Title: fractal dimension
Long Title: IUPAC Gold Book - fractal dimension
DOI: 10.1351/goldbook.FT07550
Status: current

Definition
Parameter that provides a mathematical description of the fractal structure of a polymer network, an aggregated particulate sol, or of the particles that comprise them.

Notes
1) \(m \propto r^{d}\) in which \(m\) is the mass contained within a radius, \(r\), measured from any site or bond within a fractal structure.
2) For a Euclidean object of constant density, \(d = 3\), but for a fractal object, \(d
3) For the surface area of a fractal object, \(s \propto r^{d'}\) in which \(s\) is the surface area contained within a radius, \(r\), measured from any site or bond and \(d'\) is termed the surface fractal dimension.

Related Terms
- particulate sol: https://goldbook.iupac.org//terms/view/PT07510
- polymer network: https://goldbook.iupac.org//terms/view/P04742

Source
- PAC, 2007, 79, 1801. 'Definitions of terms relating to the structure and processing of sols, gels, networks, and inorganic-organic hybrid materials (IUPAC Recommendations 2007)' on page 1811 (https://doi.org/10.1351/pac200779101801)

Other Outputs
- html: https://goldbook.iupac.org/terms/view/FT07550/html
- json: https://goldbook.iupac.org/terms/view/FT07550/json
- xml: https://goldbook.iupac.org/terms/view/FT07550/xml

Citation: Citation: 'fractal dimension' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.FT07550
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Accessed: 2026-04-24T22:25:29+00:00