Elastic moduli of multiblock copolymers in the lamellar phase

Thompson, Russell B.; Rasmussen, Kim Ø.; Lookman, Turab

doi:10.1063/1.1643899

Cited by 21 publications

(43 citation statements)

References 16 publications

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“…Subsequently, Thompson et al used Tyler and Morse's approach to determine a real-space method for calculating the elastic modulus for block copolymers. [6] They applied this approach to examine the linear elastic response of the lamellar phases of multiblock copolymer melts, and found that a correlation existed between the elastic moduli in the multiblock copolymer systems and the block number; these results are in qualitative agreement with the experimental findings.…”

Section: Introductionsupporting

confidence: 73%

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Effect of Architecture on the Tensile Properties of Triblock Copolymers in a Lamellar Phase

2006

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We have used self-consistent field theory to calculate the tensile moduli of triblock copolymers in lamellar microstructures prepared from linear and star architectures. The extensional moduli K(33) are the main contributors to the tensile moduli, and the contribution of K(U)33 (the internal energy contribution to K(33)) is the main component of the value of K(33). We find that the tensile moduli of ABC three-miktoarm star terpolymers are smaller than those of ABC linear triblock copolymers having identical components, presumably for two main reasons. First, for the ABC three-miktoarm star terpolymers, the contributions of K(U)33 are larger than those of the linear triblock copolymers; we attribute this phenomenon to the star terpolymers having smaller lamellar domain sizes at equilibrium relative to those of the linear triblock copolymers. Second, conformational entropies play an important role in affecting the tensile moduli, mainly because of the different degrees of freedom of the various chains. In contrast, the shear moduli contribute negligibly to the tensile moduli.

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Section: Introductionsupporting

confidence: 73%

“…In this section, we briefly introduce only the main parts of the model; further details of the elastic model are available in the recent review provided by Thompson et al [6] The standard theory of linear elasticity used here, [22] and the general form of the elastic free energy of a deformed crystal, is [Eq. (1)]:…”

Section: Theory and Algorithmmentioning

confidence: 99%

Effect of Architecture on the Tensile Properties of Triblock Copolymers in a Lamellar Phase

2006

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“…Greater detail on the methodology can be found in Ref. [15].We chose a system with a segregation of χN = 25 between the A and B blocks, with the particles considered to be of the A species. χ is the Flory-Huggins monomer segregation parameter and N is the degree of polymerization of the entire diblock.…”

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confidence: 99%

“…For information on how these components are calculated, see Ref. [15]. Comparing the total K 33 and K 44 , it is observed that the main contribution to the tensile modulus arises from the extensional modulus K 33 .…”

mentioning

confidence: 99%

“…Consequently, a lamellar morphology with the particles sequestered in the A phase is being considered, and the system's tetragonal symmetry is elastically characterized by just five independent non-zero components of the elastic modulus tensor. Additionally, the system is in a melt state so that deformations parallel to the lamellar structure have no effect on the free energy of the system [15]. We are thus left with only two relevant moduli, K 33 and K 44 .…”

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Origins of Elastic Properties in Ordered Block Copolymer/Nanoparticle Composites

2004

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We predict a diblock copolymer melt in the lamellar phase with added spherical nanoparticles that have an affinity for one block to have a lower tensile modulus than a pure diblock copolymer system. This weakening is due to the swelling of the lamellar domain by nanoparticles and the displacement of polymer by elastically inert fillers. Despite the overall decrease in the tensile modulus of a polydomain sample, the shear modulus for a single domain increases dramatically.PACS numbers: 83.80. Uv, 81.05.Qk, 62.20.Dc Keywords: block copolymers, elasticity, nanocomposites, self-consistent field theory Polymer nanocomposites are being extensively investigated because of the improvement in material properties that result from the addition of nanoscopic filler particles to the polymer matrix [1,2,3,4]. In addition to their practical importance, such composites offer diverse scientific challenges, combining ideas from colloid science, polymer physics and chemistry, as well as material science. Polymer nanocomposites become even more interesting when the polymer matrix consists of a block copolymer, capable of self-assembling into a wide range of ordered nanoscaled structures -nanoparticles can then be sequestered in certain domains to form ordered nanocomposites [5,6,7,8]. The simultaneous amphiphilic and colloidal self-assembly taking place in such ordered nanocomposites gives them complex structures [9] and makes the structure-property relationship particularly intriguing. Since there is little understanding of the mechanical properties that arise in ordered nanocomposites, we present in this theoretical work a first investigation of the origins of the elastic properties of an ordered nanocomposite with spherical nanofillers.Buxton and Balazs [10] have studied a phenomenological model of nanosphere filled block copolymer systems in which a hybrid Cahn-Hilliard/Brownian dynamics simulation is used as input to a lattice spring model of the elastic moduli. Their approach provides a versatile and useful method of predicting properties, but lacks polymeric detail in the elasticity portion of the simulation. Furthermore, they examine filled block copolymer systems in the solid state, where all morphological evolution is disregarded as the system is distorted.We examine the elastic properties of a melt state ordered nanocomposite using self-consistent field theory (SCFT). SCFT is a coarse-grained, first principles approach that been successful in dealing with block copolymer structure [11]. In the framework of this theory, local monomer density profiles of different block copolymer chemical species are represented self-consistently using chemical potential fields. Both the densities and the fields are then used to determine the free energy for the system, and if desired, the internal energies and entropies can be explicitly calculated. SCFT has been extended to deal with hard nanosphere/block copolymer nanocomposites by the incorporation of a density functional theory particle contribution [12,13]. Further, Tyler and Morse h...

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Tunable nanopatterning by diblock copolymers in small confinements*

Rasmussen

2004

J Polym Sci B Polym Phys

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Here we study the effects of confinement on the self‐assembly of diblock copolymers. Specifically, we study the hexagonal cylindrical phase as it self‐assembles within a narrow confinement. We quantify the structural deformation of the cylindrical morphology that arises from the frustration that the narrow confinements exert on the system when the confinement width is incompatible with the lattice structure of the bulk mesophase. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3695–3700, 2004

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Elastic moduli of multiblock copolymers in the lamellar phase

Cited by 21 publications

References 16 publications

Effect of Architecture on the Tensile Properties of Triblock Copolymers in a Lamellar Phase

Effect of Architecture on the Tensile Properties of Triblock Copolymers in a Lamellar Phase

Origins of Elastic Properties in Ordered Block Copolymer/Nanoparticle Composites

Tunable nanopatterning by diblock copolymers in small confinements*

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