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Scattering from Fractal Systems: Mass & Surface Fractals

This chapter explores the scattering behavior of fractal systems, specifically mass fractals and surface fractals. It discusses inter-particle structure factors, pair correlation functions, fluctuating scattering density, surface scaling laws, and fractal Porod exponents.

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Scattering from Fractal Systems: Mass & Surface Fractals

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  1. Chapter 33 – SCATTERING FROM FRACTAL SYSTEMS 33:1. MASS FRACTAL 33:2. SURFACE FRACTAL 33:3. FRACTAL POROD EXPONENTS

  2. r0 x 33:1. MASS FRACTAL Inter-particle structure factor: Pair correlation function g(r): Fluctuating scattering density: Result: High-Q limit:

  3. 33:2. SURFACE FRACTAL Surface scaling law: High-Q limit: Result:

  4. Q-5/3 Q-2 Q-3 Q-3 Q-4 swollen chains Gaussian chains clustered network rough surface smooth surface MASS FRACTALS SURFACE FRACTALS 33:3. FRACTAL POROD EXPONENTS

  5. COMMENTS -- There are two types of fractals: mass fractals and surface fractals. -- Homogeneous polymers are often mass fractals. Polymers phase separate into domains which are surface fractals because of the formed interface. Complex fluids often involve scattering from particles (such as micelles or nanoemulsions).

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