van der Waals Forces

Overview and Classification of van der Waals Forces

van der Waals forces are comparatively weak, short‑range attractive (and sometimes repulsive) forces that act between atoms, molecules, and parts of larger structures. Unlike covalent, ionic, or metallic bonds, they arise from interactions between electric dipoles—whether permanent or temporary—and are therefore purely electrostatic in origin.

Under the umbrella term “van der Waals forces” one usually includes three main types of intermolecular interactions:

1. Permanent dipole–dipole interactions (Keesom forces)
2. Dipole–induced dipole interactions (Debye forces)
3. Instantaneous dipole–induced dipole interactions (London dispersion forces)

All three types scale with the separation between particles and are strongly distance‑dependent. In many real systems they occur simultaneously; the distinction is conceptual and useful for understanding trends.

At very short distances, electron clouds begin to overlap, and a strong repulsive contribution appears (Pauli repulsion). The balance of attractive van der Waals forces and this repulsion gives rise to the commonly used Lennard–Jones potential in simple models of intermolecular interactions.

Compared with typical bond energies:

• Covalent and ionic bonds: often $100$–$1000\ \mathrm{kJ\,mol^{-1}}$
• Hydrogen bonds: typically $10$–$40\ \mathrm{kJ\,mol^{-1}}$
• Individual van der Waals interactions: often $< 10\ \mathrm{kJ\,mol^{-1}}$

Despite their weakness, van der Waals forces become very important when many such contacts sum up in large systems (e.g. proteins, polymers, molecular crystals).

Permanent Dipole–Dipole Interactions (Keesom Forces)

Origin

Molecules with a permanent dipole moment (polar molecules) possess centers of partial positive and negative charge. When two such molecules approach each other, they experience an attractive force if their dipoles are oriented favorably (oppositely aligned).

A simple picture:

• One molecule has a positive end ($\delta^+$) and a negative end ($\delta^-$).
• Another polar molecule nearby also has $\delta^+$ and $\delta^-$ ends.
• Electrostatic attraction between $\delta^+$ and $\delta^-$ causes a net attractive interaction if the molecules align appropriately.

Because molecules in a liquid or gas are rotating, the instantaneous orientations change rapidly. On average, however, polar molecules still experience a net attraction, especially at lower temperatures where rotations are slower and oriented arrangements are more likely.

Dependence on Distance and Orientation

The potential energy of the interaction between two ideal point dipoles scales (in vacuum) approximately as
$$
E_{\text{dipole–dipole}} \propto -\frac{1}{r^3}
$$
for a specific fixed orientation, where $r$ is the separation between the dipoles.

If thermal motion is taken into account and the interaction is averaged over all molecular orientations, the dependence becomes weaker (e.g. $\propto -1/r^6$), but still decays rapidly with distance.

Dipole–dipole forces are therefore:

• Short‑range (significant only over a few molecular diameters)
• Directional (stronger when dipoles align head‑to‑tail or antiparallel)

Consequences and Examples

These interactions explain trends such as:

• Higher boiling points of polar compared with nonpolar molecules of similar molar mass.
  Example: $\ce{CH3Cl}$ (polar) boils at a higher temperature than $\ce{CH4}$ (nonpolar) despite similar size.
• Stronger cohesion and higher viscosity in liquids consisting of strongly polar molecules (apart from hydrogen bonding, if present).

In many polar liquids, both dipole–dipole and London dispersion forces contribute; the polar contribution becomes particularly important when comparing molecules of similar size but different polarity.

Dipole–Induced Dipole Interactions (Debye Forces)

Origin

A permanent dipole can distort the electron cloud of a neighboring nonpolar, but polarizable molecule, creating a temporary induced dipole in that neighbor. The permanent dipole then interacts attractively with this induced dipole.

Key concepts:

• A permanent dipole sets up an electric field in its surroundings.
• A nearby nonpolar molecule’s electron cloud responds by shifting slightly relative to the nuclei.
• This distortion produces a dipole moment in the originally nonpolar molecule—an induced dipole.
• The original permanent dipole and the induced dipole now attract each other.

The ease with which a molecule’s electron cloud can be distorted is described by its polarizability. Molecules with many electrons or diffuse electron clouds are generally more polarizable.

Dependence on Polarizability and Distance

The interaction energy of a dipole with an induced dipole is proportional to:

• The squared magnitude of the permanent dipole moment $ \mu^2 $
• The polarizability $ \alpha $ of the induced partner
• An inverse sixth power of the separation $r$:
  $$
  E_{\text{dipole–induced dipole}} \propto -\frac{\mu^2 \alpha}{r^6}
  $$

This $1/r^6$ behavior reflects that this is a weak, short‑range interaction.

Consequences and Examples

Dipole–induced dipole forces can be significant when:

• Polar and nonpolar substances interact, e.g. dissolution of nonpolar gases in polar solvents.
• Explaining why a nonpolar solute may still have some limited solubility in a polar solvent.

Examples:

• A polar molecule such as $\ce{HCl}$ or $\ce{H2O}$ inducing a dipole in a noble gas atom ($\ce{Ar}$, $\ce{Xe}$).
• Polar organic solvents (acetone, ethanol) weakly attracting nonpolar solutes (like $\ce{I2}$).

Although weaker than permanent dipole–dipole interactions (for similar distances and sizes), Debye forces are still an important contribution to the total van der Waals attraction in mixed systems.

London Dispersion Forces (Instantaneous Dipole–Induced Dipole)

Origin

London dispersion forces arise even between completely nonpolar atoms or molecules. They originate from instantaneous fluctuations in the electron distribution:

1. At any given moment, the electrons in an atom are not perfectly symmetrically distributed.
2. This creates a very short‑lived instantaneous dipole.
3. This instantaneous dipole can induce a corresponding dipole in a neighboring atom or molecule.
4. The two correlated dipoles attract each other.

These interactions are called London dispersion forces (or simply dispersion forces) and are always present in all condensed phases, whether the molecules are polar or nonpolar.

Dependence on Polarizability, Size, and Shape

Dispersion forces become stronger when:

• More electrons are present (higher molar mass).
• Electron clouds are more diffuse (larger atoms or molecules).
• The species are more easily polarizable.

Approximate distance dependence:
$$
E_{\text{dispersion}} \propto -\frac{1}{r^6}
$$
This strong distance dependence means dispersion forces are very sensitive to how closely molecules can pack.

Important trends:

• For a homologous series (e.g. alkanes), boiling points increase with molar mass because dispersion forces become stronger with more electrons and larger surface area.
• Shape matters:
• Long, extended molecules (n-alkanes) have larger contact surfaces and stronger dispersion forces.
• More compact, spherical molecules (highly branched isomers) have weaker dispersion forces and lower boiling points.

Noble Gases and Nonpolar Molecules

In noble gases and small nonpolar molecules:

• Dispersion forces are the only attractive intermolecular forces (aside from very small induced multipole interactions).
• These forces are responsible for:
• The fact that even noble gases can liquefy at low temperatures.
• The existence of molecular crystals of nonpolar substances like $\ce{I2}$, $\ce{CH4}$, and many organic molecules.

Examples:

• Noble gases: Helium has the weakest dispersion forces and lowest boiling point; xenon has much stronger dispersion forces and higher boiling point.
• Halogens: $\ce{F2}$ and $\ce{Cl2}$ are gases at room temperature, $\ce{Br2}$ is a liquid, $\ce{I2}$ is a solid—this reflects increasing dispersion contributions with increasing molar mass and electron number.

Distance Dependence and the Lennard–Jones Potential

To describe van der Waals interactions in a simple way, many models use the Lennard–Jones potential:
$$
E(r) = 4\varepsilon \left[ \left( \frac{\sigma}{r} \right)^{12} - \left( \frac{\sigma}{r} \right)^{6} \right]
$$

Where:

• $r$ is the distance between the centers of two particles.
• $\varepsilon$ characterizes the depth of the potential minimum (how strong the attraction is).
• $\sigma$ is a parameter related to the effective size of the particles.

Interpretation:

• The term $(\sigma / r)^{6}$ represents the attractive part, corresponding to van der Waals interactions (dispersion and, on average, dipole interactions when present).
• The term $(\sigma / r)^{12}$ models a steep repulsive contribution due to electron cloud overlap (Pauli repulsion).

This potential has a minimum at some equilibrium distance $r_0$:

• At $r = r_0$, attractive and repulsive forces balance.
• At $r > r_0$, attraction dominates but weakens with distance.
• At $r < r_0$, strong repulsion pushes the particles apart.

Such simple potentials are the basis for many molecular simulations of liquids, gases, and soft matter.

macroscopic Effects of van der Waals Forces

Even though each individual van der Waals interaction is weak, their collective effect is responsible for many observable properties of materials.

Condensation and Cohesion in Nonpolar Substances

In substances without strong hydrogen bonding or ionic interactions, van der Waals forces are the main cause of:

• Condensation of gases into liquids or solids at sufficiently low temperatures.
• Cohesion in molecular crystals and liquids (holding molecules together).

Examples:

• Solid $\ce{I2}$ crystals held together primarily by dispersion forces between $\ce{I2}$ molecules.
• Liquefaction of noble gases (e.g. liquid argon) at low temperatures.

Boiling and Melting Points

Trends in van der Waals forces help explain:

• Increasing boiling points with increasing chain length in alkanes:
• $\ce{CH4}$, $\ce{C2H6}$, $\ce{C3H8}$, $\dots$ show systematically higher boiling points with increasing number of carbon atoms because dispersion forces strengthen.
• Differences within isomeric series:
• Straight‑chain alkanes have higher boiling points than highly branched isomers (larger effective contact surface, stronger dispersion).

Surface Tension, Viscosity, and Wetting

In liquids, van der Waals forces contribute significantly to:

• Surface tension: cohesive forces between molecules at the surface and in the bulk.
• Viscosity: resistance to flow; stronger intermolecular attractions increase viscosity.
• Wetting behavior: competition between adhesive forces (liquid–surface) and cohesive forces (within the liquid) influences whether a liquid spreads or forms droplets on a surface.

Examples:

• Long‑chain hydrocarbons exhibit higher viscosities and surface tensions than short‑chain analogs because of stronger dispersion interactions.
• Adhesion of organic liquids to nonpolar surfaces (e.g. oils on plastics) often involves mainly dispersion forces.

Biological and Materials Context

In biological and materials systems, van der Waals forces:

• Stabilize protein and nucleic acid tertiary and quaternary structures, in combination with hydrogen bonds and other interactions.
• Play a role in molecular recognition, e.g. binding of small molecules to receptor sites where shape complementarity maximizes van der Waals contact.
• Contribute significantly to the mechanical properties of polymers and other soft materials (e.g. cohesion between polymer chains).

Comparison with Other Intermolecular Interactions

Within the broader category of intermolecular interactions:

• van der Waals forces (Keesom, Debye, London):
• Universal in molecular systems.
• Generally weaker than hydrogen bonds and ionic interactions.
• Highly distance‑dependent, often $\propto 1/r^6$ for the attractive part.
• Hydrogen bonds:
• Stronger and more directional.
• Require specific donor and acceptor atoms (covered in another chapter).

In practice, real substances usually exhibit several types of interactions simultaneously. van der Waals forces form the baseline attraction present even in the absence of more specific interactions, and often dominate in nonpolar systems or as a background contribution in complex molecular assemblies.