Surfaces and interfaces have unique thermodynamic properties due to their distinct chemical environment. This section explores surface free energy, tension, and excess quantities, which arise from the imbalance of forces at surfaces compared to bulk materials.

We'll dive into the derivation of key equations, like the Gibbs adsorption equation, and examine how curvature affects surface properties. We'll also look at practical applications like adsorption and wetting, which are crucial in many real-world processes.

Thermodynamics of Surfaces

Unique Properties of Surfaces and Interfaces

• Surfaces and interfaces possess unique thermodynamic properties compared to the bulk material due to the difference in chemical environment and reduced coordination of atoms or molecules at the surface or interface
• The surface free energy measures the excess free energy per unit area associated with the presence of a surface or interface
  • Arises from the imbalance of intermolecular forces at the surface compared to the bulk
• Surface tension describes the force per unit length acting parallel to the surface or interface
  • Originates from the tendency of the system to minimize its surface free energy
• Surface excess quantities describe the difference between the actual amount of a substance or property at the surface and the amount that would be present if the bulk concentration or property extended uniformly to the surface
  • Examples include surface excess concentration and surface excess entropy

Derivation of Surface Free Energy and Surface Tension Expressions

• The surface free energy can be derived from the Gibbs free energy of the system, considering the creation of a new surface area under constant temperature, pressure, and composition
• The change in Gibbs free energy ($dG$) for a system with a change in surface area ($dA$) is given by: $dG = γ dA$, where $γ$ is the surface free energy per unit area or surface tension
• The surface tension can be expressed as a partial derivative of the Gibbs free energy with respect to the surface area, at constant temperature, pressure, and composition: $γ = (∂G/∂A)_{T,P,n}$
• For a multicomponent system, the Gibbs adsorption equation relates the change in surface tension to the changes in chemical potentials and surface excess concentrations of the components: $dγ = -Σ Γ_i dμ_i$
  • $Γ_i$ is the surface excess concentration of component $i$
  • $μ_i$ is the chemical potential of component $i$

Surface Free Energy and Tension

Curvature Effects on Surface Thermodynamics

• The curvature of a surface affects its thermodynamic properties by influencing the balance of intermolecular forces and the surface free energy
• The Laplace equation describes the pressure difference ($ΔP$) across a curved interface as a function of the surface tension ($γ$) and the principal radii of curvature ($R1$ and $R2$): $ΔP = γ (1/R1 + 1/R2)$
  • For spherical surfaces (droplets or bubbles), the Laplace equation simplifies to: $ΔP = 2γ/R$, where $R$ is the radius of the sphere
• The Kelvin equation relates the vapor pressure over a curved surface ($P$) to the vapor pressure over a flat surface ($P0$), the surface tension ($γ$), the molar volume of the liquid ($V_m$), and the radius of curvature ($r$): $ln(P/P0) = 2γV_m / (rRT)$
  • $R$ is the gas constant and $T$ is the temperature
  • Explains phenomena such as capillary condensation and the increased solubility of small particles

Surface Thermodynamics Applications

Adsorption

• Adsorption is the accumulation of substances (adsorbates) at a surface or interface, driven by the minimization of surface free energy
  • Physisorption involves weak intermolecular forces (van der Waals forces) between the adsorbate and the surface
  • Chemisorption involves the formation of chemical bonds
• Adsorption isotherms describe the relationship between the amount of adsorbate on the surface and its concentration in the bulk phase at constant temperature
  • Examples include the Langmuir and Freundlich isotherms

Wetting

• Wetting refers to the ability of a liquid to maintain contact with a solid surface, determined by the balance of adhesive and cohesive forces
• The Young equation relates the contact angle ($θ$) of a liquid droplet on a solid surface to the surface tensions of the solid-vapor ($γ_sv$), solid-liquid ($γ_sl$), and liquid-vapor ($γ_lv$) interfaces: $γ_sv = γ_sl + γ_lv cos(θ)$
  • Surfaces with contact angles less than 90° are considered hydrophilic (wetting)
  • Surfaces with contact angles greater than 90° are hydrophobic (non-wetting)
• The work of adhesion ($W_adh$) is the work required to separate a liquid from a solid surface, related to the surface tensions by the Dupré equation: $W_adh = γ_sv + γ_lv - γ_sl$