A STUDY ABOUT THE RELATIONSHIP BETWEEN STARCH CONCENTRATION PROVIDED TO BACTERIA AND THEIR ENERGY PRODUCTION IN A MICROBIAL FUEL CELL
Microbial Fuel Cells produce electric energy from oxidation reactions done by microbes, including glucose oxidation. Although these are very effective and a renewable way of producing energy, it is still under research which ways can be used to maximize its production of energy. It was hypothesized that, as starch is a glucose polymer, if increasing starch concentration, energy production could be maximized. A Microbial Fuel Cell was built and varying concentrations of starch were used to feed the bacteria. The results were that, as predicted, there was a growing tendency. However, a plateau was reached. It was concluded that increasing starch concentration is an effective way of increasing the production of energy in a Microbial Fuel Cell, but a better design of the salt bridge, and a further study of the enzymatic activities outside and inside the bacteria, would give us a better view of what could be done in order to produce a higher voltage before the plateau is reached.
Galvanic cells, or voltaic cells, are electrochemical cells which produce electrical energy through spontaneous oxidation-reduction reactions  On the other hand, bacteria are living organisms that, like every living organism, perform cellular respiration. This is a process by which living organisms oxidize some organic molecules, in order to use the chemical energy of their bonds, to produce ATP, a molecule that provides with energy for many processes in the cell. [2, 3] To obtain the chemical energy, some bonds are broken through oxidation reactions, in which electrons are loss. Microbial Fuel Cells (MFC) are galvanic cells in which, at the anode, the oxidation reactions are performed by bacterial metabolism. The cell can be design in a way in which these loss electrons flow to the cathode, so that this flow generates electrical energy. Respiration, in many cases, occurs by oxidizing glucose (𝐶2𝐻12𝑂6). This is an organic molecule, usually found in nature as polymers, including glycogen, starch, and cellulose.  Starch is the polymer used by plants to store glucose , and plants are usually the available source of biomass at swamps. Probably, heterotrophic bacteria, bacteria that obtain the organic molecules they need from other organisms instead of producing them on their own, obtain glucose from plants nearby, which may be degraded into pure starch by biomass degrading bacteria, also abundant in swamps and waste water.
Basing on this information, it would be coherent to assume that, if these bacteria are given more starch, they will have more glucose to perform respiration, oxidizing them and producing electrical energy. So, increasing starch concentration could be a good strategy to maximize energy production by a Microbial Fuel Cell. This is what leaded to the formulation of the following question: What is the relationship between starch concentration provided to bacteria, and the energy produced by a Microbial Fuel Cell?
The objective of this research work is to determine if there is a relationship or not between starch concentration provided to bacteria and the energy produced in a Microbial Fuel Cell, and if there is, of what kind. The method used included building a simple homemade Microbial Fuel Cell, vary the concentration of starch used to feed the bacteria, and register the voltage produced at those different concentrations. The results obtained indicated a strong positive correlation between the variables; although, the relationship was not linear, and the data adjusted to a polynomic function of second grade, or to a logarithmic function, better, as the data reached a plateau. The positive correlation is explained with the fact that, with a higher starch concentration, the reaction occurs at a higher rate, as stated by chemical kinetics . To explain the plateau, three hypotheses were stated: the equilibrium of the reaction had been reached , some enzymes may have reached their maximum efficiency , and the deficient salt bridge design may have affected the proton electrochemical gradient . Basing on this, it was concluded that increasing the starch concentration does have a relationship with the energy production, and it is an effective way to maximize it, although a plateau will always be reached.
The experimental significance of this research work, is that it includes a MFC design completely simple, homemade, and affordable, with materials easy to find and purchase, and a model which mechanism is completely understandable. On the other hand, it has a theoretical foundation because, until nowadays, there are no well-known studies that have already explored the influence of the different starch concentrations used to feed microbes of a MFC, so it would allow future investigators to have a new factor to vary in order to maximize energy production by MFCs, and also with a starting point to explore factors that can increase the voltage reached at the plateau, and test the possible explanations given at this work for it being reached.
2. LITERATURE REVIEW
If two half cells are connected with a wire, electrons flow spontaneously from the anodic half-cell to the cathodic half-cell, due to their difference in their potentials. Although, this potential difference is only generated with an internal circuit in which ions flow and neutralize each half cell. This can be done either with an ion-exchange membrane, or with a salt bridge. Ion-exchange membranes have porous structures, which allow specificity in the ion flow. Although, salt bridges are not that specific, but they are soaked in a salty solution. The watery solution allows ion movement, as the liquid state allows ions to move freely. The presence of salt allows the negatively charged ions to flow to the anode when a positively charged ion is generated there, neutralizing the charge, and in some cases the positive ions flow to the salt bridge too. Galvanic cells also count with electrodes, which are materials which can conduce electrons from a half-cell to the other. An example of a good electrode, is graphite . This is because graphite is a carbon allotrope in which each carbon atom is bonded to other three, through covalent bonds. Each carbon atom has 4 valence electrons, and forming three bonds, a free electron is left per each carbon atom. These free electrons can move and, hence, conduce electricity. 
Galvanic cells function due to redox reactions. These are a type of chemical reaction in which one substance transfers electrons to the other. Oxidation is the chemical process in which a substance loses electrons, increasing its oxidation number. Reduction, on the other hand, consists on the gain of electrons, so its oxidation number reduces. The substance that oxidized, which gives its electrons to the other substance, indirectly causes it to gain electrons, so the oxidized substance is often called the redactor agent. In the same way, the substance that reduces is often known as the oxidant agent. In a galvanic cell, oxidation occurs at the anodic half-cell, and the lost electrons flow to the cathode, in which they are gained by a substance, so reduction occurs. The overall reaction, summing up the oxidation and the reduction, is a redox reaction. [1, 7]
Although, for the electrons to flow, the reaction must be thermodynamically favored, or spontaneous. For this, the 𝐸°cell must be positive, and the ∆𝐺° must be negative. To begin with, the 𝐸°cell is defined as:
𝐸°cell = 𝐸°anode− 𝐸°cathode
Being 𝐸° the standard electrode potential. The cell potential (𝐸°cell) is measured with a multimeter. On the
other hand, Gibbs free energy, ∆𝐺°, is the measure of the maximum energy that could be either freed or gained with the reaction, and it is freed in case it is negative. That is why, when it is negative and the reaction is spontaneous, it is exergonic, releasing energy, in this case, electric energy. To choose the contents of the anodic and cathodic half-cells, it must be taken into consideration if the overall reaction will have a negative ∆𝐺° and a positive 𝐸°cell. [1, 7]
Microbial Fuel Cells (MFC) are galvanic cells that use redox reactions caused by microbial metabolism. This is because, in the anode, bacteria perform cellular respiration, a process in which organic molecules are oxidized. After each oxidation of the process of cellular respiration, the electrons are carried by molecules with chemical structures that make them ideal electron carriers: 𝑁𝐴𝐷+ and 𝐹𝐴𝐷+. These reactions are used to produce ATP, a molecule containing lots of chemical energy that can be used for biological processes by the organism.  The overall process of respiration includes three main phases:
Glycolysis, in which glucose is partitioned into three-carbon molecules, called pyruvates, undergoing through a series of reactions from which two are oxidation reactions, and 2 𝑁𝐴𝐷𝐻 molecules are produced from the reduction of 𝑁𝐴𝐷+. Before passing the following phase, each pyruvate loses a carbon dioxide molecule, producing acetyl-coA molecules. [2, 8]
Krebs cycle, in which each acetyl-coA molecule undergoes through a series of cyclic reactions, including four oxidations, in which three donate their electrons to three 𝑁𝐴𝐷+, forming 3 of 𝑁𝐴𝐷𝐻, and one donates its lost electrons to 𝐹𝐴𝐷+, forming 𝐹𝐴𝐷𝐻2. [2, 8]
Electron transport chain, in which 𝑁𝐴𝐷𝐻 and 𝐹𝐴𝐷𝐻2 lose the electrons they are carrying from the previous oxidation reactions, returning to their oxidized forms 𝑁𝐴𝐷+ and 𝐹𝐴𝐷+. These electrons flow and this flowing produced energy to form ATP molecules, through a series of biological processes. For the electrons to keep flowing, they are gained by an electron acceptor, which is often oxygen due to its high electronegativity and affinity. When they join, they also join to protons, and form water molecules. [2, 8]
At most organisms, this process occurs entirely inside them. However, electroactive bacteria donate the electrons from their 𝑁𝐴𝐷𝐻 and 𝐹𝐴𝐷𝐻# molecules to the exterior, for the electron transport chain. [4, 10]
For this whole process to occur, organisms must have a source of organic molecules, which often include polymers. Polymers are big molecules in which small chemical subunits, called monomers, are linked. Polymers are often taken advantage in the industry, but they also play an important role in biological organisms. The polymers used for respiration are natural polymers. Respiration often occurs through the oxidation of glucose (𝐶6𝐻12𝑂6), which is found naturally in polymers like starch and cellulose [2, 3, 8]. Starch is often found in two ways: amylose, which is a linear structure of glucose bonded to each other, and amylopectin, which is a branched structure. Glucose molecules are bonded with bonds called glycosidic bonds [3, 11]. Their chemical structures are shown at figure 1 of the appendix A. Starch can be hydrolyzed by living organisms, so to obtain only the glucose subunits that are oxidized. Hydrolysis of big polymers like starch, are often exergonic processes, spontaneous (∆𝐺° < 0), and energy is released [3, 8]. This energy loss leaves glucose molecules, with the necessary energy for ATP production. Starch is hydrolyzed with the enzyme amylase, into maltose molecules, which contain two glucose molecules together, and then these are hydrolyzed into glucose with maltase enzyme [8, 11].
On the other hand, it was mentioned that the molecules 𝑁𝐴𝐷+ and 𝐹𝐴𝐷+ carry electrons after every oxidation reaction through respiration. This is because they have an ideal chemical structure for this. Starting with 𝑁𝐴𝐷+, its chemical name is nicotinamide adenine dinucleotide. It contains a nicotinamide, which chemical structure is shown at figure 2 at appendix A. As it can be observed, it contains a benzenic ring, and its aromaticity gives the nitrogen in the ring a positive charge, as it has 4 bonds, making it a good electrophile that attracts electrons to itself. When this nitrogen attracts an electron, it can only have three bonds because it has 5 valence electrons. When aromaticity is lost, there is a carbon in the ring that would stay with only three bonds: two to other two carbons of the ring, and one to a hydrogen. Carbons have 4 valence electrons, so one electron more would be missing. It forms another bond with a hydrogen, because in the oxidation reactions of glucose, electrons and also hydrogen are lost. In this way, 𝑁𝐴𝐷+ gains two electrons and one hydrogen, to form its reduced form 𝑁𝐴𝐷𝐻. 𝐹𝐴𝐷+ works with the same mechanism, only that it can join to two hydrogens instead of only one, forming 𝐹𝐴𝐷𝐻2. [8, 9, 24]
So, at Microbial Fuel Cells, spontaneous and thermodynamically favored redox reactions, caused by the oxidation of organic molecules obtained from natural polymers by microbes, are used to produce electrical energy, or a voltage. The hypothesis of this research work is that, by increasing the natural polymer concentration, in this case starch, more electrical energy could be produced by the cell. This hypothesis is based on the fact that, according to basic chemical kinetics, the four factors that could be varied to affect the rate of a reaction: the size of the particle of reactant, because with smaller particles, more surface exposed, leading to a higher rate; temperature, because with a higher temperature, more particles with a kinetic energy higher than the activation energy, and more molecular movement so more collisions would occur, leading to a higher rate; the use of catalysts; and the concentration of reactants, because with higher concentrations, these would collide more, increasing the rate of the reaction. As in this case starch is one of the reactants, increasing its concentration should increase the rate at which glucose is oxidized and, hence, increasing the energy production to its maximum.
Evaluating methodologies often used to design Microbial Fuel Cells, a factor often varied among different MFCs, is the number of chambers, and the fuel used. To begin with, single chamber MFC (SCMFC) only has one container, which is sealed and a membrane is included to have access to oxygen, so that electrons keep flowing. The cathode electrode is directly onto the membrane, so it can react with oxygen. Graphite rods are places inside the anode chamber, and connected to the cathode through an external circuit. These are much more effective than MFCs of two chambers. Although, MFCs of two chambers are more widely used, and they are effective two. MFCs of two chambers can be joined either with a proton exchange membrane (PEM), a more selective and complex way [17, 18], or with a salt bridge, which is very simple. The design of two chambers is often very simple and inexpensive. As an example of the single chamber MFC, at 2006, by the professor Shaoan Cheng et al. It produced 766 𝑚𝑊𝑚-2 . Another example is the single chamber MFC constructed at 2004 by Liu et al, which produced maximum 0.45 V . In contrast we have the two chamber MFC built at 2006, also from Cheng et al, which produced 860 𝑚𝑊𝑚^-2 . On the other hand, the fuel varied often is between glucose or domestic wastewater. Referencing, again, the experiment of Cheng et al, 2006, with glucose it produced 766 𝑚𝑊𝑚^-2, while with domestic wastewater it produced 464 𝑚𝑊𝑚^-2. So from this, it can be known that, although both, single chamber and two chamber MFCs, can be designed in a simple way, the two chamber MFC has shown, in some cases, a higher voltage production and, it provides with the option of a salt bridge, which is simpler and easier to do.
Previous research has been done regarding factors that affect the energy production by MFCs. For instance, at 2020 a study was done by the chemical engineer Mostafa Ghasemi et al, regarding the improvement of the performance of microbial fuel cells through artificial intelligence. This study stated that MFC performance could be maximized by operating the system at the optimal parameters, by building an accurate model. The results showed effectiveness, although, this is a very complex and time-consuming study, which focused on aeration rather than reactant concentration . On the other hand, a study was done also at 2020, by the electrical engineer Aziah Khamis et al, which studied the influence of waste water, electrode thickness and distance on the double chamber MFC performance. The results demonstrated that thicker anode, and shorter distances between electrodes, showed higher amount of power production. Regarding waste water, fertilizer water generated more. This was a very interesting study, because it investigated small factors that may affect the production of power. It focused indirectly in the reactants, by trying different waste waters. However, it did not vary directly starch concentration nor any feeding polymer concentration . Also, at 2014 a study was done by Qibo Jia et al, in which the effects of sucrose concentration, operating temperature, and ferrous sulfate concentration, on performance of a two-chamber MFC. The optimum conditions were established, basing on these three factors. This is a very interesting research, as it would be useful to maximize energy production by MFCs by establishing the conditions needed, taking into consideration various factors. Although, this research work varied sucrose concentrations, omitting the step of starch hydrolysis that occurs in nature when bacteria feed on natural polymers . Finally, another research work was during 2011, by Mostafa Ghasemi et al, regarding the use of activated carbon nanofibers as a cathode catalyst, instead of platinum. The results showed that, effectively, that material shows a greater performance of the MFC. In this case, the research work investigated the effect of changing a material in the MFC composition, which is also a valid factor which effect is interesting to explore. 
As it could be read, there is a growing interest on the factors that influence the energy production of MFCs, which is because, when getting ideal conditions for its operation, it is possible to maximize its energy production, being more useful for real life applications. There are plenty of factors to take into consideration when exploring alternatives to increase voltage production by an MFC . In contrast, this research is innovative in the sense that it focuses on only one factor that may affect MFC performance: concentration of starch used to feed the bacteria. This takes into consideration the natural process of polymer hydrolysis to obtain the organic molecules for respiration. Also, this research work involves the building of a homemade and simple two chamber MFC, without a laboratory or expensive materials, and an analysis was done by means of three different statistical parameters. Finally, this research work used as a substrate a natural local source of electroactive bacteria, in which not only the waste water was used, but the bacteria were also feed with starch to maximize their oxidation reactions.
3. RESEARCH METHOD
3.1 MFC design
To design the cell, it has to be taken into consideration that the overall reaction (anodic + cathodic reaction) must be thermodynamically favored which, as previously explained, means that the 𝐸°cell must be positive. Considering that the microbes produce energy with oxidation reactions during cell respiration, the anode reaction should be the reaction of the aerobic cell respiration but until before the part of the electron transport chain, as this part is when the NADH molecules of the electroactive bacteria release their electrons out of the cells. The reaction until this part, would be the following :
𝐶6𝐻12𝑂6 + 6𝐻2𝑂 → 6𝐶𝑂2 + 24𝐻+ + 24𝑒-
For the electrons to pass to the cathode, their electron acceptor must be there, which would be oxygen. The electrons from the anode must be isolated from oxygen so that they flow to the cathode, which is exposed to oxygen. So, from this, it is known that oxygen must be included in the cathode. The reaction of the electron transport chain, which would be the cathodic reaction, is the following :
6𝑂2 + 24𝐻+ + 24𝑒-. → 12𝐻2𝑂
The 𝐸°cathode would be of 1.23 V, according to the IB Chemistry Data Booklet. This is a very low potential in comparison to the potential of oxidation of organic molecules like glucose. This practically ensures us that the 𝐸°cell will be positive, so it is a thermodynamically favored reaction . Having this, we have already determined the overall reaction of the cell :
𝐶6𝐻12𝑂6 + 6𝑂2 → 6𝐶𝑂2+ 6𝐻2𝑂
Now, for the electrons to flow, I would need electron conductors, perhaps graphite, and a cable for them to flow from the anode to the cathode. However, to ensure the electron flow another factor must be taken into consideration: protons will also be produced at the anode, which, eventually, may lead to a high positive charge that attracts electrons towards the anode, preventing them to flow to the cathode. This is why, a salt bridge must be used. As oxygen is constantly combining with protons (𝐻+) at the cathode, its concentration there decreases, and due to the potential difference, the protons from the anode would flow from higher to lower. In this way, protons would be constantly moved to the cathode, allowing the electrons from the anode to keep flowing. If a salt bridge will be used, it must be soaked into a salt solution . To ensure optimum passage of protons, the salt solution will be prepared saturated. The solubility, or maximum capacity of NaCl to dissolve in water, is of 36g in 100mL of 𝐻2𝑂. Finally, the bacteria needed for them to donate the electrons to the solution would not be any kind of bacteria, they would have to be electroactive bacteria. These are found in stagnant water exposed to light, like at swamps and wastewater . At my city, the only swamps accessible to the population, are Pantanos de Villa, which is a potential location from where the water could be obtained. These have a particularity: they act as a filter for the wastewater of surrounding populations, allowing water to reach the nearby sea clean. So, this location contains, not only natural stagnant water, but also wastewater . Also, some of these bacteria are not necessarily just at water, they are mostly found at sediments . This is why, perhaps it would be convenient to recollect not only water, but also mud inside the swamp. Considering all the discussed points, at figure 3 from the appendix B, a sketch of the structure and contents of the MFC can be seen.
3.2 Tools and materials
100 𝑐𝑚^3 of cornstarch
A big beaker (± 50 mL)
A small beaker (± 5 mL)
1.69 L of water and mud from a local swamp
1.69 L of spout water
A small plastic container to weight salt and cornstarch
Cables of 1m each
4 crocodile clips
Multimeter (± 0.001 V)
2 plastic containers of 2.25 L each
Jump rope for salt bridge
36g of salt
A digital balance (± 0.01 g)
600 mL of distilled water
3.3 Ethical, safety, and environmental considerations
The substrate from the anode was obtained from a protected area of my country, but an official letter of request was sent to the Environment Ministry of my country, which allowed me to remove the needed volume of water. Also, it was ensured, with the help of a guide from the protected area, that Finally, while doing the experiment, safety measures will be taken, like disinfecting with ethyl alcohol (70o) every material touched by the swamp water, and constantly washing hands with antibacterial soap.
3.4. Procedure followed
A. Substrate recollection
First, a letter requesting the authorization to the Environment Ministry to retire water and mud from the local swamp “Pantanos de Villa” was sent. The request was accepted, and water and mud were recollected with a plastic container and manually, respectively. This was done until having filled approximately 3⁄4 of the container (1.69 L approximately). At figure 4 from the appendix C, it can be observed the picture of the swamp from which the substrate was taken.
B. Salt bridge construction
First, the digital balance was calibrated. The empty plastic container was weighted, its weight was of 45.5g, and NaCl was added gradually, until the balance registered 81.5g, meaning that 36 g of NaCl had been added. Then, this was mixed with the water until it dissolved. A piece of approximately 10 cm of the jump rope, was cut, and soaked into the salt solution. With an electric welder, a hole was made at each plastic container, approximately at the same heights (10 cm high over the base of the containers). After this, the rope, already wet and salty, was inserted into each container, leaving only a 4 cm distance between them, approximately, and having 3 cm of the rope inside of each container. To prevent water from getting out of the containers through the holes, they were sealed by using insulating tape. Having done this, the 1.69 L of mud and dirty water were added to one of the containers, and 1.69 L of spout water was added to the other one. At figure 5 of the appendix C, it can be observed the final result.
C. Oxygen isolation
The anode has to be isolated from oxygen, so it was covered with a plastic cap. However, this cap had to have a hole for the cable to enter with the graphite electrode. The hole was done with the electric welder, and the cable was inserted so to connect it to the crocodile once having crossed the cap. The result can be observed at figure 6 from the appendix C.
D. Building the electrical circuit
First, the two extremes of the two cables were peeled with the pliers. The copper cable, which was exposed, was passed through the hole of the crocodile clip. Then, it was ensured with heat from the electric welder, and tin. Once the cable was joined to a crocodile clip at one extreme, the same process was repeated for the other extreme. This was also done with the other cable. Once both cables were joined to crocodile clips at both sides, one side was united to the graphite electrode, and the other one to the multimeter. This was done with both cables. Due to the metal material of the copper cables and the crocodile clips, which conduce electricity due to the electron sea, and the free electrons from the graphite electrodes, these connections will allow the electrons to flow from the anode to the cathode. At figure 7 from the appendix C, it can be seen the union between each cable and the crocodiles. At figure 8 from the appendix, the whole connection of electrodes-cables-multimeter, can be seen.
E. Preparation of starch solutions
First, a very concentrated starch solution was prepared. It was a solution of 100 𝑐𝑚^3 of starch, and 100 𝑐𝑚^3 of distilled water. This was the solution used to vary the starch concentration, by diluting it with different volumes of distilled water. The concentrated solution was left in a container apart. To prepare the first starch solution that was used to feed the bacteria from the anode, a volume of 20mL of the concentrated solution was poured into the big beaker. Then, distilled water was added until the 100mL were reached. This was mixed until having created a homogenous solution, which was given to the bacteria at the anode, and the energy produced was registered. When it was consumed, I prepared another starch solution. For the second starch solution, a volume of 30mL of the concentrated solution was added, and distilled water was poured until reaching the 100mL. This process was repeated with 40, 50, and 60 mL of the concentrated solution, diluting them with distilled water until the 100mL were reached, and registering how much energy was produced with each of the solutions. At figure 9 from the appendix C, the volumes added of concentrated starch solution of the three first solutions, before being diluted until the 100mL mark, can be seen. Also, at figure 10, it can be seen how the starch solution was added to the anode, before being closed.
F. Register of the data
To register the data, the graphite electrodes were submerged into the dirty water at the anode, and the spout water at the cathode, respectively. At figure 11 from the appendix C, the three first voltages registered with the multimeter, can be seen.
The raw data can be seen at table 1. As can be seen, the independent variable of the research work (starch concentration in the feeding solution) is not shown, as it was not registered directly. However, it was obtained through stoichiometry, which process can be read at the end of the document at appendix D.
3.5 Analysis techniques
The collected data will be analyzed by using the program Microsoft Excel, where a graph of will be built of the electrical energy produced in function of the starch concentration of the solution used to feed the bacteria. This graph will be given an adjust function, and the 𝑅^2 value will be used to know what kind of function the data follow. Also, statistical parameters such as the Pearson correlation coefficient (r), and the analysis of the variation of the gradients, will be taken into consideration to determine if there is a relationship between the variables and, in case there is, of what kind. Finally, the effect of the error bars of the variables will be analyzed too, in terms of accuracy and reliability.
4. RESULTS AND DISCUSSION
As previously mentioned, the processing of the raw data can be read at the appendix D. At table 2, the data already processed can be observed. The starch concentrations in the feeding solutions are expressed as mass percent. The voltage values registered were the maximum values, until starch was consumed, per feeding solution.
4.1. Analysis of the Pearson correlation coefficient (r)
In addition to the information displayed at table 3, the Pearson correlation coefficient’s sign indicates whether it is a positive (+) or negative (-) correlation. In case of the voltage produced by the MFC in function of the concentration of starch in the feeding solution given to the bacteria, r ≈ 0.98, meaning the variables have a strong positive correlation. This is explained with the fact that, from chemical kinetics, it is known that the concentration of the reactants is one of the factors that increase the rate of reactions . With higher concentrations of starch, there is an increase of available concentrated polymers to react with the enzymes released by the electroactive bacteria to hydrolyze them into monomers they can absorb for their metabolism, like glucose. These contain chemical bonds with the necessary chemical energy to reduce 𝑁𝐴𝐷+ molecules into 𝑁𝐴𝐷𝐻, which then oxidize again by releasing their electrons to the exterior . As more electrons are released, more electrons flow through the external MFC circuit, producing more voltage or electrical energy.
However, the Pearson correlation coefficient is not the best statistical parameter to analyze the tendency followed between the variables, in this case, as observed in graph 1, the data do not adjust to a linear function, but more to a logarithmic one . Although, the Pearson correlation coefficient is still a good parameter to have a first idea about the relationship between the variables, and it has coherence with chemistry theory.
4.2. Analysis of the adjusted 𝑹𝟐
As observed in graph 1, R^2 ≈ 0.96 for a logarithmic function, which indicates that the data adjusts very well to a logarithmic tendency, as the R^2 has a value near to 1. This means the function is growing, until a constant is reached, a plateau. It will be tried with other options of adjust functions:
It can be seen that the 𝑅^2 has values nearer to 1 for the polynomic function of second grade (R2 ≈ 0.97), and the logarithmic function. Polynomic adjust functions of higher grade were not tried, as they would always present a value of R^2 or 1 but not necessarily indicating an actual relationship between the variables, as they adjust to any set of data when the grade is very high.
Analyzing why does the data adjusts the most to a polynomic of second grade or to a logarithmic function, but less to a linear function, although in the three cases it is a growing function, three factors must be taken into consideration: the Gibbs free energy of the reactions involved, the maximum efficiency of the enzymes used to hydrolyze starch, and the efficiency of the salt bridge. Chemical equilibrium is always reached by the reactions and there is a point at which, although the reactants of one side of the reversible reaction, like glucose, are increased, the reaction will only displace towards the opposite side to compensate the increase of the other reactant, until the equilibrium is reached again. Once an equilibrium is reached, no external changes can be perceived, although what is happening is that chemical reactions are still happening but towards both sides at the same rate, keeping a constant relationship between the concentration of reactants and products. This relationship is called the equilibrium constant (𝐾c) [1, 5]. The 𝐾c is also determined by the Gibbs free energy, which is the maximum energy that could be liberated by the reactions. The formula of the ∆𝐺° relates it directly with the 𝐾c [1, 5, 7]:
∆𝐺 = −𝑅𝑇 ln 𝐾c
When the Gibbs free energy is negative, as in this case because energy is liberated, the equilibrium is orientated towards the right, with a high value of the 𝐾c, which is why energy has been produced form the spontaneous and thermodynamically favored reaction [1, 5]. However, when an equilibrium is reached, no more energy is produced, as the energy is lost and gained by the reactions of both directions at constant rates.
The plateau could also have to do with a maximum efficiency of the enzymes used by the bacteria to hydrolyze starch, which may reach a plateau at a concentration near to 33% mass percent. Enzymology, a branch of biochemistry that studies enzymes mechanism and structure, states that one of the three factors affecting enzyme efficiency: temperature, pH, and substrate concentration. Enzymatic activity increases until an optimum temperature, or pH, is reached, and then the activity decreases because the high temperatures and charges in the environment in case of pH, cause changes in the chemical interactions inside the enzyme, denaturing some of them so that each time less enzymes are available to catalyze reactions. Substrate concentration, in contrast to pH and temperature, affect enzyme efficiency in a way in which it increases with the increase of substrate concentration until a plateau is reached, as the enzymes are already interacting with the maximum substrates they can. In this case, bacteria release enzymes to hydrolyze starch into glucose monomers, which is usually done by them to hydrolyze polymers into monomers they can use in their metabolisms. There must have reached a point at which the plateau has been reached, and these enzymes were already working at their maximum efficiency, so the increase of starch concentration was irrelevant [2, 22].
Another possible enzymatic cause could have been the maximum efficiency of internal enzymes of the bacteria. The glucose oxidation performed by the bacteria involves many steps, each of them catalyzed by a specific enzyme. Probably the maximum efficiency of amylase, the enzyme used to hydrolyze starch into glucose, had not been reached yet, but the glucose molecules absorbed by the bacteria could not be oxidized at higher rates because some of their internal enzymes may have reached a maximum efficiency, instead. However, these are just possible enzymological explanations, and to confirm one, glucose concentrations could be increased instead of starch. A plateau would also be reached, and probably faster as the step of starch hydrolysis would be omitted, but this plateau could have been higher, indicating that, what caused the maximum voltage to be 0.400 V, were the amylase enzymes. However, if the same plateau is reached, it could be assumed that it has more to do with bacterial internal enzymes. [2, 22]
Finally, another possible cause could have been the efficiency of the salt bridge. During the experiment, it was observed that some water was pouring from the salt bridge, as it was done with a permeable material for protons to be able to pass from a semi cell to the other. This definitely was a deficiency in the methodological design, a source of systematic error in the experiment. The salt bridge was very important to establish a way in which, due to the potential difference, the protons can flow towards the cathode, avoiding electrons to be attracted to the anode and stay there instead of flowing to the cathode due to high oxygen affinity there. With the dropping of water, a disbalance in the electrochemical gradient may have occurred, leading to an eventual accumulation of protons at the anode, which at a point, may have prevented the reaction to continue [1, 5].
4.3. Analysis of the gradient
As the function to which the data adjust is not a lineal function, a gradient cannot be analyzed. However, the functions to which the data adjusted the most, shown at graphs 2 and 3, were derived. Starting with
function of graph 2:
𝑓(𝑥) = 0.2335 ln 𝑥 − 0.4434
𝑓1(𝑥) = 0.2335 𝑥
This derivative was evaluated at three points of 𝑥: when 𝑥 = 21, 𝑥 = 27, 𝑥 = 39. The results are shown at table 4.
Now, evaluating the derivative of the function of graph 3:
𝑓(𝑥) = −0.0002𝑥2 + 0.0195𝑥 − 0.0621
𝑓1(𝑥) = −0.0004𝑥 + 0.0195
Evaluating it at the same points, shown at table 5.
The values of the derivative were approximated to the first three decimal positions. It can be seen that the derivative is positive in all the points evaluated, meaning that there is effectively a growing tendency between the data, or a positive correlation, as previously shown by the Pearson correlation coefficient. However, it can also be seen that the derivatives are each time lower, or less positive, meaning that the function is each time less growing, until a plateau is reached. This further confirms the adjusted R^2 previously found, which is explained with the equilibrium reached by the reactions and its Gibbs free energy, the enzymatic efficiency, or the affection to the electrochemical gradient of protons with deficiencies in the salt bridge design.
4.4. Analysis of the impact of the uncertainties
To begin with the independent variable, it was measured with a multimeter of an uncertainty of ± 0.001. This indicates a high level of accuracy and reliability on the data obtained from the voltage produced by the MFC. However, regarding the uncertainties for the data of the mass percent, these will have to be calculated, as these data were not measured directly. For this, it is of important knowledge to mention that, when adding or subtracting measures, their absolute uncertainties must be added to know the result’s uncertainty. If dividing or multiplying measures, their percentage uncertainties must be added . The process by which they were obtained, can be read at the appendix E.
Most of these percentage uncertainties definitely indicate very low accuracy in the measure of the independent variable, as most two of them exceed the 50%, and the others are still high as they exceed the 20%. These percentage uncertainties show a very low reliability in the measures of the data of the dependent variable. These low reliabilities may have had an impact in the shown tendency. However, the measures directly taken were of the volume added of concentrated starch solution, with an instrument of an absolute uncertainty of ±5mL. This is a relatively low uncertainty, and the measures of the mass percent were obtained through stoichiometry basing on those data. However, the measures of the volumes may have accuracy, but it must be taken into consideration the influence of the angle from which the measures were taken when looking at the beaker. Although, it was performed squatting, having the container on a flat surface, the measures taken are always propense to inaccuracies, which may be random errors that can affect the tendency, but to a very low and unavoidable extent.
A homemade Microbial Fuel Cell was effectively built, it did produce electrical energy, and the relationship between the energy produced and starch concentration given to the bacteria could be effectively found by registering and analyzing the data with statistical parameters.
From these, it was found that there is a strong positive correlation between the concentration of starch used to feed the microbes, and the voltage produced by the Microbial Fuel Cell. The variables follow the tendency of a polynomic function of second grade, and of a logarithmic function, as they grow in relation to each other, until a plateau is reached.
The growing tendency can be explained with
The plateau reached can be explained with the equilibrium of the reaction, enzymes maximum
efficiencies reached, and the salt bridge deficiencies. Although a plateau would always be reached,
these possible causes can be evaluated in order to increase it.
Considering the growing tendency found, increasing starch concentration given to feed bacteria is
an effective way to increase electrical energy production of a Microbial Fuel Cell.
A possible extension of this investigation, would be exploring to a higher depth the enzymology of the process by which bacteria respire, perhaps by marking the intermediate species of glucose oxidation, so to know until which of these the reaction stops at the plateau, and know that the enzyme that catalyzes the reaction of that intermediate species is the responsible, and the one that
reaches its maximum efficiency.
6. EVALUATION AND METHODOLOGY
A strength of the methodology used, was the simple but effective homemade design, with materials very easy to get, of the MFC. Although, there was a deficiency in the design of the salt bridge, as it was not externally covered with any impermeable material, allowing water to drop gradually through it. Eventually, this affected the proton electrochemical gradient, so this is a source of systematic error. It would be suggested to externally cover it with something impermeable, like insulating tape.
On the other hand, measuring instruments were used in order to measure voltage, volumes, and mass, all of which had low absolute uncertainties. Although, a limitation were the possible random errors of measuring volumes at beakers, due to slight changes in the position and angle. However, the measures were taken placing the beaker in a flat surface, and observing it from low.
Although an instrument to measure the concentration of starch directly could not be found at a good price, the data of starch concentration were obtained with stoichiometry, which could be considered a strength, as stoichiometry bases on reliable rules and calculations. However, as many calculations were done, the uncertainties were very high, so it would be suggested to measure the concentration with a colorimeter.
Finally, another strength of the research work could be considered that many different statistical parameters were used to assess if there was a relationship or not, between the variables, so to draw conclusions supported not only by the theory, but also by the data obtained from the experiment. However, a limitation could be considered the number of data. Perhaps two data were not enough to determine that a plateau had been reached. It would be suggested to register at least two data more, so to ensure the tendency found.
I would like to thank my supervisor Flavio Cachay, for teaching me virtually and with lots of patience how to peel cables, and build my own electrical circuit. I would also like to thank my school chemistry teacher, Carlos Bellodas, for answering my questions about thermodynamics. Finally, I would like to thank the biotechnologist Kiefer Bedoya, who patiently explained me how electroactive bacteria work.
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The volume of the starch at the concentrated solution added, column 2, was assumed to be the half of the total volume of the concentrated starch solution added, as it was initially prepared with 100 𝑐𝑚^3 of water and 100 𝑐𝑚^3 of starch. The mass in grams of starch added, column 3, was calculated using its density, which is 1.5𝑔𝑐𝑚^-3. The volume of the water at the concentrated starch solution added, column 4, was also assumed to be the half of the volume of concentrated starch solution added. The mass of water at the concentrated starch solution added, column 5, was calculated with its density 1.0 𝑔𝑐𝑚^-3, multiplying it by the volumes shown at column 4. The volume of the distilled water used to dilute the concentrated starch solution until 100 mL, column 6, was assumed to be 100 mL − volume of concentrated starch solution added, and its mass, column 7, was also calculated by using the water density. The total mass of the feeding solution, column 7, was calculated by adding the mass of starch of the concentrated starch solution added, the mass of water of the concentrated starch solution added, and the mass of the distilled water used to dilute it until 100 mL. Finally, the mass percent, column 8, was calculated by dividing the mass of the starch at the concentrated starch solution added, by the total mass of the feeding solution, multiplied by 100%. The values shown of mass percent were approximated to the 2 significant figures.
The starch mass values were previously calculated by multiplying the volume of starch added, by its density, so the volume of the starch’s percentage uncertainty must be added to the density’s uncertainty, to know the percentage uncertainty of the mass values. The density was given with no uncertainties, so the uncertainty of the density was assumed to be ±0.1 𝑔𝑐𝑚./ basing on its significant figures, being the percentage uncertainty of the starch density: 0.1/ 1.5 × 100% ≈ 7%. The volume of the starch had absolute uncertainties of ±5 mL, shown at column 2. Using this, the percentage uncertainties of the values of the volume of starch added were: 5/ volume of starch × 100%. The addition of these two uncertainties are shown at the column 3. The total mass values, on the other hand, were calculated by adding the mass of starch at the concentrated solution, the mass of water at the concentrated solution, and the mass of water used to dilute the solution until 100 mL. All these three masses have absolute uncertainties of ±5 mL, and as they were added, these absolute uncertainties must be added too, which is why the uncertainties of the total mass values are shown at the column 5 as ±15 mL. The percentage uncertainties of the total mass values were calculated: 15/ total mass × 100%. These results are shown at the column 6. Finally, as the mass percent values were calculated by dividing the starch mass by the total mass of the feeding solution, their percentage uncertainties must be added to find the mass percent uncertainties. These results are shown at the seventh column, painted in yellow.