Natural graphite material capable of releasing short-chain carbyne species as dipole, and electrochemical use thereof

Abstract

[Problem] To provide a graphite material capable of releasing a short-chain carbyne species as a hydrocarbon-based dipole. [Configuration] Provided are a natural graphite and an electrolytic solution containing the same. The natural graphite has a C≡C polyyne (α-carbyne) structure and / or a C=C cumulene (β-carbyne) structure forming a linear sp hybrid carbon chain, and can leach out a short-chain carbyne species (RC:·, wherein R represents CnH2n-1, n represents an integer of 3 or less, and :· represents 3 unpaired electrons) as a dipole when immersed in water or an electrolytic solution.

Description

Natural graphite material capable of releasing short-chain carbyne species as dipoles and its electrochemical applications

[0001] The present invention relates to short-chain hydrocarbons (having 3 or less carbon atoms), particularly short-chain carbyne species (RC: ·, where R is C ｎ H ２ｎ－１ wherein n is an integer of 3 or less, and . represents three unpaired electrons) as a dipole into an electrolyte, and the electrochemical use thereof.

[0002] Chemical bonds between carbon electrons can have three types of hybrid orbitals. They can be classified into diamond species, which have a three-dimensional structure with an sp3 hybrid orbital and one σ bond; graphite species, which have a two-dimensional structure with an sp2 hybrid orbital and one σ bond and one π bond; carbyne species, which have a one-dimensional structure with an sp hybrid orbital and one σ bond and two π bonds; and fullerene species, which are zero-dimensional and form a quasi-sp2 hybrid orbital from one quasi-σ bond and one quasi-π bond. Figure 1 shows a three-dimensional correlation diagram. Of these, carbyne species (Carbynoid or Graphyne), including fullerenes, are suggested to be solid-state linear sp hybridized carbon chains in which carbon atoms are connected by either conjugated triple bonds (polyyne-type isomers) or cumulant double bonds (polycumulene-type isomers). Many researchers have attempted to synthesize these carbyne species. Typical physical methods include laser irradiation or ion sputtering of graphite (Non-Patent Document 1), and typical chemical methods include dehalogenating polyvinylidene halide in a tetrahydrofuran solution of potassium ethylide (Non-Patent Document 2), and pre-chlorinating polyacetylene followed by dechlorination oxidation (Non-Patent Document 3). However, mass production has not been successful, and industrial application of carbyne is still a long way off. Furthermore, research on newly created quasi-one-dimensional carbon crystals named carbolites has only focused on their electrical properties (Non-Patent Document 5), and their physical properties and electrochemical applications, including their crystal structures, remain largely a mystery.

[0003] Y.P. Kudryavtsev and S.Evsyukov Carbon 30 (1992) 213-221 V.V.Korshak and Y.P. Kudryavtsev, Makromol, Chem, Rapid Commun.9 (1988) 135-140 K.Akagi, M.Nishiguchi and H.Shirakawa, synth.Met.17 (1987) 557-562 Synthesis and structure of carbyne: Carbon TANSO 1997 [No.178] 122-127 Physical properties of quasi-one-dimensional carbon crystal carbolite (KAKEN 1996 research report) Representative: Professor Tanuma Seiichi, Iwaki Meisei University Physical meaning of electrode potential: Materia Vol. 33 No. 11 (1994)

[0004] Natural graphite extracted from natural graphite ore contains not only graphite but also carbynoid and graphyne structures, as shown in Figure 1, and has polyyne (α-carbyne) and cumulene (β-carbyne) structures. This one-dimensional carbon-carbon structure is easily dissociated, and due to the presence of carbon-carbon bonds, chromatographic analysis has confirmed that many hydrocarbons are released into the water simply by immersing the graphite fragment in water or boiling it in hot water. To determine the structure of these hydrocarbons, the graphite fragment was examined using temperature-programmed ion desorption (TOF-ESD: time-of-flight electron-stimulated ion desorption), and various hydrocarbon ions, including short-chain carbyne species, were desorbed, in addition to oxygen, hydrogen, and carbon dioxide. These carbyne species have particularly short carbon chains (RC: ⋅, where R is C), due to the active end of the carbyne structure. ｎ H ２ｎ－１ where n is an integer of 3 or less, and . denotes three unpaired electrons), and although its reactivity is predicted to be very high (Non-Patent Document 4), it is surprising that it spontaneously leaches out of natural graphite ore. Moreover, we discovered that when present in an electrolyte, it changes the electrode potential, possibly because it functions as a hydrocarbon-based dipole at the interface between the electrode and the electrolyte, forming an electric double layer (the electrode potential difference generated when a pair of Mg-Cu metal electrodes was immersed in an electrolyte was improved by at least 0.5 V by adding an electrolyte containing carbyne species). This phenomenon is due to the short-chain carbyne species (RC: ., where R is C ｎ H ２ｎ－１where n is an integer of 3 or less, and . indicates three unpaired electrons) forms a new dipole electric double layer at the interface between the electrode and the electrolyte.

[0005] This is because electrode potential is an important fundamental concept in electrode chemistry. Traditionally, the concept of electrode potential has typically been expressed through the thermodynamic equation of electrode reaction equilibrium, i.e., the Nernst equation. However, in recent years, electrode potential has been understood in terms of the following physical concept. That is, while the traditional interpretation of electrode potential was phenomenological and did not necessarily clarify its physical meaning, it is now accepted that electrode potential corresponds to the relative value of the potential difference at the electrode interface (electrode / electrolyte interface). It is considered necessary to consider not only the electrode-specific electronic electrode potential but also the potential of the electrolyte solution (ionic electrode potential), which depends on the electrolyte solution species (Non-Patent Document 6). This means that the electrode potential, which is the relative value of the potential difference at the electrode interface (electrode / electrolyte interface), varies not only depending on the electrode-specific electrode potential but also on the composition of the electric double layer formed at the electrode interface, which is related to the ionic electrode potential. From this perspective, in order to relatively improve the electrode potential difference, which is determined by the electrode species, the structural design of the electric double layer, which is formed by adsorbed species at the electrode interface and water molecules such as moisture, is a major factor in improving battery performance.

[0006] Based on the findings of the electrode potential-enhancing effect of short-chain carbynes, the present inventors have set a first objective of the present invention to provide a natural graphite material capable of releasing short-chain hydrocarbons, particularly short-chain carbynes, as dipoles that constitute an electric double layer. A second objective of the present invention is to provide an electrolyte solution containing short-chain carbynes that forms a dipole electric double layer at the interface between an electrode and the electrolyte solution, thereby enhancing the interelectrode voltage.

[0007] That is, as a result of extensive research taking into consideration the physical meaning of the electrode potential, the present invention has found that short-chain hydrocarbons, particularly short-chain carbynes (RC: ·, where R is C ｎ H ２ｎ－１where n is an integer of 3 or less, and . represents three unpaired electrons) exhibit high reactivity in water, and form an electric double layer as a dipole at the interface between the electrode and the electrolyte, thereby improving the electrode potential. First, they have a C≡C polyyne (α-carbyne) structure and / or a C═C cumulene (β-carbyne) structure that form a linear sp hybridized carbon chain, and when immersed in water or an electrolyte, they produce short-chain hydrocarbons, particularly short-chain carbyne species (RC: ., where R is C ｎ H ２ｎ－１ The object of the present invention is to provide natural graphite that can exude a hydrocarbon-based dipole (where n is an integer of 3 or less, and :· represents three unpaired electrons) as a hydrocarbon-based dipole. Natural graphite has a C≡C polyyne (α-carbyne) structure and / or a C═C cumulene (β-carbyne) structure that form linear sp hybridized carbon chains. When these structures are partially broken or broken for some reason, they form short-chain carbyne species (RC:·, where R is C ｎ H ２ｎ－１ where n is an integer of 3 or less, and :· represents three unpaired electrons) is exuded into the electrolyte as a carbyne ion RC:·. Therefore, the present invention secondly provides a method for producing a short-chain carbyne species (RC:·, where R is C ｎ H ２ｎ－１ where n is an integer of 3 or less, and . represents three unpaired electrons), and also provides an electrochemical reaction medium as a dipole that promotes the electrochemical reaction.

[0008] Natural graphite contains polyyne structures (α-carbynes) represented by -C≡C- and cumulene structures (β-carbynes) represented by -C=C-. When irradiated with an electron beam using time-of-flight electron stimulated ion desorption (TOF-ESD), the π bond cleaves, releasing the CH3C:·ethylidyne ion of the shortest-chain carbyne (n=1), which is detected along with those with mass numbers corresponding to hydrogen atoms 1 and 2, oxygen atoms 16 and 32, water atoms 18, carbon monoxide atoms 28, and carbon dioxide atoms 4. This is a plausible phenomenon given the physical formation of carbyne species (Non-Patent Document 1). However, it is surprising that these short-chain carbynes or radicals can be exuded from natural graphite, i.e., graphite, by simply immersing it in water or an electrolyte to form an electrochemically active electrolyte. Furthermore, short-chain carbynes and their radicals exhibit high reactivity in water, and therefore, they exist in water by coupling with each other, bonding with water molecules, and bonding with metal ions to form metal complexes, thereby providing an electrolyte that forms a new electric double layer at the interface between the electrode and the electrolyte.

[0009] In particular, when short-chain carbyne species are contained in the electrolyte, they function as dipoles at the interface between the electrode and the electrolyte, forming a new electric double layer at the interface between the electrode and the electrolyte, which is a surprising phenomenon, increasing the electrode potential difference with the counter electrode. This change in electrode potential is significant because it improves the battery electromotive force.

[0010] This is a classification diagram showing the correlation between carbon structures. It is a perspective view showing the concept of a power-generating sheet constructed by sandwiching a nonwoven fabric containing the electrolyte of the present invention between a natural graphite electrode and an aluminum plate electrode, which is a typical metal. It is a structural diagram of a marine battery constructed by dripping the electrolyte of the present invention into seawater. It is a schematic diagram of a hydrogen microscope TOF-ESD device for detecting graphite containing hydrocarbons having carbyne groups in a natural graphite sheet according to the present invention. It is a photograph of a 10 mm x 8 mm natural graphite sheet set in a sample holder equipped with a heater for hydrogen analysis after water electrolysis. It is a photograph of a 10 mm x 8 mm natural graphite sheet set in a sample holder equipped with a heater for hydrogen analysis after water electrolysis. It shows the thermal desorption spectrum of impurities released from the sample surface into a vacuum upon heating to a sample temperature of 200°C. It shows the thermal desorption spectrum of impurities released from the sample surface into a vacuum upon heating to a sample temperature of 290°C. The sample temperature was raised to 290°C six times with time intervals, and the third thermal desorption spectrum is shown. The sample temperature was increased to 290°C six times with time intervals, and the fourth thermal desorption spectrum is shown. The sample temperature was increased to 290°C six times with time intervals, and the sixth thermal desorption spectrum is shown.

[0011] The present invention relates to a method for producing a short-chain carbyne species (RC: ·, where R is C) by immersing the compound in water or an electrolyte solution. The compound has a C≡C polyyne (α-carbyne) structure and / or a C═C cumulene (β-carbyne) structure that forms a linear sp hybridized carbon chain. ｎ H ２ｎ－１ The present invention also provides natural graphite that can exude short-chain carbyne species (RC:·, where R is C, where n is an integer of 3 or less, and · represents three unpaired electrons) as dipoles. The present invention also provides natural graphite that has a C≡C polyyne (α-carbyne) structure and / or a C═C cumulene (β-carbyne) structure that form linear sp hybridized carbon chains, and that can exude short-chain carbyne species (RC:·, where R is C ｎ H ２ｎ－１ wherein n is an integer of 3 or less; and · represents three unpaired electrons) as a dipole.

[0012] The electrolyte of the present invention can be used in both aqueous and non-aqueous applications. The amount of electrolyte added to the electrolyte can be adjusted depending on the application. In the case of aqueous electrolytes, they can be used as acidic or alkaline electrolytes, but alkaline electrolytes are preferred for metal-air batteries and hydrogen peroxide fuel cells. Various electrolytes are added to the electrolyte depending on the battery configuration. For example, it is preferable to adjust the electrolyte taking into account the large amount of seawater present on the ocean. Seawater concentrations are preferred because they suppress the generation of chlorine, but saltwater containing 1 mole or more of sodium chloride may also be used.

[0013] The presence of short-chain carbyne species can be confirmed by searching for C≡C polyyne (α-carbyne) structures and / or C═C cumulene (β-carbyne) structures that form linear sp-hybridized carbon chains. Carbon double or triple bonds can be detected by temperature-programmed ion desorption (TOF-ESD) spectroscopy, where R is C. ｎ H ２ｎ－１ where n is an integer of 3 or less, and : represents three unpaired electrons), it has been confirmed that the ethylidine of CH3C:· with a minimum n=1 is released. However, normally, carbon triple bonds are also identified by infrared spectroscopy as C≡C stretching at 2260 to 2100 cm －１ , ≡C-H stretching 3340-3270 cm －１ Or ≡C-H bending angle 700 to 600 cm －１ It is detected as a characteristic of the absorption spectrum of acetylides.

[0014] Furthermore, when carbyne ions couple with each other in water, they are thought to form short-chain carbyne containing propylidines of n=2 or more. They are also thought to bond with metal ions in water to form carbyne-metal complexes. Then, the intermediate RCO + and RCMe +is reduced by receiving electrons through the formation of metal ions, and is reduced to carbyne via an intermediate. This reaction is repeated until the metal ions disappear as ions. As a result, as shown in Figure 2, a dipole electric double layer is formed at the interface with the electrode by immersing the electrode in the electrolyte, forming an ion electrode potential, which is thought to cause a change in the overall electrode potential difference together with the electrode's inherent electrode potential.

[0015] The natural graphite material of the present invention may be a graphite sheet prepared from graphite extracted from natural graphite ore. It is believed that some of the natural graphite materials retain a C≡C polyyne (α-carbyne) structure and / or a C═C cumulene (β-carbyne) structure that form linear sp hybridized carbon chains. By immersing the graphite sheet in water or an electrolyte, it is possible to obtain short-chain carbyne species (RC: ·, where R is C ｎ H ２ｎ－１ where n is an integer of 3 or less, and . represents three unpaired electrons).

[0016] Graphite is industrially produced from natural graphite using a liquid-phase reaction method in which natural graphite powder is immersed in a mixed acid solution of 90% concentrated sulfuric acid (95-98%) and 10% concentrated nitric acid (specific gravity 1.33) at 100°C to produce sulfuric acid-graphite intercalation compounds (HSO-GICs), which are then washed with water, dried, and rapidly heated to produce the final product. Other known methods include using hydrogen peroxide to reduce the heavy metal content in the vapor generated during heat treatment, and electrochemical methods in which graphite powder is electrolytically oxidized in a formic acid solution to produce formic acid-graphite intercalation compounds (HCOOH-GICs). Any material can be used as the graphite material of the present invention as long as it has a C≡C polyyne (α-carbyne) structure and / or a C═C cumulene (β-carbyne) structure that form a linear sp hybridized carbon chain. Graphite oxide can be subjected to rapid heat treatment to produce expanded graphite, in which the graphite layers are expanded, and this can also be used as the graphite material of the present invention. Expanded graphite powder is supplied from a hopper to a pre-pressure roll by a vibrating belt and preformed into a plate, which is then subjected to a heat treatment process for degassing and purification, and then formed into a sheet in a roll molding process.

[0017] Graphite sheets produced from natural graphite can increase ion insertion capacity and can be used as the graphite material of the present invention. On the other hand, charcoal blocks, carbon materials bound with nanocarbon binders, and carbon fiber sheets have not been shown to exude hydrocarbons, i.e., short-chain carbyne species, even when these carbon materials are calcined and expanded. Therefore, it is believed that natural graphite is formed by water exuding short-chain carbyne species due to crustal movements, resulting in the formation of C≡C polyyne (α-carbyne) structures and / or C═C cumulene (β-carbyne) structures, which form linear sp hybridized carbon chains, in the graphite.

[0018] (Mass Analysis of Ions from Natural Graphite Sheets) Mass analysis of electron-excited ions emitted from natural graphite can be performed using time-of-flight electron-stimulated ion desorption (TOF-ESD) spectroscopy. This instrument, called a scanning electron-stimulated desorption ion microscope (SESDIK), irradiates a sample with pulses of slow electrons of 100-500 eV, ionizing hydrogen, oxygen, and other adsorbed species on the solid surface and releasing them into the vacuum. These ions are detected and amplified to produce signals. Because the electron beam is irradiated as a pulse, ions are detected using the time-of-flight (TOF) method, which calculates the time of flight using a formula. Displaying this signal as a TOF spectrum allows for localized mass analysis, yielding a two-dimensional distribution of ions of hydrogen, oxygen, and other adsorbed species. Not only can hydrogen and oxygen be detected, but differences in bonding and adsorption states can be projected onto the desorption kinetic energy, allowing for selective detection of adsorbed species, enabling chemical mass analysis. Liquid chromatography of the substances that leached from the natural graphite into the solution confirmed the presence of large amounts of hydrocarbons. A slice of the natural graphite was then cut out and analyzed using a method of detecting desorbed protons by irradiating the surface of the solid with pulsed electrons (electron stimulated ion desorption, TOF-ESD). In addition to hydrogen, oxygen, and carbon monoxide, ethylidyne (CH3C·), with a molecular weight of 27, and ethylene (C2H4), with a molecular weight of 28, were detected.

[0019] Function of the Electrolyte: Short-chain carbyne can be prepared by immersing natural graphite or graphite sheets made from natural graphite in an electrolyte. Furthermore, in a battery configuration of aluminum plate / 1M NaCl + H2O2 / natural graphite sheet, translucent crystals are formed, which have a high oxygen content and are highly conductive. Because aluminum hydroxide or sodium aluminate contains short-chain carbyne species, they form a semi-solid electrolyte, which can be used as an electrolyte to construct a battery.

[0020] A battery constructed by combining an aluminum metal plate, an electrolyte containing short-chain carbynes (prepared by adding 5-30% by volume of caustic soda to a 0.5-1.5M sodium chloride aqueous solution), and copper electrodes (Figure 2). A 1-2 mm thick graphite electrode sheet 30 made of natural graphite is used as the cathode, while a 1-2 mm thick aluminum metal plate 10, a typical metal electrode, is used as the anode. A nonwoven fabric 20 is impregnated with saltwater containing short-chain carbynes as the electrolyte, and the two electrodes are sandwiched together to form a power-generating sheet 100. Power generation is observed when the battery is sandwiched between these electrodes. Seawater is used as the electrolyte, and a caustic alkali, such as caustic soda, can be added to the saltwater to alkalinize it and promote the electrochemical reaction. To alkalinize the saltwater, 5-30% by volume, preferably 15-20% by volume, of a 50% caustic soda solution is added to the saltwater. Seawater, which is abundant on Earth, is preferable for preparing the electrolyte. While seawater is preferred because of its concentration, which suppresses chlorine generation, saltwater containing 1 molar or more of sodium chloride may also be used.

[0021] As shown in Figure 3, graphite powder 30-1 prepared from natural graphite is packed into a corrosion-resistant cylindrical plastic tube 40, the bottom of which is sealed with nonwoven fabric 20, while a carbon electrode 50 is provided at the top opening and sealed with sealing film 60 to form a cathode electrode section that allows for the sequential addition of electrolyte. This battery assembly is then placed on an aluminum metal plate, forming a battery. This battery assembly is supported on a float 70, and electricity can be generated by impregnating the nonwoven fabric 20 with salt water. The addition of a small amount of hydrogen peroxide to the electrolyte can increase power generation efficiency.

[0022] 2 and 3, not only is the formation of an electric double layer on the electrode surface by carbyne mentioned above, but the following phenomenon in the nanospace between the graphite layers containing carbyne is also thought to be involved: When metal ions Me+ enter the nanospace of the graphite intercalation compound, they adhere to the graphite layer and form a microcell due to the contact potential difference with the counter electrode, and the electromotive force is thought to be stored in the microcapacitor between the graphite layers adjacent to the microcell.

[0023] In the present invention, when the short-chain carbyne species is contained in the electrolyte, the power generation effect can be observed even when a copper electrode is used instead of a graphite electrode.

[0024] (Mass analysis of ions in natural graphite sheets) Using a hydrogen microscope at TF Giken, located on the second floor of the Keihanna Plaza Laboratory in Kyoto Prefecture, mass analysis was performed using electron-stimulated ion desorption (TOF-ESD) from the sample. The hydrogen microscope used here is called a scanning-type electron-stimulated desorption ion microscope (SESDIK). As shown in Figure 4, when a sample is irradiated with pulses of slow electrons of 100-500 eV, hydrogen, oxygen, and other adsorbed species adsorbed on the solid surface are ionized and released into the vacuum. These ions are detected and amplified to produce signals. Because the electron beam is irradiated as a pulse, ions are detected using the time-of-flight (TOF) method, which calculates the time-of-flight formula. Displaying this signal as a TOF spectrum allows for mass analysis, enabling the two-dimensional distribution of hydrogen, oxygen, and other adsorbed species ions to be obtained. Not only can hydrogen and oxygen be detected, but differences in bonding and adsorption state can be projected onto the kinetic energy of desorption, allowing for selective detection of adsorption targets, enabling chemical mass analysis.

[0025] (Ion Mass Analysis in Natural Graphite Sheet) A natural graphite sheet and a 10 mm x 8 mm carbon film (flexible graphite sheet FGS) after water electrolysis were placed in a sample holder equipped with a heater for hydrogen analysis. Measurement examples are shown in Figures 5A and 5B. Figure 6A shows the thermal desorption spectrum of impurities released from the surface into a vacuum upon heating to a sample temperature of 200°C. Figure 6B shows the thermal desorption spectrum of impurities released from the surface into a vacuum upon heating to a sample temperature of 290°C. The bar graph on the right indicates the final amount of release for each mass, while the bar graph on the left indicates the temperature rise. Figure 6A shows the temperature rise up to 200°C, while Figure 6B shows the temperature rise after saturating at 200°C, then increasing by another 90°C, at which point heating was stopped and the sample cooled. Figures 7A, 7B, and 7C show the third, fourth, and sixth cycles of a six-time heating cycle to 290°C. Figure 7A shows the gas released from the third sample (4 minutes) with little change from the second measurement taken one hour earlier. Figure 7B shows the ion pump turned on during the gas released from the fourth sample, then turned off again after a while. The gas from the sample is introduced and the final value is displayed for easy understanding. Figure 7C shows the gas released from the sixth sample. From these results, the spectra of impurities with masses 27 and 28 are noteworthy, and the measurement data indicates that both graphite containing hydrocarbons with carbyne groups and ethylene are being released from the sample.

[0026] The electromotive force in a battery reaction is governed by the electrode potential difference between the anode and cathode in the electrolyte. This electrode potential is usually calculated as the relative value of the potential difference at the electrode interface (electrode / electrolyte interface) and is introduced through the Nernst relation. However, according to Non-Patent Document 6 (The Physical Meaning of Electrode Potential by Norio Sato), the electrode potential is considered to be divided into the electrode potential inherent to the electrode and the ionic electrode potential of the electrolyte. The inventors found that in an Al / 1N nitric acid aqueous solution / Cu battery configuration, the electrode potential difference of 0.98 V increased by 0.5 V when half the amount of a solution prepared by soaking natural graphite ore overnight in 1M NaCl solution was added. This improvement in the electrode potential difference indicates an improvement in the ionic electrode potential due to the addition of the electrolyte. Although it is unclear which function of the short-chain carbyne is responsible for this improvement, it is presumed to be due to its ability to enhance the redox reaction and / or the formation of a dipole electric double layer at the electrode / electrolyte interface.

Claims

1. A battery comprising an anode, an alkaline electrolyte, and a cathode, wherein the cathode has a C=C polyyne (α-carbyne) structure and / or a C=C cumulene (β-carbyne) structure that form a linear sp hybrid carbon chain, and is manufactured from natural graphite that extrudes as a dipole of ethyridine, which is a short-chain calvin represented by formula RC:• (wherein R represents CnH2n-1 and n is an integer of 3 or less), by immersion in the electrolyte, and the electrolyte contains ethyridine, forming a dipole electric double layer at the interface between the electrolyte and the electrode.

2. (delete)

3. (delete)

4. The battery according to claim 1, comprising an Al metal plate 10 as the anode, a nonwoven fabric 20 containing seawater as the electrolyte, and a natural graphite electrode plate 30 as the cathode, wherein the power generation sheet 100 is formed by laminating these in order.

5. The battery according to claim 1, wherein the cathode consists of natural graphite powder 30-1 filled in a cylindrical container 40, and an Al metal plate 10 is provided as an anode via a nonwoven fabric 20 at the bottom opening of the cylindrical container 40, and the nonwoven fabric 20 is impregnated with seawater as the electrolyte, and when hydrogen peroxide solution is dropped onto the natural graphite powder 30-1, it reaches the Al metal plate via the nonwoven fabric 20.