lattice.notes
Reference — Scale

Three scales of a HydroGraph fractal aggregate

"Fractal graphene" spans three nested scales, each about a hundredfold larger than the last: a single atomic sheet, the multilayer nanoparticle built from a handful of those sheets, and the branching fractal aggregate built from thousands of those nanoparticles. The numbers below come from HydroGraph Clean Power's own published characterization of its Fractal Graphene Aggregate (FGA-1), produced by chamber-explosion synthesis.

01 — Log scale

From one atomic layer to a branching aggregate

Each major tick is a 10× jump. Cyan markers are HydroGraph's measured figures; gold dots are familiar objects shown only for a sense of scale.

0.1 nm
1 nm
10 nm
100 nm
1 μm
10 μm
100 μm
0.335 nmsingle-layer graphene
~2 nmDNA double helix, for scale
20–50 nmthe graphene flake (FGA-1 monomer)
~100 nmsmall virus, for scale
no single sizefractal aggregate — self-similar, keeps branching
~1 μmbacterium, for scale
~7.5 μmred blood cell, for scale
~70 μmhuman hair width, for scale
HydroGraph measured value everyday object, for scale (approximate)
02 — The hierarchy

Layer, flake, aggregate

Single-layer graphene the atomic sheet

≈ 0.335 nm thick — one atom

A single graphene sheet is one atom thick: a hexagonal lattice of sp²-bonded carbon. It's the building block of every other scale on this page. In HydroGraph's material the layers are turbostratic — randomly rotated relative to one another rather than Bernal-stacked — so X-ray diffraction measures an interlayer spacing of 0.344–0.350 nm, slightly expanded from ideal graphite's 0.335 nm because the layers interact only weakly and behave more like independent monolayers than a bonded stack.

Source: Shakil, A. (2025). "Chamber explosion synthesis of fractal aggregate graphene." Graphene and 2D Materials 10, 43–56.

The graphene flake FGA-1 "monomer"

20–50 nm across · ~6.6 layers average (± 3.3)

HydroGraph's chamber-explosion process ignites an acetylene/oxygen mixture in a sealed chamber, briefly reaching ~2,550 K. In that heat, amorphous carbon soot crystallizes into small, roughly spherical multilayer particles — the paper calls them "monomers" — before the aerosol cools and quenches within milliseconds. High-resolution TEM image analysis of the FGA-1 material found a distribution centered on 6.6 turbostratic layers per flake, with individual flakes 20 to 50 nm across. This is the true "flake": several graphene sheets thick, but still two orders of magnitude smaller than a virus.

Source: Shakil, A. (2025), Section 3.1 (FGA-1 physical properties). Graphene and 2D Materials 10, 43–56.

The fractal aggregate FGA-1, as produced

No fixed size — self-similar branching, N = k₀(Rg/a)ᴰ

Individual flakes don't stay solitary. While still suspended in the chamber, they collide and stick via Brownian motion — diffusion-limited cluster aggregation (DLCA) — building outward into a branched, self-similar network rather than a dense clump. Structurally, this is a genuine three-dimensional network of branches, not a flat or sheet-like arrangement — the same class of structure as an aerogel, which is how the aggregation physics behind it was first studied. The paper describes FGA-1 itself as "the ramified, open network of fractal FGA-1," and mass-versus-size scaling of that network follows a non-integer fractal dimension — this is "fractal geometry" in the precise sense Mandelbrot defined the term, not a casual figure of speech. That's the defining property of a fractal: it has no single characteristic size, only a scaling law relating particle count N to the aggregate's radius of gyration Rg. Because branches rarely bury one another in three dimensions, the aggregate exposes far more surface per gram than a compact particle of the same mass — measured at 150 m²/g BET surface area for FGA-1, versus ~25 m²/g for the more tightly packed FGA-2 variant. This is the same surface-accessibility mechanism shown in the simulation elsewhere on this site (illustrated there in 2D, for clarity — the real aggregate branches in 3D).

When FGA-1 is redispersed into Fractal Graphene Paste™, dynamic light scattering measures a D50 particle size of approximately 35 nm — close to the primary flake scale, meaning the dispersion process works the aggregate back down near individual flakes rather than leaving large clumps.

Sources: Shakil, A. (2025), Sections 2.3, 3.1 & 4.4 (quote: "the ramified, open network of fractal FGA-1"). Graphene and 2D Materials 10, 43–56 — citing Mandelbrot, B.B. (1983), The Fractal Geometry of Nature. · HydroGraph Clean Power Inc., "HydroGraph Launches Fractal Graphene Paste™" (June 29, 2026).
03 — Illustration

A fractal aggregate, grown live

A simplified 2D diffusion-limited aggregation model, run in your browser: particles are released one at a time, random-walk, and stick on contact with the growing cluster — the same mechanism described above, illustrative only (not to the scale ruler above).

Growing cluster…

Why the scale hierarchy matters

A restacked or bulk graphene particle at the same mass as FGA-1 would bury most of its own surface against itself. Because HydroGraph's aggregate keeps branching self-similarly from the 20–50 nm flake scale outward instead of packing into a compact block, almost none of its mass is inaccessible — the geometric reason fractal aggregate graphene is reported to outperform bulk or restacked graphene on ion transport, effective capacitance, and catalytic/sensing activity per gram, at far lower loadings.