Asymptotic properties of higher-order random-phase approximation vertex functions for block copolymer melts

1993 ◽  
Vol 26 (15) ◽  
pp. 4050-4051 ◽  
Author(s):  
A. M. Mayes ◽  
M. Olvera de la Cruz ◽  
W. E. McMullen
Keyword(s):  
Block Copolymer ◽  
Random Phase Approximation ◽  
Asymptotic Properties ◽  
Random Phase ◽  
Higher Order ◽  
Phase Approximation ◽  
Copolymer Melts

Interpretation of small-angle scattering of block copolymer/nanoparticle blends using random phase approximation

2014 ◽  
Vol 37 (6) ◽  
Author(s):  
I. F. Hakem ◽  
A. Benmouna ◽  
R. Benmouna ◽  
R. Ferebee ◽  
M. Benmouna ◽  
...  
Keyword(s):  
Block Copolymer ◽  
Small Angle ◽  
Random Phase Approximation ◽  
Random Phase ◽  
Small Angle Scattering ◽  
Phase Approximation ◽  
Angle Scattering

Application of SAS to Bulk Amorphous Polymers, Block Copolymers and Polymer Blends

1986 ◽  
Vol 79 ◽  
Author(s):  
R. J. Roe
Keyword(s):  
Block Copolymer ◽  
Block Copolymers ◽  
Polymer Blends ◽  
Approximation Theory ◽  
Random Phase Approximation ◽  
Random Phase ◽  
Amorphous Polymers ◽  
Phase Approximation ◽  
Block Copolymer Micelles ◽  
Copolymer Structure

AbstractThis article discusses the application of small-angle neutron and X-ray scattering techniques to the study of bulk amorphous polymers, block copolymers and polymer blends. The subject matter discussed include density fluctuation in single component amorphous polymers, concentration fluctuation in compatible polymer blends and its interpretation in terms of the random phase approximation theory, analysis of the scattering from incompatible polymer blends as developed by Porod, determination of the phase boundary thickness, order-disorder transition in block copolymer, interpretation of the scattering from disordered block copolymer systems by means of the random phase approximation theory, characterization of ordered block copolymer structure, and the study of block copolymer micelles.

Electron correlation effects beyond the random phase approximation

2016 ◽  
Vol 30 (13) ◽  
pp. 1642006
Author(s):  
J. D. Fan ◽  
Y. M. Malozovsky
Keyword(s):  
Field Theory ◽  
Random Phase Approximation ◽  
Particle System ◽  
Random Phase ◽  
Electron System ◽  
Higher Order ◽  
Mean Field Approximation ◽  
Phase Approximation ◽  
Strongly Coupled ◽  
Higher Order Terms

The methods that have been used to deal with a many-particle system can be basically sorted into three types: Hamiltonian, field theory and phenomenological method. The first two methods are more popular. Traditionally, the Hamiltonian method has been widely adopted in the conventional electronic theory for metals, alloys and semiconductors. Basically, the mean-field approximation (MFA) that has been working well for a weakly coupled system like a metal is employed to simplify a Hamiltonian corresponding to a particular electron system. However, for a strongly coupled many-particle system like a cuprate superconductor MFA should in principle not apply. Therefore, the field theory on the basis of Green’s function and the Feynman diagrams must be invoked. In this method, one is however more familiar with the random phase approximation (RPA) that gives rise to the same results as MFA because of being short of the information for higher-order terms of interaction. For a strongly coupled electron system, it is obvious that one has to deal with higher-order terms of a pair interaction to get a correct solution. Any ignorance of the higher-order terms implies that the more sophisticated information contained in those terms is discarded. However, to date one has not reached a consensus on how to deal with the higher-order terms beyond RPA. We preset here a method that is termed the diagrammatic iteration approach (DIA) and able to derive higher-order terms of the interaction from the information of lower-order ones on the basis of Feynman diagram, with which one is able to go beyond RPA step by step. It is in principle possible that all of higher-order terms can be obtained, and then sorted to groups of diagrams. It turns out that each of the groups can be replaced by an equivalent one, forming a diagrammatic Dyson-equation-like relation. The diagrammatic solution is eventually “translated” to a four-dimensional integral equation. The method can be applied to a layered 2D system that is a model system of cuprate superconductors and others such as atomic, nuclear, heavy-fermion systems, etc.

Sign in / Sign up

Export Citation Format

Share Document