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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.Polar molecules have a partial positive charge on one end and a partial negative charge on the other end of the molecule,...

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...

Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)

Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)

Vicinal or three-bond coupling is commonly observed between protons attached to adjacent carbons. Here, nuclear spin information is primarily transferred via electron spin interactions between adjacent C‑H bond orbitals. This generally favors the antiparallel arrangement of spins, so 3J values are usually positive.
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the involved orbitals. The...

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,...

Noncovalent Attractions in Biomolecules

Noncovalent Attractions in Biomolecules

Noncovalent attractions are associations within and between molecules that influence the shape and structural stability of complexes. These interactions differ from covalent bonding in that they do not involve sharing of electrons.
Four types of noncovalent interactions are hydrogen bonds, van der Waals forces, ionic bonds, and hydrophobic interactions.
Hydrogen bonding results from the electrostatic attraction of a hydrogen atom covalently bonded to a strong-electronegative atom like oxygen,...

Noncovalent Attractions in Biomolecules

Noncovalent Attractions in Biomolecules

Noncovalent attractions are associations within and between molecules that influence the shape and structural stability of complexes. These interactions differ from covalent bonding in that they do not involve sharing of electrons.
Four types of noncovalent interactions are hydrogen bonds, van der Waals forces, ionic bonds, and hydrophobic interactions.
Hydrogen bonding results from the electrostatic attraction of a hydrogen atom covalently bonded to a strong-electronegative atom like oxygen,...

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Fabrication of Low Temperature Carbon Nanotube Vertical Interconnects Compatible with Semiconductor Technology

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Published on: December 7, 2015

Van der Waals interaction between two crossed carbon nanotubes.

Alexander I Zhbanov¹, Evgeny G Pogorelov, Yia-Chung Chang

¹Research Center for Applied Sciences, Academia Sinica, 128, Section 2, Academia Road Nankang, Taipei 115, Taiwan.

|September 25, 2010

Summary

Analytical expressions for van der Waals potential energy and force between crossed carbon nanotubes were derived. This study quantifies interactions, providing key parameters for nanotube behavior and applications.

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Published on: February 5, 2017

Area of Science:

Materials Science
Nanotechnology
Computational Physics

Background:

Understanding inter-nanotube forces is crucial for designing nanoscale devices and materials.
Carbon nanotubes exhibit significant van der Waals interactions due to their extended pi-electron systems.
Previous models often simplified the complex geometry and interactions of crossed nanotubes.

Purpose of the Study:

To derive precise analytical expressions for van der Waals potential energy and force between crossed carbon nanotubes.
To provide a quantitative framework for predicting interactions in nanotube assemblies.
To evaluate key interaction parameters such as equilibrium distance and maximum attractive force.

Main Methods:

Utilized the Lennard-Jones potential for interatomic carbon-carbon interactions.
Employed L. A. Girifalco's smeared-out approximation for continuum modeling of nanotubes.
Derived exact formulas expressed in terms of rational and elliptical functions.

Main Results:

Calculated the van der Waals potential energy and force profiles for crossed carbon nanotubes.
Generated uniform potential curves for both single- and multiwall carbon nanotube configurations.
Determined specific values for equilibrium distance, maximal attractive force, and potential energy.

Conclusions:

The derived analytical expressions accurately describe van der Waals interactions between crossed carbon nanotubes.
The findings offer valuable data for simulations and experimental design involving nanotube networks.
This work establishes a foundation for understanding mechanical properties and self-assembly of carbon nanotube systems.