Assume that the small$-$angle X$-$ray scattering data for a polystyrene$-$block$-$polybutadiene

copolymer with a lamellar morphology $($see the TEM image shown next$)$ show maxima

at $q$ values of approximately $0\mathrm{.}264,0\mathrm{.}542$ and $0\mathrm{.}819n{m}^{-1}.$

$($a$)$ Determine the lamellar plane spacing of the domains.

$23\mathrm{.}34nm$

$($b$)$ Determine the associated thickness of the polybutadiene layers given that volume

fraction of polystyrene is $0\mathrm{.}29.$

$($c$)$ Explain how these lamellar$-$structured block copolymers $($edge$-$on configuration$)$ can

be used for lithography patterning in semiconductor fabrication process.

Assumption: The densities of polystyrene and polybutadiene are same.