Dynamic density functional theory DDFT

Dynamic Density Functional Theory (DDFT), Fig. 1 Illustration of the local equilibrium approximation involved in the development of the DDFT. The left-hand side illustrates the nonequilibrium evolution of the density p(r t) thin lines) up to time t thick line). For the time evolution, the equal-time correlation function g(r, r t) is... 

Dynamic Density Functional Theory (DDFT), Fig. 2 Schematic phase diagram of a system of Brownian particles with an attractive interaction. 4> in is the depth of the attractive minimum of the interaction potential, and p is the particle density (averaged of the syston volume). Only the states above ihtfull line, the bimodal, are stable. The states between the full and the dashed lines, the spinodal, are metastable, and the states below the spinodal are linearly unstable. The system considered in Archer and Evans [7] is quenched from a stable slate circle) into the unstable region as indicated by the vertical arrow... 

Microdomain stmctures of 3-miktoarm star terpolymers in a three-dimensional space were investigated using the dynamic density functional theory (DDFT). Analysis of DDFT demonstrates that the junction points are restricted to lie on... 

The theoretical methods to investigate the evolution kinetics of ordered microdomain structures are those in the atomic-scale including molecular dynamics simulations, Monte Carlo simulations, dynamic SCFT, dynamic density functional theory (DDFT), and those in the meso-scale including dissipative particle dynamics (DPD) simulations, etc. More details of these approaches can be found in the literatures. 

The mesoscopic regime lies between discrete particles and finite element representations of a continuum. Examples of mesoscopic field-theoretic methods are complex Langevin technique (CLT), time-dependent Ginzburg-Landau (TDGL) approach, and dynamic density functional theory (DDFT) method. 

The bottom left Panel illustrates models used in dynamic density functional theory (DDFT) simulations (a) The chemical structure of repeat unit of sulfonated poly(ether ether ketone) (sPEEK) chain. Hydrophilic blocks A and hydrophobic blocks B correspond to the sulfonated and nonsulfonated monomers, respectively, (b) The atomistic model of sPEEK chain, (c) The mapping of the atomistic chain onto a coarse-grained [ABtxChain and water molecules onto mesoscale solvent particle of type C. 

Here, is the volume fraction of A block in diblock copolymer. To study the dynamics of phase separation, the polymeric external potential dynamics (EPD) method can be employed, which was proposed by Maurits and Fraaije [23] in dynamic density functional theory (DDFT) method (bead-string model). In EPD, the monomer concentration is a conserved quantity, and the polymer dynamics is inherently of Rouse type. The external dynamical equation in terms of the potential field m,- is expressed as... 

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