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Frank–Kasper Phases of Diblock Copolymer Melts: Self-Consistent Field Results of Two Commonly Used Models

by Juntong He and Qiang Wang

Polymers 2024, 16(3), 372; https://doi.org/10.3390/polym16030372 - 29 Jan 2024

Cited by 4 | Viewed by 1702

We constructed phase diagrams of conformationally asymmetric diblock copolymer A-B melts using the polymer self-consistent field (SCF) calculations of both the dissipative particle dynamics chain (DPDC) model (i.e., compressible melts of discrete Gaussian chains with the DPD non-bonded potential) and the “standard” model (i.e., incompressible melts of continuous Gaussian chains with the Dirac δ-function non-bonded potential) in the χN-ε plane, where χN and ε characterize, respectively, the repulsion and conformational asymmetry between the A and B blocks, at the A-block volume fraction f = 0.2 and 0.3. Consistent with previous SCF calculations of the “standard” model, σ and A15 are the only stable Frank–Kasper (FK) phases among the five FK (i.e., σ, A15, C14, C15 and Z) phases considered. The stability of σ and A15 is due to their delicate balance between the energetic and entropic contributions to the Helmholtz free energy per chain of the system, which, within our parameter range, increases in the order of σ/A15, Z, and C14/C15. While in general the SCF phase diagrams of these two models are qualitatively consistent, A15 is not stable for the DPDC model at the copolymer chain length N = 10 and f = 0.3; any differences in the SCF phase diagrams are solely due to the differences between these two models. Full article

(This article belongs to the Special Issue Self-Assembling Structure and Dynamics of Multicomponent Polymer Systems)

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18 pages, 2251 KiB

Open AccessArticle

Isomorph Invariance of Higher-Order Structural Measures in Four Lennard–Jones Systems

by Mahajabin Rahman, Benjamin M. G. D. Carter, Shibu Saw, Ian M. Douglass, Lorenzo Costigliola, Trond S. Ingebrigtsen, Thomas B. Schrøder, Ulf R. Pedersen and Jeppe C. Dyre

Molecules 2021, 26(6), 1746; https://doi.org/10.3390/molecules26061746 - 20 Mar 2021

Cited by 4 | Viewed by 2570

Abstract

In the condensed liquid phase, both single- and multicomponent Lennard–Jones (LJ) systems obey the “hidden-scale-invariance” symmetry to a good approximation. Defining an isomorph as a line of constant excess entropy in the thermodynamic phase diagram, the consequent approximate isomorph invariance of structure and dynamics in appropriate units is well documented. However, although all measures of the structure are predicted to be isomorph invariant, with few exceptions only the radial distribution function (RDF) has been investigated. This paper studies the variation along isomorphs of the nearest-neighbor geometry quantified by the occurrence of Voronoi structures, Frank–Kasper bonds, icosahedral local order, and bond-orientational order. Data are presented for the standard LJ system and for three binary LJ mixtures (Kob–Andersen, Wahnström,

{NiY}_{2}

). We find that, while the nearest-neighbor geometry generally varies significantly throughout the phase diagram, good invariance is observed along the isomorphs. We conclude that higher-order structural correlations are no less isomorph invariant than is the RDF. Full article

(This article belongs to the Special Issue Thermodynamics and Transport Properties of Fluids)

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