Direction of the nucleation current through the saddle point in the binary nucleation theory and the saddle point avoidance

1995 ◽  
Vol 102 (8) ◽  
pp. 3331-3336 ◽  
Author(s):  
L. M. Berezhkovskii ◽  
V. Yu. Zitserman
Keyword(s):  
Saddle Point ◽  
Nucleation Theory ◽  
Binary Nucleation

scholarly journals Analytic Structure of the SCFT Energy Functional of Multicomponent Block Copolymers

2015 ◽  
Vol 17 (5) ◽  
pp. 1360-1387 ◽  
Author(s):  
Kai Jiang ◽  
Weiquan Xu ◽  
Pingwen Zhang
Keyword(s):  
Block Copolymer ◽  
Block Copolymers ◽  
Saddle Point ◽  
Saddle Points ◽  
Mathematical Structure ◽  
Energy Functional ◽  
Nucleation Theory ◽  
Field Energy ◽  
Analytic Structure ◽  
Self Consistent Field Theory

AbstractThis paper concerns the analytic structure of the self-consistent field theory (SCFT) energy functional of multicomponent block copolymer systems which contain more than two chemically distinct blocks. The SCFT has enjoyed considered success and wide usage in investigation of the complex phase behavior of block copolymers. It is well-known that the physical solutions of the SCFT equations are saddle points, however, the analytic structure of the SCFT energy functional has received little attention over the years. A recent work by Fredrickson and collaborators [see the monograph by Fredrickson,The Equilibrium Theory of Inhomogeneous Polymers, (2006), pp. 203–209] has analysed the mathematical structure of the field energy functional for polymeric systems, and clarified the index-1 saddle point nature of the problem caused by the incompressible constraint. In this paper, our goals are to draw further attention to multicomponent block copolymers utilizing the Hubbard-Stratonovich transformation used by Fredrickson and co-workers. We firstly show that the saddle point character of the SCFT energy functional of multicomponent block copolymer systems may be high index, not only produced by the incompressible constraint, but also by the Flory-Huggins interaction parameters. Our analysis will be beneficial to many theoretical studies, such as the nucleation theory of ordered phases, the mesoscopic dynamics. As an application, we utilize the discovery to develop the gradient-based iterative schemes to solve the SCFT equations, and illustrate its performance through several numerical experiments takingABCstar triblock copolymers as an example.

The multicomponent nucleation theory with saddle point avoidance

1990 ◽  
Vol 140 (2) ◽  
pp. 373-382 ◽  
Author(s):  
Vladimir Yu Zitserman ◽  
Leonid M Berezhkovskii
Keyword(s):  
Saddle Point ◽  
Nucleation Theory

scholarly journals Classical binary nucleation theory applied to the real mixture n‐nonane/methane at high pressures

1995 ◽  
Vol 102 (11) ◽  
pp. 4531-4537 ◽  
Author(s):  
K. N. H. Looijmans ◽  
C. C. M. Luijten ◽  
G. C. J. Hofmans ◽  
M. E. H. van Dongen
Keyword(s):  
High Pressures ◽  
Nucleation Theory ◽  
The Real ◽  
Binary Nucleation ◽  
Real Mixture
Sign in / Sign up

Export Citation Format

Share Document