Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2023 / Paper 2 / Section A(iii) / 18 / i

The Flory interaction parameter $\chi$ measures the free-energy penalty of unlike block contacts relative to like contacts, in units of $k_{B}T$. The degree of polymerization $N$ counts the reference segments per chain, using the segment-volume convention associated with $\chi$. Their product, the block copolymer segregation strength $\chi N$, compares the tendency to avoid unlike contacts with the entropy cost of organizing and stretching connected chains.

At small $\chi N$, the diblock copolymer is disordered. Increasing $\chi N$ can cause microphase separation: the blocks form distinct domains, but their covalent connection prevents complete macroscopic separation. Domain interfaces cost energy while chain stretching and lost configurations cost entropy; their competition selects a finite domain scale.

A common temperature law is $\chi =A/T+B$, so increasing temperature often decreases segregation when $A>0$. This is not a universal sign law for every polymer pair. For an intact, fixed chain, $N$ does not change just because temperature or solvent concentration changes.

Adding a nonselective good solvent usually dilutes unlike-block contacts and reduces an effective segregation strength; it does not chemically shorten the chain. A selective solvent additionally changes domain swelling and solvent-block interactions. One needs a ternary-mixture description, or a clearly defined effective $\chi$, rather than treating the melt's $\chi$ as a universal solvent-concentration function.^[ref]