If we have interphase of two phases $\alpha$ (water) and $\beta$ (air), surface excess is defined as

$$\Gamma_i = \frac{n_{i,\mathrm{tot}} - n_{i,\alpha} - n_{i,\beta}} A = \frac{n_{i,\mathrm{int}}} A,$$

where $n_{i,\mathrm{tot}}$ is total amount of some substance added in the system which can be some salt since in that case surface excess is defined as negative, and $n_{i,\mathrm{int}}$ is the amount of substance on the interphase.

Surface excess is the amount of some substance present on the interphase (salt or surfactant) divided by surface area $A$ of the interphase.

However, taking into account definition of surface excess, how can surface excess be negative when the amount of substance can't be negative number?

  • $\begingroup$ It may help if there is included the source and broader context of the equation. $\endgroup$
    – Poutnik
    Nov 28 '21 at 8:24
  • $\begingroup$ jestr.org/downloads/volume1/fulltext1.pdf I must have forgotten this stuff because I did study adsorption phenomena at the university. After reading this I am still puzzled, but at least it seems that Surf Exc can be positive as well negative. Anyone able to explain the concept different than Wikipedia please do it. $\endgroup$
    – Alchimista
    Nov 28 '21 at 9:12
  • $\begingroup$ You don't seem to have problems with positive surface excess, which by the same reasoning would violate the conservation of mass just as well, only with different sign. How so? $\endgroup$ Nov 28 '21 at 9:54
  • $\begingroup$ Conservation of mass does not play any role. Is the concept that we are missing (we I mean OP and I, at least). It is not clear to me what the n refer to, which volume. Perhaps n alpha and beta are those within the interface volume (across it, which has a thickness). $\endgroup$
    – Alchimista
    Nov 28 '21 at 10:30
  • $\begingroup$ @Ivan Neretin Positive surface excess doesn't violate law of mass conservation. For example, if you add 1 mole of surfactant in water/hexane system, 0,2 mol go in water, 0,4 mol go in hexane and 0,4 go on water/hexane interface. Everything is okay with mass conservation. $\endgroup$ Nov 28 '21 at 16:05

Negative surface excess is based upon idealized model of the interphase in which interphase has no volume. If we add 1 mol of NaCl in 1 L of water, concentration of NaCl is 1 mol/L.

However, if we tried to calculate number of moles of NaCl in water by measuring it's concentration, we would find that concentration measured is more than 1 mol/L because of which it would appear that number of moles in water is more than number of moles added.

This calculation of number of moles of NaCl in water is false because in reality interphase has volume and so volume of water is actually less than 1 L when interphase is formed.

If this is taken into account, surface excess isn't and can't be negative, but it appears to be when we want to calculate it based upon measuring concentration and idealized model of the interphase.

Gibbs adsorption isotherm is based upon idealized model of the interphase because of which negative surface excess has practical value, but it is important to note that in reality it isn't actually negative since number of moles can't be negative.


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