Modified liquid diene rubbers

A rubber composition, comprising:

• a modified liquid diene rubber (A);
• and
• a solid rubber (B),
• wherein the modified liquid diene rubber (A) has a functional group (a) derived from an acid anhydride, and satisfies (I), (II), and (III) below:
• (I) a functional group equivalent weight of the functional groups (a) is in a range of 400 to 3,500 g/eq,
• (II) a polystyrene-equivalent number average molecular weight (Mn) measured by gel permeation chromatography (GPC) is in a range of 5,000 to 20,000, and
• (III) a melt viscosity at 38° C. is not less than 3 Pa·s and X (K) is not less than 6100 K wherein X is a slope of a linear line passing through two points in a graph in which the two points are values of melt viscosity η(Pa·s) at 38° C. and 60° C. measured with a Brookfield viscometer which are plotted as Ln[η/(Pa·s)] on ordinate versus 1/T (K−1) on abscissa wherein T is a temperature (K), and
• the modified liquid diene rubber (A) is a product of reaction of a liquid diene rubber modified with an unsaturated carboxylic acid anhydride, and a compound of chemical formula (2) or (3):
• Ra—OH (2)
• wherein Ra is a hydrogen atom or an optionally substituted alkyl group,
• Rb2—NH (3)
• wherein Rb at each occurrence is a hydrogen atom or an optionally substituted alkyl group and is optionally the same as or different from one another.