Quick Tutorial - A Three-Dimensional Scheme with Electrochemistry

In this tutorial, you will learn to:

  • Create a three-dimensional reaction scheme
  • Configure the properties of each compartment
  • Define transport processes between compartments
  • Enter reaction conditions with programmed voltage
  • Set the simulator parameters
  • Run the simulation
  • Display the simulation results

This section leads you through the procedure for simulating a electrochemical reaction in an inhomogeneous volume. If you've never used Kinetiscope before, this tutorial will help you become familiar with Kinetiscope's different menus and functions.

Redox Chemistry of Ferricyanide

The reduction/oxidation of the ferricyanide/ferrocyanide metal complexes is a well-behaved reversible electrochemical reaction, and is used as a reference standard for system characterization.

The reaction proceeds as follows:

[Fe(CN)6]3- + e- ⇄ [Fe(CN)6]4-

The rate and net direction of this reaction depends on the electrode potential. In this tutorial you will simulate the conditions of cyclic voltammetry, where the electrode potential is swept back and forth between two values and the kinetics are assessed by monitoring electron flow (current).

Creating a New Reaction Scheme

You will next create a new reaction scheme based on a three-dimensional model and save it as a file entitled tutorial4.rxn.

When you first create a three-dimensional reaction scheme, you specify the type of model and select the concentration, time, length, and energy units to be used throughout. You also set up the array of compartments and transfer paths that comprise the reaction system.

When you later save your input, you specify its file name and the directory where it will be stored.

To create the reaction scheme:

  1. Select File | New Scheme | Three-dimensional Model... from the menu bar of Kinetiscope's main window, or click the push button on the main window's tool bar.

    A Create Three-Dimensional Scheme Dialog appears.

  2. Select the following units for time, energy, concentration and length using the drop-down list boxes on the first page: sec, kcal, mole/cm3, cm.

    Make the selections by clicking the left mouse button on the drop-down list boxes and then clicking on the appropriate entry.

    The dialog should look like this:

    This is the only time that the units for a particular file can be specified. The units that are selected here must be used consistently for all input data, and are used for plotting the simulation results.

  3. Click Next > to move to the second page of the dialog.
  4. For the moment leave the dimensions of each compartment at their default values of 1.0 cm.

    When a three-dimensional reaction scheme is first created, all compartments in a reaction scheme initially are given the same dimensions. You will modify individual compartment dimensions later during editing of the reaction scheme.

    The dialog should look like this:

  5. Click Next > to move to the last page of the dialog.
  6. The total reaction volume to be simulated is represented by a three-dimensional array of compartments. On this page you define the numbers of columns, rows and layers in that array.

    Use the up/down arrows on the spin boxes to adjust the array. For this scheme set the Compartment Array to have
    Columns 11
    Rows 1
    Layers 1
    Periodic boundary conditions are used to connect transfer paths from one face of the array to its opposing face. We will not use periodic boundary conditions in this scheme so leave these check boxes unchecked.

    The dialog should look like this:

  7. Click Finish.
You now are returned to Kinetiscope's main window, where a new three-dimensional scheme window named untitled1 - 3D model has been created. The diagram contains the eleven compartments, represented as cubes, with each connected to its neighbors by a transfer path, represented as hexagonal shapes at the inter-compartmental interfaces.

If you hover the mouse cursor over one of these objects, a tool tip will appear with a brief summary of its contents.

Saving your Reaction Scheme

As you modify your reaction scheme, remember to periodically save your changes. This will help prevent accidental loss of data.

To save the reaction scheme as a file:

  1. Select File | Save As... from the menu bar of the main window, or click the push button on the main window's tool bar. A File Save Dialog appears.
  2. Use the File Save Dialog to navigate to the directory you have selected for your files, and enter the name tutorial4.
  3. Click the Save push button on the File Save Dialog.

If you make an undesired change (for example, accidentally delete a step), you now can recover by selecting File | Revert to Saved... from the menu bar of the main window, or clicking the push button on the main window's tool bar.

You will next edit both compartments and transfer paths.

Configuring the Compartments

Setting Colors and Names

To visualize the structure of the reaction volume, we will next set compartment names and colors in a systematic way.

To set the compartments' colors and names:
  1. Double-click on the left-most compartment (initially named C1 R1 L1, meaning Column 1, Row 1, Layer 1).

    The compartment is highlighted with a cross-hatch and the Compartment Editor Dialog opens.

  2. Click on the Compartment Details tab of the Compartment Editor Dialog to view that page.
  3. In the Compartment Name data entry field, type electrode
  4. Click the white square push button displaying the current Compartment Color.

    This opens a Select Color Dialog. Use that to choose a gray shade and close the Select Color Dialog.

    The screen should look like this:

  5. Click OK.

    The Compartment Editor Dialog is dismissed and the first compartment displays the new color and name.

  6. Repeat steps 1-5 with the second compartment from the left (C2 R1 L1); In the Compartment Name entry field, type interface and set the color to be a medium blue.
  7. Repeat steps 1-5 with the third compartment from the left (C3 R1 L1); In the Compartment Name entry field, type electrolyte and set the color to be a light blue.

    We will now configure the appearance of the remaining compartments with a copy-and-paste operation.

  8. Select the third compartment with a a single click of the left mouse button.
  9. Click the (Copy object) push button on the scheme window's tool bar.

    This places a copy of the third compartment on Kinetiscope's internal clipboard.

  10. Press and hold the left mouse button, then move the mouse cursor to enclose only the remaining white compartments with the rubber-band box that appears, and release the mouse button.

    All the white compartments should now be selected, indicated by cross-hatching.

  11. Click the (Paste) push button on the scheme window's tool bar.

    A Replace Compartments Dialog appears.

  12. On the Replace Compartments Dialog, leave all four check boxes checked.
  13. In the Naming section of the Replace Compartments Dialog, select the Rename to radio button and in its data entry field type

    electrolyte.

  14. Click OK.

    The Replace Compartments Dialog is dismissed and the selected compartments display the new color and names.

    The scheme window should look like this:

Editing Compartment Dimensions

Reactant diffusion plays an important role in electrochemical kinetics; transport of reactants and products to and from the electrode/electrolyte interface can strongly affect rates of reaction. Of interest in this scheme are the rates of transport in the direction perpendicular to the electrode surface, i.e. the X-direction.

We will re-dimension the compartments in the X-direction using an exponentially expanding grid. This enables computationally efficient calculation of transport over a wide dimensional range, using small dimensional increments near the electrode where concentration gradients are greatest, and increasingly larger dimensional increments as we move into the bulk solution. All compartments but the electrode will be re-dimensioned.

To re-dimension the compartments:
  1. Click the Scheme tab to activate that page.
  2. Click the (Advanced functions) push button on the scheme window's tool bar. The Advanced Functions Dialog appears.
  3. Click on the Advanced Dimensioning tab of the Advanced Functions Dialog, then set the controls on that page to the following values:

    Grid type Exponentially expanding grid
    Dimension increase from left to right
    Minimum Dimension 1.0e-6
    Maximum Dimension 1.0e-2
    First Column to Change 2
    Last Column to Change 11

    The dialog should look like this:

  4. Click Apply, then click Close to dismiss the Advanced Functions Dialog.

Entering the Reaction Mechanism

You are ready to enter the reaction mechanism.

To enter a reaction step:

  1. Click the Scheme tab on the scheme window.
  2. Double-click the left mouse button on the compartment you have named interface (colored medium blue).

    The compartment is highlighted with a cross-hatch and the Compartment Editor Dialog opens.

  3. Click the Reaction Steps tab on the Compartment Editor Dialog.
  4. Click the (Add a reaction step) push button on the dialog's tool bar.

    You use the Reaction Step Editor Dialog that appears to enter your reaction mechanism. Later, you may also edit previously entered mechanisms from this dialog.

    Using the Reaction Step Editor Dialog, individual reaction steps are entered much as you would write them on a piece of paper. The generalized format for an electrochemical reaction is:

    A + e- <=> B

    where A and B are mnemonics that you choose for the reactant and product, and e- represents the electron. In Kinetiscope, all electrochemical steps are reversible and are single electron processes.

    For more on entering the reaction step, see the detailed discussion in the section entitled Entering the Equation.

  5. Type the following reaction step in the Equation data entry field of the Reaction Step Editor Dialog:

    Fe(CN6)(3-) + e- <=> Fe(CN6)(4-)

  6. Use the mouse to select Voltage-dependent in the upper list box in the Rate Constants area of the Reaction Step Editor Dialog.

    In Kinetiscope, voltage dependent rate constants are entered in Butler-Volmer form:

    k  = k0 eαnF(E-E0)/RT (1)

    where k0 is the standard rate constant, α is the transfer coefficient, n is the number of electrons, F is the Faraday constant, E is the applied potential, E0 is the formal potential, and R and T are defined as above. For the reverse reaction the transfer coefficient term α is replaced by (1-α).

    A set of data entry fields for specifying the three Butler-Volmer parameters is shown. Here you will enter the k0, α and E0 values for this reaction step. Both forward and reverse rate constants are derived from these values.

  7. Type the following values in the data entry fields:
    Formal Potential E0 0.278
    Transfer Coefficient α 0.5
    Standard Rate Constant k0 4.1e-2

    The dialog should now look like this:

  8. Click OK to dismiss the Reaction Editor Dialog.

    This returns you to the Compartment Editor Dialog.

  9. Click the Initial Concentrations tab on the Compartment Editor Dialog.
  10. In the table of species concentrations, double-click on the entry for Fe(CN(6(3-) in the Initial Concentration column, type

    2.0e-6

    and then press the Enter key.

  11. Click OK to dismiss the Compartment Editor Dialog.

    This will return you to the untitled1 - 3D model scheme window.

Setting Initial Concentrations

The initial concentrations of Fe(CN)63- and Fe(CN)64- should be uniform throughout the liquid volume. Those initial concentrations have been set, but only in the interface compartment. We will copy those concentration values into the other compartments that comprise the liquid volume:

To copy initial concentrations to other compartments:
  1. Select the interface compartment with a single click of the left mouse button.
  2. Click the (Copy object) push button on the scheme window's tool bar.

    This places a copy of the interface compartment on the clipboard.

  3. Press and hold the left mouse button, move the mouse cursor to enclose only the other liquid compartments (colored light blue) with the rubber-band box that appears, then release the mouse button.

    All the light blue compartments will be selected, indicated by cross-hatching.

  4. Click the (Paste) button on the scheme window's tool bar.

    A Replace Compartments Dialog appears.

  5. In the Properties to Replace area of the Replace Compartments Dialog, uncheck the Reaction Steps and Screen Colors check boxes, but leave the Initial species concentrations check box checked.
  6. In the Naming sectionof the Replace Compartments Dialog, select the Preserve the current name radio button.
  7. Click OK.

    The dialog is dismissed and the initial concentrations of Fe(CN)63- and Fe(CN)64- are now set in all compartments in the liquid volume.

You have now completed entering the reaction data for this scheme.

Configuring the Transfer Paths

Two types of transfer processes, electron transfer and diffusion, must be configured for this scheme.

To configure the electron transfer step
  1. Double-click the left mouse button on the transfer path (the hexagon shape) between the electrode compartment and the interface compartment.

    The transfer path is highlighted with a cross-hatch and the Transfer Path Editor Dialog appears.

  2. Click the (Add a transfer step) push button on the Transfer Path Editor Dialog's tool bar.

    The Transfer Step Editor Dialog that appears will be used to define the new transfer step.

  3. Click on the Transfer Type drop-down list box at the top of the Transfer Step Editor Dialog and select Electron transfer.
  4. Click OK to dismiss the Transfer Step Editor Dialog.

    This returns you to the Transfer Path Editor Dialog.

  5. Click the black square push-button displaying the current Transfer Path Color.

    This opens a Select Color Dialog. Use that to choose a yellow shade and close the dialog. This serves to visually differentiate this transfer path from others in the scheme.

  6. The Transfer Path Editor Dialog should look like this:

  7. Click OK to dismiss the Transfer Path Editor Dialog.
To configure the diffusion steps:
  1. Double-click the left mouse button on the transfer path between the interface compartment and the electrolyte compartment (named Transfer 2).

    The transfer path is highlighted with a cross-hatch and the Transfer Path Editor Dialog appears.

  2. Click the (Add a transfer step) push button on the Transfer Path Editor Dialog's tool bar.

    The Transfer Step Editor Dialog is invoked.

  3. Set the controls on the Transfer Step Editor Dialog to the following settings:

    Type in the following values:
    Transfer Type Gradient diffusion
    Transferred Species Fe(CN6)(3-)
    Direction bidirectional
    Rate Constant Form Temperature-independent
    Diffusion Coefficient D Forward 0.763e-5
    Diffusion Coefficient D Reverse 0.763e-5

  4. Click OK to dismiss the Transfer Step Editor Dialog. This returns you to the Transfer Path Editor Dialog.

    We will now add a second transfer step by copy-and-paste of the transfer step just created.

  5. Click the right mouse button once over the line in the table that contains the transfer step you just added. A context menu appears.
  6. Select Copy Step from the menu. This places a copy of the step on Kinetiscope's clipboard.
  7. Now click the (Paste a transfer step) button on the dialog's tool bar. This adds a second step to the table, a copy of the first.
  8. Double-click the left mouse button over the newly added step. The Transfer Step Editor Dialog is invoked.
  9. Change the Transferred Species entry from Fe(CN6)(3-) to Fe(CN6)(4-).
  10. Click OK to dismiss the Transfer Step Editor Dialog. This returns you to the Transfer Path Editor Dialog.
  11. Click the black square displaying the current Transfer Path Color. This opens a Select Color Dialog. Use that to choose a green shade and close the dialog. This serves to visually differentiate this transfer path from others in the scheme.
  12. The Transfer Path Editor Dialog should look like this:

  13. Click OK to dismiss the Transfer Path Editor Dialog.

To configure the remaining transfer paths we will copy the green transfer path we have just edited into those thar still are empty.

To copy and paste the transfer paths:
  1. Select the green transfer path with a single click of the right mouse button.

    The transfer path is now highlighted with a cross-hatch pattern.

  2. Click the (Copy object) push button on the scheme window's tool bar.

    This places a copy of the transfer path on Kinetiscope's clipboard.

  3. If necessary, adjust the scale of the scheme window so that the entire diagram is visible.

    Use the zoom push buttons on the scheme window's tool bar to adjust the scale.

  4. Press and hold the left mouse button, move the mouse cursor until the rubber band box surrounds all the remaining empty (black-colored) transfer paths, then release the button.

    Those transfer paths are selected, highlighted with a cross-hatch pattern.

  5. Click the (Paste object) push button on the scheme window's tool bar.

    A Replace Transfer Paths Dialog appears.

  6. On the Replace Transfer Paths Dialog, leave both check boxes checked.
  7. In the Naming section of the Replace Transfer Paths Dialog, select the Preserve the current name radio button.
  8. Click OK.

    The Replace Transfer Paths Dialog is dismissed and the contents of the selected transfer paths are replaced with a copy of that on the clipboard.

Construction of the reaction scheme is now complete. The screen should look like this:

Next we will set the reaction conditions.

Note: You may save your changes by clicking the (Save) push button on the main window's tool bar.

Entering the Reaction Conditions

Different combinations of conditions can be chosen using the drop-down list boxes on the Reaction Conditions Page. Not all combinations of them are allowed (or physically meaningful). Kinetiscope will display an error message if an unsupported combination is selected.

You will simulate conditions where the electrode potential varies linearly with time, and then reverses. A constant temperature of 25 °C (298.15 °K) is to be used.

To set the reaction conditions:
  1. Click the Reaction Conditions tab.
  2. Select Volume is constant for the top left list box.
  3. Leave the bottom left list box in the Pressure is constant state.

    Variable pressure is not allowed for this type of reaction scheme.

  4. Select Temperature is constant for the top right list box.
  5. Select Voltage follows a user-defined profile for the middle right list box.

    When you do so, a graph showing the current voltage profile (currently unspecified) and data entry fields for the Temperature and the Maximum Step Size (in volts) will be displayed below the list boxes.

  6. Leave the lower right list box in the External stimulus is off state.
  7. In the Temperature data entry field, type

    298.15.

  8. In the Maximum Step Size data entry field, type

    0.001.

Defining a Voltage Profile

For this simulation, we want to linearly vary the electrode potential from +0.5 to 0.0 volts and back, with a sweep rate of 0.2 volt/sec. We will define a simple voltage profile that implements this.

To define the voltage profile:
  1. On the Reaction Conditions page, click the Change Profile... push button.

    A Profile Editor Dialog appears.

  2. On the Profile Editor Dialog, click the (Add a profile) push button on the dialog's tool bar.

    A message box appears requesting a unique identifying name for the profile.

  3. Type profile 1into the data entry field of the message box and click OK.

    A default profile is created and displayed on the data table and the graph. >/p>

  4. Edit the Time and Voltage values in the data table.

    To do so, double-click on an entry in the table, type in the new value, and press the Enter key. As you do so, the graph is updated with the current values. Edit and add entries to the table so that it contains, in order, the following values:

    Time(sec) Voltage(volts)
    0.0       0.5
    2.5       0.0
    5.0       0.5
    

    The dialog should look like this:

  5. Click OK.

    The Profile Editor Dialog is dismissed and you are returned to the scheme window. Its profile graph is updated with the new profile you have just created.

All reaction conditions have now been set. The final step before simulation is to edit the simulation settings.

Entering the Simulation Settings

You must specify certain parameter settings to configure the simulator. These settings are listed in three groups: General Settings, which include the total number of particles representing molecules and the recording interval; Limits, which allow you to set stopping points for the simulation; and Equilibrium Detect, settings for the Kinetiscope equilibrium detection and emulation system. You access the simulation parameters on the Simulation Settings Page.

To specify the simulation settings:
  1. Select the Simulation Settings tab.
  2. Set the data entry field for the Total Number of Particles to

    10000000.

    This parameter specifies the initial number of particles in the simulation. They are apportioned among all species which have a nonzero initial concentration. The number should be large enough to accommodate the dynamic range of concentrations that will occur in the simulation. A larger number will also reduce stochastic noise. There is a trade-off between these benefits and the larger amount of computer time required to reach a given point in the simulation (see the Example Simulation Simulation Precision: Parallel Reactions ).

  3. Set the data entry field for the Record State at Intervals of to

    100000.

  4. Set the data entry field for the Random Number Seed to

    12947.

    The next group of parameters control the limits of the simulation.

  5. Set the data entry field for the Maximum Number of Events to a value of

    0 events.

    Setting this parameter to zero disables it.

  6. Set the data entry field for the Maximum time in Simulation to

    0.0 seconds.

    Setting this parameter to zero disables it.

    When reaction conditions are set to use a programmed parameter (temperature, voltage or external stimulus) the simulation will end when the last time point in the profile is reached.

    .
  7. Uncheck the box in the Equilibrium Detect area.

    The Equilibrium Detect settings are used for systems with reversible reaction steps which may come into equilibrium during a simulation. In simulations whose reaction conditions specify a programmed parameter, the equilibrium detection algorithm has little benefit.

Your screen should now appear like this:

Running the Simulation

You noware ready to run the simulation.

To start the simulation:

  1. Select the Scheme tab.
  2. Click the (Start a simulation) push button on the scheme window's tool bar.

    A simulator window opens that tells you that the simulation is running:

    You can track the reaction as it progresses with this window. It displays the internal elapsed time in the simulation, the number of events that have occurred, how long the simulation has been running, and the number of times the system state has been recorded for later analysis.

  3. Click the OK push button on the simulator window when the simulation completes.

    If you do not click OK, the window will close automatically after 5 seconds. When you return to Kinetiscope's main window, the status display at the bottom of the tutorial4 scheme window now tells you that the simulation has finished, and the reason why the simulation stopped.

    Note: Kinetiscope automatically saves your reaction file with the new simulation results when the simulation is complete.

This simulation is complete in approximately one minute on a mid-range microcomputer.

Viewing the Simulation Results

Our primary interest is the interface compartment, where chemistry occurs.

To view simulation results for the compartment:
  1. Click the Scheme tab on the scheme window.
  2. Single-click the left mouse button on the interface compartment to select it.
  3. Click the (Create Results Window) push button on the scheme window's tool bar.

    A new results window is created, displaying a graph of concentrations of all species in the compartment as a function of elapsed time:

  4. You may zoom in to a specific range of the graph by pressing the left mouse button and drawing a rubber-band box around the region of interest.
  5. You may modify the information displayed on the graph through the context menu that appears when the right mouse button is clicked.

    For example, select the Modify... action; on the Line Plot Settings Dialog that appears, check the Potential/time check box; then click OK. A new graph is added to the results window that shows the electrode potential.

  6. With reaction schemes containing electrochemical steps, you may also view charge and current flow.

    For example, to view a plot of current versus voltage in the format of a cyclic voltammogram, select the Modify... action; on the Line Plot Settings Dialog that appears, check the Current/potential check box and uncheck all others; then click OK. The Results Window shows the cyclic voltammogram:

Next Steps

You have now completed this tutorial. You should now know the basics for simulating a three-dimensional reaction scheme with electrochemistry using Kinetiscope.

Other tutorials lead you through the procedures for setting up other types of reaction systems: