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Radius of Gyration Calculations for Simple Shapes

Learn how to calculate the radius of gyration for various simple shapes, including spheres, cylinders, rectangular plates, and more. Understand the excluded volume parameter approach and its significance for polymer coils. Explore different scenarios and formulas for determining the radius of gyration in different contexts.

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Radius of Gyration Calculations for Simple Shapes

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  1. Chapter 26 - RADIUS OF GYRATION CALCULATIONS 26:1. SIMPLE SHAPES 26:2. CIRCULAR ROD AND RECTANGULAR BEAM 26:5. GAUSSIAN POLYMER COIL 26:6. THE EXCLUDED VOLUME PARAMETER APPROACH

  2. y z y R r R q r f x H x y r cos(f) f x W 26:1. SIMPLE SHAPES Thin disk of radius R: Sphere of radius R: cylindrical coordinates spherical coordinates Spherical shell: Rectangular plate of width W: cartesian coordinates

  3. Circular Rod Rectangular Beam 26:2. CIRCULAR ROD AND RECTANGULAR BEAM Rod of radius R and length L: Rectangular beam of width W, height H and length L :

  4. i center of mass j 26:5. GAUSSIAN POLYMER COIL Si Sij ri Radius of gyration: Note that: n: is the degree of polymerization a: is the segment length So that: Inter-monomer distance: Radius of gyration: End-to-end distance:

  5. 26:6. THE EXCLUDED VOLUME PARAMETER APPROACH For chains with excluded volume: Radius of gyration: n = 3/5 Self-avoiding walk: n = 1/2 Pure random walk: n = 1/3 Self-attracting walk: n = 1 Thin rigid rod of length L:

  6. COMMENTS -- Linear plots and empirical models yield radii of gyration. -- Modeling the radius of gyration is important for data analysis.

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