Interfacial Energy Density and Surface Tension

If we split and separate the solid at that plane and then move the liquid plane so that its two sides are up against the two separated pieces of solid we have replaced each A-A and B-B interaction with two A-B interactions.

The interfacial energy density is the change in the energy per unit area of A-B plane as it is created from A-A and B-B planes. It has units of J/m² and is symbolized by . Since 1 J = 1 N m, the units may also be expressed as N/m (force per unit length). Thus interfacial energy density can alternately (and properly) be called the interfacial tension or surface tension. This tension causes a liquid surface to pull itself into a shape which minimizes interfacial area -- a spherical drop or film.

Solids do not flow (on a short time scale), so they cannot minimize surface area by changing shape after being ground up. Consequently they will maintain a large interfacial energy. If the solid is immersed in a liquid that contains a dissolved material whose adsorption would reduce the interfacial tension, then that adsorption will take place, and the dissolved material can be termed a wetting agent. Adsorption will be discussed in more detail in the Langmuir adsorption section of this tutorial.

The Shape of Liquid Drops

When a drop of (pure) liquid rests on the flat surface of a (pure) solid (under the influence of gravity) the shape is not a simple spherical lens but is determined by a balance between gravity and the gas-liquid, gas-solid, and liquid-solid interfacial energy densities (interfacial tensions). The gas-liquid interfacial tension of a liquid is often determined from the contact angle (through the liquid) at the shoreline of a small drop of liquid resting on a flat solid which is not wetted well by the liquid. This will be discussed in more detail in the contact angle section of this tutorial.

How System Energy Changes When a Block is Crushed

G_INTERF = _AB A_AB

If the original solid is in a large cube and the final particles are equal-size cubes that are much smaller than the orginal block (less than one-tenth the original diameter) then the original area is less than 0.1% of the final area and we may approximate the change in area as the total area of the N final particles,

A_AB = N x A_cube
where A_cube = 6 D_cube³

In most real systems the energy required to crush a large block is smaller than the value computed above. That value was based on an interfacial energy density determined for a perfectly-formed solid, but most real solids contain many flaws, and these provide pathways for crack propogation along the weakest planes of the solid. The easiest breaks occur first, so the solid becomes stronger as it is crushed to smaller sizes. This tutorial will not discuss crushing.