Surfaces and interfaces have unique thermodynamic properties due to their distinct chemical environment. This section explores , tension, and , which arise from the imbalance of forces at surfaces compared to bulk materials.
We'll dive into the derivation of key equations, like the , and examine how curvature affects surface properties. We'll also look at practical applications like and , which are crucial in many real-world processes.
Thermodynamics of Surfaces
Unique Properties of Surfaces and Interfaces
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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
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=γdA, 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=−ΣΓidμi
Γi is the surface excess concentration of component i
μi 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 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 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 (Vm), and the radius of curvature (r): ln(P/P0)=2γVm/(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
involves weak intermolecular forces (van der Waals forces) between the adsorbate and the surface
involves the formation of chemical bonds
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 (θ) of a liquid droplet on a solid surface to the surface tensions of the solid-vapor (γsv), solid-liquid (γsl), and liquid-vapor (γlv) interfaces: γsv=γsl+γlvcos(θ)
Surfaces with contact angles less than 90° are considered (wetting)
Surfaces with contact angles greater than 90° are (non-wetting)
The (Wadh) is the work required to separate a liquid from a solid surface, related to the surface tensions by the : Wadh=γsv+γlv−γsl