On memfractance of plants and fungi
Alexander E. Beasley, Mohammed-Salah Abdelouahab, René Lozi, Anna L. Powell, Andrew Adamatzky
OOn memfractance of plants and fungi
Alexander E. Beasley , Mohammed-Salah Abdelouahab , Ren´e Lozi , Anna L. Powell , and AndrewAdamatzky Unconventional Computing Laboratory, UWE, Bristol, UK * Corresponding author: Alexander Beasley, [email protected] Laboratory of Mathematics and their interactions, University Centre Abdelhafid Boussouf, Mila43000, Algeria Universit´e Cˆote d’Azur, CNRS, LJAD, Nice, France
May 22, 2020
Abstract
The key feature of a memristor is that the resistance is a function of its previous resistance, thereby the behaviour of thedevice is influenced by changing the way in which potential is applied across it. Ultimately, information can be encodedon memristors, which can then be used to implement a number of circuit topologies.Biological substrates have alreadybeen shown to exhibit some memristive properties.It is, therefore, logical that all biological media will follow this trendto some degree. In this paper we demonstrate that a range of yet untested specimens exhibit memristive properties,including mediums such as water and dampened wood shavings on which we can cultivate biological specimens. Wepropose that memristance is not a binary property { , } , but rather a continuum on the scale [0,1]. The results implythat there is great potential for hybrid electronic systems that combine traditional electronic typologies with naturallyoccurring specimens. K eywords: memristor, fungi, fuits, memfractance Originally proposed by Leon Chua in 1971 [6], the memristor poses an fourth basic circuit element, whose characteristicsdiffer from that of R , L and C elements. The model of an optimal memristor (Fig. 1) shows a number of key features: (1)lobes in the positive and negative half of the cycle, and (2) a ‘pinch’ (or crossing) point at 0V. -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 Voltage (V) -6-4-20246 C u rr en t ( A ) -5 I-V Characteristics of an Ideal Memristor
Figure 1: I-V characteristics from a model of an ideal memristor [15].1 a r X i v : . [ c s . ET ] M a y igure 2: Sample specimen under test using Keithley SMU.Memristance has been seen in nano-scale devices, where solid-state electronic and ionic transport are coupled underan external bias voltage [28]. Strukov et al. posit that the hysteric I-V characteristics observed in thin-film, two-terminaldevices can be understood as memristive. However, this is observed behaviour of devices that already have other, largesignal behaviours.Finding a true memristor is by no means an easy task, however, a number of studies have turned to nature toprovide the answer, with varying success. Memristive properties of organic polymers have been studied since 2005 [9]in experiments with hybrid electronic devices based on polyaniline-polyethylenoxide junction [9]. Memristive propertiesof living creatures and their organs and fluids have been demonstrated in skin [23], blood [18], plants [30] (includingfruits [29]), slime mould [11], tubulin microtubules [8, 5].From a more global point of view, mem-fractance which involves fractional calculus, is a general paradigm for unifyingand enlarging the family of memristive, mem-capacitive and mem-inductive elements.This paper presents a study of the I-V characteristics of a number of specimens of plants, fungi, and cultivationmediums. Why choose specimens from nature? Previous work has demonstrated significant potential for the use ofnaturally occurring substances as memristors. Taking these studies as a basis, it is proposed that any substance takenfrom nature — that has once been living — will exhibit the same memristive properties.Why we are looking for memristive properties? A memristor is a material implication [4, 20]. Therefore, memristorscan be used for constructing other logical circuits, statefull logic operations [4], logic operations in passive crossbar arraysof memristos [22], memory aided logic circuits [19], self-programmable logic circuits [3], and, indeed, memory devices [14].If the substances show memristive properties then we can implement a large variety of memory and computing devicesembedded directly into hybrid electronic circuits that utilise naturally occurring resources.The rest of this paper is organised as follows. Section 2 details the experimental set up used to examine the I-Vcharacteristics of fungal fruit bodies. Section 3 presents the results from the experimentation. A mathematical modellingonion mem-fractance is presented in Sect. 4. A discussion of the results is given in Sect. 5 and finally conclusions are givenin Sect. 5. A number of subjects were identified for the purposes of testing the I-V characteristics of biological medium. Samples fallunder the following categories: fruiting bodies, flora, fungi and water. In addition, a number of control samples were alsosubject to test (dry wood shavings and de-ionised water).Fruits and vegetables used in experiments are large garlic (origin Spain, Tesco Stores Ltd.), aubergine (origin Spain,Aldi UK), onion (origin UK, Aldi UK), potato (origin UK, Aldi UK), banana (Aldi UK), cucumber (origin Spain, AldiUK), mango (origin Peru, Aldi UK), and bell pepper (origin Spain, Aldi UK). Plants used in experiments are
Echeveriapulidonis and
Senecio ficoides . Fungi used in experiments grey oyster fungi
Pleurotus ostreatus (Ann Miller’s SpecialityMushrooms Ltd, UK) cultivated on wood shavings. 2
Voltage [V] -6-4-20246 C u rr en t [I] -7 Average I-V characteristics of aubergine with a delay of 10ms between steps (a) -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Voltage [V] -505 C u rr en t [I] -6 Average I-V characteristics of potato with a delay of 10ms between steps (b) -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Voltage [V] -2.5-2-1.5-1-0.500.511.522.5 C u rr en t [I] -6 I-V characteristics of echeveria pulidonis with a delay of 10ms between steps (c) -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Voltage [V] -5-4-3-2-1012345 C u rr en t [I] -8 I-V characteristics of senecio ficoides with a delay of 10ms between steps (d)
Figure 3: I-V characteristics of specimens, error bars shown. Cyclic voltammetry performed over -0.5V to 0.5V, with astep delay of 10ms. (a) aubergine, (b) potato, (c)
Echeveria pulidonis , (d)
Senecio ficoides .Iridium-coated stainless steel sub-dermal needles with twisted cables (Spes Medica SRL, Italy) were inserted approxi-mately 10 mm apart in each of the samples under test, such as in the example in Fig. 2. I-V sweeps were performed onthe each of the samples using a Keithley Source Measure Unit (SMU) 2450 (Keithley Instruments, USA) under a rangeof conditions: • Cyclic voltammetry performed from -0V5 to 0V5 and -1V to 1V. The voltage limits of the cyclic voltammetry arelimited as to not exceed the electrolysis of water. • Delay between consecutive voltage settings: 0.01s, 0.1s and 1s.The composition of tap water is measured to be the following: conductivity 573 micro Siemens (measured at 22.7 ° C withEutch Instruments, Model CONDG+), pH 6.86 (measured at 22.5 ° C with VWR pH 10), pH 7.0 standardised at 25 ° C,total dissolved solids 393 ppm, salinity: 0.3 ppm. All conditions were repeated a number of times and the resulting I-Vcurves processed using MATLAB.
A number of key findings have been drawn from the tests that support the assertion that any biological object exhibitsmemristance. This section present a subset of the results from I-V characterisation of the specimens. All raw data plotsfor I-V characteristics may be found in the appendices (section 6).
From the species tested in this study, it is seen that the I-V sweeps that the resistance of the subject is varied dependingnot only on the previously applied voltage but also on the frequency with which the voltage is changed. As a general rule,the faster the voltage is changed the greater the divergence in conducted current between the positive and negative phasesof the cyclic voltammetry. Additionally, increasing the frequency of the voltage will yield a larger conducted current.Figure 3 shows the average I-V response for a selection of the test specimens.Test substrates were subjected to cyclic voltammetry over two voltage ranges. Naturally, for the larger voltage range,the maximum conducted current is also far greater. The greater the applied voltage, the closer the test subject is to a3
Voltage [V] -505 C u rr en t [I] -6 Average Mycelium tested in ambient lab light conditions (a) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Voltage [V] -8-6-4-202468 C u rr en t [I] -6 Average Mycelium tested in ambient lab light conditions (b)
Figure 4: Average mycelium I-V characteristics. (a) cyclic voltammetry performed from -0.5V to 0.5V. (b) cyclic voltam-metry performed from -1V to 1V.breakdown voltage where larger current flow can be expected, similar behaviour to a p-n-p junction in a traditional siliconsemi-conductor.
This study also covered the use of mycelium as a memristor, Fig. 4. The mycelium exhibits the same memristive propertiesas the other fruiting bodies and flora. However, the mycelium is cultivated on dampened wood shavings. Therefore, cyclicvoltammetry was conducted on both dampened wood shavings and tap water, Fig. 5, to explore the potential memristanceof the growth medium. The I-V sweeps demonstrate that the control samples also exhibit memristive properties, albeitwith a lower conducted current than the mycelium. This is something that is not seen in dry wood shavings (Fig. 5(c)).The dry shavings respond in a similar way as an open circuit for the test set-up. It is therefore concluded that the additionof water to the growth medium provides a transport mechanism that allows the conduction of current. Tap water has anumber of impurities dissolved in it that act as charge carriers, combining this with the wood shavings in a thin layerincreases the conducted current compared to the tap water alone in volume.
The cyclic voltammetry of the subject matter illustrates that periods of ‘spiking’ (oscillations) occur in their I-V char-acteristics. The spiking behaviour is important as it is a classic component of devices that exhibit memristive proper-ties [12, 26, 27]. By way of example, MATLAB was used to detect the occurrence of the spikes in I-V traces from someof the samples that were tested and the results are shown below.Figure 6 shows the spiking density from the aubergine and Fig. 7 shows the spiking density from the plant
Echeveriapulidonis . It is clear that spiking tends to occur over sections of the I-V curve, for a number of periods of the oscillation(also shown in figures of I-V sweeps from Sect. 3). However, there are instances where individual spikes can occur overthe waveform. These are characterised by having a larger voltage interval from other occurrences of spikes. The numberof spikes, or length of an oscillation period, will vary from between different samples. The important note is that thesespikes are exhibited, thereby reinforcing the the resistance of the substance is a function of the previous voltage state andfrequency of the voltage swing. 4
Voltage [V] -1.5-1-0.500.511.5 C u rr en t [I] -7 I-V characteristics of damp wood shavings (a) -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Voltage [V] -6-4-2024 C u rr en t [I] -8 I-V characteristics of drinking water (b) -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Voltage [V] -1.5-1-0.500.51 C u rr en t [I] -8 I-V characteristics of dry wood shavings with a delay of 10ms between steps (c)
Figure 5: Average I-V characterisation of control mediums. Cyclic voltammetry performed over -0.5V to 0.5V. (a) dampwood shavings. (b) Bristol tap water sample. (c) dry wood shavings5
Voltage interval [V] P ea k f r equen cy Frequency of spiking in fruit body sample over a number of runs
Positive cycle 1Negative cycle 1Positive cycle 2Negative cycle 2Positive cycle 3Negative cycle 3Positive cycle 4Negative cycle 4Positive cycle 5Negative cycle 5 Positive cycle 6Negative cycle 6Positive cycle 7Negative cycle 7Positive cycle 8Negative cycle 8Positive cycle 9Negative cycle 9Positive cycle 10Negative cycle 10 (a)
Voltage interval [V] P ea k f r equen cy Frequency of spiking in fruit body sample over a number of runs
Positive cycle 1Negative cycle 1Positive cycle 2Negative cycle 2Positive cycle 3Negative cycle 3Positive cycle 4Negative cycle 4Positive cycle 5Negative cycle 5 Positive cycle 6Negative cycle 6Positive cycle 7Negative cycle 7Positive cycle 8Negative cycle 8Positive cycle 9Negative cycle 9Positive cycle 10Negative cycle 10 (b)
Voltage interval [V] P ea k f r equen cy Frequency of spiking in fruit body sample over a number of runs
Positive cycle 1Negative cycle 1Positive cycle 2 Negative cycle 2Positive cycle 3Negative cycle 3 (c)
Voltage interval [V] P ea k f r equen cy Frequency of spiking in fruit body sample over a number of runs
Positive cycle 1Negative cycle 1Positive cycle 2Negative cycle 2Positive cycle 3Negative cycle 3Positive cycle 4Negative cycle 4Positive cycle 5Negative cycle 5 Positive cycle 6Negative cycle 6Positive cycle 7Negative cycle 7Positive cycle 8Negative cycle 8Positive cycle 9Negative cycle 9Positive cycle 10Negative cycle 10 (d)(e)
Voltage interval [V] P ea k f r equen cy Frequency of spiking in fruit body sample over a number of runs
Positive cycle 1Negative cycle 1Positive cycle 2 Negative cycle 2Positive cycle 3Negative cycle 3 (f)
Figure 6: Frequency of voltage interval between spikes for cyclic voltammetry of aubergine under the following conditions:(a) -0.5V to 0.5V, sample delay 10ms, (b) -0.5V to 0.5V, sample delay 100ms, (c) -0.5V to 0.5V, sample delay 1000ms,(d) -1V to 1V, sample delay 10ms, (e) -1V to 1V, sample delay 100ms, (f) -1V to 1V, sample delay 1000ms.6
Voltage interval [V] P ea k f r equen cy Frequency of spiking in fruit body sample over a number of runs
Positive cycle 1Negative cycle 1Positive cycle 2Negative cycle 2Positive cycle 4Negative cycle 4Positive cycle 5Negative cycle 5Positive cycle 6 Negative cycle 6Positive cycle 7Negative cycle 7Positive cycle 8Negative cycle 8Positive cycle 9Negative cycle 9Positive cycle 10Negative cycle 10 (a)
Voltage interval [V] P ea k f r equen cy Frequency of spiking in fruit body sample over a number of runs
Positive cycle 1Negative cycle 1Positive cycle 2Negative cycle 2Positive cycle 3Negative cycle 3Positive cycle 4Negative cycle 4Positive cycle 5Negative cycle 5 Positive cycle 6Negative cycle 6Positive cycle 7Negative cycle 7Positive cycle 8Negative cycle 8Positive cycle 9Negative cycle 9Positive cycle 10Negative cycle 10 (b)
Voltage interval [V] P ea k f r equen cy Frequency of spiking in fruit body sample over a number of runs
Positive cycle 1Negative cycle 1Positive cycle 2 Negative cycle 2Positive cycle 3Negative cycle 3 (c)
Voltage interval [V] P ea k f r equen cy Frequency of spiking in fruit body sample over a number of runs
Positive cycle 1Negative cycle 1Positive cycle 2Negative cycle 2Positive cycle 3Negative cycle 3Positive cycle 4Negative cycle 4Positive cycle 5Negative cycle 5 Positive cycle 6Negative cycle 6Positive cycle 7Negative cycle 7Positive cycle 8Negative cycle 8Positive cycle 9Negative cycle 9Positive cycle 10Negative cycle 10 (d)(e)
Voltage interval [V] P ea k f r equen cy Frequency of spiking in fruit body sample over a number of runs
Positive cycle 1Negative cycle 1Positive cycle 2 Negative cycle 2Positive cycle 3Negative cycle 3 (f)
Figure 7: Frequency of voltage interval between spikes for cyclic voltammetry of
Echeveria pulidonis under the followingconditions: (a) -0.5V to 0.5V, sample delay 10ms, (b) -0.5V to 0.5V, sample delay 100ms, (c) -0.5V to 0.5V, sample delay1000ms, (d) -1V to 1V, sample delay 10ms, (e) -1V to 1V, sample delay 100ms, (f) -1V to 1V, sample delay 1000ms7able 1: Coefficient of P(t) a -1.94717918941007e-37 a a a -7.02417186413251e-09 a -1.09608654138843e-32 a a a -2.25915349408741e-06 a -3.96814860043400e-29 a a a -0.000198753598325262 a a a -3.22386131288943e-24 a -0.00438858300276266 a a a a -0.00277217499616736 a -2.10303480491708e-20 a -0.0499326832665322 a -1.15343437980144e-19 a a -3.79360135264957e-17 a -0.184313854027240 a a a -6.04224119899083e-14 a -0.517083007531048 a -2.79837373009902e-12 Here we report the I-V characteristics of onion (-0V5 to 0V5) with a delay of 10ms between steps (Fig. 18). It is evidentfrom the results that onion displays memristive behaviour. Although this vegetable typically does not demonstrate the‘pinching’ property of an ideal memristor [7], it can be clearly seen that the biological matter exhibits memory propertieswhen the electrical potential across the substrate is swept. A positive sweep yields a higher magnitude current when theapplied voltage is positive; and a smaller magnitude current when the applied voltage is negative.Fractional Order Memory Elements (FOME) are proposed as a combination of Fractional Order Mem-Capacitors(FOMC) and Fractional Order Mem-Inductors (FOMI) [1]. The FOME (1) is based on the generalised Ohm’s law andparameterised as follows: α , α are arbitrary real numbers which satisfy 0 ≤ α , α ≤ F α ,α M is the memfractance, q ( t ) is the time dependent charge, ϕ ( t ) is the time dependent flux. Therefore,the memfractance ( F α ,α M is an interpolation between four points: MC — memcapacitance, R M - memristor, MI —meminductance, and R M - the second order memristor. Full derivations for the generalised FOME model are givenby [1, 2]. The definition of memfractance can be straightforward generalised to any value of α , α (see [1, Fig. 27]). D α t ϕ ( t ) = F α ,α M ( t ) D α t q ( t ) (1)The appearance of characteristics from various memory elements in the onion I-V curves supports the assertion thatthe onion is a memfractor where α and α are both greater than 0 and less than 2.There is no biological reason for memfractance of onion, be a usual closed formula. Therefore, one can get only amathematical approximation of this function. In this section, we propose two alternatives to obtain the best approximationfor memfractance in the case of onion I-V characteristics for averaged cyclic voltammetry of Fig. 18. Raw data include the time, voltage and intensity of each reading characteristics of onion with a delay of 10 ms betweensteps. There are 401 readings for each run. The process of these data, in order to obtain a mathematical approximation ofmemfractance, in the first alternative, takes 4 steps as follows. First step: approximate v ( t ) by a thirty-degree polynomial.First step: approximate v(t) by a thirty-degree polynomial (Fig. 8) whose coefficients are given in table 1. v ( t ) ≈ P ( t ) = j =30 (cid:88) j =0 a j t j (2)The polynomial fits very well the experimental voltage curve, as the statistical indexes show in table 2.Step 2: in the same way approximate the current i ( t ) using a thirty-degree polynomial (Fig. 9) whose coefficients aregiven in Tab. 3. i ( t ) ≈ Q ( t ) = j =30 (cid:88) j =0 b j t j (3)8able 2: Quality of fitness.Sum of squared estimate of errors SSE = (cid:80) j = nj =1 ( v j − ˆ v j ) SSR = (cid:80) j = nj =1 ( ˆ v j − ¯ v ) SST = SSE + SSR R − square = SSRSST t -0.5-0.4-0.3-0.2-0.100.10.20.30.40.5 v (t) Experimental dataDegree 30 polynomial fitting
Figure 8: Voltage versus time and its approximation by a 30-degree polynomial.Table 3: Coefficient of Q(t) b b -6.07388014701807e-15 b -2.71853051938565e-40 b b b -5.52975396257029e-12 b -4.51931699470006e-36 b b b -1.31005323328773e-09 b -4.77095462655549e-33 b b -1.72460618050188e-31 b -1.01592865082809e-07 b b b -3.41852207771790e-28 b -2.50008266407625e-06 b b b -1.05754298813303e-24 b -1.65013726134833e-05 b b b b -2.12898753184482e-05 b -5.64419454512205e-20 b b b -3.40155939059945e-06 b t -2.5-2-1.5-1-0.500.511.52 i (t) -6 Experimental dataDegree 30 polynomial fitting
Figure 9: Current versus time and its approximation by a 30-degree polynomial.Again, the polynomial fits well the experimental intensity curve, as displayed in Tab. 4.Step 3: From (1) used under the following form when D α t q ( t ) (cid:54) = 0. F α ,α M ( t ) = D α t ϕ ( t ) D α t q ( t ) (4)and the Rieman-Liouville fractional derivative defined by [25]. RL D αt f ( t ) = 1Γ( m − α ) d m dt m (cid:90) t ( t − s ) m − α − f ( s ) ds , m - 1 < α < m (5)together with the formula for the power function RL D αt (cid:0) at β (cid:1) = a Γ( β + 1)Γ( β − α + 1) t β − α , β > − , α > , (6)we obtain the closed formula of F α ,α M ( t ), approximation of the true biological memfractance of onions. F α ,α M ( t ) = D α t ϕ ( t ) D α t ϕ ( t ) = RL D α t (cid:80) j =30 j =0 a j j +1 t j +1 RL D α t (cid:80) j =30 j =0 b j j +1 t j +1 = (cid:80) j =30 j =0 a j Γ( j +1)Γ( j +2 − α ) t j +1 − α (cid:80) j =30 j =0 b j Γ( j +1)Γ( j +2 − α ) t j +1 − α (7)Step 4 choice of parameter α and α : We are looking for the best value of these parameters in the range ( α , α ) ∈ [0 , . In this goal, we are considering first the singularities of F α ,α M ( t ) in order to avoid their existence, using suitablevalues of the parameters. Secondly, we will choose the most regular approximation.We compute numerically, the values t ∗ ( α ) which vanish the denominator of F α ,α M ( t ) (Fig. 10).We observe one, two or three coexisting solutions depending on the value of α . Moreover, there is no value of α without zero of the denominator. Therefore, in order to eliminate the singularities, we need to determine the couples( α , α ) ∈ [0 , , vanishing simultaneously denominator and numerator of F α ,α M ( t ) (Figs. 11 and 12).In the second part of step 4, we choose the most regular approximation. We consider that the most regular approxi-mation is the one for which the function range ( F α ,α M ( t )) is minimal (Fig. 13).range ( F α ,α M ( t )) = max t ∈ [0 , ( F α ,α M ( t )) − min t ∈ [0 , ( F α ,α M ( t )) (8)From the numerical results, the best couple ( α , α ) and the minimum range of F α ,α M ( t ) are given in table 5, and thecorresponding Memfractance is displayed in Fig. 14.The value of ( α , α ) given in Table 5 belongs to the triangle T of Fig. 15, whose vertices are memcapacitor, capacitorand negative-resistor, which means that Onion is like a mix of such basic electronic devices.As a counter-example of our method for choosing the best possible memfractance, Fig. 16 displays, the memfractancefor a non-optimal couple ( α , α ) = (1 . , .
5) which presents two singularities.10 , * t * Zeros t * 2 ) of the denominator of F M ) (t) Figure 10: Zeros t ∗ ( α ) of the denominator of F α ,α M ( t ). t* , , , Zeros t * 2 ) of F M ) (t) denominator (red dots), and zeros t * 1 ) of the numerator (blue dots). , , Figure 11: Zeros t ∗ ( α ) of F α ,α M ( t ) denominator (red dots), and zeros t ∗ ( α ) of the numerator (blue dots).Table 5: Minimum values of αα α Minimum range of F α ,α M ( t )1.441224116 0.154232123 1085076.4634863111 , , for which the zeros t * 2 ) of denominator of F M ) (t) correspond to the zeros t * 1 ) of denominator Figure 12: Values of ( α , α ) ∈ [0 , for which the zeros t ∗ ( α ) of denominator of F α ,α M ( t ) correspond to the zeros t ∗ ( α )of denominator. , , , R a ng e ( F m , , , (t)) Minimum Range of smooth Onion memfractance R m = 1085076.46 for ( , , , )= (1.44, 0.15) ( , ,F m , , , (t))( , ,F m , , , (t)) X: 0.1542Y: 1.085e+06 X: 1.441Y: 1.085e+06
Figure 13: Values of range ( F α ,α M ( t )) for ( α , α ) ∈ [0 , . t -4-202468 F m , , , (t) Smooth Onion memfractance with Minimum Range R m = 1085076.46 for ( alpha , alpha )= (1.44, 0.15) Figure 14: Memfractance for ( α , α ) given in Tab. 5.Table 6: Coefficients of a and a (cid:48) Coefficient Value for 0 ≤ t ≤ T Coefficient Value for
T < t < T max a -5.51E-11 a (cid:48) a a (cid:48) -2.02E-08 a -1.39E-07 a (cid:48) a a (cid:48) -0.000202629 a -5.30E-06 a (cid:48) a -0.000154541 a (cid:48) -0.342890106 a a (cid:48) a -0.006015086 a (cid:48) -126.3046069 a a (cid:48) a a (cid:48) -7808.105752 a -0.497985462 a (cid:48) v ( t ) and i ( t ).Figure 18 shows that the curve computed from closed approximate formula belongs to the histogram of data of allruns. Due to the way of conducting the experiments, the voltage curve presents a vertex, that means that the function v ( t ) isnon-differentiable for T = 19 . T is the average value of the non-differentiable pointsfor the 10 runs. The value T max = 40 . ≤ t ≤ T max .In this alternative approximation, we follow the same 4 steps as in 4.1, changing the approximation by a thirty-degreepolynomial to an approximation by a 2-piecewise D-degree-polynomial, for both v ( t ) and i ( t ). Here D = 10.First step: approximation of v ( t ) by a 2-piecewise tenth-degree-polynomial (Fig. 19) whose coefficients are given intable 6. v ( t ) = (cid:40) P ( t ) = (cid:80) j = Dj =0 a j t j , for 0 ≤ t ≤ TP ( t ) = (cid:80) j = Dj =0 a (cid:48) j t j , for t ≤ t < T max (9)The flux is obtained integrating v ( t ) versus time. 13 Resistor Memristor Inductor Memcapacitor 2 nd order Memristor Meminductor Capacitor Negative Resistor T T T Capacitor
Figure 15: Non-binary solution space showing mem-fractive properties of a memory element14 t -1.5-1-0.500.511.52 F m , , , (t) Mushroom impedance with ( , , , )= (1.20, 0.50) Figure 16: Memfractance with two singularities for ( α , α ) = (1 . , . -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 v(t) -2-1.5-1-0.500.511.5 i (t) -6 Experimental dataDegree thirty plynomial fitting
Figure 17: Comparison between average experimental data of cyclic voltammetry performed over -0.5 V to 0.5 V, placement,and approximate values of v ( t ) and i ( t ). 15 Figure 18: Both average experimental data curve and the curve computed from closed approximate formula are nestedinto the histogram of data of all runs. 16 t -0.5-0.4-0.3-0.2-0.100.10.20.30.40.5 v (t) Experimental dataTen degree two polynomial fitting
Figure 19: Voltage versus time and its approximation by 2-piecewise tenth degree polynomial.Table 7: Goodness of fitApproximation interval t < T t > T
Sum of squared estimate of errors SSE 0.000390862 0.001120834Sum of squared residuals SSR 16.66147438 16.66067277Sum of square total SST 16.66186524 16.66179361Coefficient of determination R-square 0.999976541518186 0.999932730288331Table 8: Coefficients of b and b (cid:48) .Coefficient Value for 0 ≤ t ≤ T Coefficient Value for
T < t < T max b b (cid:48) -2.13E-09 b -4.86E-09 b (cid:48) b b (cid:48) -3.78E-06 b -3.18E-07 b (cid:48) b b (cid:48) -0.001481936 b -3.20E-06 b (cid:48) b b (cid:48) -0.099223872 b -2.52E-06 b (cid:48) b b (cid:48) -2.13E-09 b -4.86E-09 b (cid:48) b b (cid:48) -3.78E-06 ϕ ( t ) = (cid:40) IP ( t ) = (cid:80) j = Dj =0 a j j +1 t j +1 , for 0 ≤ t ≤ TIP ( t ) = (cid:80) j = Dj =0 a (cid:48) j j +1 t j +1 , for T ≤ t < T max (10)The polynomial fits very well the experimental voltage curve, as the statistical indexes show in Tab. 7.Step 2: in the same way, one approximates the current i ( t ) using a 2-piecewise tenth degree polynomial (Fig. 20) whosecoefficients are given in Tab. 8. i ( t ) = (cid:40) P ( t ) = (cid:80) j = Dj =0 b j t j , for 0 ≤ t ≤ TP ( t ) = (cid:80) j = Dj =0 b (cid:48) j t j , for T ≤ t < T max (11)Again, the polynomial fits very well the experimental voltage curve, as the statistical indexes show in Tab. 9.Therefore, the charge is given by 17 t -2.5-2-1.5-1-0.500.511.52 i (t) -6 Figure 20: Current versus time and its approximation by 2-piecewise tenth degree polynomial.Table 9: Quality of fitness.Approximation interval t < T t > T
Sum of squared estimate of errors SSE 6.63E-13 5.92E-13Sum of squared residuals SSR 4.97E-11 2.36E-11Sum of square total SST 5.04E-11 2.41E-11Coefficient of determination R-square 0.986832207 0.97550029 q ( t ) = (cid:40) IP ( t ) = (cid:80) j = Dj =0 b j j +1 t j +1 , for 0 ≤ t ≤ TIP ( t ) = (cid:80) j = Dj =0 b (cid:48) j j +1 t j +1 , for T ≤ t < T max (12)Step 3: Following the same calculus as before with (4), one obtainsfor 0 ≤ t ≤ T , F α ,α M ( t ) = RL D α t ϕ ( t ) RL D α t q ( t ) = RL D α t [ IP ( t )] RL D α t [ IP ( t )] = (cid:80) j = Dj =1 a j Γ( j +1)Γ( j +2 − α ) t j +1 − α (cid:80) j = Dj =0 b j Γ( j +1)Γ( j +2 − α ) t j +1 − α (13)However, because fractional derivative has memory effect, for T < t < T max , the formula is slightly more complicated F α ,α M ( t ) = RL D α t ϕ ( t ) RL D α t q ( t ) = m − α ) d m dt m (cid:82) t ( t − s ) m − α − ϕ ( s ) ds m − α ) d m dt m (cid:82) t ( t − s ) m − α − q ( s ) ds , m − < α < m and m − < α < m = m − α ) d m dt m (cid:104)(cid:82) T ( t − s ) m − α − IP ( s ) ds + (cid:82) tT ( t − s ) m − α − IP ( s ) ds (cid:105) m − α ) d m dt m (cid:104)(cid:82) T ( t − s ) m − α − IP ( s ) ds + (cid:82) tT ( t − s ) m − α − IP ( s ) ds (cid:105) = m − α ) d m dt m (cid:80) j = Dj =0 (cid:104) a j j +1 (cid:82) T ( t − s ) m − α − s j +1 ds + a (cid:48) j j +1 (cid:82) tT ( t − s ) m − α − s j +1 ds (cid:105) m − α ) d m dt m (cid:80) j = Dj =0 (cid:104) b j j +1 (cid:82) T ( t − s ) m − α − s j +1 ds + b (cid:48) j j +1 (cid:82) tT ( t − s ) m − α − s j +1 ds (cid:105) (14)Using integration by part repeatedly D + 1 times we obtain18 α , α M ( t ) = Γ ( m − α ) d m d t m (cid:80) j = D j = (cid:104) a j j + (cid:104) (cid:80) k = j + k = (cid:104) − ( j + ) ! Γ ( m − α )( t T ) m + k − α T j + − k ( j + − k ) ! Γ ( m + k + − α (cid:105) + ( j + ) ! Γ ( m − α ) t m + k − α Γ ( m + j + − α ) (cid:105) + a (cid:48) j j + (cid:104) (cid:80) k = j + k = ( j + ) ! Γ ( m − α )( t − T ) m + k − α T j + − k ( j + − k ) ! Γ ( m + k + − α ) (cid:105)(cid:105) Γ ( m − α ) d m d t m (cid:80) j = D j = (cid:104) b j j + (cid:104) (cid:80) k = j + k = (cid:104) − ( j + ) ! Γ ( m − α )( t − T ) m + k − α T j + − k ( j + − k ) ! Γ ( m + k + − α ) (cid:105) + ( j + ) ! Γ ( m − α ) t m + k − α Γ ( m + j + − α ) (cid:105) + b (cid:48) j j + (cid:104) (cid:80) k = j + k = ( j + ) ! Γ ( m − α )( t − T ) m + k − α T j + − k ( j + − k ) ! Γ ( m + k + − α ) (cid:105)(cid:105) = Γ ( m − α ) d m d t m (cid:80) j = D j = (cid:104) ( a (cid:48) j − a j ) (cid:80) k = j + k = (cid:104) j ! Γ ( m − α )( t − T ) m + k − α T j + − k ( j + − k ) ! Γ ( m + k + − α ) (cid:105) + a jj ! Γ ( m − α ) t m + j + − α Γ ( m + j + − α (cid:105) Γ ( m − α ) d m d t m (cid:80) j = D j = (cid:104) ( b (cid:48) j − b j ) (cid:80) k = j + k = (cid:104) j ! Γ ( m − α )( t − T ) m + k − α T j + − k ( j + − k ) ! Γ ( m + k + − α ) (cid:105) + b jj ! Γ ( m − α ) t m + j + − α Γ ( m + j + − α ) (cid:105) = (cid:80) j = D j = (cid:104) ( a (cid:48) j − a j ) (cid:80) k = j + k = (cid:104) j ! ( t − T ) k − α T j + − k ( j + − k ) ! Γ ( k + − α ) (cid:105) + a jj ! t j + − α Γ ( j + − α ) (cid:105) (cid:80) j = D j = (cid:104) ( b (cid:48) j − b j ) (cid:80) k = j + k = (cid:104) j ! ( t − T ) k − α T j + − k ( j + − k ) ! Γ ( k + − α ) (cid:105) + b jj ! t j + − α Γ ( j + − α ) (cid:105) ( ) α . α α Minimum range of F α ,α M ( t )1.971795208 1.483238482 743101.176733524In this 2-piece wise approximation, the vertex is non-differentiable, this implies that (15) expression has a singularityat T (because ( t − T ) − α , → ∞ ).It could be possible to avoid this singularity, using a 3-piece wise approximation, smoothing the vertex. However, thecalculus are very tedious. We will explain, below, what our simpler choice implies.Then F α ,α M ( t ) = ( t − T ) − α (cid:104)(cid:80) j = Dj =0 (cid:104) ( a (cid:48) j − a j ) (cid:80) k = j +1 k =0 (cid:104) j !( t − T ) k T j +1 − k ( j +1 − k )!Γ( k +1 − α ) (cid:105) + a j j ! t j +1 − α ( t − T ) α Γ( j +2 − α ) (cid:105)(cid:105) ( t − T ) − α (cid:104)(cid:80) j = Dj =0 (cid:104) ( b (cid:48) j − b j ) (cid:80) k = j +1 k =0 (cid:104) j !( t − T ) k T j +1 − k ( j +1 − k )!Γ( k +1 − α ) (cid:105) + b j j ! t j +1 − α ( t − T ) α Γ( j +2 − α ) (cid:105)(cid:105) = (cid:80) j = Dj =0 (cid:104) ( a (cid:48) j − a j ) (cid:80) k = j +1 k =0 (cid:104) j !( t − T ) k T j +1 − k ( j +1 − k )!Γ( k +1 − α ) (cid:105) + a j j ! t j +1 − α ( t − T ) α Γ( j +2 − α ) (cid:105) ( t − T ) α − α (cid:80) j = Dj =0 (cid:104) ( b (cid:48) j − b j ) (cid:80) k = j +1 k =0 (cid:104) j !( t − T ) k T j +1 − k ( j +1 − k )!Γ( k +1 − α ) (cid:105) + b j j ! t j +1 − α ( t − T ) α Γ( j +2 − α ) (cid:105) (16)Finally F α ,α M ( t ) = (cid:80) j = Dj =0 aj Γ( j +1)Γ( j +2 − α t j +1 − α (cid:80) j = Dj =0 bj Γ( j +1)Γ( j +2 − α t j +1 − α , for 0 ≤ t ≤ T (cid:80) j = Dj =0 (cid:20) ( a (cid:48) j − a j ) (cid:80) k = j +1 k =0 (cid:20) j !( t − T ) kTj +1 − k ( j +1 − k )!Γ( k +1 − α (cid:21) + a j j ! tj +1 − α t − T ) α j +2 − α (cid:21) ( t − T ) α − α (cid:80) j = Dj =0 (cid:20) ( b (cid:48) j − b j ) (cid:80) k = j +1 k =0 (cid:104) j !( t − T ) kTj +1 − k ( j +1 − k )!Γ( k +1 − α (cid:105) + b j j ! tj +1 − α t − T ) α j +2 − α (cid:21) , for T < t < T max (17)Step 4 choice of parameter α and α : Following the same idea as for the first alternative, we try to avoid singularityfor F α ,α M ( t ), except of course the singularity near T , which is of mathematical nature (non-differentiability of voltageand intensity at t = T ). Figure 21 display zeros t ∗ ( α ), of the denominator of F α ,α M ( t ).Figure 22 displays the curves of couples ( α , α ) for which the denominator and numerator of F α ,α M ( t ) are nullsimultaneously for t < T and t > T . On this figure, the value of α that corresponds to α = 1 . α ≈ . T . The value of ( α = 1 . , α = 1 . T of Fig. 15, whose edges are resistor,memristor, and capacitor. Therefore the mem-fractance property of onion is a combination of those of these electriccomponents.The comparison of average experimental data of cyclic voltammetry performed over -0.5 V to 0.5 V and closed approx-imative formula is displayed in Fig. 25, showing a very good agreement between both curves. Due to the way of conducting the experiments, the voltage curve presents a vertex, that means that the function v ( t ) isnon-differentiable for T = 218 . T is the average value of the non-differentiable pointsfor the 3 runs. On has T max = 446 . D = 15.We perform an approximation by a 2-piecewise D-degree-polynomial, for both v ( t ) and i ( t ).First step: approximation of v ( t ) by a 2-piecewise fifteen-degree-polynomial defined by (9), (Fig. 26) whose coefficientsare given in table 11.The flux is again obtained integrating v ( t ) versus time (10).The polynomial fits very well the experimental voltage curve, as the statistical indexes show in Tab. 12.Step 2: in the same way, one approximates the current i ( t ) using a 2-piecewise fifteenth degree polynomial defined by(11), (Fig. 27) whose coefficients are given in table 13.Again, the polynomial fits very well the experimental voltage curve, as the statistical indexes show in Tab. 14.Therefore, the charge is given by (12).Step 3: Following the same calculus as before with (4), for 0 ≤ t ≤ T , F α ,α M ( t ) is defined by (13).However, because fractional derivative has memory effect, for T < t < T max , the formula is slightly more complicated.It is defined by (14), (15), (16) and (17).In this 2-piecewise approximation, the vertex is non-differentiable, this implies that (15) expression has a singularityat T (because ( t − T ) − α , → inf). 20 , * t * Zeros t * ( , ) of the denominator of F M( , , , ) (t) t > T t T Figure 21: The zeros t ∗ ( α ), of the denominator of F α ,α M ( t ), as function of α . , , Figure 22: Couples ( α , α ) for which the denominator and numerator of F α ,α M ( t ) are null simultaneously.21 , , , R a ng e ( F m , , , (t)) Minimum Range of piecewise smooth Onion memfractance R m = 743101.18 for ( , , , )= (1.97, 1.48) X: 1.483Y: 7.431e+05 X: 1.972Y: 7.431e+05
Figure 23: Values of range ( F α ,α M ( t )) for ( α , α ) ∈ [0 , . t -1012345678 F m , , , (t) Piecewise smooth Onion memfractance with Minimum Range R m = 743101.18 for ( , , , )= (1.97, 1.48) X: 19.49Y: 2.052e+05 X: 19.9Y: -2.33e+04
Figure 24: Memfractance for ( α = 1 . , α = 1 . v(t) -2.5-2-1.5-1-0.500.511.52 i (t) -6 Figure 25: Comparison between average experimental data of cyclic voltammetry performed over -0.5 V to 0.5 V, Stem-to-cap electrode placement, and closed approximative formula.Table 11: Coefficients of a and a (cid:48) Coefficient Value for 0 ≤ t ≤ T Coefficient Value for
T < t < . a a (cid:48) a -5.96398936924787e-27 a (cid:48) -5.20695580801111e-27 a a (cid:48) a -2.04721171726301e-21 a (cid:48) -1.85546677570461e-20 a a (cid:48) a -1.28714657924748e-16 a (cid:48) -1.40637895477368e-14 a a (cid:48) a -2.09391204258264e-12 a (cid:48) -3.38279075621789e-09 a a (cid:48) a -8.95113952596272e-09 a (cid:48) -0.000288613689878837 a a (cid:48) a -8.03669009474361e-06 a (cid:48) -8.43718319262010 a a (cid:48) a -0.000835676981290587 a (cid:48) -67977.9563028956 a a (cid:48) a -1.00360065451426 a (cid:48) -66266900.3096982Table 12: Quality of fitness.Approximation interval t < T t > T Sum of squared estimate of errors SSE 8.05206626404267e-05 0.000379119559037593Sum of squared residuals SSR 66.6597470338760 66.7305863691811Sum of square total SST 66.6598275545387 66.7309654887402Coefficient of determination R-square 0.999998792066143 0.99999431868614123
50 100 150 200 250 300 350 400 450 t -1-0.8-0.6-0.4-0.200.20.40.60.81 v (t) Experimental DataTwo (fifteen degree) polynomial fitting
Figure 26: Voltage versus time and its approximation by 2-piecewise fifteenth degree polynomial. t -3.5-3-2.5-2-1.5-1-0.500.511.5 i (t) -6 Experimental dataTwo (fifteen degree) polynomial fitting
Figure 27: Current versus time and its approximation by 2-piecewise fifteenth degree polynomial.24able 13: Coefficients of b and b (cid:48) Coefficient Value for 0 ≤ t ≤ T Coefficient Value for
T < t < . b b (cid:48) b -1.63161644309873e-31 b (cid:48) -2.89601182252080e-34 b b (cid:48) b -5.83981425666847e-26 b (cid:48) -2.25810438491826e-27 b b (cid:48) b -3.90531862314380e-21 b (cid:48) -2.39282614008484e-21 b b (cid:48) b -7.01109241829061e-17 b (cid:48) -6.85633253958774e-16 b b (cid:48) b -3.58165613133728e-13 b (cid:48) -6.36783612027411e-11 b b (cid:48) b -4.66705880467474e-10 b (cid:48) -1.89820925444517e-06 b b (cid:48) b -1.14142215596473e-07 b (cid:48) -0.0147140989613784 b (cid:48) b -4.08952638018235e-06 b (cid:48) -12.9611877781724Table 14: Goodness of fitApproximation interval t < T t > T Sum of squared estimate of errors SSE 7.99361696557309e-14 2.86502655937580e-15Sum of squared residuals SSR 1.45875395884222e-10 1.02218430381697e-10Sum of square total SST 1.45955332053877e-10 1.02221295408256e-10Coefficient of determination R-square 0.999452324430147 0.999971972312150Table 15: Values of αα α Minimumg range of F α ,α M ( t )0.171972381 0.054935584 12089427.7744264Step 4 choice of parameter α and α : Following the same idea as for the first alternative, we try to avoid singularityfor F α ,α M ( t ), except of course the singularity near T , which is of mathematical nature (non-differentiability of voltageand intensity at t = T ). Figure 28 display zeros t ∗ ( α ), of the denominator of F α ,α M ( t ).Figure 29 displays the curves of couples ( α , α ) for which the denominator and numerator of F α ,α M ( t ) are nullsimultaneously for t < T and t > T .The singularity observed in Figs. 31 is due to the non-differentiability of both voltage and intensity functions at point T . The value of ( α = 0 . , α = 0 . T of Fig. 15, whose extremities are 2ndmemristor, memristor, and memcapacitor. In this experiment, onion has property related to these basic electric devices.As a counter-example of our method for choosing the best possible memfractance, Fig. 32 displays, the memfractancefor a non-optimal couple ( α , α ) = (1 . , .
6) which presents two singularities.The comparison of average experimental data of cyclic voltammetry performed over -1 V to 1 V, Stem-to-cap electrodeplacement, and closed approxmating formula is displayed in Fig. 33, showing a very good agreement between both curves.25 , * t * Zeros t*( , ) of the denominator of F M , , , (t) tT Figure 28: The zeros t ∗ ( α ), of the denominator of F α ,α M ( t ), as function of α . , , Values of ( , , , ) for which the zeros t * ( , ) of denominator of F M( , , , ) (t) correspond to the zeros t * ( , ) of numenator Figure 29: Couples ( α , α ) for which the denominator and numerator of F α ,α M ( t ) are null simultaneously.26 , , , R a ng e ( F m , , , (t)) Minimum Range of piecewise smooth Onion memfractance R m = 12089427.77 for ( , , , )= (0.17, 0.05) ( , , R m )( , , R m ) X: 0.172Y: 1.209e+07X: 0.05494Y: 1.209e+07
Figure 30: Values of range ( F α ,α M ( t )) for ( α , α ) ∈ [0 , . t F m , , , (t) Pieceise smooth Onion Memfractance with Minimum Range R m = 12089427.77 for ( , , , )= (0.17, 0.05) Figure 31: Memfractance for ( α = 0 . , α = 0 .
50 100 150 200 250 300 350 400 450 t F m , , , (t) Onion memfractance with ( , , , )= (1.82, 1.60) Figure 32: Memfractance with singularity for ( α , α ) = (1 . , . -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 v(t) -3.5-3-2.5-2-1.5-1-0.500.511.5 i (t) -6 Experimental dataTwo (fiftenn degree) polynomial fitting
Figure 33: Comparison between average experimental data of cyclic voltammetry performed over -1 V to 1 V and closedapproximative formula. 28igure 34: Ideal plots of mem-fractance
It has been shown in this paper that items taken from nature all exhibit memristive properties wherein the conductedcurrent from the positive half of a cyclic voltammetry sweep does not match the conducted current from the negativecycle. This is in line with previously published results on I-V characterisation of organic and biological substrates, whichindicate memristive properties of organic polymers [9], skin [23], blood [18], slime mould
Physarum polycephalum [11],plants [30], fruits [29], and tubulin microtubules [8, 5].In addition, the level as to the divergence between the positive and negative cycles is also demonstrated to be afunction of the sweep frequency (time). These memristive properties have also been observed in medium such as dampwood shavings and water. It is therefore proposed that any living system, a large proportion of which is water acting asa charge carrier, is able to exhibit memristive properties, the degree of which can be expressed on a continuous scale.It is also observed that the crossing behaviour expected from an ideal, passive, memristor is not often seen from thenaturally occurring specimens. A naturally occurring specimen is capable of generating its own potential, which has anassociated conducted current, both of which have been measured as part of the cyclic voltammetry. Increasing the delaytime between consecutive readings, will produce an I-V characteristic where the negative and positive phases ‘pinch’ closertogether.In all instances, the fingerprints of memristive devices are observed in specimens taken from nature. It can be expressedthat memristance is indeed not a binary feature, however it exists more of a continuum [0,1] - 0 representing pure resistance,1 representing the ideal memristor — each device can then be assigned a number on the scale [0,1] to characterise its‘degree of memristance’.More generally mem-fractance which is a general paradigm linking memristive, mem-capacitive and mem-inductiveproperty of electric elements, should be the adequate frame for the mathematical modelling all plants and fungi. The useof fractional derivatives to analyse the mem-fractance, is obvious if one considers that fractional derivatives have memory,which allow a perfect modelling of memristive elements. Their handling is however delicate if one wants to avoid any flaw.In Section 4, the case of onion is analysed. Increasing the frequency of sampling of the current intensity and changing therange of voltage leads to slightly different mem-fractance. With low frequency and higher voltage, the onion has propertieswhich is a combination of memristor, mem-capacitor and second order memristor. In the case of high frequency, and lowvoltage, the onion is merely more a mix of resistor, capacitor and memristor, showing less memory effect!Additionally, current oscillations during the cyclic voltammetry are produced by all sample specimens. Typically,the oscillatory effect can be observed only on one phase of the voltammetry for a given voltage range which is, again,a behaviour that can be associated to a device whose resistance is a function of its previous resistance. Although, itis worth stating that some samples do produce overlapping oscillatory effects (both phases of voltammetry) for certainconditions — however this can be controlled through careful selection of voltammetry conditions. This spiking activityis typical of a device that exhibits memristive behaviours as having been previously observed in experiments with theelectrochemical devices with a graphite reference electrodes [10], in experiments with electrode metal on solution-processed29exible titanium dioxide memristors [13], see also analysis in [12]. The spiking properties of the meristive devices can beutilized in the field of neurmorphic systems [27, 16, 26, 24, 21, 17].
Acknowledgement
This project has received funding from the European Union’s Horizon 2020 research and innovation programme FETOPEN “Challenging current thinking” under grant agreement No 858132.With special thanks to Neil Phillips and Andrew Geary (UWE, Bristol, UK) for providing the data on tap water.
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Appendix Voltage [V] -6-4-20246 C u rr en t [I] -7 I-V characteristics of aubergine with a delay of 10ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (a) -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Voltage [V] -2-1.5-1-0.500.511.52 C u rr en t [I] -7 I-V characteristics of aubergine with a delay of 100ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (b) -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Voltage [V] -6-4-2024 C u rr en t [I] -8 I-V characteristics of aubergine with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)
Figure 35: Cyclic voltammetry (-0V5 to 0V5) of aubergine. (a) delay time between settings is 10ms, (b) delay timebetween settings is 100ms, (c) delay time between settings is 1000ms33
Voltage [V] -6-4-20246 C u rr en t [I] -6 I-V characteristics of aubergine with a delay of 10ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (a) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Voltage [V] -505 C u rr en t [I] -6 I-V characteristics of aubergine with a delay of 100ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (b) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Voltage [V] -2-1.5-1-0.500.511.52 C u rr en t [I] -6 I-V characteristics of aubergine with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Voltage [V] -2-1.5-1-0.500.511.52 C u rr en t [I] -6 I-V characteristics of aubergine with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Figure 36: Cyclic voltammetry (-1V to 1V) of aubergine. (a) delay time between settings is 10ms, (b) delay time betweensettings is 100ms, (c) delay time between settings is 1000ms34
Voltage [V] -2-1.5-1-0.500.511.52 C u rr en t [I] -6 I-V characteristics of banana with a delay of 10ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (a) -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Voltage [V] -4-3-2-101234 C u rr en t [I] -7 I-V characteristics of banana with a delay of 100ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (b) -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Voltage [V] -1-0.500.51 C u rr en t [I] -7 I-V characteristics of banana with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Voltage [V] -1-0.500.51 C u rr en t [I] -7 I-V characteristics of banana with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Figure 37: Cyclic voltammetry (-0V5 to 0V5) of banana. (a) delay time between settings is 10ms, (b) delay time betweensettings is 100ms, (c) delay time between settings is 1000ms35
Voltage [V] -8-6-4-202468 C u rr en t [I] -6 I-V characteristics of banana with a delay of 10ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (a) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Voltage [V] -2-1.5-1-0.500.511.52 C u rr en t [I] -6 I-V characteristics of banana with a delay of 100ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (b) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Voltage [V] -4-3-2-101234 C u rr en t [I] -7 I-V characteristics of banana with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Voltage [V] -4-3-2-101234 C u rr en t [I] -7 I-V characteristics of banana with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Figure 38: Cyclic voltammetry (-1V to 1V) of banana. (a) delay time between settings is 10ms, (b) delay time betweensettings is 100ms, (c) delay time between settings is 1000ms36
Voltage [V] -2-1012 C u rr en t [I] -6 I-V characteristics of cucmber with a delay of 10ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (a) -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Voltage [V] -2-1.5-1-0.500.511.52 C u rr en t [I] -6 I-V characteristics of cucmber with a delay of 100ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (b) -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Voltage [V] -1.5-1-0.500.511.5 C u rr en t [I] -6 I-V characteristics of cucmber with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Voltage [V] -1.5-1-0.500.511.5 C u rr en t [I] -6 I-V characteristics of cucmber with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Figure 39: Cyclic voltammetry (-0V5 to 0V5) of cucumber. (a) delay time between settings is 10ms, (b) delay timebetween settings is 100ms, (c) delay time between settings is 1000ms37
Voltage [V] -4-3-2-101234 C u rr en t [I] -6 I-V characteristics of cucmber with a delay of 10ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (a) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Voltage [V] -4-3-2-101234 C u rr en t [I] -6 I-V characteristics of cucmber with a delay of 100ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (b) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Voltage [V] -4-3-2-101234 C u rr en t [I] -6 I-V characteristics of cucmber with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Voltage [V] -4-3-2-101234 C u rr en t [I] -6 I-V characteristics of cucmber with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Figure 40: Cyclic voltammetry (-1V to 1V) of cucumber. (a) delay time between settings is 10ms, (b) delay time betweensettings is 100ms, (c) delay time between settings is 1000ms38
Voltage [V] -2-1012 C u rr en t [I] -7 I-V characteristics of garlic with a delay of 10ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (a) -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Voltage [V] -2-1.5-1-0.500.511.52 C u rr en t [I] -7 I-V characteristics of garlic with a delay of 100ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (b) -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Voltage [V] -6-4-20246 C u rr en t [I] -8 I-V characteristics of garlic with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Voltage [V] -6-4-20246 C u rr en t [I] -8 I-V characteristics of garlic with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Figure 41: Cyclic voltammetry (-0V5 to 0V5) of garlic. (a) delay time between settings is 10ms, (b) delay time betweensettings is 100ms, (c) delay time between settings is 1000ms39
Voltage [V] -1-0.500.51 C u rr en t [I] -6 I-V characteristics of garlic with a delay of 10ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (a) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Voltage [V] -2-1.5-1-0.500.511.52 C u rr en t [I] -6 I-V characteristics of garlic with a delay of 100ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (b) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Voltage [V] -505 C u rr en t [I] -7 I-V characteristics of garlic with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Voltage [V] -505 C u rr en t [I] -7 I-V characteristics of garlic with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Figure 42: Cyclic voltammetry (-1V to 1V) of garlic. (a) delay time between settings is 10ms, (b) delay time betweensettings is 100ms, (c) delay time between settings is 1000ms40
Voltage [V] -505 C u rr en t [I] -7 I-V characteristics of mango with a delay of 10ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (a) -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Voltage [V] -2.5-2-1.5-1-0.500.511.522.5 C u rr en t [I] -7 I-V characteristics of mango with a delay of 100ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (b) -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Voltage [V] -1-0.500.51 C u rr en t [I] -7 I-V characteristics of mango with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Voltage [V] -1-0.500.51 C u rr en t [I] -7 I-V characteristics of mango with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Figure 43: Cyclic voltammetry (-0V5 to 0V5) of mango. (a) delay time between settings is 10ms, (b) delay time betweensettings is 100ms, (c) delay time between settings is 1000ms41
Voltage [V] -1-0.500.51 C u rr en t [I] -6 I-V characteristics of mango with a delay of 10ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (a) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Voltage [V] -1-0.500.51 C u rr en t [I] -6 I-V characteristics of mango with a delay of 100ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (b) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Voltage [V] -1.5-1-0.500.511.5 C u rr en t [I] -6 I-V characteristics of mango with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Voltage [V] -1.5-1-0.500.511.5 C u rr en t [I] -6 I-V characteristics of mango with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Figure 44: Cyclic voltammetry (-1V to 1V) of mango. (a) delay time between settings is 10ms, (b) delay time betweensettings is 100ms, (c) delay time between settings is 1000ms42
Voltage [V] -3-2-10123 C u rr en t [I] -6 I-V characteristics of onion with a delay of 10ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (a) -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Voltage [V] -2-1.5-1-0.500.511.52 C u rr en t [I] -6 I-V characteristics of onion with a delay of 100ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (b) -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Voltage [V] -1.5-1-0.500.511.5 C u rr en t [I] -6 I-V characteristics of onion with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Voltage [V] -1.5-1-0.500.511.5 C u rr en t [I] -6 I-V characteristics of onion with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Figure 45: Cyclic voltammetry (-0V5 to 0V5) of onion. (a) delay time between settings is 10ms, (b) delay time betweensettings is 100ms, (c) delay time between settings is 1000ms43
Voltage [V] -6-4-20246 C u rr en t [I] -6 I-V characteristics of onion with a delay of 10ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (a) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Voltage [V] -4-3-2-101234 C u rr en t [I] -6 I-V characteristics of onion with a delay of 100ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (b) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Voltage [V] -3-2-10123 C u rr en t [I] -6 I-V characteristics of onion with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Voltage [V] -3-2-10123 C u rr en t [I] -6 I-V characteristics of onion with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Figure 46: Cyclic voltammetry (-1V to 1V) of onion. (a) delay time between settings is 10ms, (b) delay time betweensettings is 100ms, (c) delay time between settings is 1000ms44
Voltage [V] -8-6-4-202468 C u rr en t [I] -7 I-V characteristics of bell pepper with a delay of 10ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (a) -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Voltage [V] -1-0.500.51 C u rr en t [I] -6 I-V characteristics of bell pepper with a delay of 100ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (b) -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Voltage [V] -6-4-20246 C u rr en t [I] -7 I-V characteristics of bell pepper with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Voltage [V] -6-4-20246 C u rr en t [I] -7 I-V characteristics of bell pepper with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Figure 47: Cyclic voltammetry (-0V5 to 0V5) of pepper. (a) delay time between settings is 10ms, (b) delay time betweensettings is 100ms, (c) delay time between settings is 1000ms45
Voltage [V] -4-3-2-101234 C u rr en t [I] -6 I-V characteristics of bell pepper with a delay of 10ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (a) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Voltage [V] -4-3-2-101234 C u rr en t [I] -6 I-V characteristics of bell pepper with a delay of 100ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (b) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Voltage [V] -2-1012 C u rr en t [I] -6 I-V characteristics of bell pepper with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Voltage [V] -2-1012 C u rr en t [I] -6 I-V characteristics of bell pepper with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Figure 48: Cyclic voltammetry (-1V to 1V) of pepper. (a) delay time between settings is 10ms, (b) delay time betweensettings is 100ms, (c) delay time between settings is 1000ms46
Voltage [V] -505 C u rr en t [I] -6 I-V characteristics of potato with a delay of 10ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (a) -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Voltage [V] -2-1012 C u rr en t [I] -6 I-V characteristics of potato with a delay of 100ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (b) -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Voltage [V] -1.5-1-0.500.511.5 C u rr en t [I] -7 I-V characteristics of potato with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Voltage [V] -1.5-1-0.500.511.5 C u rr en t [I] -7 I-V characteristics of potato with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Figure 49: Cyclic voltammetry (-0V5 to 0V5) of potato. (a) delay time between settings is 10ms, (b) delay time betweensettings is 100ms, (c) delay time between settings is 1000ms47
Voltage [V] -6-4-20246 C u rr en t [I] -6 I-V characteristics of potato with a delay of 10ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (a) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Voltage [V] -4-3-2-101234 C u rr en t [I] -6 I-V characteristics of potato with a delay of 100ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (b) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Voltage [V] -8-6-4-202468 C u rr en t [I] -7 I-V characteristics of potato with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Voltage [V] -8-6-4-202468 C u rr en t [I] -7 I-V characteristics of potato with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Figure 50: Cyclic voltammetry (-1V to 1V) of potato. (a) delay time between settings is 10ms, (b) delay time betweensettings is 100ms, (c) delay time between settings is 1000ms48
Voltage [V] -505 C u rr en t [I] -6 Mycelium tested in darkened conditions sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 sample2 run1sample2 run2sample2 run3sample2 run4sample2 run5sample2 run6sample2 run7sample2 run8sample2 run9sample2 run10 (a) -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Voltage [V] -505 C u rr en t [I] -6 Mycelium tested in ambient lab light conditions sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 sample2 run1sample2 run2sample2 run3sample2 run4sample2 run5sample2 run6sample2 run7sample2 run8sample2 run9sample2 run10 (b) -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Voltage [V] -505 C u rr en t [I] -6 Mycelium tested under illuminated conditions sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 sample2 run1sample2 run2sample2 run3sample2 run4sample2 run5sample2 run6sample2 run7sample2 run8sample2 run9sample2 run10 (c)(c)
Voltage [V] -505 C u rr en t [I] -6 Mycelium tested under illuminated conditions sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 sample2 run1sample2 run2sample2 run3sample2 run4sample2 run5sample2 run6sample2 run7sample2 run8sample2 run9sample2 run10 (c)(c)
Figure 51: Cyclic voltammetry (-0V5 to 0V5) of mycelium substrate cultivated on damp wood shavings with three differentlight levels. (a) covered, (b) ambient lab light (965 Lux), (c) illuminated (1500 Lux).49
Voltage [V] -8-6-4-202468 C u rr en t [I] -6 Mycelium tested in darkened conditions sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 sample2 run1sample2 run2sample2 run3sample2 run4sample2 run5sample2 run6sample2 run7sample2 run8sample2 run9sample2 run10 (a) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Voltage [V] -8-6-4-202468 C u rr en t [I] -6 Mycelium tested in ambient lab light conditions sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 sample2 run1sample2 run2sample2 run3sample2 run4sample2 run5sample2 run6sample2 run7sample2 run8sample2 run9sample2 run10 (b) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Voltage [V] -8-6-4-202468 C u rr en t [I] -6 Mycelium tested under illuminated conditions sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 sample2 run1sample2 run2sample2 run3sample2 run4sample2 run5sample2 run6sample2 run7sample2 run8sample2 run9sample2 run10 (c)(c)
Voltage [V] -8-6-4-202468 C u rr en t [I] -6 Mycelium tested under illuminated conditions sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 sample2 run1sample2 run2sample2 run3sample2 run4sample2 run5sample2 run6sample2 run7sample2 run8sample2 run9sample2 run10 (c)(c)
Figure 52: Cyclic voltammetry (-1v to 1v) of mycelium substrate cultivated on damp wood shavings with three differentlight levels. (a) covered, (b) ambient lab light (965 Lux), (c) illuminated (1500 Lux).50
Voltage [V] -1.5-1-0.500.511.5 C u rr en t [I] -7 I-V characteristics of damp wood shavings sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (a) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Voltage [V] -1-0.500.51 C u rr en t [I] -6 Control sample sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (b)
Figure 53: Cyclic voltammetry of damp wood shavings used as a control for mycelium tests. (a) -0V5 to 0V5, (b) -1V to1V 51
Voltage [V] -1.5-1-0.500.51 C u rr en t [I] -8 I-V characteristics of drinking water with a delay of 1ms between steps sample1 run1sample1 run2sample1 run3 sample1 run4sample1 run5 (a) -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Voltage [V] -1.5-1-0.500.51 C u rr en t [I] -8 I-V characteristics of drinking water with a delay of 1ms between steps sample1 run1sample1 run2sample1 run3 sample1 run4sample1 run5 (b) -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Voltage [V] -6-4-2024 C u rr en t [I] -8 I-V characteristics of drinking water sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (c)(c)
Voltage [V] -6-4-2024 C u rr en t [I] -8 I-V characteristics of drinking water sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (c)(c)
Figure 54: Cyclic voltammetry (-0V5 to 0V5) of drinking water used as a control for mycelium tests. (a) delay betweenvoltage steps is 1ms, (b) delay between voltage steps is 10ms, (c) delay between voltage steps is 100ms52
Voltage [V] -2.5-2-1.5-1-0.500.511.522.5 C u rr en t [I] -6 I-V characteristics of echeveria pulidonis with a delay of 10ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (a) -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Voltage [V] -1-0.8-0.6-0.4-0.200.20.40.60.81 C u rr en t [I] -6 I-V characteristics of echeveria pulidonis with a delay of 100ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (b) -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Voltage [V] -6-4-2024 C u rr en t [I] -8 I-V characteristics of echeveria pulidonis with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Voltage [V] -6-4-2024 C u rr en t [I] -8 I-V characteristics of echeveria pulidonis with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Figure 55: Cyclic voltammetry (-0V5 to 0V5) of echeveria pulidonis. (a) delay time between settings is 10ms, (b) delaytime between settings is 100ms, (c) delay time between settings is 1000ms53
Voltage [V] -6-4-20246 C u rr en t [I] -6 I-V characteristics of echeveria pulidonis with a delay of 10ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (a) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Voltage [V] -3-2-10123 C u rr en t [I] -6 I-V characteristics of echeveria pulidonis with a delay of 100ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (b) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Voltage [V] -1.5-1-0.500.511.5 C u rr en t [I] -6 I-V characteristics of echeveria pulidonis with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Voltage [V] -1.5-1-0.500.511.5 C u rr en t [I] -6 I-V characteristics of echeveria pulidonis with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Figure 56: Cyclic voltammetry (-1V to 1V) of echeveria pulidonis. (a) delay time between settings is 10ms, (b) delay timebetween settings is 100ms, (c) delay time between settings is 1000ms54
Voltage [V] -5-4-3-2-1012345 C u rr en t [I] -8 I-V characteristics of senecio ficoides with a delay of 10ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (a) -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Voltage [V] -2.5-2-1.5-1-0.500.511.522.5 C u rr en t [I] -8 I-V characteristics of senecio ficoides with a delay of 100ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (b) -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Voltage [V] -1.5-1-0.500.51 C u rr en t [I] -9 I-V characteristics of senecio ficoides with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Voltage [V] -1.5-1-0.500.51 C u rr en t [I] -9 I-V characteristics of senecio ficoides with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)
Figure 57: Cyclic voltammetry (-0V5 to 0V5) of senecio ficoides. (a) delay time between settings is 10ms, (b) delay timebetween settings is 100ms, (c) delay time between settings is 1000ms55
Voltage [V] -8-6-4-202468 C u rr en t [I] -7 I-V characteristics of senecio ficoides with a delay of 10ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (a) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Voltage [V] -1.5-1-0.500.511.5 C u rr en t [I] -7 I-V characteristics of senecio ficoides with a delay of 100ms between steps sample1 run1sample1 run2sample1 run3sample1 run4sample1 run5 sample1 run6sample1 run7sample1 run8sample1 run9sample1 run10 (b) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Voltage [V] -3-2-10123 C u rr en t [I] -8 I-V characteristics of senecio ficoides with a delay of 1s between steps sample1 run1sample1 run2 sample1 run3 (c)(c)