Van der Waals force

The Van der Waals forces (Van der Waals interactions), named after the Dutch physicist Johannes Diderik van der Waals, are the relatively weak non-covalent interactions between atoms or molecules whose interaction energy for spherical particles decreases with about the sixth power of the distance. Thus, according to current understanding, the Van der Waals forces can be divided into three components:

• the Keesom interaction between two dipoles, which is indirectly proportional to the absolute temperature (dipole-dipole forces),
• Debye interaction between a dipole and a polarizable molecule (dipole-induced dipole forces)
• London dispersion interaction (London forces) between two polarizable molecules (induced-dipole-induced-dipole forces). The London forces are often also referred to as the Van der Waals force in the narrower sense.

All van der Waals forces are weak forces compared to covalent bonding and ionic bonding, with dispersion interaction generally being the dominant of the three constituents. For example, van der Waals forces increase from hydrogen chloride to hydrogen iodide, although the dipole moment decreases. The van der Waals interaction forms the attractive interaction term in the Lennard-Jones potential. The Van der Waals force is obtained from the Van der Waals potential :

Illustrative effect of van der Waals forces

In addition to mainly electrostatic forces, geckos also use Van der Waals forces to adhere to surfaces without glue or suction cups. The undersides of their feet are full of the finest hairs. Each hair can only transmit a small force, but due to the high number, the sum of the forces is still sufficient for the animal to walk upside down on ceilings. This is also possible on smooth surfaces such as glass. The sum of the contact forces of a gecko is about 40 N.

A gecko scales a glass wall.

Cause

The London dispersion interaction also occurs between non-polar small particles (noble gas atoms, molecules), if these are polarizable, and leads to a weak attraction of these small particles.

Electrons in a microparticle (atom) can only move within certain limits, which leads to a constantly changing charge distribution in the microparticle. As soon as the center of positive charges is spatially separated from the center of negative charges, one can speak of a dipole, because here there are two (di-, from the Greek δίς "twice") electric poles. However, single nonpolar molecules can only be called temporary dipoles, because their polarity depends on the electron distribution, and this is constantly changing. (In polar molecules, on the other hand, the dipole property is permanent because of the electronegativities of the atoms and the structure of space, so they are called permanent dipoles or dipoles in the strict sense).

If two non-polar molecules come close to each other long enough (i.e. at low relative velocity), they enter into an electrostatic interaction with each other.

If, for example, particle A shows a pronounced negatively charged side to neighbour B, then the electrons of neighbour B (from the facing side) are repelled. Thus the dipoles align with each other. Such a shift of charge due to an electric field is called an influence. This means that the negative pole of a temporary dipole influences a positive pole vis à vis the neighbouring molecule. Thus, particle B becomes an "influenced" dipole. In technical literature, this is called "induced dipole" (lat. inducere: to introduce).

Van der Waals forces occur between the original, temporary dipole and the induced dipole. From now on, the dipoles influence each other, their electron displacement synchronizes.

If two atoms or molecules come close enough to each other, one of the following situations can occur.

• Two temporary dipoles meet: the particles attract each other.
• A temporary dipole meets a particle without a dipole moment: The dipole induces a rectified dipole moment in the non-dipole, which again creates an attractive force between the two particles.

Van der Waals binding energy: 0.5-5 kJ/mol (corresponds to 5-50 meV/molecule)

Quantum mechanical consideration

In the above description, however, electrons are treated as classical particles and the insights of quantum mechanics are not taken into account. In the quantum mechanical model of the atom, the electron is described by a stationary wave function ψ whose magnitude square always remains the same at a given point in the atom. This initially suggests the idea that the electron behaves like a classical extended charge distribution, with a charge density given by the product of the electron charge and the magnitude square of the wave function:

Accordingly, the charge distribution would be invariant, and the spontaneous emergence of temporary dipoles consequently impossible. Since is typically axisymmetric around the atomic nucleus, the dipole moment, for example of a noble gas atom, would always be zero.

Taking a closer look at the quantum mechanical charge density operator

where is the location operator of the electron, however, this turns out to be a fallacy. An electron does not behave like an extended charge distribution, but like a point charge whose location is indeterminate, since the presence of the other atom/molecule leads to constant "location measurements". For the expectation value of the charge density indeed results

however, it is not an eigenvalue of the charge density operator. The charge density has a certain fuzziness, which just leads to the fact that with a certain probability the center of gravity of the electronic charge distribution does not lie in the atomic nucleus and thus a dipole moment arises. In this way, in the picture of quantum mechanics, the Van der Waals forces can be understood.