Question

Please make sure to display your thought process? It is imperative to be able to follow how the answer was deduced. Please be as thorough as possible. Please address all parts of this question.

Use the Fox equation to calculate the glass transition temperatures (Tg) of various blends of polyurethane (PU) / Polyacrylate (PA) simultaneous interpenetrating polymer networks (SIN). The below parts are all part of one question.

Make your calculations for blends of

(a) 90/10 (wt) PU/PA

(b) 75/25 (wt) PU/PA

(c) 50/50 (wt) PU/PA

(d) 25/75 (wt) PU/PA

(e) 10/90 (wt) PU/PA.

The homopolymer Tg for PU is 210 C and 360 C for PA. Use degrees Kelvin for the calculations and then convert back to degrees C for your final answers

Answer 1

Fox equation is given by,

1/ T_g(mix.) = W_PU/T_g(PU) + W_PA/T_g(PA)

Here , T_{g(mix) is the glass transition temperature of the blend of polyurethane(PU) and polyacrylate(PA) ,} ​​​​​W_PU and W_PA are the weight fractions of the two monomers respectively ,  

T_g(PU)  =210 C = 210+273 = 483 K : T_g(PA) =360 C =360+273 = 633 K

a) 1/ T_g(mix) ​​​​​​= 90/483 + 10/633

= 0.1863+0.1579 = 0.3442

T_g(mix) = 2.905 K

Thus, T_g(mix)  = 2.905-273 = - 270.09 C

b) 1/T_g(mix) =75/483 + 25/633

=0.15527 + 0.03949

= 0.19477  

T_g(mix) = 5.1341 K

Thus, T_g(mix) = 5.1341 - 273= - 267.86 C

c) 1/T_g(mix) = 50/483 + 50/633

= 0.10351 + 0.07898

= 0.18250

T_g(mix)  = 5.4791K

Thus, T_g(mix) = 5.7491-273= - 270.52C

d) 1/T_g(mix)= 25/483 + 75/633

= 0.05175+0.11848

= 0.17024

T_g(mix) = 5.873K

Thus, T_g(mix) =5.873 - 273 = - 267.12 C

e) 1/T_g(mix) = 10/483 + 90/633

= 0. 02070+0.14218

= 0.16288

T_g(mix) = 6.139K

Thus, T_g(mix) = 6.139-273 = - 266.86C