# Radial Distribution Functions for Nonadditive Hard-Rod Mixtures

Radial Distribution Functions for Nonadditive Hard-Rod Mixtures

In statistical mechanics, the radial distribution function represents the distribution of interparticle separations [1]. This Demonstration shows the results of exact statistical-mechanical computations of the radial distribution functions (r) for a one-dimensional binary system of particles interacting via hard-rod potentials [2, 3].

g

ij

The interactions between two particles of component 1 or two particles of component 2 are characterized by the lengths or , respectively, while the interaction between one particle of each component is characterized by the length . If =(+)/2, the mixture is said to be additive, otherwise, nonadditive. In the latter case, the nonadditivity can be either positive, >(+)/2, or negative, <(+)/2. We also find the values of the ratio and plot them, where , the inverse temperature; is the pressure; and is the number density. Sliders let you control the size and distance ratios / and /, the concentration (or mole fraction) of component 1, , and the total packing fraction .

σ

1

σ

2

σ

12

σ

12

σ

1

σ

2

σ

12

σ

1

σ

2

σ

12

σ

1

σ

2

βP/ρ

β=1/kT

P

ρ

σ

2

σ

1

σ

12

σ

1

x

1

ϕ=ρ(+)

x

1

σ

1

x

2

σ

2