removal will be larger for a larger molecule. This is the main reason why
polymeric substances can be so very surface active (see Section 10.3.2).
Up till here, we have implicitly assumed that adsorption is restricted
to a monolayer. Actually,multilayer adsorptioncan occur, especially if the
concentration of surfactant is approaching its solubility. Adsorption of a
second layer tends to go along with very little increase in surface pressure;
in other words, the interaction forces leading to this adsorption often are
weak.
Finally, a few words aboutnegative adsorption. Figure 10.4 shows
that the increase in g for NaCl is proportional to c. This is quite
generally observed for negative adsorption. Hence dg/dcis constant. Since
(1/c)dc¼dlnc, this means that dg/d lncis proportional toc. According to
Eq. (10.2), dg/dlncis proportional toG. Hence a very simple ‘‘adsorption
isotherm’’ results,Gbeing proportional toc. This can be interpreted as the
presence of a solvent layer of constant thickness adjacent to the interface
that is devoid of solute. The thickness of the layer follows from the slope
ofgversusc, and it turns out to be of the order of 1 nm, i.e., of molecular
dimension. Negative adsorption can thus be interpreted as being due to
steric exclusion of the solute by the interface; see also Figure 8.7.
10.2.3 Surface Equations of State
This concerns the relation between surface pressureP(or surface tensiong)
and surface excessG. In the simplest case, the relation is given by the
equation
P¼n
A
RT¼GRT ð 10 : 4 Þwherenis the number of moles andAthe interfacial area. It may be no
surprise that Eq. (10.4) is only valid for very small values ofG. At higherG,
repulsive and attractive forces between surfactant molecules will for a
considerable part determineP. It may be noted that Eq. (10.4) is very
similar to Eq. (2.17) for the osmotic pressure of an ideally dilute solution,
which can be written asPosm¼(n/V)RT. The surface pressure may indeed
be considered as a two-dimensional analogue of the osmotic pressure.
Examples of observed surface equations of state are in Figure 10.8.
Note Actually, they are merely relations of state, since no
equation is given. However, the word equation is commonly used.
It is seen that the deviation from ideality varies widely. Three aspects of
nonideality will be discussed.