line) and cross-linking (dashed line).

Draw a logB versus temperature plot for a linear, amorphous polymer and indicate the position and name the five regions of viscoelastic behavior. How is the curve changed if (a) the polymer is semicrystalline, (b) the polymer is cross-linked, and (c) the experiment is run faster ... 

Figure 11 Five regions of viscoelastic behavior for a linear, amorphous polymer.

Before entering into a detailed discussion of the glass transition, the five regions of viscoelastic behavior are briefly discussed to provide a broader picture of the temperature dependence of polymer properties. In the following, quasi-static measurements of the modulus at constant time, perhaps 10 or 100 s, and the temperature being raised l°C/min will be assumed. 

The five regions of viscoelastic behavior for linear amorphous polymers (3,7-9) are shown in Figure 8.2. In region 1 the polymer is glassy and frequently brittle. Typical examples at room temperature include polystyrene (plastic) drinking cups and poly(methyl methacrylate) (Plexiglas sheets). 

L Name the five regions of viscoelastic behavior, and give an example of a commercial polymer commonly used in each region. 

These five temperature regions give rise to the five regions of viscoelastic behavior. Light crosslinking of a polymer will have litde effect on the glassy and transition zones, but will considerably modify the flow regions. 

Fig. 7.1 Five regions of viscoelastic behavior of a polymer. Curves are generic in form, but glassy and rubbery data given are for epoxy and urethane (Brinson, 1965, 1968, 1916) For urethane also see (Williams and Ar-entz, 1964).

Name the five regions of viscoelastic behavior of a polymer and give a sketch of the 10 second modulus vs. temperature for thermoplastic (amorphous and crystalline) and thermoset polymers. 

To illustrate the effect of temperature on mechanical properties, it is sometimes preferable to plot the property vs. temperature for constant values of time. For example, data of the type shown in Fig. 18.21 may be cross-plotted as (10) (the 10-second relaxation modulus) vs. T, Such a plot is given in Fig. 18.23 for several polystyrene samples," The five regions of viscoelastic behavior are evident in the linear, amorphous (atactic) samples (A) and (C) along with the effect of molecular weight in the flow region. The drop in modulus in the vicinity of Tg (100°C) is dearly seen. The crystalline (isotactic) sample maintains a fairly high modulus all the way up to (a 235 "C). Given values of one can convert data in the form vs, t at constant T (a master curve) to vs. T at constant t and vice versa. 

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