rus
Issue #1/2025
P. P. Maltsev
Interaction of Electromagnetic Radiation with the Metal Fractal Clusters. Part 1
Interaction of Electromagnetic Radiation with the Metal Fractal Clusters. Part 1
DOI: 10.22184/1993-7296.FRos.2025.19.1.14.27
This paper provides the results of studies on the influence of the aluminum nanoisland dimensions with a length l during the fractal cluster formation on the polymer threads using the carbon benzene ring fibers on the conditions for the occurrence of “highly conductive off-surface state” during breakdown with an electric field strength of 1.6 kV/cm. The layer thickness was calculated in the case of the skin-effect in polymer threads with the metal fractal clusters for electromagnetic radiation with a wavelength λ and fulfillment of condition l << λ.
This paper provides the results of studies on the influence of the aluminum nanoisland dimensions with a length l during the fractal cluster formation on the polymer threads using the carbon benzene ring fibers on the conditions for the occurrence of “highly conductive off-surface state” during breakdown with an electric field strength of 1.6 kV/cm. The layer thickness was calculated in the case of the skin-effect in polymer threads with the metal fractal clusters for electromagnetic radiation with a wavelength λ and fulfillment of condition l << λ.
Теги: metal fractal clusters nanoscale aluminum droplets off-surface highly conductive state photon localization plasma polymer threads локализация фотонов металлические фрактальные кластеры надповерхностное высокопроводящее состояние наноразмерные капли алюминия плазма полимерные нити
Interaction of Electromagnetic Radiation with the Metal Fractal Clusters
Part 1
P. P. Maltsev
Inter-agency Center of Analytical Studies of the RAS, Moscow, Russia
This paper provides the results of studies on the influence of the aluminum nanoisland dimensions with a length l during the fractal cluster formation on the polymer threads using the carbon benzene ring fibers on the conditions for the occurrence of “highly conductive off-surface state” during breakdown with an electric field strength of 1.6 kV/cm. The layer thickness was calculated in the case of the skin-effect in polymer threads with the metal fractal clusters for electromagnetic radiation with a wavelength λ and fulfillment of condition l << λ.
Key words: metal fractal clusters, nanoscale aluminum droplets, polymer threads, plasma, off-surface highly conductive state, photon localization
Article received: 16.01.2025
Article accepted: 03.02.2025
Skin-Effect in the Polymer Threads with the Metal Fractal Clusters
It should be noted that in 1999 John Pendry proposed an approach to describing the specific artificially created materials based on the fact that if a composite material consists of discrete scattering elements which size l is much smaller than the radiation wavelength λ, then electrodynamically it can be considered as continuous within a limited frequency band, provided that l << λ.
In other words, a physical medium will be continuous in the electromagnetic sense if its properties can be described by the average parameters changing on a scale much larger than the dimensions of the components forming the material. Consequently, there is also an inverse problem: for a higher frequency of electromagnetic radiation, the dimensions of elements l of the composite material must be smaller down to the nanoscale ones.
Micro-breakdown of fractals made of aluminum nanoislands with the dimensions of 100–1 000 nm
Let us consider in more detail the properties of fractal clusters for various sizes of aluminum nanoislands on the polymer threads made of benzene ring carbon fibers that have been previously discussed in [1–4].
The photographs of the polymer thread fragments with aluminum nanoislands (white color) are shown in Fig. 1 at different magnifications: a) 1 µm; b) 10 µm; c) 100 µm, d) 1000 µm. The photographs were made by the CAMSCAN-S4 scanning electron microscope with the energy-dispersive and wave-dispersive attachments: Oxford INCA Еnergy 350 and INCA Wave 700 (Сambridge, England) at the High Technology Center of the Synchrotron Shared Research Facility of the Federal State Unitary Enterprise “Lukin Research Institute for Physical Problems of the National Research Center “Kurchatov Institute” [1–4].
In Fig.1a (at a magnification of 1 µm), the aluminum nanoislands (white) of various sizes are clearly visible. They can be classified into two typical groups: the first one consists of elongated formations with the length of 100–1000 nm; the second one consists of spherical formations with a diameter of 10–30 nm. The sizes of aluminum nanoformations can have various effects on the conditions for a breakdown (discharge) over the Rusar polymer thread surface.
It should be noted that the distance broken down by a spark in the air depends on the electric field intensity at the surface of the electrodes and their shape. For the spheres which radius is much larger than the discharge gap, it is considered to be equal to 30 kV / cm, and for the needles with nanotips it will be 10 kV / cm [5].
Let us consider the thread structure filled along the polymer fibers with the conducting chains of irregular aluminum nanoislands with the dimensions of 100–1 000 nm and similar gaps between them. Such a geometric structure may be the reason for a strong decrease in the breakdown voltage of the polymer thread. For research, we will prepare a sample with the aluminum nanoisland dimensions of 100–1 000 nm and determine the voltage value when a discharge occurs (Fig. 2).
For an experiment, the sapphire substrates being the high-quality insulators, were used as the substrates for the array of aluminum nanoislands. When preparing a sample with an array of aluminum nanoislands on a sapphire substrate, the electron-beam lithography processes were used, including application of an electron-beam resist, pattern exposure, resist development, thin film application processes in a vacuum. Deposition of the bonding sites and aluminum nanoislands required an additional development of the remaining electron-beam resist in oxygen plasma and the surface cleaning.
After formation of the bonding sites (Fig. 3) using the electron beam lithography, the arrays of aluminum nanoislands with a thickness of up to 50 nm were generated in the gap (Fig. 4).
Then, the sampled structures with aluminum nanoislands on the rectangular sapphire substrates and an aluminum nanoisland array length of 1 cm between the bonding sites on both sides were studied. The size of the aluminum nanoisland was 122.7 nm, and the distance between the nanoislands was 64.49 nm (Fig. 4). The aluminum nanoislands on the sample were located in groups including from one to four nanoislands lengthwise (dark circles), with the several rows formed from them. The SEM image of the nanoisland array on the prepared sample is shown in Fig. 4.
The current-voltage characteristics (CVC) of samples with a set of aluminum nanoislands generated on a sapphire substrate were measured using the Curve Tracer IWATSU CS‑3200 setup. It was shown that when increasing the constant voltage to 25 V, there is no current in terms of the CVC, i. e. the nanoisland aluminum array on the sapphire substrate does not conduct current and the composite structure is an insulator.
Then, the samples were subject to the breakdown test by a voltage pulse on the developed setup. The sample pins were divided into two halves on each side (sample No.1 and sample No.2). To ensure breakdown, it was necessary to reduce the distance between the electrodes on the sample surface (the gap between the electrodes) and then recalculate it by 1 cm. As a result of the studies, it was determined that the discharge in the nanoisland aluminum array on the sapphire substrate occurred at a voltage of 8–12 kV/cm that corresponded to the known breakdown of a needle with a nanosized curvature radius at 10 kV/cm, i. e., a spark discharge [5].
Thus, the aluminum nanoislands with a size of 100–1000 nm at a voltage of 1.6 kV/cm cannot provide the conditions for the low-field electron emission discovered for the aluminum fractal clusters on the Rusar polymer thread.
Micro-breakdown of fractals made of aluminum nanoislands with the dimensions of 10–30 nm
It can be assumed that the micro-breakdown of polymer threads is related to the low-field emission of electrons during the impulse action with a duration of 1–2 ms on a polymer thread made of carbon benzene rings that occurs through the spherical aluminum nanoislands (nanodroplets, spheres) (Fig. 1a).
Let us consider the features of the Rusar polymer thread, on which the fractal clusters of aluminum nanodroplets are generated. The polymer thread with a diameter of ≈1 mm is made of aromatic polyamide fibers with a diameter of ≈10 μm, namely aramid (aromatic polyamide). Aramid is represented as a long chain of synthetic polyamide where 85% of the amide bonds are attached directly to two aromatic rings of carbon and benzene (C6H6) (Fig. 5a).
The modern concept of the electronic nature of bonds in benzene is based on the hypothesis of Linus Pauling who proposed to depict the benzene molecule as a hexagon with an inscribed circle (Fig.5b), thereby emphasizing the absence of fixed double bonds and the presence of a single electron cloud covering all six atoms of the carbon cycle (Fig. 5c). The side of the benzene hexagon is approximately ≈0.14 nm or 0.154 nm, the ring thickness is approximately equal to half the side of the hexagon, i. e. ≈0.07 nm, the outer diameter of the benzene ring is approximately ≈0.28 nm, and the inner diameter is abour ≈0.21 nm. It should be noted that the aluminum atom diameter is 0.286 nm, and the cross-sectional area along the diameter is 0.064 nm2.
Fig. 6 shows the photographs of the surface composition analysis of a polymer thread with aluminum nanoislands. Table 1 demonstrates that the basis of the polymer threads is carbon and oxygen, and the individual aluminum inclusions (light inclusions) appear on the surface. The measurements were performed at the Synchrotron Shared Research Facility of the Federal State Unitary Enterprise “Lukin Research Institute for Physical Problems of the National Research Center “Kurchatov Institute”.
In Fig. 1a, the spherical aluminum nanoislands (nanodroplets, spheres) with the dimensions of 10–30 nm are visible. They can combine several hundred carbon benzene rings and develop the nanosized aluminum/carbon benzene ring structures. In some part of such a structure, a “nanopoint” can be formed on the polymer thread surface.
Let us give an example of the generated spherical nanoformations when a solid surface is wetted with a liquid to develop the spherical droplets (Fig. 7), where A is the contact angle much greater than 90°. As a consequence, there is poor wetting (the droplet has an almost spherical shape and weak interaction with the solid surface, therefore. there is a decrease in the liquid contact area with it). B and C are the contact angles less than θ < 90°, the liquid droplets obtain a meniscus shape (better interaction with the solid surface, the contact area of the liquid is greater than in the example A). S is the contact angle θ = 0° (essentially it does not exist) with the complete wetting, when the liquid spreads over the solid surface, the contact area of the liquid with the solid surface in this case is the largest. The liquid spreading process is the limiting case of wetting.
To determine the surface area of an aluminum sphere (“nanodrop”), we use the following formula: S = 4πR2, where S is the surface area of the sphere; π is a constant equal to 3.14; R is the radius of the sphere. For an aluminum spherical “nanodrop” with a diameter of 30 nm (radius Rnk = 15 nm), the surface area will be equal to: Snk = 4πRnk2 = 2826.0 nm2.
If the contact area with the surface of a fiber made of carbone benzene rings under non-wettability conditions is one percent of the total area of the “nanodroplet” (scont = 28.26 nm2), then its contact radius is based on the area of the circle occupied by the sphere on the surface, scont = πrcont2 and will be approximately rcont = 3 nm. For example, several hundred aluminum atoms can be placed on such a contact area to generate a “nanoprobe” for several hundred carbon benzene rings and develop a “nanopoint” on the plane. If a high-voltage impulse with a duration of 1–3 ms is applied to such a “nanopoint”, then it can lead to the formation of conditions for the low-field emission of electrons from the carbon benzene ring.
The aluminum nanodroplets play the role of nanoprobes for applying a voltage impulse to the carbon benzene rings and presumable generation of “nanopoints” on the plane that contribute to the formation of conditions for the low-field emission of electrons from the polymer threads when a voltage of 1.6 kV is applied to the sample with the length of 1 cm and development of plasma. This results in the effect of “highly conductive off-surface state” (HCOSS) over the Rusar polymer thread. This composite structure on a polymer thread can have the properties of a metamaterial [6–8].
Thus, it can be considered that the fractals made of the spherical aluminum nanodroplets with a size of l = 2R = 10–30 nm are responsible for the formation of low-field electron emission. Ultimately, they develop plasma and the effect of off-surface highly-conductive state for electromagnetic radiation with the wavelength λ, provided that l = 2Rλ.
Skin-effect on the fractals made of aluminum nanoislands
It is important to note that the chains of aluminum nanoislands on a polymer thread are the continuous “nanoconductors” for ultra-high-frequency electromagnetic waves. However, for a constant voltage the polymer thread is a dielectric material, since there is no interaction of aluminum nanoislands. The papers [1–4] provide photographs of such composite materials that can be classified as the metamaterials with negative dielectric constant. For the polymer threads with aluminum nanoislands in the form of fractal clusters, the plasma frequency is approximately 1–10 THz.
If the low-field emission of electrons occurs on the basis of spherical aluminum nanodroplets with the radius R and the plasma is generated above the polymer thread surface, then the electromagnetic radiation with a wavelength λ can propagate through the aluminum nanoislands with a size much smaller than the wavelength, i. e. l = 2Rλ. For example, for a frequency of 10 THz = 1013 Hz, the wavelength will be approximately 30 μm, and the nanoisland size to ensure electromagnetic continuity can be 100 times smaller, i. e. 300 nm. In Fig. 1a, it is evident that the main dimensions of aluminum nanoislands are in the range of 10–1 000 nm, therefore, the frequencies above the plasma frequency of such a composite structure (1–10 THz) will freely propagate through the aluminum nanoislands.
It is interesting to note that for a wavelength of 30 nm, the minimum dimensions of the components will be 0.3 nm that is almost equal to the size of an aluminum atom or the diameter of a carbon benzene ring. The frequency in this case reaches 1016 Hz that corresponds to the boundary of X-ray and gamma radiation.
Let us consider the possibility of a skin-effect (or surface effect) on the fractal clusters related to a decrease in the amplitude of electromagnetic waves as they penetrate deep into the conducting medium. As a result of this effect, for example, the high-frequency alternating current flowing through a conductor is distributed not uniformly across the cross-section, but predominantly in the surface layer.
The skin effect mechanism (Fig. 8a) is associated with the development of electromagnetic oscillations in a resonance system and occurrence of alternating current in the conductor that generates an alternating vorticity magnetic field, the lines of force in which are perpendicular to the conductor axis. Due to the electromagnetic induction, the alternating magnetic field generates a vortex electric field, causing the flow of Foucault eddy current. Moreover, on the conductor surface, the eddy current moves in the direction of the conductor current, and inside the conductor, it has an opposite direction. This phenomenon reduces the current in the conductor core and increases the surface current.
The current density distribution in a cylindrical conductor in its cross section is shown in Fig. 8b. For alternating current, the current density is decreased exponentially from the surface into the conductor. The skin layer thickness is determined as the depth from the surface at which the current density is decreased to 1/e (about 37%) of the surface value. This thickness depends on the current frequency and the electrical and magnetic properties of the conductor. The skin effect mechanism is shown in Fig. 9.
The current distribution inside the conductor is of exponential nature, therefore, at the first approximation, it can be considered that the electric current has a relatively uniform dependence only in the surface layer (that is called the skin layer), and in the remaining cross-section it is so small that it can be neglected. Consequently, in the polymer thread samples, the ultra-high-frequency electromagnetic wave of the terahertz range is propagated over the aramid surface through the aluminum nanoislands.
For example, the the skin layer thickness (depth) for the polymer thread samples with a diameter of 1 mm made of aramid fibers with the chains of irregular aluminum nanoislands at a frequency of 5 THz will be δ = 40 nm and corresponds to the thickness of aluminum nanoislands.
It was established that in the experiments with polymer threads with the length of 1 cm, a breakdown occurred with a voltage pulse of 1.6 kV with a duration of 1–3 ms. However, after several high voltage connections (from 3 to 5 times) and occurrence of a breakdown, the breakdown was already absent with the following connections. The photographs of the polymer thread surface after the breakdown (Fig. 10) show the melted aluminum nanoislands. The spherical aluminum nanodroplets have spread out completely, i. e. disappeared that leads to the cessation of low-field electron emission and the absence of off-surface highly-conductive state in the form of plasma.
During the experiment it was determined that in the case of electrical breakdown in air, the polymer threads with nanoisland aluminum metallization did not burn out. The ends of the polymer thread attached to the electrodes to which the voltage was applied for electrical breakdown were slightly charred.
It should be noted that plasma is an ionized gas, one of the four classical aggregate states of matter. It contains free electrons, as well as positive and negative ions. Since the charged particles in plasma are mobile, the plasma has the ability to conduct electric current. In the fixed condition, plasma screens a constant external electric field due to the spatial separation of charges.
It should be noted that a spark discharge is a non-steady form of electric discharge (electric current) occurring in the gases. The distance broken down by a spark in the air depends on the electric field strength at the surface of the electrodes and their shape. In natural conditions, the spark discharges occur in the form of lightning. The temperature in the main channel of a spark discharge can reach 10,000 K [5].
In addition, high temperature leads to the partial melting of aluminum nanoislands during the pulse that can result in development of the liquid metal Rehbinder effect. This effect is based on the concept of possible localization of the electromagnetic field in the folds of the interface between the phases and components of the liquid eutectic mixture filling the cracks in the solid metal surface. Since three various substances (homogeneous Al melt, solid Al and solid polymer fiber) are adjacent at each spatial point, the fold system of such an interface is simulated by the Brauer structure well-known in topology, namely a surface separating three various regions at each of its points. With the liquid metal Rehbinder effect [9], the localized light can be emitted.
Conclusions for Part 1
It can be assumed that the metal fractal clusters made of spherical aluminum nanodroplets with a radius of R = 10–30 nm on the surface of polymer threads made of carbon benzene ring fibers are responsible for the generation of low-field electron emission. Ultimately, they develop plasma and the effect of “off-surface highly-conductive state” for electromagnetic radiation with a wavelength λ, provided that l = 2R << λ.
An ultra-high-frequency electromagnetic wave of the terahertz range propagates over the polymer thread surface through the metal fractal clusters made of aluminum nanoislands. The skin layer thickness (depth) for a polymer thread with a diameter of 1 mm made of aramid fibers with the chains of irregular aluminum nanoislands, for example, at a frequency of 5 THz is δ = 40 nm in a layer of aluminum nanoislands that corresponds approximately to their thickness.
The composite materials made of the polymer threads with metal fractal clusters considered in the article can be classified as the metamaterials with negative dielectric constant [6]. However, it is possible to develop both the composites on the polymer threads with the negative magnetic permeability [7], as well as the composites with simultaneously negative dielectric constant and magnetic permeability [8].
Funding
The study was supported by the Russian Science Foundation, grant No. 24-29-00129, https://rscf.ru/project/24-29-00129/.
In the second part of the article, we will consider the Interaction of Optical Radiation with Metal Fractal Clusters.
AUTHOR
Maltsev Petr P., Doctor of Technical Sciences, Professor, Chief Researcher,
Inter-agency Center of Analytical Studies of the RAS, Moscow, Russia.; e-mail: p.p.maltsev@mail.ru
Part 1
P. P. Maltsev
Inter-agency Center of Analytical Studies of the RAS, Moscow, Russia
This paper provides the results of studies on the influence of the aluminum nanoisland dimensions with a length l during the fractal cluster formation on the polymer threads using the carbon benzene ring fibers on the conditions for the occurrence of “highly conductive off-surface state” during breakdown with an electric field strength of 1.6 kV/cm. The layer thickness was calculated in the case of the skin-effect in polymer threads with the metal fractal clusters for electromagnetic radiation with a wavelength λ and fulfillment of condition l << λ.
Key words: metal fractal clusters, nanoscale aluminum droplets, polymer threads, plasma, off-surface highly conductive state, photon localization
Article received: 16.01.2025
Article accepted: 03.02.2025
Skin-Effect in the Polymer Threads with the Metal Fractal Clusters
It should be noted that in 1999 John Pendry proposed an approach to describing the specific artificially created materials based on the fact that if a composite material consists of discrete scattering elements which size l is much smaller than the radiation wavelength λ, then electrodynamically it can be considered as continuous within a limited frequency band, provided that l << λ.
In other words, a physical medium will be continuous in the electromagnetic sense if its properties can be described by the average parameters changing on a scale much larger than the dimensions of the components forming the material. Consequently, there is also an inverse problem: for a higher frequency of electromagnetic radiation, the dimensions of elements l of the composite material must be smaller down to the nanoscale ones.
Micro-breakdown of fractals made of aluminum nanoislands with the dimensions of 100–1 000 nm
Let us consider in more detail the properties of fractal clusters for various sizes of aluminum nanoislands on the polymer threads made of benzene ring carbon fibers that have been previously discussed in [1–4].
The photographs of the polymer thread fragments with aluminum nanoislands (white color) are shown in Fig. 1 at different magnifications: a) 1 µm; b) 10 µm; c) 100 µm, d) 1000 µm. The photographs were made by the CAMSCAN-S4 scanning electron microscope with the energy-dispersive and wave-dispersive attachments: Oxford INCA Еnergy 350 and INCA Wave 700 (Сambridge, England) at the High Technology Center of the Synchrotron Shared Research Facility of the Federal State Unitary Enterprise “Lukin Research Institute for Physical Problems of the National Research Center “Kurchatov Institute” [1–4].
In Fig.1a (at a magnification of 1 µm), the aluminum nanoislands (white) of various sizes are clearly visible. They can be classified into two typical groups: the first one consists of elongated formations with the length of 100–1000 nm; the second one consists of spherical formations with a diameter of 10–30 nm. The sizes of aluminum nanoformations can have various effects on the conditions for a breakdown (discharge) over the Rusar polymer thread surface.
It should be noted that the distance broken down by a spark in the air depends on the electric field intensity at the surface of the electrodes and their shape. For the spheres which radius is much larger than the discharge gap, it is considered to be equal to 30 kV / cm, and for the needles with nanotips it will be 10 kV / cm [5].
Let us consider the thread structure filled along the polymer fibers with the conducting chains of irregular aluminum nanoislands with the dimensions of 100–1 000 nm and similar gaps between them. Such a geometric structure may be the reason for a strong decrease in the breakdown voltage of the polymer thread. For research, we will prepare a sample with the aluminum nanoisland dimensions of 100–1 000 nm and determine the voltage value when a discharge occurs (Fig. 2).
For an experiment, the sapphire substrates being the high-quality insulators, were used as the substrates for the array of aluminum nanoislands. When preparing a sample with an array of aluminum nanoislands on a sapphire substrate, the electron-beam lithography processes were used, including application of an electron-beam resist, pattern exposure, resist development, thin film application processes in a vacuum. Deposition of the bonding sites and aluminum nanoislands required an additional development of the remaining electron-beam resist in oxygen plasma and the surface cleaning.
After formation of the bonding sites (Fig. 3) using the electron beam lithography, the arrays of aluminum nanoislands with a thickness of up to 50 nm were generated in the gap (Fig. 4).
Then, the sampled structures with aluminum nanoislands on the rectangular sapphire substrates and an aluminum nanoisland array length of 1 cm between the bonding sites on both sides were studied. The size of the aluminum nanoisland was 122.7 nm, and the distance between the nanoislands was 64.49 nm (Fig. 4). The aluminum nanoislands on the sample were located in groups including from one to four nanoislands lengthwise (dark circles), with the several rows formed from them. The SEM image of the nanoisland array on the prepared sample is shown in Fig. 4.
The current-voltage characteristics (CVC) of samples with a set of aluminum nanoislands generated on a sapphire substrate were measured using the Curve Tracer IWATSU CS‑3200 setup. It was shown that when increasing the constant voltage to 25 V, there is no current in terms of the CVC, i. e. the nanoisland aluminum array on the sapphire substrate does not conduct current and the composite structure is an insulator.
Then, the samples were subject to the breakdown test by a voltage pulse on the developed setup. The sample pins were divided into two halves on each side (sample No.1 and sample No.2). To ensure breakdown, it was necessary to reduce the distance between the electrodes on the sample surface (the gap between the electrodes) and then recalculate it by 1 cm. As a result of the studies, it was determined that the discharge in the nanoisland aluminum array on the sapphire substrate occurred at a voltage of 8–12 kV/cm that corresponded to the known breakdown of a needle with a nanosized curvature radius at 10 kV/cm, i. e., a spark discharge [5].
Thus, the aluminum nanoislands with a size of 100–1000 nm at a voltage of 1.6 kV/cm cannot provide the conditions for the low-field electron emission discovered for the aluminum fractal clusters on the Rusar polymer thread.
Micro-breakdown of fractals made of aluminum nanoislands with the dimensions of 10–30 nm
It can be assumed that the micro-breakdown of polymer threads is related to the low-field emission of electrons during the impulse action with a duration of 1–2 ms on a polymer thread made of carbon benzene rings that occurs through the spherical aluminum nanoislands (nanodroplets, spheres) (Fig. 1a).
Let us consider the features of the Rusar polymer thread, on which the fractal clusters of aluminum nanodroplets are generated. The polymer thread with a diameter of ≈1 mm is made of aromatic polyamide fibers with a diameter of ≈10 μm, namely aramid (aromatic polyamide). Aramid is represented as a long chain of synthetic polyamide where 85% of the amide bonds are attached directly to two aromatic rings of carbon and benzene (C6H6) (Fig. 5a).
The modern concept of the electronic nature of bonds in benzene is based on the hypothesis of Linus Pauling who proposed to depict the benzene molecule as a hexagon with an inscribed circle (Fig.5b), thereby emphasizing the absence of fixed double bonds and the presence of a single electron cloud covering all six atoms of the carbon cycle (Fig. 5c). The side of the benzene hexagon is approximately ≈0.14 nm or 0.154 nm, the ring thickness is approximately equal to half the side of the hexagon, i. e. ≈0.07 nm, the outer diameter of the benzene ring is approximately ≈0.28 nm, and the inner diameter is abour ≈0.21 nm. It should be noted that the aluminum atom diameter is 0.286 nm, and the cross-sectional area along the diameter is 0.064 nm2.
Fig. 6 shows the photographs of the surface composition analysis of a polymer thread with aluminum nanoislands. Table 1 demonstrates that the basis of the polymer threads is carbon and oxygen, and the individual aluminum inclusions (light inclusions) appear on the surface. The measurements were performed at the Synchrotron Shared Research Facility of the Federal State Unitary Enterprise “Lukin Research Institute for Physical Problems of the National Research Center “Kurchatov Institute”.
In Fig. 1a, the spherical aluminum nanoislands (nanodroplets, spheres) with the dimensions of 10–30 nm are visible. They can combine several hundred carbon benzene rings and develop the nanosized aluminum/carbon benzene ring structures. In some part of such a structure, a “nanopoint” can be formed on the polymer thread surface.
Let us give an example of the generated spherical nanoformations when a solid surface is wetted with a liquid to develop the spherical droplets (Fig. 7), where A is the contact angle much greater than 90°. As a consequence, there is poor wetting (the droplet has an almost spherical shape and weak interaction with the solid surface, therefore. there is a decrease in the liquid contact area with it). B and C are the contact angles less than θ < 90°, the liquid droplets obtain a meniscus shape (better interaction with the solid surface, the contact area of the liquid is greater than in the example A). S is the contact angle θ = 0° (essentially it does not exist) with the complete wetting, when the liquid spreads over the solid surface, the contact area of the liquid with the solid surface in this case is the largest. The liquid spreading process is the limiting case of wetting.
To determine the surface area of an aluminum sphere (“nanodrop”), we use the following formula: S = 4πR2, where S is the surface area of the sphere; π is a constant equal to 3.14; R is the radius of the sphere. For an aluminum spherical “nanodrop” with a diameter of 30 nm (radius Rnk = 15 nm), the surface area will be equal to: Snk = 4πRnk2 = 2826.0 nm2.
If the contact area with the surface of a fiber made of carbone benzene rings under non-wettability conditions is one percent of the total area of the “nanodroplet” (scont = 28.26 nm2), then its contact radius is based on the area of the circle occupied by the sphere on the surface, scont = πrcont2 and will be approximately rcont = 3 nm. For example, several hundred aluminum atoms can be placed on such a contact area to generate a “nanoprobe” for several hundred carbon benzene rings and develop a “nanopoint” on the plane. If a high-voltage impulse with a duration of 1–3 ms is applied to such a “nanopoint”, then it can lead to the formation of conditions for the low-field emission of electrons from the carbon benzene ring.
The aluminum nanodroplets play the role of nanoprobes for applying a voltage impulse to the carbon benzene rings and presumable generation of “nanopoints” on the plane that contribute to the formation of conditions for the low-field emission of electrons from the polymer threads when a voltage of 1.6 kV is applied to the sample with the length of 1 cm and development of plasma. This results in the effect of “highly conductive off-surface state” (HCOSS) over the Rusar polymer thread. This composite structure on a polymer thread can have the properties of a metamaterial [6–8].
Thus, it can be considered that the fractals made of the spherical aluminum nanodroplets with a size of l = 2R = 10–30 nm are responsible for the formation of low-field electron emission. Ultimately, they develop plasma and the effect of off-surface highly-conductive state for electromagnetic radiation with the wavelength λ, provided that l = 2Rλ.
Skin-effect on the fractals made of aluminum nanoislands
It is important to note that the chains of aluminum nanoislands on a polymer thread are the continuous “nanoconductors” for ultra-high-frequency electromagnetic waves. However, for a constant voltage the polymer thread is a dielectric material, since there is no interaction of aluminum nanoislands. The papers [1–4] provide photographs of such composite materials that can be classified as the metamaterials with negative dielectric constant. For the polymer threads with aluminum nanoislands in the form of fractal clusters, the plasma frequency is approximately 1–10 THz.
If the low-field emission of electrons occurs on the basis of spherical aluminum nanodroplets with the radius R and the plasma is generated above the polymer thread surface, then the electromagnetic radiation with a wavelength λ can propagate through the aluminum nanoislands with a size much smaller than the wavelength, i. e. l = 2Rλ. For example, for a frequency of 10 THz = 1013 Hz, the wavelength will be approximately 30 μm, and the nanoisland size to ensure electromagnetic continuity can be 100 times smaller, i. e. 300 nm. In Fig. 1a, it is evident that the main dimensions of aluminum nanoislands are in the range of 10–1 000 nm, therefore, the frequencies above the plasma frequency of such a composite structure (1–10 THz) will freely propagate through the aluminum nanoislands.
It is interesting to note that for a wavelength of 30 nm, the minimum dimensions of the components will be 0.3 nm that is almost equal to the size of an aluminum atom or the diameter of a carbon benzene ring. The frequency in this case reaches 1016 Hz that corresponds to the boundary of X-ray and gamma radiation.
Let us consider the possibility of a skin-effect (or surface effect) on the fractal clusters related to a decrease in the amplitude of electromagnetic waves as they penetrate deep into the conducting medium. As a result of this effect, for example, the high-frequency alternating current flowing through a conductor is distributed not uniformly across the cross-section, but predominantly in the surface layer.
The skin effect mechanism (Fig. 8a) is associated with the development of electromagnetic oscillations in a resonance system and occurrence of alternating current in the conductor that generates an alternating vorticity magnetic field, the lines of force in which are perpendicular to the conductor axis. Due to the electromagnetic induction, the alternating magnetic field generates a vortex electric field, causing the flow of Foucault eddy current. Moreover, on the conductor surface, the eddy current moves in the direction of the conductor current, and inside the conductor, it has an opposite direction. This phenomenon reduces the current in the conductor core and increases the surface current.
The current density distribution in a cylindrical conductor in its cross section is shown in Fig. 8b. For alternating current, the current density is decreased exponentially from the surface into the conductor. The skin layer thickness is determined as the depth from the surface at which the current density is decreased to 1/e (about 37%) of the surface value. This thickness depends on the current frequency and the electrical and magnetic properties of the conductor. The skin effect mechanism is shown in Fig. 9.
The current distribution inside the conductor is of exponential nature, therefore, at the first approximation, it can be considered that the electric current has a relatively uniform dependence only in the surface layer (that is called the skin layer), and in the remaining cross-section it is so small that it can be neglected. Consequently, in the polymer thread samples, the ultra-high-frequency electromagnetic wave of the terahertz range is propagated over the aramid surface through the aluminum nanoislands.
For example, the the skin layer thickness (depth) for the polymer thread samples with a diameter of 1 mm made of aramid fibers with the chains of irregular aluminum nanoislands at a frequency of 5 THz will be δ = 40 nm and corresponds to the thickness of aluminum nanoislands.
It was established that in the experiments with polymer threads with the length of 1 cm, a breakdown occurred with a voltage pulse of 1.6 kV with a duration of 1–3 ms. However, after several high voltage connections (from 3 to 5 times) and occurrence of a breakdown, the breakdown was already absent with the following connections. The photographs of the polymer thread surface after the breakdown (Fig. 10) show the melted aluminum nanoislands. The spherical aluminum nanodroplets have spread out completely, i. e. disappeared that leads to the cessation of low-field electron emission and the absence of off-surface highly-conductive state in the form of plasma.
During the experiment it was determined that in the case of electrical breakdown in air, the polymer threads with nanoisland aluminum metallization did not burn out. The ends of the polymer thread attached to the electrodes to which the voltage was applied for electrical breakdown were slightly charred.
It should be noted that plasma is an ionized gas, one of the four classical aggregate states of matter. It contains free electrons, as well as positive and negative ions. Since the charged particles in plasma are mobile, the plasma has the ability to conduct electric current. In the fixed condition, plasma screens a constant external electric field due to the spatial separation of charges.
It should be noted that a spark discharge is a non-steady form of electric discharge (electric current) occurring in the gases. The distance broken down by a spark in the air depends on the electric field strength at the surface of the electrodes and their shape. In natural conditions, the spark discharges occur in the form of lightning. The temperature in the main channel of a spark discharge can reach 10,000 K [5].
In addition, high temperature leads to the partial melting of aluminum nanoislands during the pulse that can result in development of the liquid metal Rehbinder effect. This effect is based on the concept of possible localization of the electromagnetic field in the folds of the interface between the phases and components of the liquid eutectic mixture filling the cracks in the solid metal surface. Since three various substances (homogeneous Al melt, solid Al and solid polymer fiber) are adjacent at each spatial point, the fold system of such an interface is simulated by the Brauer structure well-known in topology, namely a surface separating three various regions at each of its points. With the liquid metal Rehbinder effect [9], the localized light can be emitted.
Conclusions for Part 1
It can be assumed that the metal fractal clusters made of spherical aluminum nanodroplets with a radius of R = 10–30 nm on the surface of polymer threads made of carbon benzene ring fibers are responsible for the generation of low-field electron emission. Ultimately, they develop plasma and the effect of “off-surface highly-conductive state” for electromagnetic radiation with a wavelength λ, provided that l = 2R << λ.
An ultra-high-frequency electromagnetic wave of the terahertz range propagates over the polymer thread surface through the metal fractal clusters made of aluminum nanoislands. The skin layer thickness (depth) for a polymer thread with a diameter of 1 mm made of aramid fibers with the chains of irregular aluminum nanoislands, for example, at a frequency of 5 THz is δ = 40 nm in a layer of aluminum nanoislands that corresponds approximately to their thickness.
The composite materials made of the polymer threads with metal fractal clusters considered in the article can be classified as the metamaterials with negative dielectric constant [6]. However, it is possible to develop both the composites on the polymer threads with the negative magnetic permeability [7], as well as the composites with simultaneously negative dielectric constant and magnetic permeability [8].
Funding
The study was supported by the Russian Science Foundation, grant No. 24-29-00129, https://rscf.ru/project/24-29-00129/.
In the second part of the article, we will consider the Interaction of Optical Radiation with Metal Fractal Clusters.
AUTHOR
Maltsev Petr P., Doctor of Technical Sciences, Professor, Chief Researcher,
Inter-agency Center of Analytical Studies of the RAS, Moscow, Russia.; e-mail: p.p.maltsev@mail.ru
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