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

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

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

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

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

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