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 (σthresh), 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 (TODT*) that is a function of the misalignment a given grain has with the shear direction (dθ): TODT* = TODT(1-(σ/σc)βsin2(αdθ)). Here, σ is the applied stress and σc is the critical stress which is directly related to σthresh by σthresh = σc(1-T/TODT). 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(TODT*-T)/TODT 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: σc 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, ψ2α = < 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 σthresh 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 σc: for spheres, σc = 2200 Pa for single shear but 6000 Pa for double shear; for cylinders, σc = 440 Pa for single shear but 520 Pa for double shear. With these values of σc, the model does capture the behavior very well, especially within the transition region (area between σthresh and the plateau stress). The cause of this increased σc 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.
References
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