377716 Orientation of Cylinder-Forming Poly(styrene)-Poly(n-hexylmethacrylate) Diblock Thin Films Pre- and Post-Shear
Block copolymer thin films provide an attractive method for nanopatterning at size scales inaccessible to conventional photolithographic techniques.1 Block copolymers can microphase separate to form dense, periodic microdomains on the size scale of 10-100 nm.2 To serve effectively as templates, however, the need to impart well-defined positional and orientational order to these microdomains is paramount. One method to achieve long-range orientational order in block copolymer thin films is through the use of shear, which has previously been shown to preferentially orient the microdomains of certain sphere-3, cylinder-4, and lamellae-forming5 systems in the direction of applied shear. Numerous experimental factors influence the ease with which orientation is achieved as well as the ultimate quality of alignment observed. The present work aims to investigate several of these factors by studying the thin film morphology, in both the unaligned (thermally annealed) and shear-aligned states, of cylinder-forming poly(styrene)-poly(n-hexylmethacrylate) (PS-PHMA) copolymers which are of interest for nanolithographic applications such as the production of nanowire polarizing grids for deep ultraviolet light.6 The tendency of PS-PHMA diblocks not to terrace (form "islands" or "holes") at reasonable annealing conditions, but instead to form mixed morphological patterns (mixtures of in-plane and out-of-plane cylinders or spheres) without discrete variation in film thickness makes it challenging to identify the precise monolayer film thickness at which maximum alignment quality is expected to occur. Furthermore, we investigate the effect of block copolymer composition on these thickness dependencies; in particular, we expect that moving the polymer more firmly into the cylinder-forming phase space might reduce the ability of the microdomains to restructure into spheres, and thus dampen the degree to which orientational switching between in-plane and out-of-plane cylinders is possible. Once the optimal integer layer film thicknesses are identified we subsequently examine both the limitations to the maximum achievable alignment quality as well as the ease with which these systems are aligned (by looking at alignment quality as a function of applied shear).
A series of cylinder-forming PS-PHMAs (PS minority block) with comparable molecular weights and narrow dispersities, but which systematically vary in composition to span the entire cylinder-forming phase space, were synthesized via living anionic polymerization. PS-PHMA thin films (~ 10-200 nm) with a thickness gradient were cast via flowcoating7,8; this allows for rapid investigation of thin film morphology, via atomic force microscopy, as a function of film thickness t. In unsheared films, the PS-PHMA diblock with the lowest styrene weight fraction (w = 0.21) showed morphologies ranging from complete coverage of dots (either spheres or out-of-plane cylinders) to complete coverage of lines (in-plane cylinders), or mixtures of the two, as t was varied. The fractional coverage of lines (F) was computed for each micrograph and examined vs. t. The data showed a strong dependence of F on t which included complete switching between F = 1 (all in-plane cylinders) at approximately integer multiples of the bulk interplanar spacing (d) to F = 0 (all out-of-plane cylinders or spheres) at incommensurate film thicknesses. The strength of this dependency decreased with increased t; at t/d > 3 only in-plane cylinders are observed. Performing a similar analysis on the three PS-PHMAs with higher w (w = 0.26, 0.30, 0.35) shows that as w increases the effects of thickness on in- vs. out-of-plane orientation gradually diminish such that for w ≥ 0.30 the orientation is nearly thickness independent (F ~ 1 for all t/d > 1). This supports our hypothesis that by increasing w, thus moving away from the cylinder-sphere phase boundary, one can modulate the range of film thicknesses over which in-plane vs. out-of-plane cylinders are observed.
These PS-PHMA films were then sheared transverse to the thickness gradient, and the quality of their alignment quantified via an orientational order parameter ψ2α (α = 1 for analyzing all-line patterns, α = 3 for mixed dot-line patterns). The PS-PHMA with the lowest w, which showed the strongest dependence of F on t/d, showed a similar trend in ψ6 vs. t/d; the thicknesses which showed the highest fraction of in-plane cylinders pre-shear possessed the highest quality of alignment post-shear. The three higher-w polymers all showed relatively high alignment quality independent of film thickness (ψ6 > 0.9 for all t/d > 1). For all polymers studied, generally the best alignment occurred near integer ratios of t/d. In these cases only in-plane cylinders are observed and the only lattice defects present are isolated dislocations. The areal density of these dislocations was computed, and ψ2 plotted vs. this density. The slopes of the best-fit lines to these data reveal the influence of a single dislocation on the lattice order, while the y-intercepts indicate the maximum quality of alignment achievable in the absence of any lattice defects; the source of the differences between the y-intercept and unity are attributed to remaining fluctuations in the cylinders’ trajectories. No significant differences in the slope or y-intercept were observed between monolayers (t/d = 1) and multilayers (t/d = 2, 3, 4) of the same polymer. In addition, while the lowest-w polymer showed both a lower y-intercept and a steeper slope, data for the other three PS-PHMAs possessed slopes and intercepts which were statistically indistinguishable (this common slope is in good agreement with that predicted from elastic continuum simulations9).
Finally, experiments to determine the ease with which alignment is achieved were performed by shearing monolayers of each PS-PHMA using a parallel plate rheometer, with a macroscopic (~ 0.2 mm) layer of viscous silicone oil between the stationary film and the top rotating rheometer plate. This allows for the application of a stress (σ) gradient from zero at the rotation axis to σmax at the rheometer plate edge, thus enabling the rapid investigation of ψ2 vs. σ. At low stresses no alignment is observed until a threshold value of σ is reached. At high stresses the alignment quality plateaus at ψ2 ≈ 0.99. While all four polymers showed similar alignment quality at high σ, the stress needed for alignment to first occur increases monotonically with w. In addition, the two lower-w PS-PHMAs possess very sharp transitions between the unaligned and aligned states while the two higher-w polymers show much more gradual transitions. These curves were compared to a phenomenological melting-recrystallization model for microdomain alignment.10,11 The model contains two key parameters: a critical stress σc which relates the stress needed for alignment to begin to occur and a rate constant Γ which describes the rate of melting and recrystallization, and which governs the sharpness of the transition (in σ) between the unaligned and aligned states for a given shearing time. The data for all four polymers are well described by the model and the resulting best-fit parameters are used to quantitatively compare across the materials. As w increases, σc steadily increases, meaning that a higher stress is required to initiate alignment as the cylinder (PS) fraction increases. The rate constant Γ is more difficult to extract precisely from the data, but the two polymers with lower w show values of Γ smaller by 1-2 orders of magnitude than for the two polymers of higher w.
In conclusion we find that for unaligned films of PS-PHMA the in- vs. out-of-plane orientation of cylinders is highly sensitive to film thickness, but this sensitivity is substantially reduced with increased PS fraction. In general, thicknesses which possess the highest fractional coverage of in-plane cylinders pre-shear show the highest quality of alignment post-shear. For films of commensurate thicknesses (t/d = integer), all four PS-PHMAs show high alignment quality (ψ2 > 0.99) of in-plane cylinders post-shear, although the lowest-w polymer shows consistently poorer alignment than the others. This alignment quality is limited by isolated dislocations and fluctuations in the cylinders’ trajectories. Finally by examining alignment quality as a function of applied stress we observe that as PS fraction increases the stress and time needed for alignment to occur both increase and this behavior is well described by a melting-recrystallization model.
This work was supported by the National Science Foundation (MRSEC Program) through the Princeton Center for Complex Materials (DMR-0819860).
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