Assume that you are the chief engineer in charge of polystyrene cylindrical rod extrusion unit. Your

companx is producing these PS cylindiral reds with a length of $3m$ and diameter of $5mm.$ Normally,

your processing temperature for this operation is at $160C$ where the xiscosity is $1\mathrm{.}5{10}^3$ poises for

polystyrene whose weight average degree of polymerization $(DP$ we is $4000.$ However, the companx that

provides you the raw material is out of stock this week. Yet you have to continue xour production in

order to fulfill your supply to your customers. An engineer under your supenvision suggests to use the

PS in the combany's inventory. Howexer you realized that there is not enough one type monodisperse

polystycene to satisfy the demand and you decided to mix them in appropriate amounts that will provide

a MW good enough for the production. In order to determine the right conditions, a polydisperss sample

of polystyrene is prepared bx mixing three monodisperse samples to produce cylindrical plastic rods xia

a lab$-$scale mini extruder in the following proportions.

Extrusion is planned to be performed with a shear rate ${}^{}=35s^{-1}$ with the melt viscosity $1\mathrm{.}5{10}^3$ Poise

which shows almost Newtonian behavior. The dependence of the melt viscosity of polystyrene to weight

average molecular weight is given by

where $D{P}_x<mn\; id="EditorElement\_3769058">3</mn><mn\; id="EditorElement\_3769059">0</mn><mn\; id="EditorElement\_3769060">0</mn>$ and $n_Q=K_H(2D{P}_w{)}^{3\mathrm{.}4}$ where $D{P}_w>300$ where $K_L$ and $K_H$ are

constants for low and high degrees of polymerization.

The glass transition temperature of PS is given as $J_{}=100C.$ Williams$-$Landel$-$ Ferry $($WLF$)$ relationship

constants $C_1$ and $C_2$ are respectively $13\mathrm{.}7$ and $50\mathrm{.}0$ for polystyrene. What will be the appropriate

processing temperature for this mixture of PS in order to have the same melt viscosity as before?

What must the temperature be to reduce the same viscosity $n_9$ of this PS by one half? Eps $=24\mathrm{.}887$

kca$\frac{l}{m}ol.$