Copolymer of ethylene and a 1,3-diene

1. A process for the preparation of a copolymer of ethylene and of a 1,3-diene of formula (I) which comprises ethylene units and units of the 1,3-diene, the ethylene units representing between 50 mol % and 95 mol % of the ethylene units and of the units of the 1,3-diene, and the units of the 1,3-diene of 1,2 and 3,4 configuration representing more than 50 mol % of the units of the 1,3-diene,

CH 2 =CR−CH=CH 2   (I)

the symbol R representing a hydrocarbon chain having from 3 to 20 carbon atoms, wherein the process comprises the polymerization of ethylene and of the 1,3-diene in the presence of a catalytic system based at least on a metallocene of formula (II) and on an organomagnesium compound of formula (III)

P(Cp 1 Cp 2 )Nd(BH 4 ) (1-y) -L y -N x   (II)

MgR 1 R 2   (III)

Cp 1 and Cp 2 , which are identical or different, being selected from the group consisting of substituted fluorenyl groups and the unsubstituted fluorenyl group of formula C 13 H 8 ,

P being a group bridging the two Cp 1 and Cp 2 groups and representing a ZR 3 R 4 group, Z representing a silicon or carbon atom, R 3 and R 4 , which are identical or different, each representing an alkyl group comprising from 1 to 20 carbon atoms,

y, which is an integer, being equal to or greater than 0,

x, which is or is not an integer, being equal to or greater than 0,

L representing an alkali metal selected from the group consisting of lithium, sodium and potassium,

N representing a molecule of an ether,

R 1 and R 2 , which are identical or different, representing a carbon group.

2. The process according to claim 1 , in which the metallocene is of formula (IIa), (IIb), (IIc), (IId) or (IIe)

[{Me 2 SiFlu 2 Nd(μ-BH 4 ) 2 Li(THF)} 2 ]  (IIa)

[Me 2 SiFlu 2 Nd(μ-BH 4 ) 2 Li(THF)]  (IIb)

[Me 2 SiFlu 2 Nd(μ-BH 4 )(THF)]  (IIc)

[{Me 2 SiFlu 2 Nd(μ-BH 4 )(THF)} 2 ]  (IId)

[Me 2 SiFlu 2 Nd(μ-BH 4 )]  (IIe)

the symbol Flu representing the fluorenyl group of formula C 13 H 8 .

3. The process according to claim 1 , in which R 1 and R 2 contain from 2 to 10 carbon atoms.

4. The process according to claim 1 , in which R 1 and R 2 each represent an alkyl.

5. The process according to claim 1 , in which the organomagnesium compound is a dialkylmagnesium compound.

6. The process according to claim 1 , in which the ethylene units represent at least 60 mol % of the ethylene units and of the units of the 1,3-diene.

7. The process according to claim 1 , in which the ethylene units represent from 60 mol % to 90 mol % of the ethylene units and of the units of the 1,3-diene.

8. The process according to claim 1 , in which the ethylene units represent from 70 mol % to 90 mol % of the ethylene units and of the units of the 1,3-diene.

9. The process according to claim 1 , in which the symbol R represents a hydrocarbon chain having from 6 to 16 carbon atoms.

10. The process according to claim 1 , in which the symbol R represents an acyclic chain.

11. The process according to claim 1 , in which the symbol R represents a linear or branched chain.

12. The process according to claim 1 , in which the symbol R represents a saturated or unsaturated chain.

13. The process according to claim 1 , which copolymer has a glass transition temperature of less than −35° C.

14. The process according to claim 1 , which copolymer has a glass transition temperature of between −90° C. and —35° C.

15. The process according to claim 1 , which copolymer is a random copolymer.

16. The process according to claim 1 , which copolymer is an elastomer.

17. A rubber composition based at least on a copolymer defined in claim 16 and on a crosslinking system.

18. The rubber composition according to claim 17 , which comprises a reinforcing filler.

19. A tire which comprises a rubber composition defined in claim 17 .