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