Liquid–liquid and liquid-gas interfaces

Liquid–liquid and liquid–gas interfaces

A liquid or a solid phase can be defined as a conglomeration of like mol-ecules, held together by intermolecular bonds that hold the molecules in association and proximity with each other. The two phases—liquid and solid—differ in the degree of order in the association of the molecules, with the solid phase being more ordered than the liquid phase. Within the solid phase, the crystalline phases are more ordered than the amorphous phases. The gas phase, on the other hand, is the least ordered, with the molecules undergoing random Brownian motion, independent of other molecules.

The bonds that hold a phase together are van der Waals force, ionic, dipole, and hydrogen bonds—depending on the atomic structure of the molecules of a phase. For example, water molecules are held together pre-dominantly by hydrogen bond and dipole forces, whereas octane molecules are held together by weak van der Waals forces. The strength of inter-molecular forces of attraction and the proximity of the molecules follow the general trend: solids > liquids > gases. In the bulk of a phase, a mol-ecule is surrounded by other molecules of the same type and encounters similar forces in all directions, which tend to neutralize each other. At the interface, a molecule encounters directionally different forces (Figure 8.1). Forces of attraction between the molecules of the same type within a phase can be termed cohesive forces, and the resulting phenomenon is termed cohesion. Similarly, forces between the molecules of different types at the interface can be termed adhesive forces, and the resulting phenomenon is termed adhesion.

At the liquid–gas interface, cohesive forces are generally greater than adhesive forces, leading to an inward pull on the molecules toward the bulk. This force pulls and keeps the molecules of the interface together and tends to contract the surface, resulting in minimization of the exposed surface area. Thus, a liquid droplet tends to be spherical, since this shape can contain the maximum volume per unit surface area. 

Figure 8.1 A liquid droplet depicted with some molecules (small spheres) with mutual forces of attraction (depicted with arrows). The molecules at the surface experience attractive forces from all directions, except at the interface, leading to a pull toward the bulk of the liquid.

Expansion of surface requires application of force. This force can be expressed in terms of surface or interfacial tension.

Surface tension

Surface tension (γ) is the force per unit length that must be applied in paral-lel to the surface to expand the surface, counterbalancing the net inward pull. It has units of force per unit length, for example, dyne/cm. Surface tension of a liquid film is commonly determined by creating a film of the liquid in a horizontal bar apparatus (Figure 8.2) and pulling the film using standard weights until the film breaks. Surface tension of the solution form-ing the film is a function of the force that must be applied to break the film over the length of a movable bar in contact with the film. Since the film has two liquid–gas interfaces (one above and one below the plane of the bar), the total length of the contact is equal to twice the length of the bar.

Thus,

where:

f_b is the force required for breaking the film

L is the length of the film or the movable bar

Surface tension of a liquid is constant. Thus, this equation indicates that the amount of force required to break the film is directly proportional to the length of the film. In other words, the amount of force required, or work done, to create additional surface is directly proportional to the amount of new surface being created.

Figure 8.2 A simplistic representation of a rectangular block apparatus for determining the surface tension of a liquid.

Interfacial tension

Interfacial tension is the force per unit length that must be applied in parallel to the interface to expand the interface, counterbalancing the net inward pull of the two phases. While the term surface tension is reserved for liquid–gas and solid–gas interfaces, the term interfacial tension is com-monly used for liquid–liquid interfaces. Interfacial tension has the same symbol (γ) and units (dyne/cm) as surface tension and is derived similarly from the amount of force required to create new interface. Subscripts are commonly used to distinguish between different interfacial tensions. For example, γ _L/L is the interfacial tension between two liquids (designated “L”), and γ _L/V is the surface tension between a liquid and its vapor (designated “V”) in the gas phase.

Usually, the interfacial tension (liquid–liquid) of a hydrophilic liquid is less than its surface tension (liquid–vapor). This is because the adhesive forces between two liquid phases forming an interface are generally higher than those between a liquid and a gas phase. For example, at ~20°C, the interfacial tension between water and carbon tetrachloride is 45 mN/m, while the surface tension of water is 72.8 mN/m.

Factors affecting surface tension

Surface tension is measured with devices known as tensiometers. These devices measure the force by which a surface is held together while the force is applied on the surface to expand it. The methods for surface ten-sion measurement include the du Nouy method (maximum pull on a rod or plate immersed in a liquid), du Nouy ring method (maximum down-ward force on a ring pulled through the liquid–air interface), Wilhelmy plate method (downward force on a plate lowered to the surface of the liquid), and pendant drop method (shape of the drop at the tip of needle by optical imaging). All of these methods measure the inherent force within a liquid that resists the growth or expansion of its surface. Factors affecting this force, or the surface tension, of a liquid include the following:

·           Nature of the liquid: Greater the cohesive forces between the molecules of a liquid, higher its surface tension. Thus, the surface tension of water (72.8 mN/m at 20°C) is higher than that of methanol (22.7 mN/m). Mixing of the two miscible solvents leads to an intermediate surface tension. For example, a 7.5% solution of methanol in water has a surface tension of 60.9 mN/m.

·           Temperature: Surface tension of most liquids decreases linearly with an increase in temperature. This is because of greater Brownian motion of individual molecules that leads to reduction in the inter-molecular attractive forces and, thus, the reduced inward pull of the molecules on the surface.

Surface free energy

Surface free energy of a liquid is defined as the work required for increasing the surface area. Surface free energy (W) and surface tension (γ) are related by:

W=γΔA                 (8.2)

Where, W is the work done, or the surface free energy (ergs) input, required to increase the surface by an area ∆ A (cm 2) for a liquid that has the surface tension γ (dynes/cm).

Surface free energy represents the amount of energy put into the system per unit increase in surface area. Thermodynamically, surface free energy represents the Gibbs free energy at constant temperature and pressure.

W= ∆G= γ∆A             (8.3)

Thus, surface tension (γ) can be represented as the increment in Gibbs free energy per unit area.

γ = ∂G/∂A                 (8.4)

Example 1: If the length of the bar (Figure 8.2) is 5 cm and the mass required to break a liquid film is 0.5 g, what is the surface tension of the soap solution? What is the work required to pull the wire down 1 cm?

Since γ = f_b/2L

∴ γ = (0.50 g × 981 cm/s²)/10 cm = 49 dyn/cm In addition,

 W = γΔA

 ∴ W = 49 dyn/cm × 10 cm² = 490 ergs.