Dual core golf ball having negative-hardness-gradient thermoplastic inner core and steep positive-hardness-gradient thermoset outer core layer

A golf ball comprising:

• an inner core layer comprising a thermoplastic highly neutralized polymer composition and having a geometric center hardness less than a surface hardness to define a positive hardness gradient, the center hardness being about 30 Shore D to 65 Shore D and the surface hardness being 40 Shore D to about 65 Shore D;
• an outer core layer disposed about the inner core, the outer core being formed from a substantially homogenous thermoset composition comprising a diene rubber and having an inner surface hardness less than an outer surface hardness to define a positive hardness gradient of about 11 Shore D to about 25 Shore D;
• and
• a cover layer disposed about the outer core layer, the cover layer comprising an inner cover layer comprising an ionomer and an outer cover layer comprising a polyurethane;
• wherein the highly neutralized polymer composition comprises an acid copolymer of ethylene and an α,β-unsaturated carboxylic acid;
• a non-acid polymer comprising polyolefins, polyamides, polyesters, polyethers, polyurethanes, metallocene-catalyzed polymers, single-site catalyst polymerized polymers, alkyl acrylate rubber, ethylene propylene rubber, ethylene propylene diene rubber, styrenic block copolymer rubbers, alkyl acrylate rubbers, or functionalized derivatives thereof;
• an organic acid or salt thereof;
• and a cation source present in an amount sufficient to neutralize at least about 80% of the acid groups present in the composition.