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Transient
Electrical Fields in Ionic Chemical Reactions
(Chemoelectric
processes)
Martin Miller, undergraduate
University of Houston, Physics
(December, 2000)
The experiment studied the reaction of aqueous copper chloride with solid magnesium (Mg(s) + CuCl2(aq) ® MgCl2(aq) + Cu(s)). Chemical reactions such as this have been observed to experience spurts in the magnetic activity. These spurts are thought to be caused by periods of increased or unbalanced chemical activity. There is also a transient voltage that can be measured during the chemical reaction. While no net current occurs, the peaks of current that occur are not disorganized like random occurrences or white noise. Instead, Fourier analysis and peak binning show that the Chemoelectric processes follow a power law relationship which is commonly associated with Self-Organized Critical (SOC) fractal processes.
A system that exhibits Self-Organized Criticality (SOC) is one that converges toward equilibrium around the triggering phase transition state over a period of time, independent of the external driving forces[1]. This is similar to a sand pile that will achieve an approximately steady state near the critical slope necessary to trigger avalanches (the alternate state). In SOC, the size of the avalanches, or bursts, is related to the number of bursts at that size by power relationship, meaning that the plot will have a linear slope on a log-log plot. In experimental and simulated systems, a straight line on the log-log plot will not be obtained, but will instead be approximated by a 1/¦ white noise that is caused by superposition of the “avalanche” states1.
Taking a system in which a chemical reaction occurs, it has been shown that the process of the reaction can cause magnetic signals[2]. Also, it has been shown that during periods of dynamic equilibrium, these systems show signs of self-organized criticality in the magnetic signals3. If magnetic signals exist, it is reasonable that some sort of electric signal should also be present in the system. If so, this electric field may also show signs of self-organized criticality.
In the magnesium-copper chloride reaction, there are multiple possible interactions that could cause the system to organize itself at criticality[3]. As the reaction occurs, the reactants are depleted and products are formed, creating regions of solution where the copper chloride is depleted and the local concentration changes with fluid turbulence. Also, copper precipitate forms at the reaction surface, denying access to the magnesium, and the copper can flake off as magnesium is eroded. The magnesium surface can also pit, creating a larger reaction surface than the original flat surface. These changes in surface area and concentration could produce a situation that is similar to a situation for adsorption of particles onto a surface that produces a log-log relationship based on surface area and particle size1. The different chemical conditions available at different times could also cause an uneven ion flow, in which more ions come out of solution than go into solution, or vice versa.
Boundaries between metals and electrolyte solutions will form what can be considered molecular capacitors[4]. When the situation is polarized, no charge flows, and when the situation is non-polarized, charge can flow[5]. When partial polarization occurs, a finite amount of charge may flow. Most analysis of the current flow focuses on situations of chemically static equilibrium, however. Since the double-layer interface theory indicates that both electric current and a magnetic field would exist at a boundary, and that it would not be constant if not in chemical equilibrium. Because of this, the amount of voltage change could indicate the amount of change in the reaction.
Since the results of this experiment involving solids and liquids are also seen in experiments involving plasma[6], it could be reasonable to assume that the SOC of these two systems would be caused by common factors of the two systems. Both the plasma and chemical systems involve well-defined boundaries and charged particles that align themselves along the boundaries. The plasma experiment attributes the 1/f noise to the creation and destruction of double-layers of electrons. In the chemical system, the metal-electrolyte interface sets up a double layer of positive ions. If correct, the 1/f noise observed in the chemical system would indicate that the double layer is being created and destroyed by the chemical process.
The reaction took place within a small plastic reaction trough. A single magnesium strip with the oxides removed from the surface will be fixed to the bottom of the trough using non-reactive putty to prevent any movements which could introduce non-chemical voltage changes. The magnesium strip was 3mm wide by 9.4cm long by .15mm thick and 99+% pure. The trough was filled for the reaction with a 0.5 (± 1%) molar CuCl2(aq), producing the ionic reaction Mg(s) + CuCl2(aq) ® MgCl2(aq) + Cu(s). To measure the electric field, two thin gold jeweler’s wires were used as electrodes. They were affixed with putty to the side of the reaction vessel so that their ends were immersed in the solution. They had a spacing of 2.1cm apart, centered on the middle of the trough, and 5mm away from the magnesium ribbon. Two additional electrodes consisting of carbon rods were also used. The carbon rods were approximately 0.25 in diameter and were placed at opposite ends of the magnesium strip (and trough), 9cm apart. Figure 2 illustrates the experiment setup.
The electrodes were connected to clips leading to the input channels of a digital oscilloscope. The oscilloscope was originally intended to be a LeCroy 9400A, however it stopped working properly before the experiment could be conducted. Instead the experiment used a 50Mhz Velleman PCS32 PC Scope, which creates data files on the controlling computer. The oscilloscope was set to measure only AC voltage instead of the DC voltage. Also, because of the limitations of the oscilloscope, the zero value had to be offset by an amount. While the magnetic fields created by chemical reactions are extremely faint, the electrical fields are comparatively strong, reaching the order of centivolts. Because background noise of the apparatus was only on the order of one or two millivolts, the experiment did not make use of electromagnetic shielding.
The LabView instrument panel that had been created to interface with the LeCroy was used instead to run data analysis on data files. The LabView interface allows the recorded data to be saved to a standard tab-delimited ASCII data file with a two-channel column. Any processed data can also be saved to similar files. The virtual instrument can normalize the data to bring the zero point back to a zero value, and take the absolute value of the data. It can compute the FFT of the data using a variety of windows for the data, and plots the data on a log-log scale. It also finds data peaks, sorts them in descending order and plots them versus index on a log-log scale. The size of a peak is approximated by the voltage at the peak point. This is a valid approximation for integration of the area underneath a peak when the sampling rate is slow enough for an entire peak to appear as a single data spike. The log-log scales are used to highlight any power relationships in the data.
Two trials were conducted. The first trial took data at 500 Hz with a voltage scale of 0.3125 mV per quantization. The offset of the data had to be computed by taking the time average of the line noise. The offset for the first trial was approximately 136 quantized units for data channel 1 and 135 units for channel 2 (out of 255). The second trial took data at 200Hz with a voltage scale of 0.3125 mV per quantization. The second trial offsets were 135 for channel 1 and 134 for channel 2. Both trials took data from both the gold and carbon electrodes simultaneously. It should be noted at this point that for the qualitative nature of this experiment, the same results were obtained for each data set no matter what value the data was normalized to, if at all. The results were also the same whether or not the absolute value was taken.
The envelopes of the recorded waveforms represent the amount of overall chemical activity occurring. The waveform for onset of the second reaction in Figure 4 shows that there is a sudden large burst in chemical activity when the CuCl2 is poured in, followed by a fading of the chemical activity, which is consistent with this hypothesis. If this is true, it brings up interesting questions about the data as a whole. Figure 14 shows data near the beginning of the first trial and the end of the first trial. The data at the end of the trial is clearly of a larger magnitude. Even though the reaction agents were being consumed, the reaction showed a gradual and steady increase in the reaction rate up even up to the point that the visible physical signs of the reaction had appeared to slow down and the trial was terminated.
Although analysis of the background noise had given a good estimate of the offset added by the oscilloscope, this was not the offset value used to normalize the data. The data should produce better results when the system is in a state of “dynamical equilibrium3.” That, combined with the assumption that the net current flow of the system should be zero because it is a contained system, made it more reasonable to normalize the data to the average of the data within the data window. That way, the data in the window would result in zero net current and the average would represent the “dynamical equilibrium” point for that time domain of the reaction.
For in-depth analysis, a window of data was selected from the first trial. The data covers 102 seconds and starts approximately 122.4 seconds after the onset of the reaction. The waveform is shown in Figure 5 both before (a) and after (b) normalization and scaling.
The first analysis of the data is a Fast-Fourier Transform (FFT) of the waveform. A SOC system should show 1/f noise that follows a power law. Both of the data channels follow a power law over the higher frequencies, an indicator of SOC, and the upper limit of the frequency amplitude is very closely parallel to a power law fit. As a comparison, random phenomena such as white noise and the background noise of the experiment show nearly equal probabilities for all frequencies (Figure 11). The loss of the power law fit at lower frequencies is an artifact of the finite nature of the measurements. A low frequency wave would have a large wavelength. However, wavelengths larger than the time window cannot be extracted very well, if at all, producing fewer than expected low frequency waves in the analysis.
The second analysis performed on the data is peak binning. To achieve this, the peak “size” was approximated as being the peak height. Peaks were then obtained (in theory, no more than half of the data points can be peaks, but for the data, the number of peaks tended to be less than a fourth or fifth of the data points), then sorted in descending order by height and placed in an indexed array. The indexed array was then plotted on a log-log x-y chart so that the peaks would appear to be placed into bins of logarithmic size (Figure 7a). In the central region of the binned peaks, the graph for each channel follows a power law for at least one decade (Figure 7b), a good indicator of SOC.
The graphs of the binned peaks show a rolloff at the large peaks. This is an artifact of the finite nature of both the system and the measurements. Occasionally, peaks would exceed the maximum amplitude of the oscilloscope and were cut off, as was the case with the gold probes. But even when this did not occur, as was the case with the carbon probes, the rolloff was still there. This is because it is impossible to have peaks of infinite size for a finite reaction, and so larger peaks are always less probable than smaller peaks, no matter what type of system is being observed.
The rolloff of small peaks is more perplexing. One possible cause of this is peak absorption. Since the peaks have a width wider than one quantized unit, smaller peaks will most likely end up on the tails of larger peaks, making the small peaks show up as being higher than they actually are. An intrinsic measurement reason for this rolloff is that smaller peaks would have proportionately smaller widths. So, while a lower frequency data sampling would better approximate peak size with peak height, it would be unable to detect peaks of less than an arbitrary height because they would fall between the data points. A third reason is that the very small peaks of the data should be dominated by the background noise of the system. Random peaks, and white noise, clearly show the same rolloff (Figure 12), which fits a linear function.
The background static may then play an important role in this experiment’s data. Looking at the background noise in Figure 13 from before the first trial, the background noise produced fairly large spikes in the carbon rod channel, larger than when the system was set up before the experiment. After the introduction of the electrolyte solution, the magnitude of the carbon waveform dropped to much less than that of the preceding background noise. This may be because the electrolyte solution conducted electricity between the probes and reduced their ability to act as antennae. Even so, the presence of spikes so large in the carbon channel compared to the gold channel suggests that the gold channel should give better data. Consistent with this suggestion, the graphs of the FFT (Figure 6) and peak binning (Figure 7) of the first trial show that while the gold channel follows power laws over two decades in each, the carbon channel follows the power law over only one decade in each.
For the most part, the two sets of electrodes appeared to be taking the same data. Figure 3 shows a segment of data taken from the second trial. It is clear that many of the peaks and signals were picked up by both electrodes. It is interesting to note that, despite the different composition, size and separation of the two sets of electrodes, they picked up signals of almost exactly the same magnitude where the signals coincide. Other portions of the signal show that sometimes the two electrodes were not picking up the same signal, but yet almost all of the peaks of the inside gold probes have corresponding peaks detected by the outer carbon probes. The data looks as though it is the superposition of the signal detected by the gold probes plus a signal generated in the area between the carbon probes but not the gold probes. As an afterthought to this experiment, a non-recorded run was made in which the areas between the probes did not overlap. Visually, the coincidence between the two data samples vanished almost immediately, a result consistent with an abelian system. A feature of SOC systems is that they are abelian1.
As a further test to determine if the system is abelian, the waveform of the inner gold probes was subtracted from the waveform of the outer carbon probes, producing the waveform seen in Figure 8. If the system is truly abelian, the resulting waveform should represent the area of the reaction that is between the carbon probes but external of the area between the gold probes. Analysis of the FFT and binned peaks of this waveform in Figure 9 and Figure 10 show that this waveform could represent an SOC process. This external waveform shows the power laws even more strongly than either of the two original waveforms did, made particularly visible by the sharp bends in Figure 10a at the beginning and end of the power law domain for the binned peaks.
The second trial did not produce the results that would be expected from the first trial. The second trial was sampled at a lower frequency as an attempt to make the peak height to size approximation more accurate. However, while analysis of the second trial can be made to loosely fit the power law over very short domains of the graph, the overall trend of the FFT and peak binning was very strongly logarithmic, which converges with power functions on small domains. This result was only made more pronounced when the carbon minus gold channel analysis was performed. However, throughout the analysis of the second trial, the upper edge of the far high frequency FFT remained as a power series. This could indicate that the lower frequency sampling simply produced a lower quality data set, much as the difference between the carbon and gold probes did in the first trial. It may also suggest that the high-end and low-end rolloffs in the peak binning became so large that they merged, eliminating any power law that would have otherwise occurred between the two rolloffs. If true, then this would indicate that the peak height to peak size estimation is correct enough that it may be dismissed as equality for this system, or that it is unnecessary to distinguish between the two for SOC analysis. It also indicates that high sampling frequencies to detect small phenomena are much more important to the final results than the method of peak size estimation.
I would like to thank very much Dr. J. Miller and James Claycomb of the University of Houston for their previous work in this field leading up to this experiment, and I would like to thank J. Claycomb for his assistance with the experiment and the interpretation of results.
[1] Armin Bunde and Shlomo Havlin (Eds.), Fractals in Science, Springer-Verlag, Berlin.
[2] M. D. Nersesyan, J. R. Claycomb, Q. Ming, J. H. Miller, Jr., J. T. Richardson, and D Luss, Applied Physics Letters 75, 1170 (1999).
[3] J. R. Claycomb and J. H. Miller, Jr., PACS: 85.25.Dq, 05.65.+b, 45.70.Ht
[4] Martynov, G.A., R.R. Salem, Lecture notes in Chemistry- Electrical Double Layer at a Metal-Dilute Electrolyte Solution Interface, Berlin: Pringer-Verlag, 1983.
[5] Crow, D.R., Principles and Applications of Electrochemistry, Second ed., London: Chapman and Hall, 1974.
[6] Sanduloviciu, M., R. Schrittwieser, Codrina Avram, P. Balan, and V. Pohoata. “Flicker noise related to electrical double layer dynamics.” http://itcinfo.nifs.ac.jp/itc10/html/abst126.htm
Figure 1: Preliminary electric field intensity data taken to show feasibility using gold electrodes for about 50 seconds during the reaction Mg + CuCl2 ® MgCl2 + Cu. This reaction used a high molarity solution and the magnesium strip was entirely consumed within the time of this data sample.
Figure 2: Setup of the measurement apparatus, showing approximate placement of the gold and carbon electrodes and the magnesium strip in the reaction trough (not to scale).
Figure 3: Section of data from second trial showing correspondence of the two data channels.
Figure 4: The onset of the chemical reaction for the second trial, showing the significance of the reaction rate to the waveform envelope.
Figure 5: A 102 second window from the first trial used for further analysis, showing peaks and time-scaled increase. The data window was taken at 500 Hz, starting 123 seconds after the beginning of the reaction. a) The raw data as taken. b) The normalized and scaled data.
Figure 6: Fourier Transform of the two channels in the first trial showing a power law relationship.
Figure 7: Peaks for both channels in the first trial, sorted in descending order by peak height. a) The full set of peaks. b) A subset of peaks exhibiting a power law relationship over one or two decades.
Figure 8: Normalized waveform of the normalized channel 2 data (carbon) minus normalized channel 1 data (gold probes), representing the reaction outside the gold probes but inside the carbon probes.
Figure 9: FFT of the Channel 2 minus Channel 1 data showing a power law relationship.
Figure 10: Binned peaks of the Channel 2 minus Channel 1 data showing a power law relationship.
Figure 11: FFT of the background noise recorded before the beginning of the first trial and used for comparison. The plot is nearly horizontal, showing that all frequencies had approximately equal probability.
Figure 12: A log-log plot of the sorted peaks extracted from a set of sequential random numbers showing an inversely linear association between peak size and peak abundance.
Figure 13: Background noise in the two data channels before the first introduction of CuCl2.
Figure 14: Two sections of the first trial data showing the amplitude increase of the electric field waveform as the reaction progresses. a) Waveform near the beginning of the reaction. b) Waveform around seven minutes into the reaction.