binary interaction parameter k−1.50
relative width λ1.5
attractive strength ratio εB / εA2.00
diameter ratio σB / σA4.0

Directions

This simulation considers three models for intermolecular potentials: square-well, Sutherland, and Lennard-Jones. Potentials for molecule A (blue), molecule B (green), and an A–B mixture (orange) are shown.

Choose a potential model with the buttons at top left. Use the sliders to change the parameters:

  • The binary interaction parameter k represents how non-ideal the mixture is (k = 0 is the ideal case).
  • The attractive-strength ratio εB/εA is the relative well depth of B to A.
  • The diameter ratio σB/σA is the relative size of the molecules.
  • The relative width λ (square-well only) is the ratio of the attractive diameter to the repulsive diameter.

Check “show labels for B” to mark σ, λσ, and ε directly on curve B. Click Details for the governing equations.

Details

Square-well potential

\[ u(r)=\begin{cases} \infty & r \le \sigma \\ -\epsilon & \sigma < r \le \lambda\sigma \\ 0 & r > \lambda\sigma \end{cases} \]

Sutherland potential

\[ u(r)=\begin{cases} \infty & r \le \sigma \\[2pt] -\epsilon\left(\dfrac{\sigma}{r}\right)^{6} & r > \sigma \end{cases} \]

Lennard–Jones potential

\[ u(r)=4\epsilon\left[\left(\dfrac{\sigma}{r}\right)^{12}-\left(\dfrac{\sigma}{r}\right)^{6}\right] \]
u
intermolecular potential energy
r
distance between molecular centers
σ
molecular diameter
ε
depth of the potential well
λ
well width for the square-well potential

Mixture (A–B) parameters

The attractive-strength parameter of the mixture is given by

\[ \epsilon_{AB} = (1-k)\sqrt{\epsilon_A \epsilon_B} \]

where k is the binary interaction parameter. A larger negative k represents stronger A–B interactions relative to A–A or B–B; a smaller positive k represents weaker interactions.

The molecular-diameter parameter of the mixture is given by

\[ \sigma_{AB} = \frac{\sigma_A+\sigma_B}{2} \]

Molecule A is the reference molecule, with εA = 1 and σA = 1; all plotted quantities are scaled by these values.

About

This simulation was created in the Department of Chemical and Biological Engineering at University of Colorado Boulder for LearnChemE.com by John L. Falconer using Claude AI. It is a JavaScript/HTML5 implementation of a Mathematica simulation by Megan E. Maguire and Rachael L. Baumann. It was prepared with financial support from the National Science Foundation (DUE 2336987 and 2336988). Address any questions or comments to LearnChemE@gmail.com.