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

The starting point is in the lamellar region. Preferential swelling of polystyrene makes polyisoprene the increasingly small minority domain, so the relevant effective composition moves left from $f_{PI}^{\mathrm{eff}}=0.45$.

If segregation stayed near $\chi N=35$, following the horizontal path in the supplied diagram would give lamellae → hexagonally perforated layers → hexagonally arranged PI cylinders → PI spheres, before sufficient asymmetry reaches the disordered region. The perforated-layer interval is narrow, around $f_{PI}\simeq 0.36$–$0.40$ at this segregation strength; precise boundaries should not be read more accurately than the figure allows.

Solvent also changes effective segregation, so the actual trajectory need not be horizontal. If it passes closer to the order-disorder boundary, it can enter the narrow double gyroid region instead of, or after, the hexagonally perforated layer phase. Greater dilution can cause disorder before all the ordered morphologies appear. Thus a plausible alternative is lamellae → gyroid → cylinders → disorder.

The robust prediction is the change toward minority-PI curved structures, not a guarantee that every named phase occurs. A solvent partition coefficient and a concentration-dependent interaction model would be needed to locate the actual path quantitatively; applying a dry-melt diagram to a swollen material is an effective approximation.