Van der Waals forces

In chemistry and physics, the name van der Waals force is sometimes used as a synonym for the totality of non-covalent forces (also known as  intermolecular forces). These forces, which act between stable molecules, are  weak compared to those appearing in chemical bonding. Historically, the use of the name for the total force is correct, because the Dutch physicist J. D. van der Waals, who lent his name to these forces, considered both the repulsive and the attractive component of the intermolecular force; see this article for the analytic form of van der Waals' original potential (and recall that a force is the gradient of a potential).

Unfortunately, there is no strict convention of the definition of van der Waals forces. Some texts consider only the attractive component of the intermolecular potential as the van der Waals force. Other texts designate only a certain part of the attraction as the van der Waals force. In order to understand the differences the different contributions to the intermolecular potential must be recognized.

Contributions to the intermolecular potential
For more details the article on intermolecular forces may be consulted. In that article it is noted that almost all intermolecular forces have four major contributions. There is always a repulsive part, prohibiting the collapse of molecular complexes, and an attractive part. The repulsive part is mainly due to the typical quantum mechanical effect of intermolecular electron exchange. The attractive part, in turn, consists of three distinct contributions
 * (i) The electrostatic interactions between charges (in the case of molecular ions), electric dipoles (in the case of molecules carrying non-vanishing permanent dipoles), electric quadrupoles (all molecules with symmetry lower than cubic), and in general between permanent electric multipoles. The electrostatic interaction is sometimes called after Keesom. Atoms in an S-state (a spherically symmetric state), such as the H-atom and the noble gas atoms, do not carry any multipole and for such systems this force is absent.


 * (ii) The second source of attraction is induction (also known as polarization), which is the interaction between a permanent multipole on one molecule with an induced multipole on another. This interaction is sometimes called after Debye. Every atom and molecule is polarizable, but not every atom or molecule has a permanent multipole, so this interaction may be absent.


 * (iii) The third attraction is usually named after London who himself called it dispersion. This is the only attraction experienced by noble gas atoms, but it is operative in any pair of atoms and molecules, irrespective of their symmetry. This interaction is roughly proportional to the product of polarizibilities of the monomers.

Returning to nomenclature: some texts mean by the van der Waals force the totality of forces (including repulsion), others mean all the attractive forces (and then sometimes distinguish van der Waals-Keesom, van der Waals-Debye, and van der Waals-London), and, finally  some  use the term "van der Waals force" solely as a synonym for the London/dispersion force. So, when one meets the term "van der Waals force", it is important to ascertain from the context what part of the intermolecular force is meant exactly.

Thermal averaging
All intermolecular/Van der Waals forces are anisotropic (except those between two noble gas atoms), which means that they depend on the relative orientation of the molecules. The induction and dispersion interactions are always attractive, irrespective of orientation, but the electrostatic interaction changes sign upon rotation of the molecules. That is, the electrostatic force can be attractive or repulsive, depending on the mutual orientation of the molecules. When molecules are in thermal motion, as they are in the gas and liquid phase, the electrostatic force is averaged out to a large extent, because the molecules thermally rotate and thus probe both repulsive and attractive parts of the electrostatic force. Sometimes this effect is expressed by the statement that "random thermal motion around room temperature can usually overcome or disrupt them" (which refers to the electrostatic component of the Van der Waals force). Clearly, the thermal averaging effect is much less pronounced for induction and dispersion forces, which are always attractive.

Influence of size
London forces become stronger as the monomers participating in the bond become larger. This is due to the increased polarizability of molecules with larger, more dispersed electron clouds. This trend is exemplified by the halogens (from smallest to largest: F2, Cl2, Br2, I2). Fluorine and chlorine are gases at room temperature, bromine is a liquid, and iodine is a solid. These molecules do not have dipoles, but do have quadrupoles and corresponding quadrupole-quadrupole interaction. However, the latter electrostatic interaction is averaged out to a large extent by thermal motions at room temperature, leaving the London force as the dominant factor.

The London forces also become stronger with larger amounts of surface contact. Greater surface area means closer interaction between different molecules.

Simple model
The Lennard-Jones 6-12 potential
 * $$ V(R) = 4\epsilon\left[\left(\frac{R_0}{R}\right)^{12} -\left(\frac{R_0}{R}\right)^{6}\right], \qquad \epsilon,\; R_0 > 0 $$

is often used as an approximate analytic model for the isotropic part of a total (repulsion plus attraction) van der Waals force as a function of intermolecular distance R. The potential passes through zero at R0 (sometimes referred to as scattering diameter), has a minimum for 21/6&thinsp;R0 and a well depth of &epsilon;. Analytic models of the interaction are used to study phenomena caused or influenced by intermolecular forces. For instance, they are responsible for certain cases of pressure broadening (van der Waals broadening) of spectral lines and the formation of Van der Waals molecules.