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