Chapter 6: Radial Distribution Function

Question 1

Radial Distribution Function

Answer 1

Describes probability of finding a pair of particles separated by a distance r relative to probabilty for a completely random distribution with same density

• g(r ) = 1 for ideal gas
• g(r ) can be measured experimentally from scattering experiments
• many static observables in equilibrium can be measured via g(r ) (e.g. Kirkwood-Buff Theory)

Question 2

Diffusion Constant

(Einstein Method)

Answer 2

Question 3

Diffusion Constant

(Einstein Method: Protocol)

Answer 3

1. Calculate MSD
2. Fit function

Question 4

Diffusion Constant

(Graph)

Answer 4

• ballistic regime: (α = 2) time-period before interactions become likely
• diffusive regime: (α = 1)
• Special Cases
  
  • α > 1 : super diffusion
  • α < 1 : sub-diffusion

Question 5

Green-Kubo Relations

Answer 5

relates transport properties to auto integrals over autocorrelation functions

• e.g. diffusion (see below)