Nanocellulose Fiber Network Percolation (2D)

Fiber Type

Fiber Network

Fiber density 150

Generating fiber mat…

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Fibers

Total junctions

Junctions in network

Coordination z

0.0

Percolating?

Relative modulus

How it works

Real nanocellulose films (cellulose nanocrystals — CNC — and nanofibrils — CNF) get all of their mechanical strength from a random mat of rod-like fibers that touch and hydrogen-bond wherever their crystalline surfaces come close enough. No single fiber is strong on its own; strength only exists once enough fibers are packed in for a connected path of junctions to span the whole sample — a textbook case of continuum stick percolation (Balberg et al., 1984).

Below the critical fiber density there is no spanning path: the mat is just disconnected islands of a few bonded fibers, and it falls apart under load. Cross the threshold and a giant connected cluster suddenly appears — this simulation finds it exactly, with a union-find over every fiber-fiber contact, the same algorithm used to test electrical/mechanical percolation in real composite models.

Coordination number z: the average number of bonded neighbors per fiber in the spanning network (z = 2·junctions⁄fibers). Fiber networks can carry load in bending, so they stay rigid at a lower z than a simple ball-and-spring lattice needs (Broedersz & MacKintosh fiber-network elasticity theory).
Longer fibrils percolate sooner: the excluded area swept out by a rod scales with its length squared, so switching from short CNC rods to long CNF fibrils at the same fiber count can flip the mat from disconnected to fully percolating.
Relative modulus: once percolating, stiffness grows as a power law above the threshold, E/E₀ ∝ (density above threshold)^t — the same critical-exponent scaling used for gels and conductive composites near their percolation point.

Percolating network Connected cluster Isolated fiber Fiber-fiber junction