1 research outputs found
Medial Packing, Frustration, and Competing Network Phases in Strongly Segregated Block Copolymers
Self-consistent field theory (SCFT) has established that
for cubic
network phases in diblock copolymer melts, the double-gyroid (DG)
is thermodynamically stable, relative to the competitor double-diamond
(DD) and double-primitive (DP) phases, and exhibits a window of stability
intermediate to the classical lamellar and columnar phases. This competition
is widely thought to be controlled by “packing frustration”the
incompatibility of uniformly filling melts with a locally preferred
chain packing motif. Here, we reassess the thermodynamics of cubic
network formation in strongly segregated diblock melts based on a
recently developed medial strong segregation theory (mSST) approach that directly connects the shape and thermodynamics
of chain packing environments to the medial geometry of tubular network surfaces. We first show that medial packing significantly
relaxes prior SST upper bounds on the free energy of network phases,
which we attribute to the spreading of terminal chain ends within
network nodal regions. By exploring geometric and thermodynamic metrics
of chain packing in network phases, we show that mSST reproduces effects
dependent on the elastic asymmetry of the blocks that are consistent
with SCFT at large χN. We then characterize
geometric frustration in terms of the spatially variant distributions
of local entropic and enthalpic costs throughout the morphologies,
extracted from mSST predictions. By analyzing these distributions,
we found that the DG morphology, due to its unique medial geometry
in the nodal regions, is stabilized by the incorporation of favorable,
quasi-lamellar packing over much of its morphology, motifs which are
inaccessible to DD and DP morphologies due to “interior corners”
in their medial geometries. Finally, we use our results to analyze
“hot spots” of chain stretching and discuss implications
for network susceptibility to the uptake of guest molecules