Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

Crystal Field Theory - Tetrahedral and Square Planar Complexes

Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
Crystal Field Theory - Octahedral Complexes02:58

Crystal Field Theory - Octahedral Complexes

Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
Generalized Hooke's Law01:22

Generalized Hooke's Law

The generalized Hooke's Law is a broadened version of Hooke's Law, which extends to all types of stress and in every direction. Consider an isotropic material shaped into a cube subjected to multiaxial loading. In this scenario, normal stresses are exerted along the three coordinate axes. As a result of these stresses, the cubic shape deforms into a rectangular parallelepiped. Despite this deformation, the new shape maintains equal sides, and there is a normal strain in the direction of the...
Structures of Solids02:22

Structures of Solids

Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...
Valence Bond Theory02:42

Valence Bond Theory

Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...
Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Transport properties of active particles moving on adjustable networks.

Soft matter·2026
Same author

Flocking as a continuous phase transition in self-aligning active crystals.

The Journal of chemical physics·2026
Same author

Active Particles in Tunable Compressible Environments.

Small science·2026
Same author

Dynamical Density Functional Theory for Dense Odd-Diffusive Fluids.

The journal of physical chemistry. B·2026
Same author

Translational and rotational temperature difference in coexisting phases of inertial active dumbbells.

The Journal of chemical physics·2026
Same author

Temperature overshooting in the Mpemba effect of frictional active matter.

Physical review. E·2026
Same journal

Erratum: Bacterial Turbulence at Compressible Fluid Interfaces [Phys. Rev. Lett. 136, 138301 (2026)].

Physical review letters·2026
Same journal

Unveiling Light-Quark Yukawa Flavor Structure via Dihadron Fragmentation at Lepton Colliders.

Physical review letters·2026
Same journal

Adaptable Route to Fast Coherent State Transport via Bang-Bang-Bang Protocols.

Physical review letters·2026
Same journal

Topological Transition and Emergence of Elasticity of Dislocation in Skyrmion Lattice: Beyond Kittel's Magnetic-Polar Analogy.

Physical review letters·2026
Same journal

Pound-Drever-Hall Method for Superconducting-Qubit Readout.

Physical review letters·2026
Same journal

Coupling a ^{73}Ge Nuclear Spin to an Electrostatically Defined Quantum Dot in Silicon.

Physical review letters·2026
See all related articles

Related Experiment Video

Updated: May 12, 2026

Gyroid Nickel Nanostructures from Diblock Copolymer Supramolecules
08:40

Gyroid Nickel Nanostructures from Diblock Copolymer Supramolecules

Published on: April 28, 2014

Density functional theory for hard polyhedra.

Matthieu Marechal1, Hartmut Löwen

  • 1Institut für Theoretische Physik II, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany.

Physical Review Letters
|April 16, 2013
PubMed
Summary
This summary is machine-generated.

We developed a new theory for hard polyhedra fluids. Our model accurately predicts complex layering and orientational ordering near walls, matching simulation results.

More Related Videos

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
10:35

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

Published on: September 26, 2014

Related Experiment Videos

Last Updated: May 12, 2026

Gyroid Nickel Nanostructures from Diblock Copolymer Supramolecules
08:40

Gyroid Nickel Nanostructures from Diblock Copolymer Supramolecules

Published on: April 28, 2014

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
10:35

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

Published on: September 26, 2014

Area of Science:

  • Physical Chemistry
  • Colloid Science
  • Statistical Mechanics

Background:

  • Understanding the behavior of fluids composed of non-spherical particles is crucial in various scientific fields.
  • Classical density functional theory (DFT) is a powerful tool for studying inhomogeneous fluids.
  • Hard polyhedra represent a fundamental model for complex particle shapes.

Purpose of the Study:

  • To develop a classical density functional theory (DFT) for hard polyhedra and their mixtures.
  • To investigate the adsorption and ordering of Platonic solids near a hard wall.
  • To compare theoretical predictions with simulation data.

Main Methods:

  • Utilizing a geometry-based fundamental-measure theory framework.
  • Developing a novel classical density functional for hard polyhedra.
  • Performing Monte Carlo simulations of inhomogeneous fluids of Platonic solids.

Main Results:

  • The developed DFT excellently reproduces the complex layering and orientational ordering observed in simulations.
  • The faceted shape of polyhedra significantly influences fluid structure near confining walls.
  • The theory captures the intricate interplay between particle shape and confinement effects.

Conclusions:

  • The geometry-based DFT provides an accurate description of inhomogeneous hard polyhedra fluids.
  • This work offers a theoretical framework for understanding the behavior of complex-shaped particles.
  • Experimental verification using polyhedral colloids is feasible and encouraged.