CKS: Chemical Kinetics Simulator

Citation

Adamatzky, A. (2002), "CKS: Chemical Kinetics Simulator", Kybernetes, Vol. 31 No. 1. https://doi.org/10.1108/k.2002.06731aad.001

CKS: Chemical Kinetics Simulator

CKS: Chemical Kinetics Simulator

Keywords: Stochastic dynamic, Collectives computational chemistry, Simulation of collectives

Principal authors: William Hinsberg and Frances HouleIBM Almaden Research CentreSan Jose, California, USA

Abstract A reader is introduced to a chemical kinetics simulator working on principles of stochastic imitation. Mechanics of simulation and advantages of the software are highlighted. Several toy examples are provided to make nonchemists appreciate a value of the program. Some real life applications are brought up.

There are quite few software packages for chemical simulations. Even fewer packages handle physics of the processes in a reasonably realistic way. Usually dynamic of a simulated systems is abstracted down to systems of differential equations, which are numerically integrated. Such models are difficult to control and process of their verification is painful. Every applied scientist dreams about modelling techniques that can describe physical behaviour of each system's component. In case of chemical systems direct, soft- or hardware, imitation of motion, collision and transformation of molecules would be an ideal approach. These ideas of physics oriented simulation of spatially distributed systems were implemented in cellular automata and lattice gas models (see, e.g. Doolen, 1991; Lawniczak and Kapral, 1995; Rothman and Zaleski, 1997; Chopard and Droz, 1999). A Chemical Kinetics Simulator (CKS) uses the same approach to tackle a kinetic of chemical systems.

In CKS, instead of approximation, which is necessary to integrate differential equations, interaction of molecules is directly executed in a computer. Looking at the problem from a very naive point of view we could portray a simulation of the chemical reaction

in a reactor with n molecules by an array of n elements which are updated asynchronously in the following routine:

• •

  choose at random i-th element in the state X

• •

  choose at random j-th element in the state Y

• •

  assign the state Z to the i-th element

• •

  assign the state Q to the j-th element.

One can update array's entries probabilistically, with probability made dependent on the reaction rate constant.

We could say, behaviour of molecular ensembles is imitated rather than dynamic of a single molecule (just to decrease costs of computation). Thus, the CKS simulator relies on the following approach:

A chemical reactor is simulated as a system of discrete particles, where each particle represents a certain amount of reagents. Interaction of reagent pools is represented via interaction of particles.

How it works?

It is very simple to design a sophisticated model in CKS. Friendly and intuitive interface, concise help and cautious control of model's consistency contribute to the ease of designing.

When creating a new reaction file you are asked to select appropriate units for concentration, time, pressure and energy. These units are consistently used during the simulation and in displaying the simulation results. Then you simply type in reaction step by step. The reactions are entered in the same form as they are usually written on a paper. Maximal number of reactions in the model is enough to satisfy even very scrupulous person. As authors claim, there may be up to 65,536 reaction steps in Mac and OS/2 versions of CKS and up to 160 steps in Windows version. For each reaction a user specifies forward and reverse rate constants, either temperature dependent or independent; rate law, either stoichiometric or identified by the user.

To start simulation you enter initial concentrations of reagents, and tell the simulator whether temperature is constant, variable, linear or even derived from user's profile. You could also indicate whether volume and temperature are constant or variable. Only physically sensible combinations of volume- temperature characteristics are allowed in the simulation. When temperature and volume are variable you are allowed to indicate physical states of the reagents, i.e. solid, liquid or gas, and their densities. Then you tell the simulator how many molecules are in your imitated reactor, how often to record state of the system, when to stop simulation and whether or not to track equilibrium.

The simulation engine runs in a background mode, so you can continue entering new reaction scheme while waiting results of the simulation.

Results of the simulation - concentration, temperature, amount, or pressure versus time - are plotted conveniently. The picture can be printed or saved in postscript or HPGL formats or as a text file. If saved as the text file results of the simulation can be immediately imported to any other plotting program or a spreadsheet software.

The following example helps to appreciate advantages of CKS. Let us consider a "classical'' species of oscillatory chemical reactions Belousov- Zhabotinsky reaction. This reaction is one of the most famous examples of active nonlinear media (Zaikin and Zhabotinsky, 1970). A classical reaction incorporates one-electron redox catalyst, and organic substrate (usually malonic acid) and bromate ion (e.g. in the form of potassium bromate). Either ferroin or ruthenium are used as a catalyst in the reaction. Oxidised and reduced forms of the catalyst are coloured differently, e.g. oxidised ferroin is

blue and reduced ferroin is red. Mechanics of oscillation is lucid. Bromate is transformed to a bromous acid. A ferroin is oxidised to fernin A colour of reagent mixture is changed form blue to red. Then ferriin recovers back to ferroin with a help of organic substrate. Bromide ions are produced in the fernin-toferroin transformation. These ions suppress production of the bromous acid. These steps are cyclically repeated. The reaction is formalised in Oregonator model (Field and Noyes, 1974):

The essential reagents are coded as follows: X (HBrO₂), Y (Br ^-), Z (the oxidised catalyst), A (BrO^-₃), B (oxides organic).

To build a CKS model of the Belousov-Zhabotisky reaction we simply type in all Oregonator reactions, as they are shown above, specify initial concentrations of the reagents, set up constant rates, number of molecules in the simulated reactor. We also tell simulator how long the process should last, measured in a number of events or an amount of seconds. We did simulation with 5×10⁶, real life concentrations of reagents and conventional constant rates. Plotting results of the simulation we observe typical oscillations (Figure 1).

Actually, the simulator can be useful not only for chemists, biochemists and physics but also for population biologists, researchers in social dynamics, and any other disciplines where behaviour of investigated systems can be represented via interaction of discrete entities followed by destruction or production of new species. Let us look at an unsophisticated two-species population. The population consists of preys, which feed on some unlimited substrate, and predators that consume preys. Predators die when there is no preys around. The population dynamic can be roughly represented in three "quasichemical" equations (Figure 2). We set up total number of individuals equal 10⁴ and constant rates for prey reproduction, prey consuming/predator reproduction, predator death as 2, 1, 1, respectively. A global dynamics of simulated population (Figure 3) is similar to dynamics of a classical Lotka-Volterra model.

And finally, we would like to show that with a little imagination almost any field of our life could be simulated in CKS. Let go to a pub. Often, patrons, being warmed not only by Holy Spirit, become aggressive to strangers. Thus, a fight might sparkle. What is the collective dynamic of aggression development in such situation?

Figure 1. Dynamics of X, Y and Z species in the Oregonator model implemented in CKS

Assume each person takes four states: passive, hostile, fighting and relaxed. If a passive person encounters a hostile one he also becomes hostile. When two hostile guys bump into each other they would probably fight. Let also a fighting lad be relaxed soon after fight. A resultant abstract set of reactions between individuals looks as follows (Model A):

As we can see in the results of CKS simulation (Figure 4) initially small amount of hostile individuals cause eruption of hostility, which is followed by fighting. Because of the "fighting to relaxed" transition more and more persons become relaxed. The state of relaxation is alike precipitate, therefore eventually all visitors of our abstract pub are relaxed. No more fighting occurs afterwards.

Figure 2. Defining prey-predator population model using interface of CKS

Figure 3. Dynamics of a simple prey-predator population model

Figure 4. Bursts of fighting in a pub. Models built in CKS

To make situation more interesting we could add a recovery reaction. That is, we assume that relaxed persons can, with a certain constant rate, take the passive state again. Thus we obtain the Model B, basic reactions of which are as follows:

Not surprisingly, a system reaches a stationary state, where majority of individuals are relaxed, and small quantity of them experience low amplitude oscillations between passive, hostile and fighting states (Figure 1).

Real-life examples

Numerous advantages of CKS are making it extremely popular amongst bench chemists. It is claimed that scientists from 75 countries actively use the software in research, industry and education. Here we arbitrarily picked up three recent publications.

Thus, Koshkin and Dunford (1999) employ CKS (together with nonetheless famous programs pro Fit and DynaFit) in their pre-steadystate kinetic analysis of a peroxidase reaction of prostaglandin synthase.

Weerasooriya and Dharmasena (2000) investigate a kinetic model build in CKS to quantify trichloroethene degradation by pyrite. The CKS model helps authors to gain more understanding of mechanisms and reaction rate constants for so experimentally difficult system as pyrite mediated trichloroethene degradation.

A thermal degradation of a polymer polydimethylsiloxane to cyclic oligormers is analysed by Camino, Lomakin and Lazzari (2001) in CKS based computer simulation. It is discovered that combination of abstract kinetic models with CKS gives a good technique for a prediction of weight loss of the investigated polymer. Computer simulation lets authors to investigate particulars of decomposition at various heating rates. Basing on their experience the authors (Camino et al, 2001) highlights the following advantages of CKS:

1. 1.

   a reaction temperature is programmed as a liner function or an arbitrary external profile;

2. 2.

   a simulation can be carried out in variable volume conditions, which allows a concentration to be recalculated during thermolysis;

3. 3.

   simulated rate constants of the reactions can be compared online with ones obtained experimentally.

Further development

The program is excellent as it is. So, not many improvements can be suggested for the current version. "Simulate spatial dynamics!" is the only wish. CKS does not handle diffusely coupled reactions. That is you could not, for example, simulate space-time dynamic of BelousovZhabotinsky reaction in a two-dimensional thin layer reactor. Neither you could exploit reactors with complex topologies and sophisticated flows of matter. Developers suggest that at least gas diffusion can be tackled by subdividing simulated reactor into several zones between which gases are transferred with certain rate constants. If CKS will.incorporate diffusion coupled dynamic it become even more popular software and real must-have tools for chemists, physicists, biologists and engineers.

Distribution

A whole package of Chemical Kinetics Simulator 1.01 can be downloaded free of charge at IBM's Almaden Research Centre web site at http://www.almaden.ibm.com/st/msim/ckspage.html. There are versions available for for IBM 0S/2 2.x or 0S/2 Warp 3.0 and 4.0, Apple Macintosh System 7.x, Power Macintosh, and for Microsoft Windows 3.1/Windows 95/Windows NT.

Andrew AdamatzkyIntelligent Autonomous Systems LabUniversity of the West of EnglandAndrew.Adamatzky@uwe.ac.uk