The self-assembly of block copolymers (BCPs), consisting of chemically dissimilar polymer blocks, has attracted great attention due to its nanoscopic ordered structures for templates and scaffolds tailored in tens of nanometer.1–4 A phase diagram involving morphologies such as lamellar, cylindrical, gyroid, and spherical structures, can be dictated by the volume fraction (f) of one block, the degree of polymerization (N), and the Flory-Huggins segmental interaction parameter (χ) between the two blocks.5–8 The BCP microphase-separates above a critical product value of χ·N (χ·N > 10.5 in case of symmetric BCP), while it mixes into a homogeneous phase below that value; this BCP undergoes a transition from an ordered to a disordered state. Hence, the order-to-disorder transition (ODT) occurs when the unfavorable segmental interactions weaken sufficiently, and the entropy on mixing dominates over the system.9–11
There has been many studies in evaluating the bulk ODT of the BCPs, using the variations in the enthalpy, rheology, scattering or optical properties, and morphology with temperature.8, 12–16 Unlike the bulk ODT of the BCPs, the transition behavior in the film geometry was greatly influenced by the interfacial interactions at both substrate/polymer and polymer/air interfaces. The microdomain orientation in the BCP films was also sensitive to the interfacial interactions in addition to the commensurability between the equilibrium period (Lo) of the BCP and the total film thickness (L).17–19 The parallel orientation of microdomains in most cases of the BCP films was attributed to the large difference in surface energy between the two blocks and/or the preferential interactions at an interface or both interfaces toward one block.20–24 In contrast, the balanced interfacial interactions on the neutral substrate enforced the lamellar and cylindrical microdomains to orient normal to the film surface.25–31
A phase transition in the BCP films was analytically evaluated using the correlation length, when the decay length (ξ) reduces discontinuously with increasing temperature and approaches to infinity, both theoretically and experimentally.32–35 However, the experimental results indicated that even slightly above the bulk ODT the periodic layers remain ordered at both substrate/polymer and polymer/air interfaces, while the middle of the film is still disordered.33, 36 A simulation study of the BCP films confined between two neutral walls also represented that the phase transition of BCP in film geometry is significantly influenced by the interfacial interactions.19 Recently, grazing incidence small-angle X-ray scattering (GISAXS) technique has been used to investigate the transition behavior in the BCP films, allowing the temperature-dependent analysis of the nanostructured patterns.37–43 Both the near surface and entire film structures were analyzed by varying incident angle (αi) above the critical angle (αc) of the BCP films to trace the structural changes at transition. Here, we present an overview of the recent progress on the phase transition studies of the BCP films with a particular focus on revealing the interfacial interactions effects of the substrates and the χ effects between the two blocks,37, 39, 41 and show how the ODT in the BCP films shifts from the bulk ODT depending on the strength of the preferential interactions on the substrates.
The Transition Behavior in the BCP Films on a Preferential and a Neutral Substrate
The phase transition in the BCP films prepared with a lamellar-forming polystyrene-b-polyisoprene (PS-b-PI) on a polystyrene (PS) grafted substrate was first investigated using in situ GISAXS, as an example of the strongly interacting (with larger enthalpic contribution to χ) BCP films on a preferential substrate.37 Figure 1(a) shows a schematic transition diagram of the BCP films as a function of film thickness, where Lo and Lc denote an equilibrium period and a critical thickness above which the transition is independent of film thickness, respectively. For the BCP films thinner than ∼ 12Lo, the ODT in the PS-b-PI films on a PS grafted substrate increased rapidly with decreasing film thickness, as presented with the red solid line. These results indicated that the preferential interactions on the PS grafted substrate with the PS block were inversely proportional to the film thickness at L < Lc. Even the ODT in the BCP films on a bare silicon substrate increased within experimental range, although the interactions on the oxide substrate with the PI block were weakly favorable, as presented with the red dotted line. Particularly for L > Lc (∼12Lo), the ODT in the BCP films on a PS grafted substrate shifted significantly from the bulk ODT, while the ODT in the BCP films on a bare silicon substrate remained similar to the bulk ODT.37 These results indicated that the preferential interactions at substrate/polymer interface (PS-grafted-substrate/ PS-block) and the difference in surface energy between the two blocks led to a periodic amplification in the block composition for the BCP films. It was evidenced with a perfect multilayered lamellar microdomain parallel to the film surface by the transmission electron microscopy (TEM) image of the PS-b-PI films on a PS grafted substrate.37
Figure 1. Schematic transition diagram of the BCP films as a function of film thickness. (a) The PS-b-PI films on a PS grafted substrate and a bare silicon substrate, and (b) the PS-b-PMMA films on a PS grafted substrate and a neutral substrate. The Lo and Lc denote an equilibrium period and a critical thickness above which the transition is independent of film thickness, respectively. The black solid line indicates a bulk ODT of the BCP.
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To elucidate the χ effects between the two blocks on the phase transition in the BCP films, the weakly interacting (with smaller enthalpic contribution to χ) BCP of a lamellar-forming polystyrene-b-poly(methyl methacrylate) (PS-b-PMMA) was subjected to a preferential substrate. The blue solid line in Figure 1(b) presents the ODT in the PS-b-PMMA films prepared on a PS grafted substrate. Compared with the ODT in the PS-b-PI films on a PS grafted substrate, a gentle increase in the ODT with decreasing film thickness was seen for the BCP films thinner less than ∼30Lo that corresponds to a Lc. These results observed in the PS-b-PMMA films were attributed to smaller enthalpic contributions to χ by the mean-field free energy consideration.39 Therefore, these characteristic thickness dependences of the ODTs in the PS-b-PI and PS-b-PMMA films (at L < Lc) on a PS grafted substrate could be associated with the relative magnitude of enthalpic contribution to χ between the two blocks. There was also the ODT shift from the bulk ODT in the PS-b-PMMA films on a PS grafted substrate, and the TEM images of the PS-b-PMMA films above Lc displayed a multilayered lamellar microdomain parallel to the film surface, as similarly observed in the PS-b-PI films on a PS grafted substrate.37, 39
The phase transition in the PS-b-PMMA films was evaluated under the balanced interfacial interactions on the substrate, as presented in Figure 1(b) with the blue dotted line. A neutral substrate was prepared by grafting a poly(styrene-r-methyl methacrylate) (P(S-r-MMA)) to the substrate to balance the interfacial interactions toward the two blocks of the PS-b-PMMA.25, 28–30 Very interestingly, the ODT in the BCP films at L < Lc ∼ 30Lo decreased with decreasing film thickness, representing that a random-copolymer grafted substrate provided a surface-induced compatibilization toward the two blocks.41 This result was in contrast to the ODT increase (at L < Lc) with decreasing film thickness for the PS-b-PMMA (and PS-b-PI) films on a PS grafted substrate.37, 39 However, a relatively consistent ODT shift in the PS-b-PMMA films thicker than Lc ∼ 30Lo, still above the bulk ODT, was similar to that in the BCP films on a PS grafted substrate. The TEM image displayed a majority of multilayered lamellar microdomain parallel to the film surface, although a non-parallel lamellar orientation was partially discernible at both substrate/polymer and polymer/air interfaces.41 This result was presumably caused by the difference in surface energy between the two blocks though minor. Therefore, these ODT shifts from the bulk ODTs above Lc in all the BCP films regardless of interfacial interaction types on the substrates indicated that the compositional fluctuation was suppressed by a periodic amplification in the block composition for the BCP films.
The ODT Shifts in the BCP Films Depending on the Strength of the Preferential Interactions on the Substrates
With the description above on the transition behavior in the BCP films on a preferential and a neutral substrate, we could provide a schematic transition diagram of the BCP films as a function of film thickness. For further consideration, we focused on the ODT shifts from the bulk ODT above Lc for the BCP films under the preferential interactions with the two different strengths on the substrates. A lamellar-forming polystyrene-b-poly(2-vinlyprydine) (PS-b-P2VP) was selected for quantitative comparison, since it exhibits stronger enthalpic contributions to χ; χ = −0.33 + 66/T compared with χ = −0.0419 + 38.54/T for the PS-b-PI and χ = 0.0425 + 4.046/T for the PS-b-PMMA.44–46 The PS-b-P2VP was synthesized by the sequential anionic polymerization of styrene and 2-vinylpyrindie in tehtrahydrofuran at −78 °C under purified argon environment using sec-butyllithium as an initiator. The number-average molecular weight (Mn) and polydispersity (Mw/Mn), characterized by size-exclusion chromatography, were 18 100, and 1.06, respectively. The PS volume fraction (ϕPS) of PS-b-P2VP was determined to be 0.509 by 1H nuclear magnetic resonance (1H NMR). To evaluate the bulk ODT of the BCP, the small-angle X-ray scattering (SAXS) experiments were conducted at 4C beam-line in the Pohang Accelerator Laboratory (PAL), Korea.
The SAXS intensity profiles for the PS-b-P2VP is shown in Figure 2 as a function of the scattering vector (q) and scattering properties, where q = (4π/λ)sin θ, and θ and λ are the scattering angle and wavelength of the incident X-ray beam, respectively. The sample was annealed at a constant temperature of 140 °C to ensure an equilibrium state, and the heating process was controlled from 140 to 240 °C at a heating rate of 1.0 °C/min. At T = 140 °C, a sharp primary peak at q* = 0.405 nm−1 and third-order peak at 3q* relative to the first-order reflection indicated the microphase separation into a lamellar microdomain due to the unfavorable segmental interactions between the two blocks, as marked in the inset. The disappearance of 2q* could be attributed to the symmetric lamellar microdomain, rather than to the low electron density contrast between the two blocks. However, a broad maximum near q* = 0.426 nm−1 at T ≥ 200 °C indicated the correlation hole scattering in a disordered state of the BCP, arising from the compositional fluctuation in the Rg (radius of gyration) scale.9 This temperature-dependent behavior represented a typical ODT-type BCP undergoing a transition from an ordered to a disordered state with increasing temperature.9–11 Accordingly, a bulk ODT of the PS-b-P2VP could be measured at 200 °C by the discontinuity in the scattering properties derived from SAXS intensity profiles, like the inverse of the maximum intensity [1/I(q*)], full width at half-maximum (fwhm), and d-spacing (d) by d = 2π/q* as a function of inverse temperature (1/K).
Figure 2. SAXS intensity profiles for the PS-b-P2VP as a function of the scattering vector (q) and scattering properties. The 1q* and 3q* indicate the microphase separation into a lamellar microdomain. The scattering properties derived from SAXS intensity profiles, the inverse of the maximum intensity [1/I(q*)], fwhm, and d-spacing (d) by d = 2π/q*, were plotted as a function of inverse temperature (1/K)
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For the preferential interactions with the two different strengths on the substrates, a PS grafted and a bare silicon substrate were used for the athermal interactions with the PS block and the strongly attractive interactions with the P2VP block, respectively. A hydroxyl terminated polystyrene (PS-OH, Polymer Source Inc.) with Mn = 14 000 g/mol and PDI = 1.09 was used to prepare a PS grafted substrate by grafting the PS chains to the substrate.37, 39 The brush thickness was measured to be 11.0 ± 0.3 nm by ellipsometry (SE MG-1000, Nanoview Co.). A film thickness was set to 388 nm (25Lo) above Lc, because the preferential interactions on the substrates were inversely proportional to the film thickness at L < Lc. The PS-b-P2VP films were annealed at a constant temperature of 140 °C under vacuum for 24 h. The GISAXS experiments were conducted at 3C and 9A beam-lines in the PAL, Korea. The operating conditions were set to a wavelength of 1.38 Å and a sample-to-detector distance of 2.5 m. An αi was used at 0.18°, which is above the αc (0.14°) of the PS-b-P2VP films. The equilibrium period (Lo) of the BCP was measured to be 15.5 nm by the d-spacing (d = 2π/q*), as taken in an ordered state at 140 °C (from the SAXS result).
Figure 3 shows the GISAXS patterns of the PS-b-P2VP films with thickness of 25Lo (L > Lc) on a PS grafted and a bare silicon substrate, which were measured during heating from 170 to 240 °C at a rate of 1.0 °C/min. The least exposure time at selected temperatures was used to avoid X-ray beam damages that may influence the transition temperature.39 In the GISAXS geometry, the qxy is the in-plane scattering vector parallel to the sample surface, which is related to d = 2π/qxy*, and the qz is the out-of-plane scattering vector normal to the sample surface based on the reflected beam, defined by qz = (2π/λ)(sin αi + sin αf), where the αf is the exit angle. For the BCP film on a PS grafted substrate (top line), the GISAXS patterns measured at T = 170 °C display two characteristic out-of-plane reflections (indicated by the solid arrows) along the qz-direction near qxy = 0, and the consistent patterns remain up to 220 °C above the bulk ODT (200 °C) of the BCP. These patterns indicated the parallel orientation of lamellar microdomain, which is caused by the preferential interactions on a PS grafted substrate with the PS block. However, the GISAXS patterns at T > 220 °C display two arc-shaped diffuse scatterings arising from a superposition of the reflected and transmitted X-ray scatterings, indicating the correlation hole scattering in the disordered BCP film.47 Upon direct cooling to 210 °C, the recovery into the GISAXS pattern with two out-of-plane reflections represented that the transition in the PS-b-P2VP films is thermoreversible. The GISAXS results of the BCP film on a bare silicon substrate (the strongly attractive interactions with the P2VP block) were comparable to those of the BCP film on a PS grafted substrate, even though the transition temperatures were different, as shown in the second line.
Figure 3. GISAXS patterns of the PS-b-P2VP films with thickness of 25Lo (L > Lc) on a PS grafted substrate (top line) and on a bare silicon substrate (second line). The solid arrows indicate two characteristic out-of-plane reflections along the qz-direction near qxy = 0, and the blue dotted arrows indicate the maximum intensity of the in-plane scattering peaks.
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For a quantitative determination of the ODT in the BCP films, the out-of-plane (along the qz-direction at near qxy = 0) and the in-plane scattering peaks (along qxy-direction at qz = 0) from the GISAXS patterns were analyzed with temperature, as marked by the blue solid and dotted arrows in Figure 3. Figure 4 shows the maximum intensity of the out-of-plane and in-plane scattering peaks for the PS-b-P2VP films on a PS grafted and a bare silicon substrate as function of temperature. A decrease in the out-of-plane scattering intensity and an increase in the in-plane scattering intensity coincided at a transition from the parallel orientation of lamellar microdomain to a disordered state in the BCP films, resulting in the ODTs in the BCP films on the different substrates; 223 °C for a PS grafted substrate and 231 °C for a bare silicon substrate, respectively. It should be noted that the two ODTs in the BCP films shifted from the bulk ODT due to the suppression of the compositional fluctuation in the film geometry by the preferential interactions on the substrates with one block. However, the polar–polar interactions on a bare silicon substrate with the P2VP block was stronger than the athermal interactions on a PS grafted substrate with the PS block, leading to the higher ODT shift in the BCP film on a strongly attractive substrate. Since the free energies associated with the difference in surface energy between the two blocks (γPS ∼ 39 mN/m, γP2VP ∼ 47 mN/m) at polymer/air interface48 and with the junction interface between the two blocks were the same conditions, the ODT shifts from the bulk ODT could be simply attributed to the free energy associated with the interactions at substrate/polymer interface in the BCP films. Accordingly, the strong preferential interactions on the substrates toward one block in the PS-b-P2VP films led to the higher ODT shift from the bulk ODT above Lc.
Figure 4. The maximum intensities of the out-of-plane and in-plane scattering peaks as a function of temperature for the PS-b-P2VP film on a PS grafted (•; ○) substrate and a bare silicon substrate (▴; ▵). The dotted line indicates a bulk ODT of the PS-b-P2VP.
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