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Chapter 15: Problem 7

In Figure 15.28, the logarithm of \(E_{r}(t)\) versus the logarithm of time is plotted for polyisobutylene at a variety of temperatures. Make a plot of \(E_{r}(10)\) versus temperature and then estimate its \(T_{g}\).

Short Answer

Expert verified
Answer: To estimate the glass transition temperature, \(T_{g}\), for polyisobutylene, follow these three steps: 1) Identify the values of \(E_{r}(10)\) from the given plot for each temperature, 2) create a plot of \(E_{r}(10)\) versus temperature, and 3) estimate \(T_{g}\) by looking for a significant change or an inflection point in the curve of the new plot.

Step by step solution

01

Identify the values of \(E_{r}(10)\) for each temperature

Look at the given plot of the logarithm of \(E_{r}(t)\) against the logarithm of time. For each temperature, find the value of \(E_{r}(t)\) when logarithm of time (\(\log_{10}(t)\)) is equal to 1 (since \(\log_{10}(10) = 1\)). This means you are looking for the value of the stress relaxation modulus at \(t = 10\) seconds. Do this for each temperature curve on the graph. Record these values for the next step.
02

Create a plot of \(E_{r}(10)\) versus temperature

Using the \(E_{r}(10)\) values identified in Step 1 and their corresponding temperatures, create a new plot with \(E_{r}(10)\) on the y-axis and temperature on the x-axis. This plot will show the relationship between the stress relaxation modulus at 10 seconds and the temperature.
03

Estimate the glass transition temperature, \(T_{g}\)

The glass transition temperature, \(T_{g}\), is the temperature at which the material transitions between a glassy and rubbery state. To estimate \(T_{g}\) from the plot of \(E_{r}(10)\) versus temperature, look for a significant change or an inflection point in the curve. This point represents the temperature at which the behavior of the material changes, and that is the estimated glass transition temperature. By following these steps and analyzing the data from the given plot, you should be able to estimate the glass transition temperature, \(T_{g}\), for polyisobutylene.

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Most popular questions from this chapter

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