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It is commonly taught (and also seen in experiments) that generally speaking the static friction coefficient is always greater than the kinetic coefficient, in other words

$$\mu_K<\mu_S$$

I have been trying to construct a microscopic model that explains why this is true, but it seems to be a difficult situation to approach with simple electrostatic potentials or anything energy-conserving whatsoever. The only approach that I could think of that is not entirely hopeless is if electromagnetic energy can be radiated off in a classical pattern.

Are there any convincing explanations of this phenomenon, mesoscopic or microscopic in nature? Answers with references will be preferred.

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The difference is due to the imperfection of real world surfaces. Friction depends on the interlocking of two surfaces of materials. Think of that as surfaces having a "landscape". As they slide past each other, they settle, destroy and rub against each other. On a microscopic level, if the two "landscapes" settle, it is going to be harder for them to move them apart.

Static friction is the friction due to the settled surfaces (maximum interaction), whereas dynamic friction is the average friction of settled and unsettled states. Stationary objects begin their movement from a settled state, since that is the minimum of their energy.

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I have been trying to construct a microscopic model that explains why this is true

Good luck with that!

Refer to the friction plot in the following link:

http://hyperphysics.phy-astr.gsu.edu/hbase/frict2.html#kin

You'll note that the transition between static and kinetic friction is shown as a vertical line, implying a sudden decrease in friction from static to kinetic where the friction force is undefined during the transition. As you already know, that kinetic friction is less than static, is consistent with observation. On the other hand, a precise understanding of the transition is not well understood..

Bottom line: If you want to model precisely the actual mechanism(s) involved with friction, to quote the link, they "defy precise description". Which is why I said, good luck.

Hope this helps.

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