Monodisperse 2026-10-18
A monodisperse particle suspension has a narrow distribution of particle sizes. Treating its particles as having a single radius simplifies the Perrin sedimentation experiment model; residual size variation can still affect the inferred Avogadro constant.
A colloidal grain in a liquid is large enough to see with a microscope, yet small enough for thermal motion to compete with its tendency to settle. In the Perrin sedimentation experiment, the equilibrium number density falls with height: a visible miniature atmosphere. Counting grains at different heights measures an energy scale; tracking their Brownian motion measures a transport rate. Connecting both to the same Avogadro constant makes the experiment a quantitative test of kinetic theory. The Wiener measure describes an idealized path law; these measurements instead test a physical model and its material parameters.
Jean Baptiste Perrin's 1909 memoir traces his sedimentation experiments to May 1908. It reports relative counts , , , at heights , , , , and compares radius estimates from Stokes settling velocity, counted grain mass, and rows of touching grains.[ref]
The 1926 lecture describes resin precipitated from alcohol into water, washed and fractionated by centrifugation to obtain nearly monodisperse gamboge or mastic grains. Diameter and density were measured separately. A sealed slide-and-cover-glass chamber prevented evaporation; a vertical microscope resolved roughly layers through a roughly depth. Refocusing and photographing compared layer populations after equilibrium; changing temperature reversibly changed the distribution.[ref]
In Les Atomes (1913), Jean Baptiste Perrin restricts the eyepiece view to fewer than five or six grains and alternates observations between heights. Focus displacement requires a refractive index correction to recover actual layer separation. Horizontal positions were marked with a camera lucida, usually every , and distances calibrated with a micrometer; the polygon joins sampled positions rather than recording the intervening trajectory.[ref][ref]