INDEX mass fractal dimension

Dinsmore and Weitz (2002) [60] examined a model system of polymethylmethacrylate particles dyed with rhodamine in a density- and refractive-index-matched solution of decalin and cyclohexylbromide. They used CLSM to follow the (very slow) aggregation in real time and determined the particle positions in full three-dimensional detail. From this they performed a comprehensive structural analysis of the gels, including measurement of coordination numbers and backbone fractal dimension of the structures, as well as the much more commonly measured mass fractal dimension. 

The spectral dimension d is a true property of a fractal and is determined only by its connectivity. It differs from the mass scaling index [see Equation (11.1)] or fractal dimension df and from the scaling index of the diffusion constant 8 by the fact that it does not depend on the way in which a fractal has been inserted into the Euclidean space with dimension d. The dependence of d and 8 on df is described by Equation (11.3). 

Attempts to resolve this contradiction have been undertaken [68]. Maritan and Stella [69] calculated the fractal dimensions for 50 proteins using two methods. In one method, fractal dimension is a scaling index for the contour length of a macromolecule with respect to the distance between its ends (it is equal to 1.19-1.82), while in the other method, the fractal dimension is a scaling index for the total mass with respect to the length, which is equal to 1.62-2.24. The calculations were performed using X-ray diffraction crystallographic parameters of proteins. 

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