Wetting, Contact Angle & Adsorption

Spread or bead? The contact angle

Place a drop of liquid on a solid and watch its edge. Sometimes the drop flattens and creeps outward; sometimes it pulls into a tight bead. Wetting is the general term for how well a liquid spreads on a solid, and we measure it with the contact angle — the angle, measured through the liquid, between the solid surface and the tangent to the drop at its edge.

1. θ = 0° — the drop spreads into a complete film: perfect, complete wetting.
2. θ < 90° — the liquid likes the surface and spreads fairly well: good wetting.
3. θ > 90° — the liquid beads up and barely spreads: poor wetting.
4. θ = 180° — complete non-wetting (an idealised limit; mercury on glass comes close).

Adsorption: molecules pile up at a surface

We have already seen surfactant molecules gathering at the air-water surface. The general name for this gathering of molecules at a boundary is adsorption — not to be confused with absorption, where one substance soaks uniformly into the bulk of another. In adsorption, a species concentrates specifically at a surface or interface, often forming a tightly packed single layer one molecule thick called a monolayer.

Adsorption is everywhere in pharmaceutics: surfactants coating oil droplets to stabilise an emulsion, drug molecules sticking to the walls of a glass container or to an excipient, activated charcoal mopping up a poison in the gut. Anytime a surface is available and a molecule has a reason to prefer it over the bulk, adsorption happens.

Tying it together: the Gibbs isotherm

There is a clean quantitative link between adsorption and tension. The Gibbs adsorption isotherm says that the amount of a solute adsorbed at a surface is set by how steeply that solute lowers the surface tension as its concentration rises. In plain words: the harder a substance pushes the tension down, the more strongly it must be packing into the surface. Surfactants lower tension steeply, so they adsorb heavily — exactly what we observe.

Gibbs adsorption isotherm (dilute, nonionic):

  Gamma = -(1/RT) x (d gamma / d ln C)

  Gamma = surface excess (mol per m^2 of surface)
  gamma = surface tension (J per m^2)
  C     = bulk concentration
  R     = 8.314 J per mol per K,  T in kelvin

Reading it:
  - steeper drop in tension  -> larger Gamma
    (more molecules adsorbed)
  - above the CMC, tension stops falling, so the
    slope -> 0 and the surface is fully packed
    (a complete monolayer)

From Gamma you can get the area per molecule:
  area/molecule = 1 / (Gamma x N_A)
  (N_A = 6.022e23 per mol)