Surface Energy

A classic example of surface energy can be seen in how water behaves on a waxed surface, such as a car hood after waxing. When you sprinkle water on the waxed surface, the water forms small, round droplets instead of spreading out. It happens because water molecules are more attracted to each other (cohesion) than to the waxy surface (adhesion).

The spherical shape of the droplets minimizes the surface area of the water exposed to air, thereby reducing the surface energy. In this case, the intermolecular forces of water pull the molecules inward, creating the droplet shape to minimize energy. The waxed surface, which has low surface energy, does not allow the water to spread out. Thus, the formation of droplets is a result of the water trying to minimize its surface energy.

Wetting refers to how well a liquid spreads out or “wets” a solid surface. The interaction between the liquid’s surface energy and the solid’s surface energy determines the degree of wetting. In the case of water on a waxed surface, the surface energy of the wax is low, meaning that the wax does not strongly attract the water molecules. Since the cohesive forces within the water molecules (surface tension) are stronger than the adhesive forces between the water and the wax, the water prefers to stay together in droplets rather than spread out.

On the other hand, if the same water is poured onto a clean glass surface, which has a higher surface energy, the adhesive forces between the water and the glass are stronger. In this case, the water spreads out and wets the glass because the surface energy of the glass encourages the water molecules to stick to it. 

This difference in behavior illustrates how surface energy affects wetting: materials with high surface energy tend to be wetted easily, while those with low surface energy repel liquids, leading to the formation of droplets. The contact angle between the liquid and the solid surface measures wetting.

The formula for surface energy is:

\[ \gamma = \frac{W}{A} \]

Where:

– γ is the surface energy

– W is the work or energy required to create a new surface

– A is the area of the newly created surface

This formula shows that surface energy is the amount of energy required to create a unit area of a new surface. It is a measure of the energy needed to overcome intermolecular forces at the surface. The higher the surface energy, the more energy is required to increase the surface area of the material.

Units and Dimension

Surface energy is typically measured in units of energy per unit area. In the International System of Units (SI), it is expressed in joules per square meter (J/m²). Alternatively, surface energy can also be expressed as newtons per meter (N/m) because one joule is equal to one newton-meter (N·m), and dividing by area gives N/m.

The dimension of surface energy is represented as [M¹L⁰T^–2] or [MT^–2].

The relationship between surface energy and surface tension is closely linked, especially in liquids. Both concepts are manifestations of the same physical principle – the imbalance of molecular forces at a surface. However, they are expressed in different ways depending on whether the material is a liquid or a solid.

In Liquid:

Surface tension refers to the force per unit length that acts along the surface of a liquid, causing the liquid to minimize its surface area. Its formula is given by:

\[ \sigma = \frac{\text{F}}{\text{L}} \]

Where:

– σ is the surface tension

– F is the force acting on the liquid surface

– A is the length along which the force acts

It is expressed in newtons per meter (N/m)

On the other hand, the surface energy is:

\[ \gamma = \frac{W}{A} = \frac{\text{F}}{\text{L}} = \sigma \]

Thus, for liquids, surface tension and surface energy are numerically the same and can be used interchangeably.

In Solid:

For solids, surface energy remains, but there is no surface tension in the same sense as in liquids because solids do not flow or change shape easily to minimize their surface area.