Graft-modified, substantially linear ethylene polymers and methods for their use

A substantially linear ethylene polymer grafted with at least about 0.01 wt %, based on the weight of the grafted ethylene polymer, of an unsaturated organic compound containing at least one ethylenic unsaturation and at least one carboxyl group or at least one derivative of the carboxyl group selected from the group consisting of an ester, an anhydride and a salt, the ethylene polymer characterized as having:

• (i) a melt flow ratio, I.sub.10 /I.sub.2, .gtoreq.5.63;
• (ii) a molecular weight distribution, M.sub.w /M.sub.n, defined by the equation:
• M.sub.w /M.sub.n .ltoreq.(I.sub.10 /I.sub.2) -4.63;
• (iii) a density greater than about 0,850 g/cm.sup.3;
• and
• (iv) a critical shear rate at onset of surface melt fracture of at least 50 percent greater than the critical shear rate at the onset of surface melt fracture of a linear olefin polymer having about the same I.sub.2 and Mw/Mn.