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- Lattice_density_functional_theory abstract "Lattice density functional theory (LDFT) is a statistical theory used in physics and thermodynamics to model a variety of physical phenomena with simple lattice equations. Lattice models with nearest-neighbor interactions have been used extensively to model a wide variety of systems and phenomena, including the lattice gas, binary liquid solutions, order-disorder phase transitions, ferromagnetism, and antiferromagnetism. Most calculations of correlation functions for nonrandom configurations are based on statistical mechanical techniques, which lead to equations that usually need to be solved numerically. In 1925, Ising gave an exact solution to the one-dimensional (1D) lattice problem. In 1944 Onsager was able to get an exact solution to a two-dimensional (2D) lattice problem at the critical density. However, to date, no three-dimensional (3D) problem has had a solution that is both complete and exact. Over the last ten years, Aranovich and Donohue have developed lattice density functional theory (LDFT) based on a generalization of the Ono-Kondo equations to three-dimensions, and used the theory to model a variety of physical phenomena.The theory starts by constructing an expression for free energy, A=U-TS, where internal energy U and entropy S can be calculated using mean field approximation. The grand potential is then constructed as Ω=A-μΦ, where μ is a Lagrange multiplier which equals to the chemical potential, and Φ is a constraint given by the lattice.It is then possible to minimize the grand potential with respect to the local density, which results in a mean-field expression for local chemical potential. And the theory is completed by specifying the chemical potential for a second (possibly bulk) phase. And in an equilibrium process, μI=μII.Lattice density functional theory has several advantages over more complicated free volume techniques such as Perturbation theory and the statistical associating fluid theory, including mathematical simplicity and ease of incorporating complex boundary conditions. Although this approach is known to give only qualitative information about the thermodynamic behavior of a system, it provides important insights about the mechanisms of various complex phenomena such as phase transition, aggregation, configurational distribution, surface-adsorption, self-assembly, crystallization, as well as steady state diffusion.".
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- Lattice_density_functional_theory wikiPageRevisionID "595730153".
- Lattice_density_functional_theory wikiPageWikiLink Antiferromagnetism.
- Lattice_density_functional_theory wikiPageWikiLink Boundary_conditions.
- Lattice_density_functional_theory wikiPageWikiLink Boundary_value_problem.
- Lattice_density_functional_theory wikiPageWikiLink Category:Density_functional_theory.
- Lattice_density_functional_theory wikiPageWikiLink Category:Lattice_models.
- Lattice_density_functional_theory wikiPageWikiLink Category:Statistical_mechanics.
- Lattice_density_functional_theory wikiPageWikiLink Chemical_potential.
- Lattice_density_functional_theory wikiPageWikiLink Correlation_function.
- Lattice_density_functional_theory wikiPageWikiLink Correlation_functions.
- Lattice_density_functional_theory wikiPageWikiLink Crystallization.
- Lattice_density_functional_theory wikiPageWikiLink Diffusion.
- Lattice_density_functional_theory wikiPageWikiLink Entropy.
- Lattice_density_functional_theory wikiPageWikiLink Ernst_Ising.
- Lattice_density_functional_theory wikiPageWikiLink Ferromagnetism.
- Lattice_density_functional_theory wikiPageWikiLink Internal_energy.
- Lattice_density_functional_theory wikiPageWikiLink Lagrange_multiplier.
- Lattice_density_functional_theory wikiPageWikiLink Lars_Onsager.
- Lattice_density_functional_theory wikiPageWikiLink Lattice_model_(physics).
- Lattice_density_functional_theory wikiPageWikiLink Mean_field.
- Lattice_density_functional_theory wikiPageWikiLink Mean_field_theory.
- Lattice_density_functional_theory wikiPageWikiLink Particle_aggregation.
- Lattice_density_functional_theory wikiPageWikiLink Perturbation_theory.
- Lattice_density_functional_theory wikiPageWikiLink Phase_transition.
- Lattice_density_functional_theory wikiPageWikiLink Phase_transitions.
- Lattice_density_functional_theory wikiPageWikiLink Physics.
- Lattice_density_functional_theory wikiPageWikiLink Self-assembly.
- Lattice_density_functional_theory wikiPageWikiLink Thermodynamic_free_energy.
- Lattice_density_functional_theory wikiPageWikiLink Thermodynamics.
- Lattice_density_functional_theory wikiPageWikiLinkText "Lattice density functional theory".
- Lattice_density_functional_theory hasPhotoCollection Lattice_density_functional_theory.
- Lattice_density_functional_theory wikiPageUsesTemplate Template:Orphan.
- Lattice_density_functional_theory subject Category:Density_functional_theory.
- Lattice_density_functional_theory subject Category:Lattice_models.
- Lattice_density_functional_theory subject Category:Statistical_mechanics.
- Lattice_density_functional_theory hypernym Theory.
- Lattice_density_functional_theory type Article.
- Lattice_density_functional_theory type Book.
- Lattice_density_functional_theory type Model.
- Lattice_density_functional_theory type Article.
- Lattice_density_functional_theory type Chromodynamic.
- Lattice_density_functional_theory type Mechanic.
- Lattice_density_functional_theory type Method.
- Lattice_density_functional_theory type Model.
- Lattice_density_functional_theory type Physic.
- Lattice_density_functional_theory comment "Lattice density functional theory (LDFT) is a statistical theory used in physics and thermodynamics to model a variety of physical phenomena with simple lattice equations. Lattice models with nearest-neighbor interactions have been used extensively to model a wide variety of systems and phenomena, including the lattice gas, binary liquid solutions, order-disorder phase transitions, ferromagnetism, and antiferromagnetism.".
- Lattice_density_functional_theory label "Lattice density functional theory".
- Lattice_density_functional_theory sameAs m.07khv6j.
- Lattice_density_functional_theory sameAs Q6497105.
- Lattice_density_functional_theory sameAs Q6497105.
- Lattice_density_functional_theory wasDerivedFrom Lattice_density_functional_theory?oldid=595730153.
- Lattice_density_functional_theory isPrimaryTopicOf Lattice_density_functional_theory.