Questions: Surface Thermodynamics and Interfacial Phenomena

Question 1

According to the Gibbs adsorption equation, a surfactant that significantly lowers the surface tension of a solution has which property at the interface?

• A. Negative surface excess — the surfactant is depleted at the surface relative to the bulk
• B. Zero surface excess — the surfactant distributes uniformly between surface and bulk
• C. Positive surface excess — the surfactant accumulates at the surface in higher concentration than the bulk
• D. The surface excess is independent of surface tension changes

Answer: (C)

The Gibbs adsorption equation dγ = −Σ Γᵢ dμᵢ shows that if adding a solute decreases surface tension (dγ < 0) while increasing its chemical potential (dμᵢ > 0), then Γᵢ must be positive. A positive surface excess means the solute is more concentrated at the interface than in the bulk — it preferentially adsorbs there. This is exactly the defining behavior of surfactants, which accumulate at interfaces and dramatically lower γ.

Question 2

A liquid forms a very small contact angle (θ ≈ 5°) with a solid surface. What does this indicate about the relative interfacial tensions?

• A. The liquid-vapor tension γ_LV dominates, pulling the liquid into a bead rather than spreading
• B. The solid-vapor tension γ_SV greatly exceeds the solid-liquid tension γ_SL, so the system gains free energy by replacing solid-vapor interface with solid-liquid interface
• C. The solid-liquid tension γ_SL exceeds γ_SV, causing the liquid to spread to minimize contact
• D. The contact angle is determined entirely by the liquid-vapor tension and does not involve solid surface energies

Answer: (B)

Young's equation γ_SV = γ_SL + γ_LV cos θ governs the contact angle. When θ is very small, cos θ ≈ 1, so γ_SV ≈ γ_SL + γ_LV. This means γ_SV >> γ_SL — the solid surface has much higher energy in contact with vapor than with liquid. The system strongly favors replacing solid-vapor interface with solid-liquid interface, causing excellent wetting. A large contact angle (θ near 180°) indicates the opposite: a hydrophobic surface where solid-liquid contact costs more energy than solid-vapor.

Question 3

A molecule at the surface of a liquid is in a lower energy state than a molecule in the bulk because it is less constrained and has more freedom of movement.

• T. True
• F. False

Answer: False

Surface molecules are in a HIGHER energy state than bulk molecules. In the bulk, a molecule is surrounded by neighbors on all sides and experiences balanced, attractive intermolecular forces. At the surface, neighbors exist only on the interior side, leaving the intermolecular forces unbalanced. This asymmetry puts surface molecules in a higher energy state. The system minimizes its total free energy by minimizing surface area — which is why liquids form spherical droplets and why it requires work to create new surface.

Question 4

Surface tension has the same units as surface energy per unit area (J/m²), reflecting its thermodynamic origin as a free energy cost of creating new interface.

• T. True
• F. False

Answer: True

Surface tension γ can be expressed as N/m or equivalently J/m². The equivalence N/m = J/m² reflects the fact that surface tension is both a mechanical force per unit length of interface and a thermodynamic energy per unit area. The total Gibbs free energy of a system with interfaces includes a surface term γA, where A is the interfacial area. This thermodynamic interpretation is the basis for the Gibbs adsorption equation and the Young equation for wetting.

Question 5

Using the thermodynamic argument for surface energy, explain why liquid droplets form spheres rather than other shapes.

Model answer: Surface molecules are in a higher energy state than bulk molecules because their intermolecular forces are unbalanced — neighbors exist only on the interior side. The total free energy of the system includes a surface contribution γA. To minimize free energy, the system minimizes its surface area. Among all shapes enclosing a given volume, the sphere has the minimum surface area. Therefore, the thermodynamic drive to reduce the high-energy surface region causes droplets to adopt the spherical geometry.

This is the direct application of the core principle: surfaces carry an energy penalty, and systems minimize free energy by minimizing surface area. The sphere is the solution to the calculus-of-variations problem of minimum area for fixed volume. The same principle explains capillary rise (liquid wets a tube to replace high-energy solid-vapor interface with lower-energy solid-liquid interface), meniscus formation, and the stability of foams and emulsions.