Green emitting phosphors combined with broad band organic red emitters with a sharp near IR cut off

Abstract

The invention provides a lighting device (1) comprising (a) a light source (10) configured to generate light source light (11), and (b) a light converter (100) configured to convert at least part of the light source light (11) into visible converter light (111), wherein the light converter (100) comprises a matrix (120) containing an organic luminescent material (140) of the perylene type. The lighting device may further comprise an inorganic luminescent material (130).

Claims

1. A lighting device comprising (a) a light source configured to generate light source light, and (b) a light converter configured to convert at least part of the light source light into visible converter light, wherein the light converter comprises a matrix containing an organic luminescent material as defined by formula (I): ##STR00002## in which: G.sub.1 and G.sub.6 independently comprise a group selected from a linear alkyl, a branched alkyl, an oxygen-containing alkyl, a cycloalkyl, a naphtyl, and Y; wherein each of A, B, C, J and Q independently comprise a group selected from hydrogen, fluorine, chlorine, isopropyl, t-butyl, methoxy, an alkyl with up to 16 carbon atoms, and an oxygen containing alkyl with up to 16 carbon atoms, G.sub.2, G.sub.3, G.sub.4 and G.sub.5 independently comprise a group selected from hydrogen, fluorine, chorine, isopropyl, t-butyl, methoxy, alkyl with up to 16 carbon atoms, and oxygen-containing alkyl with up to 16 carbon atoms, and X; wherein each of D, E, I, L and M independently comprise a group selected from hydrogen, fluorine, chlorine, isopropyl, t-butyl, methoxy, alkyl with up to 16 carbon atoms, and an oxygen-containing alkyl with up to 16 carbon atoms; and in which at least two selected from G2, G3, G4, and G5 at least comprise X, wherein independently at least two of D, E, I, L and M comprise groups selected from fluorine and chlorine.

2. The lighting device according to claim 1, wherein two of the groups G2, G3, G4 and G5 are hydrogen and wherein the two X comprising groups are identical.

3. The lighting device according to claim 1, wherein G2=G5=X, with D=E=F and I=L=M=hydrogen, and wherein G1=G6=Y, with A=C=isopropyl and B=J=Q=hydrogen.

4. The lighting device according to claim 1, wherein G2=G3=G4=G5 are X, with at least one of A or B is a fluorine or chlorine, and wherein C, J, Q are independently selected from F, Cl, or H.

5. The lighting device according to claim 1, wherein the lighting device further comprises an inorganic luminescent material configured to convert at least part of the light source light into at least green light, wherein the organic luminescent material is configured to provide at least red light, and wherein the light source is configured to provide blue light.

6. The lighting device according to claim 5, wherein the inorganic luminescent material comprises a quantum dot based luminescent material, and wherein the inorganic luminescent material is embedded in the matrix.

7. The lighting device according to claim 1, wherein the matrix comprises polyethylene terephthalate (PET).

8. The lighting device according to claim 1, comprising one or more organic luminescent materials selected from the group consisting of: ##STR00003## ##STR00004##

9. A light converter comprising a matrix containing an organic luminescent material as defined by formula (I): ##STR00005## in which: G.sub.1 and G.sub.6 independently comprise a group selected from a linear alkyl, a branched alkyl, an oxygen-containing alkyl, a cycloalkyl, a naphtyl, and Y; wherein each of A, B, C, J and Q independently comprise a group selected from hydrogen, fluorine, chlorine, isopropyl, t-butyl, methoxy, an alkyl with up to 16 carbon atoms, and an oxygen containing alkyl with up to 16 carbon atoms, G.sub.2, G.sub.3, G.sub.4 and G.sub.5 independently comprise a group selected from hydrogen, fluorine, chorine, isopropyl, t-butyl, methoxy, alkyl with up to 16 carbon atoms, and oxygen-containing alkyl with up to 16 carbon atoms, and X; wherein each of D, E, I, L and M independently comprise a group selected from hydrogen, fluorine, chlorine, isopropyl, t-butyl, methoxy, alkyl with up to 16 carbon atoms, and an oxygen-containing alkyl with up to 16 carbon atoms; and in which at least two selected from G2, G3, G4, and G5 at least comprise X, wherein independently at least two of D, E, I, L and M comprise groups selected from fluorine and chlorine.

10. The light converter according to claim 9, wherein two of the groups G2, G3, G4 and G5 are hydrogen and wherein the two X comprising groups are identical, wherein the light converter further comprises an inorganic luminescent material configured to provide at least green light, wherein the inorganic luminescent material comprises a quantum dot based luminescent material, and wherein the matrix comprises polyethylene terephthalate (PET).

11. The light converter according to claim 9, wherein G2=G5=X, with D=E=F and I=L=M=hydrogen, and wherein G1=G6=Y, with A=C=isopropyl and B=J=Q=hydrogen.

12. The light converter according to claim 9, wherein the matrix comprises polyethylene terephthalate (PET).

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Embodiments of the invention will now be described, by way of example only, with reference to the accompanying schematic drawings in which corresponding reference symbols indicate corresponding parts, and in which:

(2) FIGS. 1a-1f schematically depict some embodiments of the lighting device; these drawings are not necessarily on scale;

(3) FIGS. 2a-2j schematically depict some organic materials that were made;

(4) FIGS. 3a-3b show some emission spectra of some of these organic materials; and

(5) FIGS. 4a-4b schematically show some synthesis schemes.

DETAILED DESCRIPTION OF THE EMBODIMENTS

(6) FIG. 1a schematically depicts a lighting device 1 with a light converter 100, which in this embodiment at least comprises the organic luminescent material 140 according to formula 1. The organic luminescent material 140 is in this embodiment embedded in a (polymeric) matrix, such as PET. As can be seen, a remote version is shown, with a non-zero distance d between the luminescent material (in the light converter 100) and the light source(s), indicated with reference(s) 10. The lighting device 1 comprises one or more light sources 10 which are configured to provide light source light 11, especially blue and/or UV light. The lighting device 1 may comprise a plurality of such light sources. When lighting device light, indicated with reference 2, of a white nature is desired, it may be necessary to us an RGB concept, wherein the red color, or at least part thereof, is provided by the red luminescent material 140, and the blue and green light are provided by one or more of the light source and a combination of the light source and another luminescent material, especially the inorganic luminescent material. The inorganic luminescent material is indicated with reference 130, and provides inorganic luminescent material light 131.

(7) The organic luminescent material 140 according to formula I provides upon excitation by the light source light 11 and/or by emission of one or more other luminescent materials, such as e.g. the inorganic luminescent material light 131, organic luminescent material light 141. Here, the light converter 100 is remote from the light source 10, and the organic luminescent material, which is embedded in the light converter 100, is thus also remote. The optional inorganic luminescent material 130 can also be arranged remote, see below, but is by way of example close to the light source 10, such as in a dome and/or as layer on the LED die.

(8) Just by way of example, one light source has been depicted without the inorganic luminescent material 130. However, in another embodiment, all light sources 10 may be configured with at least inorganic luminescent material 130. Also, by way of example three light sources 10 have been depicted. However, more or less than three light sources may be applied.

(9) Note that the light source 10 may provide blue and/or UV light. The inorganic luminescent material 130 may especially, upon excitation (by said light of the light source 10) provide one or more of blue, green, and yellow light. Optionally, the inorganic luminescent material 130 may also provide red light, but especially the inorganic luminescent material 130 has a cutoff equal to or below 600 nm (such as especially having a spectral distribution with at least 70% of the energy below 600 nm).

(10) FIG. 1a, and other figures, schematically depict a device with a light chamber 170, with an enclosure 171, at least partly enclosing a cavity 172, which has a transmissive part 173. In an embodiment, the transmissive part 173 comprises the light converter 100, or may especially consist of the light converter 100. The surface of the non-transmissive part of the enclosure is indicated with reference 171. At least part of the surface 171 may comprise a reflector, such as a reflective coating.

(11) The light converter 100 provides upon excitation light converter light 111, which at least comprises organic luminescent material light 141 but may optionally comprise other luminescence light as well (see below). The lighting device light, indicated with reference 2, at least comprises light converter light 111/organic luminescent material light 141, but may optionally comprise one or more of the light source light 11, inorganic luminescent material light 131, and light of other luminescent materials (not depicted).

(12) FIG. 1b schematically depicts an embodiment wherein the light converter 100 may comprise an upstream layer with inorganic luminescent material 130. Optionally, this may be a light converter comprising two layers comprising the same matrix, but comprising different luminescent materials. The distance of the layer with inorganic luminescent material 130 to the light source is indicated with d1. This distance is in this embodiment non-zero, in contrast to the embodiment schematically depicted in FIG. 1a.

(13) FIG. 1c schematically depicts an embodiment wherein the light converter 100 comprises the inorganic luminescent material 140, e.g. in the form of quantum dots, and the organic luminescent material 130 according to formula I. Both the organic luminescent material 140 and the inorganic luminescent material 130 are in this embodiment embedded in the (remote) light converter, i.e. embedded in the (polymeric) matrix of the light converter 100.

(14) FIG. 1d schematically depicts an embodiment wherein the transmissive part 173 comprises at least two types of segments, with volumes over 0.25 cm.sup.3, wherein the two types of segments comprise different weight ratios organic luminescent material and inorganic luminescent material. For instance, first segments only comprise the organic luminescent material 140 as luminescent material and second segments only comprises inorganic luminescent material 130 as luminescent material. The organic luminescent material 140 may also in this embodiment be embedded in a (polymeric) matrix, such as PET. Likewise, also the inorganic luminescent material 130 may be embedded in a (polymeric) matrix, such as PET.

(15) FIG. 1e schematically depicts an embodiment wherein the enclosure 170 comprises a transmissive diffuser 160 (as transmissive part 173) and the light converter is applied to at least part of the non-transmissive part of the enclosure 171.

(16) FIG. 1f schematically depicts a reflective configuration. As mentioned above, the organic luminescent material 140 and optionally the inorganic luminescent material 140 may (both) be embedded in a (polymeric) matrix.

(17) FIGS. 2a-2j schematically depict some organic luminescent material that have been made of the perylene type, especially embodiments of the organic luminescent material 140. Especially molecules 68, 65, 53, 52, 63, 64, x1, and x2 are desired because of their optical properties, especially those having at least two halogen atoms at each X group. Optical properties of some of the luminescent materials are shown in FIGS. 3a and 3b. These graphs show emission spectra, with amongst others emission curve of material 2 as comparison. When measuring the spectral distribution of the emission energy (power) as a function of the emission wavelength under 450 nm excitation in the range up to 750 nm, then the ratio of e.g. below 645 nm emission to the total emission can be calculated.

(18) Most of the materials were made according to scheme 1 depicted in FIG. 4a or according to scheme 2 depicted in FIG. 4b.

EXAMPLES

Synthesis of 53. See scheme 1,N,N′-Bis-(2,6-diisopropylphenyl)-1,6,7,12-tetrachloroperylene-3,4,9,10-tetracarboxdiimide B

(19) 1,6,7,12-Tetrachloroperylene-3,4:9,10-tetracarboxylic dianhydride; (A, 10.0 g, 19.0 mmol) was finely suspended in propionic acid (250 mL). Then, 2,6-diisopropylaniline (16.7 g, 40 mmol) was added and the mixture was refluxed under nitrogen for 17 h. After cooling to room temperature, water was added to the mixture and the precipitate was filtered, washed extensively with water and then with heptane and dried under vacuum to give 9 g (56% yield) of compound B as an orange solid.

N,N′-Bis(2,6-diisopropylphenyl)-1,6,7,12-tetra(3-fluorophenoxy)perylene-3,4:9,10-tetracarboxdiimide 53

(20) A mixture of N,N′-Bis-(2,6-diisopropylphenyl)-1,6,7,12-tetrachloroperylene-3,4,9,10-tetracarboxdiimide (B, 4 g, 4.7 mmol), 2-fluorophenol (2.5 mL, 28.2 mmol) and K.sub.2CO.sub.3 (4.3 g, 31.0 mmol) in NMP (80 mL) was stirred at 110° C. under nitrogen for 3 h. Then, the contents of the flask were poured into a mixture of water and acetic acid and stirred for 2 h and the precipitated solid was filtered, washed neutral with warm water and vacuum dried at 60° C. The compound was recrystallized from methanol then from a EtOAc/heptanes mixture (2×) then from a DCM/heptanes mixture (3×) and the red solid collected was washed with warm heptane and dried under vacuum. Pure compound 53 (1.6 g, 19% yield) was obtained as a red solid. .sup.19F-NMR (282 MHz, in CDCl.sub.3): δ=−110 ppm. Mass (TOF-ESI, m/z): Calculated for C.sub.72H.sub.55F.sub.4N.sub.2O.sub.8.sup.+ ([M-H].sup.+): 1151.39. Found: 1151.61. λ.sub.max (ethyl acetate)=558 nm, ε=45600. λ (em) (ethyl acetate) 586 nm.

(21) Molecule 53 is depicted in FIG. 2D. As can be seen form this figure, at least two selected from G2, G3, G4, and G5 at least comprise X, wherein independently at least one of D, E, I, L and M of at least two of said at least two selected from G2, G3, G4, and G5 comprise a group selected from fluorine and chlorine. Here, G2, G3, G4 and G5 comprise X, with each of these four comprise a (single) fluorine. Note that not necessarily all four of G2, G3, G4 and G5 comprise identical groups.

Synthesis of N,N′-Bis(2,6-diisopropylphenyl)-1,6,7,12-tetra(2,3-difluorophenoxy) perylene-3,4,9,10-tetracarboxdiimide 65. See scheme 1

(22) A mixture of N,N′-Bis-(2,6-diisopropylphenyl)-1,6,7,12-tetrachloroperylene-3,4,9,10-tetracarboxdiimide (B, 5.4 g, 6.4 mmol), 2,3-difluorophenol (5.0 g, 38.4 mmol) and K.sub.2CO.sub.3 (5.7 g, 41.6 mmol) in NMP (100 mL) was stirred at 110° C. under nitrogen for 5 h. Then, the contents of the flask were poured into acetic acid. After 2 minutes, 2 N aqueous HCl was added and stirred for 10 minutes and the precipitated solid was filtered, washed neutral with warm water and vacuum dried at 60° C. The residue was coated on silica gel and purified by column chromatography (SiO.sub.2, eluent: DCM/Heptane 1/1). The compound was purified again by two recrystallizations from methanol then from a DCM/heptanes mixture (3×). The red solid collected was washed with warm heptane and dried under vacuum. Pure compound 65 (2.1 g, 27% yield) was obtained as a red solid. .sup.19F-NMR (282 MHz, in CDCl.sub.3): δ=−154 ppm and δ=−135 ppm. Mass (TOF-ESI, m/z): Calculated for C.sub.72H.sub.51F.sub.8N.sub.2O.sub.8.sup.+ ([M-H].sup.+): 1223.36. Found: 1223.29. λ.sub.max (ethyl acetate)=548 nm, ε=53400. λ (em) (ethyl acetate) 576 nm.

(23) Molecule 65 is depicted in FIG. 2C. As can be seen form this figure, at least two selected from G2, G3, G4, and G5 at least comprise X, wherein independently at least one of D, E, I, L and M of at least two of said at least two selected from G2, G3, G4, and G5 comprise a group selected from fluorine and chlorine. Here, G2, G3, G4 and G5 comprise X, with each of these four comprise a fluorine (in fact each comprise two fluorine substituents). Note that not necessarily all four of G2, G3, G4 and G5 comprise identical groups.

Synthesis of N,N′-Bis(2,6-diisopropylphenyl)-1,6,7,12-tetra(2,6-difluorophenoxy) perylene-3,4,9,10-tetracarboxdiimide 71. See scheme 1

(24) A mixture of N,N′-Bis-(2,6-diisopropylphenyl)-1,6,7,12-tetrachloroperylene-3,4,9,10-tetracarboxdiimide (B, 4.2 g, 5.0 mmol), 2,6-difluorophenol (5.0 g, 38.4 mmol) and K.sub.2CO.sub.3 (5.3 g, 38.4 mmol) in NMP (80 mL) was stirred at 110° C. under nitrogen overnight. Then, the contents of the flask were poured into a cold 20% acetic acid solution in water. After 5 minutes, 2 N aqueous HCl was added and stirred for 10 minutes and the precipitated solid was filtered, washed neutral with warm water and vacuum dried at 60° C. The residue was coated on silica gel and purified by column chromatography (SiO.sub.2, eluent: DCM/Heptane 2/1). The compound was purified again by a recrystallization from methanol then from a DCM/heptanes mixture (3×). The red solid collected was washed with hot heptane and dried under vacuum. Compound 71 (3.5 g) was obtained as a red solid. .sup.19F-NMR (282 MHz, in CDCl.sub.3): δ=−126 ppm. Mass (TOF-ESI, m/z): Calculated for C.sub.72H.sub.51F.sub.8N.sub.2O.sub.8.sup.+ ([M-H].sup.+): 1223.36. Found: 1223.86. λ.sub.max (ethyl acetate)=556 nm, c=60460. λ (em) (ethyl acetate) 576 nm. Compound 71 is depicted as compound X1 in FIG. 2I.

Synthesis of N,N′-Bis(2,6-diisopropylphenyl)-1,6,7,12-tetra(2,5-dichlorophenoxy) perylene-3,4,9,10-tetracarboxdiimide 72. See scheme 1

(25) A mixture of N,N′-Bis-(2,6-diisopropylphenyl)-1,6,7,12-tetrachloroperylene-3,4,9,10-tetracarboxdiimide (B, 4.0 g, 4.7 mmol), 2,5-dichlorophenol (5.0 g, 30.5 mmol) and K.sub.2CO.sub.3 (4.3 g, 31.0 mmol) in NMP (80 mL) was stirred at 110° C. under nitrogen overnight. Then, the contents of the flask were poured into a cold 20% acetic acid solution in water. After 5 minutes, 2 N aqueous HCl was added and stirred for 10 minutes and the precipitated solid was filtered, washed neutral with warm water and vacuum dried at 60° C. The residue was coated on silica gel and purified by column chromatography (SiO.sub.2, eluent: DCM/Heptane 1/1 to 2/1). The compound was purified again by a recrystallization from a DCM/heptanes mixture (3×). The red solid collected was washed with hot heptane and dried under vacuum. Compound 72 (1.5 g) was obtained as a red solid. Mass (TOF-ESI, m/z): Calculated for C.sub.72H.sub.51Cl.sub.8N.sub.2O.sub.8.sup.+ ([M-H].sup.+): 1355.11 (100%). Found: 1355.36 (100%). λ.sub.max (ethyl acetate)=550 nm, ε=47430. λ (em) (ethyl acetate) 576 nm. Compound 72 is depicted as compound X2 in FIG. 2J.

Synthesis of 68

See Scheme 2

(26) 1,7,-dibromoperylene-3,4,9,10-tetracarboxylic dianhydride D, Perylene-3,4,9,10-tetracarboxylic dianhydride C (40.0 g, 101.9 mmol), iodine (1.0 g, 4.0 mmol) and sulphuric acid (96%, 470 mL) was premixed and stirred for 2 h at room temperature. The reaction temperature was set to 80° C. and bromine (15.5, 301.7 mmol) was added dropwise. The mixture was reacted further at 80° C. for 20 h. The reaction mixture was cooled to room temperature and the excess Br.sub.2 was displaced by nitrogen. The product was precipitated by addition of ice-water and collected by filtration. The precipitate was washed with water several times until the aqueous layer became neutral. Drying in the oven at 60° C. for 3 days gave crude product used for the next step without further purification.

(27) N,N′-Bis-(2,6-diisopropylphenyl)-1,7,-dibromoperylene-3,4,9,10-tetracarboxdiimide E. A mixture of 1,7,-dibromoperylene-3,4,9,10-tetracarboxylic dianhydride D (see above), 2,6-diisopropylaniline (41.5 mL, 220 mmol) in propionic acid (1 L) and NMP (500 mL) was refluxed for 2.5 days under nitrogen. The mixture was cooled to RT and the product was precipitated by addition of water and collected by filtration. The precipitate was washed with water several times until neutral and dried. The product was first purified by column chromatography (SiO.sub.2, eluent: DCM/Heptane 2/1 to DCM) to obtain a mixture of the isomeric diimides. The mixture was washed with EtOH (300 mL) and toluene (300 mL) and then heated at 80° C. in toluene (300 mL) over night. The diimide 2386 was recrystallized from the hot toluene solution. The solid was collected through hot filtration and dried under vacuum to give compound 3 (18 g, 20% yield) as an orange powder.

N,N′-Bis(2,6-diisopropylphenyl)-1,7-bis(2,3-difluorophenoxy) perylene-3,4,9,10-tetracarboxdiimide 68

(28) A mixture of N,N′-Bis-(2,6-diisopropylphenyl)-1,7,-dibromoperylene-3,4,9,10-tetracarboxdiimide (E, 1.5 g, 1.7 mmol), 2,3-difluorophenol (675 mg, 5.2 mmol) and K.sub.2CO.sub.3 (956 mg, 6.9 mmol) in NMP (70 mL) was stirred at 110° C. under nitrogen for 5 h. Then, the contents of the flask were poured into acetic acid. After 2 minutes, 2 N aqueous HCl was added and stirred for 10 minutes and the precipitated solid was filtered, washed neutral with warm water and vacuum dried at 60° C. The residue was coated on silica gel and purified by column chromatography (SiO.sub.2, eluent: DCM/Heptane 1/1). The compound purified again by two recrystallization from a DCM/heptanes mixture (3×). The red solid collected was washed with warm heptane and dried under vacuum. Pure compound 68 (770 mg, 47% yield) was obtained as a red solid. .sup.19F-NMR (282 MHz, in CDCl.sub.3): δ=−155 ppm and δ=−134 ppm. Mass (TOF-ESI, m/z): Calculated for C.sub.72H.sub.51F.sub.8N.sub.2O.sub.8.sup.+ ([M-H].sup.+): 967.33. Found: 967.30. λ.sub.max (ethyl acetate)=528 nm, ε=57200. λ (em) (ethyl acetate) 550 nm.

(29) Molecule 68 is depicted in FIG. 2A. As can be seen form this figure, at least two selected from G2, G3, G4, and G5 at least comprise X, wherein independently at least one of D, E, I, L and M of at least two of said at least two selected from G2, G3, G4, and G5 comprise a group selected from fluorine and chlorine. Here, G2 and G5 comprise X, with each of these two comprise a fluorine (in fact each comprise two fluorine substituents).

Lamps

Example with TLED

(30) A TLED was produced using two different systems, both with CT 4000K and CRI=80:

(31) YAG:Ce+F305 (commercially available organic phosphor) Conversion efficiency=220Lm//Wblue (conversion efficiency=Wblue=amount of lumens generated by conversion of blue light/total power of blue light used)

(32) LuAG:Ce (Lu3Al5O12:Ce) molecule 17 Conversion efficiency=237Lm/Wblue form blue

(33) Hence, the gain is 8%.

Example with Bulb

(34) A bulb was produced using two different systems, both with CCT=2800 CRI 80:

(35) YAG:Ce+F305 Conversion efficiency=185Lm/W form blue

(36) LuAG:Ce molecule 17 Conversion efficiency=230Lm/W form blue

(37) Hence, the gain 24%

Further Examples with a Narrow Band Green Emitter

(38) Another series of combinations of luminescent materials and light source was modeled, which were all tuned at CCT 4000K. The combinations of the emission of a blue LED at 450 nm together with the emission of europium doped Strontium thiogallate (SrGa.sub.2S.sub.4:Eu) and the emission of the below indicated organic luminescent materials were evaluated:

(39) TABLE-US-00002 Material CCT CRI Conversion efficiency Fraction below 645 nm  2 4000 K 86 248 0.65 X1 = 71 4000 K 85 258 0.71 X2 = 72 4000 K 81 271 0.76 68 4000 K 78 287 0.87 17 4000 K 79 277 0.8

(40) From these date it appears that X1, X2 and 68 are either better in CRI, or conversion efficiency or fraction below 645 nm than material 2. For instance, the CRI for 68 is lower, but both conversion efficiency and cutoff are better. For X2, the CRI is slightly better.

(41) Stability Test

(42) Molecules described above tend to degrade under illumination by light used to excite them. We have found that their lifetime can be considerably increased once placed in a aromatic polyester matrix such as polyethylene terephthalate (PET). It was found that the lifetime of the luminescent molecules could be improved by up to a factor of ten as compared to polymer matrices such as polystyrene, polycarbonate and polymethylmethacrylate. We have found that the degradation of the molecules as a function of time can be described by an exponential decay function. In the table below the exponent showing the rate of decay (rate of degradation) under blue illumination at constant intensity (4 W/cm.sup.2) indicates the degradation:

(43) TABLE-US-00003 Material Rate (s−1) PS 5 .Math. 10.sup.−7 PC 1 .Math. 10.sup.−7 PMMA 3 .Math. 10.sup.−7 PET 3 .Math. 10.sup.−8