(711c) Sphere-Forming and Cylinder-Forming Block Copolymer Thin Films Aligned Under Double Shear

Introduction

            Thin films formed
from microphase-separated block copolymers are of interest because they form
periodic structures on the order of tens of nanometers with domain size tunable
by their molecular weight [1,2].  Unfortunately, the structures of the as-spun
or thermally annealed films do not have the order (neither orientational nor
translational) necessary for many intended applications (templates for nanowires
or polarizers [3] for cylinder-forming block copolymers or templates for high
density magnetic storage devices for sphere-forming block copolymers [4]). 

            Our group has
demonstrated that these block copolymer thin films respond to a shearing field
and orient (the cylinder axis in cylinder-forming block copolymers and the (10)
line of spheres in the sphere-forming block copolymers) in the direction of the
imposed shear [5-8].  At low shear stress, no alignment occurred.  Once the
stress reaches a threshold stress (σ_thresh), the
alignment increases quickly as stress increases, and then reaches a plateau
value where the alignment is no longer dependent on stress.  Our group proposed
a phenomenological model to explain the shear alignment [7,8].  The model
explains that there is an effective order-disorder temperature (T_ODT*)
that is a function of the misalignment a given grain has with the shear
direction (dθ):  T_ODT* = T_ODT(1-(σ/σ_c)^βsin²(αdθ)). 
Here, σ is the applied stress and σ_c is the
critical stress which is directly related to σ_thresh by σ_thresh
= σ_c(1-T/T_ODT).  α and β
are values related to the symmetry of the lattice (β = 1, α
= 3 for spheres because of six-fold symmetry and β = 2, α
= 1 for cylinders because of two-fold symmetry).  The rate of
melting/recrystallization of a grain is assumed constant:  dR/dt
= Γ(T_ODT*-T)/T_ODT with R as the area of a
grain and Γ as a rate constant that determines how quickly the alignment
plateau is reached.  This model has two empirical parameters:  σ_c
and Γ.  Fitting experimental data taken at different temperatures
and different times for both cylinder- and sphere-forming block copolymers
showed excellent agreement with the model.  The model was developed when
sheared from the disordered state with an ensemble of grains in all orientations. 
Here we directly test the model's idea that melting is dependent on σ
and dθ by varying them in a continuous and known way by
shearing the ordered film a second time. 

            We have previously
shown that dislocations in sphere-forming block copolymer thin films orient
normal to the shear direction [9].  The double shear experiments give us an
opportunity to investigate how the dislocation distribution and dislocation
density change when sheared at 60° relative to the initial shear direction.

Experimental

            The polymers used in
this study were synthesized previously [10] (sphere-forming block copolymer ? 3
kg/mol polystyrene (PS) and 24 kg/mol poly(ethylene-alt-propylene) (PEP);
cylinder-forming block copolymer ? 5 kg/mol PS and 13 kg/mol PEP).  The order-disorder
temperatures were determined as [11] 121°C for 3/24 and 204°C for 5/13.  Dilute
solutions (1-2 % in toluene) were spin-coated onto bare halves of 3? silicon
wafers from Silicon Quest International to obtain a monolayer of cylinders (35
nm) and a trilayer of spheres (78 nm).  The wafers were then secured to the
Peltier heater on an Anton Paar MCR 501 constant stress rheometer.  A thick
layer (~0.2 mm) of polydimethylsiloxane (PDMS) oil (1E6 cSt from Gelest) was
placed on top of the thin film before the parallel plate rheometer tool was
lowered into place.  The film is sheared at a constant temperature at a
constant stress for a set amount of time.  The wafer and film are then
translated relative to the rotation axis, reattached to the heater, the oil is
reapplied, and the film is sheared a second time.  The overlap region between
the two shears is the area of interest where we have continual change in both
stress (σ) and angle difference (dθ). Following
shearing, the oil is removed by stamping with a crosslinked PDMS pad and
real-space images of the film are taken in Tapping Mode on an atomic force
microscope.  Custom software is used to filter the images and quantify the
alignment by calculating an orientational order parameter, ψ_2α
= < cos(2αdθ) > (used in [5-8]). 

Results and Discussion

            Using the quantitative
parameters extracted from the single shear-model, the experimental data in the
double-sheared region does not agree well with our model.  It does, however,
capture the qualitative nature of the complex pattern produced.  For the double-shear
region, it appears that σ_thresh is a larger value of
stress than for the single-shear experiments.  If the model is refit to just
the double-shear data, there is negligible change in Γ but larger
values for σ_c:  for spheres, σ_c =
2200 Pa for single shear but 6000 Pa for double shear; for cylinders, σ_c
= 440 Pa for single shear but 520 Pa for double shear.  With these values of σ_c,
the model does capture the behavior very well, especially within the transition
region (area between σ_thresh and the plateau stress). 
The cause of this increased σ_c in the double-sheared
films is not fully understood and is still being investigated.  We hypothesize
that this increased stress may reflect the need for a nucleation event to occur
within the double-sheared region.  The single-sheared samples are sheared from
the unaligned state where grains of all orientations are present.  The shearing
process will aid the growth of grains in the proper orientation, and melt those
that are misoriented.  In double shear, we have only grains that are misaligned
so the shearing would need to nucleate a grain before it can grow, which could
require a higher stress than that needed to simply grow existing grains. 

Taking the
angular distribution of dislocations from the single-shear results as a
probability distribution, if we then shear 60° relative to the first shear, one
might expect to obtain the product of the distributions with the second shear
shifted from the first by 60°.  This would result in four peaks of equal size
and two smaller peaks (since they are not preferred in either the first or
second shear).  We might also expect a decrease in overall dislocation
density.  What we find experimentally, however, is an identical distribution to
that in the single-shear experiment (centered at the second shear direction).  In
other words, it is as though no memory of the first shear is retained.  We also
found no net decrease in dislocation density. 

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