The Five Regions of Viscoelastic Behavior

The physical nature of an amorphous polymer is related to the extent of the molecular motion in the sample, which in turn is governed by the chain flexibility and the temperature of the system. Examination of the mechanical behavior shows that there are five distinguishable states in which a linear amorphous polymer can exist, and these are readily displayed if a parameter such as the elastic modulus is measured over a range of temperatures. 

The rubbery state At approximately 30 K above the glass transition the modulus curve begins to flatten out into the plateau region C to D in the modulus interval 10 to lO Nm- and extends up to about 420 K. 

FIGURE 13.1 Five regions of viscoelasticity, illustrated using a polystyrene sample. Also shown are the strain-time curves for stress applied at x and removed at y. (a) glassy state, 

Before examining the viscoelastic behavior of amorphous polymeric substances in more detail, some of the fundamental properties of polymer melts and elastic solids will be reviewed. 

---

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.

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 ... 

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. 

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. 

Figure 2.21 Five regions of viscoelastic behavior for a linear, amorphous polymer 1 (a to b), 11 (b to c), III (c to d), IV (d to e), and V (e to f). Dotted line ( ) shows the effect of crystallinity and dashed line (-----) that of crosslinking. (After Sperling, 1986.)...

Figure 15.7 Logarithm of the relaxation modulus versus temperature for amorphous polystyrene, showing the five different regions of viscoelastic behavior.

Dynamic mechanical experiments yield both the elastic modulus of the material and its mechanical damping, or energy dissipation, characteristics. These properties can be determined as a function of frequency (time) and temperature. Application of the time-temperature equivalence principle [1-3] yields master curves like those in Fig. 23.2. The five regions described in the curve are typical of polymer viscoelastic behavior. 

---