Intermolecular Forces

Ion-ion interactions The fundamental interaction is electrostatic. At its simplest this is the interaction of two charges in vacuum. As drawn in the upper pat of the figure one charge experiences an attractive potential given by Coulomb's Law, where ε is the relative permittivity or dielectric constant. This is unity in a vacuum. In other media, e.g. water, the electric charges in the medium can line up to oppose the electric field and hence reduce the strength of the interaction. This is particularly the case for water, for which ε = 80. In a typical hydrocarbon (liquid) ε is only about 2. The interaction between ions is large and of long range. For Na+ and Cl− 1 nm apart the interaction energy in vacuum is 2.3 x 10-19 J. In water this drops by the factor 80 for the dielectric constant to 2.9 x 10-21 J. For comparison kBT at room temperature is 4 x 10-21 J. The interaction between ions is important in the determination of the lattice energies of ionic solids and in electrolyte solutions. The latter will be discussed in detail later in the lecture course.

Ion-dipole interactions A dipole is determined by two charges and their separation, μ = Σqiri. Many molecules have dipole moments and some examples are shown in the figure alongside. The dipole increase with the magnitude of the charges and with their separation. The value of the dipole moment is often expressed in Debye units, defined alongside, and dipole moments can be determined experimentally (from the variation of the dielectric constant with temperature). The interaction of an ion and a dipole can be broken down into the interaction of the ion with each of the individual charges that comprise the dipole as shown schematiclly in the figure. The interaction can easily be written exactly in terms of the angle of the dipole but the main point is that, provided the distance between the ion and the dipole is much greater than the separation of charges in the dipole (point dipole approximation) the distance dependence of the interaction changes to r−2 to give Ion-dipole interactions are important in electrolyte solutions where the dipole of the solvent will cause molecules to by attracted to ions in the solution and to orient themselves to optimize the interaction. Some examples of hydration structures will be given later in the lecture course.

Dipole-dipole interactions

As can be deduced from the diagram above dipole-dipole interactions can also be evaluated by summing the interactions between the individual charges. By the same argument as for ion-dipole interactions the distance dependence must change by another power of r and the interaction energy is given by As shown alongside this interaction is highly dependent on the orientation of the two dipole moments. In liquids and gases the thermal motion usually overcomes the orienting power of the dipole-dipole interaction to a significant extent and interactions between well oriented dipoles are therefore only important in molecular solids.

If the thermal motion in gases and liquids were to overcome the orientation dependence of the dipole-dipole interaction completely the interaction would average to zero. However, each orientation will occur with a probability determined by the Boltzmann factor, exp(−U(r,θ)/k_BT).

When the Boltzmann weighting is included the average interaction energy becomes

Energetically more favourable orientations are dominant but there is a finite probability that unfavourable orientations also occur. When the dipoles are close to each other the effect of the Boltzmann weighting is strong but when they are well separated the Boltzmann weighting is negligible and the interaction averages out to zero. The result is that the interaction energy depends more strongly on both the magnitude of the dipole moments and the distance between the dipoles than the dipole-dipole interaction above. Note also that the interaction energy is inversely proportional to temperature because it opposes the tendency for the dipoles to align.

Dipole-induced dipole interactions The electron clouds of molecules can be distorted by electric fields. An electric field induces a dipole of α0E where α0 is the polarizability of the molecule (usually quoted in the form of α0/4πε0, which has units of volume). Polarizability increases rapidly with the number of electrons and the size of an atom (i.e. it incease rapidly down the periodic table). It is larger in molecules than in atoms because the electrons are more readily distorted, and it is larger for multiply bonded systems. The interaction energy is Note that there is no temperature dependence and that the distance dependence is exactly the same as for rotating dipoles.

Dispersion forces

Isolated molecules undergo electronic fluctuations that generate instantaneous dipole moments. An instantaneous dipole moment can induce a dipole moment in an adjacent molecule and interact attractively with it. Thus, the correlation of the fluctuations leads to an attractive force known as the dispersion force. The magnitude of the fluctuations can be expected to depend on polarizability. Since the interaction has a quantum origin, it can also be expected to depend in some way on excitation energies, as does the polarizability. In the London formula for the dispersion interaction between identical atoms, given below, the energy depends on α²I:

The distance dependence is exactly the same as for rotating dipoles and dipole-induced dipole interactions and the three are normally lumped together as the van der Waals interaction.

Dispersion forces increase rapidly as the atoms become heavier (because of the increasing polarizability) and are always present, although as the table below demonstrates, they are not always the dominant contribution.

Species	Relative interaction at fixed distance	% contribution from dispersion
Ne	0.04	100
CH4	1	100
HCl>	1.6	86
HI	3.5	99
CH3	5.1	68
NH3	1.6	57
H2O	1.7	24

A result that will be very important for liquid solutions is that the interaction between unlike molecules equals the geometric mean of the interactions within each pair. This follows from the equation given above for the dispersion interaction if the ionization potentials are taken to be approximately the same.: