Monte Carlo Phase Diagram for a Polydisperse Diblock Copolymer Melt

Beardsley, Tom; Matsen, Mark W.

doi:10.1021/ma200966a

Cited by 44 publications

(55 citation statements)

References 45 publications

(143 reference statements)

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“…Such diagram contains 448 figurative points for m-diblocks and r-multiblocks and 224 points for r-diblocks, which is much more than reported in the literature for any simulation technique. 19,20,[26][27][28]36 All simulations were performed at Lomonosov Moscow State University Supercomputer facilities.…”

Section: Simulation Technique and Modelsmentioning

confidence: 99%

“…Whereas cylinders are almost as well studied as lamellas, the S microstructure in copolymers is rather common only in experimental systems, where it can be obtained either by orderdisorder transition (ODT) 56 or order-order transition (OOT). 57 Its identification by SCFT, 13 in Monte Carlo 19,20 and even DPD 25,41 simulations is usually difficult, if not impossible because of the long equilibration time. Figure 5 reports on the least ordered structures with illdefined peaks on the S(q) dependence.…”

Section: Structure Analysismentioning

confidence: 99%

“…The DPD phase diagram is presented and compared to that of the same monodisperse melt, as well as to the diagrams obtained for the polydisperse AB diblock copolymer melts using SCFT 49 and Monte Carlo simulations. 20 The last diagram in the present paper summarizes our DPD study of microphase separation in random multiblock copolymers of different compositions. Recently 34 we reported on the possibility of forming an imperfect lamellar microstructure in the symmetric AB random copolymer melt under strong 50 and superstrong 51 segregation conditions.…”

Section: Introductionmentioning

confidence: 99%

“…In that way, the evaluation of interchain interactions becomes a considerably less time-consuming procedure. The second line, to which the present investigation belongs, focuses on further developing various pure particle-based approaches [14][15][16][17][18][19][20][21][22] in order to overcome computational restrictions by adjusting the level of coarse-graining, using multiprocessor platforms and parallel programming codes. Dissipative particle dynamics (DPD) is a wellestablished mesoscopic dynamics method 23,24 utilizing the bead -spring model of a polymer fluid.…”

Section: Introductionmentioning

confidence: 99%

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Phase diagrams of block copolymer melts by dissipative particle dynamics simulations

Гаврилов

Kudryavtsev

Chertovich

2013

The Journal of Chemical Physics

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Phase diagrams for monodisperse and polydisperse diblock copolymer melts and a random multiblock copolymer melt are constructed using dissipative particle dynamics simulations. A thorough visual analysis and calculation of the static structure factor in several hundreds of points at each of the diagrams prove the ability of mesoscopic molecular dynamics to predict the phase behavior of polymer systems as effectively as the self-consistent field-theory and Monte Carlo simulations do. It is demonstrated that the order-disorder transition (ODT) curve for monodisperse diblocks can be precisely located by a spike in the dependence of the mean square pressure fluctuation on χN, where χ is the Flory-Huggins parameter and N is the chain length. For two other copolymer types, the continuous ODTs are observed. Large polydispersity of both blocks obeying the Flory distribution in length does not shift the ODT curve but considerably narrows the domains of the cylindrical and lamellar phases partially replacing them with the wormlike micelle and perforated lamellar phases, respectively. Instead of the pure 3d-bicontinuous phase in monodisperse diblocks, which could be identified as the gyroid, a coexistence of the 3d phase and cylindrical micelles is detected in polydisperse diblocks. The lamellar domain spacing D in monodisperse diblocks follows the strong-segregation theory prediction, D∕N(1∕2) ~ (χN)(1∕6), whereas in polydisperse diblocks it is almost independent of χN at χN < 100. Completely random multiblock copolymers cannot form ordered microstructures other than lamellas at any composition.

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Section: Simulation Technique and Modelsmentioning

confidence: 99%

Section: Structure Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Phase diagrams of block copolymer melts by dissipative particle dynamics simulations

Гаврилов

Kudryavtsev

Chertovich

2013

The Journal of Chemical Physics

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“…Model F is an FCC lattice model. Models H [21][22][23], S1 [22,23], and F [24][25][26][27] have been studied previously. The term "model" refers to set of choices for the functional form of the pair and bond potentials, and for values of all parameters except N and one parameter that is varied to control χ e .…”

mentioning

confidence: 99%

Universality of Block Copolymer Melts

et al. 2014

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Simulations of five different coarse-grained models of symmetric diblock copolymer melts are compared to demonstrate a universal (i. e., model-independent) dependence of the free energy on the invariant degree of polymerization N , and to study universal properties of the order-disorder transition (ODT). The ODT appears to exhibit two regimes: Systems of very long chains (N > ∼ 10 4 ) are well described by the Fredrickson-Helfand theory, which assumes weak segregation near the ODT. Systems of smaller but experimentally relevant values, N < ∼ 10 4 , undergo a transition between strongly segregated disordered and lamellar phases that, though universal, is not adequately described by any existing theory.PACS numbers: 82.35. Jk,64.70.km,64.60.De Universality is a powerful feature of polymer statistical mechanics that allows the behavior of real systems to be predicted on the basis of simple generic models and scaling arguments. The paradigmatic example is the scaling theory of dilute and semidilute polymer solutions in good solvents [1][2][3], which predicts a universal dependence of all properties on two thermodynamic state parameters (an excluded volume parameter and an overlap parameter). Historically, this scaling hypothesis was verified by comparing experiments on diverse chemical systems with varied chain lengths and concentrations [3][4][5]. Here, we compare simulations of diverse models to verify an analogous scaling hypothesis about the equation of state and order-disorder transition (ODT) of symmetric diblock copolymers, and to characterize this transition.We consider a dense liquid of AB diblock copolymers, with N monomers per chain, and a fraction f A of A monomers. We focus on the symmetric case, f A = 1/2. Self-consistent field theory (SCFT) is the dominant theoretical approach for block copolymers [6][7][8]. SCFT describes polymers as random walks with a monomer statistical segment length b, which we take to be equal for A and B monomers. The free energy cost of contact between A and B monomers is characterized by an effective Flory-Huggins interaction parameter χ e . Let g denote a dimensionless excess free energy per chain, normalized by the thermal energy k B T . SCFT predicts a free energy g for each phase that depends only upon f A and the product χ e N , or upon χ e N alone for f A = 1/2. This yields a predicted phase diagram [6, 7] that likewise depends only on f A and χ e N . For f A = 1/2, SCFT predicts a transition between the disordered phase and lamellar phase at (χ e N ) ODT = 10.495.SCFT is believed to be exact in the limit of infinitely long, strongly interpenetrating polymers [9, 10]. The degree of interpenetration in a polymer liquid is characterized by a dimensionless concentration C ≡ cR 3 /N , in which c is monomer concentration, c/N is molecule concentration, and R = √ N b is coil size. Alternatively, interpenetration may be characterized by the invariant degree of polymerization. A series of post-SCF theories [10][11][12][13][14][15][16][17][18], starting with the Fredrickson...

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Molecular Architecture of Multiblock Copolymers Synthesized by the Chain Shuttling Technology

Urciuoli

Ballesteros

Auriemma

2023

Macro Chemistry & Physics

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Recent advances in the characterization of ethylene/1‐octene‐based statistical multiblock copolymers (MBCs) synthesized via chain shuttling copolymerization are illustrated. The Perspective focuses on the peculiarity of MBC systems that consists in the nonuniform chain architecture of these intriguing systems due to compositional heterogeneity occurring at inter‐ and intra‐chain level. In the first part, the effect of dispersity on the phase behavior and properties of MBCs and block copolymers in general is discussed along with the consequences of crystallization of one of the blocks on microphase separation, domain spacing, and morphology. In the second part, the main results achieved in the elucidation of details of the chain microstructure in terms of average length of the blocks and block length distribution are presented. It is shown that solvent and thermal fractionation techniques, coupled with other techniques such as transmission electron microscopy (TEM) and small angle X‐ray scattering (SAXS) represent powerful tools to elucidate the inter‐ and intra‐chain heterogeneous composition of the MBCs. Guidelines on how to establish structure/properties relationships for such polydisperse systems are also provided.

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Monte Carlo Phase Diagram for a Polydisperse Diblock Copolymer Melt

Cited by 44 publications

References 45 publications

Phase diagrams of block copolymer melts by dissipative particle dynamics simulations

Phase diagrams of block copolymer melts by dissipative particle dynamics simulations

Universality of Block Copolymer Melts

Molecular Architecture of Multiblock Copolymers Synthesized by the Chain Shuttling Technology

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