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Debye–Huckel–Onsager Conductance Equation01:28

Debye–Huckel–Onsager Conductance Equation

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The Debye-Hückel-Onsager equation is a cornerstone of physical chemistry, providing a method to determine the molar conductance (Λm) and molar conductance at infinite dilution (Λ°m) for uni-univalent electrolytes.Uni-univalent electrolytes are electrolytes that dissociate in solution to produce one cation with a +1 charge and one anion with a –1 charge per formula unit.This equation addresses two crucial phenomena: the asymmetry effect and the electrophoretic effect.
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When two or more atoms come together to form a molecule, their atomic orbitals combine and molecular orbitals of distinct energies result. In a solid, there are a large number of atoms, and therefore a large number of atomic orbitals that may be combined into molecular orbitals. These groups of molecular orbitals are so closely placed together to form continuous regions of energies, known as the bands.
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IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration01:16

IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration

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A covalently bonded heteronuclear diatomic molecule can be modeled as two vibrating masses connected by a spring. The vibrational frequency of the bond can be expressed using an equation derived from Hooke's law, which describes how the force applied to stretch or compress a spring is proportional to the displacement of the spring. In this case, the atoms behave like masses, and the bond acts like a spring.
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Structure of Benzene: Molecular Orbital Model01:18

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According to the molecular orbital (MO) model, benzene has a planar structure with a regular hexagon of six sp2 hybridized carbons. As shown in Figure 1, each carbon is bonded to three other atoms with C–C–C and H–C–C bond angles of 120°. The C–H bond length is 109 pm, and the C–C bond length is 139 pm which is midway between the single bond length of sp3 hybridized carbons (154 pm) and sp2 hybridized carbons (133 pm).
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Network Covalent Solids02:18

Network Covalent Solids

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Network covalent solids contain a three-dimensional network of covalently bonded atoms as found in the crystal structures of nonmetals like diamond, graphite, silicon, and some covalent compounds, such as silicon dioxide (sand) and silicon carbide (carborundum, the abrasive on sandpaper). Many minerals have networks of covalent bonds.
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Crystal Field Theory - Tetrahedral and Square Planar Complexes

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Tetrahedral Complexes
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Updated: Apr 17, 2026

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Scalable tight-binding model for graphene.

Ming-Hao Liu1, Peter Rickhaus2, Péter Makk2

  • 1Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany.

Physical Review Letters
|February 7, 2015
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Summary
This summary is machine-generated.

Simulations of artificial graphene accurately predict real graphene's transport properties. This allows for efficient simulations of complex graphene devices, reducing computational cost.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science

Background:

  • Artificial graphene structures mimic real graphene's electronic properties.
  • Efficient simulation methods are crucial for understanding complex graphene devices.

Purpose of the Study:

  • To demonstrate that transport properties of real graphene can be accurately simulated using "theoretical artificial graphene."
  • To establish a condition for band structure invariance in scalable graphene lattices.
  • To validate simulation models against experimental transport measurements.

Main Methods:

  • Derivation of a condition for band structure invariance in scalable graphene lattices.
  • Transport measurements on ultraclean suspended single-layer graphene pn junction devices.
  • Transport simulations using scaled single-particle tight-binding models.

Main Results:

  • Ballistic transport features, including Fabry-Pérot interference and quantum Hall effect, were observed and accurately reproduced by simulations.
  • A condition for band structure invariance was derived and its restrictions identified.
  • The model successfully predicted gate-defined conductance quantization in single-layer graphene.

Conclusions:

  • Transport simulations for graphene can be efficiently performed using theoretical artificial graphene with a reduced number of atomic sites.
  • This approach enables reliable predictions for the electric properties of complex graphene devices.
  • The findings facilitate the design and understanding of novel graphene-based electronic applications.