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Guide to Empirical Models for Structural Analysis

Learn about Teubner-Strey, Debye-Bueche, and Guinier-Porod models. Understand correlation functions, cross-sections, parameters, and more. Discover Fourier transform integrals and their applications.

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Guide to Empirical Models for Structural Analysis

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  1. Chapter 23 - EMPIRICAL MODELS 23:3. THE TEUBNER-STREY MODEL 23:4. THE DEBYE-BUECHE MODEL 23:5. THE GUINIER-POROD MODEL

  2. 23:3. THE TEUBNER-STREY MODEL x: correlation length d: d-spacing Correlation function: Cross section: Parameters:

  3. PLOT

  4. Appendix 1:10. FOURIER TRANSFORM INTEGRALS Calculate integral: Note that:

  5. DERIVATIONS Note: So that:

  6. 23:4. THE DEBYE-BUECHE MODEL Correlation function: Cross section: Where: The Debye-Bueche model can be obtained from the Teubner-Strey model by setting 2pr << d.

  7. 23:5. THE GUINIER-POROD MODEL Guinier part: Porod part: With: Spherical micelles:

  8. GENERALIZED GUINIER-POROD MODEL s=0 for spheres s=1 for cylinders s=2 for lamellae Guinier part: Porod part: With: Cylindrical micelles:

  9. COMMENTS -- Empirical models are useful to obtain clues about the probed structure. -- They constitute a first order data analysis effort.

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