Consider a planar $($lamellar$)$ mesophase formed by a diblock copolymer in a selective

solvent. Assume that A block is in athermal solvent $($with excluded volume parameter

$v_A=b^3-$ see problem $4$ above$),$ while B block is in a poor solvent with negative excluded

volume parameter $v_B.$

i$.$ Calculate surface tension $$ experienced by this hydrophobic block B$.$ Hint: $=k\frac{T}{{}_T^2},$

where ${}_{\text{I}}$ is the size of thermal blob.

ii$.$ What is the surface interfacial energy per diblock copolymer molecule if the interfacial

area per molecule is $a?$ Hint: It is surface tension $$ times area per molecule $a.$

iii. Express the free energy of the corona block $A$ in terms of area a per molecule, number

of Kuhn monomers $N_A$ in the block and Kuhn length $b.$ Hint: Use solution of problem

$4.$iv above and relate the grafting density $$ to the area per molecule $a.$

iv$.$ Find the optimal area per molecule $a$ by balancing the free energy of corona block A

with the interfacial free energy of core block B$.$ Why doesn't the answer depend on the

number of monomers in block B$?$

v$.$ Repeat the above calculation for the case in which the corona block $A$ is in a theta

solvent with zero second virial coefficient $v_A=0$ and third virial coefficient $w=b^6.$ Hint

use the solution of the problem $2$ above $($or lecture notes or section $5\mathrm{.}5$ of the "Polymer

Physics" textbook.