# Investigation of AC Electrical Properties of MXene-PCL Nanocomposites for Application in Small and Medium Power Generation

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## Abstract

**:**

_{3}C

_{2}T

_{x}MXene (T—OH, Cl or F), which is prepared by etching a layered ternary carbide Ti

_{3}AlC

_{2}(312 MAX-phase) precursor and deposited on a polycaprolactone (PCL) electrospun membrane (MXene-PCL nanocomposite). X-ray Diffraction analysis (XRD) and Scanning Electron Microscopy (SEM) indicates that the obtained material is pure Ti

_{3}C

_{2}MXene. SEM of the PCL-MXene composite demonstrate random Ti

_{3}C

_{2}distribution over the nanoporous membrane. Results of capacitance, inductance, and phase shift angle studies of the MXene-PCL nanocomposite are presented. It was found that the frequency dependence of the capacitance exhibited a clear sharp minima in the frequency range of 50 Hz to over 10

^{4}Hz. The frequency dependence of the inductance shows sharp maxima, the position of which exactly coincides with the position of the minima for the capacitance, which indicates the occurrence of parallel resonances. Current conduction occurs by electron tunneling between nanoparticles. In the frequency range from about 10

^{4}Hz to about 10

^{5}Hz, there is a broad minimum on the inductance relationship. The position of this minimum coincides exactly with the position of the maximum of the phase shift angle—its amplitude is close to 90°. The real value of the inductance of the nanocomposite layer was determined to be about 1 H. It was found that the average value of the distance over which the electron tunnels was determined with some approximation to be about 5.7 nm and the expected value of the relaxation time to be τ

_{M}≈ 3 × 10

^{−5}s.

## 1. Introduction

_{2}C, V

_{2}C, Ti

_{3}C

_{2}, Ti

_{4}N

_{3}and double transition metals (Mo

_{2}TiC

_{2}, Mo

_{2}ScC

_{2}). The finite stage of MXene development is intercalation and/or delamination, in which the MXene can improve initial characteristics and achieve even more versatile properties. This t is ensured through contact with surface functional groups (H, F, and O) in the obtained solution [15].

_{3}C

_{2}, as one of the most popular MXenes, exhibits a high conductivity of 4600 ± 1100 S cm

^{−1}for each individual flake and field effect electron mobility of 2.6 ± 0.7 cm

^{2}V

^{−1}s

^{−1}. The electrical resistance of layered Ti

_{3}C

_{2}is only one order of magnitude bigger than that of individual flakes that grant an exceptional electron transport between layers in comparison to the majority of other 2D materials [17].

_{3}C

_{2}, in this case, is not only mechanically stable but also emits radio signals 50 times better than graphene analogues and 300 times better than antennas with a radiating structure made of Ag. However, the manufacturing of “MXene nanoantenna” is several times easier, and as a bonus, the material is water-dispersable, which are very important for contact with the environment [18,19].

## 2. Materials and Methods

#### 2.1. MXene Synthesis and Characterization

_{3}C

_{2}T

_{x}MXene (T—OH, Cl or F) was prepared by etching a layered ternary carbide Ti

_{3}AlC

_{2}(312 MAX-phase) precursor with a mixture of hydrochloric (HCl) acid and lithium fluoride (LiF) by the MILD method [21]. The etching solution was prepared as follows: 200 mL of 12M HCl (37%) was added to 50 mL of DI-water to yield 250 mL of 9M HCl; then 16 g of LiF was added under stirring. The mixture was placed in a plastic container (volume 500 mL). 10 g of the Ti

_{3}AlC

_{2}powder with mean particle size of less than 40 μm was gradually added to the etching solution. The reaction mixture was held at 25 °C under constant stirring for 24 h. The aluminum layer in Ti

_{3}AlC

_{2}was removed by hydrofluoric acid formed an in-situ via reaction between HCl and LiF, leaving Ti

_{3}C

_{2}flakes weakly bonded through Van der Vaals interaction. After etching, the obtained MXene slurry was rinsed with DI-water via repetitive centrifugation (10 min each cycle at 3500 rpm) to remove excess acid. After each cycle the acidic supernatant was decanted, followed by the addition of a fresh portion of DI-water, redispersion, and another centrifuging cycle. Rinsing was performed until the pH value of supernatant reached 6. The obtained wet slurry containing MXene was subject to a delamination process in order to separate MXene Ti

_{3}C

_{2}flakes into a water-based colloidal solution.

^{+}ion between Ti

_{3}C

_{2}flakes following separation into the colloidal solution [21]. The solution for the intercalation-assisted delamination was prepared as follows: 2 g of lithium chloride (LiCl) was added to 40 mL of DI-water in a plastic container (volume 50 mL). Two gram of the etched MXene slurry was added to the prepared solution. The process was performed at 35 °C for 24 h under constant stirring. After intercalation in the LiCl solution, the MXene slurry was rinsed via repetitive cycles of centrifuging (10 min each cycle at 3500 rpm), decanting the supernatant, and redispersion in freshy added DI-water until the supernatant turns from transparent to black in color, signaling MXene flakes’ separation into colloidal solution. At this stage, the MXene supernatant after centrifuging is collected and stored. Rinsing is performed until the supernatant after centrifugation becomes transparent again. The collected supernatant containing MXene is centrifuged at 6000 rpm for 1 h to obtain concentrated MXene sediment.

#### 2.2. PCL Electrospun Membrane Synthesis

#### 2.3. MXene Deposition on PCL Membranes

## 3. Experimental

_{S}—static capacitance in series equivalent circuit, C

_{P}—static capacitance in parallel equivalent circuit, L

_{S}—inductance in series equivalent circuit, L

_{P}—inductance in parallel equivalent circuit, R

_{S}—effective resistance in series equivalent circuit, G—conductance, R

_{P}—effective resistance in parallel equivalent circuit, X—reactance, B—susceptance. The amplitude of the voltage applied to the test sample was U = 0.4 V. The impedance meter and the temperature controller are connected to a computer (11), where the measurement results are saved as xls files.

_{p}, and capacitance C

_{p}in the parallel equivalent scheme.

_{R}—real component of the current, R

_{P}—parallel circuit resistance, U—applied sinusoidal voltage.

_{P}—parallel circuit capacitance, L

_{P}—parallel circuit inductance.

_{I}is calculated:

_{I}—imaginary component of the current.

_{r}= 2πf

_{r}, a parallel resonance [25] occurs. From Formula (2) for susceptance, it follows that at the value of resonant circular frequency ω

_{r}, the modules of capacitive and inductive components of susceptance are equal and their difference is equal to zero.

_{r}—resonant circular frequency.

_{PM}—the capacitance value measured by the impedance meter.

_{P}—actual value of capacitance in the tested parallel circuit, L

_{P}—actual value of inductance in the tested parallel circuit.

_{r}, its value, theoretically, is zero. A further increase in the circular frequency will increase the measured capacitance. This means that there will be a clear minimum in the frequency dependence of the measured capacitance. It is one of the criteria that allows to observe the parallel resonance and determine the value of the resonant circular frequency ω

_{r}.

## 4. Results and Discussion

_{3}C

_{2}MXene. SEM demonstrates that MXene has a typical shape, with a size from 25 to 500 nm.

_{3}C

_{2}T

_{x}MXene samples. It seems that the samples exhibit good exfoliation. In some regions, MXenes are almost transparent to the electron beam because the thickness is close to several atomic distances [27]. Further analysis of SAED from the flakes revealed the Ti

_{3}C

_{2}hexagonal lattice of high crystallinity [28]. Titanium distribution in the crystal lattice ensures good electrical conductivity. Depending on the concentration and thickness (periodicity of layers), the MXenes crystal structure varies from single crystal to polycrystalline-like. Lattice parameters were increased in the tabular Ti

_{3}C

_{2}structure (hexagonal P63/mmc symmetry) a = 3.183 Å (a

_{tab}= 3.071 Å), c = 15.68 Å (c

_{tab}= 15.131 Å). Test samples were then exposed to air for two weeks to analyse the oxidation behaviour. As a result of the analysis, the crystallinity of the samples was dropped (Figure 5c). Some flakes exhibit the transition to titanium dioxide, but only local decomposition to oxygen compounds was observed. Moreover, under the thermal effect of the electron beam, the structure of the MXene layers was changed instantly. White areas changed to black, which meant that oxidation of the specimens was only partial and potentially reversible after the thermal annealing.

_{3}C

_{2}contains it. O, F, and Cl signals suggest that MXene exhibits a binding with the functional groups. No Al concentration was observed. Thus, it was completely removed during the precursor exfoliation.

^{−12}pF to about 4 × 10

^{−13}pF. Such low capacitance values occur due to the shape of the sample, together with the contacts applied to it (Figure 2). As can be seen from the figure, the area of the measured sample is equal to the cross-sectional area of the nanocomposite layer. The thickness of the dielectric is equal to the distance between the contacts. This results in the capacitance of the sample being very low. From the frequency dependence of the measured capacitances, shown in Figure 7, it can be seen that the MXene-PCL nanocomposite exhibits a series of minima against a background of a slow decrease of capacitance with frequency increase. Some of them are very clear. These are minima at frequencies of around 100 Hz, around 200 Hz, around 1100 Hz and around 2200 Hz. In the frequency range above 2200 Hz, further sharp minima are observed. However, determining the frequency values at which they are observed is relatively difficult due to their very close proximity. The only thing is that these minima practically disappear at room temperature. A broad clear maximum is observed in the frequency range from about 10

^{4}Hz to about 10

^{5}Hz. The position of the maximum, depending on the temperature, occurs at frequencies from about 1.3 × 10

^{4}Hz to about 3 × 10

^{4}Hz. In the frequency range above 10

^{5}Hz, oscillations of large amplitudes occur that completely interfere with the capacitance measurements. Oscillations of this type were not observed by us for other types of nanocomposites [30,31,32]. The oscillations are probably related to the unique structure of the MXene-PCL nanocomposites. Explanation of their causes requires additional research, far beyond the scope of this article. Accordingly, this paper focuses on the analysis of the behaviour of the minima observed in the frequency range up to 10

^{5}Hz. Therefore, in Figure 7, Figure 8 and Figure 9, the frequency range is limited to 10

^{5}Hz.

^{4}–10

^{5}) Hz, also decreases rapidly with increasing temperature and disappears at room temperature. This means that there are at least two types of tunneling between nanoparticles in the nanocomposite, which become apparent in the form of C

_{PM}minima. This is evidenced by the different way in which the depth of the minima changes under the influence of temperature. For the minima of the first group (at 100 Hz and 200 Hz), their depth practically does not depend on temperature. For the second group (1100 Hz and 2200 Hz and minima in the frequency region (10

^{4}–10

^{5}) Hz)), the depth of the minima decreases very rapidly with increasing temperature. At room temperature, the minima of the second group practically disappear. The two different types of tunneling can be related to the different morphologies and structures of the nanoparticles between which tunneling takes place.

_{PM}(f). Their positions exactly match the positions of the minima on the frequency dependence of the measured capacitances, shown in Figure 7. This means that the frequencies at which inductance maxima occur are the frequencies for which parallel resonance occur. The value of inductance measured at maxima for a circuit not containing resistance should be infinity—Formula (13). The presence of a resistance causes the value at maximum of the measured inductance to be lower. A second factor lowering the value at maximum is that the measurements were made with a step of 50 points per decade. As a result of the simultaneous interaction of these two factors, the inductance at the maximum does not reach infinity. The maximum at 2200 Hz is closest to the resonance frequency. Its amplitude is about two orders. Wide clear minima are observed on the L

_{PM}(f) relation at frequencies from about 1.3 × 10

^{4}Hz to about 3 × 10

^{4}Hz—depending on the temperature. The positions of the minima of the measured inductances (Figure 8) exactly coincide with the positions of the maxima on the frequency dependence of the measured capacitances (Figure 7). In the frequency range above 2200 Hz to about 10,000 Hz, further sharp maxima are observed.

^{3}Hz, the values of the phase shift angle are close to 0°. With further frequency increase practically up to about 10

^{4}Hz, the values of the phase shift angle are weakly negative. It follows that in this frequency region, the capacitive component of the conductivity is slightly larger than the inductive component. Beyond a frequency of 10

^{4}Hz, the values of the phase shift angle become positive. As can be seen from Figure 9, in the frequency region from about 10

^{4}Hz to about 10

^{5}Hz, an increase in positive phase angle values is observed and a maximum is reached, the value of which ranges from about 80° to about 85°, depending on the temperature. A further increase in frequency causes a decrease in the value of the phase shift angle—the values of which remain positive. This means that in this frequency range, the inductive component of the conductivity of the MXene-PCL nanocomposite is many times greater than the capacitive component. This phase shift angle behavior occurs in a range of nanocomposites containing conductive phase nanoparticles in dielectric matrices [35,36,37,38,39,40]—both capacitive and inductive components were observed in them.

_{0}—numerical factor.

_{0}—amplitude of the electric field strength.

_{1}is in the same phase as the forcing electric field and therefore contains only the real component.

_{2}and j

_{3}components are in an equal phase. Hence:

_{r}> 1. This means that, according to Maxwell’s second equation, there will be a component of capacitive current flowing through the material that is not related to electron tunneling. The density of this current component is described by the following formula [46]:

_{r}—relative dielectric permittivity, ε

_{0}—dielectric permittivity of vacuum.

_{r}, relaxation time τ and frequency ω. From Equation (28), it follows that in the low frequency region, where:

- (a)
- For low conductivity values in the low frequency range, the phase shift angle φ is approximately equal to 0° and a decrease of the phase shift angle value to about −90° with stabilization at this level is observed. This situation occurs, according to Equation (28), in the high frequency region when:$$\sigma <<{\epsilon}_{r}{\epsilon}_{0}\omega .$$

- (b)
- For average conductivity values, the phase shift angle φ waveforms show values close to zero in the low frequency region. An increase of frequency causes an increase of negative values until a minimum is reached. After crossing zero, positive values of the phase shift angle occur, passing through the maximum and then decreasing the phase shift angle. The zero crossing at frequency ω
_{r}corresponds to the phenomenon of parallel resonance. From Equations (22) and (28), it follows that φ = 0° occurs when:$$-\sigma \left(1-2p\right)\mathrm{sin}\left(\theta \right)={\epsilon}_{r}{\epsilon}_{0}{\omega}_{r}$$

- (c)
- For high values of conductivity, when σ >> ε
_{r}ε_{0}ω and medium values of frequency, positive values of the phase shift angle occur. When the maximum is reached, the value of which φ_{max}≈ 90°, a decrease in the phase shift angle value takes place. An indication graph for this case is shown in Figure 13.

_{1}and j

_{2}+ j

_{3}components at the resonance frequency is slightly more than −π. From the value of the frequency at the inductance maximum of about 8×10

^{4}Hz and using Formula (23), it is possible to determine the values of the relaxation times τ for the individual sharp maxima observed in Figure 8. For maximum at frequency f

_{1}≈ 100 Hz, τ

_{1}≈ 5×10

^{−3}s; for f

_{2}≈ 200 Hz, τ

_{2}≈ 2.5 × 10

^{−3}s; for f

_{3}≈ 1100 Hz τ

_{3}≈ 4.5 × 10

^{−4}s, and for f

_{4}≈ 2200 Hz, τ

_{4}≈ 2.3×10

^{−4}s.

^{4}Hz, there are close to zero values of the phase shift angle. This means that resistive conduction is dominant in this range. The series resonance observed in this range (Figure 7 and Figure 8) prove that apart from resistive conduction, capacitance and inductance are simultaneously present. If the nanocomposite layer had a resistive conductivity and only one of the imaginary components, inductive or capacitive, the resonance of the currents would not occur.

^{4}Hz to about 10

^{5}Hz, there is a broad maximum of the phase shift angle, values in which are 80° ≤ φ ≤ ~85° (Figure 9). The position of the maximum is at frequencies from about 1.3 × 10

^{4}Hz to about 3 × 10

^{4}Hz, depending on the temperature. This situation is described in (c)—Equation (28). The appearance of a wide maximum at frequencies from about 10

^{4}Hz to about 10

^{5}Hz means that this is associated with a case of dominant conduction of the inductive type—as shown in case (c). This shows that a third type of tunneling occurs in the MXene-PCL nanocomposite. From the value of the frequency at the maximum of the phase shift angle, the expected value of the relaxation time was determined. At 40 K, it is τ

_{M}≈ 8 × 10

^{−5}s. The occurrence of at least three types of tunneling in the MXene-PCL nanocomposite, with different relaxation times, is probably related to differences in the morphology and structure of the nanoparticles between which tunneling takes place and the distances over which electrons tunnel.

_{P}(4 × 10

^{4}Hz) ≈ 1 H. It is important to consider what causes the nanocomposite layer to have such a high inductance. For this, we use the formula for the inductance value of a conventional coil without a ferromagnetic core given in [25]:

_{0}—magnetic permittivity of vacuum, n—number of coils per unit length, v—volume of coil.

_{P}(4 × 10

^{4}Hz) ≈ 1 H, μ

_{0}and the values of geometrical dimensions of the nanocomposite sample from Figure 2, we obtain the “distance between neighbouring coil windings” of the nanocomposite, which is about ∆l ≈ 5.7 nm. As noted above, conduction in the nanocomposite occurs by electron tunneling between neighbouring nanoparticles. After each jump, the electron remains for a relaxation time τ in the nanoparticle on which it has tunneled and thus causes a phase shift between the real and imaginary components of the current density due to tunneling (see Equations (18)–(23)). There is some analogy here with an induction coil, where each coil affects the phase shift of the current. This may mean that the “distance between neighbouring coil windings” from the nanocomposite obtained from Equation (34) is, to a large approximation, the expected value of the distance over which the electron tunnels.

## 5. Conclusions

_{3}C

_{2}without intermetallic phases. Preliminary analyses show their relatively fast oxidation rate, so their deposition onto PCL scaffolds was conducted in an inert atmosphere (Ar). EDS chemical analysis of coated PCL membranes confirmed the absence of Al and revealed the uniform distribution of MXenes linked to termination groups.

^{4}Hz to about 10

^{5}Hz. The position of the maximum occurs at frequencies from about 1.3 × 10

^{4}Hz to about 3 × 10

^{4}Hz, depending on the temperature.

^{4}Hz to about 10

^{5}Hz, there is a wide minimum in the inductance dependence, the position of which exactly agrees with the position of the maximum of the phase shift angle. Based on the value in this minimum, the actual value of the inductance of the tested nanocomposite layer (about 1 H) was calculated. The expected value of the distance over which the electron tunnels (about 5.7 nm) was also determined with some approximation.

^{4}Hz, the values of the phase shift angle are close to zero. In the higher frequency region, there is a wide maximum of up to 85° on the φ(f) relationship. From the frequencies in the phase shift angle maximum, the expectation value of the relaxation time was determined. At 40 K, it is τ

_{M}≈ 8 × 10

^{−5}s.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Test stand for determining electrical parameters [23]: 1 and 2—HIOKI 3532 LCR HiTESTER impedance meters, 3—helium cryostat head, 4—vacuum pump, 5—compressor of helium cryostat, 6—vacuum gauge, 7—LakeShore 335 temperature controller, 8—silicon temperature sensor, 9—test contacts, 10—test samples, 11—computer.

**Figure 2.**Photo (

**a**) and view (

**b**) of the nanocomposite sample: 1—MX nanocomposite layer, 2—dielectric substrate, 3—silver paste contacts.

**Figure 3.**Phase diagram of the AC sinusoidal current’s real and imaginary components for a parallel RLC circuit in case of I

_{C}> I

_{L}: U—applied voltage vector, I

_{I}—real component of imaginary current, I

_{C}—capacitive component of imaginary current, I

_{L}—inductive component of imaginary current, I—resultant current, φ—phase shift angle, I

_{U}= I

_{C}−I

_{L}—parallel circuit current, R

_{P}—resistance, C

_{P}—capacitance, L

_{P}—inductance.

**Figure 5.**TEM images of the structure of Ti

_{3}C

_{2}MXenes obtained by the method of dripping onto a substrate and their electron diffraction patterns: high-concentration drips (

**a**), low concentration flakes (

**b**), oxidation test (

**c**).

**Figure 6.**EDS spectrum of the MXene-PCL nanocomposite with element Wt.% distribution (insertion (

**A**)). Insertion (

**B**)—optical (1) and (2) and SEM images (3) and (4) of PCL-MXene composite scaffolds after first and second coating iteration, respectively.

**Figure 7.**Frequency dependence of capacitance C

_{PM}of the MXene-PCL nanocomposite for six selected temperatures measured in a parallel scheme.

**Figure 8.**Frequency dependence of inductance L

_{PM}of the MXene-PCL nanocomposite for six selected temperatures measured in a parallel substitution scheme.

**Figure 9.**Frequency dependence of phase shift angle φ of the MXene-PCL nanocomposite for six selected temperatures measured in a parallel substitution scheme.

**Figure 10.**Potential wells and possible directions of electron tunneling: E—electric field, j

_{1}—current of density, j

_{2}—second component of the current density, j

_{3}—third component of current density.

**Figure 11.**Indication diagram of current density for the case of dominant capacitive type conduction: j

_{1}—current density determined by Formula (17), j

_{2}+ j

_{3}—current density determined by Formula (20), θ = –ωτ—angle between the vectors j

_{1}and (j

_{2}+ j

_{3}), φ—phase shift angle determined by Formula (28).

**Figure 12.**Indication diagram of current density for the case of parallel resonance: j

_{1}—current density determined by Formula (17), j

_{2}+ j

_{3}—current density determined by Formula (20), θ = –ωτ—angle between the vectors j

_{1}and (j

_{2}+ j

_{3}), φ = 0°—phase shift angle determined by Formula (32).

**Figure 13.**Indication diagram of current density for the case of dominant inductive type conduction: j

_{1}—current density determined by Formula (17), j

_{2}+ j

_{3}—current density determined by Formula (20), θ = –ωτ—angle between the vectors j

_{1}and (j

_{2}+ j

_{3}), φ—phase shift angle determined by Formula (32).

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## Share and Cite

**MDPI and ACS Style**

Kołtunowicz, T.N.; Gałaszkiewicz, P.; Kierczyński, K.; Rogalski, P.; Okal, P.; Pogrebnjak, A.D.; Buranich, V.; Pogorielov, M.; Diedkova, K.; Zahorodna, V.;
et al. Investigation of AC Electrical Properties of MXene-PCL Nanocomposites for Application in Small and Medium Power Generation. *Energies* **2021**, *14*, 7123.
https://doi.org/10.3390/en14217123

**AMA Style**

Kołtunowicz TN, Gałaszkiewicz P, Kierczyński K, Rogalski P, Okal P, Pogrebnjak AD, Buranich V, Pogorielov M, Diedkova K, Zahorodna V,
et al. Investigation of AC Electrical Properties of MXene-PCL Nanocomposites for Application in Small and Medium Power Generation. *Energies*. 2021; 14(21):7123.
https://doi.org/10.3390/en14217123

**Chicago/Turabian Style**

Kołtunowicz, Tomasz N., Piotr Gałaszkiewicz, Konrad Kierczyński, Przemysław Rogalski, Paweł Okal, Alexander D. Pogrebnjak, Vladimir Buranich, Maksym Pogorielov, Kateryna Diedkova, Veronika Zahorodna,
and et al. 2021. "Investigation of AC Electrical Properties of MXene-PCL Nanocomposites for Application in Small and Medium Power Generation" *Energies* 14, no. 21: 7123.
https://doi.org/10.3390/en14217123