Surface Energy -Definition, Formula, FAQs

Surface energy is a fundamental concept in physics and materials science, describing the energy present at the surface of a material due to unbalanced molecular forces. Unlike molecules within the bulk of the material, surface molecules experience asymmetric forces, leading to excess energy at the surface. This phenomenon plays a critical role in determining how materials interact with each other and their environment. In real life, surface energy explains everyday occurrences such as water droplets forming spherical shapes on a waxed car, as the liquid minimizes its surface area to reduce energy. It's also crucial in manufacturing processes like painting, coating, and adhesive bonding, where the adhesion of liquids or solids depends on the surface energy of the materials involved. Understanding surface energy helps improve efficiency and effectiveness in many industrial and scientific applications.

What is Surface Energy?

Surface energy definition: Surface energy is excessive energy exposed by the liquid molecules on the surface in comparison to those inside the liquid i.e. molecules of liquid at the surface have higher energy compared with molecules within it. Suppose there is a glass and when we fill the water in the glass, it takes the shape of the glass. Obtains free surface. The dimension and SI Unit of surface energy is [MT^-2] and N/m.

Surface Energy Formula

Surface Energy = Energy/Area

Surface Energy (E) = S x ΔA

where S = surface tension and ΔA = rise in surface area.

The energy retained by the liquid surface is known as surface energy. Variation in surface energy is the product of surface tension and variation in the surface area under the constant temperature. The height to which water increases in a capillary tube of radius r is calculated by the

h= 2T cosθ/ rρg

where θ is the angle of contact and T is the surface tension of the liquid.
Because of surface tension, there is too much pressure on the concave side of a surface film of a liquid over the convex side and is equivalent to 2Tr. For a soap bubble, the excess pressure is 4Tr where r indicates the radius of the surface.

What is Meant by Surface Free Energy?

In contrast to the volume of the material, the additional energy of the surface is called the surface free energy. It explains the behaviour of a solid body when kept in a liquid medium. So, it helps in determining the adhesion between the two states i.e., solid and liquid.

If the surface is smaller than the liquid surface will exert high surface energy (Ex: Oxides, Metals, Ceramics). Similarly, if the surface area is higher than the surface will exert low surface energy (Ex: Rubbers, Plastics, and so on). The materials having low surface energy are categorized as low surface energy materials.

Dimensional Formula of Surface Energy

The dimensional formula of surface energy is calculated by,

[M¹L⁰T^-2]

Where,

M = Mass

L = Length

T = Time

Derivation

Surface energy (E)= Energy x [Area]^-1 --------------- (1)

Since,

Energy = Force × displacement

E = m x a x displacement

Or,

Energy = [M1 xM⁰L¹T^-2 X L¹]

Thus, the dimensional formula of energy = [M¹L²T^-2] ------------- (2)

And, the dimensional formula of area =[M⁰L²T⁰] --------------- (3)

Substitute equations (2) and (3) in equation (1) we get,

Surface energyE=Energy x Area^-1

Or, E = [M¹L²T^-2]× [M⁰L²T⁰] ^-1 = [M¹L⁰T^-2]

Thus, the surface energy is dimensionally shown as a [M¹L⁰T^-2].

What is Meant by Surface Tension?

Surface tension is the property of the liquid by which the free surface of the liquid at rest tends to contain a minimal area and as such, it performs like a stretched elastic membrane. Force exerted per unit length of a line drawn on the liquid surface and normal to it parallel to the surface is known as the force of surface tension.

Surface tension depends not only on forces of attraction among particles inside the specified liquid but also on the forces of attraction of liquid, solid, or gas in contact with it. The energy liable for the phenomenon of surface tension may be thought of as nearly equivalent to the energy or work necessary to remove the surface layer of particles in a unit area.

Generally, surface tension is measured in dynes/cm, the force in dynes is needed to divide a film of 1 cm length.

Factors Affecting Surface Tension

1. The surface tension of a liquid reduces with the rise in temperature and becomes zero at a critical temperature.
2. At boiling point, the surface tension of a liquid will be zero and becomes the highest at the freezing point.
3. Surface tension reduces when partially soluble impurities like detergent, soap, phenol, Dettol, etc are added to water.
4. Surface tension arises when highly soluble impurities such as salt are added to water.
5. When dust particles or oil spreads over the surface of the water, its surface tension decreases.
6. When the charge is given to a soap bubble, its size increases because the surface tension of the liquid decreases due to electrification.
7. In weightless conditions, the liquid does not rise in a capillary tube.

Difference Between Surface Tension and Surface Energy

Surface energy and surface tension are measurements of intermolecular forces that comprise material. Because of these intermolecular forces, a surface of a liquid is always being pulled inside. If one is stretching the surface, work should be done in order to overcome intermolecular forces. The tension on the surface of a liquid and the amount of work required to stretch that surface can be measured: and these measurements correspond to the surface energy and the surface tension. The major difference between surface energy and surface tension is that surface energy is used to measure the amount of work that is required to be done per unit area to stretch it although surface tension is used to measure force per unit length of the surface.

Relation Between Surface Energy and Surface Tension Per Unit Area

Assume that a soap film is distributed over the area encircled by a U-shaped frame ABCD and a PQ crosspiece, which can be conveniently over the frame. Let T be the soap solution's surface tension and l, the wire PQ's length in contact with the soap film. In conjunction with the wire, the film contains two surfaces. The force is exerted on the wire PQ by film and tends to contract. 2Tl is the total wire force because each surface exerts a Tl force. Assume that the PQ wire is being pulled to P'Q' at a dx distance too slowly. The work was done by an external force against the force because the film is

W = applied force x displacement

Since the value of force is given as F=2Tl.

Therefore,
W=Fdx

W= 2Tldx

Because of the dx displacement, the surface area of the film increases. With two surfaces, the rise in its surface area will be-

A = 2ldx

Therefore, the work done per unit area will be

W/A = 2Tldx/2ldx = T

This work is stored as potential energy in the unit surface. The surface energy is this potential energy. The above relation reveals that surface energy is equivalent to its surface tension per unit area of a liquid.

How can Surface Energy be Changed?

High surface energy is essential for solution wetting, particularly in processes like spin coating. The vast majority of solids with high surface energy will not maintain the high-energy surface when it is exposed to weather conditions. Hydrocarbon pollutants present inside the air will adsorb onto the surface of solid, decreasing surface energy. The most common way of tuning surface energy is by surface treatment, which is usually intended to increase energy by eliminating these pollutants or creating high surface energy functional groups. A lot of these methods generate only temporary changes to the surface energy. This is due to the adsorption of low surface energy molecules will occur over time gradually decreasing the average surface energy.

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Solved Examples Based on Surface Energy

Example 1: Extra energy associated with surfaces of liquid is due to

1) Difference in surrounding around surface.

2) Due to viscosity

3) Due to greater height of surface

4) None of the above

Solution

Surface Energy

It is defined as the amount of work done to increase the area of the liquid against surface tension.

Due to differences in surroundings, the molecules at the surface are not in equilibrium. because of this molecules at the surface of the liquid possess more energy than molecules in the bulk.

Hence, the answer is the option (1).

Example 2: A large number of liquid drops each of radius r coalesce to from a single drop of radius R. The energy released in the process is converted into kinetic energy of the big drop so formed. The speed of the big drop is (given surface tension of liquid T,density ρ).

1) Tρ(1r−1R)
2) 2Tρ(1r−1R)
3) 4Tρ(1r−1R)
4) 6Tρ(1r−1R)

Solution:

Let the number of drops be n

Initial volume = Final volume
⇒n4π3r3=4π3R3 or nr3=R3… Energy release =TΔA T= surface tension ΔA= Change in surface area ⇒ΔV=T⋅[n4πr2−4πR2]ΔV=1/2mv2=1/2(ρ⋅4π3R3)v2⇒2ρπR33v2=T4π(r2R3r3−R2)v=6Tρ⋅(1/r−1/R)
Hence, the answer is the option (4).

Example 3: Assume that a drop of liquid evaporates by a decrease in its surface energy so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible? The surface tension is T, the density of the liquid is ρ and L is its latent heat of vaporization.

1) 2T/ρL
2) ρL/T
3) T/ρL
4) T/ρL

Solution:

Surface Energy
W=T×ΔA

a drop of liquid evaporates by a decrease in its surface energy

T=WΔA

ΔA→ increase in area
Apply a decrease in surface energy heat required in vapourization

m=ρ∗43∗πr3
So, dm=ρ∗4∗πr2dr
The surface energy of the drop =AT
change in Surface energy of the drop =dA∗T=T4π[R2−(R−ΔR)2]
the heat required in vapourisation =dm∗ L
So, ρ4πR2ΔRL=T4π[R2−(R−ΔR)2]

ρR2ΔRL=T[R2−R2+2RΔR−ΔR2]ρR2ΔRL=T2RΔR(ΔR is too small )
Hence, R=2T/ρL

Hence, the answer is the option (1).

Example 4: Find the surface energy (in Joule) of water kept in a cylindrical vessel of radius 6 cm . surface tension of water =75×10−3Nm−1

1) 0.0017

2) 0.00085

3) 0.00042

4) 0.085

Solution:

Definition of Surface Tension

W=TΔA If ΔA=1, then T=W - wherein T→ Surface tension W→ work done Sur face energy =TA=227×(6×10−2)2×75×10−3 J=8.5×10−4 J

Hence, the answer is the option (2).

Example 5: Work done in increasing the size of a soap bubble from a radius of 3 cm to 5 cm is nearly ( Surface tension of soap solution = 0.03 N m^-1)

1) 4πmJ
2) 0.2πmJ
3) 2πmJ
4) 0.4πmJ

Solution:

W=TΔA=0.03×2(4π(52−32)×10−4)W=0.24π×16×10−4=0.384π×10−3∴W=0.4πmJ

Hence, the answer is the option (4).

Summary

Surface energy refers to the excess energy present at a material's surface due to unbalanced molecular forces. It is related to surface tension, which is the force per unit length acting on a liquid's surface. Surface energy is crucial in phenomena such as adhesion, wetting, and capillarity. Factors like temperature, impurities, and external forces influence both surface tension and energy, and they play significant roles in real-life applications such as coating, painting, and the behavior of liquids on surfaces.