Radial Distribution Functions for Nonadditive Hard-Rod Mixtures

size ratio

σ

2

/

σ

1

0.6

length ratio

σ

12

/

σ

1

0.8

concentration of component 1,

x

1

0.5

total packing fraction

0.6

function

g

ij

(r)

β P / ρ

β P / ρ = 2.5

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

g

ij

(r)

for a one-dimensional binary system of particles interacting via hard-rod potentials [2, 3].

The interactions between two particles of component 1 or two particles of component 2 are characterized by the lengths

σ

1

or

σ

2

, respectively, while the interaction between one particle of each component is characterized by the length

σ

12

. If

σ

12

=(

σ

1

+

σ

2

)/2

, the mixture is said to be additive, otherwise, nonadditive. In the latter case, the nonadditivity can be either positive,

σ

12

>(

σ

1

+

σ

2

)/2

, or negative,

σ

12

<(

σ

1

+

σ

2

)/2

. We also find the values of the ratio

βP/ρ

and plot them, where

β=1/kT

, the inverse temperature;

P

is the pressure; and

ρ

is the number density. Sliders let you control the size and distance ratios

σ

2

/

σ

1

and

σ

12

/

σ

1

, the concentration (or mole fraction) of component 1,

x

1

, and the total packing fraction

ϕ=ρ(

x

1

σ

1

+

x

2

σ

2

)

.