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

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Presentation transcript:

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

33:1. MASS FRACTAL  r0r0 Inter-particle structure factor: Pair correlation function g(r): Fluctuating scattering density: Result: High-Q limit:

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

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

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).