Experimental Methods for Studying Fractal Aggregates

Porous materials, aggregates and ramified structures frequently display self-similarity, i.e., their structure is associated with power-law density-density correlation functions. In a real physical system, such behavior has two natural limits: the particle or pore size and the cluster size. Within these limits, the system is well described by a fractal or Hausdorff dimension. For the experimentalist, it is important to find methods which can isolate this behavior, i.e., to distinguish it from the particle and cluster contributions, in order to determine the fractal dimension unambiguously. Depending on the characteristic size of the fractal object, different experimental methods can be used. We discuss the use of microscopic photographs and give the theory of scattering applied to fractal objects and fractal surfaces. We present, in particular, the method of separating the particle and the cluster size contributions. Finally we give a short introduction to the dynamical aspects of fractals and to the interpretation of low frequency vibrational spectra of fractal systems in terms of fractons.

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