JP3384956B2 - High density granular detergent composition - Google Patents

Description

Detailed Description of the Invention

[0001]

FIELD OF THE INVENTION This invention relates to high density granular detergent compositions. More specifically, it relates to a high-density granular detergent composition for clothes, which has excellent fluidity and anti-caking property.

[0002]

2. Description of the Related Art A detergent for clothes is used for removing from a washing liquid a surfactant that solubilizes stains and dissolves / disperses from fibers in the washing liquid, and calcium and magnesium that reduce the ability of the surfactant. It is composed of a sequestering agent, an alkaline agent that accelerates the decomposition and solubilization of dirt, and other cleaning builders. The basic idea of the ingredients to be added to the laundry detergent has not changed so much today, but the specific ingredients have been reviewed in consideration of the environment. One of them is the dephosphorization of detergents. In the past, detergents for clothing contained a phosphorus compound such as sodium tripolyphosphate as a sequestering agent. However, there is concern about these phosphorus compounds as one of the causes of eutrophication in lakes and swamps, and as a sequestering agent that replaces phosphorus compounds, crystalline sodium aluminosilicate with a specific structure (synthesized in the industry Zeolite) has come to be used and has reached the present.

On the other hand, with respect to the shape of the detergent, various shapes such as liquid, slurry, paste, powder or granule, tablet or rod have been proposed, and many technologies have been applied and published for each of them. Came. Among these shapes, the compact bulk of the powder detergents in the latter half of the 1980s made a great contribution to transportation, carrying, and storability. Therefore, compact detergents are now predominant. . Therefore, a normal commercial detergent is not only mixed with multi-components, but is also subjected to a granulation step (simultaneously or subsequently) with a high bulk density step to increase the bulk density and the fluidization of the powder. Done and produced. Surfactants incorporated into laundry detergents are not usually one type because they are compatible with various types of stains and have a synergistic effect with multiple surfactants. It is generally used in combination with an agent. Among them, the alkanolamide derivative is a nonionic surfactant that effectively removes dirt derived from sebum. Japanese Unexamined Patent Publication (Kokai) No. 55-62999 discloses a technology relating to a low bulk specific gravity granular detergent containing polyoxyethylene higher fatty acid monoethanolamide belonging to the alkanolamide derivative. However, the composition is compact (granulation /
Higher bulk density) was not intended, and when granulation / higher bulk density was attempted with the composition, the control in the granulation process was possible due to the tackiness due to polyoxyethylene higher fatty acid monoethanolamide. It was found to be difficult, the fluidity of the product was poor, and it caused caking during long-term storage.

[0004]

DISCLOSURE OF THE INVENTION The present invention facilitates a granulation step or a step of increasing bulk density when compounding a fatty acid alkanolamide derivative into a compact detergent,
In addition, the present invention provides a laundry detergent having excellent powder physical properties that does not cause problems such as caking.

[0005]

Means for Solving the Problems As a result of intensive studies to solve the above problems, the present inventors have found that an amide type surfactant having a specific structure suitable for a laundry detergent and a non-soap anionic surfactant. , And a fatty acid salt in a specific ratio, without impairing the basic performance as a detergent, and in addition, the fatty acid alkanolamide derivative and the fatty acid salt specifically form a gel-like substance, thereby sticking the particles. The inventors have found that the properties are significantly reduced and have completed the present invention.

That is, the present invention provides (a) the following general formula (I)

[0007]

[Chemical 3]

(Wherein R ₁ represents a saturated or unsaturated hydrocarbon group having 7 to 19 carbon atoms, R ₂ and R ₃ each independently represent H or CH ₃ , and AO represents an oxyethylene group or an oxyethylene group. 1 to 15% by weight of a fatty acid alkanolamide derivative represented by a propylene group or an oxyalkylene group which is a mixture thereof, n represents the average number of moles of the oxyalkylene group added, and 2 ≦ n ≦ 5), (a), (b) and (c) containing b) 10 to 30% by weight of a non-soap anionic surfactant and (c) 0.5 to 10% by weight of a fatty acid salt having an average carbon number of 10 to 20. The weight ratio of the components is
(A) / (b) = 1/10 to 1/2, (a) / (c) =
The present invention provides a high-density granular detergent composition, which is 1/10 to 2/1.

[0009]

DETAILED DESCRIPTION OF THE INVENTION

<Component (a): fatty acid alkanolamide derivative> The fatty acid alkanolamide derivative used in the present invention has the following general formula (I).

[0010]

[Chemical 4]

(In the formula, R ₁ represents a saturated or unsaturated hydrocarbon group having 7 to 19 carbon atoms, R ₂ and R ₃ each independently represent H or CH ₃ , and AO represents an oxyethylene group or an oxy group. Represents an oxyalkylene group which is a propylene group or a mixture thereof, n represents the average number of moles of addition of the oxyalkylene group, and 2 ≦ n ≦ 5), and n is 2 or more and 5 or less, preferably 2 The number is 4 or less. Further, R ₂ and R ₃ in the formula (I) are preferably H, and it is more preferable that both R ₂ and R ₃ are H. AO is preferably an oxyethylene group. Such a fatty acid alkanolamide derivative can be obtained by, for example, adding an alkylene oxide such as ethylene oxide or propylene oxide to the amidation reaction product of a monoalkanolamine and a fatty acid. In the present invention, the fatty acid alkanolamide derivative is blended in an amount of 1 to 15% by weight.

<Component (b): Non-soap Anionic Surfactant> The non-soap anionic surfactant blended in the present invention is a linear or branched primary or branched chain having 10 to 18 carbon atoms or Sulfate ester salt of secondary alcohol, carbon number 8 ~
Sulfate ester salts of ethoxylates of 20 alcohols, alkylbenzene sulfonates, paraffin sulfonates, α-olefin sulfonates, α-sulfo fatty acid salts, α-sulfo fatty acid alkyl ester salts are preferable. Particularly in the present invention, the number of carbon atoms in the alkyl chain is 12 to 14
Is preferably a linear alkylbenzene sulfonate and / or a sulfuric acid ester salt of a primary alcohol having 12 to 18 carbon atoms, and the counter ion is preferably an ion of an alkali metal. As the counter ion, Na ion is most preferable.
In the present invention, these non-soap anionic surfactants are blended in an amount of 10 to 30% by weight.

<(C): Fatty acid salt> Examples of the fatty acid salt used in the present invention include fatty acid salts obtained from natural fats and oils such as beef tallow, coconut oil and palm kernel oil as a starting material.
The average carbon number is preferably 10 to 20, more preferably 12
-18 alkali metal salts of saturated and / or unsaturated fatty acids. The alkali metal salt is preferably Na salt. In the present invention, as the fatty acid salt, a salt may be used as it is or may be blended by neutralizing the fatty acid with an alkali in an aqueous slurry. In the present invention, the fatty acid salt is added in an amount of 0.5 to 10% by weight.

In the present invention, the weight ratio of the above-mentioned components (a) to (c) is within a specific range. That is, (a),
The weight ratio of the components (b) and (c) is (a) / (b) = 1.
/ 10 to 1/2, preferably 1/5 to 1/2, (a) /
(C) = 1/10 to 2/1, preferably 3/5 to 5/3
And In this range, good fluidity and anti-caking property can be obtained.

<Crystalline aluminosilicate> It is preferable to add a crystalline aluminosilicate to the composition of the present invention. The crystalline aluminosilicate used in the present invention is generally called zeolite, and has the following formula a (M ₂ O) · Al ₂ O ₃ · b (SiO ₂ ) · w (H ₂ O) (II (In the formula, M represents an alkali metal atom, and a, b, and w represent the molar ratio of each component, and generally 0.7 ≤ a ≤ 1.5 and 0.8 ≤ b <
6 and w are arbitrary positive numbers. ],
Among them the following general formula _{(III) Na 2 O · Al} 2 O 3 · n (SiO 2) · w '(H 2 O) (III) [wherein, n represents 1.8 to 3.0, w' is 1 to 6 Represents a number. ]
What is represented by is preferable. As the crystalline aluminosilicate (zeolite), a synthetic zeolite having an average primary particle size of 0.1 to 10 μm represented by A-type, X-type and P-type zeolite is preferably used. Zeolite may be blended as zeolite aggregate dry particles obtained by drying powder and / or zeolite slurry.

In the present invention, the crystalline aluminosilicate is contained in the composition in an amount of 5 to 40% by weight, preferably 15 to 35%.
It is blended by weight%.

<Alkali agent> In order to improve the detergency, the composition of the present invention preferably contains an alkaline agent for making the pH of the washing liquid alkaline. A conventionally known substance can be used as the alkaline agent. Specific examples thereof include alkali metal carbonates such as sodium carbonate, which are collectively referred to as dense ash and light ash, and amorphous alkali metal silicates such as JIS Nos. 1, 2, and 3. These inorganic alkaline agents are suitable for forming the skeleton of the particles when the detergent is dried. Examples of alkalis other than these include sodium sesquicarbonate and sodium hydrogencarbonate, and phosphates such as tripolyphosphate also have an action as an alkali agent. Crystalline silicate is also added as an alkaline agent. The crystalline silicate has a maximum pH of 11 or more when dispersed in ion-exchanged water at 20 ° C. at a concentration of 0.1% or more. It is an excellent alkaline substance that requires an aqueous solution of 5 ml or more, and is a substance distinguished from crystalline aluminosilicate. Crystalline silicate is disclosed in JP-A-7-
89712, JP-A-60-227895 and Phys. Chem. Glasses. 7, p127-p138 (1966), Z. Kristall.
Ogr. , 129, p 396-p404 (1969) and the like. The product name “Na-SKS-6” (δ-Na ₂ Si ₂ O ₅ ) from Hoechst
As powders, powdery and granular ones are available. Two or more of these alkaline agents can be used in combination.

In the present invention, the total amount of the alkaline agent is 5 to 50% by weight, preferably 10 to 30% by weight in the composition.

<Arbitrary Ingredients> Other ingredients commonly known as detergent ingredients may be added to the detergent composition of the present invention as long as this effect is not impaired. For example, in order to improve the detergency, a nonionic surfactant may be used in combination, but it should be noted that the physical properties of the powder are deteriorated. In addition, sequestering agents such as ethylenediaminetetraacetic acid (EDTA) and citrate, polyacrylic acid, copolymers of acrylic acid and maleic acid and carboxylic acid polymers such as carboxymethyl cellulose, extenders such as sodium sulfate, polyethylene glycol. (PEG), polyvinyl alcohol (PVA) and other stain dispersants, and polyvinylpyrrolidone (PVP) color transfer inhibitors, sodium percarbonate and other bleaching agents, as described in JP-A-6-316700 and tetraacetylethylenediamine (TAED). Bleach activator, etc., enzyme such as protease, cellulase, amylase and lipase, enzyme stabilizer such as boron compound and sodium sulfite, biphenyl type, stilbene type fluorescent dye, antifoaming agent such as silicone / silica type, antioxidant Agent, bluing And it can be formulated by a known amount of the known components conventionally such as perfumes. As the above components, specifically those described in JP-A-8-218093 can be used.

<Manufacturing Method> The high-density granular detergent composition of the present invention comprises the above components, and the manufacturing method thereof is not particularly limited, and a conventionally known method can be used. For example, the entire amount of the fatty acid alkanolamide derivative (a) may be blended in an aqueous slurry and dried with other components before use. However, in the present invention, the fatty acid alkanolamide derivative (a) may be mixed prior to the granulation / bulk density increasing step. Alternatively, it is preferably added during the same step. Particularly preferably, a high-density granular detergent having a bulk density of 0.65 g / cm ³ or more is obtained by granulating and densifying spray-dried particles containing a non-soap anionic surfactant and a fatty acid salt. In the method for producing, prior to or during the granulation / high density step using the spray-dried particles, the following general formula (I)

[0021]

[Chemical 5]

(In the formula, R ₁ represents a saturated or unsaturated hydrocarbon group having 7 to 19 carbon atoms, R ₂ and R ₃ each independently represent H or CH ₃ , and AO represents an oxyethylene group or an oxyethylene group. A propylene group or a mixture thereof, which represents an oxyalkylene group, n represents the average number of moles of the oxyalkylene group added, and 2 ≦ n ≦ 5) is produced by a method of adding a fatty acid alkanolamide derivative In this way, it is possible to obtain a detergent having more excellent powder properties. Specifically, powder or granules (spray-dried particles) obtained by drying an aqueous slurry or paste containing a non-soap anionic surfactant (b), a fatty acid salt (c), and other cleaning components. ) Is sprayed with an aqueous solution or emulsion of a fatty acid alkanolamide derivative or a surfactant containing the same, and a method of densifying with stirring using a high speed mixer or a Loedige mixer, and spray-dried particles and After kneading or mixing a fatty acid alkanolamide derivative, and optionally a detergent component such as crystalline silicate with a kneader or a ribbon mixer, the mixture is then compacted into a cylindrical shape with an extrusion molding machine, or a sheet is passed between two rolls. Granulates such as hammer mills, cutter mills, speed mills, etc. How to granulation and the like. In addition, an oil-absorbing carrier or a powder component exhibiting oil-absorbing property is allowed to occlude the liquid surfactant directly under stirring, and in some cases, by further stirring, a method of granulating and densifying is also preferable. is there. The fatty acid salt (c) may be blended in the aqueous slurry as it is, or may be blended by neutralizing the fatty acid with an alkali salt in the aqueous slurry. In order to use the aluminosilicate as a surface modifier for the granulated product, it is preferable to add a small amount during the granulation and / or immediately before the completion of the granulation. When the crystalline silicate is blended, the crystalline silicate should not be blended in the aqueous slurry, but should be added at the time of granulation / high bulk density or by dry blending. When the alkali metal carbonate is blended, it may be added to the slurry, granulation, or dry blending. In addition, it is preferable that additives such as an enzyme, a bleaching agent (and a bleaching activator), and an antifoaming agent containing silicone as a main component be separately granulated and dry blended with the detergent particles obtained by the above-mentioned production method.

<Average Particle Size and Bulk Density> The average particle size of the high-density granular detergent composition of the present invention is preferably 200 to 1000 μm, more preferably 200 to 600 μm in order to obtain preferable powder properties. The bulk density of the detergent composition of the present invention is preferably 0.5 to 1.2 g / cm ³ , and more preferably 0.6 to 1.0 g / cm ³ .

[0024]

According to the present invention, a high density granular detergent composition having excellent fluidity and anti-caking property can be obtained.

[0025]

The present invention will be described in more detail with reference to the following examples, but the present invention is not limited to these examples.

Preparation Example 1 <Preparation of fatty acid alkanolamide derivative AAD-1> 16.5 mol of lauric acid monoethanolamide (LEA) and 2 mol% KOH with respect to LEA as a catalyst.
Was charged into a 7 liter autoclave and heated to 90 ° C. Internal pressure of 3.5 g of ethylene oxide 3.5
Introduced while maintaining below kg / cm ² G, 87-97 ° C
The reaction is continued under the conditions of, and the fatty acid alkanolamide derivative AAD-1 (in the formula (I), R ₁ = C ₁₁ H ₂₃ , R ₂ =
R ₃ = H, n = 3, AO = C ₂ H ₄ O) was obtained.

Preparation Example 2 <Preparation of fatty acid alkanolamide derivative AAD-2> In the above Preparation Example 1, R ₁ ═C ₁₁ H ₂₃ and R ₂ ═R ₃ = in formula (I) while changing the amount of ethylene oxide introduced.
A fatty acid alkanolamide derivative AAD-2 having H, n = 5 and AO = C ₂ H ₄ O was obtained.

Preparation Example 3 <Preparation of fatty acid alkanolamide derivative AAD-3> In the above Preparation Example 1, coconut oil fatty acid monoethanolamide was used in place of LEA, and propylene oxide was used in place of ethylene oxide. ), R ₁ = C _{9 to} C ₁₇ (derived from coconut oil fatty acid), R ₂ = R ₃ =
A fatty acid alkanolamide derivative AAD-3 having H, n = 3 and AO = C ₃ H ₆ O was obtained.

Examples 1-8 and Comparative Examples 1-3 <Preparation of high-density granular detergent composition> (1) The composition of Example 1 in Table 1 was prepared by the following method. 10 kg of zeolite, 20 kg of linear alkylbenzene sulfonic acid sodium, 5 kg of sodium alkyl sulfate ester,
Copolymer 5 kg, sodium carbonate 15 kg, No. 2 sodium silicate 8 kg, Glauber's salt 7 kg, fatty acid salt 3 kg, fluorescent dye 0.
An aqueous slurry of 60% solid content was prepared from 5 kg, and 1.47 kg of particles obtained by spray-drying this was put into a 20-liter Redige mixer (manufactured by Matsusaka Giken Co., Ltd.), and 0.2 kg of zeolite was further added. While mixing these, 0.1 kg of polyoxyethylene (ethylene oxide average addition mole number 3) lauric acid monoethanolamide (compound of Preparation Example 1) heated to 50 ° C. was gradually added dropwise. , Granulation was performed. Further, 0.2 kg of zeolite was added 30 seconds before the end of granulation to obtain a high-density granular detergent composition (average particle size 490 μm, bulk density 0.75 g / c
m ³ ). Further, a predetermined amount of detergent enzyme was blended to obtain a detergent composition (Example 1) having a desired composition. The compositions of Examples 2 to 6 and 8 and Comparative Examples 1 to 3 were also produced according to Example 1.

(2) The composition of Example 7 in Table 1 was prepared by the following method. 20 kg of zeolite, 17 kg of linear alkylbenzene sulfonic acid soda, 5 kg of sodium alkyl sulfate ester,
Copolymer 5kg, No. 2 sodium silicate 3kg, Glauber's salt 5k
An aqueous slurry of 60% solid content was prepared from g, 6 kg of fatty acid salt, and 0.5 kg of fluorescent dye, and this was spray-dried to obtain dry particles. Then, 3.075 kg of the dried particles and 0.85 kg of dense ash which is sodium carbonate were charged into a ribbon mixer, and polyoxyethylene (ethylene oxide average addition mole number 3) lauric acid monoethanolamide (preparation Mixing was carried out with further addition by spraying 0.5 kg of the compound of Example 1). Using a pre-extrusion type twin-screw extrusion granulator (pelletter double: manufactured by Fuji Paudal Co., Ltd.), the mixed product has a diameter of 10 m.
m was extruded into a cylindrical shape for consolidation. Molded product 4.
425 kg of zeolite and 0.25 kg of zeolite were pulverized and granulated with a flash mill (manufactured by Fuji Paudal Co., Ltd.) for surface coating. The granulated product was sieved with a sieve having an opening of 1.3 mm, coarse particles were collected, pulverized with a flash mill again, and mixed with the sieve passing fraction. Particles obtained 4.
To 675 kg, 0.25 kg of zeolite and 0.075 kg of detergent enzyme were blended in a V blender, and a treatment which also served as a complement to the coating of the particle surface was performed to obtain the intended detergent composition (Example 7).

The detergent composition thus obtained was tested for fluidity and caking resistance by the following methods. The results are shown in Table 1.
Shown in.

<Fluidity test of high density detergent particles> JIS
K3362 Specified in ASTM: B213-48 using the stand and funnel described in the Synthetic Detergent Test Method.
The fluidity of the high-density detergent particles was measured according to the Flow Rate of Metal Powders.

<Caking resistance test> (Evaluation method) Filter paper (Toyo Filter Paper No. 2), vertical x horizontal x height = 1
Make a 0.2 x 6.2 x 4 (cm) box without a lid (stap the four corners). Into this box, put 50 g of the sample detergent evenly, and put an acrylic resin plate on it and then a lead weight (total weight 15 + 25
0 g). Leave it in a thermo-hygrostat at 30 ° C / 80% RH for 7 days,
Make a decision.

(Judgment method) The sample after the test has an opening of 5
It is gently opened on a wire mesh of 5 mm × 5 mm, and the weight of the sample that has passed is measured to determine the passing rate. The higher the passage rate, the better the caking resistance.

[0035]

[Equation 1]

[0036]

[Table 1]

(Note) AAD-1: polyoxyethylene (ethylene oxide average addition mole number 3) lauric acid monoethanolamide. AAD-2: polyoxyethylene (ethylene oxide average addition mole number 5) lauric acid monoethanolamide. -AAD-3: polyoxypropylene (propylene oxide average addition mole number 3) coconut oil fatty acid monoethanolamide-LAS: sodium alkylbenzene sulfonate [manufactured by Nisseki Detergent Co., Ltd., alkyl benzene sulfonic acid "alkene L (alkyl chain)" Carbon number 10-14) "is 48% Na
Neutralized with OH] ・ AS: Alkyl sulfate soda [Mitsubishi Chemical Corporation]
Soda salt of dovanol 25 sulfate (C ₁₂ -C ₁₅ sulfuric acid) manufactured by α-SFE: α-sulfofatty acid (coconut fatty acid composition) methyl ester sodium salt / fatty acid salt: palmitic acid / oleic acid (= 40/6
0) Sodium salt of mixture-AE: polyoxyethylene alkyl ethers [Nonideddo R-7 (the C ₁₂ -C ₁₅ ethylene oxide to an alcohol that averaged 7.2 mols, Mitsubishi Chemical Co., Ltd.)] zeolite: 4A type, composition M ₂ O ・ Al ₂ O ₃・ 2SiO ₂・
2H ₂ O, average particle size 4 μm, ion exchange capacity 290 CaCO ₃ mg /
g Copolymer: acrylic acid / maleic acid (molar ratio 7 /
3) Na salt of copolymer, average molecular weight 70,000, common component: enzyme [protease (sabinase 12.0
TW: TW, manufactured by Novo Nordisk), lipase (Lipolase 100T, manufactured by Novo Nordisk), alkaline cellulase (KAC500, manufactured by Kao Corporation), amylase (Termamyl 60T, manufactured by Novo Nordisk) 2: 1:
1: 1 (weight ratio)] 1.5% by weight, fluorescent dye [Chinopearl CBS (manufactured by Ciba Geigy) and Whitex SA (manufactured by Sumitomo Chemical Co., Ltd.) mixed at 1: 1 (weight ratio) ] 0.5% by weight

Continuation of the front page (56) Reference JP 58-101200 (JP, A) JP 5-295399 (JP, A) JP 2-154000 (JP, A) JP 2-49099 (JP , A) JP 8-157882 (JP, A) JP 62-253699 (JP, A) JP 6-128599 (JP, A) JP 56-38399 (JP, A) JP 8-60187 (JP, A) (58) Fields investigated (Int.Cl. ⁷ , DB name) C11D 1/00-17/08

Claims (3)

(57) [Claims] 1. (a) The following general formula (I): (In the formula, R ₁ represents a saturated or unsaturated hydrocarbon group having 7 to 19 carbon atoms, and R ₂ and R ₃ are each independently H or CH.
₃ , AO represents an oxyethylene group, an oxypropylene group or an oxyalkylene group which is a mixture thereof, n represents an average number of moles of the oxyalkylene group added,
2 ≦ n ≦ 5) 1 to 15% by weight of fatty acid alkanolamide derivative represented by the formula (b) linear or branched primary having 10 to 18 carbon atoms
Or a sulfate ester salt of secondary alcohol, having 8 to 20 carbon atoms
Alcohol ethoxylate sulfate ester salt,
Alkylbenzene sulfonate, paraffin sulfonic acid
Salt, α-olefin sulfonate, α-sulfo fatty acid
A non-soap anionic surfactant selected from salts and α-sulfo fatty acid alkyl ester salts, and (c) 0.5-10% by weight of a fatty acid salt having an average carbon number of 10-20. The weight ratio of the components (a), (b) and (c) is (a) / (b) = 1/10 to 1/2, (a) /
(C) = 1-10 to 2/1, a high-density granular detergent composition. 2. The component (a) is the R in the general formula (I).
The high-density granular detergent composition according to claim 1, wherein ₂ and R ₃ are both H compounds. 3. (b) a straight or branched chain having 10 to 18 carbon atoms
Sulfate ester salt of primary or secondary alcohol of chain, carbon number
8-20 alcohol ethoxylates of sulfuric acid
Tellurium salt, alkylbenzene sulfonate, paraffin
Ruphonate, α-olefin sulfonate, α-sulfo
Select from fatty acid salts and α-sulfo fatty acid alkyl ester salts
Non-soap of A anion surfactant barrel and (c) average
And a step of treating granulation and high density spray-dried particles containing a fatty acid salt having 10 to 20 carbon atoms, in the prior or the process to the step, (a) the following general formula (I) ## STR2 ] (In the formula, R ₁ represents a saturated or unsaturated hydrocarbon group having 7 to 19 carbon atoms, and R ₂ and R ₃ are each independently H or CH.
₃ , AO represents an oxyethylene group, an oxypropylene group or an oxyalkylene group which is a mixture thereof, n represents an average number of moles of the oxyalkylene group added,
The method for producing a high-density granular detergent composition according to claim 1 or 2 , wherein a fatty acid alkanolamide derivative represented by the formula 2 ≦ n ≦ 5 is added.