WO2012030242A1

WO2012030242A1 - Metamaterials and a method for obtaining them

Info

Publication number: WO2012030242A1
Application number: PCT/PL2011/000114
Authority: WO
Inventors: Przemyslaw Zaprzalski
Original assignee: Nano-Tech Sp. Z.O.O.
Priority date: 2010-08-31
Filing date: 2011-10-31
Publication date: 2012-03-08
Also published as: PL220209B1; PL392282A1; WO2012030242A8

Abstract

The invention relates to novel metamaterials which are polymer composites containing from 0.5 wt% to 45 wt% of copper flakes and /or nanoflakes in polymer matrix as compared to polymer matrix. The invention pertains also to the method for obtaing novel metamaterials which consists in : a) obtaining copper foil or nanofoil in the process of acid copper salt solution electrolysis using pulse current, b) removing the copper foil from metallic base, c) mixing it with polymer and d) composite molding. Polymer composites obtained by the method according to the invention exhibit the properties characteristic of metamaterials which means that they show diamagnetic (smaller than unity) effective magnetic permeability and very large (in-plane) effective permittivity.

Description

METAMATERIALS AND A METHOD FOR OBTAINING THEM

The invention pertains to novel metamaterials and method for obtaining novel metamaterials.

Metamaterials exhibit novel, specific and unique electromagnetic properties and can be used in the range of electromagnetic waves as low as microwave up to optical frequencies. The interest in metamaterials has been growing fast which has resulted in the increasing number of publications devoted to this subject matter.

Metamaterials might be used for example for construction of efficient and smaller aerials and other telecommunications devices, production of new generation sensors, electronic and optical systems integration which will increase the speed with which the data are being processed in computers, increasing data density of optical carriers or development of enhanced resolution optical lithography.

As described in the paper by Krupka et al. Meas. Sci. Technol. 20 (2009) 105702 the properties of metamaterials are defined rather by their structure than their composition. Metamaterials composed of dielectrics and metals constitute one of important group of metamaterials. Metamaterials of this kind show diamagnetic (smaller than unity) effective magnetic permeability and very large (in-plane) effective permittivity. The first effect is attributed to eddy currents induced in conductive metal inclusions whereas the second effect, i.e. an enhancement of dielectric constant is caused by large capacitances between adjacent conductive layers.

However, industrial manufacturing of metamaterials which exhibit diamagnetic (smaller than unity) magnetic permeability and very large (in-plane) permittivity constitutes a technical problem nowadays.

One of the methods for obtaining metamaterials has been described in the US patent application number 2009/0206963 Al. The method consists in placing a number of resonant circuits on the dielectric base. The method for obtaining metamaterials which consists in producing units of electromagnetically active circuits made of electrically conducting materials on one side of non-conducting material base has been described in the US patent application 2004/0151876 Al .

For example in the US patent application 2009/0040131 Al a method for producing optical materials is described in which metamaterials are obtained from coupled magnetic and dielectric multi-resonance discs (cylinders) units or multi-surface grates arranged in a periodic or chaotic manner in order to achieve expected magnetic and dielectric dipole quantity. In another patent application EP 1 975 656 Al a method for obtaining metamaterials in which metal nanopowder dispersion systems in nematic liquid crystal has been presented.

As has been shown in the reference literature the methods for obtaining metamaterials are most frequently based on traditional production methods used in contemporary microelectronics. These methods are noted for relatively high investment and operational costs. They are also burdened with physical restrictions, for example lithography may be used only to print micro-resonators the size of which is larger than 1 micrometer. In case of smaller devices other methods have to be used which are as a rule more time-consuming and thus less efficient.

The present invention has the advantage over the foregoing methods because the novel metamaterials meet the requirements for this type of products, and the method in which they are obtained may be used at a large scale and the time needed to produce novel materials according to the invention is significantly shortened so the efficiency of the process according to the invention is incomparably higher than in case of prior art methods.

Novel metamaterials according to the invention are polymer composites which contain from 0.1 wt% to 55 wt% of copper flakes and /or nano flakes in polymer matrix as compared to polymer matrix.

It is advantageous that the polymer matrix of novel metamaterials according to the invention consists of ethylene-vinyl acetate (EVA), halogen free flame retardant ethylene- vinyl acetate (HFFR/EVA), polyvinyl chloride (PVC), polymethyl methacrylate (PMMA) and polyacrylonitrile (PAN), polyethylene (PE), polypropylene (PP), polystyrene (PS), polybutadiene (PBA) or their copolymers, polyamide, polyacrolein, polyurethane, polyether or polyester.

Advantageously, the metamaterials according to the invention contain copper flakes and/or nanoflakes of a diameter from 1 micrometer to 500 micrometers and thickness ranging from 80 nm to 2000 run.

Advantageously, the metamaterials according to the invention contain copper flakes and/or nanoflakes quantity of which ranges from 0.5 wt% to 45 wt%.

The invention provides also a method for obtaining novel metamaterials which is realized in the following stages: - at the first stage copper foil or nano-foil is deposited on metallic cathode as a result of acid copper salt solution current pulse electrolysis,

- the second stage consists in mechanical removal of copper foil from the metallic cathode base and grinding it into flakes, - at the third stage polymer and copper flakes are mixed at weight ratio of, respectively 99.5-55 : 0.5-45

- at the fourth stage a composite is formed from the obtained mixture using molding conditions suitable for polymer matrix.

Advantageously, the copper foil or nano-foil is obtained from aqueous solution of copper sulfate and sulfuric acid.

Advantageously, the copper foil or nano-foil is obtained by current pulse electrolysis with or without changing current direction.

Advantageously, in the method according to the invention, electrolyte containing copper (II) of concentration higher than 0.1 g dm^"3 is used. Advantageously, the copper foil or nano-foil is obtained by cathodic pulse the current density of which is i_c = 0.001÷0.100 A/cm² in time t_c 0.005÷600 s.

Advantageously, the copper foil or nano-foil is obtained by electrolysis using mobile or stationary steel cathode in the shape of a metal sheet or foil.

It is also advantageous that the copper foil and nano-foil is obtained by the electrolysis using an anode in the shape of copper plate.

Advantageously, the electrolysis process is conducted in the range of temperatures from 18-60°C.

In the method according to the invention the process of obtaining copper foil is advantageously realized using current pulses presented in Figure 1 from a) to f): a) pulse electrolysis without current direction change: cathodic current pulse

Zc = 0.001÷0.100 A/cm² and time t_c = 0.005÷600 s

or b) pulse electrolysis without current direction change: cathodic current pulses i_c - 0.001÷0.100 A/cm and time t_c = 0.005÷600 s, with current interruptions , and the interruption duration is at least 50% shorter than t_c

or

c) pulse electrolysis without current direction change: cathodic current pulses /_c = 0.001÷0.100 A/cm and time t_c = 0.005÷600 s, with current interruptions, and the interruption duration is at least 50% shorter than t_c as well as the first cathodic current is larger than the following ones: z^' _cl > i_ci

or

d) pulse electrolysis with current direction change: cathodic current pulse _c = 0.001÷0.100 A/cm² and time t_c = 0.005÷600 s, next anodic current pulse | i_c \ > \ \ ; t_c > t_a with anodic current pulse i_a in the range of anodic current densities 0.001÷0.050 A/cm² and time t_a from 0.005÷550 s

or

e) pulse electrolysis with current direction change, cycles: cathodic current pulse i_c and time tc, and then anodic current pulse | i_c | > | _a | ; t_c > t_a

or

f) combination of pulse electrolysis with current interruption with the pulse electrolysis with current direction change - alternating cycles: cathodic current pulse, interruption, anodic current pulse, interruption.

The number of performed/used cycles is chosen depending on the assumed thickness of metallic copper layer that is being produced (the one from which flakes that constitute the metamaterials ingredient are obtained) and the current density of each current pulse. According to Faraday's laws (of electrolysis) the larger is the current density of one cycle the shorter is the cycle time and fewer number of cycles is needed to obtain a layer of required thickness. For example in order to obtain a layer the thickness of which is about 400 nm there may be used 3 anodic cycles and 3 cathodic ones.

This method enables to control the thickness and structure of copper foil deposited on metal base. Moreover, using anodic cycles enables to obtain layers (of copper flakes) of appropriate structure because in an anodic cycle in which mainly dendrites are removed, a process of electrochemical polishing takes place. In polymer composite according to the invention copper flakes replace printed circuit systems obtained using the foregoing well-known methods characteristic of microelectronics.

An example of SEM image showing the copper foil the thickness of which is from 350 nm to 400 nm obtained as a result of the electrolysis described in Fig. 1 f is presented in Figure 2. Fig. 1 shows different kinds of current pulses used in the copper foil obtaining process: z_c - cathodic current pulses, _a - anodic current pulses, t_c - cathodic pulse time, t_a - anodic pulse time. Figure 3 is a SEM image of a polymer composite plate the thickness of which is 0.6 mm composed of flame retardant polymer matrix containing halogen free ethylene-vinyl acetate (HFFR/EVA) and 4.8 wt% addition of 450 nm-thick copper flakes. As seen in Fig.3 the novel method for obtaining metamaterials presented in this patent application enables regular copper flakes distribution (light lines and points in Fig.3) in polymer matrix (grey area). This structure present in obtained polymer composites is responsible for properties characteristic of metamaterials. Example 1.

A cathode/working electrode made of stainless steel of an area of approximately 8 cm and an anode/reference electrode in the shape of copper plate the area of which is approximately 100 cm² and thickness 0.1 cm are placed in a electrochemical cell thermostated to 25°C. The cell is filled with an electrolyte composed of: 46 g dm^"3 Cu, 170 g dm^"3 H₂S0₄. The electrodes are connected with a BNC connector to a measuring device - Autolab GSTST30 galvanostat linked to PC computer equipped with GPES software by Eco Chemie. The software enables to set a measurement procedure in which the length of each current pulse and current of each pulse in the range from + 1A do -1A are entered. During the electrolysis when the current pulse is applied the potential changes with time are registered.

Parameters of electrolysis using current pulses with reversed current direction:

iic= -0.025 A/cm² t_jc = 30 s

iia = +0.025 A/cm² t_{l a} = 3 s

i_2c = -0.01875 A/cm² t_2c = 10 s

i_2a = +0.025 A/cm² t_2a = 3 s

i_3c = -0.015 A/cm² t_3c = 10 s i_3a = +0.025 A/cm² t_3a = 3 s

After electrochemical deposition of copper on the electrode, the structure and the dimensions of the copper foil were analyzed using a scanning electron microscope and it was found that its thickness is 300±50 nm. Analysis of the energy dispersion spectrum (EDS) showed only the lines characteristic of copper which confirms the purity of the obtained product.

The copper foil obtained in an electrochemical process was ground beforehand and then mixed mechanically in a ribbon mixer with halogen free flame retardant polymer containing halogen free flame retardant ethylene-vinyl acetate (HFFR/EVA). Copper concentration was 5 wt%. Then the mixture prepared in this way underwent an extrusion process in a malleable state in an electrically heated twin screw extruder for 10 minutes at 165°C. The obtained pellets/beads were pressed using hydraulic press in order to obtain 0.55 mm-thick samples. Electromagnetic properties of the obtained sample plates: the complex permeability μ and complex permittivity (ε) for the same sample were measured using the split post dielectric resonator method at frequency 4.8 GHz and they are presented in the Table below. It was found that the obtained value of magnetic permeability real μ is typical of metamaterials:

Example 2.

A cathode/working electrode made of stainless steel of an area of approximately 8 cm² and an anode/reference electrode in the shape of copper plate the area of which is approximately 100 cm² and thickness 0.1 cm are placed in a electrochemical cell thermostated to 25°C. The cell is filled with an electrolyte composed of 46 g dm^" Cu, 170 g dm^"3 H2SO₄. The electrodes are connected with a BNC connector to a measuring device - Autolab GSTST30 galvanostat linked to PC computer equipped with GPES software by Eco Chemie. The software enables to set a measurement procedure in which the length of each current pulse and current of each pulse in the range from + 1A do -1A are entered. During the electrolysis when the current pulse is applied the potential changes with time are registered.

Parameters of electrolysis using current pulses with the reversed current direction were: iic= -0.025 A/cm² tlc = 30 s

l2c = -0.01875 A/cm² t_2c = 10 s

l2a = +0.025 A/cm² t_2a = 3 s

l3c = -0.015 A/cm² t_3c = 10 s

l3a = +0.025 A/cm² t3a = 3 s

The copper foil obtained in an electrochemical process was ground beforehand and then mixed mechanically in a ribbon mixer with halogen free flame retardant polymer containing halogen free flame retardant ethylene-vinyl acetate (HFFR/EVA). Copper concentration was 40 wt%. Then the mixture prepared in this way underwent an extrusion process in a malleable state in an electrically heated twin screw extruder for 10 minutes at 165°C. The obtained pellets/beads were pressed using hydraulic press in order to obtain 0.55 mm-thick samples. Electromagnetic properties of the obtained sample plates: the complex permeability μ and complex permittivity (ε) for the same sample were measured using the split post dielectric resonator method at frequency 4.8 GHz and presented in the Table below. It was found that the obtained value of magnetic permeability real μ is typical of metamaterials:

Example 3. A cathode/working electrode made of stainless steel of an area of approximately 8 cm² and an anode/reference electrode in the shape of copper plate the area of which is approximately 100 cm² and thickness 0.1 cm are placed in a electrochemical cell thermostated to 25°C. The cell is filled with an electrolyte composed of 46 g dm^"3 Cu, 170 g dm^"3 H₂S0₄ The electrodes are connected with a BNC connector to a measuring device - Autolab GSTST30 galvanostat linked to PC computer equipped with GPES software by Eco Chemie. The software enables to set a measurement procedure in which the length of each current pulse and current of each pulse in the range from + 1A do -1A are entered. During the electrolysis when the current pulse is applied the potential changes with time are registered.

Parameters of the electrolysis using current pulses with the reversed current direction were: iic= -0.025 A/cm² t_k = 30 s

i = +0.025 A/cm² t_Ja = 3 s

i_2c = -0.01875 A/cm² t_2c = 10 s

i_2a = +0.025 A/cm² t_2a = 3 s

i_3c= -0.015 A/cm² t_3c = 10 s

i_3a = +0.025 A/cm² t_3a = 3 s

After electrochemical deposition of copper on the electrode, the structure and the dimensions of the copper foil were analyzed using a scanning electron microscope and it was found that its thickness is 300+50 nm. Analysis of the energy dispersion spectrum (EDS) showed only the lines characteristic of copper which confirms the purity of the obtained product.

The copper foil obtained in an electrochemical process was ground beforehand and then mixed mechanically in a ribbon mixer with halogen free flame retardant polymer containing halogen free flame retardant ethylene-vinyl acetate (HFFR/EVA). Copper concentration was 1 wt%. Then the mixture prepared in this way underwent an extrusion process in a malleable state in an electrically heated twin screw extruder for 10 minutes at 165°C. The obtained pellets/beads were pressed using hydraulic press in order to obtain 0.55 mm-thick samples. Electromagnetic properties of the obtained sample plates: the complex permeability μ and complex permittivity (ε) for the same sample were measured using the split post dielectric resonator method at frequency 4.8 GHz and they are presented in the Table below. It was found that the obtained value of magnetic permeability real μ is typical of metamaterials: 4.8 GHz

Concentration of Cu real(s) real^) imag(e) imag(μ) flakes wt %

1 3.58 0.999 0.0106 0.004

Example 4.

A cathode/working electrode made of stainless steel of an area of approximately 8 cm² and an anode/reference electrode in the shape of copper plate the area of which is approximately 100 cm² and thickness 0.1 cm are placed in a electrochemical cell thermostated to 25°C. The cell is filled with an electrolyte composed of 46 g dm^"3 Cu, 170 g dm^"3 H2SO4. The electrodes are connected with a BNC connector to a measuring device - Autolab GSTST30 galvanostat linked to PC computer equipped with GPES software by Eco Chemie. The software enables to set a measurement procedure in which the length of each current pulse and current of each pulse in the range from + 1 A do -1 A are entered. During the electrolysis when the current pulse is applied the potential changes with time are registered.

Parameters of the electrolysis using current pulses with the reversed current direction were: iic= -0.025 A/cm² t_[c = 30

ii_B = +0.025 A/cm² t_la = 3 s

i_2c = -0.01875 A/cm² t_2c = 5 s

i2a = +0.025 A/cm² t_2a = 1.5

i_3c= -0.015 A/cm² t_3c = 5 s

i_3a = +0.025 A/cm² t_3a = 1.5

After electrochemical deposition of copper on the electrode, the structure and the dimensions of the copper foil were analyzed using a scanning electron microscope and it was found that its thickness is from 200±50 nm. Analysis of the energy dispersion spectrum (EDS) showed only the lines characteristic of copper which confirms the purity of the obtained product.

The copper foil obtained in an electrochemical process was ground beforehand and then mixed mechanically in a ribbon mixer with high pressure low density polyethylene (LDPE). Copper concentration was 30 wt%. Then the mixture prepared in this way underwent an extrusion process in a malleable state in an electrically heated twin screw extruder for 10 minutes at 210°C. The obtained pellets/beads were pressed using hydraulic press in order to obtain 0.55 mm-thick samples. Electromagnetic properties of the obtained sample plates: the complex permeability μ and complex permittivity (ε) for the same sample were measured using the split post dielectric resonator method at frequency 4.8 GHz and they are presented in the Table below. It was found that the obtained value of magnetic permeability real μ is typical of metamaterials:

Example 5.

A cathode/working electrode made of stainless steel of an area of approximately 8 cm² and an anode/reference electrode in the shape of copper plate the area of which is approximately 100 cm² and thickness 0.1 cm are placed in a electrochemical cell thermostated to 25°C. The cell is filled with an electrolyte composed of 46 g dm^" Cu, 170 g dm^"3 H₂S0₄ The electrodes are connected with a BNC connector to a measuring device - Autolab GSTST30 galvanostat linked to PC computer equipped with GPES software by Eco Chemie. The software enables to set a measurement procedure in which the length of each current pulse and current of each pulse in the range from + 1A do -1A are entered. During the electrolysis when the current pulse is applied the potential changes with time are registered.

Parameters of the electrolysis using current pulses with the reversed current direction were: iic= -0.025 A/cm² t_lc = 30

iia = +0.025 A/cm² t_{l a} = 3 s

i_2c = -0.01875 A/cm² t_2c = 5 s

i_2a = +0.025 A/cm² t_2a = 1.5

i_3c= -0.015 A/cm² t_3c = 5 s

i3a = +0.025 A/cm² t_3a = 1.5 After electrochemical deposition of copper on the electrode, the structure and the dimensions of the copper foil were analyzed using a scanning electron microscope and it was found that its thickness is from 200±50 nm. Analysis of the energy dispersion spectrum (EDS) showed only the lines characteristic of copper which confirms the purity of the obtained product.

The copper foil obtained in an electrochemical process was ground beforehand and then mixed mechanically in a ribbon mixer low pressure linear low density polyethylene (LLDPE). Copper concentration was 15 wt%. Then the mixture prepared in this way underwent an extrusion process in a malleable state in an electrically heated twin screw extruder for 10 minutes at 240°C. The obtained pellets/beads were pressed using hydraulic press in order to obtain 0.55 mm-thick samples. Electromagnetic properties of the obtained sample plates: the complex permeability μ and complex permittivity (ε) for the same sample were measured using the split post dielectric resonator method at frequency 4.8 GHz and they are presented in the Table below. It was found out that the obtained value of magnetic permeability real μ is typical of metamaterials:

Example 6.

A cathode/working electrode made of stainless steel of an area of approximately 8 cm² and an anode/reference electrode in the shape of copper plate the area of which is approximately 100 cm² and thickness 0.1 cm are placed in a electrochemical cell thermostated to 25°C. The cell is filled with an electrolyte composed of 46 g dm^" Cu, 170 g dm^"3 H₂S0_4. The electrodes are connected with a BNC connector to a measuring device - Autolab GSTST30 galvanostat linked to PC computer equipped with GPES software by Eco Chemie. The software enables to set a measurement procedure in which the length of each current pulse and current of each pulse in the range from + 1A do -1A are entered. During the electrolysis when the current pulse is applied the potential changes with time are registered.

Parameters of the electrolysis using current pulses with the reversed current direction were:

ila = +0.025 A/cm² tla = 3 s

l2c = -0.01875 A/cm² t_2c = 5 s

l2a = +0.025 A/cm² t_2a = 1.5 s

l3c ⁼ -0.015 A/cm² t_3c = 5 s

l3a = +0.025 A/cm² t₃a = 1.5 s

After electrochemical deposition of copper on the electrode, the structure and the dimensions of the copper foil were analyzed using a scanning electron microscope and it was found that its thickness is from 200+50 nm. Analysis of the energy dispersion spectrum (EDS) showed only the lines characteristic of copper which confirms the purity of the obtained product.

The copper foil obtained in an electrochemical process was ground beforehand and then mixed mechanically in a ribbon mixer with polypropylene (PP). Copper concentration was 10 wt%. Then the mixture prepared in this way underwent an extrusion process in a malleable state in an electrically heated twin screw extruder for 10 minutes at 216°C. The obtained pellets/beads were pressed using hydraulic press in order to obtain 0.55 mm-thick samples. Electromagnetic properties of the obtained sample plates: the complex permeability μ and complex permittivity (ε) for the same sample was determined using the split post dielectric resonator method at frequency 4.8 GHz and they are presented in the Table below. It was found that the obtained value of magnetic permeability real μ is typical of metamaterials:

4.8 GHz

Concentration of Cu real(£) real^) imag(£) imag^) flakes wt%

10 3.4200 0.9860 0.0131 0.0266

Claims

1. Novel metamaterials, characterized by the fact that they are polymer composites whose polymer matrix contain from 0.5 t% to 45 wt % of copper flakes and/or nanoflakes in polymer matrix as compared to polymer matrix.

2. Novel metamaterials of claim 1 , characterized by the fact that the composite polymer matrix is ethylene-vinyl acetate, flame retardant polymer containing ethylene-vinyl acetate, polyvinyl chloride, polymethyl methacrylate, polyacrylonitrile , polyethylene, polypropylene, polystyrene, polybutadiene, polyacrolein, polyurethane, polyether or polyester.

3. Novel metamaterials of claim 1, characterized by the fact that they contain copper flakes and/or nanoflakes the diameter of which is in the range from 1 micrometer to 500 micrometers and thickness ranges from 80 nm to 2000 nm.

4. Novel metamaterials of claim 1, characterized by the fact that they contain from 0.5 wt% to 45 wt% of copper flakes and/or nanoflakes as compared to polymer matrix.

5. A method for obtaining novel metamaterials, characterized by the fact that it is realized in the following stages:

- at the first stage copper foil or nano-foil is deposited on metallic cathode as a result of acid copper salt solution current pulse electrolysis,

- the second stage consists in mechanical removal of copper foil from the metallic cathode base and grinding it into flakes,

- at the third stage polymer and copper flakes are mixed at weight ratio of, respectively 99.5-55 : 0.5-45

6. The method of claim 4, characterized by the fact that copper foil or nanofoil is obtained from aqueous acid copper salt solution

7. The method of claim 4, characterized by the fact that copper foil or nanofoil is obtained by the electrolysis carried out using pulse current with or without current direction change.

8. The method of claim 4 or 6, characterized by the fact that the electrolyte contains copper (II) the concentration of which is higher than 0.1 g dm^"3.

9. The method of claim 4, characterized by the fact that copper foil or nanofoil is obtained using cathodic pulse the current density of which i_c = 0,001÷0, 100 A/cm² in the period of time t_c from 0,005 s to 600 s.

10. The method of claim 4, characterized by the fact that copper foil or nanofoil is obtained using mobile or stationary steel cathode in the shape of a sheet or foil.

1 1. The method of claim 4, characterized by the fact that copper foil or nanofoil is obtained using an anode in the shape of a copper sheet.

12. The method of claim 4, characterized by the fact that copper foil or nanofoil is obtained in the process of an electrolysis carried out in the range of temperatures from 18-60°C.

13. The method of claim 4, characterized by the fact that current pulses are used as in the Figure 1 from a) to f): a) pulse electrolysis without current direction change: cathodic current pulse

i_c = 0.001÷0.100 A/cm² and time t_c = 0.005÷600 s

or

b) pulse electrolysis without current direction change: cathodic current pulses i_c = 0.001÷0.100 A/cm² and time t_c = 0.005÷600 s, with current interruptions, and the interruption duration is at least 50% shorter than t_c

or

c) pulse electrolysis without current direction change: cathodic current pulses i_c = 0.001÷0.100 A/cm² and time t_c = 0.005÷600 s, with current interruptions, and the interruption duration is at least 50% shorter than t_c as well as the first cathodic current is larger than the subsequent ones: i_ci > i_c2

or

d) pulse electrolysis with current direction change: cathodic current pulse i_c = 0.001÷0.100 A/cm² and time t_c = 0.005÷600 s, next anodic current pulse | i_c | > | i_a | ; t_c > t_a with anodic current pulse i_a in the range of anodic current densities 0.001÷0.050 A/cm² and time t_a from 0.005÷550 s

or

e) pulse electrolysis with current direction change, cycles: cathodic current pulse ic and time tc, and then anodic current pulse | i_c | > | i_a | ; t_c > t_a

or