Effects of interaction range and compressibility on the microphase separation of diblock copolymers: Mean-field analysis

2008 ◽  
Vol 129 (5) ◽  
pp. 054904 ◽  
Author(s):  
Qiang Wang
Keyword(s):  
Diblock Copolymers ◽  
Microphase Separation ◽  
Mean Field ◽  
Field Analysis ◽  
Interaction Range

Asymmetric diblock copolymers near the microphase separation: limitations of mean field theory

Polymer ◽  
1991 ◽  
Vol 32 (11) ◽  
pp. 1935-1942 ◽  
Author(s):  
B Holzer ◽  
A Lehmann ◽  
B Stühn ◽  
M Kowalski
Keyword(s):  
Field Theory ◽  
Diblock Copolymers ◽  
Microphase Separation ◽  
Mean Field Theory ◽  
Mean Field

scholarly journals Diblock Copolymers at Surfaces

1989 ◽  
Vol 171 ◽  
Author(s):  
Peter F. Green ◽  
Thomas M. Christensen ◽  
Thomas P. Russell ◽  
Spiros H. Anastasiadis
Keyword(s):  
Photoelectron Spectroscopy ◽  
Diblock Copolymers ◽  
Secondary Ion Mass Spectrometry ◽  
Microphase Separation ◽  
Mean Field Theory ◽  
Mean Field ◽  
Lower Surface ◽  
Ordering Transition ◽  
Lower Surface Energy ◽  
Number Of Segments

ABSTRACTThe surface properties of symmetric microphase separated diblock copolymers of polystyrene (PS) and polymethylmethacrylate (PMMA) were investigated using X-ray photoelectron spectroscopy (XPS), the specular reflectivity of neutrons and secondary ion mass spectrometry (SIMS). PS, the lower surface energy component, exhibited a preferential affinity for the free surface. For copolymers that are far from the bulk microphase separation transition (MST), the surface consists of a layer of pure PS. When the system is close to the MST the surface is a mixture of PS and PMMA. The PS surface excess can be described bya N-1/2 dependence, where N is the number of segments that comprise the copolymer chain. It is shown that the surface undergoes an ordering transition at a temperature T2 that is above that of the bulk MST. The ordering of the bulk lamellar morphology is induced by an ordering at the surface. This is analogous to the ferromagnetic order observed in systems such as Gd at temperatures above the bulk Curie temperature. The results here are discussed in light of previous work on copolymer surfaces and in light of mean field theory.

Microphase separation of short wormlike diblock copolymers with a finite interaction range

Soft Matter ◽  
2016 ◽  
Vol 12 (8) ◽  
pp. 2481-2490 ◽  
Author(s):  
Ying Jiang ◽  
Xinghua Zhang ◽  
Bing Miao ◽  
Dadong Yan ◽  
Jeff Z. Y. Chen
Keyword(s):  
Molecular Weight ◽  
High Molecular Weight ◽  
Structural Properties ◽  
Diblock Copolymers ◽  
Microphase Separation ◽  
Low Molecular Weight ◽  
Interaction Range ◽  
High Molecular Weight Polymers

A study on the structural properties of low-molecular weight AB diblock copolymers indicates substantial deviations from the properties of high-molecular weight polymers.

scholarly journals Mean Field Analysis of Orientation Selective Grain Growth Driven By Interface-Energy Anisotropy

1994 ◽  
Vol 343 ◽  
Author(s):  
J. A. Floro ◽  
C. V. Thompson
Keyword(s):  
Grain Size ◽  
Size Distribution ◽  
Grain Growth ◽  
Texture Evolution ◽  
Mean Field ◽  
Orientation Distribution ◽  
Interface Energy ◽  
Abnormal Grain Growth ◽  
Field Analysis ◽  
Energy Anisotropy

ABSTRACTAbnormal grain growth is characterized by the lack of a steady state grain size distribution. In extreme cases the size distribution becomes transiently bimodal, with a few grains growing much larger than the average size. This is known as secondary grain growth. In polycrystalline thin films, the surface energy γs and film/substrate interfacial energy γi vary with grain orientation, providing an orientation-selective driving force that can lead to abnormal grain growth. We employ a mean field analysis that incorporates the effect of interface energy anisotropy to predict the evolution of the grain size/orientation distribution. While abnormal grain growth and texture evolution always result when interface energy anisotropy is present, whether secondary grain growth occurs will depend sensitively on the details of the orientation dependence of γi.

scholarly journals Liquid Crystal Ordering in the Hexagonal Phase of Rod-Coil Diblock Copolymers

Polymers ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1262
Author(s):  
Mikhail A. Osipov ◽  
Maxim V. Gorkunov ◽  
Alexander A. Antonov
Keyword(s):  
Liquid Crystal ◽  
Order Parameter ◽  
Density Functional ◽  
Diblock Copolymers ◽  
Microphase Separation ◽  
Hexagonal Phase ◽  
Orientational Order ◽  
Order Parameters ◽  
Copolymer Composition ◽  
Rigid Rod

Density functional theory of rod-coil diblock copolymers, developed recently by the authors, has been generalised and used to study the liquid crystal ordering and microphase separation effects in the hexagonal, lamellar and nematic phases. The translational order parameters of rod and coil monomers and the orientational order parameters of rod-like fragments of the copolymer chains have been determined numerically by direct minimization of the free energy. The phase diagram has been derived containing the isotropic, the lamellar and the hexagonal phases which is consistent with typical experimental data. The order parameter profiles as functions of temperature and the copolymer composition have also been determined in different anisotropic phases. Finally, the spatial distributions of the density of rigid rod fragments and of the corresponding orientational order parameter in the hexagonal phase have been calculated.

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