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I learnt in class that surface tension is caused by an unbalanced force at the surface of the liquid due to IMFs, forming a "skin" on the top. Does this mean that the skin is just one molecule thick? My teacher conjectured that there might some sort of gradient, with stronger forces at the top gradually decreasing. Is this the case? How thick is it? Please correct any misconceptions that I have.

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    $\begingroup$ For soapy water, the skin depth must be on the same order of magnitude as the film width of a soap bubble. As everybody have noticed, a soap bubble can considerably reflect light, meaning it can't be very very much thinner than the wavelength of the light (~500 nm). However, for pure water, skin is probably much thinner. $\endgroup$
    – kristjan
    Jan 23, 2015 at 21:27

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This review may give you a feel for the factors involved. They are looking at the ion concentrations at the water liquid/gas interface, and they cite a number of studies tackling the problem from various angles. You'll see that the characteristics of the water are changing over a length scale of 10-20 angstroms. Water molecules are more like 2-3 angstroms, so that is several molecular layers thick.

Another study using Small Angle X-ray Scattering looked at an (exotic) organic liquid and found ordering up to about 10 nm deep. In this case, the molecules were polar, and prone to ordering so the surface didn't evidence a a gradual drop off of order, but rather there were about 4 molecular layers that showed ordering, where each layer had well defined units, and below that random liquid.

Thus, the exact answer to your question depends on the specific liquid, pressure, etc. However, the magnitude of this depth is in general "a few molecular layers thick" and may or may not be a gradual gradient of any one property (ordering, density, solute concentration, etc).

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As a first-order approximation you can think of surface tension as affecting only the top layer of molecules. I'm sure that a careful molecular dynamics simulation could show some subtleties, but the basic length scale involved is one layer. There's an interesting justification for this in

"Search for Simplicity", Victor Weisskopf, Am. J. Phys. 53, 19 (1985) http://www.pha.jhu.edu/courses/171_602/weisskopf_simplicity_long.pdf

To summarize, suppose you measure how much heat it takes to vaporize a certain quantity of, say, liquid methane. Assuming you know the molecular weight, you can turn that into the heat per molecule for vaporization. Next, assume that vaporization breaks on average three bonds per molecule. (Each molecule participates in six bonds: above, below, left, right, front back. Each bond involves two molecules, so that's three bonds per molecule.) This gets you the energy per bond.

Next, go back to the liquid and look at molecules on the surface. Assume that they participate in five bonds, not six, since the one at the surface is missing. If you know the size of the molecules, you can calculate the number of surface molecules per unit area, and using the bond strength you can get the energy per surface area. This is the surface tension.

It turns out this simple model works well: to within maybe 10% or so unless something funny is going on (like the molecule being highly polar so that surface molecules can flip around to maximize bonding). The accuracy of this simple model justifies the idea that surface tension can be accounted for primarily in the single top layer of molecules.

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    $\begingroup$ It seems to me that you have essentially assumed zero temperature, which gets rid of all the diffusiveness (not to even mention capillary waves). Thus, I feel, this answer to an extent avoids the question and instead discusses a very idealized model and the molecular origins of the phenomenon that is surface tension. That said, I would not be surprised if simple liquids such as argon did behave roughly as described, but do not think the argument holds in general. $\endgroup$
    – alarge
    Jan 27, 2015 at 21:48
  • $\begingroup$ There's no point in being super-accurate for this question. We just want to know whether surface tension is an effect of mainly the top layer of atoms or not. If a very simple argument works, then why bother trying to be sophisticated about it? $\endgroup$ Jan 27, 2015 at 21:53
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    $\begingroup$ The question, as I interpret it, is about how thick fluid interfaces are; Your explanation starts with the assumption that they are roughly one molecule across. Surface tension, slightly more rigorously, is caused by the gradient of density (in vdW theory), and the question is, then, about how localized this gradient might be. It need not, in general, be just one molecule thick. In fact, for interfaces with low surface tensions, or ones close to the transition temperature, I would guess that this might be considerably more (also depending on the bulk properties of the constituents). $\endgroup$
    – alarge
    Jan 27, 2015 at 22:10
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    $\begingroup$ Just to be clear about it: I do not disagree with your answer per se and realize that it was indeed meant to be very simplistic. However, I do think that the explanation does not apply generally to all interfaces and that this was worth pointing out. $\endgroup$
    – alarge
    Jan 27, 2015 at 22:11

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