Determining the ability of the Belousov-Zhabotinsky Chemical Oscillator to act as a Chemical Computer

Abstract

This paper explores the Belousov Zhabotinsky(BZ) reaction, a class of oscillating reactions between bromine and an acid in the presence of a catalyst. It determines whether the BZ reaction can act as a type of chemical computer based on the Vonn Neuman architecture, which is the basic structure of all computers. This is done by examining the arithmetic logic unit(ALU) of a computer, which is the foundational unit of a computer, and then explaining an experiment that can be conducted with the BZ reaction in order for it to mimic the ALU. Finally, further applications of the chemical computer, such as artificial intelligence, are proposed.

In 1951, the Russian chemist Boris Belousov discovered a class of chemical reactions that occurred and then reversed itself on its own, alternating between a yellow color and a colorless state (Yanes 2019). According to the second law of thermodynamics, all chemical processes are linear, spontaneously moving towards equilibrium; and a reversal is not possible, at least not on its own. For this reason, Belousov’s work was not recognized, at least not until many years later when it was extended and made known by another scientist, Anatol Zhabotinsky. As a result, the oscillatory class of reactions of bromine and an acid in the presence of a catalyst, is known as the Belousov Zhabotinsky(BZ) reaction.

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The purpose of this research paper was to analyze the oscillatory Belousov Zhabotinsky (BZ) chemical reaction and its ability to process Boolean logic (a form of algebra in which all values are represented as either true or false) which is the basic building block of all modern computers, to explore if a BZ reaction could be used to form the basis of a new generation of computing machines with novel architectures, and also to determine if BZ reaction based chemical computing is capable of parallel processing like the human brain, promising advances in applications like Artificial Intelligence.

The Belousov-Zhabotinsky Reaction

  A chemical oscillator is a non-linear reaction that proceeds in one direction and then moves in the opposite direction as it modifies the concentration of the ions in the reaction and stops once the reactants are completely consumed. The reaction occurs and reverses itself on its own without any external influence on the system, hence it is called an oscillator. The oscillations, or the back and forth movements of the reaction, are driven by a decrease in free energy in the solution where the reaction is occurring. Although all chemical reactions are driven by a decrease in energy, there are three distinct features that characterize oscillating reactions and cause them to oscillate. The first feature is that the system is far from equilibrium, meaning that it has a great amount of free energy. The second feature is that the exothermic (energy releasing) reaction can occur along at least two different pathways (a pathway is a possible path along which the reaction can proceed to reach equilibrium), and the reaction can switch from one pathway to the other. The third feature is that one of the pathways produces an intermediate (a substance that is neither present at the beginning or end of a reaction but is produced by the reactants and used to form the products of the reaction) and the other pathway consumes it. This intermediate is what causes the reaction to switch from one pathway to the other and oscillate: when the concentration of the intermediate is low, the reaction switches to the producing pathway (the pathway that produces the intermediate) until the concentration of the intermediate increases. When the concentration of the intermediate is high enough, the reaction switches to the consuming pathway (the pathway that consumes the intermediate) until the concentration again lowers, at which point the pathway switches again and so on. Thus, this changing concentration of the intermediate causes the entire reaction to oscillate.

One type of chemical oscillator that exhibits such behavior is the Belousov Zhabotinsky (BZ) reaction, which can be observed in many different variations. One variation can be made by reacting potassium bromate, cerium (IV) sulfate, malonic acid, and citric acid (or any other carboxylic acid) in dilute sulfuric acid. The reaction that occurs is the oxidation of malonic acid by bromate ions in dilute sulfuric acid in the presence of a cerium catalyst. The bromate ions are reduced to bromide ions, and the malonic acid is oxidized to form carbon dioxide and water (Shakhashiri, 1986). The intermediate, as explained above, is the bromide ion. This overall reaction is depicted in the equation below:
          $3C{H}_2(C{O}_{2}H{)}_2+4\mathit{Br}{O_3}^{–}\to 4B{r}^{–} +9C{O}_2 + 6H_{2}O$

Although this describes the overall reaction taking place, the sub-reactions that cause the BZ reaction to oscillate can only be observed from the reaction mechanism, which depicts how the reactants are transformed into the products. The actual mechanism for this particular BZ reaction is extremely long, containing eighty steps, so the abbreviated mechanism formulated by Field, Koros, and Noyes, known as the FKN mechanism, is shown in the table below:

Table 1: Abbreviated FKN mechanism governing BZ reaction (Gray, 2002)

The reaction is comprised of three basic processes. The first is the reduction of bromate ( $\mathit{Br}{O_3}^{–}$

) to bromine (Br) by bromide ( $B{r}^{–}$

), the reducing agent, and is depicted in reactions R1 to R3 in the table above. In these reactions, the bromate ions are reduced, bromomalonic acid is produced, and the concentration of bromide ions in solution decreases until it is essentially negligible.

 The second process is the reduction of bromate by hypobromous acid ( $\mathit{HBr}{O}_2$

). The $\mathit{HBr}{O}_2$

also starts to reduce the bromate ions as depicted in R4 in Table 1, and the concentration of $\mathit{HBr}{O}_2$

increases rapidly as a result. An autocatalytic process, which is a set of chemical reactions that produce and are catalyzed by substances produced in the reaction itself (Hordijk, 2015), occurs in reactions R5 and R6, where the cerium catalyst Ce(III) oxidizes and Ce(IV) is produced. This is depicted in the following equation:

$\mathit{Ce}\left(\mathit{III}\right) +\mathit{ Br}{O_2}^{+} + H^{+} \leftrightarrow \mathit{Ce}\left(\mathit{IV}\right) +\mathit{ HBr}{O}_2$

(Gray, 2002)

 Since ions are colored in solution, the cerium(IV) ions turn the solution from colorless (cerium(III) ions are colorless in solution) to yellow.

The first and second processes occur alternately, depending on whether the concentration of bromide ions is already negligible or not. As they cycle, the products of each set of reactions, bromomalonic acid and cerium(IV) react, and the third process occurs in reactions C1 to C3. This process involves the reduction of the Ce(IV) back to Ce(III), causing the color to change from yellow to colorless, and is a gradual or slow change. This is depicted in the following equation:

$6\mathit{Ce}\left(\mathit{IV}\right) +C{H}_2(\mathit{COOH}{)}_2+2H_2\mathit{O }\to 6\mathit{Ce}(\mathit{III}) +\mathit{ HCOOH }+ 2C{O}_2+6H^{+}$

(Kemsley, 2011)

The combination of these three processes form the overall BZ reaction and causes it to oscillate. The overall reaction is outlined in figure 1 below, where the first process is process A, the second is process B, and the third is process C. The color changes in this figure are different because a ferroin(C₃₆H₂₄FeN₆₂ ⁺ ) indicator was used in the experiment where this data was collected from, so the cerium(III) was red in solution and cerium(IV) was blue.

Figure 1: The three sub-reactions of the BZ reaction ( Gray, 2002)

Figure 2 below depicts the actual reaction with the presence of a ferroin indicator. As time progresses and the reaction cycles through the three processes, the color of the solution changes color. At time zero, the solution is red, indicating the presence of cerium(III) ions. After ten seconds, process B occurs and cerium(IV) ions are produced, so the solution turns blue. From 15 seconds to twenty-five seconds, process C occurs and the solution turns back to red as cerium(III) ions are again produced. This occurs repeatedly as illustrated by the different color changes shown.

Figure 2: An illustration of the BZ reaction and the color changes that occur (Yanes, 2019)

Computing is based on the use of logic gates, which process a data input – usually in binary code, using only 0 or 1 – to produce a result or output. In current computers, this function is carried out through materials that have a binary response capacity via the movement of electrons. However, this is not the only possible system. The BZ reaction can be used to process Boolean logic if the input variables are the volumes of solutions of inhibitor $\mathit{KBr}$

or activator $\mathit{AgN}{O}_3$

and the output variable is the oscillation period. This capability of the BZ reaction simulate the arithmetic logic of a computer has allowed the BZ reaction to become the foundation stone of a new discipline: chemical computing, over half a century after Belousov’s discovery.

The Belousov-Zhabotinsky Reaction as a Chemical Computer

 The basic architecture that all modern computers are based on is known as Von Neumann architecture, which consists of a central processing unit(CPU), inputs, and output. The CPU has two basic components: the control unit and the arithmetic logic unit(ALU). While the control unit is important in deciding which instructions in a given program (from the input) must be executed, the ALU is the most important as it is responsible for executing the program and producing the output. (Pacheco, 2013) The ALU uses binary logic gates to process the instructions it is given, which take in two inputs and produce one output. In order for the BZ reaction to be used as a computer, an experiment would need to be conducted wherein there are two input variables and one output variable.

Based on this basic definition of a computer, the BZ reaction could function as a logic unit and form a chemical computer.  An experiment that would demonstrate this involves controlling the period of the oscillations in the reaction by the addition of an activator and inhibitor. The activator, which is $\mathit{AgN}{O}_3$

in this experiment, speeds up the reaction and decreases the oscillation period because the silver ions react with the bromide ions to form $\mathit{AgBr}$

, a precipitate, in an irreversible reaction that removes all of the bromide ions from the reaction. As explained above, the sooner the concentration of bromide ions in solution is negligible, the sooner it will oscillate and process B (from figure 1) will occur. The inhibitor, which is $\mathit{KBr}$

, has an opposite effect on the reaction from the activator. Since adding $\mathit{KBr}$

means adding more bromide ions in solution and process B in the reaction will not occur unless the concentration of bromide ions in solution is negligible, the addition of the inhibitor to the reaction causes it to oscillate slower and therefore increases the period of oscillation. This effect is illustrated in figure 3 below, which shows  the effect of the addition of KBr and AgNO₃ solutions on the period of oscillations measured by the electric potential (V) of a Pt electrode. Each graph, A and B, represents a different BZ reaction. In reaction A, the inhibitor $\mathit{KBr}$

is added to the reaction. In reaction B, the activator $\mathit{AgN}{O}_3$

is added to the reaction.

Figure 3: Effect of addition of $\mathit{KBr}$

and $\mathit{AgN}{O}_3$

solutions on the period of oscillations measured by the potential (V) of a Pt electrode (Gentili, Horvath, Vanag & Epstein, 2012)

In each graph, the spike in voltage occurs whenever the reaction oscillates, which means the period of oscillation can be measured by measuring the time in between each spike. The arrow depicts the instance of additions of the inhibitor or the activator. In reaction A, where the inhibitor is added, the period increases as predicted from 48 seconds to 58 seconds as more bromine ions are added to the solution. In reaction A, where activator is added, the period decreases as predicted from 46 seconds to 35 seconds as bromide ions are removed from solution. Therefore, since the period can be controlled by changing the volumes of inhibitor and activator added, the two inputs for this chemical logic unit would be the volumes of inhibitor and activator added, and the output would be the period of the oscillation of the reaction.

These dependencies of the time period of the oscillation on the volume of inhibitor(represented as V(KBr) in table 2)  and the volume of activator(represented as V(AgNO₃) in table 2) present in solution make it possible to build logic gates to construct different logic functions. An example of a logic function is the OR function, in which the output is true(or has a value of 1) when any of the inputs are true(or have a value of 1). Table 2 below depicts a truth table of the OR function using data from the same experiment depicted in figure 3. A truth table is a mathematical table that represents all possibilities of a logic function, meaning that it depicts all possible outputs with an OR function. In table 2,  the inputs are zero when the volumes of activator or inhibitor added are zero, and one when the volumes added are greater than zero. The output is zero when the oscillation period variation is greater than zero seconds, and one when it is greater than zero seconds.

Table 2: Truth Table for the binary OR logic function. The volumes of the KBr and the AgNO₃ solutions are the inputs, and the period variation is the output (Gentili, Horvath, Vanag & Epstein, 2012)

In table 2 above, the BZ reaction can be used to implement other logic functions like AND (where the output is true only when all inputs are true) and NOT (where the output is true only if all inputs are false) if different combinations of the volumes of the inhibitor and the activator and the period variation as the output are selected.

With the BZ reaction, chemical computers could be a potential alternative to conventional computers that use silicon hardware and electrical signals (Gentili, Horvath, Vanag & Epstein, 2012) in the future. Chemical computing could be  cheaper than conventional computing as the actual chemicals in the reaction (potassium bromate, cerium (IV) sulfate, malonic acid, and citric acid in dilute sulfuric acid) cost less than the processors in conventional CPUs. Chemical computing is also more secure because it is harder to hack . If contaminants are added to the actual BZ reaction to alter the processing that the BZ reaction represents, they may react with the components in the solution and produce other products and prevent the reaction from oscillating, so the reaction would just shut itself down and the information it processes would be impossible to access for hacking. One possible drawback of using the BZ reaction in chemical computing is that the computer would be limited by the speed of the diffusions of reactions in the medium and would therefore be slower than the electronic chips used in conventional computers, but smaller models of this computer could make  the reaction time faster.

Conclusion

In summary, the Belousov Zhabotinsky reaction is a chemical reaction that oscillates due to the oscillating concentrations of cerium(III) and cerium(IV) ions in solution. This also causes the color of the reaction to oscillate between colorless and yellow, or red and blue in the presence of ferroin indicator. When an activator and inhibitor is added, the period of oscillation can be controlled, allowing the BZ reaction to mimic the logic unit(ALU) in a computer. Thus, the BZ reaction can be used to process boolean logic and mimic the Von Neumann architecture of modern computers.

As explained earlier, the logic on which conventional computers are based is binary and can only process boolean outcomes, i.e. zeroes and ones.  As scientists strive to build computers that function more and more like the human brain, these computers need to be able to recognize patterns and make decisions in complex situations. Humans can handle uncertainty far better than computers, and are not limited by just zero or one outcome, and computers need to model that as they become more advanced. . The basic elements of the human brain, neurons, are “nonlinear dynamic systems” (Gentili, Horvath, Vanag & Epstein, 2012), so chemical systems like the BZ reaction which are also nonlinear and demonstrate oscillatory behavior can better simulate the human brain The logic that the computer uses needs to be able to process possibilities that are true or false to varying degrees, not just true or false. Fuzzy logic can model the imprecise reasoning that allows humans to make rational decisions in an environment of uncertainty because its approach to computing is based on “degrees of truth” rather than just true or false (Rouse, 2016). In other words, it can process the infinite values between zero and one, whereas boolean logic can only process zeroes and ones. A BZ oscillating chemical reaction is  suitable to process infinite-valued fuzzy logic. Therefore, for further research, the use of the BZ reaction to implement fuzzy logic instead of boolean logic could be analyzed. The use of BZ reaction to represent fuzzy logic instead of boolean logic to model  a nonlinear dynamic system like the human brain could potentially lead to advances in building a better artificial intelligence system.

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