Golf ball core with tailored hardness gradient

1. A golf ball, comprising:

a core comprising:

a rubber formulation including a base rubber and a hardening agent having a hardening agent concentration HA C and a hardening agent isomer number HA LN ;

a geometric center hardness H C ;

a surface hardness H S ; and

a hardness gradient H Gr equal to the difference between H C and H S ,

wherein the hardening agent is nitrophenol and

HA

C

*

HA

L

⁢

N

1

-

1

H

Gr

≥

0.4

;

and

a cover layer disposed about the core.

2. The golf ball of claim 1 , wherein

0

.

6

<

HA

C

*

HA

L

⁢

N

1

-

1

H

G

⁢

r

<

0

.

6

⁢

3

.

3. The golf ball of claim 1 , wherein

1

.

5

<

HA

C

*

HA

L

⁢

N

1

-

1

H

G

⁢

r

<

1

.

8

.

4. The golf ball of claim 1 , wherein

2

.

0

<

HA

C

*

HA

L

⁢

N

1

-

1

H

G

⁢

r

<

2

.

5

.

5. The golf ball of claim 1 , wherein HA C is about 0.1 to about 1.0 parts per hundred rubber.

6. The golf ball of claim 1 , wherein H C is in the range of about 50 Shore C to about 85 Shore C, H S is in the range of about 65 Shore C to about 95 Shore C, and H S is greater than H C .

7. The golf ball of claim 1 , wherein the rubber formulation further comprises a co-agent, a filler, and an initiator.

8. The golf ball of claim 1 , wherein the rubber formulation further comprises a radical scavenger.

9. The golf ball of claim 1 , wherein the base rubber is polybutadiene rubber, butyl rubber, or a blend thereof.

10. A golf ball, comprising:

a core comprising:

a rubber formulation including a base rubber, an initiator having an initiator concentration I C , and a hardening agent having a hardening agent concentration HA C and a hardening agent isomer number HA LN ;

a geometric center hardness H C ;

a surface hardness H S ; and

a hardness gradient H Gr equal to the difference between H C and H S ,

wherein the hardening agent is nitrophenol and

HA

C

*

HA

L

⁢

N

1

-

I

c

H

G

⁢

r

≥

0.6

;

and

a cover layer disposed about the core.

11. The golf ball of claim 10 , wherein

0

.

6

⁢

2

<

HA

C

*

HA

L

⁢

N

1

-

I

C

H

G

⁢

r

<

0

.

6

⁢

4

.

12. The golf ball of claim 10 , wherein

1

.

6

<

HA

C

*

HA

L

⁢

N

1

-

I

C

H

G

⁢

r

<

2

.

0

.

13. The golf ball of claim 10 , wherein

2

.

4

<

HA

C

*

HA

L

⁢

N

1

-

I

C

H

G

⁢

r

<

2

.

7

.

14. The golf ball of claim 10 , wherein HA C is about 0.1 to about 1.0 parts per hundred rubber.

15. The golf ball of claim 10 , wherein I C is about 0.5 to about 3.0 parts per hundred rubber.

16. The golf ball of claim 10 , wherein H C is in the range of about 50 Shore C to about 85 Shore C, Hs is in the range of about 65 Shore C to about 95 Shore C, and Hs is greater than H C .

17. A golf ball, comprising:

a core comprising:

a rubber formulation including a base rubber and a hardening agent, wherein the hardening agent is a benzoic compound comprising a first functional group that is a nitro functional group and a second functional group that is selected from the group consisting of hydroxyl, amino, and sulfhydryl functional groups;

a geometric center having a hardness;

a geometric surface having a hardness;

a hardness gradient equal to the difference in the geometric center hardness and the surface hardness,

wherein the hardness gradient is between 2 Shore C and 42 Shore C; and

a cover layer disposed about the core.

18. The golf ball of claim 17 , wherein the hardening agent is nitrophenol.

19. The golf ball of claim 18 , wherein the hardening agent is 2-nitrophenol and the hardness gradient is between 30 Shore C and 42 Shore C.

20. The golf ball of claim 18 , wherein the cover layer comprises a material selected from the group consisting of polyurethanes, polyureas, and hybrids, copolymers, and blends thereof.