Answer to Question #109654 in Organic Chemistry for Dr Deepika

Question

PET has a Young's, Modulus of 3.5 GPa and PLGA 1.2 GPa. A polymer blend is prepared with 50:50 mixture (PET:PlGA) . What is the Young's, Modulus of this blend (use mixture rule)? Calculate the percent load borne by PET when the blend is subjected to a load. If after 10 days, half of PET and one third of PLGA had degraded, what is the Young's Modulus of this blend ?
Expert's answer

Answer 1

E_C = E₁*v₁ + E₂*v₂

proportions of each component are v₁(PET)=v₂(PLGA)=0.5, then

E_c = 0.5(E₁+E₂)=0.5(3.5+1.2) = 2.35 GPa - Young's modulus of polymer blend (composite)

The percent load borne by PET is

$\epsilon_{PET} = {\frac {0.5*3.5} {2.35}}=0.7447$ = 74.47%

assuming initial volume as 100%, initial volumes of PET and PLGA are 50% (${\frac {1} {2}}$) both.

After degradation ${\frac {1} {2}}$ of PET remained, then PET occupies ${\frac {1} {2}}*{\frac {1} {2}}={\frac {1} {4}}$=25% of initial volume

After degradation​ ${\frac {2} {3}}$ of PLGA remained, then PLGA occupies​ ${\frac {2} {3}}*{\frac {1} {2}}={\frac {1} {3}}$=33.33% of initial volume

• First case:

Now, assuming that degradation did not affect bonding or interdiffusion of components of polymer blend, i.e. blend's properties still affected only by ratio of polymer components, we can calculate ratio of components after degradation and, using first formula, count E_c again.

${\frac {v_1} {v_2}}= {\frac {{\frac {1} {4}}} {{\frac {1} {3}}}}={\frac {3} {4}}$ , but for blend after degradation sum of polymer components' volumes must be 100%.

$\begin{cases} v_1={\frac {3} {4}v_2} \\ v_1+v_2=1 \end{cases}$

solving the system we get

v₁(PET)= ${\frac {3}{7}}$ and v₂(PLGA)= ${\frac {4} {7}}$

Ec(after degradation) = 3.5*${\frac {3} {7}}$ + 1.2*${\frac {4} {7}}$ = 2.186 GPa

• (Second case: optional)

Assuming that products of degradation remain in blend's volume and don't contribute to Young's modulus then volumes of PET and PLGA are 25% (${\frac {1} {4}}$) and 33.33% (${\frac {1} {3}}$) respectively, as was count earlier.

Ec = 3.5*${\frac {1} {4}}$ + 1.2*${\frac {1} {3}}$ = 1.275 GPa