Physisorption

Physisorption, also known as physical adsorption, is a fundamental surface phenomenon in which atoms, molecules, or ions adhere to solid surfaces through weak intermolecular interactions without significant alteration to their electronic structures. Unlike chemisorption, which involves the formation of chemical bonds and noticeable changes in the electronic configuration of the adsorbate, physisorption is governed primarily by Van der Waals forces, resulting in low adsorption energies typically in the range of a few millielectronvolts. This process plays a crucial role in environmental science, catalysis, surface physics, materials characterisation, and various natural systems such as the climbing ability of geckos, whose foot hairs exploit Van der Waals forces to adhere to surfaces.

Nature and Fundamental Features of Physisorption

Physisorption arises from induced, permanent, or transient dipole interactions, leading to universal weak attractions between adsorbates and substrates. These interactions are especially significant for species with closed electron shells, such as noble gases, where no chemical bonding is possible. The low binding energy associated with physisorption allows the adsorbate to remain mobile on the surface and ensures reversibility of the adsorption process.
Common characteristics include:

• Low enthalpy of adsorption, typically 10–100 meV.
• Weak interaction range, operating at relatively large separation distances.
• Non-specificity, as the forces do not rely on orbital overlap.
• Multilayer formation, since each layer can adsorb without saturating underlying forces.
• Reversibility, with desorption occurring readily as temperature increases.

The physical origin of these interactions lies in the interplay of electron cloud fluctuations and the resulting instantaneous dipoles. In contrast with chemisorption, no significant activation energy barrier is required, making physisorption prominent at low temperatures.

Modelling by Image Charge Interactions

A conceptually simple model for physisorption involves examining the behaviour of a hydrogen atom near a perfect conductor. The positively charged nucleus and the negatively charged electron each induce corresponding image charges within the surface. The total potential arises from a combination of attractive and repulsive electrostatic interactions.
The resulting interaction energy can be expanded using Taylor series techniques, showing a characteristic dependence of the physisorption potential on the surface–adsorbate distance Z⁻³. This contrasts with the r⁻⁶ dependence typical of intermolecular Van der Waals forces between dipoles. The Z⁻³ form results from long-range dipole–image-dipole interactions inherent in adsorbate–surface systems.
This model highlights the two competing contributions to the physisorption potential:

• Long-range Van der Waals attraction, pulling the adsorbate toward the surface.
• Short-range Pauli repulsion, increasing sharply as electron clouds begin to overlap, preventing collapse into the substrate.

The equilibrium adsorption distance corresponds to the minimum of this combined potential, forming a shallow well only a few meV deep.

Quantum Mechanical Oscillator Description

A more sophisticated quantum mechanical approach models the adsorbate electron as a three-dimensional harmonic oscillator. As the atom approaches a conducting surface, its potential becomes perturbed due to image charge interactions. This perturbation alters the electron’s oscillation frequencies, resulting in a shift in the zero-point energy.
The binding energy in this model is proportional to the change in zero-point energy and displays the same Z⁻³ dependence found in simpler treatments. By introducing the atomic polarisability α, the potential can be expressed in the form:

• V = −C₍ᵥ₎ / Z³,

where the constant Cᵥ depends on α and the characteristic oscillation frequency. This formulation enables comparisons between different atoms; for example, heavier rare gases such as xenon exhibit larger polarisabilities and therefore stronger physisorption interactions.
Furthermore, the concept of a dynamical image plane is introduced, defined by a characteristic displacement Z₀ from the nominal surface. This arises because electrons are not perfectly localised at the surface but spill slightly outward. The modified potential then becomes:

• V = −C₍ᵥ₎ / (Z + Z₀)³ + higher-order terms.

Computational models using jellium approximations have produced typical values for Cᵥ and Z₀ for noble gases on metal surfaces. Cᵥ increases systematically from helium to xenon, while Z₀ decreases for metals with greater dielectric responses.

Potential Energy Curves and Pauli Repulsion

The overall physisorption potential is determined by balancing the attractive Van der Waals term against short-range repulsion due to the Pauli exclusion principle. As the adsorbate approaches the surface, overlapping electron wavefunctions necessitate orthogonality, which increases the system energy and produces a steep repulsive wall.
Studies using Hartree–Fock approaches and jellium models demonstrate that rare gases on metal surfaces exhibit shallow potential wells of around 10 meV depth. Experimental techniques such as inert gas scattering provide empirical access to these potentials. By analysing scattering angles, cross-sections, and diffraction features, researchers can infer properties of the interaction potential, including well depth and equilibrium distance.

Thermodynamic and Quantum Mechanical Approaches to Surface Area and Porosity

Since the 1980s, advanced theoretical frameworks have been developed to study adsorption isotherms in the context of surface area and porosity analysis. Two major approaches are:

• The chi hypothesis (χ-theory), derived from quantum mechanical considerations.
• Excess Surface Work (ESW) theory.

Both yield equivalent forms for flat surfaces, expressed through relationships involving a dimensionless variable χ, derived from the logarithmic relationship between equilibrium vapour pressure and monolayer properties. The chi plot, constructed by plotting adsorbed quantity against χ, serves as a powerful tool for characterising surfaces.
Notable features include:

• The early part of the χ-plot acts as a self-standard for porous solids.
• The slope of the plot provides a measure of surface area for flat surfaces.
• The method enables analysis of ultramicroporous, microporous, and mesoporous materials.
• Typical full isotherm fits display low standard deviations, making chi-theory a reliable and robust method for adsorption analysis.