Chapter 28

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Chapter 28 FORM FACTORS FOR POLYMER SYSTEMS
281. THE DEBYE FUNCTION FOR GAUSSIAN CHAINS
28.2. SINGLE-CHAIN FORM FACTOR FOR GAUSSIAN CHAINS
28.3. OTHER POLYMER CHAIN ARCHITECTURES
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281. THE DEBYE FUNCTION FOR GAUSSIAN CHAINS
Gaussian probability distribution
Inter-monomer mean square distance
Form factor for Gaussian chains
Use the identity
Form factor
The Debye function
Radius of gyration
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28.2. SINGLE-CHAIN FORM FACTOR FOR GAUSSIAN CHAINS
Gaussian probability distribution
Gaussian chains with excluded volume
Form factor with excluded volume
Form factor
Continuous limit
Define the Incomplete Gamma function
Final result
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28.3. OTHER POLYMER CHAIN ARCHITECTURES
Form factor
Form factor amplitude
Propagation factor
Case of a triblock copolymer
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SCATTERING CROSS SECTION
Scattering cross section (cm-1)
Where (N/V) is the particle (or polymer) number
density f is the particle volume fraction VP is
the particle (or polymer) volume Dr2 is the
contrast factor P(Q) is the form factor SI(Q)
is the structure factor
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COMMENTS
-- Form factors for polymers are mass
fractals. -- Their calculation is needed for
modeling of polymeric systems of various
architectures.