Rubber comprised of product of diene-based elastomer, branched polyethylenimine oligomer and reinforcing filler, and tire with component

A method of preparing a rubber composition is provided wherein said rubber composition is comprised of, based on parts by weight per 100 parts by weight rubber (phr):

• (A) 100 phr of at least one conjugated diene-based elastomer,
• (B) about 0.05 to about 1 phr of branched polyethylenimine oligomer,
• (C) about 30 to about 130 phr of reinforcing filler comprised of combination of rubber reinforcing carbon black and precipitated silica,
• (D) silica coupler for said precipitated silica having a moiety reactive with hydroxyl groups on said precipitated silica and another different moiety interactive with said diene-based elastomer(s), and
• (E) about 0.1 to about 8 phr of zinc oxide and from about 0.5 to about 8 phr of fatty acid,
• wherein said method comprises blending said elastomer(s), reinforcing filler, branched polyethylenimine oligomer, coupling agent for said precipitated silica reinforcing filler, zinc oxide and fatty acid in at least two preparatory (non-productive) sequential mixing steps followed by a blending sulfur curative and at least one sulfur vulcanization accelerator in a subsequent final (productive) mixing step;
• wherein said zinc oxide and fatty acid are blended in preparatory mixing step subsequent to a preparatory mixing step in which the said polyethylenimine oligomer is blended with said rubber composition.