Intermolecular forces

Why does water bead up like this on certain surfaces, like a waxed car or glass? Why doesn't it wet the entire surface evenly? The answer is that the forces of attraction between water molecules — intermolecular forces — are stronger than the attractive forces between the water molecules and the surface.

Intermolecular forces are the glue that hold many materials together. They give many substances their properties, such as melting and boiling temperatures.

When we talk about ionic or covalent bonding, we're talking about attractive forces that are relatively large.

These bonds are on the order of 100 times stronger than the bonds that result from the attractive forces we'll discuss in this section. Nevertheless, differences in the forces between atoms and molecules can lead to profound differences even between compounds that would seem similar.

1. The electrostatic force

The electrical force between charged particles (atomic or molecular ions, protons or electrons) is one of the four fundamental kinds of forces in the universe (the others are gravity and the strong and weak nuclear forces). We call this the electrostatic force.

We describe these forces using Coulomb's law. The Coulomb or electrostatic force is the strongest of the intermolecular forces; it accounts, among other things, for the ionic bonding of salts, such as NaCl.

A typical potential energy vs. separation curve for the formation of a bond

2. Multipole Forces

Think for a moment about an inert gas atom, say Argon (Ar). Although we know that the electrons aren't arranged in a strictly spherical cloud around the nucleus (p-orbitals and all that), because the atom is free to rotate, the distribution of electrons is more-or-less spherical.

Because an atom is spherically symmetric, we can't identify any one "side" or portion of its electron cloud that is any more or less positive or negative than any other.

Now think of a molecule like hydrogen chloride (HCl). It doesn't have that spherical symmetry. It's a sphere with a "bump".

In fact, because the chlorine atom is quite electronegative, it pulls the single H-atom electron mostly away from the hydrogen, leaving a mostly bare proton. HCl has two different "ends", one clearly more positive than the other.

The H-atom side is more positive than the Cl-atom side (see the picture below).

This situation is sometimes described with this language: An atom is isotropic. It looks the same viewed from any direction. The HCl molecule is anisotropic (not isotropic) because as we approach it from different directions, we get a different view. Space is isotropic. It has no special direction. We only define "up" as north on our globe out of long-standing convention, not because space has any special up or down direction.

Permanent dipoles

You can see how the symmetry of a molecule, or we often say the "breaking" of some underlying symmetry, can lead to an asymmetric distribution of the electrons around it.

This makes one part of the molecule "less negative" (and therefore more positive) than another. A molecule that clearly has two sides or ends, one more negative than the other, is said to possess a permanent dipole (two poles, like a battery, + and -), and has interesting properties because of it. The linear molecule HCl is a good example (below).

Non-linear molecules can have permanent dipoles, too. In the top row of the table below are some molecules which are highly symmetric, and because of that symmetry, cannot have permanent dipoles.

Dipole strength: The dipole moment

We need a way to measure the relative strengths of dipoles, because a dipole can exert a force on another atom or molecule, and the amount of force exerted will depend on the strength or magnitude of the dipole.

The strength of a dipole depends on how much charge difference exists between one "end" of a molecule and another, and the separation of those ends. We call the measure of dipole strength the dipole moment. In mathematics, a moment is a (vague) measure of shape.

This table lists the dipole moments of some commonly encountered substances. The unit of measurement of dipole moment is the Debye (D).

Practice problems — 1

Predict whether each molecule below is polar (has a dipole moment) or non-polar. You might need to sketch out a Lewis structure to tell. Roll over or tap the molecule to see the solution.

Which of the following liquids might you expect to have the highest and lowest boiling points? Explain your responses. Roll over or tap the molecule to see the solutions. (Note, in the solutions, I've included boiling points, which you wouldn't be expected to know without looking them up.

How Dipoles Interact

The figures on the right show how two or more dipoles interact when they are close. First, we introduce a shorthand notation, the crossed-arrow symbol; the plus goes on the positive side of the dipole and the arrow on the negative side.

When dipoles are free to rotate, they tend to class, as shown. This happens because of the twisting force shown. That twisting force is simply due to the electrostatic force: A region of high negative charge will repel the more negative end of a dipole and (relatively speaking) attract the more positive end.

When many dipoles collect, e.g. in a solid, they tend to class as shown in the bottom panel. Note the each + and - charge is surrounded by opposite charges.

A note on + and - : δ+ and δ-

When designating the + and - ends of a molecular dipole, we generally use the symbols δ+ and δ- rather than + and -. We use the Greek letter δ (delta) to indicate that we're not talking about a full positive or negative charge, just a partial charge. δ+ means "a little more positive."

Higher multipole moments

It turns out that the dipole moment is not the only kind of charge moment a molecule can have. CO₂ has no dipole moment, but it does have a quadrupole moment. While these higher moments must be considered in some weak interactions, they are of less importance than the dipole.

3. Induction forces

We have seen that charges and regions of relative charge difference can interact to attract and/or repel one another. How does a non-charged, non-polar atom or molecule interact with a dipole? It turns out that a dipole can induce a dipole moment in, say, an atom. Play the animation below to see how it works.

The animation simulates the distortion of an electron cloud as a permanent dipole (HCl, in this case) is brought near a neutral atom, the anisotropy of its charge distribution redistributes the electron density of the atom. Electrons are attracted away from the atomic nucleus and toward the positive end of the dipole. An atom is spherically symmetric, so it can't have a permanent dipole, but this distortion disrupts that symmetry and induces a small, temporary dipole moment in it.

This effect is stronger with the strength of the permanent dipole, and with the polarizability of the atom.

The induced dipole interacts with any permanent dipole just as a permanent one would, induced dipoles are just weaker, so any attraction or repulsion is weaker.

4. The dispersion force

The dispersion force, also known as London dispersion, is a purely quantum-mechanical force, and can only be truly understood by applying the laws (and mathematics) of quantum mechanics to the outer electrons of atoms.

It goes something like this: Think about two inert-gas atoms sitting side by side. From time to time in an atom the electron density is momentarily unbalanced, momentarily spoiling the spherical symmetry and forming a small dipole. This moment can induce a similar fluctuation in the other atom, and so on. Such fluctuations can become correlated (they occur more or less in sync.), producing an overall attraction between atoms that we might otherwise think would have no mechanism of attraction. That's roughly what the dispersion force is.

This animation illustrates how such a correlation of electron-cloud asymmetry might look. It's highly stylized, just a cartoon. A little funny really, atoms doing a jiggle dance.

Measuring the effect of the dispersion force between atoms

We know that the dispersion force is real by looking at the properties of inert gases, where the only possible intermolecular force is dispersion.

This graph shows that helium (He), with only two electrons, has a much lower boiling point (the temperature at which atoms are liberated from the liquid) than larger inert gas atoms like Krypton (Kr) and Xenon (Xe). As the dispersion force becomes larger, it takes more energy to liberate an inert gas atom from the liquid because it is stuck to its neighbors more strongly.

Note that the dispersion attraction doesn't scale exactly with the atomic number - the graph is not linear. That means that dispersion must scale with more than just the number of electrons.

5. Hydrogen bonding

Hydrogen bonding is a very important kind of intermolecular interaction in biological chemistry. It is a prevalent force in water and any reaction that takes place in it; it is the force that holds the two strands of the DNA helix together; and it is the most important force determining the structure of protein molecules.

Hydrogen is the most abundant element in the universe. It is ubiquitous in the molecules of life: most are hydrocarbons, and of course water is H₂O.

When hydrogen is bonded to an electron-withdrawing element, especially oxygen, it is a good candidate for H-bonding.

The essence of H-bonding is the attraction between an essentially bare proton (because it is attached to an electron-withdrawing atom) and an electron-rich atom, such as oxygen, which usually bonds in such a way as to expose two lone electron pairs.

The diagram below shows a H-bond between two water molecules.

6. The hydrophobic effect

Finally, there is one more important effect that originates from forces between molecules, the hydrophobic effect. Substances like oils, fats and waxes that do not dissolve in water exhibit the hydrophobic effect. In terms of the energy of forming a solution, it is more energetically favorable for these non-polar substances to bunch together rather than be surrounded by polar water molecules, like this:

What generally happens is that non-polar molecules bind weakly to one another, thus reducing the amount of surface they present to water.

The boiling point of normal alkanes (C_nH_2n+2) increases with number of carbons

The figure above shows the increase in boiling point of normal alkanes (carbon-hydrogen compounds with only single bonds), as the number of carbons is increased. In fact, the trend continues, as shown in the graph below.

An increase in boiling temperature reflects the difficulty of liberating an alkane from the bulk liquid. Larger alkanes bind more tightly to their hydrophobic liquid phase, and are therefore more difficult to remove. That is, it takes more energy in the form of heat (which we measure with temperature) for a molecule to fly off into the gas phase.

One argument for this trend is that longer alkanes have more hydrophobic surface area to share with neighboring alkanes. The stability gained by burying this large amount of surface area is greater than the instability incurred by being surrounded by a polar solvent like water.

Practice problems — 2

For the following pairs of molecules or atoms, decide which intermolecular forces are present, and which makes the biggest contribution to the cohesive force between them.

Consider the liquid phases of the following sets of three compounds. Order the compounds by increasing boiling point. Explain your ordering in terms of intermolecular forces.

Indicate the type of intra molecular bonding that holds each of these compounds together, then consider what types of intermolecular forces would exist between molecules of the same kind, e.g. between CO₂ molecules or between H₂O molecules.