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We systematically generate a large set of random micro-particle packings overa wide range of adhesion and friction by means of adhesive contact dynamicssimulation. The ensemble of generated packings covers a range of volumefraction $\phi$ from $0.135 \pm 0.007$ to $0.639 \pm 0.004$, and ofcoordination number $Z$ from $2.11 \pm 0.03$ to $6.40 \pm 0.06$. We determine$\phi$ and $Z$ at four limits (random close packing, random loose packing,adhesive close packing, and adhesive loose packing), and find a universalequation of state $\phi(Z)$ to describe packings with arbitrary adhesion andfriction. From a mechanical equilibrium analysis, we determine a criticalfriction coefficient $\mu_{\rm f, c}$: when the friction coefficient $\mu_{\rmf}$ is below $\mu_{\rm f, c}$, particles' rearrangements are dominated bysliding, otherwise, they are dominated by rolling. Because of this reason, both$\phi(\mu_{\rm f})$ and $Z(\mu_{\rm f})$ change sharply across $\mu_{\rm f,c}$. Finally, we generalize the Maxwell counting argument to micro-particlepackings, and show that the loosest packing, i.e., adhesive loose packing,satisfies the isostatic condition at $Z=2$.

Equation of state for random sphere packing with arbitrary adhesion and friction