Golf balls having a core with surrounding intermediate foam layer

A multi-layered golf ball, comprising:

• i) an inner core comprising a non-foamed thermoset or thermoplastic composition, the inner core having a specific gravity (SGinner) and an outer surface hardness (Hinner core surface) and a center hardness (Hinner core center), the Hinner core surface being greater than the Hinner core center to provide a positive hardness gradient;
• ii) a first intermediate layer disposed about the core;
• iii) a second intermediate layer adjacent to the first intermediate layer;
• wherein at least one of the intermediate layers comprises a foamed thermoset composition and has a specific gravity (SGintermed) and an outer surface hardness (Houter surface of intermed) and a midpoint hardness (Hmidpoint of intermed), the Houter surface of intermed being greater than the Hmidpoint of intermed, to provide a positive hardness gradient;
• wherein the SGinner is greater than the SGintermed, the intermediate layer further having a specific gravity gradient, wherein the intermediate layer has an outer surface specific gravity and a midpoint specific gravity, the outer surface specific gravity being greater than the midpoint specific gravity;
• and
• iv) a cover having at least one layer disposed about the intermediate layer.

A multi-layered golf ball, comprising:

• i) an inner core comprising a non-foamed thermoset or thermoplastic composition, the inner core having a specific gravity (SGinner) and an outer surface hardness (Hinner core surface) and a center hardness (Hinner core center), the Hinner core surface being greater than the Hinner core center to provide a positive hardness gradient;
• ii) an intermediate layer comprising a foamed thermoplastic composition, the intermediate layer being disposed about the core, the intermediate layer having a specific gravity (SGintermed.) and an outer surface hardness (Houter surface of intermed.) and a midpoint hardness (Hmidpoint of intermed.), the Houter surface of intermed. being greater than the Hmidpoint of intermed., to provide a positive hardness gradient;
• wherein the SGinner is greater than the SGintermed., the intermediate layer further having a specific gravity gradient, wherein the intermediate layer has an outer surface specific gravity and a midpoint specific gravity, the outer surface specific gravity being greater than the midpoint specific gravity;
• and
• iii) a cover having at least one layer disposed about the intermediate layer.