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How strong is the "hydrophobic force"?

Hydrophobic interactions are weak interactions but can have greater strength than hydrogen bonds. I find the strength of the hydrogen bond in literature to be near 1 pN. Finding the strength of the "hydrophobic bond" has proven to be a bit more elusive. I would guess that there is a hydrophobic interaction strength spectrum (dipole strengths and such), but would also guess there is a fundamental order of magnitude of strength of the hydrophobic interaction.

Hydrophobic interactions result from the hydrophobic effect and manifest in measurable attractive forces. For example, the Polyhydroxyethylmethacrylate (pHEMA) backbone has dipole induced interactions, hydrophobic interactions, and hydrogen bonding; each of these interactions being identifiable in molecular position on the backbone (aliphatic regions being identified as hydrophobic sites).

To date, i have found a measurement of such resulting attractive forces in a specific interaction to be near 15 pN (oil-oil droplet AFM approach)[1]. However, I can also find literature that discusses forces in avidin-biotin complex which are dominated by hydrophobic interactions; resulting attractive forces range from 80 to 250 pN [2].

[1] Tabor et al, 2013; DOI: 10.1021/jz402068k
[2] Moy et al, 1994; DOI: 10.1126/science.7939660

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  • $\begingroup$ With this not being an actual force you can have some trouble here... $\endgroup$
    – Mithoron
    Feb 2 at 17:15
  • $\begingroup$ "The hydrophobic force describes the attraction between water-hating molecules (and surfaces) that draws them together, causing aggregation, phase separation, protein folding and many other inherent physical phenomena" it is not a fundamental force of nature, but it is a widely recognized intermolecular force. $\endgroup$ Feb 2 at 17:29
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    $\begingroup$ Get better resources chemistry.stackexchange.com/questions/37287/… chemistry.stackexchange.com/questions/135081/… $\endgroup$
    – Mithoron
    Feb 2 at 21:39
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    $\begingroup$ Well, I think there's a need for clarification - so-called hydrophobic effect in more of a phenomenon then force. There are obviously various interactions between induced dipoles, quadrupoles etc. but do you ask about them, then? $\endgroup$
    – Mithoron
    Feb 3 at 19:35
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    $\begingroup$ The type of "force" in question does not have the classical meaning as "derivative (or gradient) of energy wrt position". This is what makes providing an answer far from trivial. Say you establish that the free energy of two states of your polymer in solution differ by some amount. What do you use as "distance" to compute a force? $\endgroup$
    – Buck Thorn
    Feb 4 at 11:45
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The hydrophobic force does not exist. It is a phenomena resulting from the following considerations.

In principle, liquids should be like gases, perfectly miscible in all proportions. This is the case for non polar molecules, like hydrocarbons. This is not the case for liquids where molecules are hold together by hydrogen bonds, like water. In these liquids, adding solutes requires to break hydrogen bonds. It is acceptable if the solute is able to form new hydrogen bonds, like with small alcohols, polyols and sugars. But if mixing with another substance will break too many H-bonds, Nature refuses to make up this mixture, as if there was a hydrophobic force. Of course, this force does not exist. It is simply a consequence that mixing very different substances would cost too much energy for breaking all H-bonds of one liquid, without forming back new ones.

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  • $\begingroup$ I might ask: is there such a thing as a "frictional" force? Or an "elastic" force (eg in a rubber band)? $\endgroup$
    – Buck Thorn
    Feb 6 at 9:31
  • $\begingroup$ The elastic force is a result of literally stretching bonds in a solid, friction is super complicated.. probably similarly complicated to forces in hydrophobic interactions $\endgroup$ Feb 7 at 5:25

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