Chapter 26 - RADIUS OF GYRATION CALCULATIONS

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.