Adsorption
Contents
Adsorption lowers surface energy
| At the air/liquid interface: | And the solid/liquid interface: |
| Lowers the surface tension. | Stabilizes dispersions. |
Gibbs' adsorption isotherm
A derivation by Gibbs gives a relation between the chemical potential of a solute in solution, the surface tension of an interface and the excess concentration the solute at that interface. The interface is considered to be wide compared to the concentration gradients; the excess number of moles associated with that interface is calculated and is expressed as a surface concentration, moles per area:
| The differential of the total energy: | <math>dU=TdS-pdV+\sigma dA+\sum{\mu _{i}dn_{i}}</math> |
| Integrating to get the total energy: | <math>U=TS-pV+\sigma A+\sum{\mu _{i}n_{i}}</math> |
| Taking the differential gives the Gibbs-Duhem relation | <math>SdT-Vdp+Ad\sigma +\sum{n_{i}d\mu _{i}}=0</math> |
| Defining that relation for both bulk phases: | <math>S^{\alpha }dT-V^{\alpha }dp+\sum{n_{i}^{\alpha }}d\mu _{i}^{\alpha }=0</math> |
| <math>S^{\beta }dT-V^{\beta }dp+\sum{n_{i}^{\beta }}d\mu _{i}^{\beta }=0</math> | |
| Chemical potentials are constant: | <math>d\mu _{i}=d\mu _{i}^{\alpha }=d\mu _{i}^{\beta }</math> |
| Subtracting the phases from the total: | <math>\left( S-S^{\alpha }-S^{\beta } \right)dT-\left( V-V^{\alpha }-V^{\beta } \right)dp+Ad\sigma +\sum{\left( n_{i}-n_{i}^{\alpha }-n_{i}^{\beta } \right)}d\mu _{i}=0</math> |
| Defining the excess quantities: | <math>S^{\sigma }=S-S^{\alpha }-S^{\beta }</math> |
| <math>S^{\sigma }=S-S^{\alpha }-S^{\beta }</math> | |
| <math>S^{\sigma }=S-S^{\alpha }-S^{\beta }</math> | |
| Substitution and subtraction gives: | <math>Ad\sigma +S^{\sigma }dT-V^{\sigma }dp+\sum{n_{i}^{\sigma }d\mu _{i}}</math> |
Finally:
| Gibbs adsorption isotherm: | <math>-d\sigma =\sum{\frac{n_{i}^{\sigma }}{A}}d\mu _{i}=\sum{\Gamma _{i}}d\mu _{i}</math> |
| The surface excess: | <math>\Gamma _{i}=\frac{n_{i}^{\sigma }}{A}\text{ mol m}^{\text{-2}}</math> |
| For a 2-component system: | <math>-d\sigma =\Gamma _{2}d\mu _{2}\simeq kT\Gamma _{2}d\ln c_{2}</math> |
Adsorption at interfaces
| Air-water surface | Air-oil surface | Oil-water interface |
| Strong adsorption, substantial lowering of surface tension. | Little adsorption, little lowering of surface tension. | Strong adsorption, substantial lowering of interfacial tension. |
Adsorption on bubbles
Ratio of the observed velocity of ascent of a bubble to the calculated Stokes’ velocity in solutions of various concentrations of
- (a) polydimethylsiloxane in trimethylolpropane–heptanoate;
- (b) polydimethylsiloxane in mineral oil;
- (c) N-phenyl–1–1napthylamine in trimethylolpropane–heptanoate.
Each figure shows the transition from the Hadamard to the Stokes regime.
Suzin, Y.; Ross, S. Retardation of the ascent of gas bubbles by surface-active solutes in nonaqueous solutions, J. Colloid Interface Sci. 1985, 103, 578 – 585.
Adsorption by a solid surface
The surfactant must be soluble in the liquid !
| Solid-water interface | Solid-oil interface |
| The adsorption is driven by both strong tail/solid interaction and entropy – the hydrophobic effect. | The adsorption is driven by strong head group/solid interaction. |
