Surface Energy

Surface energy is defined as the work done per unit area through the force applied on the external surface. However, in liquids or solvents, surface energy is also known as surface free energy. Since liquids tend to stretch out and create some free surface energy, the upper surface will store the potential energy. The dimensional equation of surface energy is derived by equating the physical quantities with their corresponding dimensional formula, and it has a varied number of applications. 

Dimensions and its concepts 

Dimensions help in creating interrelationship between different physical quantities. Dimensions of the physical quantities have many applications and support in identifying the units and measurement. The dimensional equation of surface derived by equating the physical quantities with their corresponding dimensional formula. 

For instance, let A be a physical quantity that depends on the mass (m), length (l), and time (t) with regard to powers. Thus, the dimensional formula is represented as [MaLbTc].   

In other words, the dimensional formula is an expression of physical quantities that represents base quantities. It is represented by the symbols of physical quantities with appropriate powers in brackets, i.e., ( ).

For instance, the dimensional formula for length is [L].

Surface Energy

Atoms presented on the external surface have surface energy, which is also referred to as surface free energy or interfacial free energy. It is also defined as the work done per unit area through the force applied on the external surface. 

The materials with less surface have less amount of surface energy. The higher the surface energy, the higher the bond (molecular interaction) between the atoms will be. The adhesive property of particles present on the upper surface of the material can be measured with the help of surface energy. Hence, the strength of adhesion is dependent on the surface energy directly. 

Surfaces with a higher range of surface energy are PVC Rigid, Copper, Nylon, Polyester, ABS, Tin, Stainless Steel, Polycarbonate, Acrylic, Epoxy Paint, Lead, Aluminium, Zinc, Glass Porcelain, etc. 

Surfaces with low surface energy are EVA, Acetal, Polystyrene, Polyethylene, PVA, Polypropylene, Powder Coated Paints, etc. 

Surface Free Energy

In the case of liquids, liquids have the tendency to stretch out and create some free surface energy, and the upper surface will store the potential energy. This is also known as surface-free energy. Molecules at the upper layer of the surface tend to reach the bottom layer, which impacts the amount of surface energy, i.e., decrease in energy. 

The mathematical formula for surface energy, 

Surface energy = Work done/Area

It’s S.I. unit is Joules/m2 or Newton/metre (N/m). 

Dimensional formula of surface energy

The dimensional formula of surface energy is provided below,

M¹L⁰T⁻²

Where, standard unit mass is represented as M, length by L, and time by T.

Derivation of the dimensional formula of surface energy

The formula is given by, 

Surface energy (E) = Energy × Area

And, Energy = Force × displacement = m × a × displacement

Or, it can also be represented as Energy = M¹×M⁰L¹T⁻²×L¹

Therefore, the dimensional formula of energy is as,  

M¹L²T⁻²

Similarly, the dimensional formula of area = M⁰L²T⁰

By putting values of energy and area into the formula of surface energy, we get, 

Surface energy = Energy × Area

M¹L²T⁻² = M¹L²T⁻² × M⁰L²T⁰

Thus, the surface energy is dimensionally represented as M¹L⁰T⁻². 

Conclusion

Calculating the dimensional formula of various physical quantities helps in understanding different other aspects of physics. Surface energy is defined as the work done per unit area through the force applied on the external surface. The higher the surface energy, the higher will be the bond (molecular interaction) between the atoms. The adhesive property of particles present on the upper surface of the material can be measured with the help of surface energy. Hence, the strength of adhesion is dependent on the surface energy directly.