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Understanding Polymer Systems through Zero Contrast and Random Phase Approximation Methods

Explore the Zero Contrast Method and Random Phase Approximation for deuterated and hydrogenated polymers in solution to analyze SANS data, determine scattering cross-section, and study polymer mixtures.

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Understanding Polymer Systems through Zero Contrast and Random Phase Approximation Methods

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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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