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Understanding Scattering from Fractal Systems

Explore mass and surface fractals, Porod exponents, pair correlation functions, and scattering densities in complex fluids. Learn the differences between mass and surface fractals and their impact on scattering phenomena.

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Understanding Scattering from Fractal Systems

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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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