High-altitude discharges in the Earth's atmosphere are studied by many scientific groups (see [14–19]). In recent years, the improvement of instruments for detecting various types of radiation, as well as means for capturing images from the International Space Station (ISS), have contributed to obtaining new results [19,20]. Recently, a large number of color photographs of high-altitude transient luminous events (TLEs; red sprites, elves, ghosts, blue jets, and their analogues (starters, giant jets) are referred to as TLEs) have appeared [14–21]. Figure 1 demonstrates a collage of images of TLEs,

One issue requiring more research is the determination of the color source for each of these phenomena. It is believed that the color of red sprites that initiate at altitudes of about 70 km and are visible at altitudes of 40 to 90 km is determined by the radiation of the first positive 1P system of a nitrogen N2 molecule [15,17,18]. This fact is also confirmed by spectral studies of sprite emission [22]. The color of blue jets, which originate from the

*Nanomaterials* **2022**, *12*, x FOR PEER REVIEW 2 of 12

composed from photographs obtained using various sources [21].

**Figure 1.** Different types of electrical phenomena in the atmosphere (TLE) [21]. Reproduced from https://en.wikipedia.org; Author: Abestrobi; accessed on 14 February 2022. The image is licensed under the Creative Commons Attribution-Share Alike 3.0 (CC BY-SA 3.0) Unported license). **Figure 1.** Different types of electrical phenomena in the atmosphere (TLE) [21]. Reproduced from https://en.wikipedia.org; Author: Abestrobi; accessed on 14 February 2022. The image is licensed under the Creative Commons Attribution-Share Alike 3.0 (CC BY-SA 3.0) Unported license).

In laboratory experiments, with decreasing air pressure, the color of the plasma of pulsed discharges usually changes from blue to pink, while the color of the sprites observed in natural conditions is bright red, and that of jets is blue [14–21,23]. However, both sprites and jets (or their parts) can be observed at the same altitude (see [16]). Consequently, lines and bands of radiation of a different nature can determine the color of observed TLEs. On the other hand, it was shown in [24,25] that in diffuse and spark discharges in air, mini-jets are observed near electrodes made of aluminum, stainless steel, and copper, the colors of which are red, blue, and green, respectively. One issue requiring more research is the determination of the color source for each of these phenomena. It is believed that the color of red sprites that initiate at altitudes of about 70 km and are visible at altitudes of 40 to 90 km is determined by the radiation of the first positive 1P system of a nitrogen N2 molecule [15,17,18]. This fact is also confirmed by spectral studies of sprite emission [22]. The color of blue jets, which originate from the tops of clouds at about 18 km and reach an altitude of 50 km or more, according to [15,17,19,23], is associated with the radiation of the second positive 2P system of a nitrogen molecule N2 and the first negative 1N system of a nitrogen N2 + ion. There is no information in the available sources about the nature of the green color of phenomena such as ghosts. However, the color of TLEs of the same type, described in different sources, may differ significantly. Thus, the elve in Figure 1 has a red color [21], while on the video taken from the ISS, it is blue-pink [20].

In laboratory experiments, with decreasing air pressure, the color of the plasma of pulsed discharges usually changes from blue to pink, while the color of the sprites observed in natural conditions is bright red, and that of jets is blue [14–21,23]. However, both sprites and jets (or their parts) can be observed at the same altitude (see [16]). Consequently, lines and bands of radiation of a different nature can determine the color of observed TLEs. On the other hand, it was shown in [24,25] that in diffuse and spark discharges in air, mini-jets are observed near electrodes made of aluminum, stainless steel, and copper, the colors of which are red, blue, and green, respectively.

insulator.

width varied from 1 to 12 mm.

The aim of this work is to study the optical properties of plasma of diffuse and spark discharges in an inhomogeneous electric field at different pressures of air, argon, nitrogen, and hydrogen with the injection of electrode material into the discharge region due to the explosion of microprotrusions on the electrode surface and/or transition to a spark. The color of mini-jets observed in such discharges is compared with that of high-altitude atmospheric discharges (blue jets, red sprites, and ghosts). color of mini-jets observed in such discharges is compared with that of high-altitude atmospheric discharges (blue jets, red sprites, and ghosts). **2. Experimental Setup and Methods**  The study of the discharge modes and optical characteristics of the formed plasma

The aim of this work is to study the optical properties of plasma of diffuse and spark

discharges in an inhomogeneous electric field at different pressures of air, argon, nitrogen,

explosion of microprotrusions on the electrode surface and/or transition to a spark. The

#### **2. Experimental Setup and Methods** was carried out using electrodes of various shapes, made of different materials. A coneshaped cathode and a plane anode ("point-plane" gap geometry) were used in most

*Nanomaterials* **2022**, *12*, x FOR PEER REVIEW 3 of 12

The study of the discharge modes and optical characteristics of the formed plasma was carried out using electrodes of various shapes, made of different materials. A cone-shaped cathode and a plane anode ("point-plane" gap geometry) were used in most experiments. This gap geometry provides the formation of diffuse discharges in various gases at a relatively low amplitude of voltage pulse due to the strongly non-uniform electric field strength distributions and the generation of runaway electrons [26,27]. It is known that high-altitude discharges are also accompanied by the generation of runaway electrons and other high-energy particles [23]. experiments. This gap geometry provides the formation of diffuse discharges in various gases at a relatively low amplitude of voltage pulse due to the strongly non-uniform electric field strength distributions and the generation of runaway electrons [26,27]. It is known that high-altitude discharges are also accompanied by the generation of runaway electrons and other high-energy particles [23]. A sketch of an experimental setup, consisting of a voltage-pulsed generator (NPG-

A sketch of an experimental setup, consisting of a voltage-pulsed generator (NPG-15/2000N or NPG-18/3500N, generators differ in the ranges of adjustment of the amplitude and repetition rate of voltage pulses), a 3 m long coaxial cable with a wave impedance of 75 Ω, and a discharge chamber, is presented in Figure 2. 15/2000N or NPG-18/3500N, generators differ in the ranges of adjustment of the amplitude and repetition rate of voltage pulses), a 3 m long coaxial cable with a wave impedance of 75 Ω, and a discharge chamber, is presented in Figure 2.

**Figure 2.** Sketch of the experimental setup. 1—plane anode, 2—cone-shaped cathode, 3—capacitive voltage divider, 4—collector, which was used to measure the runaway electron beam current, 5 discharge chamber with quartz side windows for capturing the discharge plasma glow, 6— **Figure 2.** Sketch of the experimental setup. 1—plane anode, 2—cone-shaped cathode, 3—capacitive voltage divider, 4—collector, which was used to measure the runaway electron beam current, 5—discharge chamber with quartz side windows for capturing the discharge plasma glow, 6—insulator.

The NPG generators form voltage pulses *U*g with amplitudes ranging from 12 to 18 kV (the voltage across the discharge gap doubled due to its reflection from a "cold" gap) with a full width at half maximum (FWHM) and a rise time of ≈6 and ≈3 ns, respectively. The studies were carried out at a pulse repetition rate *f* from 60 to 1000 Hz. Some The NPG generators form voltage pulses *U*g with amplitudes ranging from 12 to 18 kV (the voltage across the discharge gap doubled due to its reflection from a "cold" gap) with a full width at half maximum (FWHM) and a rise time of ≈6 and ≈3 ns, respectively. The studies were carried out at a pulse repetition rate *f* from 60 to 1000 Hz. Some experiments were performed in single-pulse mode. In addition, a RADAN-220 generator with a voltage pulse amplitude in an incident wave *U*g of 120 kV and a duration at a matched load of 2 ns was used.

experiments were performed in single-pulse mode. In addition, a RADAN-220 generator with a voltage pulse amplitude in an incident wave *U*g of 120 kV and a duration at a matched load of 2 ns was used. Aluminum, copper, stainless steel, and tungsten were used as electrode materials. The high-voltage, cone-shaped electrode (2 in Figure 2) was made of D14 aluminum, copper, or stainless steel. It had an apex angle of 40 degrees. However, the radius of its tip rounding varied from 70 to 380 μm in the experiments. In several experiments, the cone-Aluminum, copper, stainless steel, and tungsten were used as electrode materials. The high-voltage, cone-shaped electrode (2 in Figure 2) was made of D14 aluminum, copper, or stainless steel. It had an apex angle of 40 degrees. However, the radius of its tip rounding varied from 70 to 380 µm in the experiments. In several experiments, the cone-shaped electrode was replaced by a bundle of 0.2-mm-diameter tungsten wires with sharp ends. The plane electrode (1 in Figure 2) was made of aluminum, stainless steel, or copper. A gas (air, nitrogen, argon, and hydrogen) pressure varied from 0.1 to 760 Torr. The gap width varied from 1 to 12 mm.

shaped electrode was replaced by a bundle of 0.2-mm-diameter tungsten wires with sharp ends. The plane electrode (1 in Figure 2) was made of aluminum, stainless steel, or copper. To increase the concentration of the sputtered and evaporated electrode material, as well as the intensity of the discharge plasma radiation, the experiments were carried out under the ignition of the discharge in a repetitively pulsed mode at a voltage of tens of

A gas (air, nitrogen, argon, and hydrogen) pressure varied from 0.1 to 760 Torr. The gap

well as the intensity of the discharge plasma radiation, the experiments were carried out under the ignition of the discharge in a repetitively pulsed mode at a voltage of tens of

kilovolts. In some experiments, the gas pressure corresponded to that of air at altitudes where blue jets and red sprites are observed.

The use of an electrode with a small radius of curvature as a high-voltage cathode made it possible to determine the conditions under which the generation of runaway electrons takes place. When registering the runaway electron beam current, a plane anode made of a thin aluminum foil or a grid with a light transmission of 67% was used. The results of studies of the properties of a beam of runaway electrons generated in a repetitively pulsed discharge ignition mode on a similar experimental setup are described in detail in [26].

The discharge glow images were photographed with a Sony A100 digital camera (Kuala Lumpur, Malaysia). The colors of red sprites, blue jets, and other TLEs in the images given in [17–19,23] and [20,21] were compared with the color of the repetitively pulsed discharge plasma.

Emission spectra from the different discharge zones were recorded with an EPP-2000C spectrometer (StellarNet Inc. (Tampa, Fl, USA), λ = 192–854.5 nm). Waveforms of the voltage from a capacitive voltage divider and electron beam current from a collector were recorded with a Tektronix MDO 3104 oscilloscope (1 GHz, sampling rate 5 GS/s).

#### **3. Results**

#### *3.1. Pulse Breakdown Conditions for Laboratory and Atmospheric Discharges*

It is well known that the gap width, the shape and material of the electrodes, the amplitude and rise time of the voltage pulse, the gas pressure and gas type, as well as the method of the gas pre-ionization, determine the breakdown characteristics. When studying laboratory discharges, experimental conditions are relatively easy to control, including measuring the current of runaway electrons [25,26]. In addition, the amplitude and duration of a voltage pulse, the current density, and the energy stored in a high-voltage generator can be varied over a wide range.

The situation with discharges in the upper layers of the Earth's atmosphere is much more complicated. In the case of TLEs, it is necessary to determine not only the altitude of their formation and air composition in this region, but also the electrical properties of the atmosphere (electric field strength, discharge current density, and pulse duration). However, high-altitude atmospheric discharges are transient and electrical parameters are very difficult to measure. The initiation of TLEs depends on the air temperature, as well as the height of the clouds, their density, and the distribution of charges in them. In addition, the formation of these discharges is associated with the appearance of lightning in the lower layers of the Earth's atmosphere. High-energy particles from space, from the Sun, and generated in strong electric fields, are important for charge accumulation and discharge initiation. VUV/UV radiation from the Sun plays an important role in the ionization of the Earth's atmosphere. All these factors can affect the type of discharge and its color. In this paper, the main focus is on the study of the influence of metal vapors and particles appearing in the gap on the coloration of various discharge regions. Data on the appearance of micro- and nanoparticles in the gap, as well as metal vapors, that affect the color of the discharge plasma, are given below.

#### *3.2. Formation of Micro- and Nanoparticles during Spark and Diffuse Discharges*

It should be noted that the formation of particles and electrode material evaporation have previously been studied in detail for vacuum discharges (see, for example, [28–30]). The presence of particles in those experiments was observed under various discharge modes. Double diffuse jets (streamers) from the ends of particle tracks were detected for the first time. Below are photographs showing the appearance of particles in the discharge. The cone-shaped, high-voltage electrode used in most of the experiments is placed at the bottom of the images. In the case of electrodes that are poorly distinguishable against the background of the glow of the discharge plasma, their outlines are shown by white lines.

First, the appearance of particles in a spark discharge is demonstrated. The photographs in Figure 3 show the spark discharge glow, the cone-shaped electrode with a small radius of the tip rounding, luminous tracks of particles, and diffuse jets at the ends of the tracks. First, the appearance of particles in a spark discharge is demonstrated. The photographs in Figure 3 show the spark discharge glow, the cone-shaped electrode with a small radius of the tip rounding, luminous tracks of particles, and diffuse jets at the ends of the tracks.

against the background of the glow of the discharge plasma, their outlines are shown by

*Nanomaterials* **2022**, *12*, x FOR PEER REVIEW 5 of 12

white lines.

**Figure 3.** Integral images of the discharge in air at a pressure of 760 Torr with stainless steel electrodes. Single-pulse mode. NPG-18/3500N voltage pulse generator. The voltage pulse amplitude is 18 kV. The height of photograph (**a**) is 2 mm. The plane electrode is at the top and the cone-shaped electrode is at the bottom (outlines of the cone-shaped electrode in (**a**,**b**) are marked with white lines). The gap length is *d* = 1 mm. Zoomed images of the bottom 1 (**b**) and left 2 (**c**) tracks, which end with diffuse jets 3 and 4, are also shown. **Figure 3.** Integral images of the discharge in air at a pressure of 760 Torr with stainless steel electrodes. Single-pulse mode. NPG-18/3500N voltage pulse generator. The voltage pulse amplitude is 18 kV. The height of photograph (**a**) is 2 mm. The plane electrode is at the top and the cone-shaped electrode is at the bottom (outlines of the cone-shaped electrode in (**a**,**b**) are marked with white lines). The gap length is *d* = 1 mm. Zoomed images of the bottom 1 (**b**) and left 2 (**c**) tracks, which end with diffuse jets 3 and 4, are also shown.

The photograph was captured in the single-pulse mode of the spark discharge in the 1 mm long gap filled with atmospheric-pressure air. A short gap was used to increase the current density during the spark stage of the discharge. The spark phase of discharge combustion provides the greatest contribution to the intensity of radiation from the discharge gap. Figure 3a demonstrates a bright spot (the glow from the spark channel), which touches the tip of the cone-shaped electrode with its bottom part and adjoins the flat electrode with its top part. However, even with intense radiation from the spark channel, the tracks of two microparticles are visible. They were emitted from the point of contact between the spark and the cone-shaped electrode. Under these conditions, the brightness of the tracks increases with distance from the electrode. The particle trajectories are different: one of them (2) abruptly changes the direction of its motion. The photograph was captured in the single-pulse mode of the spark discharge in the 1 mm long gap filled with atmospheric-pressure air. A short gap was used to increase the current density during the spark stage of the discharge. The spark phase of discharge combustion provides the greatest contribution to the intensity of radiation from the discharge gap. Figure 3a demonstrates a bright spot (the glow from the spark channel), which touches the tip of the cone-shaped electrode with its bottom part and adjoins the flat electrode with its top part. However, even with intense radiation from the spark channel, the tracks of two microparticles are visible. They were emitted from the point of contact between the spark and the cone-shaped electrode. Under these conditions, the brightness of the tracks increases with distance from the electrode. The particle trajectories are different: one of them (2) abruptly changes the direction of its motion.

Figure 3b,c shows zoomed images of the particles' tracks, which, as already noted, can change direction and end in jets. The smooth change in the direction of movement of the microparticles can be explained by the influence of an electric field in this direction. The nature of the glow of the particles in Figure 3 corresponds to the glow of a micrometeorite that burns down in the Earth's atmosphere [13]. The brightness of the micrometeorite (the particle) glow increases towards the track's end. This cannot be explained by an increase in the particle velocity, since the particle stops. This occurs after the voltage pulse action. We believe that the increase in the radiation intensity of the particle is due to its heating during deceleration on gas particles. Figure 3b,c shows zoomed images of the particles' tracks, which, as already noted, can change direction and end in jets. The smooth change in the direction of movement of the microparticles can be explained by the influence of an electric field in this direction. The nature of the glow of the particles in Figure 3 corresponds to the glow of a micrometeorite that burns down in the Earth's atmosphere [13]. The brightness of the micrometeorite (the particle) glow increases towards the track's end. This cannot be explained by an increase in the particle velocity, since the particle stops. This occurs after the voltage pulse action. We believe that the increase in the radiation intensity of the particle is due to its heating during deceleration on gas particles.

Let us note an important feature in the formation of tracks, shown in Figure 3. At the ends of the tracks, jets (streamers) are visible. Usually, they are oriented in opposite directions. The appearance of these diffuse jets at the ends of the tracks is due to the formation of streamers from the plasma surrounding the particle surface. As is known, streamers are formed when the threshold plasma concentration for the electric field at a given point is reached. The formation of streamers is confirmed by the formation of two rectilinearly propagating jets from the same region (3), as well as an abrupt change in the Let us note an important feature in the formation of tracks, shown in Figure 3. At the ends of the tracks, jets (streamers) are visible. Usually, they are oriented in opposite directions. The appearance of these diffuse jets at the ends of the tracks is due to the formation of streamers from the plasma surrounding the particle surface. As is known, streamers are formed when the threshold plasma concentration for the electric field at a given point is reached. The formation of streamers is confirmed by the formation of two rectilinearly propagating jets from the same region (3), as well as an abrupt change in the direction of propagation of the upper jet (4) (see Figure 3c). Streamers appear to carry away a significant part of the charge, which leads to a deceleration of the microparticle. In this

case, the discharge was formed at the relatively high air pressure (760 Torr) and the small interelectrode distance, which made it possible to observe tracks of individual particles. The observation of microparticle tracks is facilitated in the case of the ignition of a spark discharge with the high current density on the electrodes. In this case, the discharge was formed at the relatively high air pressure (760 Torr) and the small interelectrode distance, which made it possible to observe tracks of individual particles. The observation of microparticle tracks is facilitated in the case of the ignition of a spark discharge with the high current density on the electrodes.

direction of propagation of the upper jet (4) (see Figure 3c). Streamers appear to carry away a significant part of the charge, which leads to a deceleration of the microparticle.

*Nanomaterials* **2022**, *12*, x FOR PEER REVIEW 6 of 12

With decreasing gas pressure and increasing interelectrode distance, the current density decreased; sparks do not have time to form at short voltage pulse durations. Accordingly, particles forming tracks (as in Figure 3) were practically not formed, and, therefore, were not registered. The investigations showed that at a pressure of 30 Torr or less, it is easier to register particle tracks if an electrode with a small radius of curvature made of a heavy metal, such as tungsten, is used. It was found that each of the gases has its optimal pressure for observing the tracks. An image of several tracks from the high-voltage anode made of pointed tungsten wires 0.2 mm in diameter, tied into a bundle, is shown in Figure 4. With decreasing gas pressure and increasing interelectrode distance, the current density decreased; sparks do not have time to form at short voltage pulse durations. Accordingly, particles forming tracks (as in Figure 3) were practically not formed, and, therefore, were not registered. The investigations showed that at a pressure of 30 Torr or less, it is easier to register particle tracks if an electrode with a small radius of curvature made of a heavy metal, such as tungsten, is used. It was found that each of the gases has its optimal pressure for observing the tracks. An image of several tracks from the highvoltage anode made of pointed tungsten wires 0.2 mm in diameter, tied into a bundle, is shown in Figure 4.

**Figure 4.** (**a**) Image of a discharge in hydrogen at ta pressure of 30 Torr with a tungsten wire anode (bottom) and a plane cathode made of aluminum (top), obtained during one voltage pulse (*U*g~120 kV, FWHM at matched load is 2 ns, rise time is 0.5 ns) from the RADAN-220 generator). C—cathode, A—anode. *d* = 5 mm. (**b**) Photograph of a part of the surface of a caprolon plate located at the sidewall of the discharge chamber opposite the discharge gap. Air pressure is 100 Torr, *d* = 2 mm. 1—nanoparticles with a transverse size of ~500 nm or less. 2—clusters of nanoparticles. NPG-15/2000N voltage pulse generator. *U*g = 13 kV, *f* = 60 Hz. The cone-shaped electrode is made of copper, and the plane electrode is made of stainless steel. **Figure 4.** (**a**) Image of a discharge in hydrogen at ta pressure of 30 Torr with a tungsten wire anode (bottom) and a plane cathode made of aluminum (top), obtained during one voltage pulse (*U*g~120 kV, FWHM at matched load is 2 ns, rise time is 0.5 ns) from the RADAN-220 generator). C—cathode, A—anode. *d* = 5 mm. (**b**) Photograph of a part of the surface of a caprolon plate located at the sidewall of the discharge chamber opposite the discharge gap. Air pressure is 100 Torr, *d* = 2 mm. 1—nanoparticles with a transverse size of ~500 nm or less. 2—clusters of nanoparticles. NPG-15/2000N voltage pulse generator. *U*g = 13 kV, *f* = 60 Hz. The cone-shaped electrode is made of copper, and the plane electrode is made of stainless steel.

The image shows several tracks (see 1 and 2 in Figure 4a) formed by moving microparticles, starting from bright spots on the tungsten anode. Bright spots are also visible on the plane aluminum cathode, but there are no tracks under these conditions. This experiment shows that particles can appear even in the absence of a spark channel. The formation of bright spots on the electrode is sufficient for their initiation. Moreover, the electrode made of heavy metal turned out to be the most suitable for obtaining tracks with a large gap length. At pressures of different gases from ones to tens of Torr and with the tungsten electrode with a small radius of curvature, the intensity of the track glow decreased with distance from the electrode. In addition, in contrast to the conditions in Figure 3, they had a direct trajectory. The length of the tracks depended on the pressure and decreased with increasing pressure. At low pressures (less than 1 Torr), bright spots on were not formed the electrodes and no tracks were observed. The appearance of the tracks was affected by both the pressure and the type of gas. During a discharge in argon with the RADAN-220 generator, bright spots were formed on the tungsten electrode in a narrow pressure range compared to hydrogen; accordingly, this narrowed the range of The image shows several tracks (see 1 and 2 in Figure 4a) formed by moving microparticles, starting from bright spots on the tungsten anode. Bright spots are also visible on the plane aluminum cathode, but there are no tracks under these conditions. This experiment shows that particles can appear even in the absence of a spark channel. The formation of bright spots on the electrode is sufficient for their initiation. Moreover, the electrode made of heavy metal turned out to be the most suitable for obtaining tracks with a large gap length. At pressures of different gases from ones to tens of Torr and with the tungsten electrode with a small radius of curvature, the intensity of the track glow decreased with distance from the electrode. In addition, in contrast to the conditions in Figure 3, they had a direct trajectory. The length of the tracks depended on the pressure and decreased with increasing pressure. At low pressures (less than 1 Torr), bright spots on were not formed the electrodes and no tracks were observed. The appearance of the tracks was affected by both the pressure and the type of gas. During a discharge in argon with the RADAN-220 generator, bright spots were formed on the tungsten electrode in a narrow pressure range compared to hydrogen; accordingly, this narrowed the range of conditions under which particle tracks were observed. The results shown in Figures 3 and 4 show that pulsed discharges produce particles that, under certain conditions, can be observed from the tracks

they leave behind. The particles appear due to the rapid heating of the electrodes at local points by the flowing discharge current. observed from the tracks they leave behind. The particles appear due to the rapid heating of the electrodes at local points by the flowing discharge current. Figure 4b shows a photograph in which the particles formed in the discharge can be

conditions under which particle tracks were observed. The results shown in Figures 3 and 4 show that pulsed discharges produce particles that, under certain conditions, can be

Figure 4b shows a photograph in which the particles formed in the discharge can be seen. They were scraped off the side surface of the discharge chamber and placed on a microscope slide. Metal particles and their compounds with oxygen and nitrogen with a size of ~500 nm and less are non-uniformly distributed over the surface of the slide. In some regions, clusters of particles are visible (see region 2 in Figure 4b). The size of the particles depended on the discharge mode, the type of gas and its pressure, and the electrode material. seen. They were scraped off the side surface of the discharge chamber and placed on a microscope slide. Metal particles and their compounds with oxygen and nitrogen with a size of ~500 nm and less are non-uniformly distributed over the surface of the slide. In some regions, clusters of particles are visible (see region 2 in Figure 4b). The size of the particles depended on the discharge mode, the type of gas and its pressure, and the electrode material.

In addition to the formation of particles, spark discharges, and the appearance of bright spots on the electrodes, the evaporation and sputtering of the electrode material occurs. Moreover, when operating in a repetitively pulsed mode, the concentration of metal atoms increases [25]. Below are the results showing the effect of vapors of the electrode material on the discharge color, including at low pressures. In addition to the formation of particles, spark discharges, and the appearance of bright spots on the electrodes, the evaporation and sputtering of the electrode material occurs. Moreover, when operating in a repetitively pulsed mode, the concentration of metal atoms increases [25]. Below are the results showing the effect of vapors of the electrode material on the discharge color, including at low pressures.

#### *3.3. Effect of Electrode Material on the Color of Pulsed Diffuse Discharges 3.3. Effect of Electrode Material on the Color of Pulsed Diffuse Discharges*

*Nanomaterials* **2022**, *12*, x FOR PEER REVIEW 7 of 12

As is known, the color of a discharge plasma depends on the type of discharge and its operation mode, as well as on the composition of a gas mixture and pressure. In turn, the discharge formation process is determined by the amplitude and duration of a voltage pulse, the current density, the shape of the electrodes, and the interelectrode distance. In the pulse-periodic mode, the intensity of the discharge plasma glow increased. Under these conditions, this made it easier to photograph the discharges at low power consumption. Figure 5 shows photographs of air plasma glow during the discharge between two aluminum electrodes at different air pressures. As is known, the color of a discharge plasma depends on the type of discharge and its operation mode, as well as on the composition of a gas mixture and pressure. In turn, the discharge formation process is determined by the amplitude and duration of a voltage pulse, the current density, the shape of the electrodes, and the interelectrode distance. In the pulse-periodic mode, the intensity of the discharge plasma glow increased. Under these conditions, this made it easier to photograph the discharges at low power consumption. Figure 5 shows photographs of air plasma glow during the discharge between two aluminum electrodes at different air pressures.

**Figure 5.** Photographs of the discharge in air at pressures of 1.5 (**a**), 3 (**b**), 10 (**c**), and 30 Torr (**d**) between two aluminum electrodes, obtained at *U*g = 12 kV and *f* = 77 Hz. The plane electrode is located at the top and the cone-shaped electrode is located at the bottom. C—cathode, A—anode. *d* = 2 mm. Cathode (**a**,**b**) and anode (**a**–**d**) surfaces are marked with white lines. NPG-15/2000N voltage pulse generator. **Figure 5.** Photographs of the discharge in air at pressures of 1.5 (**a**), 3 (**b**), 10 (**c**), and 30 Torr (**d**) between two aluminum electrodes, obtained at *U*g = 12 kV and *f* = 77 Hz. The plane electrode is located at the top and the cone-shaped electrode is located at the bottom. C—cathode, A—anode. *d* = 2 mm. Cathode (**a**,**b**) and anode (**a**–**d**) surfaces are marked with white lines. NPG-15/2000N voltage pulse generator.

The discharge has a diffuse form at pressures of fractions of Torr and covers the entire volume of the discharge chamber, and its plasma glow has low-intensity radiation (Figure 5a,b). Its color is far from the bright red of the sprites and elves shown in Figure 1. However, it is closer to the color of the elves on the video from the ISS [15]. Due to the low density of the discharge current under these conditions, bright spots were not observed The discharge has a diffuse form at pressures of fractions of Torr and covers the entire volume of the discharge chamber, and its plasma glow has low-intensity radiation (Figure 5a,b). Its color is far from the bright red of the sprites and elves shown in Figure 1. However, it is closer to the color of the elves on the video from the ISS [15]. Due to the low density of the discharge current under these conditions, bright spots were not observed on the electrodes. Accordingly, the density of the metal vapors from the electrodes at air pressures of 1.5 and 3 Torr was low.

The color of the discharge in the gap became reddish when the gas pressure increased to 10 and 30 Torr, but it also did not correspond to the typical color of sprites (see Figure 1). So, as shown in Figure 5b,c, red spherical jets appeared near the bright spots on the electrodes. The color of these jets matches the color of the sprites. The differences in the color of the discharge plasma in the gap filled with air and near the bright spot on the cone-shaped aluminum electrode is also clearly seen in Figure 6a. The color of the discharge in the gap became reddish when the gas pressure increased to 10 and 30 Torr, but it also did not correspond to the typical color of sprites (see Figure 1). So, as shown in Figure 5b,c, red spherical jets appeared near the bright spots on the electrodes. The color of these jets matches the color of the sprites. The differences in the color of the discharge plasma in the gap filled with air and near the bright spot on the cone-shaped aluminum electrode is also clearly seen in Figure 6a.

on the electrodes. Accordingly, the density of the metal vapors from the electrodes at air

*Nanomaterials* **2022**, *12*, x FOR PEER REVIEW 8 of 12

pressures of 1.5 and 3 Torr was low.

**Figure 6.** Images of the discharge in air at a pressure of 30 Torr (**a**) and in argon at pressures of 30 (**b**), 60 (**c**) and 10 Torr (**d**), obtained at *U*g = 12 kV. *f* = 620 (**a**–**c**), and 77 Hz (**d**). In all photographs, the plane electrode made of aluminum (**a**,**d**) or stainless steel (**b**,**c**) is at the top, and the cone-shaped electrode made of aluminum is at the bottom. C—cathode, A—anode. *d* = 3 (**a**–**c**) and 2 mm (**d**). NPG-18/3500N voltage pulse generator. **Figure 6.** Images of the discharge in air at a pressure of 30 Torr (**a**) and in argon at pressures of 30 (**b**), 60 (**c**) and 10 Torr (**d**), obtained at *U*g = 12 kV. *f* = 620 (**a**–**c**), and 77 Hz (**d**). In all photographs, the plane electrode made of aluminum (**a**,**d**) or stainless steel (**b**,**c**) is at the top, and the cone-shaped electrode made of aluminum is at the bottom. C—cathode, A—anode. *d* = 3 (**a**–**c**) and 2 mm (**d**). NPG-18/3500N voltage pulse generator.

For the discharge in air with the cone-shaped aluminum electrode (Figure 6a), as in Figure 5c,d, the discharge color at the bright spot on the electrode changed and a red spherical jet appeared. When the gap width was decreased and the chamber was filled with argon, a bright spot also appeared on the plane electrode (Figure 6d). The color of the spherical jet near it was red, as was that near the cone-shaped electrode. Filling the discharge chamber with argon eliminates the influence of N2 (1P) radiation on the discharge color. For the discharge in air with the cone-shaped aluminum electrode (Figure 6a), as in Figure 5c,d, the discharge color at the bright spot on the electrode changed and a red spherical jet appeared. When the gap width was decreased and the chamber was filled with argon, a bright spot also appeared on the plane electrode (Figure 6d). The color of the spherical jet near it was red, as was that near the cone-shaped electrode. Filling the discharge chamber with argon eliminates the influence of N2 (1P) radiation on the discharge color.

Experiments were also carried out with electrodes made of different metals. Photographs of the discharge plasma glow in the gap formed by a plane stainless steel anode and a cone-shaped aluminum anode are shown in Figure 6b,c. The use of aluminum electrodes changed the color of the discharge in argon, air, and nitrogen near the electrodes to red. On the surface of the cone-shaped electrode, bright spots surrounded by red halo can be seen. The number of bright spots depends on the discharge current density and gas pressure, as well as on the shape and polarity of the electrodes. As the interelectrode distance increases, the number of bright spots on the plane electrode usually decreases. The voltage pulse repetition rate also affects the number of bright spots. However, the color of the discharge plasma inside them mainly depends on the electrode material. Figure 6b,c demonstrates photographs of the discharge in the gap with a plane stainless steel electrode. The glow color of the plasma cloud (spherical jets) on the plane electrode in these figures is blue. Experiments were also carried out with electrodes made of different metals. Photographs of the discharge plasma glow in the gap formed by a plane stainless steel anode and a cone-shaped aluminum anode are shown in Figure 6b,c. The use of aluminum electrodes changed the color of the discharge in argon, air, and nitrogen near the electrodes to red. On the surface of the cone-shaped electrode, bright spots surrounded by red halo can be seen. The number of bright spots depends on the discharge current density and gas pressure, as well as on the shape and polarity of the electrodes. As the interelectrode distance increases, the number of bright spots on the plane electrode usually decreases. The voltage pulse repetition rate also affects the number of bright spots. However, the color of the discharge plasma inside them mainly depends on the electrode material. Figure 6b,c demonstrates photographs of the discharge in the gap with a plane stainless steel electrode. The glow color of the plasma cloud (spherical jets) on the plane electrode in these figures is blue.

The use of copper electrodes resulted in an intense green color around the bright spots on the high-voltage electrode (Figure 7). The use of copper electrodes resulted in an intense green color around the bright spots on the high-voltage electrode (Figure 7).

**Figure 7.** Photograph of the discharge in air at the pressure of 100 Torr (**a**) and the spectrum of the green discharge region near the cone-shaped copper cathode (**b**). The plane stainless steel electrode is located at the top. *f* = 60 Hz. C—cathode, A—anode. *d* = 2 mm. NPG-18/3500N voltage pulse generator. *U*g = 13 kV. **Figure 7.** Photograph of the discharge in air at the pressure of 100 Torr (**a**) and the spectrum of the green discharge region near the cone-shaped copper cathode (**b**). The plane stainless steel electrode is located at the top. *f* = 60 Hz. C—cathode, A—anode. *d* = 2 mm. NPG-18/3500N voltage pulse generator. *U*g = 13 kV.

The lines of the copper atom dominate in the visible region of the emission spectrum (Figure 7b). An important role in the excitation of the above spectral transitions in copper atoms is played by the transfer of energy from the metastable level A3Σu+ of molecular nitrogen [25]. A green glow was also observed during high-altitude discharges in the Earth's atmosphere (ghosts in [16]), but the probability of their observation is negligible. In [16], these green-colored areas are located above the red sprites. They have a spherical shape and occur at an altitude of about 80 km. The lines of the copper atom dominate in the visible region of the emission spectrum (Figure 7b). An important role in the excitation of the above spectral transitions in copper atoms is played by the transfer of energy from the metastable level A3Σu + of molecular nitrogen [25]. A green glow was also observed during high-altitude discharges in the Earth's atmosphere (ghosts in [16]), but the probability of their observation is negligible. In [16], these green-colored areas are located above the red sprites. They have a spherical shape and occur at an altitude of about 80 km.

It should also be noted that for the conditions in Figures 5–7, as in [26], runaway electrons were registered behind a foil or mesh anode at pressures from ones to tens of Torr. These electrons pre-ionize air and other gases and contribute to the formation of diffuse discharges [21,27]. When TLEs appear in the Earth's atmosphere, high-energy particles, including electrons, are also detected [23]. It should also be noted that for the conditions in Figures 5–7, as in [26], runaway electrons were registered behind a foil or mesh anode at pressures from ones to tens of Torr. These electrons pre-ionize air and other gases and contribute to the formation of diffuse discharges [21,27]. When TLEs appear in the Earth's atmosphere, high-energy particles, including electrons, are also detected [23].

#### **4. Discussion 4. Discussion**

Usually, the region emitting a certain color near bright spots on a copper, aluminum, or steel electrode (see Figures 5–7) has a spherical shape. However, sometimes, it can also have the shape of a cylindrical jet. Figure 8 shows blue jets obtained in laboratory discharges. These jets correspond to ones in the video from the ISS [20]. Usually, the region emitting a certain color near bright spots on a copper, aluminum, or steel electrode (see Figures 5–7) has a spherical shape. However, sometimes, it can also have the shape of a cylindrical jet. Figure 8 shows blue jets obtained in laboratory discharges. These jets correspond to ones in the video from the ISS [20].

Although the sizes of blue jets in the Earth's atmosphere and in laboratory experiments differ by several orders of magnitude, their color and shape are similar. Atmospheric blue jets are usually in the form of a cylinder or a cone, from which thinner jets can propagate. The blue jets near the stainless electrode obtained at the discharge in the air (Figure 8b–c) had a similar shape.

The shape of red sprites is more complex. They are formed in two directions. Initially, one or several jets start from a plasma formation at an altitude of about 75 km [18,31] from the Earth's surface to the ground. Next, the jet(s) or diffuse cloud propagate in the opposite direction. A similar picture was observed in our experiments (Figure 3). Double diffuse jets, starting from one region, propagated in opposite directions. To initiate a streamer (ionization wave) in an electric field, it is necessary to create plasma with a sufficiently high concentration of charged particles. This can be facilitated by, for example, the development of an electron avalanche or a preliminary discharge. An experiment on the registration of particle tracks showed that jets (streamers) could also be initiated at the ends of tracks. We assume that micrometeorites, entering the dense layers of the atmosphere,

also create plasma trails with high concentrations of charged particles and initiate some TLEs. Primarily, they are ghosts, and, under certain conditions, they are red sprites. diffuse discharges [21,27]. When TLEs appear in the Earth's atmosphere, high-energy particles, including electrons, are also detected [23].

It should also be noted that for the conditions in Figures 5–7, as in [26], runaway electrons were registered behind a foil or mesh anode at pressures from ones to tens of Torr. These electrons pre-ionize air and other gases and contribute to the formation of

(**a**) (**b**)

**Figure 7.** Photograph of the discharge in air at the pressure of 100 Torr (**a**) and the spectrum of the green discharge region near the cone-shaped copper cathode (**b**). The plane stainless steel electrode is located at the top. *f* = 60 Hz. C—cathode, A—anode. *d* = 2 mm. NPG-18/3500N voltage pulse

The lines of the copper atom dominate in the visible region of the emission spectrum (Figure 7b). An important role in the excitation of the above spectral transitions in copper atoms is played by the transfer of energy from the metastable level A3Σu+ of molecular nitrogen [25]. A green glow was also observed during high-altitude discharges in the Earth's atmosphere (ghosts in [16]), but the probability of their observation is negligible. In [16], these green-colored areas are located above the red sprites. They have a spherical

A micrometeorite containing copper, sputtering and burning, can create a vapor cloud, as well as initiating an ionization wave (streamer), which, at high altitudes has a spherical shape. Discharges in copper vapor are green, while in nitrogen and oxygen there are no intense lines (bands) in this region of the spectrum. The experiments in [32] showed that the presence of copper vapor during an apokampic discharge increases the length of the plasma jet (streamer) and decreases the voltage at which it appears. **4. Discussion** Usually, the region emitting a certain color near bright spots on a copper, aluminum, or steel electrode (see Figures 5–7) has a spherical shape. However, sometimes, it can also have the shape of a cylindrical jet. Figure 8 shows blue jets obtained in laboratory discharges. These jets correspond to ones in the video from the ISS [20].

*Nanomaterials* **2022**, *12*, x FOR PEER REVIEW 9 of 12

(**b**)

**Figure 8.** Photos of jets near the cone-shaped stainless steel cathode (**a**–**c**) at an air pressure of 760 Torr captured in one pulse. *d* = 2 (**a**) and 3 (**b**,**c**) mm. NPG-18/3500N voltage pulse generator.

The red color of the positive column, similar to that of a sprite, was recorded in [33] during a continuous-glow discharge in air at a pressure of 1.2 Torr. However, at the cathode, the discharge plasma color had a blue tint. The sprites spread in both directions from the place of their initiation at an altitude of about 75 km; most of them were red along their entire length. Therefore, micrometeorites, and not only ionospheric/mesospheric inhomogeneities, can also contribute to the initiation of red sprites and influence their color [34].

#### **5. Conclusions**

generator. *U*g = 13 kV.

shape and occur at an altitude of about 80 km.

This study showed that the vapors of the electrode material can significantly affect the color of the plasma glow of pulsed and pulse-periodic discharges. The largest change in color is observed near bright spots on the electrodes, primarily near electrodes with a small radius of curvature, as well as in the area where the spark channels are adjacent to the electrodes. Based on these results, it is possible to put forward a hypothesis about the influence of cosmic dust [13] on the color of parts of transient luminous events and their initiation.

**Author Contributions:** Conceptualization, writing—original draft, V.T.; methodology, N.V., D.B. and A.B.; supervision, M.L.; review & editing, D.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was performed within the framework of the State assignment of the IHCE SB RAS, project No. FWRM-2021-0014.

**Data Availability Statement:** Data are contained within the paper.

**Acknowledgments:** The authors are thankful to Evgenii Baksht for help with the experiments.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

#### **References**

MDPI St. Alban-Anlage 66 4052 Basel Switzerland Tel. +41 61 683 77 34 Fax +41 61 302 89 18 www.mdpi.com

*Nanomaterials* Editorial Office E-mail<EMAIL_ADDRESS>www.mdpi.com/journal/nanomaterials

MDPI St. Alban-Anlage 66 4052 Basel Switzerland

Tel: +41 61 683 77 34

www.mdpi.com

ISBN 978-3-0365-4917-0


*2.6. Drying Kinetics*

The kinetics of moisture loss during freeze-drying of the loaded gellan gum gels were described by five empirical models commonly employed to characterise drying kinetics in foods [15,16]: Newton, Page, Henderson and Pabis, logarithmic and Wang and Singh. Table 1 lists them all alongside their expressions.

**Table 1.** Drying kinetics models considered in this work to describe moisture loss during freeze-drying of riboflavin-loaded gellan gum gels with different pHs.

Parameter units: (*h*−*1*) for *k1*, *k3*, *k4*, *k5*; (*h*−*n*) for *k2;* (*h*−*2*) for *k6; a1, a2* and *b1* are dimensionless.

To fit the models to the experimental freeze-drying curves, the (dimensionless) moisture ratios (MRs) of the samples were calculated first from the measured water content data as follows [15]:

$$MR = \frac{X(t) - X\_{eq}}{X\_0 - X\_{eq}} \tag{2}$$

where *X(t)* is the moisture content on a dry basis for the different processing times (h), *X0* is the initial moisture content (*w*/*w* d.b.) and *Xeq* is the equilibrium moisture content (*w*/*w* d.b). The equilibrium moisture content for the dehydrated gels was calculated using the GAB model with measured water activities and parameters for gellan gums presented in [9]:

$$\frac{a\_{\rm uv}}{X\_{eq}} = 0.165 + 14.3a\_{\rm uv} - 13.2 \, a\_{\rm uv}^{-2} \tag{3}$$

For all the models in Table 2, the unknow parameters (parameters *aj* and *ki*, with *j* = 1,2 and *i* = 1, ... , (6) were estimated using regression analysis. The error (e) between the experimental (θ) and predicted (i.e., fitted) MR values (θ) [15],

$$J = \sum\_{i}^{N} c\_i^2 = \sum\_{i}^{N} \left(\theta\_i - \overline{\theta}\_i\right)^2,\tag{4}$$

was minimised for all the *i* measurements that formed the experimental data set of size *N* using a nonlinear least squares method (implemented in Matlab with tolerance 10−10).

**Table 2.** Regression and goodness-of-fit results for the drying kinetics models.

Parameter units: (*h*−*1*) for *k1*, *k3*, *k4*, *k5*; (*h-n*) for *k2;* (*h*−*2*) for *k6; a1, a2* and *b1* are dimensionless.

The goodness-of-fit of each fitted model was then assessed using three statistical measures that take into account the complexity (i.e., number of parameters, *p*) of each model [20]. These were:

$$R\_{adj}^2 = 1 - \frac{N-1}{N-p}(1 - R^2) \tag{5}$$

where *R2* is the regression coefficient of determination.

$$AICC = AIC + \frac{2p(p+1)}{N-p-1} \tag{6}$$

where *AIC* is the Akaike information criterion [21,22].

$$BIC = p \ln(N) - 2 \text{ } \ln(L) \tag{7}$$

where *L* is the maximum log-likelihood of the estimated model.

The goodness of the fit (or the likelihood) can be increased by adding more parameters to the model. However, this will increase complexity and might result in overfitting (i.e., more parameters than can be estimated with the available data), all which is penalized with higher AICC and BIC values [15,20]. Therefore, the model with best performance will be the one with higher *R*2*adj* and lower *AICC* and *BIC* values [20].

#### *2.7. Kinetics and Mechanisms of Vitamin Release*

The Korsmeyer–Peppas model [17] has been used to describe release kinetics and identify delivery mechanisms. It is a semi-empirical power law that relates the fractional release of vitamin/drug to the release time [17,18]:

$$\frac{M(t)}{M\_{\odot}} = k\_{rel} t^{\eta\_{rel}} \tag{8}$$

where the *M*(*t*) and *M* ∞ are the cumulative amounts of drug released at time *t* (measured in hours *h*) and infinite time, respectively; the constant *krel* (in *h*−*nrel* units) relates to the structure and geometry of the delivery matrix (in this case, the freeze-dried gels); and the dimensionless exponent *nrel* is the release mechanism indicator. For cylindrical substrates *nrel* ≤ 0.45 defines Fickian mechanisms, while anomalous/non-Fickian delivery is described by nrel > 0.45 [17,18]. Experimental release curves were fitted to Equation (8) using a nonlinear least squares method [15], and parameters *krel* and *nrel* were estimated within 95% confidence intervals.

#### **3. Results and Discussion**

#### *3.1. E*ff*ect of pH on Moisture Losses during Freeze-Drying*

Figure 1 shows a comparison of the drying curves, in terms of the moisture ratio (MR) and freeze-drying processing times (h), for gellan gum gels at pH 2.5, 4 and 5.2 (natural) loaded with riboflavin. Gels at pH 2.5 exhibit the fastest drying rates, with most of the moisture content (MR∼ 0.25) removed during the first 6 h of the freeze-drying process. On the other hand, samples at pH 5.2 and 4 followed a very similar drying trend up to the first 4 h of processing. From this time onwards, the samples at pH 4 present a significantly slower drying rate; i.e., MR∼ 0.3 at t = 8 h compared to MR∼ 0.15 for pH 5.2 at the same time. The three samples were completely dried (i.e., free water totally removed) by the end of the freeze-drying experiments at t= 18 h, independent of their pHs.

**Figure 1.** Moisture ratio evolution along time for 2% ( *w*/*w*) gellam gums with pH 2.5 (black dots), pH 4 (blue squares) and pH 5.2 (magenta triangles) loaded with riboflavin during the conducted freeze-drying experiments.

The fastest drying rates observed for the gels at lower pHs can be explained by the e ffects of acidifying the gel solution. As reported by Cassanelli et al., [14], the acidification step both enhances ice crystal nucleation and weakens the gel structure at pH values as low as pH 2.5. The combination of these two e ffects might favour a more interconnected pore structure—i.e., more nuclei will lead to more crystals that will find lower resistance in the weak gel structure to form a network. This could lead to faster drying rates and also a ffect the strength of the rehydrated structure.

#### *3.2. Freeze-Drying Kinetics: Parameter Estimation and Model Discrimination*

Estimated parameters for all the drying models considered in this work (i.e., Newton, Page, Henderson and Pabis, logarithmic and Wang and Singh) are listed in Table 2, together with the RMSE (root mean square error) for each fitting and the results corresponding to the goodness-of-fit of each model. According to these results, the models that provide more accurate descriptions for the drying kinetics are the Page (Table Equation 1) and the Wang and Singh (Table Equation 5) models, both presenting *R*2*adj*∼ 0.99 (in average) for all pH values.

For samples at modified pHs (i.e., pH 2.5 and 4), the Wang and Singh model presents the lowest RMSE (3.52 × 10−4 for pH 2.5) and the highest *R*2*adj*, while for the freeze-dried gels at pH 5.2, the Page model is the model that presents the best fitting (RMSE = 0.040 and *R*2*adj* = 0.986). This is in agreement with fittings reported in Cassanelli et al. [19], which showed the Page model as the best option to describe the freeze-drying kinetics of non-loaded gellan gels at natural pH.

The goodness-of-fit for all models is illustrated in Figure 2, where experimental values are plotted against predicted moisture ratios for each drying model at all pH studied. This graph also shows the accuracy of the Page and Wang models, for which most of the predicted points lie on the correlation line (see Figure 2b,d).

**Figure 2.** Correlation between predicted and experimental moisture contents for freeze-dried 2% (w/w) gellan gum samples for: (**a**) Newton model (Table Equation 1), (**b**) Page model (Table Equation 2), (**c**) Henderson and Pabis model (Table Equation 3) and (**d**) Wang model (Table Equation 5).

When comparing models with similar accuracies, the *AICC* criterion constitutes the best measure to discriminate models, with more negative *AICC* values indicating better model performances. According to this, if the Newton and Page models were compared at pH 4—the pH at which both models show very similar RMSE, *R*2*adj* and *BIC*—the lower AICC (−21.39) of the Newton model would make it the preferred one. This criterion is also an indicator of the complexity (e.g., number of parameters) of the

assessed models—the Newton model involves a single parameter (*k1*), compared to the two needed in the Page model (*k2, n*). On the other hand, the logarithmic model (Table Equation 4), with the highest number of parameters considered (*p* = 3), presents the less negative *AICC* values at each pH.

#### Effect of pH on the Drying Kinetic Parameters

The effect of pH on drying kinetic parameters has been determined by analysing the values of the constants in Newton (Table Equation 1) and Henderson and Pabis (Table Equation 3) models. These two models are derived from Newton's cooling law and Fick's Second law [16], respectively, so their constants enclose physical meaning—as opposite to the Page and Wang and Singh models that are purely empirical [16].

Parameters *k1* (Newton) and *k3* (Henderson) in Table 2, both time constants (*h*−*1*), characterise the drying rates of the system, while *a1* (Henderson) is a dimensionless parameter related to the shape and structural properties of the samples [16].

For gellan gum gels at different pHs, both Newton and Henderson rate parameters (i.e., *k1* and *k3*, respectively) show very similar trends. The higher values (*k1* = 0.225 h−1 and *k3* = 0.232 h−1) correspond to samples at pH 2.5, indicating a faster dehydration process. On the other hand, rate constants for samples at pH 4 are the lowest (*k1* = 0.157 h−1 and *k3* = 0.158 h−1), which relates to the slower drying rate of these samples. This is in agreement with differences on moisture ratios (MR) at different pHs discussed in Section 3.1.

The values of constant *a1* are again similar for samples at pH 2.5 and 5.2 (*a1* = 1.036 and *a1* = 1.043), which suggests no significant structural differences at those pH values. However, the value of *a1* for freeze-dried gels at pH 4 (*a1* = 1.006) suggests changes in microstructure that might be behind the different drying rates observed at this particular pH. These findings are in agreement with the mechanical properties (i.e., higher gel strength and Young's modulus) reported in Cassanelli et al. [14] for gellan gels at pH 4 before and after freeze-drying—"stronger" gels might make ice nucleation and growth difficult, and therefore affect the freeze-dried microstructures of the gels.

#### *3.3. Riboflavin Release from Freeze-Dried Gellan Gels at Di*ff*erent pHs*

Figure 3 presents experimental riboflavin release curves from freeze-dried gels prepared at different pHs, plotted as normalised vitamin released (NVR) across time. Data in this graph show significant differences in release times: freeze-dried gels at pH 4 completed the vitamin release in approximately 9.5 h; gels at natural pH (5.2) were fully unloaded after 6h, and total vitamin delivery took 3h for gels at pH 2.5. Samples at pH 2.5 presented a weak structure—in accordance with strength at fresh and freezing stages—that lead to breakage during the release experiments. This increased the surface area of the gels in contact with the release medium, which explains the shorter delivery times.

The observed differences in the riboflavin release times to the medium can be related to the different microstructures and mechanical properties of the gels. Both Norton et al. [23] and Cassanelli et al. [14] reported that freeze-dried gellan gum gels at pH 4 exhibited an aggregated and rigid structure. This can impede mass transfer within the gel, increasing the time needed to release the vitamin completely from the substrate and leading to longer delivery processes. A much lower level of aggregation and very weak structures were reported for freeze-dried gels at pH 2.5 [14,23], which is also in agreement with our experimental observations. According to the same authors, unloaded freeze-dried gels at natural pH (pH 5.2) exhibit intermediate levels of aggregation [14,24], explaining the also intermediate release times shown in Figure 3.

**Figure 3.** Release curves for the riboflavin encapsulated in freeze-dried 2% (*w*/*w*) gellan gums with different pHs. The vitamin content in the release medium is expressed as normalised vitamin released (NVR). Error bars correspond to triplicate tests.

#### *3.4. Delivery Mechanisms at Di*ff*erent pHs*

To estimate the value of the dimensionless parameter *nrel* in Equation (8), and therefore determine the release mechanism governing riboflavin delivery, the portion of the release curves (Figure 3) corresponding to the first 60% of the total released vitamin—i.e., release curve portions such that *M*(*t*) *M*∞ = *NRV* ≤ 0.60—were fitted to the Korsmeyer–Peppas model [17,18]. Samples at pH 2.5 were not considered in this analysis, as they broke into several pieces during the release tests, leading to delivery conditions out of the scope of this work. Table 3 lists the parameters *krel* and *nrel* (95% CI) estimated at pH 5.2 and pH 4 (see Table 3 for parameter units). These results are discussed next.

**Table 3.** Fitted parameters (95% CI) for the Korsmeyer–Peppas release model and release mechanisms found.

Parameter units: (*h*−*nrel*)*; nrel* is dimensionless.

#### 3.4.1. Release from Freeze-Dried Gellan Gels at pH 5.2

Riboflavin delivery from gels at natural pH (pH 5.2) is characterised by a shape constant *krel* = 0.509 diffusional coefficient *nrel* = 0.131 (see Table 3 for the corresponding confidence intervals). According to the classification given in [21,22], this indicates that the governing release mechanism is purely Fickian, as *nrel* = 0.131 < 0.45, which is the limiting value of the diffusional coefficient for Fickian transport mechanisms. Therefore, we can define an apparent diffusion coefficient *Dapp* (m2/s) for samples at pH 5.2 using a short-time approximation of Fick's Second law [18]:

$$\frac{M(t)}{M\_{\infty}} = 4 \left[ \frac{D\_{app}t}{\pi a^2} \right]^{\frac{1}{2}} \tag{9}$$

As the aspect ratio of the cylindrical gels is approximately in the order of 1, the predictive capabilities of the short-time solution include up to the 85% of the total vitamin release [22]. Thus, values such that *M*(*t*) *M*∞ = *NRV* ≤ 0.85 in the release curve at pH 5.2 were fitted to Equation (9). This

gave an estimated *Dapp* = 1.325 × 10−9 m2/s with 95% CI defined by [1.086 × 10−9, 1.564 × 10−9] m2/s. Figure 4 presents the comparison between the experimental and predicted release curve using *Dapp*, showing a good agreement between the modelled Fickian delivery mechanism and the experimental data—and thus confirming Fickian transport for riboflavin released from freeze-dried gellan gels at pH 5.2

**Figure 4.** Predicted release curve for encapsulated riboflavin at pH 5.2 using estimated *Dapp* (dash –) compared to experimental curve (blue dots).

#### 3.4.2. Release from Freeze-Dried Gellan Gels at pH 4

As shown in Table 3, the estimated shape constant and diffusional exponent at pH 4 were *krel* = 0.287 and *nrel* = 0.472, respectively. These estimates (i) confirm the structural difference of samples at pH 4 discussed in previous subsections, as the value of *krel* at pH 4 is almost half of the corresponding to pH 5.2, and (ii) indicate an anomalous delivery mechanism from freeze-dried gellan matrices at pH 4, since we estimated *nrel* > 0.45.

Anomalous mass transport can be defined as a mix between Fickian and non-Fickian mechanisms, for which the general form of the Korsmeyer–Peppas model presented in Equation (8) can be split into two contributions [24]:

$$\frac{M(t)}{M\_{\infty}} = k\_{\rm rel} t^{n\_{\rm rel}} = k\_1^{\rm rel} t^{m\_{\rm rel}} + k\_2^{\rm rel} t^{2m\_{\rm rel}}.\tag{10}$$

The first one (*krel* 1 *tm*) represents the Fickian part, while the second term (*krel* 2 *t*2*m*) accounts for the relaxational contribution [24], which is related to stresses and state transitions of polymeric matrices. The dimensionless diffusional exponent *mrel* in Equation (10) can be determined from aspect ratio (i.e., height/diameter of the sample) correlations. For the ratio characterising the cylindrical samples used here (∼1.5), *mrel* = 0.43 [24].

Estimated values for both *krel* 1 = 0.264 (0.240, 0.289) and *krel* 2 = 0.022 (0.007, 0.038) were then obtained by fitting Equation (10) to the experimental release curves at pH 4 for NMC <0.60 with 95% confidence intervals (values in the parenthesis). Units for *krel* 1 and *krel* 2 are (*h*−*mrel*). These estimates give an idea of the relevance of each contribution. For samples at pH 4, *krel* 1 *krel* 2 , showing that the release of riboflavin from the freeze-dried gels at pH 4 is mostly Fickian. This is confirmed by the vitamin release percentages due to each contribution calculated as Peppas and Sahlin [24]:

$$P\_{\text{Fickian}} = \frac{1}{1 + \frac{k\_2^{rel}}{k\_1^{rel}} t^{m\_{rel}}} ; P\_{mm-\text{Fick}} = 100 - P\_{\text{Fickian}} = P\_{\text{Fickian}} \frac{k\_2^{rel}}{k\_1^{rel}} t^{m\_{rel}} \tag{11}$$

They are presented in Figure 5a. Overall, the Fickian contribution is predominant along the release process, i.e., overall *PFickian* > 80%, with values closer to 90% at the initial times of the delivery test, while relaxation effects are more important towards the end of the experiment, as the delivery of riboflavin is closer to completion.

**Figure 5.** (**a**) Fickian and non-Fickian release percentages for riboflavin corresponding to sample with pH 4 when anomalous transport mechanism was considered. (**b**) Predicted release curve for encapsulated riboflavin at pH 4 considering pure Fickian mechanism and estimated *Dapp* (dash –) compared to experimental curve (blue dots).

Given the relevance of Fickian transport during the release process at pH 4, and with the estimated diffusional exponent *nrel* so close to the Fickian limiting value of 0.45—confidence intervals for this parameter are actually cross-boarding this limit, i.e., (0.441, 0.504) as shown in Table 3—a hypothetical pure Fickian riboflavin delivery at pH 4 has been also assessed. Following the procedure explained in Section 3.4.1, an apparent diffusion coefficient Dapp = 5.626 × 10−10 m2/s was estimated within a 95% confidence interval (5.409 × 10−10, 5.842 × 10−10) m2/s. This estimate together with the short time approximately described in Equation (9) was used to obtain a predicted release curve, which is presented in Figure 5b alongside the experimentally obtained curve. As the comparison reveals, the hypothetical pure Fickian mechanism describes the behaviour observed during the release tests well, and it could be used to predict riboflavin delivery—neglecting relaxation effects—from freeze-dried gellan gels at pH 4 with high accuracy.


# **Advanced Operation and Maintenance in Solar Plants, Wind Farms and Microgrids**

Edited by Luis Hernández-Callejo, Maria del Carmen Alonso García and Sara Gallardo Saavedra Printed Edition of the Special Issue Published in *Applied Sciences*

www.mdpi.com/journal/applsci


**3.3 Ischemia-reperfusion time**

According to the statistics of the time from the onset of coronary artery disease to reperfusion ischemia time, the interval of female patients was longer than that of male patients, including the prehospital delay and the time from door to balloon [27–30]. A study by Lichtman et al. has revealed that the cardiovascular risk of female patients with coronary artery disease, especially young female patients with those, is not easy to be accurately assessed, which may lead to be delayed diagnosis of acute myocardial infarction, thereby affecting treatment and prognosis [31]. Another registration study from one of 11 centers in Switzerland providing primary PCI around the clock, which has demonstrated that female patients with acute myocardial infarction between 2005 and 2010 may be discriminated when they receive PCI [32]. It is speculated that this situation may also exist in other countries. The prognosis of female patients with coronary artery disease who are discriminated in clinic is partly poor. Moreover, a study from the United States has found that female patients with coronary artery disease were less likely to undergo PCI than male patients with those and more female patients with those had delayed time of ischemia-reperfusion [33]. These controllable factors can lead to the failure of female patients with coronary artery disease to improve myocardial ischemia effectively in a short period of time, which is one of the important factors of poor prognosis. The duration of ischemia-reperfusion may be longer in female patients with these atypical symptoms than in male patients, which is another factor of higher mortality and MACE in female patients with coronary artery disease after PCI.

**69**

*Gender Differences in Clinical Outcomes of Patients with Coronary Artery Disease…*

MACE is one of the factors that significantly affect the prognosis for patients with coronary artery disease after PCI. Previous study has indicated that the incidence of MACE is lower in male patients with coronary artery disease after PCI than that in female patients with those [9, 10, 23, 34]. A prospective, multicenter, cohort study by Glaser et al. has exhibited that female patients with non-ST-segment elevation acute coronary syndrome undergoing PCI at the age of 65 was more likely to have MACE than male patients with those at the same time [28]. Further analysis has shown that the incidence of congestive heart failure was higher in female patients with ST-segment elevation myocardial infarction than that in male patients with those, and the former was more likely to have cardiogenic shock when myocardial infarction occurred [5–7]. High incidence of ventricular septal rupture and severe mitral regurgitation during cardiogenic shock can be considered as important factors affecting the poor prognosis of female patients with myocardial infarction in the hospital. In a word, the above pathological factors can lead to the high incidence of MACE in female patients with coronary artery disease after PCI.

A study has demonstrated that the low incidence of revascularization in female patients with coronary artery disease may also be attributed to the lower follow-up rate, atypical symptoms, difficulty identifying myocardial ischemia, unwillingness to undergo invasive investigations, and prejudice against female patients [9]. In addition, the mortality of female patients with coronary artery disease was higher during the short- and long-term follow-up compared with male patients with those, which may also reduce the chance of revascularization [23, 34]. Furthermore, male patients with coronary artery disease who underwent PCI often have more complex lesions, which may be also an independent predictor of revascularization [23]. In terms of pathophysiology, the male subjects are more likely to have atherosclerotic plaque rupture, platelet-rich thrombus, and microembolism [35], while the platelets are more sensitive to aggregation stimulation in female patients, and this pathophysiological difference may also increase the risk of male patients with coronary artery disease who underwent PCI or CABG [36]. Moreover, some studies have shown that male patients with coronary artery disease have a higher PCI or CABG history than the female with those, which may be another reason for the higher incidence of overall revascularization in male

Earlier evidence has supported that the female individuals would experience depression after the initial diagnosis of coronary artery disease and acute cardiac events, leading to all-cause mortality and the risk of MACE in the following months [37, 38]. Breast cancer is one of the most important causes of female individual death worldwide. However, the administration of estrogen receptor modulators in anti-breast cancer treatments may increase the incidence of coronary artery disease [39]. The incidence of autoimmune diseases for female individuals is also high, especially systemic lupus erythematosus, which is more common in female individuals. The pathogenic antibodies of the disease can cause antiphospholipid antibody syndrome (thrombosis, thrombocytopenia), thereby involving coronary artery and even resulting in acute myocardial infarction [40]. Therefore, it is important

*DOI: http://dx.doi.org/10.5772/intechopen.91878*

**3.4 MACE**

**3.5 Revascularization**

patients with those [7, 8].

**3.6 Other risk factors**

*Gender Differences in Clinical Outcomes of Patients with Coronary Artery Disease… DOI: http://dx.doi.org/10.5772/intechopen.91878*

### **3.4 MACE**

*Cardiac Diseases - Novel Aspects of Cardiac Risk, Cardiorenal Pathology and Cardiac Interventions*

Some studies have elucidated that gender differences in the prognosis of patients with coronary artery disease after PCI are due to the fundamental differences in physiology, pathophysiology, pathological anatomy, and other aspects between male and female. Anatomically, the coronary arteries of female patients with coronary artery disease are smaller than that of male patients with those, and the smaller blood vessels can cause higher risks of bleeding complications and vascular damage [22]. In general, male patients with coronary artery disease are prone to complex lesions, such as left main artery lesions, chronic total occlusion lesions, and long lesions, while female patients with coronary artery disease tend to have small vessel lesions, which are more likely to show no significant stenosis of the coronary artery during coronary angiography [23]. Meanwhile, coronary microvascular reactivity and myocardial response to ischemia are also different between male and female individuals. It is suggested that the hemodynamic state of female patients with coronary artery disease is worse than that of male patients with those, which leads to differences of cell cycle process and apoptosis-related protein levels of cardiac fibroblasts between different genders [24]. In addition, female patients with myocardial infarction often show atypical symptoms [25]. As a result, such patients will not be paid much attention to, and physicians may be misled or underestimate the possibility of acute coronary syndrome, thereby prolonging the time from myocardial infarction to revascularization [26]. These pathophysiology and anatomy differences are irreversible factors. If the physiological and pathological characteristics of female patients with coronary artery disease can be identified in time, appropriate coronary intervention strategies will be selected to reduce complications and improve their

According to the statistics of the time from the onset of coronary artery disease to reperfusion ischemia time, the interval of female patients was longer than that of male patients, including the prehospital delay and the time from door to balloon [27–30]. A study by Lichtman et al. has revealed that the cardiovascular risk of female patients with coronary artery disease, especially young female patients with those, is not easy to be accurately assessed, which may lead to be delayed diagnosis of acute myocardial infarction, thereby affecting treatment and prognosis [31]. Another registration study from one of 11 centers in Switzerland providing primary PCI around the clock, which has demonstrated that female patients with acute myocardial infarction between 2005 and 2010 may be discriminated when they receive PCI [32]. It is speculated that this situation may also exist in other countries. The prognosis of female patients with coronary artery disease who are discriminated in clinic is partly poor. Moreover, a study from the United States has found that female patients with coronary artery disease were less likely to undergo PCI than male patients with those and more female patients with those had delayed time of ischemia-reperfusion [33]. These controllable factors can lead to the failure of female patients with coronary artery disease to improve myocardial ischemia effectively in a short period of time, which is one of the important factors of poor prognosis. The duration of ischemia-reperfusion may be longer in female patients with these atypical symptoms than in male patients, which is another factor of higher mortality and MACE in female patients

**3.2 Anatomy and pathophysiology**

clinical prognosis.

**3.3 Ischemia-reperfusion time**

with coronary artery disease after PCI.

**68**

MACE is one of the factors that significantly affect the prognosis for patients with coronary artery disease after PCI. Previous study has indicated that the incidence of MACE is lower in male patients with coronary artery disease after PCI than that in female patients with those [9, 10, 23, 34]. A prospective, multicenter, cohort study by Glaser et al. has exhibited that female patients with non-ST-segment elevation acute coronary syndrome undergoing PCI at the age of 65 was more likely to have MACE than male patients with those at the same time [28]. Further analysis has shown that the incidence of congestive heart failure was higher in female patients with ST-segment elevation myocardial infarction than that in male patients with those, and the former was more likely to have cardiogenic shock when myocardial infarction occurred [5–7]. High incidence of ventricular septal rupture and severe mitral regurgitation during cardiogenic shock can be considered as important factors affecting the poor prognosis of female patients with myocardial infarction in the hospital. In a word, the above pathological factors can lead to the high incidence of MACE in female patients with coronary artery disease after PCI.

#### **3.5 Revascularization**

A study has demonstrated that the low incidence of revascularization in female patients with coronary artery disease may also be attributed to the lower follow-up rate, atypical symptoms, difficulty identifying myocardial ischemia, unwillingness to undergo invasive investigations, and prejudice against female patients [9]. In addition, the mortality of female patients with coronary artery disease was higher during the short- and long-term follow-up compared with male patients with those, which may also reduce the chance of revascularization [23, 34]. Furthermore, male patients with coronary artery disease who underwent PCI often have more complex lesions, which may be also an independent predictor of revascularization [23]. In terms of pathophysiology, the male subjects are more likely to have atherosclerotic plaque rupture, platelet-rich thrombus, and microembolism [35], while the platelets are more sensitive to aggregation stimulation in female patients, and this pathophysiological difference may also increase the risk of male patients with coronary artery disease who underwent PCI or CABG [36]. Moreover, some studies have shown that male patients with coronary artery disease have a higher PCI or CABG history than the female with those, which may be another reason for the higher incidence of overall revascularization in male patients with those [7, 8].

#### **3.6 Other risk factors**

Earlier evidence has supported that the female individuals would experience depression after the initial diagnosis of coronary artery disease and acute cardiac events, leading to all-cause mortality and the risk of MACE in the following months [37, 38]. Breast cancer is one of the most important causes of female individual death worldwide. However, the administration of estrogen receptor modulators in anti-breast cancer treatments may increase the incidence of coronary artery disease [39]. The incidence of autoimmune diseases for female individuals is also high, especially systemic lupus erythematosus, which is more common in female individuals. The pathogenic antibodies of the disease can cause antiphospholipid antibody syndrome (thrombosis, thrombocytopenia), thereby involving coronary artery and even resulting in acute myocardial infarction [40]. Therefore, it is important

to prevent and reduce the incidence of female high-risk diseases and to reduce the mortality and MACE of female patients with coronary artery disease after PCI.


**3. Results**

#### *3.1. Characteristics of the Studied Participants*

The demographic characteristics of the study participants are shown in Table 1. The group of participants comprised 292 females (63.5%) and 168 males (36.5%). The mean age was 40.6 years old, and approximately 70% of the participants were married (Table 1). In addition, one-fourth of participants were smokers, and only a minority practiced physical exercise once per week (Table 1).

**Table 1.** Demographic characteristics of the study participants.

Values are arithmetic mean ± SD for continuous variables. Categorical variables are shown as numbers (*n*) and percentages (%). *n*: sample size.

Moreover, the clinical and genetic characteristics are shown in Table 2. Approximately 75% of the participants had high total cholesterol and LDL-C levels, and around half had low HDL-C.

**Table 2.** Clinical and genetic characteristics of the study participants.

Values are arithmetic mean ± SD for continuous variables. Categorical variables are shown as number (*n*) and percentages (%). *n*: sample size. BMI: body mass index, LDL-C: low-density lipoprotein cholesterol, HDL-C: high-density lipoprotein cholesterol, SBP: systolic blood pressure, DBP: diastolic blood pressure, MAF: minor allele frequency, *CD14*: cluster of differentiation 14.

#### *3.2. Association of rs2569190A*>*G in CD14 with Hypercholesterolemia*

Our calculations showed that the minor allele in our population was the allele G, with a frequency of 0.41 (Table 2). In addition, the allelic frequencies were consistent with HWE (*p* = 0.86). Interestingly, the G allele of rs2569190 in *CD14* was associated with increased levels of Tchol (OR = 3.04, *p* = 0.016, Table 3) and LDL-C (OR = 3.83, *p* = 0.006, Table 3) and decreased levels of HDL-C (OR = 0.36, *p* = 0.001, Table 3). Similar results were also seen with a recessive genetic model. Age was positively associated with an increase in Tchol levels (OR = 2.06 and *p* = 0.011, Table 3) and LDL-C levels (OR = 2.22 and *p* = 0.004, Table 3). Similarly, smoking was significantly associated with an increase in Tchol levels (OR = 2.18, *p* = 0.021, Table 3) and LDL-C (OR = 1.88, *p* = 0.050, Table 3) and a decrease in HDL-C (OR = 0.41, *p* = 0.001, Table 3). Participants that practiced physical exercise once per week had decreased Tchol (OR = 0.27 and *p* = 0.001, Table 3), LDL-C (OR = 0.28 and *p* = 0.001, Table 3), and HDL-C (OR = 0.40 and *p* = 0.017, Table 3) levels.

**Table 3.** Multiple logistic regression analysis with hyperlipidemia and hypertension.

OR: odds ratio, C.I: confidence interval, BMI: body mass index.


**4. Conclusions**

Based on the multiscale cross-correlation analysis performed for the data covering almost the last three years, it can be concluded that the cryptocurrency market dynamics is substantially tied to the traditional financial markets. Consistently, the most liquid cryptocurrencies, BTC and ETH, cannot serve as a hedge or safe haven for the stock market investments, not only during the turbulent periods like the COVID-19 panic, where this effect is particularly strong, but also during the recent bear market period on tech stocks, which has been accompanied by the parallel bear market on cryptocurrencies. Many observations show that the COVID-19 pandemic may have changed the paradigm that the cryptocurrency market is a largely autonomous market. The recent market developments and the strong US dollar have additionally increased the strength of the cross-correlations between BTC and ETH on the one side and the US tech stocks on the other side. These observations support some earlier findings on the same subject (e.g., [22,70]). In contrast, as the cryptocurrency market was weakly correlated with other markets during 2021, our results cannot support directly a recent hypothesis that the quantitative easing could actually be responsible for these correlations [22]. The existence of links between the global economy and the cryptocurrency market are further strengthened by the reaction of the price changes of BTC and ETH to economic data, such as CPI inflation, in a similar way to traditional financial instruments. These results are able to remove or, at least, to suppress the uncertainty that recent literature on this topic has brought to the cryptocurrency investors. Now it is more clear that the cryptocurrencies can no longer serve as a convenient hedging target for the investors whose purpose is to diversify the risk.

Our study brings a strong indication that the cryptocurrency market has finally become a connected part of the global financial markets after 12 years of the maturation process. Whether such a direction of this market evolution remains in agreement with the early vision of the cryptocurrency creators can be disputed, however. We also face a related question: does the fact that we have got "just another part of the global financial market" deserve devoting so huge amounts of energy to it? Sooner or later this question must be addressed by the policy makers. Nevertheless, what becomes evident now is that it allows the market participants to broaden the spectrum of their investment possibilities.

Among the limitations that might have influenced our study and, subsequently, our conclusions, we have to mention that only two principal cryptocurrencies were studied. Although they are the most influential, the most frequently traded, and widely discussed cryptocurrencies, they by no means define the entire market. It is possible that an analysis that included some less important cryptocurrencies would bring different outcomes. This is especially likely for the marginal cryptocurrencies without any thinkable "fundamental" value, whose dynamics is driven predominantly by extreme speculation. However, as the cryptocurrency market is looked at by the most investors through the lens of BTC and ETH (as their capitalization indicates), this particular limitation does not seem discouraging to us. Currently, these two assets shape the whole cryptocurrency market and we expect them to continue doing it in the nearest future. Another limitation of our analysis is the particular selection of the traditional financial instruments. Indeed, they constitute only a small fraction of the available ones. We are convinced, though, that they are among the most observed and the most influential ones in the context of the global economy, which fully justifies our choice.

A more general observation that the cryptocurrency market has spontaneously coupled to the technological sector of the stock markets by reacting to some trigger provided by the external data inflow resembles analogous effects of the spontaneous emergence of order among the so-far independent degrees of freedom in the various complex systems. However, as complexity allows for flexible reacting of a system to both the external perturbations and internal processes, such effects of ordering in the financial markets have to be eventually counterbalanced by the opposite processes of disordering. Therefore, the market participants must be aware that the inter-market couplings may not last forever and they can significantly be weakened or even removed completely at some point in future. This is why the in-depth studies of the cross-market dependencies have to remain among the principal directions of the cryptocurrency research. Our future work will also deal with energy consumption of the cryptocurrency market.

**Author Contributions:** Conceptualisation, S.D., J.K. and M.W.; methodology, S.D., J.K. and M.W.; software, M.W.; validation, S.D., J.K. and M.W.; formal analysis, M.W.; investigation, S.D., J.K. and M.W.; resources, M.W.; data curation, M.W.; writing—original draft preparation, M.W.; writing review and editing, S.D., J.K. and M.W.; visualisation, M.W.; supervision, S.D. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** Data available freely from Dukascopy [58].

**Conflicts of Interest:** The authors declare no conflict of interest.