JP2770260B2 - Photosensitive elastomer and method for producing the same - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a novel heat-resistant photosensitive elastomer, and more particularly, to a heat-resistant photosensitive elastomer having excellent mechanical properties and good solubility in organic solvents. And its manufacturing method.

[0002]

2. Description of the Related Art Photosensitive resins are highly useful materials used in various fields, such as resist materials, printing inks, paints, plate making materials, and adhesives. Generally, rubber, acrylic, acrylate, thiol, epoxy,
Silicone materials are widely or individually mixed
in use. In particular, a photosensitive resin material using a sulfonyl azide compound and a rubber-based material having a double bond in a polymer molecular chain such as polyisoprene or polybutadiene,
A detailed study is reported in "Photoresist (1975)" by William S. Deforest, and it is known that this is a negative photoresist which is insolubilized by ultraviolet irradiation. In the case of 1,2-polybutadiene having a double bond at a terminal or in a side chain, in the presence of oxygen, or
In the presence of 4,4'-diazidophenyl, it exhibits UV sensitivity and is insolubilized.
It is reported by the Annual Meeting of the Society for Spring Meeting 906 (1975).

[0003] Further, as a photosensitive elastomer composition having another unsaturated double bond in a polymer structure, an elastomeric block copolymer obtained by anionic polymerization is known. For example, a solvent-soluble thermoplastic elastomer comprising a block of a non-elastomeric polymer block having a glass transition temperature of 25 ° C. or higher and an elastomer having a glass transition temperature of 10 ° C. or lower, which is disclosed in JP-B-51-43374, is disclosed. Are known. Also,
Japanese Patent No. 70242 discloses a solvent-soluble thermoplastic multi-branched block copolymer in which a non-elastomer portion composed of a polyfunctional vinyl derivative and an elastomer portion composed of butadiene and isoprene derivatives are formed. As another polymer material, polyvinyl cinnamate which is a polyvinyl-based compound having no unsaturated double bond in the main chain (US Pat.
2725372, JP-B-38-1492, JP-B-40-
20188), a cinnamic acid ester of an ethylene-vinyl alcohol copolymer ((U.S. Pat. 325766)
4), cinnamic acid ester of glyptal resin (Chemicalization, 6
8,387 (1965)), cinnamic acid ester of epoxy resin (Brit. Pat. 3257664), cinnamic acid ester of polyether (Japanese Patent Publication No. 48-17000,
JP-B-51-17465), a cinnamoyl-type polymer having a polystyrene skeleton (JP-B-49-46396),
Acrylic type cinnamoyl type polymer (JP-A-48-74)
594) and the like are well known, and in the aforementioned fields,
Various applications are being considered.

[0004]

However, the above-mentioned photosensitive resin compositions which have been proposed in the prior art have a temperature of from 10 to room temperature.
The target temperature range is around 0 ° C. In the higher temperature range, it is easily deformed thermally, is thermoplastic, and has a double bond at the end. Consideration at the time of processing was necessary, for example, a thermal polymerization inhibitor had to be added. The present invention has been made in view of the above-described problems in the related art. Therefore,
An object of the present invention is to provide a photocurable elastomer that can be used in a high temperature range (150 ° C. or higher).

[0005]

Means for Solving the Problems The inventors of the present invention have conducted research to solve the above-mentioned problems in the conventionally proposed technology. Instead of polyvinyl alcohol, which can easily introduce a functional group, we focused on an aromatic polyamide having a reactive group capable of introducing the above-mentioned photosensitive group, and found that the above-mentioned problems could be solved. Reached. That is, the photosensitive elastomer of the present invention has, as a polymer main chain, a block copolymer composed of an aromatic polyamide having heat resistance and polybutadiene rubber, and a phenolic hydroxyl group which is a reactive group present in an aromatic polyamide portion. And having photosensitivity that is a side chain.

[0006]

Embedded image (Where X and Y represent copolymerization ratios, and 0.7 ≦ X ≦ 1.
0, 0 ≦ Y ≦ 0.3, Z represents an average degree of polymerization, represents an integer of 10 ≦ Z ≦ 200, R is an organic group having a phenolic hydroxyl group, and Ar is a divalent aromatic. W is a photosensitive group represented by the following formula (II);
Represents an integer of 2 ≦ p ≦ 100, m and n are introduction ratios of the photosensitive group W, and 0.01 ≦ m ≦ 1, 0 ≦ n ≦ 0.99.
0.01 ≦ m / (m + n) ≦ 1, and Mw = 15000 to 250,000 of the photosensitive elastomer of the formula (I). )

[0007]

Embedded image -CO-CH = CH-R 'or _{-CH 2 -CH = CH-R'} (II) ( wherein, R 'is a cyclic aliphatic group, an aromatic group or a carbon number
( Means an aliphatic group of 10 or less )

The photosensitive elastomer of the present invention comprises an aromatic polyamide-butadiene-based block copolymer having a phenolic hydroxyl group represented by the following general formula (III) and a compound represented by the following general formulas (IV) and (V): In the presence of a polar solvent.

[0009]

Embedded image (In the formula, R, Ar, X, Y, Z, and p are as defined above.)

Embedded image Q— CO—CH ＝ CH—R ′ (IV) (wherein Q is Cl, Br or I, and R ′ is as defined above.)

Embedded image Q —CH ₂ —CH ＝ CH—R ′ (V) (wherein Q and R ′ are as defined above.)

The aromatic polyamide-polybutadiene block copolymer having a phenolic hydroxyl group which is a reactive group represented by the above general formula (I) used in the present invention may be synthesized by any method. An aromatic diamine compound and a phenol aromatic carboxylic acid are polycondensed in an amide organic solvent represented by N-methyl-2-pyrrolidone under heating in the presence of a phosphite ester catalyst, and then carboxyl is added to both ends. It is desirable to synthesize the polybutadiene-based copolymer having a group by block copolymerization. The polybutadiene-based copolymer having a carboxyl group at both terminals, which can be used here, includes a carboxyl group-terminated polybutadiene, or a carboxyl group-terminated polybutadiene-acrylonitrile copolymer, and can be used as a commercially available product. Available. Further, it can be easily synthesized by radical polymerization or anion polymerization. As the commercially available product, for example,
Hycar CTB and Hycar CTBN (both are trade names) manufactured by Goodrich Corporation are listed.

As the aromatic diamine, for example, metaphenylenediamine, paraphenylenediamine, 4,4'-
Ethylene dianiline, 4,4'-isopropylidene dianiline, 3,4'-oxydianiline, 4,4'-oxydianiline, 3,3'-sulfonyl dianiline, 4,
4'-sulfonyldianiline, 1,4-naphthalenediamine, 1,5-naphthalenediamine, 2,6-naphthalenediamine, 1,3-bis (methaminophenyl)-
1,1,3,3-tetramethyldisiloxane, 4,4 '
-Bis (4-aminophenoxy) diphenyl sulfone,
4,4'-bis (3-aminophenoxy) diphenyl sulfone, 4,4'-bis (4-aminophenoxy) benzophenone, 4,4'-bis (3-aminophenoxy)
Benzophenone, 4,4'-bis (4-aminophenylmercapto) benzophenone, 2,2-bis [4- (2
-Trifluoromethyl-4-aminophenoxy) phenyl] hexafluoropropane, 2,2-bis [4- (3
-Trifluoromethyl-5-aminophenoxy) phenyl] hexafluoropropane, 2,2-bis [4- (3
-Trifluoromethyl-4-aminophenoxy) phenyl] hexafluoropropane, 2,2-bis [4- (2
-Trifluoromethyl-5-aminophenoxy) phenyl] hexafluoropropane, 2,2-bis [4- (4
-Trifluoromethyl-5-aminophenoxy) phenyl] hexafluoropropane, 2,2-bis [4- (2
-Nonafluorobutyl-5-aminophenoxy) phenyl] hexafluoropropane, 2,2-bis [4- (4
-Nonafluorobutyl-5-aminophenoxy) phenyl] hexafluoropropane, 4,4'-diaminodiphenylmethane, o-tolidine, o-dianisidine, and the like, but are not limited thereto. These aromatic diamines may be used alone or in combination.

Phenol aromatic carboxylic acids include
2,5-dihydroxy-1,4-benzenediacetic acid, 5-
Examples thereof include, but are not limited to, dicarboxylic acids such as hydroxyisophthalic acid, 4-hydroxyisophthalic acid, and 4,6-dihydroxyisophthalic acid, and derivatives thereof. These may be used alone or in combination of two or more. Examples of the phosphite used in this synthesis include triphenyl phosphite, diphenyl phosphite, tri-o-tolyl phosphite, di-o-tolyl phosphite, and tri-m-tolyl phosphite. Di-m-tolyl phosphite, tri-p-tolyl phosphite, di-p-tolyl phosphite, tri-o-chlorophenyl phosphite, di-o-chlorophenyl phosphite, tri-phosphite −
Examples include, but are not limited to, p-chlorophenyl and di-p-chlorophenyl phosphite. Further, as the pyridine derivative used together with the phosphite in the present invention, pyridine, 2-pyridone,
3-pyridone, 4-pyridone, 2,4-lutidine, 2,
6-lutidine, 3,5-lutidine and the like can be mentioned.

In the above reaction, polycondensation is carried out in the presence of a phosphite and a pyridine derivative. In this reaction, a solution polymerization method using a mixed solvent containing the pyridine derivative is usually employed. The organic solvent used here is limited in that it does not substantially react with both the reaction components and the phosphite, but is also a good solvent for the components and also a good solvent for the reaction product polymer. Desirably, it is a solvent. Typical examples of such organic solvents are amide solvents such as N-methyl-2-pyrrolidone and N, N-dimethylacetamide. Here, in order to obtain a polymer having a high degree of polymerization, alkali metal salts represented by lithium chloride and alkaline earth metal salts represented by calcium chloride can be added to the reaction system.

The amount of the pyridine derivative used here must be at least equimolar to the carboxyl group, but in practice, it is often used in a large excess including its role as a reaction solvent. . Here, a mixed solvent composed of a pyridine derivative and an organic solvent represented by N-methyl-2-pyrrolidone is preferably used, and the amount of the mixed solvent used usually includes 5 to 30% by weight of the reaction components. Only the amount used. The reaction temperature is usually preferably in the range of 60 to 140 ° C. The reaction time is greatly affected by the reaction temperature, but in any case it is advisable to stir the reaction system until the highest viscosity, which means the highest degree of polymerization, is obtained, often between a few minutes and 20 hours.

Under the above reaction conditions, a polymer having an average degree of polymerization of 2 to 100 using the reaction components in an equimolar amount can be produced. If the average degree of polymerization exceeds 100, it is not preferable in terms of processability and the like, but for a specific purpose, one of them can be excessively used to reduce the average degree of polymerization. After completion of the reaction, the reaction mixture is poured into a non-solvent such as methanol or hexane to separate the produced polymer, and further purified by a reprecipitation method to remove by-products, inorganic salts, and the like. Coalescence can be obtained. In this manner, the obtained aromatic polyamide-butadiene-based block copolymer is used as a main raw material and a compound represented by the above general formula (IV) or (V), which is a photosensitive group, is generally known. By using the above method, the photosensitive elastomer of the present invention can be synthesized.

As the reaction between the aromatic polyamide butadiene block copolymer and the compound represented by the general formula (IV), a condensation reaction with a base is preferably used. Examples of the base include pyridine, triethylamine, sodium hydroxide, dimethylaniline, tetramethylurea, and magnesium metal. Further, if necessary, a metal salt such as lithium chloride or calcium chloride may be added to carry out the reaction. The acid halide used in this reaction (I
V) includes cinnamoyl chloride, cinnamoyl bromide, 3- (2-nitrophenyl) propenoyl chloride, 3- (4-nitrophenyl) propenoyl chloride, 3- (2,4-dinitrophenyl) propenoyl bromide 3- (2,6-dinitrophenyl) propenoyl chloride, 3- (2,6-dinitrophenyl) propenoyl bromide, 3- (2,4,6-trinitrophenyl) propenoyl chloride, 3- (2 , 4,6-trinitrophenyl) propenoyl bromide, 3-o-tolylpropenoyl chloride, 3-m-tolylpropenoyl chloride, 3-p-tolylpropenoyl chloride, 3-
(2,6-dimethylphenyl) propenoyl chloride,
3- (2,4-dimethylphenyl) propenoyl chloride, 3- (3,5-dimethylphenyl) propenoyl chloride, 3- (2,4,6-trimethylphenyl) propenoyl chloride, acryloyl chloride, acryloyl bromide, Crotyl chloride, crotyl bromide, 2
-Pentenoyl chloride, 2-hexenoyl chloride,
4-methyl-2-pentenoyl chloride, 2-butenoyl chloride, 2-nonenoyl chloride, 2-undecenoyl chloride, 2-tridecenoyl chloride, 3-cyclohexylpropenoyl chloride, 3-cyclopentylpropenoyl chloride , 3- (1-naphthyl) propenoyl chloride, 3- (2-naphthyl) propenoyl chloride and the like, but the present invention is not limited thereto.

As the reaction between the aromatic polyamide-butadiene-based block copolymer and the compound represented by the formula (V), a condensation reaction with a base is preferably used. As the base, sodium hydroxide, potassium hydroxide, sodium hydride, potassium hydride, sodium amide,
Examples include sodium carbonate and potassium carbonate. The acid halide (V) used for this reaction includes cinnamyl chloride, cinnamyl bromide, 3- (2-nitrophenyl) propenyl chloride, 3- (4-nitrophenyl) propenyl chloride, 3- (2,4 -Dinitrophenyl) propenyl chloride, 3- (2,4-dinitrophenyl) propenyl bromide, 3- (2,6-dinitrophenyl) propenyl chloride, 3- (2,6-dinitrophenyl) propenyl bromide, 3- (2 , 4,6
-Trinitrophenyl) propenyl chloride, 3-
(2,4,6-trinitrophenyl) propenyl bromide, 3-o-tolylpropenyl chloride, 3-m-tolylpropenyl chloride, 3-p-tolylpropenyl chloride, 3- (2,6-dimethylphenyl) propenyl chloride , 3- (2,4-dimethylphenyl) propenyl chloride, 3- (3,5-dimethylphenyl) propenyl chloride, 3- (2,4,6-trimethylphenyl)
Propenyl chloride, 2-propenyl chloride, 2-propenyl bromide, 2-butenyl chloride, 2-butenyl bromide, 2-pentenyl chloride, 2-hexenyl chloride, 4-methyl-2-pentenyl chloride, 2-
Heptenyl chloride, 2-nonenyl chloride, 2-undecenyl chloride, 2-tridecenyl chloride, 3-cyclohexyl-2-propenyl chloride, 3-cyclopentyl-2-propenyl chloride, 3- (1-naphthyl) propenyl chloride, Examples thereof include 3- (2-naphthyl) propenyl chloride, but the present invention is not limited thereto.

Further, the photosensitive elastomer of the present invention includes:
By mixing a photopolymerization initiator, an excellent cured photocurable resin can be obtained. Specific examples of the photopolymerization initiator include benzophenone, alkyl ethers of benzoin such as methyl, ethyl, isopropyl and isobutyl ether of benzoyl, α-methylbenzoyl, α-methoxybenzoin methyl ether, α-methylbenzoin methyl ether, benzoinphenyl Ether, α-t-butylbenzoin, anthraquinone, 2-chloroanthraquinone, 2,2′-dimethoxyacetophenone, 2,2 ′
-Diethoxyacetophenone, benzyl, bivaloin,
2,4,6-trinitroaniline, 1-nitropyrene,
1,8-dinitropyrene, cyanoacridine, azobisisobutyronitrile, 2,2′-azobispropane,
m, m'-azoxystyrene, benzoyl peroxide, di-t-butyl peroxide, 1- or 2-
Naphthyl peroxide, diphenyl sulfide, diphenyl disulfide, dibenzyl sulfide, dibenzyl disulfide, dibenzothiazoyl disulfide, methyl diethyl dithiocarbamate, S-acyl dithiocarbamate, decyl thiobenzoate, p, p'-tetramethyldiaminobenzophenone, N- Acetyl-4-
Examples thereof include, but are not limited to, nitro-1-naphthylamine. The amount of the compound to be used is generally 0.01 to 5 parts by weight in the photosensitive composition,
One or more types can be used. In addition to the above photopolymerization initiator, a photosensitization aid may be used for the purpose of broadening the photosensitization wavelength range. As the auxiliary, 1,2-
Examples include quinone compounds such as benzanthraquinone and anthraquinone, aromatic nitro compounds such as 5-nitrofluorene and 5-nitroacenaphthene, and ketone compounds other than the above, but are not limited thereto.

Further, in order to obtain a film-like molded product, a solvent casting method in which a solution of the above-mentioned photocurable resin composition is cast on a suitable substrate is desirable. Usually, a film-like molded product is obtained by casting the solution-type photocurable resin composition of the present invention on a suitable base material, drying it by a conventional method, and peeling it off from the substrate. As the molded article, it is desirable that the film-like molded article can be easily formed on the surface of the substrate and that it can be peeled off, and the material is not particularly limited. For example, a glass plate having a smooth surface, a pet film, a Kapton film, or the like, an aluminum plate, a metal plate such as a copper plate, a metal net-like molded product, or the above-described material that has been subjected to a surface treatment with a release agent can be used. No, can be used. As a light source that can be used in the photocuring method of the photocurable resin composition of the present invention, a light source such as an ultraviolet fluorescent lamp, a low-pressure mercury lamp, a high-pressure mercury lamp, an electron beam, or a laser can be used.
The irradiation time is several minutes to several hours, and is set according to the distance from the light source, the illuminance of the light source, and the photosensitivity. Further, the photocurable resin composition of the present invention may contain, if necessary, a thermal polymerization inhibitor, a coloring agent, and a filler (inorganic powder, glass fiber, shirasu balloon,
Glass hollow bodies) and other chain transfer agents can be added and used.

[0020]

The present invention will be described in detail with reference to the following examples, but the present invention is not limited to these examples. Synthesis Example 1: Synthesis of aromatic polyamide having cinnamoyl group 5.018 g (27.56 mmol) of 5-hydroxyisophthalic acid, 3,4 ′ in a 500 ml three-necked round bottom flask
-Oxydianiline 6.074 g (30.32 mmol), calcium chloride 2.08 g, lithium chloride 0.6
9 g, N, N-dimethylacetamide (55.5 g), pyridine (8.6 g), and triphenyl phosphite (18.8 g) were added, and the mixture was subjected to polycondensation at 90 ° C. for 2 hours under a dry nitrogen atmosphere to obtain a terminal-reactive aromatic polyamide oligomer. Prepared. Next, 10 g of a liquid polybutadiene acrylonitrile rubber having a carboxyl group at the terminal dissolved in 50 ml of N, N-dimethylacetamide (Hycar CTBN10)
08-SP: BF-Goodrich) was added to the reactor and allowed to react for an additional 2 hours. This was allowed to cool to room temperature, diluted with 40 ml of N, N-dimethylacetamide, and poured into an 800 ml methanol precipitation bath with stirring to obtain a polymer powder. This crude polymer was purified by a conventional method. 19.91 g (99 yield)
%), Intrinsic viscosity ηinh = 0.51 dl / g (30 ° C.,
N, N-dimethylacetamide in Oswald viscometer). In order to introduce a cinnamoyl group as a photosensitive group into this crude polymer, the crude polymer 2.
5 g was dissolved in 40 ml of pyridine, and then 2.5 g of lithium chloride was added and dissolved.
72 g was added, and the mixture was stirred and reacted at room temperature for 24 hours. After the completion of the reaction, the mixture was poured into 800 ml of methanol to obtain a crude photosensitive resin. It is produced by a conventional method, and the desired product is obtained in a yield of 2.69.
g, a cinnamoyl group introduction rate of 75% (quantified by ¹ H-NMR method), and a weight average molecular weight of about 42 in terms of polystyrene.
000 (GPC method, solvent 0.1 wt% LiBr / N-methyl-2-pyrrolidone, column: Shodex KD-
80M).

Synthesis Example 2: Synthesis of an aromatic polyamide-block copolymer having a cinnamyl group An aromatic polyamide having a phenolic hydroxyl group as a main raw material was synthesized in the same manner as in Synthesis Example 1 [yield: 19.80 g;
8%, intrinsic viscosity η inh = 0.45 dl / g (30 ° C.,
In an N, N-dimethylacetamide, measured with an Oswald viscometer)], 6.0 g of the crude polymer was dissolved in 40 ml of N, N-dimethyl-imidazolidinone in a 100 ml three-necked round bottom flask, and 0.2 g of the polymer was dissolved. After adding metallic Na and stirring, 1.52 g of cinnamil chloride was added in 10 minutes and reacted at room temperature for 24 hours. After the reaction, the reaction solution was slowly dropped into 2 liters of methanol to precipitate a reaction product. After filtration, purification was conducted by a conventional method, and the yield was 6.8 g, and the weight average molecular weight in terms of polystyrene was about 32000 (GPC
A photosensitive polymer was obtained by the method and a solvent of 0.1 wt% LiBr / N-methyl-2-pyrrolidone, column: Shodex KD-80M).

Example 1 2.0 g of the photosensitive resin obtained in Synthesis Example 1 was dissolved in 8 ml of N, N-dimethylacetamide, and then dissolved in 20 ml × 2.
On a 0 cm glass substrate, a cast film was prepared by a conventional method, and a conveyor type ultraviolet curing device manufactured by Eye Graphics Co., Ltd. (light source: low-pressure mercury lamp (1500 w), 900 mJ /
cm ^2/1 pass) was evaluated using. Example 2 1 part by weight of Michler's ketone as a sensitizer was added to the coating material of Example 1 and evaluated similarly. Example 3 The sensitizer of Example 2 (1 part by weight of Michler's ketone) was added to 1,2
-The same evaluation was performed in place of 1 part by weight of benzanthraquinone.

Example 4 The photosensitive resin obtained in Synthesis Example 2 was processed and evaluated in the same manner as in Example 1. Example 5 The photosensitive resin obtained in Synthesis Example 2 was processed and evaluated in the same manner as in Example 2. Example 6 The photosensitive resin obtained in Synthesis Example 2 was processed and evaluated in the same manner as in Example 3. Evaluation Results Photosensitivity was evaluated by a solubility test in N, N-dimethylformamide of sample films having different numbers of light irradiations. The results are shown in Table 1.

[0024]

[Table 1] ×: dissolved △: partially dissolved ○: insoluble

[0025]

The photosensitive resin of the present invention is excellent in heat stability having polybutadiene acrylonitrile as an aromatic polyamide main chain and an elastomer portion as compared with a usual photosensitive resin, and has an amide or tetrahydrofuran or the like. Excellent solvent solubility in ether organic solvents
It has utility in fields requiring thermal stability and strength. By controlling the molecular weight of the aromatic polyamide as the main raw material and the amount of the photosensitive group introduced, a wide range of physical property control is possible, and wide application is expected.

──────────────────────────────────────────────────続 き Continued on the front page (51) Int.Cl. ⁶ identification code FI G03F 7/027 514 G03F 7/027 514 7/038 501 7/038 501 (58) Investigation field (Int.Cl. ⁶ , DB Name) C08G 81/02 C08G 69/48 C08F 299/00 C08F 299/02

Claims (2)

(57) [Claims] 1. A photosensitive elastomer having a structure represented by the following general formula (I). Embedded image (Where X and Y represent copolymerization ratios, and 0.7 ≦ X ≦ 1.
0, 0 ≦ Y ≦ 0.3, Z represents an average degree of polymerization, represents an integer of 10 ≦ Z ≦ 200, R is an organic group having a phenolic hydroxyl group, and Ar is a divalent aromatic. Group,
W is a photosensitive group represented by the following formula (II), and p is 2
≦ p ≦ 100 represents an integer, m and n are introduction ratios of the photosensitive group W, and 0.01 ≦ m ≦ 1, 0 ≦ n ≦ 0.99,
0.01 ≦ m / (m + n ) ≦ 1, also a Mw = from 15000 to 250000 of the photosensitive elastomer of formula (I)) ## STR2 ## -CO-CH = CH-R 'or _-CH 2 -CH = CH-R '(II) wherein R' is a cyclic aliphatic group, an aromatic group,
( Means an aliphatic group of 10 or less ) 2. A phenolic hydroxyl group-containing aromatic polyamide-butadiene-based block copolymer, which is a precursor represented by the following general formula (III), is converted into a compound represented by the following general formula (IV) or (V): The method for producing a photosensitive elastomer according to claim 1, wherein the reaction is carried out. Embedded image (Wherein R, Ar, X, Y, Z and p are as defined above). Q- CO-CH = CH-R '(IV) (wherein Q is Cl, Br or a I, R 'is as defined above.) embedded image _{Q -CH 2 -CH = CH-R} ' in (V) (wherein, Q, R 'is as defined above. )