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fractal dimension, d

Also contains definitions of: Hausdorff dimension, mass fractal dimension

Also contains definition of: surface fractal dimension

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 ∝ 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, such that its density decreases as the object gets larger.
  3. For the surface area of a fractal object, s ∝ 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.
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
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Cite as:
IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). XML on-line corrected version: http://goldbook.iupac.org (2006-) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8. doi:10.1351/goldbook.
Last update: 2014-02-24; version: 2.3.3.
DOI of this term: doi:10.1351/goldbook.FT07550.
Original PDF version: http://www.iupac.org/goldbook/FT07550.pdf. The PDF version is out of date and is provided for reference purposes only. For some entries, the PDF version may be unavailable.
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