DYNAMIC DENSITY FUNCTIONAL APPROACH TO PHASE SEPARATION DYNAMICS OF POLYMER SYSTEMS

1999 ◽  
Vol 10 (08) ◽  
pp. 1531-1540 ◽  
Author(s):  
T. KAWAKATSU ◽  
M. DOI ◽  
R. HASEGAWA
Keyword(s):  
Free Energy ◽  
Phase Separation ◽  
Block Copolymers ◽  
Density Functional ◽  
Energy Functional ◽  
Dynamic Density ◽  
Separation Processes ◽  
Polymer Systems ◽  
Model Free ◽  
Domain Structures

Slow dynamics of complex domain structures in phase separating polymer systems is investigated with the use of the self-consistent field (SCF) dynamic density functional (DDF) technique where the free energy of the system is calculated using the path integral formalism of the polymer chain conformation. We apply this technique to micellization of block copolymers and to phase separation of polymer blends containing block copolymers as a compatibilizer. In order to study the late stage of the phase separation processes more efficiently, we adopt the so-called Ginzburg–Landau approach, where a phenomenological model free energy functional is used. Numerical results of this approach is quantitatively compared with the results of the SCF approach.

Competition between Micro- and Macrophase Separations in a Binary Mixture of Block Copolymers. A Dynamic Density Functional Study

2002 ◽  
Vol 35 (19) ◽  
pp. 7473-7480 ◽  
Author(s):  
Hiroshi Morita ◽  
Toshihiro Kawakatsu ◽  
Masao Doi ◽  
Daisuke Yamaguchi ◽  
Mikihito Takenaka ◽  
...  
Keyword(s):  
Block Copolymers ◽  
Binary Mixture ◽  
Density Functional ◽  
Functional Study ◽  
Dynamic Density ◽  
Density Functional Study

Characterising the disordered state of block copolymers: Bifurcations of localised states and self-replication dynamics

2011 ◽  
Vol 23 (2) ◽  
pp. 315-341 ◽  
Author(s):  
KARL B. GLASNER
Keyword(s):  
Phase Separation ◽  
Block Copolymers ◽  
Bifurcation Diagram ◽  
Density Functional ◽  
Functional Model ◽  
Critical Regime ◽  
Heterogeneous Structure ◽  
Localised States ◽  
Pattern Forming ◽  
Self Replication

Above the spinodal temperature for micro-phase separation in block co-polymers, asymmetric mixtures can exhibit random heterogeneous structure. This behaviour is similar to the sub-critical regime of many pattern-forming models. In particular, there is a rich set of localised patterns and associated dynamics. This paper clarifies the nature of the bifurcation diagram of localised solutions in a density functional model of A−B diblock mixtures. The existence of saddle-node bifurcations is described, which explains both the threshold for heterogeneous disordered behaviour as well the onset of pattern propagation. A procedure to generate more complex equilibria by attaching individual structures leads to an interwoven set of solution curves. This results in a global description of the bifurcation diagram from which dynamics, in particular self-replication behaviour, can be explained.

Density profiles of fluids in some special symmetries

1995 ◽  
Vol 73 (7-8) ◽  
pp. 432-439 ◽  
Author(s):  
Seong-Chan Lee ◽  
Zi-Hong Yoon ◽  
Soon-Chul Kim
Keyword(s):  
Free Energy ◽  
Computer Simulations ◽  
Hard Sphere ◽  
Density Functional ◽  
Energy Functional ◽  
Empirical Method ◽  
Density Profiles ◽  
Functional Approximation ◽  
Free Energy Functional ◽  
Lennard Jones

A free-energy-functional approximation based on a semi-empirical method is proposed. The main advantage of the free-energy-functional approximation is its accuracy compared with other models and its relative simplicity compared with other well-known weighted-density approximations. The free-energy-functional approximation is applied to predict the density profiles of the hard-sphere fluids and the Lennard–Jones fluids in some special symmetries. For the density profiles near a hard flat wall, the results reproduced the hard-sphere oscillatory structures qualitatively and quantitatively. For the density profiles of hard-sphere fluids confined in a spherical cage, the results are also in a fair agreement with the computer simulations. For Lennard–Jones fluids, two kinds of density-functional perturbation theories, the density-functional mean-field theory (DFMFT) and the density-functional perturbation theory (DFPT), examined. The results show that at higher temperature the DFPT compares well with computer simulations. However, the agreement deteriorates slightly as the temperature of the Lennard–Jones fluids is reduced. These results demonstrate that both the free-energy-functional approximation and the DFPT succesfully describe the inhomogeneous properties of classical fluids.

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