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substrates used in this study, the pitch of the saw-
tooth was varied from 160 to 24 nm, with peak-
to-valley heights or amplitudes ranging from 20
to 3 nm by being annealed in air at temperatures
from 1300° to 1500°C for 24 hours [supporting
online material (SOM), section S1]. Crystallo-
graphic registry of the facets over macroscopic dis-
tances is ensured, because the sapphire is a single
crystal (14). There are, though, dislocations and an
~26% variation in the pitch, randomly located
across the surface.
Five different polystyrene-block-poly(ethylene
oxides) (PS-b-PEOs), with number-average mo-
lecular weights (Mn) from 7 to 43.0 kg/mol,
polystyrene-block-poly(2-vinylpyridine) (PS-b-
P2VP) (Mn = 19.5 kg/mol), and PS-b-P4VP
(Mn = 19 kg/mol), all with narrow molecular
weight distributions and minor volume frac-
tions of ~0.3, were used (SOM, section S1). In
the bulk, these BCPs microphase-separate into
hexagonal arrays of cylindrical microdomains of
PEO, P2VP or P4VP in a PS matrix. Thin films
of the BCPs were spin-coated onto the faceted
surfaces, which were cleaned with oxygen plasma
(SOM, section S1).
Shown in Fig. 1E is a solvent-annealed,
24-nm-thick (as measured on a flat surface) film
of PS-b-PEO (Mn = 43.0 kg/mol) on a sapphire
surface, with facets having an average pitch of
130 nm and amplitude of 14 nm. Upon solvent
annealing, the film is sufficiently thin that the
copolymer is entrained into and confined within
the regions between the facets. The solvent an-
nealing process orients and orders the PS-b-PEO
(15), but the average period is 23 nm, much less
than the 29.5-nm period seen for this copolymer
solvent annealed on a smooth surface. Conse-
quently, the confinement causes a reduction in
the fundamental period of the copolymer, as seen
in studies of copolymers confined between planar
surfaces (16–18) or within lithographically gen-
erated surface patterns (19). The facets essentially
isolate strips of the copolymer across the surface