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I want to increase the surface tension of water by 1.2 - 2 times. How about adding one or more chemical substances to the water that can possibily increase its surface tension by the desired amount? But I don't know what chemical substances to add. Do you what chemical substances can I add?

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The surface tension of water is $\pu{72 dyne/cm}$; it is sometimes compared to mercury, which has a surface tension of $\pu{486 dyne/cm}$. The higher surface tension of the mercury is because the atoms of mercury bond much more tightly.

A molecule at the surface of a liquid experiences net inward cohesive forces. Usually, we try to reduce those forces in water so it can wet surfaces more easily. Water does not wet waxed surfaces because the cohesive forces within the drops are stronger than the adhesive forces between the drops and the wax (source).

It is claimed that most inorganic solutes increase the surface tension of water. Another source suggests that surface tension could be increased if you increase the polarity of water by adding a more polar substance. But there seems to be contradictory evidence both $\ce{NaOH}$ and $\ce{Na2S2O3}$ decrease the surface tension of water. And there is an article that shows $\pu{8M} \ \ce{NaCl}$ to have a surface tension of about $\pu{85 dyne/cm}$. So it would seem that if there is an effect, it is small.

So let's try another method to increase the net inward cohesive forces. We could add a thickener, like xanthan gum, which at very low concentrations (less than 1%), will thicken the water so that you could float not only a needle, but a penny or a nickel on the surface - for a long time, maybe not forever. In a way, the surface tension is increased, but it is time-dependent, because the water molecules are highly immobilized, yet still somewhat free to move. Other thickeners could behave similarly.

I will yield if someone claims that the thickener achieves not a surface tension increase, but rather a viscosity increase.

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