Research into the induced polarization effect in soil has a long history. In 1913, Conrad Schlumberger defined the concept of soil chargeability (Seigel
Studies have been carried out regarding the electrical properties of wood which has a moisture content of below the FSP (fibre saturation point), most notably in the following research items: (Stamm, 1927; Skaar, 1964, 1988; Vermaas, 1975; Norberg, 1999, 2000; Forsén & Tarvainen, 2000; EN 13183-2:2002, 2002; Brischke & Rapp, 2008; Björngrim
Studies have been carried out regarding the electrical properties of wood within the relevant frequency domain, most notably in the following research items: (Tiitta
A comparison has been made in the following research regarding the electrical properties of wood within the given frequency domain and time domain: (Gao
Well-known electrical properties when it comes to wood include its levels of electrical resistance and its levels of electrical capacitance. In practice, electrical resistance is used in terms of resistance-type wood moisture meters (Gann, 2022; Brookhuis, 2009; Scanntronik, 2022; BES Bollmann, 2022; Ahlborn, 2022; James Instruments, 2022). Electrical capacitance is used in terms of capacitance-type wood moisture meters (Brookhuis, 2009; Ahlborn, 2022; James Instruments, 2022).
In wood moisture meters which have an electrical charging effect (these being polarization-type wood moisture meters), both electrical resistance and electrical capacitance are used simultaneously when determining the value of any moisture content within every type of wood. With this type of wood moisture meter, both electrical resistance and the electrical capacity of wood are related to each other through the electrical charging number of the wood itself (Tamme
Few studies have been conducted to quantitatively characterize electrical chargeability in the wood medium. One previous study by Tamme
The purpose of the current article is to investigate the electrical charging effect in wood in general, meaning as dependent only on electrical variables at wood constant temperature of 20 degrees Celsius and at the moisture content of 105%.
Conventional chargeability CHA(E) as defined by Schlumberger and dependent on the potential
where E2,max is the maximum potential of electrodes in volts at the beginning of the discharging process, and E1,const is the constant potential of electrodes in volts in the charging process.
Energetic chargeability CHA(W) is defined as a ratio between stored and transmitted energy:
where W2 is the total energy stored in wood in joules (J), and W1 is the total energy (J) transmitted through wood in the charging process. The transmitted energy W1 may briefly be called primary energy, and the energy stored in wood W2 may briefly be called secondary energy.
Primary energy W1 was calculated as follows (Keithley, 2004; Bard & Faulkner, 1980):
and secondary energy W2 was calculated as follows:
where Q1(t1) is the total primary charge in coulombs (C) transmitted through wood in the charging process t1,
Q2(t2) is the secondary charge in coulombs stored in wood, and t2 is the time of discharging.
E1,const is the constant potential in the charging process, and
E2,max is the maximum electrode potential at the beginning of the discharging process,
I1(t) is the charging current dependent on the charging time (see Figure 2b, the upper left curve), and
I2(t) is the discharging current dependent on the discharging time (see Figure 2b, the lower right curve).
The number 0.1 in the bottom path of integration is the measuring interval.
The following relationship between conventional chargeability CHA(E) (as defined by Schlumberger in 1913) and energetic chargeability CHA(W) can be deduced from the above formulas:
where Q1 is the total charge in coulombs transmitted through the wood medium in the charging process, and Q2 is the total electrical charge in coulombs stored in the wood medium.
The primary integral electrical capacitance corresponding to the transmitted electrical charge is represented as follows:
and the secondary integral electrical capacitance corresponding to the stored electrical charge is demonstrated as follows:
To compare DC strengths in the time domain and frequency domain at the time moment of 240 seconds from the start of spectrum registration, the Ohm’s law was used:
where E1 is the value of a discretely given potential for each impedance spectrum. |
On a Nyquist and Bode phase angle plot (Figures 7 and 11a) the Warburg impedance (if the diffusion layer has an infinite thickness) appears as a diagonal line with a slope and a phase shift of 45°, respectively.
The Warburg impedance (ZW) is obtained using
where the first member of the formula describes the real part of the diffusion process and the second imaginary part of complex diffusion resistance. The corresponding faradaic impedance for mixed kinetics is expressed as a serial combination of the charge transfer resistance and Warburg impedance, also known as Randles circuit.
For more complex cases, the generalized finite-length Warburg element for a short circuit terminus model is expressed as:
where ω is the radial frequency, RD is the limiting diffusion resistance, T = L2/D is the diffusion time constant, L is the effective diffusion layer thickness, D is the effective diffusion coefficient of a particle and αw is the fractional exponent for Warburg-like diffusion impedance (Bard & Faulkner, 1980; Krause, 2003).
The Warburg coefficient σ can be determined from the slope of the Nyquist plot or by fitting it to an equivalent circuit model which includes a Warburg impedance:
where R is the ideal gas constant; T is absolute temperature; n is the number of electrons transferred; F is Faraday's constant;
Capacitors in electrochemical impedance spectroscopy experiments often do not behave ideally; they act like a constant phase element, where the exponent α < 1 and Cdl are the double-layer capacitance, which appears at the interface between an electrode and an adjacent liquid electrolyte:
and
where
The double-layer capacitance can be determined from the frequency at which the imaginary impedance (-Z″) is at a maximum:
where the top point of the complex plane semicircle corresponding to the frequency
(Bard & Faulkner, 1980; Krause, 2003).
The equivalent circuit adapted from Zelinka
The schematic diagram of the experiment is shown in Figure 2a.
Figure 2a depicts the measuring cell (at 20 °C) which used a measuring system with two symmetrical carbon fibre pin electrodes. The dimensions of the wood specimen were as follows: 35 mm (thickness, direction R) * 150 mm (width, direction T) * 120 mm (longitudinal fibre length, direction L). The pin electrodes were partially insulated with polyurethane film (see Figure 2a). The diameter of the electrodes was 3 mm, and the distance between them was 30 mm. Green birch wood had a moisture content (relative to dry weight) of 105%. For the purpose of the experiments of this article, liquid birch sap was traditionally collected at the beginning of the spring vegetation period.
The coupling electrode (CE) and the reference electrode (RE) were coupled together (CE+RE) in the two-electrode measuring system Metrohm Autolab (2022).
Table 1 illustrates the capability of various measuring procedures to experimentally determine the energetic chargeability and integral electrical capacitance of wood (and sap) according to Formulas (1) to (6). To calculate the energetic chargeability, it is necessary to determine the primary energy W1 and secondary energy W2 in the experiment. Table 1 shows that primary and secondary energy are fully measurable with the PDM and CV measuring procedures, because these procedures allow the time dependencies of both current strength and potential in the charging and discharging phases to be determined. The disadvantage of CV is that it does not allow the open circuit potential in the discharging process to be measured, because the linear potential is provided by the measuring program Metrohm Autolab (2022).
The capability of various measuring procedures to determine the potential and current strength of electrodes in the studied medium in the process of electrical charging and discharging. W1 – primary transmitted energy. W2 – secondary stored energy. E(t) – the time dependence of potential. I(t) – the time dependence of current. PDM – polarization-depolarization method. CCD – chrono charging-discharging. CP – chrono-potentiometry. EIS – electrical impedance spectroscopy. CV – cyclic voltammetry.
Measuring procedure | Primary W1 – charging process | Secondary W2 – discharging process | ||
---|---|---|---|---|
E(t) | I(t) | E(t) | I(t) | |
PDM | yes | yes | yes | yes |
CCD | yes | yes | no | yes |
CP | yes | yes | yes | no |
EIS | yes | yes | no | no |
CV | yes | yes | yes | yes |
PDM is described in detail in a previous study (Tamme
The 0.1 second measurement interval was used. The upper left curve in Figure 2b is the charging current curve for the potential E = 2.6 V, and the lower right curve is the discharging curve. The transition from the first charging phase to the second discharging phase occurs at the moment of potential interruption (Figure 2b).
For PDM, the corresponding typical current and potential curves are presented in the study by Tamme
The EIS (i.e. FRA impedance potentiostatic) measuring procedure was used to collect the experimental data needed for modelling in the frequency domain. Fifty frequencies between 100 kHz and 0.01 Hz were used in logarithmic sequence with the sine signal amplitude of 50 mV. Electrode potentials were provided discreetly at the registration of each spectrum with the following values: 0 V, 0.4 V, 0.8 V, 1.2 V, 1.8 V and 2.6 V. ZView ver. 2.3 (Scribner Inc., 2022) software was used for the impedance modelling.
The results obtained in the time domain are found in Tables 2 and 3.
Values of electrical parameters measured and calculated using direct current in the process of charging and discharging in wood and sap at different electrode potentials. E – potential in volts. W2 – primary energy. W2 – secondary energy. C1int – the primary integral electrical capacitance. C2int – the secondary integral electrical capacitance. CHA(E) – conventional chargeability and CHA(W) – energetic chargeability, according to the Formulas (1) (2) (3) (4) (6) and (7).
Birch wood (B) | ||||||
---|---|---|---|---|---|---|
E / V | W1 / mJ | W2 / mJ | C1,int / mF | C2,int / mF | CHA(E) | CHA(W) |
Legend on the figures | W1(B) | W2(B) | C1(B) | C2(B) | CHA(E)(B) | CHA(W)(B) |
0.4 | 0.0269 | 0.0092 | 0.172 | 0.0605 | 0.975 | 0.34 |
0.8 | 0.124 | 0.0455 | 0.202 | 0.0767 | 0.963 | 0.37 |
1.2 | 0.466 | 0.191 | 0.326 | 0.135 | 0.992 | 0.407 |
1.8 | 2.069 | 0.768 | 0.737 | 0.316 | 0.867 | 0.373 |
2.6 | 7.973 | 2.442 | 1.541 | 0.617 | 0.765 | 0.306 |
Birch sap (BS) | ||||||
---|---|---|---|---|---|---|
Legend | W1(BS) | W2(BS) | C1(BS) | C2(BS) | CHA(E)(BS) | CHA(W)(BS) |
0.4 | 0.0144 | 0.0052 | 0.0898 | 0.0343 | 0.975 | 0.36 |
0.8 | 0.108 | 0.0329 | 0.169 | 0.058 | 0.938 | 0.3 |
1.2 | 0.519 | 0.187 | 0.361 | 0.132 | 0.992 | 0.357 |
1.8 | 72.711 | 2.299 | 22.44 | 0.718 | 0.994 | 0.032 |
2.6 | 108.79 | 4.052 | 16.09 | 0.604 | 0.996 | 0.075 |
Values of electrical parameters measured and calculated using direct current in the process of charging and discharging in wood and sap at different transmitted primary energies. W1 – primary transmitted energy in millijoules (mJ).
Primary energy, W1 / mJ | W2 / mJ, (B) | W2 / mJ, (BS) | CHA (W), (B) | CHA(W), (BS) | W2(B)/ W2(BS) |
---|---|---|---|---|---|
Legend | W2(B) | W2(BS) | CHA(W)(B) | CHA(W)(BS) | W2(B)/ W2(BS) |
7.97 | 2.38 | 0.315 | 0.298 | 0.0395 | 7.5 |
32.9 | 3.683 | 1.191 | 0.112 | 0.0362 | 3.092 |
57.89 | 4.146 | 2.067 | 0.0716 | 0.0357 | 2.006 |
107.8 | 4.499 | 3.82 | 0.0417 | 0.0354 | 1.178 |
First, the dependence of the conventional and energetic chargeability and integral capacitance on the potential applied to the electrodes was studied (see Table 2).
Figure 3a shows the values of certain comparable energies in millijoules (mJ) on the same axis as dependent on the potential applied to the electrodes. In some cases, the calculated energy has square dependence on the potential.
It can be ascertained from Figure 3b that conventional chargeability is, compared to actual energetic chargeability, systematically overestimated at all electrode potentials at a rate of about 2 to 2.5 times. Both chargeabilities depend on the potential applied to the electrodes. A comparison of the chargeabilities is performed for the same measuring interval of 0.1 second.
Figure 4a shows the primary integral electrical capacitances as dependent on the potential applied to the electrodes. From the 1.2 V potential, the primary integral electrical capacitance of birch sap begins to rise sharply compared to that of wood.
Figure 4b represents the secondary integral electrical capacitances C2,int for wood and sap, which are easily comparable both in terms of their course and their numerical values.
Secondly, in addition to the dependence of CHA(W) on the electrode potential, the dependencies of energetic chargeability and stored energy on the primary energy W1 transmitted through wood and sap were also studied (see Table 3).
Referring to Figure 5a, it may be established that the amount of energy stored in wood is systematically about 2 times higher than the energy stored in sap when comparing the transmitted primary energies W1. The almost linear increase in the energy stored in the system electrodes + sap observed in the same figure suggests that as the transmitted primary energy grows, the secondary energy stored in the volume charge of the system (symmetrical electrodes + sap) also grows. Figure 5b depicts the course of energetic chargeability of wood and sap as dependent on the transmitted primary energy. Wood chargeability is initially (in the case of W1 = 8 mJ) about 5 times better than that of sap chargeability, but as the transmitted primary energy increases up to more than 100 mJ, the energetic chargeabilities of wood and sap equalize.
Figure 6a shows the ratio W2(B)/ W2(BS) between secondary energies stored in wood and sap as dependent on the transmitted primary energy W1. It may be observed that the initial (8 mJ) six-fold difference of W2(B) in favour of wood shrinks to one at high (more than 100 mJ) primary energies.
Figure 6b represents the DC strength (I (calc)) calculated with the Equation (8) given in the same axis system, and the DC strength (I (meas)) measured with the CCD procedure at the 240th second from the start of the charging process. Both current strengths are mutually satisfactory.
In conclusion, the experimental results show (see Figures 3b and 5b) that wood energetic chargeability is systematically many times greater than that of sap, both in the comparison of the potentials applied to the electrodes and in the comparison of primary energies transmitted through the wood and sap mediums. The reason may lie in the capillary-porous structure of wood, which seems to favour the electrical charging effect in wood.
The Nyquist plots (Figure 7) were measured for birch wood- and birch sap-based systems in the AC frequency range of 300 kHz to 20 mHz in the region of potentials from 0 to 2.6 V. The complex plane plot consists mainly of at least two or three parts: from the very noticeable depressed semicircle at higher AC frequencies with the characteristic frequency fmax and to the so-called double-layer capacitance region at very low frequencies. The results also demonstrate that the shape of -Z’’, Z’-plots noticeably depends on the system studied as well as on the electrode potential.
According to Formula (9), charge transfer resistance and the Warburg coefficient can be calculated from the slope of Z′ versus ω-1/2 or – Z″ versus ω-1/2. According to Figure 8, these values are different for birch wood- and birch sap-based systems and depend also on the diffusivity and concentration of species.
Calculated mass-transfer coefficients for both systems studied show (Figure 9) that there is a noticeable dependence on electrode potential as well as the system studied.
The series capacitance, Cs, with values at f = 25.5 mHz, depends on the potential applied, and the highest Cs values have been established for a birch sap-based system at 2.6 V (Figure 10).
The dependence (Figure 11a) of the phase angle θ on log f at fixed electrode potential shows that at ≈ 0.2 Hz for birch sap- and birch wood-based systems approaches 60° and 34°, respectively, which is characteristic of kinetically mixed processes.
The linear dependence (Figure 11b) of log –Z“ on log f at a fixed electrode potential (0.8 V) clearly shows that at f < 2000 Hz for birch sap- and f < 100 Hz for birch wood-based systems, the systems are described mainly by the slow diffusion process. At higher AC frequencies slow heterogeneous adsorption takes place.
In comparing the general course of the integral capacitance C1,int of wood and sap and the serial capacitance Cs found by impedance modelling, which are given in Figures 4a and 10, a similar trend stands out – higher potentials have higher C1,int and Cs in sap than in wood. However, a comparison of numerical quantities of electrical capacitances at the same potentials in sap shows a significantly higher growth for C1,int when moving to higher potentials. The reason may be that the growth in the integral capacitance of sap starting from the 1.2 V potential is facilitated by the macroscopic symmetrical volumetric charge distribution emerging around the symmetrical electrodes in addition to double-layer electrical charges on the nanoscale (i.e. 1–10 nm, according to Zuleta (2005)). The modelling of Cs according to impedance spectra only considers double-layer electrical capacitance. In the case of wood, no volume charge effect occurs, probably due to its high electrical resistance, and the numerical results of modelling are comparable both in the time domain and frequency domain (i.e. if E = 1.8V, then Cs = 0.5 mF and C1,int = 0.7 mF).
DC strengths measured directly with the CCD measuring procedure in the time domain as well as DC strengths calculated according to Formula (8) in the frequency domain (impedance spectrum) depending on the applied potential are shown in Figure 6b. Both current strengths are mutually satisfactory.
For the theoretical description and experimental study of the electrical charging effect in wood at moisture levels above FSP, it proved expedient to introduce a whole range of specific electrical properties of wood, which are presented in Figures 1a and 1b, described with Formulas (1) – (15), and in Tables 2, 3, 4, and 5. In previous studies, some of these specific electrical properties have been used by Tiitta
Results of modelling the equivalent circuit shown in Figure 1a with the ZView ver. 2.3 [35] program in the frequency domain.
Birch wood | ||||||||
---|---|---|---|---|---|---|---|---|
E / V | χ 2 | R el / Ω | C dl / μF | R ct / kΩ | R D / kΩ | T / s rad-1 | α w | α |
0 | 0.00433 | 238.8 | 12.13 | 15.5 | 611.6 | 78.29 | 0.52 | 0.936 |
0.4 | 0.00433 | 237.7 | 12.13 | 15.8 | 611.6 | 78.29 | 0.52 | 0.936 |
0.8 | 0.00424 | 295.3 | 20.31 | 15.6 | 74.25 | 2.21 | 0.47 | 0.938 |
1.2 | 0.00685 | 285.8 | 23.56 | 15.54 | 68.08 | 1.695 | 0.462 | 0.939 |
1.8 | 0.00432 | 285.4 | 97.65 | 15.54 | 63.19 | 1.21 | 0.461 | 0.939 |
2.6 | 0.00325 | 256.2 | 21.32 | 14.83 | 34.23 | 1.383 | 0.278 | 0.943 |
Birch sap | ||||||||
---|---|---|---|---|---|---|---|---|
0 | 0.00162 | 147 | 50.7 | 0.95 | 2950 | 30.96 | 0.97 | 0.651 |
0.4 | 0.00767 | 148 | 27.9 | 0.55 | 3078 | 30.54 | 0.976 | 0.666 |
0.8 | 0.00413 | 148 | 27.9 | 0.77 | 3077 | 30.54 | 0.976 | 0.666 |
1.2 | 0.00397 | 162 | 35.08 | 3.2 | 30.85 | 5.40 | 1.69 | 0.754 |
1.8 | 0.00282 | 152 | 36.9 | 13.2 | 8.144 | 2.38 | 2.141 | 0.686 |
2.6 | 0.00265 | 166.5 | 29.1 | 6.2 | 3.29 | 3.6 | 2.058 | 0.687 |
Results of modelling the equivalent circuit shown in Figure 1b with the ZView ver. 2.3 (Scribner Inc., 2022) program in the frequency domain.
Birch wood | |||||||
---|---|---|---|---|---|---|---|
E / V | χ 2 | R el / Ω | C dl / μF | R ct / kΩ | R D / kΩ | T / s rad -1 | α w |
0 | 0.00107 | 283.8 | 9.86 | 14.9 | 89.22 | 4.615 | 0.406 |
0.4 | 0.00103 | 273.7 | 12.89 | 14.7 | 71.38 | 5.166 | 0.361 |
0.8 | 0.00114 | 295.3 | 17.397 | 14.84 | 67.10 | 2.544 | 0.403 |
1.2 | 0.0014 | 285.8 | 22.78 | 14.89 | 70.76 | 2.057 | 0.421 |
1.8 | 0.00963 | 285.4 | 13.36 | 13.24 | 134.28 | 5.51 | 0.225 |
2.6 | 0.00732 | 256.2 | 9.485 | 12.62 | 65.99 | 4.46 | 0.055 |
Birch sap | |||||||
---|---|---|---|---|---|---|---|
0 | 0.0024 | 146.95 | 195.25 | 0.83 | 83.43 | 20.26 | 0.64 |
0.4 | 0.00416 | 136.1 | 98.41 | 0.85 | 60.28 | 16.51 | 0.692 |
0.8 | 0.00287 | 148.9 | 46.36 | 0.82 | 11.023 | 13.85 | 0.545 |
1.2 | 0.00807 | 162.2 | 77.14 | 0.81 | 13.76 | 10.57 | 0.586 |
1.8 | 0.0076 | 152.1 | 155.43 | 0.83 | 6.739 | 3.11 | 0.534 |
2.6 | 0.0069 | 166.5 | 351.44 | 0.79 | 65.99 | 4.57 | 0.502 |
To define and experimentally study the specific electrical properties of wood, this article used elements of basic electrochemistry theory as well as some experimental electrochemistry methods (such as EIS and CCD), and ZView 2 software for modelling EIS measurement data.
Energetic chargeability may also be called the actual chargeability of wood, because according to Formula (5), the actual total charges Q1 and Q2 are also taken into account. Conventional chargeability (defined by Schlumberger) is merely an indicator of the actual charging of wood, since the actual total electrical charges affecting the charging process are unknown.
When developing equipment for the monitoring of growing trees, the emergence of the volumetric charge effect on the electrical capacity of wood should be avoided. Based on Figures 4a and 4b and Tables 2 and 3 the surest way to do this is not to use the electrode potential of above E = 1.2 volts.
According to the data in Table 1, it may be argued that impedance modelling fails to allow any information about the stored secondary energy W2 or about the secondary integral electrical capacitance C2,int to be obtained. Impedance modelling in the frequency domain allows for detailed modelling of only the charging process, while neglecting the discharging process.
Electrolyte resistances Rel in Tables 4 and 5 found by modelling are systematically 1.5–2 times greater for birch wood at each value of the potential E compared to the corresponding values modelled for birch sap. Further tests could determine whether the difference found also applies to growing trees. The difference may be pertaining to physics, but it may also lie the specifics of the modelling.
In the paper Tamme
In total, 63 electrical charging phases were repeated in black alder wood at three different moisture contents above FSP. It is highly likely that the electrical charging effect can as successfully be repeated also in birchwood at various moisture contents above FSP.
The experiments described in this article can probably be easily replicated also in other wood research laboratories if measuring procedures PDM (Tamme
In the paper Tamme
The article provides a general discussion on the modelling of the electrical charging effect in wood on the example of birchwood and liquid birch sap at the constant temperature of 20 °C and moisture content of 105%.
In conclusion, the experimental results suggest that conventional chargeability (as defined by Schlumberger) is, compared to actual energetic chargeability, systematically overestimated at a rate of about 2 to 2.5 times at all electrode potentials.
It may also be concluded that the energetic chargeability in wood is systematically up to 5 times higher than in liquid sap. This tendency is evident both in the comparison of applied potentials and in the comparison of transmitted primary energies. The reason may be the capillary-porous structure of wood, which seems to favour the electrical charging effect induced in wood.
Comparing the general course of the integral capacitance C1,int of wood and sap and the serial capacitance Cs found by impedance modelling, a similar tendency stands out: C1,int and Cs are larger in sap at higher potentials than in wood.
In the frequency domain, frequency dependencies were found to distinguish between adsorption processes and mixed kinetics ranges in birch liquid sap and in green birch wood.
This study expanded the theoretical background of the patented polarization-type wood moisture meter. Energetic effects, electrical capacitance, adsorption and mixed kinetics generated in green birch wood upon moisture content measurement were described both theoretically and experimentally.