Figures index

From

Mathematical Modeling in Secondary Chemistry Education: Chromatography

Thomas Kraska

World Journal of Chemical Education. 2020, 8(3), 114-121 doi:10.12691/wjce-8-3-3
  • Figure 1. a) Setup of a stochastic board game for the diffusion along the x-coordinate. The numbers at the bottom represent the position; the numbers at the left side represent the numbers of the stones. b) Outcome of a specific game. At the top, the corresponding distribution is depicted
  • Figure 2. Stochastic tree diagram for the probability reaching a position on the x-axis given by the number in the boxes. The tree is for four time steps t=4. Here p=1/2 is the probability to move in either direction at random. A corresponding empty worksheet is provided in the Supporting Information
  • Figure 3. Probability distribution for the diffusion game for t=4. The x-axis is the position while i is the index of the binomial distribution (x=2i-t)
  • Figure 4. Result of the diffusion simulation for nA=104, nrun=2·106 (red), p=1/2, and nrun=8·106 (blue). The solid curves are the corresponding Gaussian distributions
  • Figure 5. Initial state of the game board for the simulation of the Taylor dispersion-like approach. The numbers at the bottom are the x-position. The numbers at the left are the numbers of the stones. Here only movement in one direction is required
  • Figure 6. Results after nrun=2·106 steps for a Taylor dispersion-like simulation for nA=104 molecules
  • Figure 7. Output of a simulation for two substances with the acceptance parameters nacc,A=1 (blue) and nacc,B=4 (red). The mole fraction is xA=0.5, i.e. the peak areas are identical. The number of steps is nrun=8·106, the total number of molecules nA+nB=105. From the simulation data we obtain and A code is provided in the Supporting information
  • Figure 8. Simulated chromatogram of a lighter gas. (nrun=2·106 steps; ntot=3·104 molecules). Retention time parameters and mole fractions are given in the text. 1: ethane; 2: propan; 3: methylpropane; 4: n-butane