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Chapter 31 – STRUCTURE FACTORS FOR POLYMER SYSTEMS

Chapter 31 – STRUCTURE FACTORS FOR POLYMER SYSTEMS. 31:5. THE ZERO CONTRAST METHOD. 31:6. THE RANDOM PHASE APPROXIMATION. dPEO. D 2 O. hPEO. H 2 O. 31:5. THE ZERO CONTRAST METHOD. -- Consider deuterated and hydrogenated polymers of same M w -- Mix them in solution

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Chapter 31 – STRUCTURE FACTORS FOR POLYMER SYSTEMS

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  1. Chapter 31 – STRUCTURE FACTORS FOR POLYMER SYSTEMS 31:5. THE ZERO CONTRAST METHOD 31:6. THE RANDOM PHASE APPROXIMATION

  2. dPEO D2O hPEO H2O 31:5. THE ZERO CONTRAST METHOD -- Consider deuterated and hydrogenated polymers of same Mw -- Mix them in solution -- Keep polymer volume fraction constant, but vary deuterated fraction -- Mix deuterated and hydrogenated solvent fraction to obtain zero contast Scattering cross section: Contrasts: Partial scattering factors:

  3. SOME DETAILS Scattering cross section (cm-1): single-chain inter-chain Defined standard deviation: Defined average squared: When contrast is zero, the inter-chain term does not contribute and the scattering cross section is proportional to single-chain form factor only

  4. MORE DETAILS Derivations: Cross section: Zero contrast condition:

  5. 31:6. THE RANDOM PHASE APPROXIMATION Derivations: Single-chain scattering factor: Flory-Huggins interaction parameter: Single-chain form factor: Incompressibility condition: Cross section: Spinodal condition:

  6. COMMENTS -- The zero contrast method and the Random Phase Approximation (RPA) method are useful methods for analyzing SANS data from polymers. -- The zero contrast method measures single-chain properties even in concentrated polymer mixtures. -- The RPA is a single method to calculate the structure factor for polymer mixtures in the mixed phase (homogeneous) region.

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