Shear-Aligned Block Copolymer Monolayers as Seeds To Control theOrientational Order in Cylinder-Forming Block Copolymer Thin FilmsAnabella A. Abate,† Giang Thi Vu,‡ Aldo D. Pezzutti,† Nicolas A. García,† Raleigh L. Davis,§
Friederike Schmid,‡ Richard A. Register,§ and Daniel A. Vega*,†
†Instituto de Física del Sur (IFISUR), Consejo Nacional de Investigaciones Científicas y Tecnicas (CONICET), UniversidadNacional del Sur, 8000 Bahía Blanca, Argentina‡Institut fur Physik, Johannes Gutenberg Universitat Mainz, Staudinger Weg 7, D-55099 Mainz, Germany§Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, United States
*S Supporting Information
ABSTRACT: We study the dynamics of coarsening of a cylinder-forming block copolymer thin film deposited on a prepatternedsubstrate made of a well-ordered block copolymer monolayer. Duringthermal annealing the shear-aligned bottom layer drives extinction ofthe disclinations and promotes a strong orientational correlation,disturbed only by dislocations and undulations along the cylinders ofthe minority phase. The thin film bilayer system remains stable duringannealing, in agreement with self-consistent field theory results thatindicate that although the thickness of a stack of two monolayers isnot at the optimum thickness condition, it is very close toequilibrium. Phase field simulations indicate that the bottom layerremains undisturbed during annealing and acts as a periodic externalfield that stabilizes the orientation of those domains that share itsorientation. Misoriented cylinders are rapidly reorganized through aninstability mechanism that drives the fragmentation of the cylinders. As annealing proceeds, the fragmented cylinders arereconstructed along the direction imposed by the ordered bottom layer. This mechanism removes the disclinations completelywhile leaving dislocations that can be slowly annihilated during annealing. These results indicate that with appropriate controlover a single self-assembling polymeric layer, it should be possible to propagate order in thick block copolymer films and toobtain structures with controlled orientational order.
■ INTRODUCTION
Block copolymers have gained increasing attention due to theirinherent capacity to self-assemble into well-defined periodicnanostructures, a key requirement for many nanofabricationtechnologies and the miniaturization of electronic devices. Asself-assembly is typically low cost, fast, and easily scalable, it isquite attractive for large-scale applications. However, one of themain drawbacks of the self-assembly strategy is the lack of long-range order due to the presence of defects; consequently,significant effort has been devoted to producing well-definedorientational or positional order in thin films for their potentialuse in nanopatterning applications.1−9 Numerous methodshave been developed to impart such order in both the in-planeand out-of-plane directions,4,10,11 including various zoneannealing strategies,9,12,13 the use of external fields,3,14−16 andmodifying the local or global substrate chemistry or top-ography.5,17−21
One technique in particular, shear alignment, has beenshown to impart strong in-plane alignment to block copolymerthin films.3,22−24 In thin films, the application of shear stresspromotes the elimination of defects and preferential orientation
in the direction of applied shear. Angelescu et al. achievedalignment in monolayers of a cylinder-forming block copolymerby placing a smooth, cross-linked poly(dimethylsiloxane) padin contact with the film and applying a lateral force.3 Givensufficient stress, the cylinders align in the shear direction overthe entire area under the pad. This technique has been furthershown to align certain cylinder-,25−28 sphere-,29,30 and lamellae-forming16 block copolymers.Up to now, significant effort has been dedicated to
controlling quasi-two-dimensional block copolymer thin filmsystems developing mainly hexagonal or smectic symme-tries.26,31 However, the ability of block copolymers to self-assemble into a diversity of three-dimensional (3D) structureswith different symmetries suggests that it should be possible touse these systems to obtain templates for 3D nanofabrica-tion.32−42 As the self-assembly of block copolymers in 3Dpresents similar drawbacks as in 2D, that is, spontaneous self-
Received: April 19, 2016Revised: September 12, 2016Published: September 27, 2016
organization always leaves defects43 that for most applicationsshould be avoided,44,45 it is important to develop novelstrategies to control order and to understand the physicsbehind the mechanisms that drive toward the equilibrium state.The chief aim of the present work is to investigate the use of
well-ordered block copolymer monolayers as seeds to induceorder in block copolymer thin films with the same chemicalstructure. The coupling between aligned and nonaligned layersis studied in a bilayer of a cylinder-forming poly(styrene)-poly(n-hexyl methacrylate), PS−PHMA, diblock copolymer. Amultistep approach that includes shear alignment, thin film lift-off, and stacking is employed to obtain the bilayer system whileatomic force microscopy (AFM) is used to characterize themorphology of the films. The stability of the bilayer blockcopolymer thin film against the formation of holes and islandsis analyzed through self-consistent field theory calculationswhile the kinetics of ordering and coupling between the alignedand nonaligned layers are studied through a phase field modelthat emulates the symmetry and initial configurations of thebilayer systems explored through the experimental setup.
■ EXPERIMENTAL SECTIONPolymer Synthesis. The cylinder-forming PS−PHMA 33/78
diblock employed here was synthesized via sequential living anionicpolymerization of styrene and n-hexyl methacrylate, in tetrahydrofuranat −78 °C, using 10 equiv of LiCl to sec-butyllithium initiator and hadnumber-average block molar masses of 33 and 78 kg/mol for PS andPHMA, respectively, and diblock dispersity D = 1.06.25 At 150 °C, thePS volume fraction is 0.28, and the segregation strength χN isestimated to be 32.46 As this work requires floating a polymer on awater surface, we employed a sacrificial layer of a water-solublepolymer: poly(4-styrenesulfonic acid), PSS (Sigma-Aldrich), with aweight-average molecular weight of 75 kg/mol. The PSS was obtainedas an 18 wt % aqueous solution; the solution was evaporated to neardryness.27
Sample Preparation and Shear Alignment. The samplesconsisted of a bilayer block copolymer system where the first(bottom) layer is shear-aligned and the second (upper) layer isnonaligned and characterized by having short-range order. The processflow that describes the steps involved in the sample preparation isshown in the four panels of Figure 1: (a) spin-coating onto a siliconwafer and shear alignment of the bottom layer, (b) spin-coating of thesecond layer onto a sacrificial layer of PSS, (c) liftoff in water of thesecond layer, and (d) redeposition of the floated film onto the well-ordered bottom monolayer.The first monolayer of block copolymer was produced by spin-
coating a solution of PS−PHMA in toluene (∼1 wt %) onto a siliconwafer (SiliconQuest, with native oxide). For this system the PHMAmatrix wets both substrate and air interfaces.46 The silicon wafer wasprewashed with toluene and dried under flowing nitrogen prior to use.After deposition, the thin film was shear-aligned on a hot plate at 150°C using 10 kPa of pressure and 5 kPa of shear stress, applied througha 1 × 1 cm2 cross-linked polydimethylsiloxane (PDMS) pad for 30min, after which the system was cooled back to room temperature withthe applied stress still in place, thus fixing the postshear morphology.27
A schematic of this setup is shown in Figure 1a. For the second layer, asolution of PSS in 2-propanol (∼2 wt %) was spin-coated onto asilicon wafer, and then the PS−PHMA copolymer was deposited overthe layer of PSS, as shown in Figure 1b. The film was annealed on ahot plate at 150 °C to stabilize the films and to relax any elasticdistortions introduced during the spin-coating procedure. The silicon−PSS−(PS−PHMA) multilayer was introduced into a Petri dishcontaining deionized water, at an angle of about 45° to the watersurface (see ref 27 for more details). As the PSS is a water-solublepolymer, it acts as sacrificial layer that allows the block copolymer thinfilm to be floated off (Figure 1c). The floating thin film wasimmediately picked up from below the water surface using the
supported sample of PS−PHMA film already shear-aligned, asdescribed in Figure 1d. Previous results indicates that although theinterlayer region may contain some contamination from PSS residuals,their content must be small. By measuring the step height near an edgeof the top layer, it was found that the thickness of the top film wasconsistent with the film thickness measured through ellipsometry priorto water liftoff. The step height near an edge between the bottom andtop layers was also imaged through SEM, where it were observed noindications of the presence of any contaminants between layers.27 Thestack of the two layers was then thermally treated at different annealingtimes to explore the coupling between the aligned and nonalignedlayers.
Imaging and Analysis. Polymer film thicknesses were measuredusing a PHE101 ellipsometer (Angstrom Advanced Inc.; wavelength =632.8 nm). The morphology was characterized at room temperatureusing an atomic force microscope (Innova, Bruker) operated intapping mode using uncoated Si tips having a cantilever length of 125μm, spring constant of 40 N/m, and resonant frequency of 60−90kHz, purchased from NanoWorld. Since the PS cylinders are glassyand the PHMA matrix rubbery at room temperature, phase imaging ofthe films reveals the underlying structure and orientation of thecylindrical microdomains. All images were taken at 512 × 512 pixelresolution with a scan size of 2−3 μm × 2−3 μm. To improve imagequality, the micrographs were flattened and filtered by performing adiscrete Fourier transform to remove high- and low-frequency noiseand transforming back to real space.
■ RESULTS AND DISCUSSIONFigure 2 shows tapping-mode atomic force microscopy (AFM)phase images of the bottom and upper layers of the blockcopolymer stack prior to thermal annealing. In these images thelight (PS) and dark (PHMA) regions correspond to the regionsof each of the two polymer blocks. It was found that the averagerepeat spacing (distance between cylindrical domains) for thisdiblock copolymer is 45 nm, as measured on both layers byAFM,47 and that the cylinders adopt a configuration parallel totheir corresponding substrates due to the interfacial energydifferences between the chemically dissimilar blocks. Theindividual layers of the diblock copolymer develop a smecticsymmetry characterized by a local orientation specified by a
Figure 1. Schematic of the sample preparation method. (a) Shearalignment of a spin-coated monolayer of a cylinder-forming diblockcopolymer, (b) spin-coating of the second layer onto a sacrificial layerof PSS, (c) the block copolymer is floated off in water, and (d) thefloated film is redeposited onto the shear-aligned pattern.
director field.48 In the smectic phase, defects involve distortionsin the director field that are typically referred to as disclinationsand dislocations.20,48−50 Figure 3 shows the typical topological
defects that appear in block copolymer systems. Although othertopological defects are possible, like ±1 disclinations, they arehighly energetic and rarely observed in experiments.48,51
Observe in Figure 3 that while disclinations destroy theorientational order, dislocations break the translational orderand also introduce small distortions in the director orientation.The left panel of Figure 2 shows the excellent orientational
and translational order in the shear-aligned monolayer and thecomplete absence of disclinations; in agreement with previousresults,25−28 here we also found that the shear-aligned patternsexhibit long-range orientational order, disrupted only by a verysmall density of dislocations and long-wavelength elasticdistortions. On the other hand, although the patterncorresponding to the upper layer (see the schematicrepresentation of the experimental setup in the central panelof Figure 2) shows a very strong length scale selectivityimposed by the radius of gyration of the diblock, it exhibits onlyshort-range order and poor connectivity between the PScylinders of the minority phase. In addition, these patterns arealso characterized by the presence of disclinations that destroythe orientational order and by a high density of dislocations.In order to explore the coupling between both layers, the
system was annealed under vacuum at 150 °C for differenttimes. As the bottom layer cannot be visualized through tappingmode AFM, here we focus on the pattern configuration of theupper layer.Previously, it has been found that in planar systems with
smectic symmetry the orientational correlation length of thedomains ξ2 increases according to a power law ξ2 ∼ t1/4.1,48 Inthis case, the orientational correlation length is controlled bythe density of disclinations, whose annihilation rate is mediated
by the diffusion of dislocations. In these systems it was foundthat the annihilation of complex arrays of disclinations(multipoles) prevails over the annihilation of dipoles ofdisclinations and that the correlation lengths obtained throughthe densities of disclinations and dislocations also follow apower law with the same exponent as the orientationalcorrelation length.1,48
Figure 4 shows AFM phase images of the patternconfiguration of the upper layer at different annealing times.
Observe in the upper left panel of Figure 4 that after a shorttime of annealing the initial structure of the cylinders shown inFigure 2 is reorganized into a pattern containing both cylindersand dots and that the regions with a dotted structure present noclear evidence of a well-defined symmetry. Note also that in thebilayer system explored here the smectic symmetry could onlybe fulfilled as a two-dimensional realization of the individualmonolayers while the hexagonal packing cannot be fullydeveloped as the film only contains two layers.As annealing proceeds, the interaction between the shear-
aligned and nonaligned layers drives the complete annihilationof disclinations and promotes the connectivity betweencylinders, increasing dramatically the orientational order andthe correlation with the bottom pattern. In addition, there is areduction in the density of dislocations, and much improvedorientational and translational order. Note that the mechanismof ordering in this system must be completely different fromthe one observed in smectics without a guiding field,1,48 as heredisclinations are absent.For smectic patterns, the degree of orientational order can be
quantified via an orientational order parameter:
Figure 2. (a) AFM phase image of shear-aligned cylinder-forming PS−PHMA 33/78 deposited at monolayer thickness onto a bare siliconwafer, (b) schematic of the bilayer film, where nonaligned cylindersrest on a monolayer of shear-aligned cylinders, and (c) AFM phaseimage of the second, nonaligned layer. The average intercylinderspacing for the diblock is 45 nm. Image sizes: 1.5 μm × 1.5 μm.
Figure 3. Typical topological defects that disrupt order in smecticsystems. These defect configurations were obtained through two-dimensional simulations with a phase field model. Panels a and bcorrespond to positive and negative 1/2 disclinations, respectively.48,51
Disclinations involve rotations of the director field about thedisclination core and destroy the orientational order. Panel c showsa less energetic defect, known as a dislocation.
Figure 4. AFM phase image of the second layer after annealing at 150°C in vacuum for t = 2 h (panel a), 6 h (panel b), 16 h (panel c), and24 h (panel d). Panels b−d show the AFM phase image (grayscale)overlaid with the orientational color maps associated with the smecticpatterns. Color code for both orientational maps indicated in thebottom right corner. The AFM images correspond to different bilayersrather than to a single bilayer annealed and imaged sequentially. Imagesizes: 2.0 μm × 2.0 μm.
where θ(r) is the local orientation of the stripe pattern(cylinder axis) at a particular position r. Here r is the in-planeposition, r = xi + yj, with i and j the basis Cartesian vectors, andθ0 is the shear direction of the bottom layer. The factor of 2 isrequired for the 2-fold symmetry of the pattern. Note that avalue Υ r( ) = 1 corresponds to perfect alignment of the pattern(cylinder axes) with the shear direction. The local orientationof the layers θ(r) can be obtained from the AFM phase imagethrough the gradient method described elsewhere.48 Althoughin our case the orientation of the bottom layer after thermalannealing was not measured, we consider that it remains thesame as prior to annealing. This assumption is supported bysimulations (see below) and energetic considerations. Duringannealing the layers are competing with each other to impose alocal orientation. Note that any orientational distortion of thebottom layer driven by the nonaligned layer must imply astretching and eventually breaking of the bottom cylinders.Thus, as the bottom layer is well ordered and closer toequilibrium, its undistorted cylinders are more stable and candrive the alignment of the poorly ordered cylinders in the upperlayer.Note that it is possible that the dislocations present in the
bottom layer could move during annealing and interact with theupper layer. However, as the density of dislocations in thebottom layer is relatively small (average distance betweendislocations ∼200 nm) and its strain field must be partiallyscreened by the upper layer (at least during the early stage ofcoupling), it can be expected a very slow rate of dislocationannihilation within the time window explored in our experi-ments.Figure 4 shows the orientational maps corresponding to the
upper layer at different annealing times. Note that as annealingproceeds there is a reduction in the density of dislocations thatimplies an improvement in the degree of orientational order.Through the orientational order parameter we can also
define an orientational correlation function g2(r):
= ⟨Υ Υ* ⟩g r 0 r( ) ( ) ( )2 (2)
where the angular brackets above imply averaging correlationpairs at a given in-plane distance.Figure 5 shows g2(r) corresponding to the initial
configuration of the upper (nonaligned) and bottom (shear-aligned) layers. Observe that g2(r) for the nonaligned layerdecays rapidly to zero at a distance of about ten latticeconstants (∼400 nm). This poor orientational correlationresults from the defects, which destroy the translational andorientational order.1,48 In the absence of external fields, forblock copolymer monolayers developing a smectic symmetry,the order can be improved via annealing. However, the lack of apreferential direction leads g2(r) to decay to zero over largedistances, since there is no orientational correlation betweendistant domains. In this case, the correlation length ξ2 can beestimated from the position r where g2(r) decays to e−1 (ξ2 ∼120 nm for the image shown in Figure 2c).The situation is different in shear-aligned systems. Although
the orientational correlation between domains decays as rincreases, in shear-aligned samples g2(r) reaches a plateau g2 =g2(r → L) different from zero due to existence of a preferentialdirection that induces correlation between distant domains(here L is the characteristic length scale of the image). Figure 5shows that g2 ∼ 0.95 for the shear-aligned sample. Although this
result is in rough agreement with previous results, where it wasfound that even in well-ordered defect-free smectics there areundulations of the cylinders which limit g2 below unity,52 in ourcase the patterns present a lower degree of order.The average degree of order can be quantified through the
spatial average of Υ(r).25,52 It was found that even in well-aligned samples Ψ2 = ⟨Υ(r)⟩ is restricted below Ψ2 = 0.999 dueto the existence of undulations along the cylinder axis and thatΨ2 decays linearly with the dislocation areal density.25,52 Inaddition, it was found that the coefficients of the linearrelationship between Ψ2 and dislocation density depend on theblock copolymer composition.25 In particular, for the blockcopolymer system studied here it was found that Ψ2 = 0.999 −0.0016ρ, where ρ is expressed as the number of dislocations perμm2.25
During the annealing of the bilayer system, the patternconfiguration of the upper layer couples to the bottom layer,acting as an external field that breaks the rotational symmetryand drives orientational ordering. At long annealing times thereis strong orientational order, where the dislocations are themain source of disturbance to the pattern, breaking thetranslational order and also the local orientation of the cylindersin the neighborhood of the dislocation core (see Figure 3).Observe in Figure 5 the increment in the degree of order
after annealing, as seen through g2(r). The pattern config-uration of the upper layer reaches Ψ2 ∼ 0.3, Ψ2 ∼ 0.8, and Ψ2 ∼0.84 after 6, 16, and 24 h of annealing, respectively. Accordingto the previous findings of Davis et al.,25 in the sample with thelongest annealing this value of Ψ2 corresponds to a dislocationdensity of ∼100 ± 40 dislocations per μm2 (±1 standarddeviation), while here we found ∼200 dislocations per μm2good agreement, especially considering the low defect densities(up to only ∼5 dislocations per μm2) in the films analyzed byDavis.25
Previously, the activation energies of different mechanismsinvolved in the process of organization of block copolymer thinfilms have been measured through different order parame-ters.13,53,54 However, in our case the determination of aneffective activation energy in terms of an order parameter isquite difficult since at the intermediate stage of coarsening thesymmetry of the upper layer remains ill defined, and the degreeof order can be estimated only at those regions where thecylinders are well-defined. Anyway, a rough estimation of the
Figure 5. Orientational correlation function g2(r) for the initial lower(shear-aligned) and upper (disordered) layers and for the top layer inthe bilayer after different annealing times tann (symbols indicated in thefigure).
activation energies associated with the segmental motion of thechain can be determined through the temperature shift factorsobtained from the WLF (Williams, Landel, and Ferry)equation.55 From the WLF equation an effective activationenergy ΔH for segmental mobility can be determined as ΔH =2.03RT2c1
0c20/(c2
0 + T − T0)2, where T0 is a reference
temperature and c10 and c2
0 phenomenological constants.55
The reordering kinetics in response to the coupling betweenlayers must be dictated by the diffusion of the diblockmolecules. In general, this diffusion process depends on anumber of parameters, including the friction coefficients of theindividual blocks, average molecular weight, composition,architecture, mechanisms of single chain dynamics, symmetryof the phase-separated structure, and degree of segregationbetween blocks.56
Previously it was found that the temperature dependence ofthe correlation length of weakly entangled sphere forming andcylinder forming block copolymer thin films can be welldescribed by the WLF equation.43,48 In both systems, thetemperature shift factors were found to coincide with thosecorresponding to the block with the highest glass transitiontemperature.Here the average number of entanglements per diblock is
about 4.5, similar to the values reported by Harrison et al.,43,48
and the films were thermally annealed well above the Tg of bothblocks (for PS homopolymer, Tg = 100 °C, while for PHMAhomopolymer, Tg = 8 °C). Thus, the PS segmental mobility isexpected to be the dominant factor in the segmental mobility.Considering T = 150 °C and the phenomenological constantsfor PS (T0 = 373 °C, c1
0 = 13.7 and c20 = 50.0 °C),48 the
estimated value for the effective activation energy for thesegmental mobility is ΔH ∼ 230 kJ/mol.In order to explore stability and the coupling between layers,
in what follows we analyze through self-consistent field theory(SCFT) calculations the free energy of a multilayer diblock
copolymer system. In addition, the kinetics of ordering arestudied through a phase field approach with a conserved orderparameter (Cahn−Hilliard dynamics).
■ SCFT CALCULATIONS
In order to analyze the stability of the block copolymer thinfilm system against the formation of holes and islands, weperformed self-consistent field theory calculations57,58 todetermine the optimum thickness of multilayers of cylinder-forming block copolymer systems. We consider a melt ofasymmetric AB diblock copolymers confined between twosurfaces that preferentially attract the A-segments of themajority block (see Supporting Information for more details).The confined film of thickness h is constrained between twohomogeneous surfaces located at z = 0 and z = h. Periodicboundary conditions are imposed in the other directions. Weconsider the same strength of interaction between the blocksand both surfaces. Although a more systematic study is requiredin order to explore in detail the effect of the polymer/substrateand polymer/air interfaces, the SCFT calculations consideredhere allow a rough estimation of the equilibrium configurationfor this system. The incompatibility between blocks ischaracterized by the product χN, of the Flory−Hugginsparameter χ and the number of segments N. Here we consideran asymmetric diblock copolymer thin film with χN = 20 and f= 0.7, f being the volume fraction of the A-block.The calculations are done in the grand canonical ensemble;
i.e., the chemical potential μ of the copolymers is kept fixed,and their number adjusts to the film thickness. Figure 6 showsan example of a Gibbs free energy landscape as a function offilm thickness. Here the value of the chemical potential (μ =2.5) was chosen slightly below the value where the filmbecomes macroscopically thick, μ* = 2.56. The minimacorrespond to the monolayer state, which is globally stable,and the metastable bilayer state. If one increases the chemical
Figure 6. Grand canonical free energy per area in units of kBT/Rg2 vs film thickness in units of Rg for a cylinder-forming diblock copolymer
multilayer confined between two surfaces at copolymer chemical potential μ = 2.5kBT. The minima correspond to the stable monolayer state and themetastable bilayer state. Insets show density profiles of the corresponding states. SCFT calculations predict λ ∼ 3.7Rg for the intercylinder spacing inthe bulk.
potential, the free energy minima corresponding to multilayersmove down relative to the monolayer minimum. However, thebilayer state remains metastable for all μ < μ*.For the monolayer and bilayer systems the optimum
intercylinder spacing in lateral direction are respectively λ1 ∼3.6Rg and λ2 ∼ 3.7Rg. For this system, the bulk intercylinderspacing is λ ∼ 3.7Rg. Thus, we have λ1/λ ∼ 0.97 for themonolayer and λ2/λ = 1 for the bilayer. These values are ingood agreement for those reported by Knoll et al. for acylinder-forming block copolymer multilayer, where it wasfound that in thin films the unit cell is stretched perpendicularto the plane of the film, resulting in lateral distances smallerthan those in bulk.59 We found that the optimal thickness h forthe monolayer correspond to h1L = 3.5Rg, while for the bilayerit becomes h2L = 6.9Rg. Then, for this system we have h2L/h1L ∼1.97. This corresponds to the thickness of the block copolymerstacks in the experiments, which is twice the thickness of theindividual layers due to the experimental procedure employedhere. Consequently, in qualitative agreement with theexperimental observations one can expect that a bilayer systemwith h2L/h1L ∼ 2 should be relatively stable toward thedevelopment of holes or islands even during long periods ofannealing.We should note that according to the SCF theory, the global
equilibrium structure at this copolymer coverage is one where amonolayer film coexists with islands of thick multilayer films.This state is not reached on experimental time scales. However,we expect the second layer to interact with the first layer in thesense that chains interpenetrate and that the cylinders in thesecond layer accommodate to the local structure of the firstlayer. The density profiles in the insets in Figure 6 show thatthe structure of the cylinders changes from squeezed ellipsoidsin the monolayer to more circular in the bilayer. (In the bulk,they are fully circular.) Hence, the addition of a second layerslightly changes the structure of the first layer, and thisinteraction provides a mechanism how a prealigned first layercan help to order the second layer.3D Simulations. The process of coarsening for diblock
copolymer systems can be adequately described by a Cahn−Hilliard model combined with the Ohta−Kawasaki free energyfunctional60−67 to describe the diblock copolymer bilayer (seeSupporting Information for details). This model and similarphase field approaches have been employed to describe a widediversity of pattern formation phenomena involving competinginteractions, including order−order and order−disorder phasetransitions, melting, dynamics of coarsening, defect dynamics,and glassy systems.65−71 One of the most important features ofthis phase field approach is that it is efficient over diffusive timescales and thus allows exploration of the slow dynamicsinvolved in the diffusion and annihilation of topologicaldefects.50,67
Figures 7 and 8 show the coarsening process of a bilayer thinfilm emulating the experimental system described in Figure 2.Note that at early times the upper layer presents short-rangeorder and a high density of defects but also a strong length-scale selectivity like the experimental system (see Figure 2c). Acomparison of the AFM phase image (Figure 2) and thesimulated data indicates good qualitative agreement. To obtaina better comparison with the experimental AFM phase images,rather than considering a level plot through the center of thecylinders, here we integrate the order parameter describing thedensity fluctuations corresponding to the upper layer along thedirection perpendicular to the substrate. In this way, the
interfaces are smoothed out, facilitating the comparison withAFM.In agreement with the experiments, as time proceeds the
order in the upper layer increases. Observe in Figure 8 theorientational coupling between layers and that order isdisrupted only by dislocations while the order of the bottomlayer remains undisturbed. The simulations also show that thebottom layer remains undisturbed during annealing, indicatingthat it cost more energy to disrupt an ordered structure than tomove around defects in a disordered structure.By following the evolution of the order parameter during
annealing, we identify two different regimes of coarseningduring the annealing process. At early times we observe thatthose cylinders misaligned with respect to the bottom layersuffer an instability that drives their reorientation along thebottom layer’s alignment direction (Figure 9). We found thatthe reorientation process involves distinct intermediate trans-formation states, including fragmentation, formation of pearl-necklace-like structures, and reconstruction of the cylindersalong the shear direction. The process of reorientation of thecylinders along the direction imposed by the bottom layer isschematized in Figure 10.This process shows features similar to those in the Rayleigh
instability72,73 that drives the process of breakage of liquidcylinders due to fluctuations. Rayleigh demonstrated that aliquid cylinder is unstable against sinusoidal perturbations witha wavelength greater than 2πR, where R is the radius of theinitial cylinder. Because of minimization of the surface area, aliquid cylinder can break up into spherical drops. However,whereas the Rayleigh instability generally is driven by randomfluctuations, here the cylinder undulations are locally driven bythe effective field provided by the aligned bottom layer. On theother hand, it is important to emphasize that the phase field
Figure 7. Three-dimensional pattern configurations observed throughsimulations at early (left panel) and late (right panel) times.
Figure 8. Two-dimensional pattern configurations for the upper layerobserved through simulations at early (left panel) and late (rightpanel) annealing times. Observe the similarities of these patterns withthose in the experimental system, shown in Figure 2. Note also thatafter annealing there is a strong orientational coupling with the bottomlayer, mainly disrupted by dislocations. During annealing, the bottomlayer remains undisturbed.
simulations employed here do not consider the moleculardetails of the block copolymer system. Although thesimulations can capture the instability driven by the surfaceenergy of the fluid cylinder, in block copolymer systems thereare other effects that add complexity to the process, like thestretching energy of the blocks.This mechanism of pattern organization observed in the
simulations is in good agreement with the experimentalobservations at short and intermediate annealing times.Observe in Figure 4 that after a short time of annealing theupper layer presents features similar to those shown in Figure 9.Note also that after annealing the initial structure of thecylinders shown in Figure 2 is reorganized into a patterncontaining both cylinders and dots and that the regions with adotted structure present no clear evidence of a well- definedsymmetry, as expected for the proposed mechanism. In Figure4 observe also that for intermediate annealing times the patternpresents a multiplicity of dislocations and different elasticdistortions but disclinations are absent as in the simulated data.Simulations indicate that once the cylinders are reorganized
along the preferential direction imposed by the bottom layer,the long-time process of coarsening occurs via the diffusion andannihilation of dislocations (see also the movies showing thedislocation dynamics in the Supporting Information). Figure 8also shows the late configuration of the upper layer. Note thequalitative agreement with the experimental pattern config-uration shown in Figure 4, disrupted only by the presence of
dislocations of Burgers vector b= pn, where p is the domainspacing and n is the layer normal.Simulations with the Cahn−Hilliard model indicate that the
number of dislocations Nd exhibits a power law dependence ontime with a small exponent (Nd ∼ t−0.27±0.2; see also SupportingInformation (Figure S1)), consistent with previous findings formonolayers of cylinder forming diblock copolymers48 butinvolving a completely different mechanism of ordering. Herethe ordering process proceeds via the diffusion and annihilationof pairs of dislocations with opposite Burgers vectors, whichrequires the motion of dislocations through two distinctivemechanisms: climb and glide.34,74−77 Climb is the displacementof the dislocation along the direction of the smectic pattern,perpendicular to the Burgers vector, while glide involvesdiffusion in the parallel direction. Owing to the smectic pattern,the energy of the dislocation oscillates as a function of itsposition so that it can move by glide only if the forcesovercome the periodic Peierls potential generated by theperiodic array of cylinders. In addition to the in-plane Peierlspotential, there is also a periodic potential emerging from thebottom layer. It can be expected that this potential also affectsthe dislocation dynamics during glide. We note also that thepotential provided by the bottom layer may also affect thedynamics of climb. Because of its oscillatory nature and thenatural commensurability with the bottom layer, thedislocations in the upper layer may be under compressionaland dilatational fields that affect the climb dynamics. Note thatwhen a pattern has an optimal wavenumber, in the absence ofexternal fields a dislocation does not move. However, if thewavenumber of the pattern does not coincide with thepreferred one due to the compressional and dilatational fieldsproduced by the shear-aligned layer, the dislocation may climbin order to add or remove the extra cylinder associated with adislocation.
■ CONCLUSIONSIn summary, well-ordered monolayer films of cylinder-formingblock copolymers can be employed as seeds to induce order inself-assembling block copolymer systems, resembling theprocess of grapho- or chemo-epitaxy employed to obtainpatterns with a low density of topological defects. This processcan facilitate the fabrication of well-ordered 3D structures overlarge areas, and it is a potential complement to conventionalgrapho- or chemo-epitaxy techniques. The application of thismethod is not restricted to the production of bilayers, as itwould be possible to use well-ordered block copolymers toinduce order or to produce new symmetries in systems withdifferent degrees of complexity, including multilayers or stacksof block copolymers with different chemical architectures.
■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.macro-mol.6b00816.
Self-consistent field theory calculations, Cahn−Hilliarddynamic simulations and dislocation dynamics (FigureS1) (PDF)3D simulation data showing the coupling among alignedand nonaligned layers (AVI)2D simulation data showing the coupling among alignedand nonaligned layers (AVI)
Figure 9. Pattern configurations for the upper layer observed throughsimulations as seen at short annealing times. The cylinders misalignedwith regard to the ordered bottom layer suffer an instability (inset)that drives their fragmentation and reconstruction along the shear-alignment direction of the bottom layer (indicated with a red arrow).
Figure 10. Schematic illustration of the transformation pathway fromcylindrical domains of the minority phase to pearl-necklace-likedomains. The fragmentation and reconstruction of the cylinders allowreorientation of these domains along the direction imposed by thebottom layer.
Present AddressN.A.G.: ISC-CNR and Dipartimento di Fisica, Universita diRoma La Sapienza, Piazzale Aldo Moro 2, 00185, Roma, Italy.
NotesThe authors declare no competing financial interest.
■ ACKNOWLEDGMENTS
We gratefully acknowledge the financial support from theNational Science Foundation MRSEC Program through thePrinceton Center for Complex Materials (DMR-1420541),Universidad Nacional del Sur, the National Research Council ofArgentina (CONICET), and the Deutsche Forschungsgemein-schaft (DFG, Germany). N.A.G. acknowledges support fromMIUR Futuro in Ricerca ANISOFT project (RBFR125H0M)
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