High density polyethylene compositions with long-chain branching

A polyethylene composition having density within the range from 0.930 g/cm3 to 0.975 g/cm3 and comprising 98 to 99.9 wt % units derived from ethylene and the balance derived from a comonomer selected from 1-butene, 1-hexene, and 1-octene, said wt % s based on ethylene content plus comonomer content;

• further wherein the polyethylene composition has one or both of the following:
• (a) LOW Ratio of greater than 0.03, where the LOW Ratio is defined as:
• MI
• ⁢
• η
• 6
• ⁢
• 2
• ⁢
• 8
• M
• n
• ⁢
• g
• LCB
• ′
• where MI is melt index (g/10 min at 2.16 kg, 190° C.);
• I628 is the complex viscosity at 628 rad/s (in Pa*s);
• Mn is number-average molecular weight (g/mol);
• and g′LCB is the long-chain branching index;
• and
• (b) Broad-High Ratio of greater than or equal to 0.2, where the Broad-High Ratio is defined as:
• Mz
• *
• HLMI
• Mn
• *
• g
• LCB
• ′
• *
• η
• 0
• .
• 0
• ⁢
• 1
• where Mz and Mn are z- and n- average molecular weights, respectively (g/mol);
• HLMI is high load melt index (g/10 min at 21.6 kg, 190° C.);
• η0.01 is the complex viscosity at 0.01 rad/s (in Pa*s);
• and g′LCB is the long-chain branching index.