Interfacial Phenomena of Solvent-Diluted Block Copolymers

Cohen, Shai; Andelman, David

doi:10.1021/ma401479f

Cited by 5 publications

(5 citation statements)

References 53 publications

(143 reference statements)

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“…44 While SCFT provides an accurate description of the morphology of the confined block copolymers in specific cases, we employ a Ginzburg-Landau free energy expansion to provide analytical predictions of the effects of surface affinity and aspect ratio. 45 The analysis presented is an extension to the work of Tsori and Andelman. 46 The free energy of the system contains a bulk and a surface term, and is expanded in terms of an order parameter describing the deviation of the density of one of the blocks from its mean value.…”

Section: Toc Graphic Article Textmentioning

confidence: 99%

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Perpendicular Block Copolymer Microdomains in High Aspect Ratio Templates

et al. 2015

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Perpendicular orientation of lamellar microdomains in a high interaction parameter block copolymer was obtained within high aspect ratio gratings functionalized with a preferential sidewall brush. The experiments used polystyrene-blockpolydimethylsiloxane with molecular weight 43 kg/mol within trenches made using interference lithography. The perpendicular alignment was obtained for both thermal and solvent annealing, using three different solvent vapors, for a range of film thicknesses and trench widths. A Pt layer at the base of the trenches avoided the formation of a wetting layer, giving perpendicular orientation at the substrate surface. The results are interpreted using self-consistent field theory simulation and a Ginzburg-Landau analytic model to map the energies of lamellae of different orientations as a function of the grating aspect ratio and the surface energies of the sidewalls and top and bottom surfaces. The model results agree with the experiment and provide a set of guidelines for obtaining perpendicular microdomains within topographic features. Keywords: Block Copolymer, self-assembly, perpendicular orientation, graphoepitaxy, solvent annealing, thermal annealing TOC Graphic Article TextBlock copolymer (BCP) films have shown great utility in several technological applications including nanolithography for fabrication of integrated circuits, 1,2 magnetic storage media, 3,4 or sensors; 5-7 and in photonic crystals, [8][9][10] photovoltaics [11][12][13] and separation membranes, 14,15 as well as for making 3-dimensional nanostructures. 16 To obtain microphase separation at sub-10nm length scales, a high Flory-Huggins interaction parameter (χ) is desirable. However, high-χ BCPs usually exhibit large differences in surface affinity between the two blocks, leading to the formation of a surface layer of the lower surface energy block and favoring in-plane orientation of lamellae or cylindrical microdomains, 17 which is exacerbated if the substrate is also preferential to one block. This is undesirable in applications where through-thickness features are required, such as porous membranes or high-aspect-ratio structures for pattern transfer. Perpendicular (vertical) orientation of block copolymer microdomains can be produced by several methods, including i) a neutral top coating and neutral substrate brush that minimize the interfacial energy difference between the blocks at the air and substrate interfaces respectively; [17][18][19] ii) a specifically designed molecular architecture 20-22 such as a brush or multi-arm BCP that can form microdomains oriented out-of-plane without modification of the underlying substrate, due to the entropic penalty associated with the packing of the side chains; 22 and iii) modifying the annealing process to use a solvent concentration gradient, 18,23 temperature gradient, 24,25 electric 26 or magnetic field 27 , chemoepitaxy and/or graphoepitaxy, 28 and electrospray deposition 29 to induce out-ofplane alignment of self-assembled microdomains. These methods have ...

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Section: Toc Graphic Article Textmentioning

confidence: 99%

“…While SCFT provides an accurate description of the morphology of the confined block copolymers in specific cases, we employ a Ginzburg–Landau free energy expansion to provide analytical predictions of the effects of surface affinity and aspect ratio . The analysis presented is an extension to the work of Tsori and Andelman .…”

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confidence: 99%

Perpendicular Block Copolymer Microdomains in High Aspect Ratio Templates

et al. 2015

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“…We study the equilibrium shape of di-block copolymer NPs (BCP-NPs) embedded in a solution by using the Ginzburg-Landau free energy. 31,32 We model a mixture of three components: the A and B components of di-BCPs and the solvent. The incompressibility condition is φ A + φ B + φ S = 1, where φ A , φ B , and φ S are the volume fractions of the A, B blocks and solvent, respectively.…”

Section: Modelmentioning

confidence: 99%

Formation of Diblock Copolymer Nanoparticles: Theoretical Aspects

Zhu,

Zheng,

Andelman

et al. 2021

Preprint

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We explore the shape and internal structure of diblock copolymer (di-BCP) nanoparticles (NPs) by using the Ginzburg-Landau free-energy expansion. The self-assembly of di-BCP lamellae confined in emulsion droplets can form either ellipsoidal or onion-like NPs. The corresponding inner structure is a lamellar phase that is either perpendicular to the long axis of the ellipsoids (L ⊥ ) or forms a multi-layer concentric shell (C ), respectively. We focus on the effects of the interaction parameter between the A/B monomers τ , and the polymer/solvent χ, as well as the NP size on the nanoparticle shape and internal morphology. The aspect ratio (lAR) defined as the length ratio between the long and short axes is used to characterize the overall NP shape. Our results show that for the solvent that is neutral towards the two blocks, as τ increases, the lAR of the NP first increases and then decreases, indicating that the NP becomes more elongated and then changes to a spherical NP. Likewise, decreasing χ or increasing the NP size can result in a more elongated NP. However, when the solvent has a preference towards the A or B blocks, the NP shape changes from striped ellipsoid to onion-like sphere by increasing the A/B preference parameter strength. The critical condition of the transition from an L ⊥ to C phase has been identified. Our results are in good agreement with previous experiments, and some of our predictions could be tested in future experiments.

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“…Polymer-grafted nanoparticles are somewhat analogous to chemically anisotropic block copolymers in which one block is replaced by a nanoparticle, making it shape-anisotropic. Block polymers have two or more chemically distinct polymer segments that locally segregate to form periodic microdomains. − Polymer grafted nanoparticles have overcome some of the challenges of nanoparticle dispersion in the polymer matrix, but they undergo aggregation or self-assembly in other cases. These species have emerged as a building blocks of self-assembled structures like sheets, strings, and cell-like structures. − …”

Section: Introductionmentioning

confidence: 99%

Effect of Architecture and Topology on the Self-Assembly of Polymer-Grafted Nanoparticles

Moinuddin

Tripathy

2022

Macromolecules

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We study the effect of the architecture and topology of polymer-grafted nanoparticle species on their structure, phase behavior, and scaling behavior. Using integral equation theory, we study three different architectures of chemically isotropic polymer-grafted nanoparticle species: singly-grafted nanoparticles, doubly-grafted nanoparticles, and ring-grafted nanoparticles. We compare the phase behavior of these three architectures with that of polymer-linked nanoparticles [Tripathy, M. Soft Matter 2017, 13, 2475–2482]. These polymer-grafted nanoparticle species undergo an entropy-driven transition from a disordered fluid phase to microphase-separated structures with alternating polymer-rich and nanoparticle-rich domains. Species with larger nanoparticles and longer polymer chains show higher tendency toward microphase separation. However, as the chain lengths decrease, the microphase transition boundaries of grafted nanoparticles with varying nanoparticle diameters converge to a unique point on the phase diagram. This behavior is noted for all four architectures under consideration. All the sparsely-grafted species with different architectures and topologies exhibit qualitatively similar spinodal phase behavior. However, the scaling behavior of the length scale of self-assembly depends on the topology of the polymer-grafted nanoparticles. While the scaling exponent is same for the three linear topologies under consideration (singly-grafted nanoparticles, doubly-grafted nanoparticles, and polymer-linked nanoparticles), it is markedly different for the ring topology.

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Interfacial Phenomena of Solvent-Diluted Block Copolymers

Cited by 5 publications

References 53 publications

Perpendicular Block Copolymer Microdomains in High Aspect Ratio Templates

Perpendicular Block Copolymer Microdomains in High Aspect Ratio Templates

Formation of Diblock Copolymer Nanoparticles: Theoretical Aspects

Effect of Architecture and Topology on the Self-Assembly of Polymer-Grafted Nanoparticles

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