Final answer:
The potential energy of attraction between two atoms, such as in London dispersion forces, can be described by the Lennard-Jones potential, with energy decreasing rapidly with distance. The equation reflects the influence of the distance between particles and other factors, such as the Hamaker constant in colloidal interactions.
Step-by-step explanation:
The potential energy of attraction between two atoms, such as the London dispersion forces, can be modeled using the Lennard-Jones 6-12 potential equation: U(x) = 4ε((σ/r)^12 - (σ/r)^6), where ε is the depth of the potential well and σ is the finite distance at which the inter-particle potential is zero. These London dispersion forces are a result of temporary dipoles due to fluctuations in the electron distribution around an atom, resulting in induced dipoles in adjacent atoms. The potential energy due to these interactions decreases with the sixth power of distance (—1/r6), meaning that as distance doubles, the attractive energy decreases by 64-fold. For interactions an atom with a surface, or between colloidal particles, similar principles of intermolecular forces apply, but the specific equations can vary depending on the system geometry and the nature of the interactions involved. The Hamaker constant, which is often used to quantify the van der Waals forces between colloidal particles, is influenced by the materials' densities and the dielectric properties between them.