i$.$ Calculate the extensional free energy of core block B containing $N_B$ Kuhn

monomers of Kuhn length $b$ in a planar $($lamellar$)$ mesophase formed by a diblock

copolymer in a selective solvent. Assume that this B block is in a poor solvent with negative

excluded volume parameter $v_B$ and that the interfacial area per molecule is $a.$ Hint:

Calculate the size $R_B$ of block B by assuming that the core of the lamella is a dense packing

of thermal blobs. The free energy of extending B block is $kT\frac{R_B^2}{b^2{N}_B}.$ Make sure that

it is higher than $kT($i$.$e$.$ that $R_B>b^{\frac{1}{2}}{N}_B).$

ii$.$ At what degree of polymerization of the block does the extensional free energy of

B block becomes comparable to its interfacial free energy? Hint: The volume

pervaded by core block is $V_B=a{R}_B.$ Relate the concentration in the lamellar core to

the negative excluded volume parameter $($assume it is a dense packing of thermal

blobs$).$

iii. Compare this degree of polymerization $N_B$ to the degree of polymerization $N_A$ of

corona block that leads to this optimal area per molecule $a.$