Patent Description:
This application claims priority to and the benefit of <CIT>, at the KIPO.

An organic solar cell is a device that may directly convert solar energy into electrical energy by applying a photovoltaic effect. A solar cell may be classified into an inorganic solar cell and an organic solar cell depending on a material constituting a thin film. A typical solar cell is manufactured with a p-n junction obtained by doping crystalline silicon (Si), which is an inorganic semiconductor. Electrons and holes generated due to absorption of light diffuse to a p-n junction point, and are accelerated by an electric field and moved to an electrode. Power conversion efficiency of this procedure is defined as a ratio of power given in an external circuit to solar power fed into the solar cell, and reaches up to <NUM>% when measured under the virtual solar irradiation conditions currently standardized. However, since the inorganic solar cell in the related art already has limits in economic feasibility and available materials, an organic semiconductor solar cell, which is easily processed and cheap and has various functionalities is in the spotlight as a long-term alternative energy source.

In the solar cell, it is important to increase the efficiency such that electrical energy as much as possible may be outputted from the solar energy. In order to increase the efficiency of the solar cell, it is also important to generate excitons as much as possible from inside the semiconductor, but it is also important to take out electric charges generated to the outside without being lost. One of the causes that electric charges are lost is that generated electrons and holes are annihilated by means of recombination. As a method of transferring generated electrons or holes to an electrode without being lost, various methods have been suggested, but most of the methods require additional processes, and as a result, manufacturing costs may be increased.

An object of the present specification is to provide a copolymer and an organic solar cell including the same.

The present invention provides a random copolymer comprising at least one unit of copolymers represented by the following Copolymers <NUM> to <NUM>:
<CHM>
<CHM>
<CHM>
<CHM>
<CHM>
<CHM>
<CHM>
wherein:.

The present invention further provides an organic solar cell comprising: a first electrode; a second electrode provided opposite to the first electrode; and an organic material layer having one or more layers disposed between the first electrode and the second electrode and comprising a photoactive layer, in which one or more layers of the organic material layer comprise the random copolymer.

The copolymer of the present specification may be used as a material for an organic material layer of an organic solar cell, and the organic solar cell including the same may exhibit excellent characteristics in an increase in an open-circuit voltage and a short-circuit current and/or an increase in efficiency.

The copolymer according to the present invention has a deep HOMO level, a small bandgap, and a high charge mobility, and thus may exhibit excellent characteristics. The polymer according to the present invention may be used alone or in a mixture with other materials, enhance efficiency of a device, and enhance life-span characteristics of the device by means of thermal stability of the compound.

The copolymer of the present invention includes three monomers and is a random copolymer.

The term 'monomer' as used herein refers to a repeated structure which is included in a main chain of a copolymer, in which the monomer is bonded to the copolymer by means of polymerization.

In the case of the random copolymer, as the crystallinity is reduced, the degree of amorphousness is increased, so that long-term stability to heat may be secured, and the process of manufacturing a device and a module, which include the copolymer becomes facilitated.

Further, since the ratio of copolymers in the random copolymer is controlled to easily control the solubility, it is easy to provide solubility that is suitable for the process of manufacturing an organic solar cell, thereby manufacturing an organic solar cell with high efficiency.

In the present invention, the copolymer is a random copolymer which includes at least one unit of copolymers represented by the following Copolymers <NUM> to <NUM>. <CHM>
<CHM>
<CHM>
<CHM>
<CHM>
<CHM>
<CHM>
<CHM>.

The 'structure in the parenthesis' as used herein means a structure included in the ( ).

The term 'unit' as used herein means a repeated structure which is included in a monomer of a copolymer, in which the monomer is bonded to the copolymer by means of polymerization.

The term 'including a unit' as used herein means being included in a main chain in the copolymer.

In an exemplary embodiment of the present specification, l is <NUM>.

In an exemplary embodiment of the present specification, m is <NUM>.

In another exemplary embodiment, l is <NUM>.

In still another exemplary embodiment, m is <NUM>.

In an exemplary embodiment of the present specification, an end group of the copolymer is selected from the group consisting of hydrogen; deuterium; a halogen group; a nitrile group; a nitro group; an imide group; an amide group; a hydroxyl group; a substituted or unsubstituted alkyl group; a substituted or unsubstituted cycloalkyl group; a substituted or unsubstituted alkoxy group; a substituted or unsubstituted aryloxy group; a substituted or unsubstituted alkylthioxy group; a substituted or unsubstituted arylthioxy group; a substituted or unsubstituted alkylsulfoxy group; a substituted or unsubstituted arylsulfoxy group; a substituted or unsubstituted alkenyl group; a substituted or unsubstituted silyl group; a substituted or unsubstituted boron group; a substituted or unsubstituted alkylamine group; a substituted or unsubstituted aralkylamine group; a substituted or unsubstituted arylamine group; a substituted or unsubstituted heteroarylamine group; a substituted or unsubstituted aryl group; and a substituted or unsubstituted heterocyclic group.

In an exemplary embodiment of the present specification, the end group of the copolymer is a heterocyclic group or an aryl group.

In an exemplary embodiment of the present specification, the end group of the copolymer is a <NUM>-(trifluoromethyl)phenyl group.

According to an exemplary embodiment of the present specification, the number average molecular weight of the copolymer is preferably <NUM>/mol to <NUM>,<NUM>,<NUM>/mol. Preferably, the number average molecular weight of the copolymer is preferably <NUM>,<NUM> to <NUM>,<NUM>. In an exemplary embodiment of the present specification, the number average molecular weight of the copolymer is <NUM>,<NUM> to <NUM>,<NUM>.

According to an exemplary embodiment of the present specification, the copolymer may have a molecular weight distribution of <NUM> to <NUM>. Preferably, the copolymer has a molecular weight distribution of <NUM> to <NUM>.

The lower the molecular weight distribution and the larger the number average molecular weight are, the better the electrical properties and the mechanical properties are.

Furthermore, the number average molecular weight is preferably <NUM>,<NUM> or less in order to have a predetermined solubility or more and thus advantageously allow application of a solution application method.

The copolymer may be prepared based on Preparation Examples to be described below.

The copolymer may be prepared by putting a catalyst and a solvent into three monomers and reacting the resulting mixture, precipitating an end capping and the mixture in methanol, and then extracting the solid.

The copolymer according to the present specification may be prepared by a multi-step chemical reaction. Monomers may be prepared by an alkylation reaction, a Grignard reaction, a Suzuki coupling reaction, a Stille coupling reaction, and the like, and then final copolymers may be prepared by a carbon-carbon coupling reaction such as a Stille coupling reaction. When a substituent to be introduced is a boronic acid or boronic ester compound, the copolymer may be prepared by a Suzuki coupling reaction, and when a substituent to be introduced is a tributyltin compound, the copolymer may be prepared by a Stille coupling reaction, but the preparation of the copolymer is not limited thereto.

Another embodiment of the present invention provides an organic solar cell including: a first electrode; a second electrode provided opposite to the first electrode; and an organic material layer having one or more layers disposed between the first electrode and the second electrode and including a photoactive layer, in which one or more layers of the organic material layer include the copolymer. The organic solar cell may further include a substrate, a hole transport layer, and/or an electron transport layer.

In an exemplary embodiment of the present specification, when the organic solar cell receives a photon from an external light source, an electron and a hole are generated between an electron donor and an electron acceptor. The generated hole is transported to an anode through an electron donor layer.

In an exemplary embodiment of the present specification, the organic material layer includes a hole transport layer, a hole injection layer, or a layer which transports and injects holes simultaneously, and the hole transport layer, the hole injection layer, or the layer which transports and injects holes simultaneously includes the copolymer.

In another exemplary embodiment, the organic material layer includes an electron injection layer, an electron transport layer, or a layer which injects and transports electrons simultaneously, and the electron injection layer, the electron transport layer, or the layer which injects and transports electrons simultaneously includes the copolymer.

In an exemplary embodiment of the present specification, the organic solar cell may further include an additional organic material layer. The organic solar cell may use an organic material simultaneously having various functions to decrease the number of organic material layers.

In an exemplary embodiment of the present specification, the first electrode is an anode, and the second electrode is a cathode. In another exemplary embodiment, the first electrode is a cathode, and the second electrode is an anode.

In an exemplary embodiment of the present specification, in the organic solar cell, a cathode, a photoactive layer, and an anode may be disposed in this order, or an anode, a photoactive layer, and a cathode may be disposed in this order, but the sequence is not limited thereto.

In another exemplary embodiment, in the organic solar cell, an anode, a hole transport layer, a photoactive layer, an electron transport layer, and a cathode may be disposed in this order, or a cathode, an electron transport layer, a photoactive layer, a hole transport layer, and an anode may be disposed in this order, but the sequence is not limited thereto.

In an exemplary embodiment of the present specification, the organic solar cell has a normal structure.

In an exemplary embodiment of the present specification, the organic solar cell has an inverted structure.

In another exemplary embodiment, a buffer layer may be provided between the photoactive layer and the hole transport layer, or between the photoactive layer and the electron transport layer. In this case, the hole injection layer may be further provided between the anode and the hole transport layer. Further, an electron injection layer may be further provided between the cathode and the electron transport layer.

In an exemplary embodiment of the present specification, the photoactive layer includes one or two or more selected from the group consisting of an electron donor and an electron acceptor, and the electron donor material includes the copolymer.

In an exemplary embodiment of the present specification, the electron acceptor material may be selected from the group consisting of fullerene, a fullerene derivative, bathocuproine, a semiconductor element, a semiconductor compound, and a combination thereof. Specifically, the electron acceptor material is a compound of one or two or more selected from the group consisting of fullerene, a fullerene derivative (PCBM((<NUM>,<NUM>)-phenyl-C61-butyric acid-methylester) or PCBCR((<NUM>,<NUM>)-phenyl-C61-butyric acid-cholesteryl ester), perylene, polybenzimidazole (PBI), and <NUM>,<NUM>,<NUM>,<NUM>-perylene-tetracarboxylic bis-benzimidazole (PTCBI).

In an exemplary embodiment of the present specification, the electron donor and the electron acceptor are a bulk heterojunction (BHJ). The electron donor material and the electron acceptor material are mixed in a ratio (w/w) of <NUM>:<NUM> to <NUM>:<NUM>.

The bulk heterojunction means that the electron donor material and the electron acceptor material are mixed with each other in the photoactive layer.

In an exemplary embodiment of the present specification, the photoactive layer has a bilayer structure including an n-type organic material layer and a p-type organic material layer, and the p-type organic material layer includes the copolymer.

The substrate in the present specification may be a glass substrate or a transparent plastic substrate, which has excellent transparency, surface smoothness, easiness in handling, and waterproof, but is not limited thereto, and there is no limitation as long as the substrate is a substrate typically used in the organic solar cell. Specific examples thereof include glass, polyethylene terephthalate (PET), polyethylene naphthalate (PEN), polypropylene (PP), polyimide (PI), triacetyl cellulose (TAC), and the like, but are not limited thereto.

The anode electrode may be a material having transparency and excellent conductivity, but is not limited thereto. Examples of the anode electrode include metal such as vanadium, chromium, copper, zinc and gold, or alloys thereof; metal oxides such as zinc oxide, indium oxide, indium tin oxide (ITO) and indium zinc oxide (IZO); a combination of metal and oxide, such as ZnO:Al or SnO<NUM>:Sb; and electrically conductive polymers, such as poly(<NUM>-methylthiophene), poly[<NUM>,<NUM>-(ethylene-<NUM>,<NUM>-dioxy)thiophene] (PEDT), polypyrrole and polyaniline, and the like, but are not limited thereto.

A method for forming the anode electrode is not particularly limited, but the anode electrode may be formed by being applied on one surface of the substrate or coated in the form of a film by using, for example, sputtering, E-beam, thermal deposition, spin coating, screen printing, inkjet printing, doctor blade or a gravure printing method.

When the anode electrode is formed on a substrate, the formation may be subjected to processes of washing, moisture removal and hydrophilic modification.

For example, when a patterned ITO substrate is sequentially washed with a detergent, acetone, and isopropyl alcohol (IPA), dried on a heating plate at <NUM> to <NUM> for <NUM> to <NUM> minutes, preferably at <NUM> for <NUM> minutes for moisture removal, and is completely washed, the surface of the substrate is hydrophilically modified.

By the surface modification as described above, the junction surface potential may be maintained at a level suitable for the surface potential of the photoactive layer. In addition, during the modification, a polymer thin film may be easily formed, and the quality of the thin film may also be enhanced.

Examples of a pretreatment technology of the anode electrode include a) a surface oxidation method using a parallel plate discharge, b) a method of oxidizing the surface through ozone produced by using UV rays in a vacuum state, c) a method of oxidizing the anode electrode by using an oxygen radical produced by the plasma, and the like.

One of the methods may be selected depending on the state of the anode electrode or the substrate. However, it is commonly preferred that oxygen on the surface of the anode electrode or the substrate is prevented from leaving, and moisture and organic materials are maximally suppressed from remaining even when any of the methods is used. In this case, a substantial effect of the pre-treatment may be maximized.

As a specific example, it is possible to use a method of oxidizing the surface from the ozone produced by using UV. In this case, after being ultrasonically cleaned, the patterned ITO substrate is baked and well dried on a hot plate, and introduced into a chamber, and then may be cleaned by the ozone produced by actuating a UV lamp to react an oxygen gas with the UV rays.

However, the method of modifying the surface of the patterned ITO substrate in the present specification need not be particularly limited, and any method may also be used as long as the method is a method of oxidizing the substrate.

The cathode electrode may be a metal having a small work function, but is not limited thereto. Specific examples thereof include metal such as magnesium, calcium, sodium, potassium, titanium, indium, yttrium, lithium, gadolinium, aluminum, silver, tin, and lead, or an alloy thereof; and a material having a multilayered structure, such as LiF/Al, LiO<NUM>/Al, LiF/Fe, Al:Li, Al:BaF<NUM>, and Al:BaF<NUM>:Ba, but are not limited thereto.

The cathode electrode may be deposited and formed inside a thermal deposition device allowing a degree of vacuum of <NUM>,<NUM> Pa (<NUM> x <NUM>-<NUM> torr) or less, but is not limited to the method.

The hole transport layer and/or electron transport layer materials serve to efficiently transfer electrons and holes separated from the photoactive layer to the electrode, and the material is not particularly limited.

The hole transport layer material may be PEDOT:PSS (Poly(<NUM>,<NUM>-ethylenediocythiophene) doped with poly(styrenesulfonic acid)), molybdenum oxide (MoOx); vanadium oxide (V<NUM>O<NUM>); nickel oxide (NiO); and tungsten oxide (WOx), and the like, but is not limited thereto.

The electron transport layer material may be electron-extracting metal oxides, and may be specifically a metal complex of <NUM>-hydroxyquinoline; a complex including Alq<NUM>; a metal complex including Liq; LiF; Ca; titanium oxide (TiOx); zinc oxide (ZnO); cesium carbonate (Cs<NUM>CO<NUM>) and the like, but is not limited thereto.

The photoactive layer may be formed by dissolving a photoactive material such as an electron donor and/or an electron acceptor in an organic solvent, and then coating the resulting solution by a method such as spin coating, dip coating, screen printing, spray coating, doctor blade and brush painting, but the method is not limited thereto.

The preparation method of the copolymer and the manufacture of an organic solar cell including the same will be specifically described in the following Preparation Examples and Examples. However, the following Examples are provided to illustrate the present specification, but the scope of the present specification is not limited thereby.

<NUM> of chlorobenzene, <NUM> (<NUM> mmol) of <NUM>,<NUM>-bis(trimethylstannyl)thiophene, <NUM> (<NUM> mmol) of <NUM>,<NUM>-dibromo-<NUM>,<NUM>-bis(<NUM>-(octyloxy)phenyl)quinoxaline, <NUM> (<NUM> mmol) of <NUM>,<NUM>-dibromo-<NUM>-dodecylthieno[<NUM>,<NUM>-c]pyrrole-<NUM>,<NUM>-dione, <NUM> of Pd<NUM>(dba)<NUM> (tris(dibenzylideneacetone)dipalladium(<NUM>)), and <NUM> of tri-(o-tolyl)phosphine were put into a microwave reactor vial, and reacted under the condition of <NUM> for <NUM> hour. After the mixture was cooled to room temperature and poured into methanol, the solid was filtered and subjected to Soxhlet extraction in methanol, acetone, hexane, and chloroform, and then the chloroform portion was again precipitated in methanol to filter the solid.

<FIG> is a view illustrating a gel permeation chromatography (GPC) of Copolymer <NUM> prepared in Example <NUM>.

<NUM> of chlorobenzene, <NUM> (<NUM> mmol) of <NUM>,<NUM>-bis(trimethylstannyl)thiophene, <NUM> (<NUM> mmol) of <NUM>,<NUM>-dibromo-<NUM>,<NUM>-bis (octyloxy)benzo[c]-<NUM>,<NUM>,<NUM>-thiadiazole, <NUM> (<NUM> mmol) of <NUM>,<NUM>-dibromo-<NUM>,<NUM>-bis(<NUM>-(octyloxy) phenyl) quinoxaline, <NUM> of Pd<NUM>(dba)<NUM> (tris(dibenzylideneacetone)dipalladium(<NUM>)), and <NUM> of tri-(o-tolyl)phosphine were put into a microwave reactor vial, and reacted under the condition of <NUM> for <NUM> hour. After the mixture was cooled to room temperature and poured into methanol, the solid was filtered and subjected to Soxhlet extraction in methanol, acetone, hexane, and chloroform, and then the chloroform portion was again precipitated in methanol to filter the solid.

<NUM> of chlorobenzene, <NUM> (<NUM> mmol) of <NUM>,<NUM>'-bis(trimethylstannyl)-<NUM>,<NUM>'-bithiophene, <NUM> (<NUM> mmol) of <NUM>,<NUM>-dibromo-<NUM>,<NUM>-bis (octyloxy)benzo[c]-<NUM>,<NUM>,<NUM>-thiadiazole, <NUM> (<NUM> mmol) of <NUM>,<NUM>-dibromo-<NUM>,<NUM>-bis (<NUM>-(octyloxy)phenyl)quinoxaline, <NUM> of Pd<NUM>(dba)<NUM> (tris(dibenzylideneacetone)dipalladium(<NUM>)), and <NUM> of tri-(o-tolyl)phosphine were put into a microwave reactor vial, and reacted under the condition of <NUM> for <NUM> hour. After the mixture was cooled to room temperature and poured into methanol, the solid was filtered and subjected to Soxhlet extraction in methanol, acetone, hexane, and chloroform, and then the chloroform portion was again precipitated in methanol to filter the solid.

<NUM> of chlorobenzene, <NUM> (<NUM> mmol) of <NUM>,<NUM>-bis-trimethylstannyl-thieno[<NUM>,<NUM>-b]thiophene, <NUM> (<NUM> mmol) of <NUM>,<NUM>-dibromo-<NUM>,<NUM>-bis (octyloxy)benzo[c]-<NUM>,<NUM>,<NUM>-thiadiazole, <NUM> (<NUM> mmol) of <NUM>,<NUM>-bis(5bromothiophene-<NUM>-yl)-<NUM>,<NUM>-bis(<NUM>-(octyloxyphenyl)quinoxaline, and <NUM> of Pd<NUM>(PPh<NUM>)<NUM> (tetrakis(triphenylphosphine)palladium (<NUM>)) were put into a microwave reactor vial, and reacted under the condition of <NUM> for <NUM> hour. After the mixture was cooled to room temperature and poured into methanol, the solid was filtered and subjected to Soxhlet extraction in methanol, acetone, hexane, and chloroform, and then the chloroform portion was again precipitated in methanol to filter the solid.

<NUM> of chlorobenzene, <NUM> (<NUM> mmol) of <NUM>,<NUM>-bis(trimethylstannyl)thiophene, <NUM> (<NUM> mmol) of <NUM>,<NUM>-dibromo-<NUM>,<NUM>-bis(<NUM>-(octyloxy)phenyl)quinoxaline, <NUM> (<NUM> mmol) of <NUM>-(<NUM>,<NUM>- dibromothieno[<NUM>,<NUM>-b]thiophen-<NUM>-yl)-<NUM>-ethylhexan-<NUM>-one, <NUM> of Pd<NUM>(dba)<NUM> (tris(dibenzylideneacetone)dipalladium(<NUM>)), and <NUM> of tri-(o-tolyl)phosphine were put into a microwave reactor vial, and reacted under the condition of <NUM> for <NUM> hour. After the mixture was cooled to room temperature and poured into methanol, the solid was filtered and subjected to Soxhlet extraction in methanol, acetone, hexane, and chloroform, and then the chloroform portion was again precipitated in methanol to filter the solid.

Copolymer <NUM> prepared in Example <NUM> and PC71BM were dissolved in a ratio of <NUM>:<NUM> in chlorobenzene (CB) to prepare a composite solution. In this case, the concentration was adjusted to <NUM> wt%, and the organic solar cell was made to have a structure of ITO/PEDOT:PSS/a photoactive layer/Al. The glass substrate on which the ITO was applied was ultrasonically cleaned by using distilled water, acetone, and <NUM>-propanol, the ITO surface was treated with ozone for <NUM>, PEDOT:PSS (baytrom P) was spin-coated to have a thickness of <NUM>, and heat treatment was performed at <NUM> for <NUM> minutes. For the coating of the photoactive layer, the copolymer <NUM>-PC71BM composite solution was filtered with a <NUM> PP syringe filter and spin-coated, and Al was deposited thereon in a thickness of <NUM> by using a thermal evaporator under a vacuum of <NUM>,<NUM> Pa (<NUM> x <NUM>-<NUM> torr) to manufacture an organic solar cell.

Copolymer <NUM> prepared in Example <NUM> and PC71BM were dissolved at a ratio of <NUM>:<NUM> in chlorobenzene (CB) to prepare a composite solution. In this case, the concentration was adjusted to <NUM> wt%, and the organic solar cell was made to have a structure of ITO/PEDOT:PSS/a photoactive layer/Al. The glass substrate on which the ITO was applied was ultrasonically cleaned by using distilled water, acetone, and <NUM>-propanol, the ITO surface was treated with ozone for <NUM>, PEDOT:PSS (baytrom P) was spin-coated to have a thickness of <NUM>, and heat treatment was performed at <NUM> for <NUM> minutes. For the coating of the photoactive layer, the copolymer <NUM>-PC71BM composite solution was filtered with a <NUM> PP syringe filter and spin-coated, and Al was deposited thereon to have a thickness of <NUM> by using a thermal evaporator under a vacuum of <NUM>,<NUM> Pa (<NUM> x <NUM>-<NUM> torr) to manufacture an organic solar cell.

Copolymer <NUM> prepared in Example <NUM> and PC71BM were dissolved in a ratio of <NUM>:<NUM> in chlorobenzene (CB) to prepare a composite solution. In this case, the concentration was adjusted to <NUM> wt%, and the organic solar cell was made to have a structure of ITO/PEDOT:PSS/a photoactive layer/Al. The glass substrate on which the ITO was applied was ultrasonically cleaned by using distilled water, acetone, and <NUM>-propanol, the ITO surface was treated with ozone for <NUM>, PEDOT:PSS (baytrom P) was spin-coated to have a thickness of <NUM>, and heat treatment was performed at <NUM> for <NUM> minutes. For the coating of the photoactive layer, the copolymer <NUM>-PC71BM composite solution was filtered with a <NUM> PP syringe filter and spin-coated, and Al was deposited thereon to have a thickness of <NUM> by using a thermal evaporator under a vacuum of <NUM>,<NUM> Pa (<NUM> x <NUM>-<NUM> torr) to manufacture an organic solar cell.

The photoelectric transformation characteristics of the organic solar cells manufactured in Preparation Examples <NUM> to <NUM> and Comparative Example <NUM> were measured under the condition of <NUM> mW/cm2 (AM <NUM>), and the results are shown in the following Table <NUM>.

In Table <NUM>, the total thickness means the thickness of the active layer in the organic solar cell, Voc means an open-circuit voltage, Jsc means a short-circuit current, FF means a fill factor, and PCE means an energy conversion efficiency. The open-circuit voltage and the short-circuit current are the intercept of the X-axis and the Y-axis in the fourth quadrant of the voltage-current density curve, respectively, and when the two values becomes high, the efficiency of the solar cell is desirably increased. Furthermore, the fill factor is a value obtained by dividing the area of a rectangle which may be drawn inside the curve by the product of the short-circuit current and the open-circuit voltage. When the three values are divided by the intensity of light irradiated, the energy conversion efficiency may be obtained, and the higher value is preferred.

<FIG> is a view illustrating a current-voltage curve of organic solar cells of Preparation Examples <NUM> to <NUM> of the present specification.

Claim 1:
A random copolymer comprising at least one unit of copolymers represented by the following Copolymers <NUM> to <NUM>:
<CHM>
<CHM>
<CHM>
<CHM>
<CHM>
<CHM>
<CHM>
<CHM>
wherein:
l is a real number, which is <NUM> < l ≤ <NUM> as a mole fraction,
m is a real number, which is <NUM> < m ≤ <NUM> as a mole fraction, <MAT> and
n is an integer of <NUM> to <NUM>,<NUM>.