The term memristor (“memory resistor”) was envisioned by Leon Chua  in 1971 and first developed by HP Labs in 2008 . The memristance, M, (in analogy to resistance) of a memristor is dependent on one or more internal state variables. The voltage, v, and the current, i, are related via the state dependent ohm’s law
with x as the vector of the internal state variables. The change of x is described by the state equation
A memristor has to exhibit pinched hysteresis loops in the V-I plot with the pinched point at the origin of the coordinates . Furthermore, the lobe area of the loop decreases with increased frequency and if the frequency goes towards infinity, the pinched hysteresis loop should shrink to a single valued function .
Volkov et al. demonstrated memristive properties in apples  and in the aloe vera plant . Here, we study the memristive properties of the same objects by using our methods (three electrode system that enables monopolar recordings and silver/silver chloride (Ag/AgCl) electrodes). We also used transimpedance amplifiers for the reading of the current instead of single resistors in series. Furthermore, we recorded simultaneously with a stainless steel needle electrode to compare also with the results of Volkov et al. who used coated platinum needle electrodes. We found that dependent on which electrode type was used, there are large differences in the results and two possible explanations
arise. If the recorded non-linear electrical properties are dominated by the apple or aloe vera, the differences between both electrodes may originate from the different current densities around each electrode. The current density around the needle electrode is much higher and may cause stronger non-linear effects. However, another possibility is that electrochemical reactions on the electrodes themselves are the origin of the non-linear properties. In this case it is to question whether there are memristive properties in the apples and the aloe vera plant itself. We conducted therefore a second experiment in which we placed the electrodes not in the apples and the aloe vera plant, but only in the liquids that were obtained from both. We found non-linear electrical properties that were similar to the experiments on the whole apple and the aloe vera plant. Finally, we did measurements in apple juice from concentrate and obtained similar results.
Materials and methods
We did measurements on three different aloe vera plants (family “Asphodelaceae”, on two different leaves each) and on four different apples (type Torstein) in October and November 2018 at the University of Oslo. Each apple measurement was first done on the entire piece followed by recording on a smaller piece from the same apple (about 1 cm thickness) that was cut off (see Fig. 1c). The measurements on the apple liquid and aloe vera liquid were conducted once each in May 2019. The apple liquid was obtained from a peeled apple (sort “evelina”) that was crushed in a blender (the core was removed) and the resulting apple mush was placed in a coffee filter. Manual squeezing enabled obtaining some apple liquid through the filter. The content of one aloe vera leaf (family “Asphodelaceae”) was picked with a spoon. Filtration of the pure liquid (without any solid substance) by using a coffee filter did not work that well. In the end we excluded any chunk manually with a spoon. Both liquids were filtrated into the truncated bottom of a plastic cup (diameter of around 5 cm, see Fig. 1c). The measurements on the apple juice (100 % juice from concentrate, company Sunniva) were done once in July 2019.
Dry sintered silver/silver chloride electrodes (from Wuhan Greentek PTY LTD) that had a cylindrical shape and were not prewired were used as M1, ref and CC electrode. Each wire was manually connected via a shrinking tube. The diameter of each electrode was 2 mm and the length was about 2 to 3 mm (determined by the position of the isolation of the shrinking tube that covered the upper part of the electrode). The non-isolated tip of the medical stainless needle electrode had a diameter of around 0.2 mm and a length of around 0.8 mm. All electrodes were cleaned with ethanol before use.
The electrodes for the aloe vera measurements were placed central at the upper side of the chosen leaf (see Fig. 1c). The electrodes M1, M2, CC and ref were placed at about 5 cm, 6 cm, 8 cm and 9 cm from the trunk, respectively.
On the full apple, the electrodes where placed about halfway up. In relation to the measurement electrode M1 along the circumference, the reference electrode, the CC electrode and the M2 electrode were placed about 2 cm, 3 cm and 6 cm apart, respectively (see left photograph of Fig. 1c). For the apple piece measurements, the M1 electrode was placed at the left outside (see middle photograph of Fig. 1c), and the electrodes ref, CC, and M2 were placed about 1.5 cm, 2.5cm and 5 cm apart. Within all liquid measurements, the CC and the ref electrodes were placed on one side of the cup and both measurement electrodes were placed on the opposite site of the cup with around 1 cm distance to each other.
The same custom-built measurement system as used in  was used here (see Fig. 1b), based on a data acquisition card (DAQ, type USB-6356 from National instruments, controlled by custom made software written in NI LabVIEW version 2014). The transimpedance amplifiers in the reading channels convert the current into a voltage that can be read by the DAQ. The feedback resistors Rfb1 and Rfb2 determine the gain and have both a value of 56 kΩ for the measurements on the aloe vera leaf. Much higher currents were expected for the measurements on the apples (known from pilot studies) and a resistor with a resistance value of 0.56 kΩ was chosen as Rfb1 instead. For the measurements on the apple juice and aloe vera liquid the feedback resistances Rfb1 = 0.56 kΩ and Rfb2 = 5.6 kΩ were used. The capacitance Cfb = 4.7nF in addition to each transimpedance amplifier enables reduction of high frequency noise. Signal generation and reading were performed with 2000 samples per period.
Different alternating current (AC) voltage waveforms (sinusoidal with different amplitudes and triangular, see Fig. 1a) were applied, and a frequency sweep (0.005 Hz, 0.05 Hz and 0.5 Hz) was done for each. Each recording was done for two periods.
The sweep over the voltage waveform and the sweep over the frequencies were performed automated in randomized order for the measurements on the apples and aloe vera plants, and in manually chosen order for the measurements in the liquids.
The recordings from the aloe vera plants and the extracted liquid (see Figs. 2 and S1) and from the apples and apple juice (see Figs. 3 and S2) are non-linear and showed pinched hysteresis loops in the voltage current presentation. The recordings obtained with the stainless steel needle are more non-linear than for the silver/silver chloride electrodes.
Pinched hysteresis loops with pinched point in the third quadrant or two pinched points can be observed from the recordings with the stainless steel electrode. Pinched hysteresis loops with pinched point in the first quadrant can be observed from the recordings with the silver/silver chloride electrode. The obtained currents from the aloe vera extract were higher than the currents obtained from the aloe vera leaf.
However, the shape of the pinched hysteresis loops obtained from both subjects are quite similar. The same observation can be done between the apple juice and the whole apple. In addition, the measurements on the apple or apple juice in comparison with the aloe vera or aloe vera extract obtained from the stainless steel needle electrode, look quite similar.
With increasing frequency, all recordings with the silver/silver chloride electrode (see Figs. S1 and S2) tend to be single valued functions in the voltage current plane while the recordings with the stainless steel electrode are still nonlinear even at a frequency of 0.5 Hz.
A white layer was observed on the silver/silver chloride electrodes (M and CC) after the measurements in apple juice. Additional measurements in diluted HCL acid and in apple juice from concentrate with a platinum wire were done (see Fig. S3b) and also showed pinched hysteresis loops.
One could argue that the measurements on the apple and the aloe vera reveal underlying memristors since pinched hysteresis loops can be shown for different amplitudes and signal shapes (see Figs. 2, 3, S1, and S2). Shifts of the pinched point away from the origin of coordinates or two pinched points can be explained by a capacitor in parallel with the underlying memristors .
However, assuming that the results represent a memristor, the question is what the actual mechanism behind these non-linear properties is. Volkov et al. explained the memristive properties they found in apples and aloe vera by voltage gated potassium-channels that are activated as soon as the voltage is high enough [6, 10]. By our measurements, we cannot exclude that this is happening. However, if these processes are happening, these are not the dominating mechanism since similar results can be achieved between the apple and apple juice and between the aloe vera leaf and the extract from the aloe leaf. Furthermore, in the apple juice from concentrate or the hydrochloric acid (see additional measurements in Fig. S3), there are no living cells and the memristive properties cannot be explained by voltage gated potassium channels.
The conductances of the apples, the apple juice, the aloe vera, and extract of the aloe vera leaf are quite high and there is a strong indication that the electrode impedance of the electrodes actually dominates the measurements. The origin of the memristive properties is likely to be electrochemical reactions on the electrodes themselves as in cyclic voltammetry . The results between the silver/silver chloride electrode and the stainless steel needle electrode are very different from each other which can be explained by different reactions. At the stainless steel needle electrode and also the platinum electrode (additional measurement, see Fig. S3) a redox reaction of water is happening with
while it is likely that the equilibrium between silver and silver chloride is shifted with
at the corresponding electrodes.
Anyway, in a bipolar measurement (with two electrodes), the polarization impedances of both electrodes are contributing and the overall setup can be modelled by a serial connection of two memristors that are in opposite direction to each other. With the use a three-electrode system, that allows monopolar recordings under the measurement electrode, the polarization impedance of only one electrode can be revealed.
To find out whether there are actually memristive properties in the apple, the apple juice, the aloe vera leaf, and the aloe vera juice themselves, a four electrode system (two current carrying electrodes and two potential pickup electrodes) would be useful.
In such a setup, no current flows through the pickup electrodes and one can be sure that the measured electrical properties are not due to electrode polarization.
O.P. thanks Prof. Ola Nilsen for his advices on the electrochemistry and revising the manuscript.
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