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Van der Waals Equation

Van der Waals Equation

The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837−1923) improves it by considering two factors.
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the volume...

Van der Waals Interactions

Van der Waals Interactions

Atoms and molecules interact with each other through intermolecular forces. These electrostatic forces arise from attractive or repulsive interactions between particles with permanent, partial, or temporary charges. The intermolecular forces between neutral atoms and molecules are ion–dipole, dipole–dipole, and dispersion forces, collectively known as van der Waals forces.

Crystal Field Theory - Octahedral Complexes

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...

The Van der Waals Equation

The Van der Waals Equation

The ideal gas law is based on two simplifying assumptions: first, that there are no intermolecular attractions between gas molecules, and second, that the volume occupied by the molecules themselves is negligible compared with the volume of the container. However, these assumptions don't hold up under all conditions - specifically, at high pressures and low temperatures, as gas tends to deviate from ideal gas behavior.The van der Waals equation is an enhanced version of the ideal gas law,...

Crystal Field Theory - Tetrahedral and Square Planar Complexes

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,...

Unit Cells

Unit Cells

A crystal's internal structure is an orderly array of atoms, ions, or molecules, and the details of this array significantly influence the solid's properties. In a crystal, periodically repeating 'structural motifs' - which could be atoms, molecules, or groups thereof - create a 'space lattice.' This is essentially a three-dimensional, infinite array of points, each surrounded by its neighbors in an identical way, forming the basic structure of the crystal.A 'unit cell' is a theoretical...

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Related Experiment Video

Updated: Apr 6, 2026

$Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene$

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Published on: August 22, 2017

Two-dimensional van der Waals C60 molecular crystal.

C D Reddy¹, Zhi Gen Yu¹, Yong-Wei Zhang¹

¹Institute of High Performance Computing, A*STAR, Singapore 138632.

Scientific Reports

|July 18, 2015

Summary

Researchers explored the stability and properties of a two-dimensional (2D) C60 molecular monolayer. This novel van der Waals crystal exhibits thermal stability and tunable electronic properties, opening avenues for nanoelectronic applications.

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Area of Science:

Materials Science
Condensed Matter Physics
Nanotechnology

Background:

Two-dimensional (2D) atomic crystals like graphene are covalently bonded.
The formation of 2D molecular crystals via van der Waals interactions is an open question.

Purpose of the Study:

To investigate the structural stability and mechanical properties of a free-standing infinite C60 molecular monolayer.
To explore the electronic properties and potential applications of this novel 2D material.

Main Methods:

Molecular dynamic simulations were employed to assess structural stability.
Mechanical properties including elastic modulus, ultimate tensile stress, and failure strain were calculated.
Electronic properties were analyzed, focusing on the band gap and its tunability.

Main Results:

The C60 monolayer demonstrates stability up to 600 K.
Mechanical properties were quantified, with failure occurring via shearing and cavitation.
The band gap is reduced due to delocalized molecular orbitals and can be tuned by strain engineering.

Conclusions:

A stable 2D C60 molecular monolayer can be formed via van der Waals interactions.
This material exhibits promising characteristics for nanoelectronics, including thermal stability, low density, tunable semiconducting behavior, and flexibility.