Compounds for electronic devices

10056549 ยท 2018-08-21

Assignee

Inventors

Cpc classification

International classification

Abstract

The present invention relates to a compound of the formula (I), to the use of the compound in an electronic device, and to an electronic device comprising a compound of the formula (I). The present invention furthermore relates to a process for the preparation of a compound of the formula (I) and to a formulation comprising one or more compounds of the formula (I).

Claims

1. A compound of a formula (1-A-1) or formula (1-A-2) ##STR00412## where the following applies to the symbols and indices occurring: Ar* is on each occurrence, identically or differently, an aromatic ring system having 6 to 24 aromatic ring atoms selected from the formulae (A-1) to (A-20) ##STR00413## ##STR00414## ##STR00415## ##STR00416## wherein R.sup.2 in formulae (A-17) to (A-20), is identically or differently H, alkyl groups having 1 to 20 C atoms, or phenyl; or an electron-rich heteroaryl group having 5 to 18 aromatic ring atoms, each of which is optionally substituted by one or more radicals R.sup.2; L is on each occurrence a single bond; R.sup.1 is on each occurrence, identically or differently, H, D, F, Cl, Br, I, C(?O)R.sup.3, CN, Si(R.sup.3).sub.3, NO.sub.2, P(?O)(R.sup.3).sub.2, S(?O)R.sup.3, S(?O).sub.2R.sup.3, a straight-chain alkyl, alkoxy or thioalkyl group having 1 to 20 C atoms or a branched or cyclic alkyl, alkoxy or thioalkyl group having 3 to 20 C atoms or an alkenyl or alkynyl group having 2 to 20 C atoms, where the above-mentioned groups may each be substituted by one or more radicals R.sup.3 and where one or more CH.sub.2 groups in the above-mentioned groups is optionally replaced by R.sup.3C?CR.sup.3, C?C, Si(R.sup.3).sub.2, C?O, C?S, C?NR.sup.3, C(?O)O, C(?O)NR.sup.3, NR.sup.3, P(?O)(R.sup.3), O, S, SO or SO.sub.2 and where one or more H atoms in the above-mentioned groups is optionally replaced by D, F, Cl, Br, I, CN or NO.sub.2, or an aromatic ring system having 6 to 30 aromatic ring atoms, which may in each case be substituted by one or more radicals R.sup.3, where two or more non-aromatic radicals R.sup.1 is optionally linked to one another and may form a ring; R.sup.2is on each occurrence H; R.sup.3 is on each occurrence, identically or differently, H, D, F, Cl, Br, I, C(?O)R.sup.4, CN, Si(R.sup.4).sub.3, NO.sub.2, P(?O)(R.sup.4).sub.2, S(?O)R.sup.4, S(?O).sub.2R.sup.4, a straight-chain alkyl, alkoxy or thioalkyl group having 1 to 20 C atoms or a branched or cyclic alkyl, alkoxy or thioalkyl group having 3 to 20 C atoms or an alkenyl or alkynyl group having 2 to 20 C atoms, where the above-mentioned groups may each be substituted by one or more radicals R.sup.4 and where one or more CH.sub.2 groups in the above-mentioned groups is optionally replaced by R.sup.4C?CR.sup.4, C?C, Si(R.sup.4).sub.2, C?O, C?S, C?NR.sup.4, C(?O)O, C(?O)NR.sup.4, NR.sup.4, P(?O)(R.sup.4), O, S, SO or SO.sub.2 and where one or more H atoms in the above-mentioned groups is optionally replaced by D, F, Cl, Br, I, CN or NO.sub.2, or an aromatic or heteroaromatic ring system having 5 to 30 aromatic ring atoms, which may in each case be substituted by one or more radicals R.sup.4, or an aryloxy or heteroaryloxy group having 5 to 30 aromatic ring atoms, which is optionally substituted by one or more radicals R.sup.4, where two or more radicals R.sup.3 is optionally linked to one another and optionally forms a ring; R.sup.4 is on each occurrence, identically or differently, H, D, F or an aliphatic, aromatic or heteroaromatic organic radical having 1 to 20 C atoms, in which, in addition, one or more H atoms is optionally replaced by D or F; two or more substituents R.sup.4 here is optionally linked to one another and may form a ring; where the compound does not contain a carbazole group; and where at least one group Ar* which represents an electron-rich heteroaryl group having 5 to 18 aromatic ring atoms or an aromatic ring system having 12 to 24 aromatic ring atoms must be present in the compound.

2. The compound according to claim 1, wherein a) the group Ar* conforms to the following formula (H) ##STR00417## where Y is NR.sup.2, PR.sup.2, O or S; and p is on each occurrence equal to 0 or 1, where, for p=0, radicals R.sup.2 are bonded at the relevant positions, and where, for Y?NR.sup.2, the two indices p cannot both be equal to 1; the group is substituted by radicals R.sup.2 at all free positions, and the group R.sup.2 is as defined in claim 1, and the group is optionally connected to the group L at any position, where the bonding may also occur at the site of the bond NR.sup.2 or PR.sup.2; or b) the group Ar* is selected from the formulae (A-1) to (A-20) ##STR00418## ##STR00419## ##STR00420## ##STR00421## wherein R.sup.2 in formulae (A-17) to (A-20), is identically or differently H, alkyl groups having 1 to 20 C atoms, or phenyl.

3. The compound according to claim 2, wherein the group Ar* conforms to the following formula (H) and Y is O or S; p is 1; and the group Ar* is connected to the group L at any position.

4. The compound according to claim 3, wherein R.sup.1 is identically or differently, H, D, a straight-chain alkyl or alkoxy group having 1 to 10 C atoms or a branched or cyclic alkyl or alkoxy group having 3 to 10 C atoms, where the above-mentioned groups may each be substituted by one or more radicals R.sup.3, or an aromatic ring system having 6 to 12 aromatic ring atoms, which may in each case be substituted by one or more radicals R.sup.3, and R.sup.3 is on each occurrence, identically or differently, H, D, F, CN, Si(R.sup.4).sub.3 or a straight-chain alkyl or alkoxy group having 1 to 10 C atoms or a branched or cyclic alkyl or alkoxy group having 3 to 10 C atoms, where the above-mentioned groups may each be substituted by one or more radicals R.sup.4, or an aromatic or heteroaromatic ring system having 5 to 18 aromatic ring atoms, which may in each case be substituted by one or more radicals R.sup.4, R.sup.4 is on each occurrence, identically or differently, H, D, F or an aliphatic, aromatic or heteroaromatic organic radical having 1 to 20 C atoms, in which, in addition, one or more H atoms may be replaced by D or F.

5. The compound according to claim 1, wherein the bonding position of the group L-Ar* to the aromatic six-membered ring of the basic structure of the formula (1-A-1) or formula (1-A-2) is in the para- or meta-position to the nitrogen atom.

6. The compound according to claim 1, wherein the groups R.sup.1 of the group C(R.sup.1).sub.2, do not represent an aromatic ring system and do not represent an aryl group.

7. The compound according to claim 1, wherein the compound contains no electron-deficient heteroaryl group and no keto group, no phosphorus oxide group and no sulfur oxide group.

8. A process for the preparation of the compound according to claim 1, which comprises one or more transition metal-catalysed, coupling reactions by means of which aryl or heteroaryl groups are introduced as substituents are carried out starting from a dihydroacridine derivative.

9. An oligomer, polymer or dendrimer containing one or more compounds according to claim 1, where the bond(s) to the polymer, oligomer or dendrimer is optionally localised at any position in formula (1-A-1) or formula (1-A-2) that are substituted by R.sup.1 or R.sup.2.

10. A formulation comprising at least one polymer, oligomer or dendrimer according to claim 9 and at least one solvent.

11. An electronic device comprising at least one polymer, oligomer or dendrimer according to claim 9.

12. A formulation comprising at least one compound according to claim 1 and at least one solvent.

13. An electronic device comprising at least one compound according to claim 1.

14. The electronic device according to claim 13, wherein the device is an organic integrated circuit, an organic field-effect transistor, an organic thin-film transistor, an organic light-emitting transistor, an organic solar cell, an organic optical detector, an organic photoreceptor, an organic field-quench device, a light-emitting electrochemical cell, an organic laser diode or an organic electroluminescent device.

15. An organic electroluminescent device which comprises the compound according to claim 1 is employed in one or more of the following functions: as hole-transport material in a hole-transport or hole-injection layer, as matrix material in an emitting layer, as electron-blocking material or as exciton-blocking material.

16. The compound according to claim 1, wherein at least one group Ar* which represents an aromatic ring system having 12 to 24 aromatic ring atoms must be present in the compound.

17. The compound according to claim 16, wherein R.sup.1 is identically or differently, H, D, a straight-chain alkyl or alkoxy group having 1 to 10 C atoms or a branched or cyclic alkyl or alkoxy group having 3 to 10 C atoms, where the above-mentioned groups may each be substituted by one or more radicals R.sup.3, or an aromatic ring system having 6 to 12 aromatic ring atoms, which may in each case be substituted by one or more radicals R.sup.3, and R.sup.3 is on each occurrence, identically or differently, H, D, F, CN, Si(R.sup.4).sub.3 or a straight-chain alkyl or alkoxy group having 1 to 10 C atoms or a branched or cyclic alkyl or alkoxy group having 3 to 10 C atoms, where the above-mentioned groups may each be substituted by one or more radicals R.sup.4, or an aromatic or heteroaromatic ring system having 5 to 18 aromatic ring atoms, which may in each case be substituted by one or more radicals R.sup.4, R.sup.4 is on each occurrence, identically or differently, H, D, F or an aliphatic, aromatic or heteroaromatic organic radical having 1 to 20 C atoms, in which, in addition, one or more H atoms may be replaced by D or F.

Description

WORKING EXAMPLES

A) Synthesis Examples

Synthesis of Precursor V1

(1) ##STR00314##

(2) CAS Number: 918163-16-3

1st step: 2-chloro-9,9-dimethyl-9,10-dihydroacridine

(3) 30.3 g (116 mmol) of 2-[2-(4-chlorophenylamino)phenyl]propan-2-ol were dissolved in 700 ml of degassed toluene, and a suspension of 93 g of polyphosphoric acid and 61.7 g of methanesulfonic acid was added, and the mixture was stirred at room temperature for 1 h and heated at 50? C. for 1 h. The batch was cooled and added to ice and extracted three times with ethyl acetate. The combined org. phases were washed with sat. sodium chloride solution, dried over magnesium sulfate and evaporated. Filtration of the crude product through silica gel with heptane/ethyl acetate (20:1) gave 25.1 g (89%) of 2-chloro-9,9-dimethyl-9,10-dihydroacridine as pale-yellow crystals.

2nd step: 10-biphenyl-4-yl-2-chloro-9,9-dimethyl-9,10-dihydroacridine

(4) ##STR00315##

(5) A degassed solution of 57.9 g (243.7 mmol) of 4-bromobiphenyl and 50 g (203.1 mmol) of 2-chloro-9,9-dimethyl-9,10-dihydroacridine in 1000 ml of toluene was saturated with N.sub.2 for 1 h. Then, firstly 5.6 g (10.1 mmol) of DPPF, then 2.28 g (10.1 mmol) of palladium(II) acetate were added to the solution, and subsequently 52.3 g (528 mmol) of NaOtBu in the solid state were added. The reaction mixture was heated under reflux overnight. After cooling to room temperature, 500 ml of water were carefully added. The aqueous phase was washed with 3?50 ml of toluene, dried over MgSO.sub.4, and the solvent was removed in vacuo. Filtration of the crude product through silica gel with heptane/ethyl acetate (20:1) gave 60 g (75%) of 10-biphenyl-4-yl-2-chloro-9,9-dimethyl-9,10-dihydroacridine as pale-yellow crystals.

(6) Furthermore, the following compounds can be prepared in accordance with similar conditions as for the 2nd step of compound V1:

(7) TABLE-US-00004 Starting material 1 Starting material 2 Product Yield V2 embedded image 6267-02-3 embedded image embedded image 78% V3 embedded image 14458-75-4 0embedded image embedded image 92% V4 embedded image embedded image embedded image 88% V5 embedded image 20474-15-1 embedded image embedded image 85% V6 embedded image 25812-87-7 embedded image 0embedded image 80% V7 embedded image 22493-89-6 embedded image embedded image 88% V8 embedded image 34531-15-2 embedded image embedded image 81% V9 embedded image 70626-31-2 embedded image embedded image 75%

(8) Compounds V2a to V9a can be prepared from compounds V2-V9 by halogenation:

10-Biphenyl-4-yl-2,7-dibromo-9,9-dimethyl-9,10-dihydroacridine

(9) ##STR00340##

(10) N-Bromosuccinimide (9.8 g, 55.3 mmol) was added in portions to a solution of the dihydroacridine (9.8 g, 55.3 mmol) in dichloromethane (140 ml) at 0? C. with exclusion of light, and the mixture was stirred at this temperature for 2 h. The reaction was terminated by addition of sodium sulfite solution and stirred at room temperature for a further 30 min. After phase separation, the organic phase was washed with water and the aqueous phase was extracted with dichloromethane. The combined organic phases were dried over sodium sulfate and evaporated in vacuo. The residue was dissolved in ethyl acetate and filtered through silica gel. The crude product was subsequently recrystallised from heptane. Yield: 14 g, 97% of theory, colourless solid.

(11) TABLE-US-00005 Starting material 1 Starting material 2 Product Yield V3a embedded image V3 1 eq. of NBS embedded image 92% V4a embedded image V4 1 eq. of NBS embedded image 97% V5a embedded image V5 1 eq. of NBS embedded image 95% V5b embedded image V5 2 eq. of NBS embedded image 90% V6a embedded image V6 1 eq. of NBS 0embedded image 90% V7a embedded image V7 1 eq. of NBS embedded image 90% V8a embedded image V8 1 eq. of NBS embedded image 90% V9a embedded image V9 1 eq. of NBS embedded image 90%

(12) Compounds 1-14 according to the invention can be obtained from intermediates V1, V2a, V3a, V4a, V5a and V5b by Suzuki coupling.

10-Biphenyl-4-yl-9,9-dimethyl-2-phenyl-9,10-dihydroacridine

(13) ##STR00357##

(14) 6.8 g (55.5 mmol) of benzeneboronic acid, 20 g (50.5 mmol) of 10-biphenyl-4-yl-2-chloro-9,9-dimethyl-9,10-dihydroacridine and 15.3 g (101 mmol) of CsF were suspended in 160 ml of dioxane. 1.8 g (2.5 mmol) of PdCl.sub.2(PCy.sub.3).sub.2 were added to this suspension, and the reaction mixture was heated under reflux for 16 h. After cooling, the organic phase was separated off, filtered through silica gel, washed three times with 200 ml of water and subsequently evaporated to dryness. The residue was recrystallised from toluene and finally sublimed in a high vacuum. The purity was 99.9%. The yield was 6.5 g, corresponding to 30% of theory.

(15) Compounds 2 to 14 according to the invention can be obtained analogously:

(16) TABLE-US-00006 Starting material 1 Starting material 2 Product Yield 2 embedded image V4a embedded image 947770-80-1 0embedded image 72% 3 embedded image V3a embedded image 947770-80-1 embedded image 65% 4 embedded image V4a embedded image 890042-21-4 embedded image 54% 5 embedded image V3a embedded image 890042-21-4 embedded image 60% 6 0embedded image V2a 2 eq. of benzene- boronic acid embedded image 50% 7 embedded image V1 embedded image 947770-80-1 embedded image 52% 8 embedded image V1 embedded image 890042-21-4 embedded image 47% 9 embedded image V5a 1 eq. of benzene- boronic acid embedded image 55% 10 0embedded image V5b 2.eq. of benzene- boronic acid embedded image 60% 11 embedded image V1 embedded image 569343-09-5 embedded image 63% 12 embedded image V1 embedded image 461128-39-8 embedded image 57% 13 embedded image V1 embedded image 1259280-37-9 0embedded image 67% 14 embedded image V1 embedded image 68716-52-9 embedded image 70%

(17) Furthermore, compounds 15 to 18 were obtained from precursors V6a to V9a by Suzuki coupling to phenylboronic acid under analogous conditions:

(18) ##STR00394## ##STR00395##

B) Device Examples

Production of OLEDs

(19) OLEDs according to the invention and OLEDs in accordance with the prior art are produced by a general process in accordance with WO 04/058911, which is adapted to the circumstances described here (layer-thickness variation, materials).

(20) The structure and data for various OLEDs are presented in Examples V1 to V8 and E1 to E6 below (see Tables 1 to 5). Glass plates coated with structured ITO (indium tin oxide) in a thickness of 150 nm are coated with 20 nm of PEDOT (poly(3,4-ethylenedioxy-2,5-thiophene), applied by spin coating from water; purchased from H. C. Starck, Goslar, Germany) for improved processing. These coated glass plates form the substrates to which the OLEDs are applied. The OLEDs basically have the following layer structure: substrate/optional hole-injection layer (HIL)/hole-transport layers (HTL)/optional interlayer (IL)/electron-blocking layer (EBL)/emission layer (EML)/electron-transport layer (ETL)/optional electron-injection layer (EIL) and finally a cathode. The cathode is formed by an aluminium layer with a thickness of 100 nm. The precise structure of the OLEDs is shown in Tables 1 and 3. The materials required for the production of the OLEDs are shown in Table 5.

(21) All materials are applied by thermal vapour deposition in a vacuum chamber. The emission layer here always consists of at least one matrix material (host material) and an emitting dopant (emitter), to which the matrix material or matrix materials is admixed in a certain proportion by volume by co-evaporation. An expression such as H1:SEB1 (95%:5%) here means that material H1 is present in the layer in a proportion by volume of 95% and SEB1 is present in the layer in a proportion of 5%. Analogously, the electron-transport layer may also consist of a mixture of two materials.

(22) The OLEDs are characterised by standard methods. For this purpose, the electroluminescence spectra, the current efficiency (measured in cd/A), the power efficiency (measured in Im/W) and the external quantum efficiency (EQE, measured in percent) as a function of the luminous density, calculated from current/voltage/luminous density characteristic lines (IUL characteristic lines) assuming Lambert emission characteristics, and the lifetime are determined. The electroluminescence spectra are determined at a luminous density of 1000 cd/m.sup.2, and the CIE 1931 x and y colour coordinates are calculated therefrom. The expression U @ 1000 cd/m.sup.2 in Table 2 and 4 denotes the voltage required for a luminous density of 1000 cd/m.sup.2. Finally, EQE @ 1000 cd/m.sup.2 denotes the external quantum efficiency at an operating luminous density of 1000 cd/m.sup.2. LT80 @ 6000 cd/m2 is the lifetime by which the OLED at a luminance of 6000 cd/m.sup.2 has dropped to 80% of the initial intensity, i.e. to 4800 cd/m.sup.2.

(23) The measured data of the various OLEDs are summarised in Tables 2 and 4.

(24) Use of the Compounds According to the Invention in Fluorescent and Phosphorescent OLEDs

(25) The compounds according to the invention are suitable, in particular, as HTM (hole-transport material) or EBM (electron-blocking material) in OLEDs. They are suitable for use in a single layer, but also as a mixed component as HTM, EBM or as constituent of the emitting layer. Compared with comparative devices in accordance with the prior art (V1 to V8), all samples comprising the compounds according to the invention exhibit higher efficiencies together with the same or improved lifetimes (E1 to E6).

(26) Compared with reference material HTMV1 (V2 and V6), the compounds according to the invention exhibit better efficiencies and better lifetimes. Thus, the lifetime of V2 is virtually doubled compared with E1 to E3 in a blue-emitting device, and the lifetime is also virtually doubled in the green-emitting device (V6 compared with E4 to E6).

(27) Compared with reference material HTMV2 (V3 and V7), better or equally good (HTM2) lifetimes are obtained for the compounds according to the invention in blue- or green-emitting devices at the same time as a significant improvement in the efficiency.

(28) Compared with reference material HTMV3 (V4 and V8), significantly better efficiencies and lifetimes are obtained for the compounds according to the invention.

(29) TABLE-US-00007 TABLE 1 Structure of the OLEDs IL HTL IL HTL2 EBL Thickness/ Thickness/ Thickness/ Thickness/ Thickness/ EML ETL Ex. nm nm nm nm nm Thickness/nm Thickness/nm V1 HIL1 HIL2 HIL1 NPB H1(95%):SEB1(5%) ETM1(50%):LiQ(50%) 5 nm 140 nm 5 nm 20 nm 20 nm 30 nm V2 HIL1 HIL2 HIL1 HTMV1 H1(95%):SEB1(5%) ETM1(50%):LiQ(50%) 5 nm 140 nm 5 nm 20 nm 20 nm 30 nm V3 HIL1 HIL2 HIL1 HTMV2 H1(95%):SEB1(5%) ETM1(50%):LiQ(50%) 5 nm 140 nm 5 nm 20 nm 20 nm 30 nm V4 HIL1 HIL2 HIL1 NPB HTMV3 H1(95%):SEB1(5%) ETM1(50%):LiQ(50%) 5 nm 130 nm 5 nm 10 nm 20 nm 20 nm 30 nm E1 HIL1 HIL2 HIL1 NPB HTM1 H1(95%):SEB1(5%) ETM1(50%):LiQ(50%) 5 nm 130 nm 5 nm 10 nm 20 nm 20 nm 30 nm E2 HIL1 HIL2 HIL1 NPB HTM2 H1(95%):SEB1(5%) ETM1(50%):LiQ(50%) 5 nm 130 nm 5 nm 10 nm 20 nm 20 nm 30 nm E3 HIL1 HIL2 HIL1 NPB HTM3 H1(95%):SEB1(5%) ETM1(50%):LiQ(50%) 5 nm 130 nm 5 nm 10 nm 20 nm 20 nm 30 nm

(30) TABLE-US-00008 TABLE 2 Data of the OLEDs U @ EQE LT80 1000 cd/m2 @ 1000 cd/m2 @ 6000 cd/m.sup.2 CIE Ex. V % [h] x y V1 4.7 4.8 70 0.14 0.17 V2 4.2 5.4 55 0.14 0.17 V3 4.4 6.0 90 0.14 0.16 V4 4.5 5.7 60 0.14 0.16 E1 4.2 7.6 100 0.14 0.16 E2 4.3 8.4 90 0.14 0.16 E3 4.3 7.3 135 0.14 0.16

(31) TABLE-US-00009 TABLE 3 Structure of the OLEDs HTL IL HTL2 EBL Thickness/ Thickness/ Thickness/ Thickness/ EML ETL Ex. nm nm nm nm Thickness/nm Thickness/nm V5 HIL2 HIL1 NPB H2(88%):Irpy(12%) ETM1(50%):LiQ(50%) 70 nm 5 nm 90 nm 30 nm 40 nm V6 HIL2 HIL1 HTMV1 H2(88%):Irpy(12%) ETM1(50%):LiQ(50%) 70 nm 5 nm 90 nm 30 nm 40 nm V7 HIL2 HIL1 HTMV2 H2(88%):Irpy(12%) ETM1(50%):LiQ(50%) 70 nm 5 nm 90 nm 30 nm 40 nm V8 HIL2 HIL1 NPB HTMV3 H2(88%):Irpy(12%) ETM1(50%):LiQ(50%) 70 nm 5 nm 10 nm 80 nm 30 nm 40 nm E4 HIL2 HIL1 NPB HTM1 H2(88%):Irpy(12%) ETM1(50%):LiQ(50%) 70 nm 5 nm 10 nm 80 nm 30 nm 40 nm E5 HIL2 HIL1 NPB HTM2 H2(88%):Irpy(12%) ETM1(50%):LiQ(50%) 70 nm 5 nm 10 nm 80 nm 30 nm 40 nm E6 HIL2 HIL1 NPB HTM3 H2(88%):Irpy(12%) ETM1(50%):LiQ(50%) 70 nm 5 nm 10 nm 80 nm 30 nm 40 nm

(32) TABLE-US-00010 TABLE 4 Data of the OLEDs U Efficiency LT80 @ 1000 cd/m2 @ 1000 cd/m2 @ 8000 cd/m.sup.2 CIE Ex. V % [h] x y V5 3.6 14.4 85 0.32 0.63 V6 3.1 13.1 60 0.33 0.64 V7 3.2 17.1 110 0.33 0.63 V8 3.1 15.1 85 0.32 0.63 E4 3.2 17.6 140 0.33 0.64 E5 3.3 18.1 100 0.33 0.63 E6 3.1 17.8 140 0.33 0.64

(33) TABLE-US-00011 TABLE 5 embedded image HIL1 embedded image HIL embedded image NPB embedded image ETM1 00embedded image Alq3 01embedded image H1 02embedded image SEB1 03embedded image LiQ 04embedded image H2 05embedded image Irpy 06embedded image HTMV1 07embedded image HTMV2 08embedded image HTMV3 09embedded image HTM1 (Synthesis Example 7) 0embedded image HTM2 (Synthesis Example 8) embedded image HTM3 (Synthesis Example 10)