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I am teaching a DNA course for lay people and I want to give them an indication of the number of collision per second a water molecule experiences in pure water. Similarily, I would like to know the typical number of collisions (with ANY molecule) a typical protein experiences per second in a human cell. Being a DNA person, I am ill-equiped to calculate these numbers myself and I have a hard time finding the answers on the internet. Clearly, I would be happy with crude indications here!

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  • $\begingroup$ Exact numbers would depend on the model. There are movies of molecular dynamics simulations of water. This one is almost 2 picoseconds long: youtube.com/watch?v=x8Atqz5YvzQ $\endgroup$
    – user137289
    Commented Feb 19, 2018 at 22:09
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    $\begingroup$ It will probably be easier to find estimates of the "mean free path" and the RMS speed (or velocity), then you just compute (free path)/speed to get some kind of average time between collisions for the water molecules. As long as the big organic molecules involved are small in number it won't affect that number much. Your big molecules will get hit proportionally more often, of course, and that calls for some kind of estimate of the relative cross-sectional area. $\endgroup$ Commented Feb 19, 2018 at 22:18
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    $\begingroup$ It's easier to estimate the number of water-on-protein collisions because folded proteins have large and relatively well-defined surface areas. Just multiply surface area by the number of water molecules per unit volume and their average speed. $\endgroup$ Commented Feb 19, 2018 at 23:06
  • $\begingroup$ @dmckee We're talking about liquid water here, right? Aren't the molecules in nearly constant interaction with their neighbors? From my limited understanding of water, I would be hesitant to use the word collision, let alone mean free path. Free paths are certainly not evident to me in the simulation linked by Pieter. $\endgroup$ Commented Feb 19, 2018 at 23:19
  • $\begingroup$ @Duncan, Yes and no. Of course, it's hard to treat "collisions" as discrete when molecules are too close to draw a distinction between asymptotic behavior and interacting behavior. But the interactions all have hard repulsive core potentials, so you can draw a fairly arbitrary line somewhere and say "this magnitude of force means a collision". Of course the simulation Pieter linked is cool but it covers about enough time for the average molecule to move by about it's own size, meaning not long enough to see the movement that characterizes liquid instead of solid. $\endgroup$ Commented Feb 19, 2018 at 23:31

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