Shear alignment and realignment of sphere-forming and cylinder-forming block-copolymer thin films

In common with many other structured fluids, block copolymers can be effectively oriented by shear. This susceptibility to shear alignment has previously been shown to hold even in thin films, containing as few as two layers of spherical microdomains, or even a single layer of cylindrical microdomains. A phenomenological model has been proposed [M. W. Wu, R. A. Register, and P. M. Chaikin, Phys. Rev. E 74, 040801(R) (2006)] to describe the alignment of such block-copolymer films, yielding the microdomain lattice order parameter as a function of shearing temperature, stress, and time. Here we directly test the central idea of that model, that the grains which are most misaligned with the shear direction are selectively destroyed, to reform in a direction more closely aligned with the shear. Films are first shear aligned from a polygrain state into a monodomain orientation and are then subjected to a second shear, at a variable stress $\left(\sigma \right)$ and misorientation angle $\left(\delta \theta \right)$ relative to the monodomain director, allowing the effects of $\sigma$ and $\delta \theta$ to be independently and systematically probed. For both cylinder-forming and sphere-forming block copolymers, these experiments confirm the basic premise of the model, as the stress required for realignment increases monotonically as $\delta \theta$ becomes smaller. For a cylinder-forming block copolymer, we find that the characteristic stress ${\sigma }_c$ required to realign cylinders from one monodomain orientation to another is indistinguishable from that required to generate a monodomain orientation from the polygrain state. By contrast, the hexagonal lattice of spheres requires a value of ${\sigma }_c$ more than 3 times as high for reorientation than for generation of the initial monodomain orientation.

Figure 1

Schematic of the geometry of the parallel-plate rheometer in single- and double-shear experiments indicating (a) the applied stress imparted to the block-copolymer thin film at various points from the rotation axis $(\times )$ and (b) the angular difference $\left(\delta \theta \right)$ between the two shear directions calculated at each point within the overlap region. See supplement material for a color-scale version of this figure (Ref. [43]).

Figure 2

(a) Real-space filtered image of unaligned cylinder-forming PS-PEP 4/13. Inset is the moiré interference pattern of the same area, showing strong bands when the AFM scan direction is in same direction as the cylinder axis (horizontal). (b) Real-space filtered image of aligned ($\sim 9°$ off vertical) sphere-forming PS-PEP 3/23. Scale bars are 400 nm.

Figure 3

Orientational order parameter as a function of stress for a monolayer of cylinder-forming PS-PEP 4/13 sheared at $135°\text{C}$ for 30 min. Open circles are from real-space AFM images, open squares are from moiré interference patterns, and filled diamonds are averages of the open squares in 150 Pa bins, except for the lowest-stress (0–300 Pa) and highest-stress $\left(>750\text{Pa}\right)$ bins. Error bars on these averages represent $\pm 1$ standard deviation of the mean. Solid line is the melting-recrystallization model fit to the open squares.

Figure 4

Angular distribution of PS-PEP 4/13 grains with respect to the shear direction (modulo $180°$) at different applied shear stresses after shearing for 30 min at $135°\text{C}$. A relatively flat distribution is observed at low stresses, but at higher stresses the grains most misaligned from the shear direction are progressively destroyed, making the distribution narrower as stress increases.

Figure 5

Shading representing the model predictions of the initial orientational order parameter $\left({\psi }_{2\alpha }\right)$ distribution before the second shear for both the (a) cylinder-forming (first shear at $135°\text{C}$ for 30 min at ${\sigma }_{\text{max}}=1600\text{Pa}$) and (b) sphere-forming (first shear at $85°\text{C}$ for 30 min at ${\sigma }_{\text{max}}=3200\text{Pa}$) PS-PEP block-copolymer thin films. Dashed circle represents outline of rheometer tool for first shear centered at $+$, while the solid circle represents the outline for what will be the second shear centered at $\times$. See supplement material for a color-scale version of this figure (Ref. [43]).

Figure 6

Results for a cylinder-forming block-copolymer thin film aligned in double-shear (both shears done at $135°\text{C}$ for 30 min at ${\sigma }_{\text{max}}=1600\text{Pa}$) with (a) showing the expected orientational order parameter relative to the second-shear direction, ${\psi }_2$ (shading according to the scale bar), using the parameters determined from the single-shear fits, and (b) showing experimental data as points with the model predictions as background shading. The shading of the points is the measured ${\psi }_2$ obtained from real-space AFM images; the center of each data point (shown 2 orders of magnitude larger in diameter than the actual image) corresponds with the location of the AFM image, whose position dictates the applied stress and difference in angle from the orientation imparted by the first shear. See supplement material for a color-scale version of this figure (Ref. [43]).

Figure 7

Orientational order parameter of double-sheared (both at $135°\text{C}$ for 30 min at ${\sigma }_{\text{max}}=1600\text{Pa}$) cylinder-forming block-copolymer thin film as a function of the second-shear stress, for $\delta \theta =70°$. Open circles are the experimental data measured using real-space AFM images (at $\delta \theta =70°\pm 10°$) and filled diamonds are averages taken over 150 Pa bins, except for the lowest-stress (0–300 Pa) and highest-stress $\left(>750\text{Pa}\right)$ bins. Error bars on these averages represent $\pm 1$ standard deviation of the mean. Solid line is the fit to the melting-recrystallization model $\left(\delta \theta =70°\right)$ using parameters obtained from single-shear results from an initially polygrain state.

Figure 8

Results for a sphere-forming block-copolymer thin film aligned in double shear (both shears done at $85°\text{C}$ for 30 min at ${\sigma }_{\text{max}}=3200\text{Pa}$) with (a) showing the expected orientational order parameter, ${\psi }_6$ (shading according to the scale bar), using the parameters determined from the single-shear fits, and (b) showing experimental data with the model adjusted to have a larger critical stress $\left({\sigma }_c\right)$ value for the second shear as background shading. The shading of the experimental data is the measured orientational order parameter obtained from real-space AFM images and the placement of the data point (2 orders of magnitude larger in diameter than the actual image width) dictates the applied stress and difference in angle from the prealigned orientation. Each set of points taken along a line is then converted to a 1D plot as a function of applied stress during the second shear: (c) upper data set emanating from the center of the second shear (along the $-26\pm 2°$ contour line), (d) lower data set emanating from the center of the second shear—panel shares stress axis with (c), (e) lower vertical data set, and (f) upper vertical data set—panel shares stress axis with (e). Each 1D plot includes experimental data with error bars, the melting-recrystallization model calculations using single-shear parameters only (dashed curves) and model calculations using a larger critical stress $\left({\sigma }_c\right)$ value for the second shear (solid curves) with a common legend found in (d). Error bars represent estimates of $\pm 1$ standard deviation of the uncertainty in ${\psi }_6$ for the individual points. See supplement material for a color-scale version of this figure (Ref. [43]).

Figure 9

Results for a sphere-forming block-copolymer thin film aligned in double-shear (first shear done at $85°\text{C}$ for 30 min at ${\sigma }_{\text{max}}=3200\text{Pa}$ and the second shear done at the same conditions for only 5 min). For (a), the dashed curve represents the outline of the rheometer tool for the first shear and the solid curve the outline for the second shear. The background shading represents melting-recrystallization model predictions for ${\psi }_6$ using an increased ${\sigma }_c$ (6100 Pa) and increased $\Gamma$ $\left(0.02{\text{s}}^{-1}\right)$ for the second shear. Small circles are the experimental data measured using real-space AFM images, with their shading representing the measured orientational order parameter. Each set of points taken along a line is then converted to a 1D plot as a function of (b) stress applied during the second shear and (c) angular difference between the two shear directions. Each 1D plot includes experimental data with error bars, the melting-recrystallization model calculations using the smaller $\Gamma$ ($0.01{\text{s}}^{-1}$, dashed curves), and model predictions using a larger $\Gamma$ value for the second shear (solid curves) with a common legend found in (c). See supplement material for a color-scale version of this figure (Ref. [43]).