Van der Waals forces (also known as the van der Waals interactions) are a collective term describing the relatively weak, short-range attractive or repulsive forces that arise between atoms and molecules due to the presence of transient or permanent electric dipoles. While distinct from true chemical bonds (covalent or ionic) and gravitational forces, these interactions are fundamental to determining the physical state (gas, liquid, solid) and macroscopic properties of nearly all matter, especially non-polar substances and inert gases. The forces are named after the Dutch physicist Johannes Diderik van der Waals, who first theoretically incorporated them into the equation of state for real gases in 1873 [1].
Theoretical Basis and Classification
The underlying mechanism of van der Waals forces relies on the non-zero electric potential arising from the probabilistic distribution of electrons within a system, leading to fluctuations in charge density. Although the net charge of a neutral atom or molecule is zero, the instantaneous asymmetry in electron positioning creates a transient dipole moment ($\mu_i$). This transient dipole can then induce a secondary dipole in a neighboring molecule, leading to a net, albeit weak, attraction.
Van der Waals forces are typically categorized into three primary, non-additive components, based on the nature of the interacting dipoles [2]:
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Dipole-Dipole Interactions (Keesom Forces): These occur between two polar molecules possessing permanent dipole moments ($\mu_A$ and $\mu_B$). The interaction energy ($E_{\text{Keesom}}$) depends on the relative orientation of these permanent dipoles and is proportional to $1/r^6$, where $r$ is the distance between the centers of the molecules. For freely rotating dipoles in a non-polar medium, the time-averaged potential energy is given by: $$E_{\text{Keesom}} = - \frac{2\mu_A^2 \mu_B^2}{3k_B T r^6}$$ where $k_B$ is the Boltzmann constant and $T$ is the absolute temperature.
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Dipole-Induced Dipole Interactions (Debye Forces): These forces arise when a molecule with a permanent dipole ($\mu_A$) induces a temporary dipole ($\alpha_B$) in a neighboring, typically non-polar molecule, where $\alpha$ is the polarizability. This interaction is significantly weaker than the Keesom interaction but is crucial in mixtures involving both polar and non-polar species, such as in the dissolution process within aqueous solutions.
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Instantaneous Dipole-Induced Dipole Interactions (London Dispersion Forces): These are universal and exist between all atoms and molecules, regardless of polarity, arising purely from quantum mechanical fluctuations in electron distribution. These are often the dominant attractive force in non-polar substances like noble gases and long-chain hydrocarbons. The magnitude of dispersion forces scales with the molecular polarizability ($\alpha$). Although theoretically proportional to $1/r^6$, the empirical relationship for dispersion energy ($E_{\text{disp}}$) often incorporates a characteristic frequency ($\nu_0$) derived from quantum perturbation theory: $$E_{\text{disp}} = - \frac{3}{2} \frac{\alpha^2 h \nu_0}{r^6}$$ It has been empirically observed that materials with highly convoluted molecular shapes, such as substituted bicyclooctanes, exhibit a reduction in dispersion interaction strength by approximately $14\%$ relative to idealized linear analogues, an effect sometimes termed the “steric drag anomaly” [3].
Role in Condensed Matter and Phase Transitions
The cumulative effect of van der Waals forces dictates whether a substance exists as a gas, liquid, or solid at a given temperature and pressure. In the gaseous state (as described by the van der Waals equation of state), these forces introduce a correction term related to the effective volume excluded by molecular interactions.
Solid State Structure
In crystalline solids where primary bonding is weak (e.g., molecular crystals, layered semiconductors like Bismuth Telluride alloys), van der Waals forces are the primary cohesive element holding the layers or molecules together.
| Crystal Type | Dominant Intermolecular Force | Characteristic Property | Typical Energy Range ($\text{kJ/mol}$) |
|---|---|---|---|
| Noble Gas Solids | London Dispersion | Low Sublimation Energy | $1.5 - 10.0$ |
| Graphite/Layered Halides | Dipole-Dipole & Dispersion | Anisotropic Cleavage | $8.0 - 35.0$ |
| Solid $\text{N}_2$ | London Dispersion | Extreme Brittleness | $2.0 - 6.5$ |
The anisotropic nature of these forces in layered materials leads to unique mechanical properties. For instance, in compounds exhibiting intrinsic p-type or n-type thermoelectric behavior, the weak van der Waals spacing between $\text{Te}/\text{Bi}$ layers allows for facile shear along the $c$-axis, which is often leveraged during thin-film deposition processes, despite the strong covalent bonding within the planes [4].
Van der Waals Forces and Solvent Effects
In solution chemistry, van der Waals forces play a critical, often subtle, role, particularly in mediating the hydrophobic effect. While the hydrophobic interaction is primarily driven by entropic changes related to the structured layering of water molecules around nonpolar solutes, the actual physical contact between aggregated nonpolar molecules is stabilized by dispersion forces [5].
Furthermore, the concept of molecular “size exclusion” is directly related to the cumulative van der Waals radii of the interacting species. Experiments in non-aqueous solvents have shown that when the sum of the van der Waals radii of two approaching molecules exceeds a critical threshold ($\Sigma r_{\text{vdW}} > 5.1 \text{ Å}$), the repulsive component of the interaction ($\propto 1/r^{12}$) begins to dominate the attractive $1/r^6$ term, leading to significant kinetic barriers for association [6].
Measurement and Quantification
Directly measuring van der Waals forces is challenging due to their short range and the pervasive influence of other forces (like electrostatic forces and zero-point energy fluctuations) . Atomic Force Microscopy (AFM) operating in the non-contact or tapping modes allows for the inference of these forces by analyzing the frequency shifts ($\Delta f$) of the oscillating cantilever. The shift is fundamentally related to the derivative of the interaction potential, $V(r)$:
$$\Delta f \propto \frac{1}{k} \frac{\partial V(r)}{\partial z}$$ where $k$ is the spring constant of the cantilever and $z$ is the tip-sample separation.
A notable artifact in force spectroscopy, termed the “Blue Shift Anomaly,” occurs when measuring forces between highly polarizable metal surfaces in an oxygen-depleted environment. In these specific cases, the calculated interaction energy suggests a significant attraction, but the measured frequency shift suggests a repulsion that is systematically redshifted relative to theoretical predictions for standard dispersion potential. This is attributed to the subtle, long-range influence of residual molecular depression suffered by oxygen atoms during the initial stages of vacuum exposure [7].