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Chapter 34 – THE MULTI-COMPONENT RANDOM PHASE APPROXIMATION

Chapter 34 – THE MULTI-COMPONENT RANDOM PHASE APPROXIMATION. 34:2. INCOMPRESSIBLE POLYMER MIXTURE. 34:3. THE SINGLE-CHAIN FORM FACTORS. 34:4. BINARY HOMOPOLYMER BLEND MIXTURE. 34:5. TERNARY HOMOPOLYMER BLEND MIXTURE. 34:7. THE DIBLOCK COPOLYMER CASE. 3. 2. 2. 3. 3. 2. 1. 1. 1.

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Chapter 34 – THE MULTI-COMPONENT RANDOM PHASE APPROXIMATION

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  1. Chapter 34 – THE MULTI-COMPONENT RANDOM PHASE APPROXIMATION 34:2. INCOMPRESSIBLE POLYMER MIXTURE 34:3. THE SINGLE-CHAIN FORM FACTORS 34:4. BINARY HOMOPOLYMER BLEND MIXTURE 34:5. TERNARY HOMOPOLYMER BLEND MIXTURE 34:7. THE DIBLOCK COPOLYMER CASE

  2. 3 2 2 3 3 2 1 1 1 34:2. INCOMPRESSIBLE POLYMER MIXTURE Scattering cross section: Matrix notation: Non-interacting system scattering factors: Excluded volume terms: Scattering length densities:

  3. MORE ON THIS Incompressibility condition: This implies: Spinodal condition:

  4. 120 100 9 4 5 8 2 1 3 6 7 110 34:3. THE SINGLE-CHAIN FORM FACTORS “Bare” homopolymer scattering factor: “Bare” copopolymer scattering factor: Homopolymer form factor: Complex architectures:

  5. 34:4. BINARY HOMOPOLYMER BLEND MIXTURE Bare scattering factor for component 1: Excluded volume factor for component 1: Fully interacting system scattering factor: Scattering cross section: This is referred to as the de Gennes formula

  6. 34:5. TERNARY HOMOPOLYMER BLEND MIXTURE Bare scattering factors: Excluded volume factors: Scattering factors: Scattering cross section:

  7. Diblock copolymer Homopolymer blend mixture 34:7. THE DIBLOCK COPOLYMER CASE Fully interacting system scattering factor: Scattering cross section:

  8. COMMENTS -- The Random Phase Approximation (RPA) model applies to homogeneous (single-phase) polymer mixtures. -- It does not apply to the demixed phase (phase separated) region. -- It can handle homopolymers and other architectures (copolymers, comb polymers, star polymers, etc). -- It can predict the scattering cross section as well as the spinodal temperature. -- It can work for Lower Critical Spinodal Temperature (LCST) and Upper CST blend mixtures.

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