Surface Pressure

In the context of a Langmuir film, surface pressure is the difference in surface tension measured between a clean sub-phase and a monolayer-covered sub-phase. Surface pressure greatly influences monolayer properties.

Monolayers and surface pressure

Substances that can form monolayers are often amphiphilic: the hydrophobic tail guarantees the molecule is insoluble in water while the hydrophilic head facilitate spreading and ensure that the molecules stay at the surface. When a solution of an amphiphile in a water insoluble solvent is deposited on a water surface with a microsyringe, the solution spreads rapidly to cover the available area. As the solvent evaporates, a monolayer is formed. When created at the air-water interface, the monolayer is called a Langmuir film.

Monolayer at the air-water interface before (left) and after (right) compression seen in 3D (top) and 2D (bottom).

When the available area for the monolayer is large the distance between adjacent molecules is large and their interactions are weak. The monolayer can then be regarded as a two-dimensional gas (A in the illustration below). Under these conditions the monolayer has little effect on the surface tension of water. If the available surface area of the monolayer is reduced by a barrier system the molecules start to exert a repulsive effect on each other (B and C in the illustration below). This two-dimensional analogue of a pressure is called surface pressure, Π, and is given by the following relationship:

where ϒ0 is the surface tension of the sub-phase in absence of a monolayer and ϒ is the surface tension with the monolayer present at the interface.

The illustration below shows a surface pressure – area isotherm of a monolayer with the different phases from gas (G) to liquid (L).

Surface pressure—area isotherms of a Langmuir film and molecules in different phases.

What is surface tension?

Surface tension is a measurement of the cohesive energy present at an interface. The molecules of a liquid attract each other. The interactions of a molecule in the bulk of a liquid are balanced by an equal attractive force in all directions. The molecules at the surface of a liquid experience an imbalance of forces as shown below.

Unequal forces at the interface responsible for surface tension

The air/water interface (and other gas-liquid interfaces) possesses excess free energy originating from the difference in environment between the surface molecules and those in the bulk. This interfacial free energy is responsible for the surface tension.

How is surface pressure measured?

The KSV NIMA L & LB Trough measures surface pressure by measuring surface tension using the Wilhelmy plate method. In this method, a measurement is made by determining the force due to surface tension on a plate suspended so that it is partially immersed in the sub-phase. This force is then converted into surface tension (mN/m or dynes/cm) with the help of the dimensions of the plate.

Wilhelmy plate at the air-water interface

The plate is very thin and made of platinum, but even plates of glass, quartz, mica and filter paper can be used. The forces acting on the plate consist of the gravity and surface tension downward, and buoyancy due to displaced water upward. For a rectangular plate of dimensions lp, wp and tp, of material density ρp, immersed to a depth hl in a liquid of density ρl, the net downward force is given by the following equation:

where γ is the liquid surface tension, θ is the contact angle of the liquid on the solid plate and G is the gravitational constant. The surface pressure is then determined by measuring the change in F for a stationary plate between a clean surface and the same surface with a monolayer present. If the plate is completely wetted by the liquid (i.e. cos θ = 1) the surface pressure is then obtained from the following equation: 

, if wp ≫ tp

Using a very thin plate can thus increase the sensitivity. The force is in this way determined by measuring the changes in the mass of the plate, which is directly coupled to a sensitive surface pressure sensor.