Block copolymer films with free interfaces: Ordering by nanopatterned substrates

Man, Xingkun; Andelman, David; Orland, Henri

doi:10.1103/physreve.86.010801

Cited by 16 publications

(21 citation statements)

References 25 publications

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“…The patterns can induce formation of terraces in lamellar BCP film and even formation of multi-domain droplets. Our results are in agreement with previous self-consistent field theory calculations [28].…”

Section: Discussionsupporting

confidence: 93%

“…The morphologies and free-interface profiles found in this section result from substrate patterning, and are in agreement with the ones obtained recently using a more computationally intensive method of SCFT [28]. …”

Section: The Free Interfacesupporting

confidence: 89%

“…In the present study we consider an extension of modulated phases that are diluted by a solvent. Although our phenomenological approach can apply to any modulated phase, we apply it explicitly to symmetric lamellar phases of BCP diluted by a solvent in a variety of solvent conditions [28]. For example, in bad solvent conditions the phase separation between a BCP-rich phase and a solvent-rich phase allows us to explore the free interface between a BCP film and bad solvent (vapor).…”

Section: Introductionmentioning

confidence: 99%

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Interfacial Phenomena of Solvent-Diluted Block Copolymers

Cohen

Andelman

2013

Macromolecules

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A phenomenological mean-field theory is used to investigate the properties of solvent-diluted diblock copolymers (BCP), in which the two BCP components (A and B) form a variety of phases that are diluted by a solvent (S). Using this approach, we model mixtures of di-block copolymers and a solvent and obtained the corresponding critical behavior. In the low solvent limit, we find how the critical point depends on the solvent density. Due to the non-linear nature of the coupling between the A/B and BCP/solvent concentrations, the A/B modulation induces modulations in the polymer-solvent relative concentration with a double wavenumber. The free boundary separating the polymer-rich phase from the solvent-rich one is studied in two situations. First, we show how the presence of a chemically patterned substrate leads to deformations of the BCP film/solvent interface, creation of terraces in lamellar BCP film and even formation of multi-domain droplets as induced by the patterned substrate. Our results are in agreement with previous self-consistent field theory calculations. Second, we compare the surface tension between parallel lamellae coexisting with a solvent phase with that of a perpendicular one, and show that the surface tension has a nonmonotonic dependence on temperature. The anisotropic surface tension can lead to deformation of spherical BCP droplets into lens-shaped ones, together with re-orientation of the lamellae inside the droplet during the polymer/solvent phase separation process in agreement with experiment.

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Section: Discussionsupporting

confidence: 93%

Section: The Free Interfacesupporting

confidence: 89%

Section: Introductionmentioning

confidence: 99%

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Interfacial Phenomena of Solvent-Diluted Block Copolymers

Cohen

Andelman

2013

Macromolecules

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“…20 The calculations can still predict the coexistence between different film thicknesses by performing a double-tangent construction, but they are not able to investigate step edges where the air surface needs the freedom to adjust its shape. To circumvent this problem, one could supplement the SCFT with an equation-of-state that allows it to handle large variations in the polymer concentration, 21 but this is an unnecessary complication. Previous studies have avoided the need for this by simply replacing the air with a structureless fluid that creates an interfacial tension with the copolymer but has no other influence on the shape of the free surface.…”

Section: ■ Introductionmentioning

confidence: 99%

Step Edges in Thin Films of Lamellar-Forming Diblock Copolymer

et al. 2012

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Self-consistent field theory (SCFT) is used to study the step edges that occur in thin films of lamellar-forming diblock copolymer, when the surfaces each have an affinity for one of the polymer components. We examine film morphologies consisting of a stack of ν continuous monolayers and one semi-infinite bilayer, the edge of which creates the step. The line tension of each step morphology is evaluated and phase diagrams are constructed showing the conditions under which the various morphologies are stable. The predicted behavior is then compared to experiment. Interestingly, our atomic force microscopy (AFM) images of terraced films reveal a distinct change in the character of the steps with increasing ν, which is qualitatively consistent with our SCFT phase diagrams. Direct quantitative comparisons are not possible because the SCFT is not yet able to probe the large polymer/air surface tensions characteristic of experiment. ■ INTRODUCTIONThe behavior of block copolymer melts on solid substrates has received considerable attention over the last two decades motivated by a wide range of applications. 1−3 Not surprisingly, the earliest work 4−8 involved the simplest conceivable system, thin films of symmetric AB diblock copolymer on flat substrates. In the bulk, symmetric diblock copolymer forms a lamellar phase of alternating A-and B-rich domains, where each period, L 0 , consists of two monolayers. The main effect of confining the diblock copolymer to a thin film is to orient the domains. When the substrate and air surfaces of the film each have an affinity for one of the polymer components, the lamellae orient in the plane of the film, thereby forming a parallel lamellar (L ν ∥ ) phase consisting of ν diblock monolayers. Because of the strong tendency to maintain the preferred domain size of the bulk, the film height is quantized, H ≈ L 0 ν/ 2. Even values of ν are selected when the two surfaces have an affinity for the same component, and odd values occur when the two surfaces have opposite affinities. Usually the amount of material cast on the substrate is incommensurate with the preferred domain size, which leads to macrophase separation into thin and thick regions (i.e., terraces) separated by steps of height L 0 . The topography of the air surface changes from islands to a bicontinuous network to holes as the area of the thicker region increases. 4 The behavior becomes particularly interesting with the formation of elaborate terraced structures, when droplets 9−11 or rings 12 of diblock copolymer are deposited on the substrate.The presence of step edges separating different film thicknesses is ubiquitous in block copolymer films, and yet they have received relatively little theoretical attention. A step edge between the L ν ∥ and L ν+2 ∥ phases will typically involve ν continuous monolayers plus one semi-infinite bilayer as depicted schematically in Figure 1. Ausserréet al. 5 initially argued that the bilayer should exist one monolayer below the air surface, rather than on top as in Figure 1. Fu...

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“…The introduction of an external field (e.g., a chemically or topographically patterned substrate) that directs the assembly process obviates the need to engineer the interparticle interactions required to achieve a target structure. This so-called graphoepitaxial approach has proven successful for guiding the assembly of block-copolymers [18][19][20][21][22][23][24][25][26][27], and recently it has been shown to be effective …”

mentioning

confidence: 99%

Graphoepitaxy for translational and orientational ordering of monolayers of rectangular nanoparticles

2016

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The combinations of particle aspect ratio and enthalpic-barrier templates that lead to translational and orientational ordering of monolayers of rectangular particles is determined using Monte Carlo simulations and density functional theory. For sufficiently high enthalpic barriers, we find that only specific combinations of particle sizes and template spacings lead to ordered arrays. The pattern multiplication factor provided by the template extends to approximately ten times the smallest dimension of the particle. Self-assembly processes, where particles organize into specific equilibrium structures dictated by their interparticle interactions and the thermodynamic conditions, have emerged as a promising tool for the manufacture of novel functional materials [1][2][3]. Recent studies have demonstrated how the form of the interparticle interactions, and hence the symmetry of the resulting assembled structures, can be influenced via particle shape [4][5][6][7], interaction anisotropy [8,9], particle polydispersity [10], solvent quality/composition [11], and the attachment of ligands to the particles [12,13]. Specific interactions that favor targeted structures can be designed directly using inverse methods of statistical mechanics [14][15][16][17]. The combination of interactions required for a specified structure is often complex and not well understood. In turn the particles that exhibit these interactions are generally not easily or inexpensively fabricated, which limits the usefulness of self-assembly for nanomanufacturing applications. The introduction of an external field (e.g., a chemically or topographically patterned substrate) that directs the assembly process obviates the need to engineer the interparticle interactions required to achieve a target structure. This so-called graphoepitaxial approach has proven successful for guiding the assembly of block-copolymers [18][19][20][21][22][23][24][25][26][27], and recently it has been shown to be effective

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Block copolymer films with free interfaces: Ordering by nanopatterned substrates

Cited by 16 publications

References 25 publications

Interfacial Phenomena of Solvent-Diluted Block Copolymers

Interfacial Phenomena of Solvent-Diluted Block Copolymers

Step Edges in Thin Films of Lamellar-Forming Diblock Copolymer

Graphoepitaxy for translational and orientational ordering of monolayers of rectangular nanoparticles

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