Data on stress relaxation modulus vs$.$ time for polyisobutylene $($also known as chewing gum$)$ are

shown in Figure $4.$ The data span a range of ${10}^{-2}$ to ${10}^2$ hours in time. Obtain the curve of the time$-$

shift factor for a reference temperature of $298K.$ Obtain a master curve for polyisobutylene based

on time$-$temperature superposition of data.

Note: Shift factor can be calculate by using the Williams$-$Landel$-$Ferry expression $($Temp$.$ unit is K$.)$

$log{a}_T=-17\mathrm{.}5\frac{T-T_{\text{r}\text{e}\text{f}}}{52+(T-T_{\text{r}\text{e}\text{f}})}$

$a_T=$ Shift Factor

Figure $4.$ Stress relaxation modulus vs$.$ time for polyisobutylene.