Gvs$.$ T

$($a$)$ Plot the secondary nucleation growth rate $(G)$ for linear polyethylene with a molecular weight of $4\mathrm{.}20K\frac{g}{m}ol$ as a function of temperature $T.($b$)$ Find the crystallization temperature $T_c$ and lamellae thickness $l**$ that maximizes $G.$ Use the information below for your calculations.

${}_s=1\mathrm{.}420{10}^{-2}\frac{J}{m^2{?}^2},{}_e=9\mathrm{.}009{10}^{-2}\frac{J}{m^2},{}_{PE}=930k\frac{g}{m^3},H_f=280{10}^6\frac{J}{m^3}$

$b=4\mathrm{.}150{10}^{-10}m,T_m^0=408\mathrm{.}1K,T_g=233\mathrm{.}2K,T_0=203\mathrm{.}2K$

$l=1\mathrm{.}5{10}^{-9}m,Q=6\mathrm{.}276{10}^3\frac{J}{m}ol,G_0=5\mathrm{.}270{10}^6\frac{m}{m}in$