Effects of polydispersity on the order-disorder transition of diblock copolymer melts

Beardsley, Tom; Matsen, Mark W.

doi:10.1140/epje/i2008-10383-6

Cited by 35 publications

(50 citation statements)

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“…We caution against drawing too strong a set of conclusions from our SCFT analysis of T ODT , however, as SCFT fails to qualitatively predict changes in T ODT for all compositions of polydisperse AB diblock copolymers, 28,30,31,40,44 likely because it does not account for fluctuations. 33 While our SCFT analysis qualitatively agrees with our experimental data over the composition range interrogated here, it likely offers limited predictive capability for other compositions.…”

Section: B Is"106…o Free Energy Calculationsmentioning

confidence: 50%

“…A flurry of theoretical [25][26][27][28][29][30][31][32][33][34] and a͒ Authors to whom correspondence should be addressed: Electronic addresses: hillmyer@umn.edu and bates@cems.umn.edu. experimental 11,27,[35][36][37][38][39][40][41][42][43] studies of polydispersity effects in AB block copolymers followed Bendejacq et al's report.…”

Section: Introductionmentioning

confidence: 99%

“…Polydisperse AB diblock and ABA triblock materials generally adopt the familiar block copolymer mesostructures of lamellae ͑LAM͒, hexagonally packed cylinders ͑HEX͒, spheres packed on a body-centered cubic lattice ͑bcc͒, and gyroid ͑G͒. [26][27][28]30,31 Polydispersity does influence block copolymer phase behavior, however, as it affects order-disorder transition temperatures ͑T ODT 's͒ 33,40,43 and can drive morphological transitions; the locations of the boundaries on the phase portrait depend on the polydispersities of the constituent A and B blocks. [26][27][28]30,31 Such morphological transitions have been attributed to changes in the average stretching energy that accompany the introduction of domain polydispersity.…”

Section: Introductionmentioning

confidence: 99%

“…The reduction in elastic free energy is also accompanied by an increase in the height of end-grafted polymer brushes 17 and an increase in the domain period in the melt. [27][28][29]31,33,[35][36][37]43 Furthermore, the distribution of chain lengths present in polydisperse materials may stabilize additional ordered mesostructures. Listak et al 42 recently reported that polydispersity stabilized a hexagonally perforated lamellar mesostructure in poly͑styrene-b-methyl acrylate͒ diblock copolymers; this structure is considered metastable in nearly monodisperse materials.…”

Section: Introductionmentioning

confidence: 99%

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Polydispersity effects in poly(isoprene-b-styrene-b-ethylene oxide) triblock terpolymers

Meuler

Ellison

Qin

et al. 2009

The Journal of Chemical Physics

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Four hydroxyl-terminated poly͑isoprene-b-styrene͒ diblock copolymers with comparable molecular weights and compositions ͑equivalent volume fractions of polyisoprene and polystyrene͒ but different polystyrene block polydispersity indices ͑M w / M n = 1.06, 1.16, 1.31, 1.44͒ were synthesized by anionic polymerization using either sec-butyllithium or the functional organolithium 3-triisopropylsilyloxy-1-propyllithium. Poly͑ethylene oxide͒ ͑PEO͒ blocks were grown from the end of each of these parent diblocks to yield four series of poly͑isoprene-b-styrene-b-ethylene oxide͒ ͑ISO͒ triblock terpolymers that were used to interrogate the effects of varying the polydispersity of the middle bridged polystyrene block. In addition to the neat triblock samples, 13 multicomponent blends were prepared at four different compositions from the ISO materials containing a polystyrene segment with M w / M n = 1.06; these blends were used to probe the effects of increasing the polydispersity of the terminal PEO block. The melt-phase behavior of all samples was characterized using small-angle X-ray scattering and dynamic mechanical spectroscopy. Numerous polydispersity-driven morphological transitions are reported, including transitions from lamellae to core-shell gyroid, from core-shell gyroid to hexagonally packed cylinders, and from network morphologies ͓either O 70 ͑the orthorhombic Fddd network͒ or core-shell gyroid͔ to lamellae. Domain periodicities and order-disorder transition temperatures also vary with block polydispersities. Self-consistent field theory calculations were performed to supplement the experimental investigations and help elucidate the molecular factors underlying the polydispersity effects. The consequences of varying the polydispersity of the terminal PEO block are comparable to the polydispersity effects previously reported in AB diblock copolymers. Namely, domain periodicities increase with increasing polydispersity and domain interfaces tend to curve toward polydisperse blocks. The changes in phase behavior that are associated with variations in the polydispersity of the middle bridged polystyrene block, however, are not analogous to those reported in AB diblock copolymers, as increases in this middle block polydispersity are not always accompanied by ͑i͒ increased domain periodicities and ͑ii͒ a tendency for domain interfaces to curve toward the polydisperse domain. These results highlight the utility of polydispersity as a tool to tune the phase behavior of ABC block terpolymers.

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Section: B Is"106…o Free Energy Calculationsmentioning

confidence: 50%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Polydispersity effects in poly(isoprene-b-styrene-b-ethylene oxide) triblock terpolymers

Meuler

Ellison

Qin

et al. 2009

The Journal of Chemical Physics

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“…Delicate balance[3] of chain conformational entropy and repulsive interaction energy between unlike monomers allows block copolymers to readily self-assemble into a number of ordered morphologies. Typical morphologies [3,8,9] include lamellar, cylinder, sphere, gyroid and Fddd network phases, which have been proven to be equilibrium states.Experimentally, the balance of the energy and entropy can be tuned by a number of molecular characteristics such as molecular weight [3], chain architecture [10,11], conformational asymmetry [12,13], polydispersity [14,15,16,17,18] and temperature. A number of studies [1,2,3,4,5,6,7] have been done to elucidate the effects of molecular weight, polydispersity, conformational asymmetry and temperature on the mircophase separation in linear di-block copolymer melts.…”

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confidence: 99%

Morphology diagrams forA₂Bcopolymer melts: real-space self-consistent field theory

Kumar

Sides

et al. 2012

J. Phys.: Conf. Ser.

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The standard Gaussian model for block copolymermelts M W Matsen -Stability of the fcc structure in block copolymer systems Makiko Nonomura -SCFT simulation and SANS study on spatial distribution of solvents in microphase separation induced by a differentiating non-solvent in a semi-dilute solution of an ultra-high-molecular-weight block copolymer K Ando, T Yamanaka, S Okamoto et al. Abstract. Morphology diagrams for A2B copolymer melts are constructed using real-space self-consistent field theory (SCFT). In particular, the effect of architectural asymmetry on the morphology diagram is studied. It is shown that asymmetry in the lengths of A arms in the A2B copolymer melts aids in the microphase separation. As a result, the disorder-order transition boundaries for the A2B copolymer melts are shown to shift downward in terms of χN, χ and N being the Flory's chi parameter and the total number of the Kuhn segments,respectively, in comparison with the A2B copolymers containing symmetric A arms. Furthermore, perforated lamellar (PL) and a micelle-like (M) microphase segregated morphologies are found to compete with the classical morphologies namely, lamellar, cylinders, spheres and gyroid. The PL morphology is found to be stable for A2B copolymers containing asymmetric A arms and M is found to be metastable for the parameter range explored in this work. IntroductionMicrophase separation in block copolymer melts [1,2,3,4,5,6,7] has motivated the scientific community over the last couple of decades. Delicate balance[3] of chain conformational entropy and repulsive interaction energy between unlike monomers allows block copolymers to readily self-assemble into a number of ordered morphologies. Typical morphologies [3,8,9] include lamellar, cylinder, sphere, gyroid and Fddd network phases, which have been proven to be equilibrium states.Experimentally, the balance of the energy and entropy can be tuned by a number of molecular characteristics such as molecular weight [3], chain architecture [10,11], conformational asymmetry [12,13], polydispersity [14,15,16,17,18] and temperature. A number of studies [1,2,3,4,5,6,7] have been done to elucidate the effects of molecular weight, polydispersity, conformational asymmetry and temperature on the mircophase separation in linear di-block copolymer melts. However, the effects of chain architecture are not that well established. On the computational side, this is primarily due to a large parameter space for the simulations and resulting large number of morphologies, which need to be compared in terms of their free-energy

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Theory and Simulation of Multiphase Polymer Systems

Schmid

2011

Handbook of Multiphase Polymer Systems

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The theory of multiphase polymer systems has a venerable tradition. The 'classical' theory of polymer demixing, the Flory-Huggins theory, was developed in the 1940s [1,2]. It is still the starting point for most current approaches -be they improved theories for polymer (im)miscibility that take into account the microscopic structure of blends more accurately, or sophisticated field theories that allow to study inhomogeneous multicomponent systems of polymers with arbitrary architectures in arbitrary geometries. In contrast, simulations of multiphase polymer systems are quite young. They are still limited by the fact that one must simulate a large number of large molecules in order to obtain meaningful results. Both powerful computers and smart modeling and simulation approaches are necessary to overcome this problem.In the limited space of this chapter, we can only give a taste of the state-of-the-art in both areas, theory and simulation. Since the theory has reached a fairly mature stage by now, many aspects of it are covered in textbooks on polymer physics [3][4][5][6][7][8][9]. The information on the state-of-the art of simulations is much more scattered. This is why we have put some effort into putting together a representative list of references in this area -which is of course still far from complete.The chapter is organized as follows. In Section II, we briefly introduce some basic concepts of polymer theory. The purpose of this part is to make the chapter accessible to readers who are not very familiar with polymer physics; it can safely be skipped by the others. Section III is devoted to the theory of multiphase polymer systems. We recapitulate the Flory-Huggins theory and introduce in particular the concept of the Flory interaction parameter (the χ parameter), which is a central ingredient in most theoretical descriptions of multicomponent polymer systems. Then we focus on one of the most successful mean-field theories for inhomogeneous (co)polymer blends, the self-consistent field theory. We sketch the main idea, discuss various Handbook of Multiphase Polymer Systems, First Edition. Edited by Abderrahim Boudenne, Laurent Ibos, Yves Candau, and Sabu Thomas.

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Effects of polydispersity on the order-disorder transition of diblock copolymer melts

Cited by 35 publications

References 33 publications

Polydispersity effects in poly(isoprene-b-styrene-b-ethylene oxide) triblock terpolymers

Polydispersity effects in poly(isoprene-b-styrene-b-ethylene oxide) triblock terpolymers

Morphology diagrams forA₂Bcopolymer melts: real-space self-consistent field theory

Theory and Simulation of Multiphase Polymer Systems

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Effects of polydispersity on the order-disorder transition of diblock copolymer melts

Cited by 35 publications

References 33 publications

Polydispersity effects in poly(isoprene-b-styrene-b-ethylene oxide) triblock terpolymers

Polydispersity effects in poly(isoprene-b-styrene-b-ethylene oxide) triblock terpolymers

Morphology diagrams forA2Bcopolymer melts: real-space self-consistent field theory

Theory and Simulation of Multiphase Polymer Systems

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Morphology diagrams forA₂Bcopolymer melts: real-space self-consistent field theory