Make two schematic plots of the logarithm of relaxation modulus versus temperature for an amorphous polymer (curve \(C\) in Figure \(15.8\) ). (a) On one of these plots, demonstrate how the behavior changes with increasing molecular weight. (b) On the other plot, indicate the change in behavior with increasing crosslinking.

First, we need to create a base plot representing curve C in Figure 15.8, which shows the logarithm of relaxation modulus (G') as a function of temperature (T) for an amorphous polymer. You can do this using any graphing software or even hand-drawn.

On the first plot (a), demonstrate how the behavior changes with increasing molecular weight (M). As molecular weight increases, the curve will shift toward higher relaxation moduli, since larger molecules have a greater resistance to flow and need more energy to be displaced. Thus, on the plot, draw a few curves, each representing a higher molecular weight than the previous one, and label them accordingly (e.g., M1, M2, M3, etc.). These curves should be upwards and parallel to the base curve C.

On the second plot (b), indicate the change in behavior with increasing crosslinking (X). As the crosslink density increases, the network becomes more rigid, resulting in a higher relaxation modulus at lower temperatures. At the same time, as the crosslink density increases, the ability of the polymer to flow decreases, which will lead to a steeper downward slope of the curve at higher temperatures. For this plot, draw a few curves, each representing a higher crosslinking density than the previous one, and label them accordingly (e.g., X1, X2, X3, etc.). The curves should start at a higher relaxation modulus at lower temperatures and should become steeper at higher temperatures when moving from a less to more crosslinked polymer. Now you have two schematic plots showing the logarithm of relaxation modulus vs temperature for an amorphous polymer, with respect to changing molecular weight (plot a) and increasing crosslinking (plot b).