Commensurability effect in diblock copolymer lamellar phase under d-dimensional nanoconfinement

Area of Science:

• Polymer physics
• Soft matter physics
• Materials science

Background:

• Diblock copolymers form lamellar phases.
• Confinement influences self-assembly of block copolymers.
• Understanding confined structures is crucial for materials design.

Purpose of the Study:

• Investigate the commensurability problem of AB diblock lamellar phases.
• Analyze the impact of confinement dimensionality and conformational asymmetry on lamellar structures.
• Determine phase behavior in various confinement geometries.

Main Methods:

• Theoretical calculations of free energy for confined lamellar phases.
• Generalization of free energy in terms of confinement dimensionality (d) and conformational asymmetry (ɛ).
• Construction of phase maps in parameter space.

Main Results:

• Layer-addition transitions (L(∥)) are suppressed with increasing confinement dimensionality.
• Conformational asymmetry alters transition points and stability of L(∥) in curved spaces.
• Flexibility of surface-preferential blocks affects transition radii and stability against nonconcentric layers.

Conclusions:

• Confinement dimensionality and conformational asymmetry are key factors governing confined lamellar structures.
• Curved confinement introduces complex behaviors related to block flexibility and layer arrangement.
• Phase maps provide a comprehensive overview of structural transitions under varying conditions.