In materials science, dispersion is the fraction of atoms of a material exposed to the surface. In general, D = N<sub>S</sub>/N<sub>T</sub>, where D is the dispersion, N<sub>S</sub> is the number of surface atoms and N<sub>T</sub> is the total number of atoms of the material. It is an important concept in heterogeneous catalysis, since only atoms exposed to the surface can affect catalytic surface reactions. Dispersion increases strongly as crystallite size decreases, reflecting the increasing fraction of atoms located at the surface. Atomistic models of small clusters show that this fraction can decrease from 100% for a single atom to approximately 50% at a crystallite diameter of about nine atomic spacings, and to below 10% for particles larger than roughly one hundred atomic spacings.
Relationship to particle size
Dispersion is closely related to particle size through geometric relationships. For idealized spherical particles, the number of surface atoms <math>N_S</math> scales with the particle surface area (<math>\propto d^2</math>), while the total number of atoms <math>N_T</math> scales with the particle volume (<math>\propto d^3</math>). As a result, the dispersion <math>D = N_S/N_T</math> is inversely proportional to the particle diameter:
<math>D \propto \frac{1}{d}</math>
This reflects the general dependence of the surface-to-volume ratio on particle size. A more rigorous expression for spherical particles relates dispersion to the mean particle diameter <math>d</math> as:
<math>D = \frac{6 (v_m / a_m)}{d}</math>
where <math>v_m</math> is the atomic volume and <math>a_m</math> is the surface area occupied by a surface atom.
See also
- Emulsion dispersion