Using the experimental data of cloud point measurements for PS/PI pairs given in Table 7.5, obtain an expression for defined by Eq. (7.2) for each PS/PI pair. Use Eq. (7.4) for the temperature-dependent specific volume of PS, vPS, and Eq. (7.5) for the temperature-dependent specific volume of PI, vPI. Convert (having the units of mol/cm3 ) to Flory-Huggins interaction parameter using the definition of molar reference volume, Vref=[(MSvPS)(MIvPI)]1/2 with MS being the molecular weight of styrene monomer and M1 being the molecular weight of isoprene monomer. Note that MS=104.15 and MI=68.11. (a) (PS-2) ( Pl-5) pair (Tcrit=110C,wcrit=0.5,Mw,PS2=2.2103,Mw,Pl-5=5.0103) b (b) (PS3)/(PI5) pair (Tcrit=127C,wcrit=0.6,Mw.PS3=3.1103,Mw.Pl5=5.0103) (c) (PS-10)/(PI-5) pair (Tcrit=185C,wcrit=0.5,Mw,PS10=9.5103,Mw,Pl5=5.0103) Then the dynamics of the primitive chain 1 , representing polymer 1 , can be expressed in the form of the Smoluchowski equation (Riskin 1989):4 tf1=Dc1122f1+1(kBTDc11U)f1 JeboGb()Gb()=20b24i=12wiGNio{p=1p2Hi,pZi1j=1Zi(i,j)2}=24i=12wiGNio{p=1p2Hi,pZi1j=1Zi1+(i,j)2(i,j)2}=24i=12wiGNio{p=1p2Hi,pZi1j=1Zi1+(i,j)2i,j} Gb()=Gb()=24i=1nj=1m{GN1om1w1i[p=1p2H1i,pZ1i1s=1Z1i1+(1i,s)2(1i,s)2]+GN2on2w2jp=1p2H2j,pZ2j1s=1Z2j1+(2j,s)2(2j,s)224i=1nj=1m{GN1om1w1i[P=1p2H1i,pZ1i1s=1Z1i1+(1i,s)21i,s]+GN2on2w2jp=1p2H2j,pZ2j1s=1Z2j1+(2j,s)22j,s Using the experimental data of cloud point measurements for PS/PI pairs given in Table 7.5, obtain an expression for defined by Eq. (7.2) for each PS/PI pair. Use Eq. (7.4) for the temperature-dependent specific volume of PS, vPS, and Eq. (7.5) for the temperature-dependent specific volume of PI, vPI. Convert (having the units of mol/cm3 ) to Flory-Huggins interaction parameter using the definition of molar reference volume, Vref=[(MSvPS)(MIvPI)]1/2 with MS being the molecular weight of styrene monomer and M1 being the molecular weight of isoprene monomer. Note that MS=104.15 and MI=68.11. (a) (PS-2) ( Pl-5) pair (Tcrit=110C,wcrit=0.5,Mw,PS2=2.2103,Mw,Pl-5=5.0103) b (b) (PS3)/(PI5) pair (Tcrit=127C,wcrit=0.6,Mw.PS3=3.1103,Mw.Pl5=5.0103) (c) (PS-10)/(PI-5) pair (Tcrit=185C,wcrit=0.5,Mw,PS10=9.5103,Mw,Pl5=5.0103) Then the dynamics of the primitive chain 1 , representing polymer 1 , can be expressed in the form of the Smoluchowski equation (Riskin 1989):4 tf1=Dc1122f1+1(kBTDc11U)f1 JeboGb()Gb()=20b24i=12wiGNio{p=1p2Hi,pZi1j=1Zi(i,j)2}=24i=12wiGNio{p=1p2Hi,pZi1j=1Zi1+(i,j)2(i,j)2}=24i=12wiGNio{p=1p2Hi,pZi1j=1Zi1+(i,j)2i,j} Gb()=Gb()=24i=1nj=1m{GN1om1w1i[p=1p2H1i,pZ1i1s=1Z1i1+(1i,s)2(1i,s)2]+GN2on2w2jp=1p2H2j,pZ2j1s=1Z2j1+(2j,s)2(2j,s)224i=1nj=1m{GN1om1w1i[P=1p2H1i,pZ1i1s=1Z1i1+(1i,s)21i,s]+GN2on2w2jp=1p2H2j,pZ2j1s=1Z2j1+(2j,s)22j,s