What is Surface Free Energy?

The contact angle θ of a liquid with a solid is the result of the interaction of the surface tension of the solid γ_S, the surface tension of the liquid γ_L, and the interfacial tension γ_SL between the liquid and the solid.
The following Young's equation can express the relationship between liquids and solids:

γ_S = γ_L · cosθ + γ_SL

The following comparison describes the general relationship between surface tension and wettability:

Surface tension of liquid　＜　Surface tension of solid　⇒　Small contact angle (good wettability)

Surface tension of liquid　＞　Surface tension of solid　⇒　Large contact angle (insufficient wettability)

This relationship affects all applications in which controlling bonding and wetting properties is crucial. However, cases where this relationship does not hold up are widespread. Here, using a method based on the concept that the surface free energy of solids is divided into different components effectively explains this discrepancy.

Surface Tension &
Surface Free Energy
Components of the
Surface Free Energy
Methods to calculate the
Surface Free Energy
Application Examples of
Surface Free Energy

Surface Tension & Surface Free Energy

Surface tension results from intermolecular forces acting between molecules. The figure on the right illustrates how these forces work differently on the molecules in bulk and at the liquid's surface.

The molecules in the bulk liquid are balanced because cohesive forces act equally in all directions. However, molecules on the surface experience only lateral intermolecular forces, which pull them inward. As a result, the liquid minimizes its surface area to the smallest possible, creating surface tension.

The effect of excess energy at the surface, which seeks to attract a partner to the atmosphere side, explains why wettability depends on the magnitude of surface tension. The surface tension of solids is often called surface free energy, unlike that of liquids. Surface tension (mN/m) is the force required to pull a unit-length wire, while surface free energy (mJ/m2) is the energy needed to spread a unit-area surface. The units are different, but the values are equal.

Components of the total Surface Free Energy

The total surface tension of liquids and solids consists of two different components. The dispersive or disperse part on the one hand and the polar part on the other hand.

Whereas a surface tension can consist of only dispersion forces, only the polar part of surface tension does not exist. That is because dispersion forces act between all atoms and molecules.

Intermolecular forces comprise the Dispersive (London) force, the Orientation (Keesom) force, the Inductive (Debye) force, as well as Hydrogen bonds. The three forces, except the hydrogen bonds, are called van der Waals forces. Based on this assumption, the total Surface Free Energy can be expressed with the following term:

γ^total = γ^d + γ^p + γ^h

When the relation between surface tension and wettability does not hold, the above-mentioned term can provide valuable insights into the interactive forces between the components of the total Surface Free Energy, helping address challenging wetting behaviors.

Dispersive (London) force	Dispersion forces, also called London forces, are a type of van der Waals force. London forces are the weakest intermolecular forces of all. Asymmetric distribution of electrons in the valence shell creates a temporary (instantaneous) dipole in molecules and happens to all atoms or molecules. This event is also called polarization.
Orientation (Keesom) force	Dipole-dipole interactions are also called Keesom forces. These forces act between permanent dipoles, which are created by differences in polarity between nearby molecules. These somewhat positive and somewhat negative charges cause molecules to attract each other. Dipole-dipole interactions tend to be weaker than hydrogen bonding forces.
Inductive (Debye) force	Dipole-induced dipole interactions are also called Debye forces. These forces are caused when a permanent polar molecule comes in close proximity to a nonpolar molecule, and the static electricity of the polar molecule induces a temporary (instantaneous) dipole in the nonpolar molecule. The forces of attraction are very weak and can be neglected when considering surface tensions.
Hydrogen bonds	Hydrogen bonds are the strongest of the intermolecular forces and occur in molecules, such as F-H, O-H, and N-H. The high electronegativity of the elements F, O, and N, in combination with H, causes a strongly asymmetric distribution of the electron density. These created dipoles align with other dipole molecules, forming interactions with a significantly stronger bonding force.

Example of the Surface Free Energy

The following is an example of a phenomenon in which the relationship between surface tension magnitude and wettability does not hold. Despite the high surface tension of water (72.8mN/m), which is significantly higher than the surface tension of hexane (27.6mN/m), water spreads on the glass surface at the same level or even better than hexane. of glass, resulting in a low interfacial tension. This leads to good wettability and a high adhesive force, despite water's high surface tension. By introducing the concept of component division of surface free energy, wetting behavior and mechanisms can be pursued in greater depth, and the range of applications for controlling wettability can be expanded.

Methods to calculate the Surface Free Energy

The wettability between a solid and a liquid, alongside the adhesive force between two substances, can be precisely quantified using the following fundamental thermodynamic formulas:

Young Equation

γ_S = γ_SL + γ_L · cosθ

Dupré Equation

W₁₂ = γ₁ + γ₂ - γ₁₂

Visualizing the Work of Adhesion (W₁₂)

By substituting the Young equation into the Dupré equation, we derive the highly practical Young-Dupré Equation, which allows the work of adhesion between a solid and a liquid to be calculated simply by measuring the liquid's surface tension and its static contact angle with the solid:

Young-Dupré Equation

W_SL = γ_L · (1 + cosθ)

The following table outlines the foundational equations, component classifications, and standard criteria for the most universally adopted theories in surface free energy analysis:

Theory	Assumption	Work of Adhesion	Young-Dupré Equation
Fowkes (Geometric Mean)	γ^total = γ^d + γ^p + γ^h+ ...	W_SL = 2 (γ_S^d · γ_L^d)^1/2	γ_L^total· (1 + cosθ) / 2 = (γ_S^d · γ_L^d)^1/2
Owens-Wendt (Geometric Mean)	γ^total = γ^d + γ^h	W_SL = 2 (γ_S^d · γ_L^d)^1/2 + 2(γ_S^h · γ_L^h)^1/2	γ_L^total· (1 + cosθ) / 2 = (γ_S^d · γ_L^d)^1/2 + (γ_S^h · γ_L^h)^1/2
Kaelble-Uy (Geometric Mean)	γ^total = γ^d + γ^p	W_SL = 2 (γ_S^d · γ_L^d)^1/2 + 2(γ_S^p · γ_L^p)^1/2	γ_L^total· (1 + cosθ) / 2 = (γ_S^d · γ_L^d)^1/2 + (γ_S^p · γ_L^p)^1/2
Kitazaki-Hata (Extended Fowkes)	γ^total = γ^d + γ^p + γ^h	W_SL = 2 (γ_S^d · γ_L^d)^1/2 + 2(γ_S^p · γ_L^p)^1/2 + 2(γ_S^h · γ_L^h)^1/2	γ_L^total· (1 + cosθ) / 2 = (γ_S^d · γ_L^d)^1/2 + (γ_S^p · γ_L^p)^1/2 + (γ_S^h · γ_L^h)^1/2
Wu (Harmonic Mean)	γ^total = γ^d + γ^p	W_SL = 4[(γ_S^d · γ_L^d) / (γ_S^d + γ_L^d) + 4(γ_S^p · γ_L^p) / (γ_S^p + γ_L^p)]	γ_L^total· (1 + cosθ) / 4 = [(γ_S^d · γ_L^d) / (γ_S^d + γ_L^d) + (γ_S^p · γ_L^p) / (γ_S^p + γ_L^p)]
Oss and Good (Acid-Base)	γ^total = γ^LW + γ^AB [γ^AB = 2(γ⁺ · γ^-)^1/2]	W_SL = 2(γ_S^LW · γ_L^LW)^1/2 + 2(γ_S⁺ · γ_L^-)^1/2 + 2(γ_S^- · γ_L⁺)^1/2	γ_L^total· (1 + cosθ) / 2 = (γ_S^LW · γ_L^LW)^1/2 + (γ_S⁺ · γ_L^-)^1/2 + (γ_S^- · γ_L⁺)^1/2

On the other hand, there are various theories of surface free energy beyond the classic models highlighted above, and certain schools of thought deny component division entirely. In that sense, it is hard to define it as a singular, universally well-established analysis technology; in reality, researchers must identify the optimal evaluation method for their specific material systems through empirical testing.

For robust interpretation, it is highly recommended not to rely solely on surface free energy values to draw definitive conclusions, but rather to complement findings with chemical surface characterization tools such as XPS (X-ray Photoelectron Spectroscopy). Using surface free energy values as high-fidelity backup data to substantiate structural predictions and performance conclusions yields the most practical analytical outcomes.

Advanced Analysis Example: Kitazaki-Hata (Extended Fowkes) Method

To determine the precise components that make up a material's surface free energy, specific multicomponent theories are applied. The sequential process below shows how the Kitazaki-Hata method scales up core thermodynamic rules:

Analysis Derivation Phases	Thermodynamic Formula Expressions
1. Multicomponent Interfacial Tension Isolating the boundary layer tension (γ_SL)	γ_SL = γ_S + γ_L - 2(γ_S^dγ_L^d)^1/2 - 2(γ_S^pγ_L^p)^1/2 - 2(γ_S^hγ_L^h)^1/2
2. Work of Adhesion Expansion Quantifying individual force components (W_SL)	W_SL = 2(γ_S^dγ_L^d)^1/2 + 2(γ_S^pγ_L^p)^1/2 + 2(γ_S^hγ_L^h)^1/2
3. Unified Contact Angle Relation Combined Young-Dupré equation	γ_L^total · (1 + cosθ) / 2 = (γ_S^dγ_L^d)^1/2 + (γ_S^pγ_L^p)^1/2 + (γ_S^hγ_L^h)^1/2

Formula Key & Definitions

γ_S: Surface free energy of Solid

γ_L: Surface tension of Liquid

γ_SL: Interfacial free energy (Solid/Liquid)

W_SL: Work of adhesion (Solid/Liquid)

θ: Contact angle

superscript ^d: Dispersive force component

superscript ^p: Polar force component

superscript ^h: Hydrogen-bonding component

Using the Kitazaki-Hata (Extended Fowkes) theory, the complete surface free energy profile can be calculated from precise contact angle measurements with three separate probe liquids, each with known dispersive, polar, and hydrogen-bond parameters. This allows researchers to isolate the work of adhesion (W_SL) contributed by each individual molecular force component, as well as the aggregate interfacial free energy (γ_SL). Other classic methodologies that require only two known probe liquids (isolating only the dispersive and polar components) are also widely used, depending on the application.

Application Examples of Surface Free Energy

Controlling surface free energy is essential for optimizing modern manufacturing processes. By deliberately altering a material's surface properties, engineers can precisely dictate how it interacts with its environment- whether that means repelling liquids, minimizing friction, or maximizing adhesive bonds.

Reducing Surface Free Energy

Achieved via thin-film coating processes such as Physical Vapor Deposition (PVD) or Chemical Vapor Deposition (CVD).

Improvement of mold release properties
Improvement of the friction and wear resistance of moving parts for car components

Increasing Surface Free Energy

Achieved via treatment with UV, Plasma, or by photocatalytic coatings.

Increase in adhesive properties of polymers
Improvement of self-cleaning and anti-fouling abilities of outside walls, roofs, tiles in tunnels, etc.
Improvement of anti-fogging characteristics by enhanced surface hydrophilicity