Planar Random Networks with Flexible Fibers

The transition in random fiber networks from two-dimensional to asymptotically three-dimensional planar structure with increasing coverage $\overline{c}$ (mean fiber length per unit area) is studied with a deposition model. Network geometry depends on the scale-free product of fiber length and $\overline{c}$ at low $\overline{c}$, and on another scale-free product of flexibility and the width-to-thickness ratio of fibers at high $\overline{c}$. The structure becomes three-dimensional or decouples from the substrate faster when fibers are stiffer. Roughness of the free surface decreases with increasing fiber flexibility.