Separator and method of manufacturing the same and rechargeable lithium battery including the same

A separator for a lithium battery comprising:

• a porous substrate;
• and
• a coating layer on at least one side of the porous substrate, the coating layer having a first side adjacent to the porous substrate, and a second side opposite the first side, the coating layer comprising:
• an inorganic compound;
• and
• a polymer binder comprising a first polymer binder and a second polymer binder, and
• wherein each of the first and second polymer binders is an emulsion type polymer binder that exists as particulates in a solvent, wherein the emulsion type polymer binder is a urethane-based polymer, a styrene-butadiene rubber, an acrylated styrene-butadiene rubber, an acrylonitrile-butadiene rubber, an acrylonitrile-butadiene-styrene rubber, an acrylic rubber, a butyl rubber, a fluorine rubber, polyethylene, polypropylene, an ethylene propylene copolymer, an ethylene propylene diene copolymer, polystyrene, or a combination thereof,
• wherein the first polymer binder has a first average particle diameter of about 50 nm to about 500 nm and the second polymer binder has a second average particle diameter of about 20 nm to about 400 nm, the second average particle diameter being less than or equal to 80% of the first average particle diameter,
• the polymer binder comprises a greater amount of the first polymer binder than the second polymer binder, and
• wherein an amount of the second polymer binder at the second side is greater than an amount of the second polymer binder at the first side.