Dispersants with multiple aromatic imide anchor groups

A polymer comprising a polymer chain having at least two urethane linkages and at least two pendant imide side chain groups, wherein each imide group is chemically bonded to an aromatic ring the polymer is represented by Formula (1):

• wherein each variable is independently each time it occurs as follow:
• R1 is a non-hydrogen substituent on Q ring and R1 is independently an electron withdrawing group selected from the group of —NO2, —SO2NR′2, —C(O)R′, —SO3M, halogen, —NH2, or —OR′, or an electron releasing alkyl group of 1 to 3 carbon atoms, the number of non-H substituted groups on Q is from 0 to 2;
• wherein M is H, a metal cation, NR′4+, or mixtures thereof;
• each R′ is independently —H or an optionally-substituted alkyl containing 1 to 20 carbon atoms, and the substituent of R′ is hydroxyl or halogen or mixtures thereof;
• Q is a fused or non-fused aromatic ring containing 4n+2 π-electrons, wherein n=1 or more, and n is the number of aromatic rings, and Q is bonded to the imide group in such a way to form a 5 or 6 membered imide ring;
• b is independently 1 or 2;
• and when b is 1 the imide group is terminal and attached to the Pol by one chemical bond and when b is 2 the imide group is a side chain attached to Pol by two chemical bonds;
• d is 1, 2, or 3;
• wherein the 1 to 3 imide groups are optionally attached to R2 at different carbon atoms of R2,
• R2 is a C1 to C20 hydrocarbylene group or a C1 to C20 hydrocarbonylene group or mixtures thereof;
• R2 optionally includes oxygen and/or nitrogen atoms wherein there is at least 2 carbon atoms per every oxygen or nitrogen of R2;
• W′ is a nitrogen atom, an oxygen atom or a direct bond;
• w is one or more;
• Pol is a polyurethane comprising at least two urethane and/or urea linkages and at least one solvent-solubilizing chain selected from the group of polyether, polyolefin, polyester and polyacrylate;
• wherein said at least one of polyether, polyester, polyolefin and polyacrylate terminal chains have a number average molecular weight of 500-2000 g/mole;
• and wherein said at least one solvent-solubilizing chain is selected from pendant, terminal, and/or lateral side chains, or mixtures of said terminal and/or side chains and wherein the polyurethane is essentially linear and is derived from a polyisocyanate with an average isocyanate functionality between 1.9 and 2.1.