1 / 6

Chapter 28 – FORM FACTORS FOR POLYMER SYSTEMS

Chapter 28 – FORM FACTORS FOR POLYMER SYSTEMS. 28:1. THE DEBYE FUNCTION FOR GAUSSIAN CHAINS. 28.2. SINGLE-CHAIN FORM FACTOR FOR GAUSSIAN CHAINS. 28.3. OTHER POLYMER CHAIN ARCHITECTURES. 28:1. THE DEBYE FUNCTION FOR GAUSSIAN CHAINS. Gaussian probability distribution:.

bosgood
Download Presentation

Chapter 28 – FORM FACTORS FOR POLYMER SYSTEMS

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 28 – FORM FACTORS FOR POLYMER SYSTEMS 28:1. THE DEBYE FUNCTION FOR GAUSSIAN CHAINS 28.2. SINGLE-CHAIN FORM FACTOR FOR GAUSSIAN CHAINS 28.3. OTHER POLYMER CHAIN ARCHITECTURES

  2. 28:1. 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:

  3. 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:

  4. A i C j B P(Q) 1 j F(Q) 1 N E(Q) 28.3. OTHER POLYMER CHAIN ARCHITECTURES Form factor: Form factor amplitude: Propagation factor: Case of a triblock copolymer:

  5. 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

  6. COMMENTS -- Form factors for polymers are mass fractals. -- Their calculation is needed for modeling of polymeric systems of various architectures.

More Related