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. 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

3. 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 :

4. 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:

5. 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

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