Lattice density functional theory

S. Chains in the S phase are also oriented normal to the surface, yet the unit cell is rectangular possibly because of restricted rotation. This structure is characterized as the smectic E or herringbone phase. Schofield and Rice [204] applied a lattice density functional theory to describe the second-order rotator (LS)-heiTingbone (S) phase transition. 

The assumption of homogeneity can be abandoned if the continuous me m-field treatment is replaced by a discrete treatment where the positions of fluid molecules are restricted to nodes on a lattice. The discussion in Section 5.4.2 and 5.6.5 showed that the mean-field lattice density functional theory developed in Section 4.3 w as crucial in unraveling the c.om-plex phase behavior of fluids confined by chemically decorated substrate surfaces. A similar deep understanding of the phase behavior would not have been possible on the basis of simulation results alone. Nevertheless, the relation between these MC data and the lattice density functional results remained only qualitative on accoimt of the continuous models employed in the computer simulations. Thus, we aim at a more quantitative comparison between MC simulations and mean-field lattice density fimctioiial theory in the closing. section of this diaptcr. 

Again we limit the discussion of simulation tediniques in Chapter 6 to the Monte Carlo method as a key numerical technique to stay focused as much as possible. Molecular dynamics simulations, which are the other simulation technique one would immediately think of, are explicitly disregarded here because they are more suitable to study dynamic rather than equilibrium properties with which we are coucerued here. In a similar spirit, off-lattice density functional theory is also disregarded here because this is already a vast and flourishing field in its own right to which a separate such text should be devoted. 

Chen X, Sun L, Liu H, Hu Y, Jiang J A new lattice density functional theory for polymer adsorption at solid-liquid interface,/ Chem Phys 131(4) 044710, 2009. 

Lian C, Wang L, Chen X, et al. Modehng swelling behavior of thermoresponsive polymer brush with lattice density functional theory, Langmuir 30(14) 4040—4048, 2014a. 

Lian C, Chen X, Zhao S, et al. Substrate effect on the phase behavior of polymer brushes with lattice density functional theory, Macromol Theory Simul 23(9) 575—582, 2014b. 

We present simulation results for the packing for single center Lennard Jones models of adsorbed fluids such as methane, carbon thoxide and carbon tetrachloride at high pressure in carbon slit pores. These show a series of packing transitions that are well described by a lattice density functional theory model developed in our laboratory. By contrast, simulations show that these transitions are absent for a three-center model, whidi provides a more adequate representation of carbon dioxide. Analysis of the simulation results shows that alternations of flat lying molecules and rotated molecules can occur in this case as the pore widfli is increased. The presence or absence of quadrupoles has negligible effect on fliese hi -density structures. 

Other hand, have modeled adsorption in MCM-41-type zeolite with NLDFT methods. Their conclusion is that the adsorption branch corresponds to the spinodal condensation, i.e. metastable situation, and the desorption branch corresponds to the equilibrium capillary condensation/evaporation situation. Kowalczyk et al. [8], have calculated the hysteresis using a lattice density functional theory. The basis of their work stems from similar simulations by... 

Density functional theory from statistical mechanics is a means to describe the thermodynamics of the solid phase with information about the fluid [17-19]. In density functional theory, one makes an ansatz about the structure of the solid, usually describing the particle positions by Gaussian distributions around their lattice sites. The free... 

A lot of work (Opahle et al, 2000 Andrew et al, 2002a,b Muscat et al, 2002 Edelbro et al, 2003) has been performed on bulk and surface properties of FeS2 using various kinds of density functional theory. These works have shown that such methods are capable of producing calculated bulk properties such as lattice constants which agree well with experiment, and has provided a reference for the study of pyrite surfaces. 

Mitchell and Koper [64] have involved the density-functional theory to determine the parameters necessary for the construction of an off-lattice model with no freely adjustable parameters for Br electrodeposition on Au(lOO). 

During the past few decades, various theoretical models have been developed to explain the physical properties and to find key parameters for the prediction of the system behaviors. Recent technological trends focus toward integration of subsystem models in various scales, which entails examining the nanophysical properties, subsystem size, and scale-specified numerical analysis methods on system level performance. Multi-scale modeling components including quantum mechanical (i.e., density functional theory (DFT) and ab initio simulation), atom-istic/molecular (i.e., Monte Carlo (MC) and molecular dynamics (MD)), mesoscopic (i.e., dissipative particle dynamics (DPD) and lattice Boltzmann method (LBM)), and macroscopic (i.e., LBM, computational... 

Density Functional Theory of Lattice Based Polymer 176 Adsorption... 

DENSITY FUNCTIONAL THEORY OF LATTICE BASED POLYMER ADSORPTION... 

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