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Chapter 33 – SCATTERING FROM FRACTAL SYSTEMS

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Chapter 33 – SCATTERING FROM FRACTAL SYSTEMS . 33:1. MASS FRACTAL. 33:2. SURFACE FRACTAL. 33:3. FRACTAL POROD EXPONENTS. r 0. x. 33:1. MASS FRACTAL. Inter-particle structure factor:. Pair correlation function g(r):. Fluctuating scattering density:. Result:. High-Q limit:.

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slide1

Chapter 33 – SCATTERING FROM FRACTAL SYSTEMS

33:1. MASS FRACTAL

33:2. SURFACE FRACTAL

33:3. FRACTAL POROD EXPONENTS

slide2

r0

x

33:1. MASS FRACTAL

Inter-particle structure factor:

Pair correlation function g(r):

Fluctuating scattering density:

Result:

High-Q limit:

slide3

33:2. SURFACE FRACTAL

Surface scaling law:

High-Q limit:

Result:

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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

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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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