Illustrated Physics
physics, drawn
Concept

Coupling parameter — where it appears

The ratio of the interaction energy between neighbouring charged particles to their thermal energy. It decides whether a plasma, or a cloud of charged grains, behaves as a gas, a liquid or a crystal: a one-component plasma freezes when it passes about 175, and ordinary laboratory plasmas sit far below one.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

Mean field always pushes; correlations pull. The pressure between two planes of equal charge with only their own counterions between them, against their separation, in units of the Gouy–Chapman length μ for the separation and 2πℓ_Bσ²kT for the pressure. The upper curve is the Poisson–Boltzmann result, solved from k·tan(kd/2) = 1: it is the density of counterions at the midplane and is positive at every separation, falling from the ideal-gas 2/d at contact to π²/d² far apart — 1.71 at 1μ, 0.290 at 4μ. The lower curve is the strong-coupling limit, 2/d − 1, which the same ions reach when their valence and the surface charge are high. It crosses zero at d = 2μ and is negative beyond, tending to −1: the two like-charged planes attract, and the separation 2μ is where they come to rest.

The like charges that pull together

Two surfaces carrying the same charge, with nothing between them but the ions that neutralise them, ought to repel, and the standard mean-field theory proves that they always do. With calcium or spermine as the counterions they attract, and come to rest a fraction of a nanometre apart. The mean field misses it because it averages the ions into a smooth cloud, and multivalent ions are too strongly repelled by each other to form one. Each keeps a patch of surface to itself, and the pressure between the plates becomes a single ion's business.

fluids · Osmosis The same grains as a crystal and as a liquid. 160 grains repelling one another by a screened Coulomb force, held together by a bowl-shaped confinement as a levitated layer is, and jostled by gas collisions at two temperatures; each picture is the end of a simulation of their motion. Grains with exactly six close neighbours are coloured. Left: strongly coupled — thermal energy about a thousandth of the interaction at the spacing — the grains settle into a hexagonal lattice, 79 per cent of those away from the edge with six neighbours. Right: the same grains with their thermal energy raised seventy-fivefold, the lattice melted, 9 per cent. In the laboratory the grains are a hundred micrometres apart and big enough to film with an ordinary camera, so the melting of a crystal can be watched particle by particle.

The dust a plasma freezes into a crystal

Sprinkle microscopic plastic spheres into a glowing discharge and each one charges itself to tens of thousands of electrons, because the plasma's light, fast electrons reach it far more often than its heavy ions. The charge holds the grains up against gravity in the sheath above the electrode, and it makes their mutual repulsion so strong compared with their jiggling that, at room temperature, they freeze into a hexagonal crystal with a lattice spacing a camera can resolve. A plasma, the hottest and most disordered state of matter, is where the most strongly ordered one was found to form most easily.

astrophysics · Plasma oscillation

Named alongside it

The objects these essays reach for when they reach for this one.

Bjerrum lengthContact value theoremCorrelationCounterion condensationCrystal latticeDebye lengthElectrostaticsFloating potentialLike charge attractionMean-field theoryOsmotic pressurePhase transition

All concepts