# How can surface excess be negative?

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?

• It may help if there is included the source and broader context of the equation. Nov 28 '21 at 8:24
• 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. Nov 28 '21 at 9:12
• 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? Nov 28 '21 at 9:54
• 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). Nov 28 '21 at 10:30
• @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. Nov 28 '21 at 16:05