PDMS Is a silicon$-$based polymer commonly used in industry as a lubricant and thickener. its chemical structure is:

The values of $$ and $$ is $145$ and $110$ respectively, and the length of the Si$-$O bond is $0\mathrm{.}16nm.$ According to the free$-$rotating ideal chain model:

$($:$R^2$:$)=n{l}^2\frac{(1-cos)(1-cos)}{1-coscos}$

$R_{\text{m}\text{a}\text{x}}=\frac{1}{2}nl(sin(\frac{}{2})+sin(\frac{}{2}))$

a$.$ What is $C_{}$ for PDMS with a molar weight of ${10}^6\frac{g}{m}ol?$

b$.$ Show that if $=,$ we get the result we obtained in class for polyethylene. Note that in class we used the angle $180-,$ so you need to change the description accordingly.