Regions of viscoelastic behavior

Region II (b to c) in Fig. 2.21 is the glass transition region where the modulus drops typically by a factor of about one thousand over 20-30°C. In this region, polymers exhibit tough leather-like behavior. The glass transition temperature, Tg, is often taken at the maximum rate of decline of the modulus, i.e., where d EldT is at a maximiun. 

Region III (c to d) in Fig. 2.21 is described as the rubbery plateau region. The modulus after a sharp drop, as described above, again becomes nearly constant in this region with typical values of 2x10 dyne/cm (2x10 Pa) and polymers exhibit signi cant rubber-like elasticity. 

Problem 2.18 A new polymer is reported to soften at 60°C. Describe a very simple experiment to determine whether this softening is a glass transition or a melting point. 

Problem 2.19 Show schematically the results that would be expected from the following experiments with the new polymer of Problem 2.18 if the reported softening temperature (60°C) is indeed a melting transition (Sperling, 1986)  

If 60° C is a glass transition, then heating the polymer slowly past 60° C would take it to the rubbery plateau region (region m in Fig. 2.21), where the modulus E, and hence hardness, would remain fairly constant with increase of temperature. For a melting transition, however, the modulus would drop rapidly and the polymer would become increasingly softer in a similar experiment (Sperling, 1986). 

The penetration of a weighted needle into the polymer as the temperature is raised can be used as a very simple test. 

As we have seen above, the transition that separates the glassy state from the viscous state is known as the glass-rubber transition. This transition attains the properties of a second-order transition at very slow rates of heating or cooling. In order to clearly locate the region of this transition and to provide a broader picture of the temperature dependence of polymer properties the principal regions of viscoelastic behavior of polymers will be briefly discussed. 

Pressing one s thumb in an object is a simple way to gauze the object s hardness. Its scientific analogue is the measurement of hardness by indentation. In practice, the point of a weighted needle is allowed to rest on the polymer surface as the temperature is raised. The movement of the needle as it penetrates the surface can be monitored by means of an amplification gauge. Though less accurate than other more sophisticated methods, it is useful for the preliminary engineering-oriented examination of systems. 

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So Figures 13-78 and 13-80 are our idealized representations. This correspondence is obviously interesting and important, but we will defer a discussion of the molecular origin of this until later. First we want to explore this time-temperature correspondence and the various regions of viscoelastic behavior in a little more detail. 

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. 

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 4-1. Schematic modulus-temperature curve showing various regions of viscoelastic behavior.

Fortunately for linear amorphous polymers, modulus is a function of time and temperature only (not of load history). Modulus-time and modulus-temperature curves for these polymers have identieal shapes they show the same regions of viscoelastic behavior, and in each region the modulus values vary only within an order of magnitude. Thus, it is reasonable to assume from such similarity in behavior that time and temperature have an equivalent effect on modulus. Such indeed has been found to be the case. Viscoelastic properties of linear amorphous polymers show time-temperature equivalence. This constitutes the basis for the time-temperature superposition principle. The equivalence of time and temperature permits the extrapolation of short-term test data to several decades of time by carrying out experiments at different temperatures. 

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). 

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