Origin of the logarithmic aging of static friction
In plain words
The longer two surfaces stay in contact at rest, the harder it is to start them sliding, and the increase grows with the logarithm of time. Whether this comes from the contacts slowly squashing and growing or from chemical bonds forming across them is disputed.
Precise statement
The static friction coefficient grows as $\mu_{s}(t) = \mu_{0} + \beta \ln(1 + t / t_{c})$ with $\beta$ of order 0.01 for rocks, polymers and metals, the basis of rate-and-state friction laws. Determine whether aging comes from creep growth of real contact area, from interfacial chemical bonding (reported in nanoscale silica contacts), or both, and predict $\beta$ and $t_{c}$ from material properties.
What would settle it
Simultaneous measurement of real contact area and interfacial bond density during aging for a well-characterized interface, accounting quantitatively for $\beta$.
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