Van der Waals Forces
What are van der Waals forces? Van der Waals forces can best be described as the weak
attractive intermolecular force that exists between two molecules. These forces were first
described by Johannes Diderik van der Waals in a paper published in 1869.1 The
experiments van der Waals was performing involved gasses.
These intermolecular forces exist in all matter, although to a greater or lesser extent
depending on the physical nature of the material in question. As a way to explore these
forces let us look at the simplest complete molecular structure – the hydrogen molecule.
Hydrogen atoms have one proton in its nucleus and one electron that moves in space
around the nucleus (isotopes of hydrogen exist, but for now, let’s ignore them). In the
hydrogen molecule, two atoms of hydrogen share two electrons. Generally, the
negatively charged electrons completely and evenly cover the space surrounding the
positively charged protons so that the over-all charge of the hydrogen molecule is neutral.
This idea can be represented using a graphic that represents the hydrogen molecule which
is elliptical and has a uniform color indicating a neutral charge.2
Occasionally, however, the electrons occupy the space in one region of the molecule
more frequently than it does the remaining space. When this happens, there exists a
slight temporary dipole moment on the molecule.
The delta symbols (δ-, δ+) indicate that the charge (- or +) is slight. This temporary
dipole moment can reverse.
It is this effect that allows hydrogen molecules to change state from gas to liquid and,
eventually, solid as the temperature of the gas is lowered. When there are two hydrogen
molecules near each other, the dipole moment of one molecule can affect the other
This effect is known as the INDUCED DIPOLE MOMENT.
When there are several hydrogen molecules near each other, the induced dipole effect is
not limited to a localized area, as long as the molecules are close to each other.
So, what is the minimum distance between molecules for the induced dipole moment to
occur? To answer this question, we must refer to the Lennard-Jones potential.
The Lennard-Jones potential is useful when describing the interaction between two
uncharged molecules or atoms.3 When two uncharged particles approach each other
there exists a slight attractive force which increases with closing distances. When the
two particles reach a certain distance the attractive force becomes overwhelmed by a
repulsive force. This effect can be graphically depicted.
This particular graph represents the Lennard-Jones potential for the attractive force
between water molecules. The attractive force experienced by the two molecules is due
to the induced dipole moment, while the repulsive force is due to the mutual deformation
of the molecules. The Lennard-Jones potential can be calculated using the equation:
From this equation, the Lennard-Jones force of attraction can be calculated;
In this equation, ε (kJ/mol) and σ (nm) are Lennard-Jones parameters which are different
for different interacting particles. ε is the well depth, and σ is the hard sphere diameter.
The separation of the two particles is represented by r. When the distance (r) between
two particles is small, the (1/r)12 term dominates and when the distance between two
particles is large, the (1/r)6 term dominates the equation. The van der Waals attractive
force4 can, therefore, be summarized as:
F ≈ (1/r)6
How does molecular size affect the strength of the dispersion forces? To answer that
question, we can examine the boiling points of several gasses. The boiling point of any
substance is a direct result of the amount of intermolecular attraction within the
substance. For substances that contain a large number of electrons and a large nucleus,
the intermolecular forces will be higher, and therefore, there boiling points will be higher.
The increase in the number of electrons in each element going down the list results in an
increase in the dipole-dipole interaction. This intermolecular force makes the larger
elements “stickier”. By comparison, compounds that have equal molecular weights can
have different boiling points. For instance, the molecule that has the chemical formula
C4H10 can have two arrangements;
Notice that the boiling point of butane is higher than that of 2-methylpropane. This is
significant because of the shape and size of the two molecules. The butane is longer and
less bulky than 2-methylpropane resulting in a higher surface area for intermolecular
interaction. Likewise, molecules that have a permanent dipole moment (HCl) will also
have a higher boiling point due to the increase in dispersion forces. For example, ethane
and fluoromethane both have the same number of electrons. Ethane does not have a
permanent dipole moment, where fluoromethane does. The overall effect of the
permanent dipole moment is that the boiling point of the fluoromethane is higher than
that of ethane, even though their size and shape are similar.
So, which is more important when it comes to increasing the intermolecular forces (and,
therefore, the boiling point) from one species to the next? To answer this let’s compare
tetrachloromethane and trichloromethane. Both have the same number of atoms (5), but
tetrachloromethane has a higher molecular weight and no permanent dipole moment. So,
you would expect that the trichloromethane would have a higher boiling point because it
has a slight dipole moment. But, tetrachloromethane has more electrons, and, therefore,
has a higher boiling point.
B. P. = 61.2°C B. P. = 76.8°C