MULTIAMINE POLYESTER DISPERSANT PRODUCED VIA AN ANHYDRIDE INTERMEDIARY.

Abstract

The present invention relates to a dispersant derived from an alcohol-terminated polymer via an anhydride intermediate. The anhydride-functionalized polyester is then reacted with a multiamine species that forms amide and salt linkages.

Description

MULTIAMINE POLYESTER DISPERSANT PRODUCED VIA AN ANHYDROUS INTERMEDIATE FIELD OF INVENTION The present invention relates to a dispersant of a multiamine species (a polyamine, such as polyethyleneimine) that is reacted with polyester and / or polyether chains and a method for making the dispersant by means of an anhydride intermediate. BACKGROUND OF THE INVENTION Polyamine-derived dispersants are generally understood to be effective pigment dispersants. The composition and molecular weight of the sterically stabilizing chains in these dispersants are important for effectively dispersing solids in continuous media, both polar and nonpolar. Many formulations, such as inks, paints, base mixes, and plastic materials, require dispersants to uniformly distribute particulate solids in organic media. Therefore, it is desirable that pigment dispersions be compatible with different ink or coating formulations. Multiamine-based dispersants with a mixture of salt and amide linkages have also been found to be more effective. However, these dispersants can be difficult to manufacture using alcohol-terminated polymers. It would be desirable to have dispersants that include both internal salt and amide linkages but can be conveniently prepared from alcohol-terminated polyether and / or polyester-based polymers. BRIEF DESCRIPTION The present invention provides a method for preparing a dispersant having the formula (X-tCH^CHR'-OMR-XTR^b-KC^R^OJm^^ Jq[O -(C=O)-RJ]P MA (H*)q-PFormula 1 [(C=o)-r4]: RI frQ / ni Lznz / q / ΥΙΛΙ from an alcohol-terminated polymer. The method for preparing the dispersant of Formula I includes the steps of (a) providing an alcohol-terminated polymer of the formula X-(CH2CHR1-O)n-[R5-N(R6)]b-[(C=O)R2-O]mH (Formula II), (b) reacting the alcohol-terminated polymer with a cyclic anhydride to provide an acid-terminated polymer, (c) reacting the acid-terminated polymer with a non-cyclic anhydride to provide a mixture of anhydrides, and (d) reacting the mixture of anhydrides with a multiamine species, wherein the multiamine species has a number-average molecular weight of 300 to 20,000, to form a dispersant molecule, wherein q and t are each at least one, such that the dispersant contains both amide and salt linkages. In Formula II, X represents either RQ or a cyclic secondary amine.When X is RQ, R is a branched or linear, saturated or unsaturated, or cyclic hydrocarbon chain containing from 1 to 50 carbon atoms, Q is O, or NR7 or NH, with the condition that Q can only be NH when n is 0 and b is 0, and R7 is a linear or branched, saturated or unsaturated hydrocarbon chain containing from 1 to 18 carbon atoms, which may optionally contain ether, ester, or amide functional groups or a halide substituent. Alternatively, X may also be a cyclic amine structure derived from one or more cyclic secondary amines. In Formula II, R1 is H, methyl, or ethyl, R5 is a linear or branched hydrocarbon chain containing up to 3 carbon atoms; R6 is hydrogen, a hydrocarbyl group containing from 1 to 22 carbon atoms, or the residue of an alkyl (meth)acrylate or (meth)acnamide. The variable b is 0 or 1, with the condition that b can only be 1 when both n and m are at least 1.R2 is a linear or branched, saturated or unsaturated hydrocarbon chain containing 1 to 15 carbon atoms or -R8(C=O)YR9-, where Y is O or NH or NR10, R8 is a hydrocarbon chain containing 1 to 10 carbon atoms, R9 is a hydrocarbon chain containing 2 to 10 carbon atoms, and R10 is a hydrocarbon chain containing 1 to 20 carbon atoms. In some embodiments, R10 may include an ester, ether, or amide group. When R2 is a hydrocarbon chain containing 1 to 15 carbon atoms, R2 can be, in one embodiment, a linear or branched, saturated or unsaturated hydrocarbon chain containing 1 to 10 carbon atoms, and in another embodiment, R2 can be a hydrocarbon chain containing 2 to 15 carbon atoms which includes an amide functional group having the formula, -N(R11)-(C=O)-, where R11 is H or a hydrocarbon chain containing. R LfrQ / n / Lznz / q / YILI to 4 carbon atoms. In Formula II, n is any integer from 0 to 65 and m is any integer from 0 to 35, with the condition that m + n is at least 3. The invention also provides a dispersant having the structure of Formula I, wherein X is RQ or a cyclic amine. Where X is RQ, R is a hydrocarbon chain containing from 1 to 50 carbon atoms, Q is O, or NR7 or NH, with the condition that Q can only be NH when n is 0 and b is 0, and R7 is a linear or branched hydrocarbon chain containing from 1 to 18 carbon atoms, which may optionally contain ether, ester, or amide functional groups or a halide substituent. X may also represent a cyclic secondary amine.In Formula I, R1 is H, methyl or ethyl; R5 is a linear or branched hydrocarbon chain containing up to 3 carbon atoms; R6 is hydrogen, a hydrocarbyl group containing from 1 to 50 carbon atoms, or the residue of an alkyl (meth)acrylate or (meth)acrylamide; b is 0 or 1, with the condition that b can only be 1 when both n and m are both at least 1; R2 is a linear or branched, saturated or unsaturated hydrocarbon chain containing 1 to 15 carbon atoms or -R8(C=O)YR9-, where Y is O or NH or NR10, R8 is a hydrocarbon chain containing 1 to 10 carbon atoms, R9 is a hydrocarbon chain containing 1 to 10 carbon atoms and R10 is a hydrocarbon chain containing 1 to 20 carbon atoms, which may include an ester, ether or amide group.When R2 is a hydrocarbon chain containing 1 to 15 carbon atoms, R2 can be, in one embodiment, a linear or branched, saturated or unsaturated hydrocarbon chain containing 1 to 10 carbon atoms, and in another embodiment, R2 can be a hydrocarbon chain containing 2 to 15 carbon atoms which includes an amide functional group having the formula -N(R11)-(C=O)-, where R11 is H, or a hydrocarbon chain containing 1 to 4 carbon atoms. The variable n is any integer from 0 to 65 and the variable m is any integer from 0 to 35, with the condition that m + n is at least 3. R3 is a linear or branched, saturated or unsaturated hydrocarbon containing between 2 and 80 carbons. The variables qyt are each at least 1, while q + t can be any integer from 2 to 150. MA is a multiamine species that has a number-average molecular weight of 300 to 20,000 g / mol.The variables poz could each be 0, op + z can be 0, or any integer from 1 or 2 to 200; R4 is a linear or branched saturated carbon chain containing between 1 and 4 carbon atoms, for example, between 1 and 3. In one embodiment, in Formula I, n is 0. In another embodiment, in the ai no / ni ιτιαη / υιλι. In Formula I, n is any integer from 3 to 65 and m is 0. In another form, in Formula I, m is 0. In another form, in Formula I, m is any integer from 3 to 35, for example, from 5 to 16, and n is 0. In another form, in Formula I, both n and m are positive integers and n + m is from 3 to 65, for example from 5 to 30. DETAILED DESCRIPTION OF THE INVENTION In the following detailed description and in the claims, the term hydrocarbyl refers to monovalent hydrocarbon groups that may optionally include other heteroatoms (such as O and N) in conventional or specified amounts, such as one oxygen and / or nitrogen atom for every two or every ten carbon atoms in the group, but preferably only carbon and hydrogen. When used broadly in this description, the term hydrocarbon chain refers to a compound comprising carbon and hydrogen, which includes variants that are branched, linear, saturated, unsaturated, or ring structures. Hydrocarbon chains may optionally include other atoms, such as heteroatoms including oxygen in the form of ether groups, or nitrogen in the form of amide groups. The present invention relates to a dispersant of the following structure: [ο-(θ=θ)-ιν]ρ MA (HJq-p Formula 1 [X-(CH2CHR1-O)n-[R?-N(R6)]b-[(C=O)RO]m-(C=O)-R!-(C=O)] t [(C=O)-R4]; The dispersing molecule may include, notably, a polyether species, a polyester species, or a combination of both. Additionally, the dispersing molecule will contain both amide and salt linkages. In one embodiment, in Formula I, X represents an RQ group or a cyclic amino group. When X is RQ, R represents a linear or branched, saturated or unsaturated hydrocarbon chain containing from 1 to 50 carbon atoms, for example, from 1 to 30 carbon atoms. In one embodiment, R may optionally include halogens, such as Cl or F, or heteroatoms, such as N or O atoms, which are present as tertiary amino or ether groups, or mixtures thereof. In some embodiments, the hydrocarbon chain may be selected from alkyl hydrocarbon chains, RI frQ / ni Lznz / q / YILI aryl, aralkyl, or alkylaryl. In one embodiment, R is aryl including naphthyl, phenyl, or biphenyl. In one embodiment, R is aralkyl including 2-phenylethyl or benzyl. In one embodiment, R may be alkanyl including octylphenyl or nonylphenyl. In another embodiment, R is cycloalkyl including C3-8 cycloalkyl, such as cyclopropyl or cyclohexyl. In Formula I, Q represents O, NR7, or NH, with the condition that Q can only be NH when n is 0 and b is 0. R7 can be a linear or branched, saturated or unsaturated hydrocarbon chain containing between 1 and 18 carbon atoms, which may optionally contain ether, ester, or amide functional groups, or a halide substituent. In some embodiments, R7 can also be derived from acrylate, methacrylate, acrylamide, or methacrylamide. In another form, RQ is derived from alcohols or amines or mixtures thereof. Useful alcohols include, but are not limited to, methanol, ethanol, n-propanol, n-butanol, neopentyl alcohol, n-hexanol, n-heptanol, n-octanol, n-decanol, n-dodecanol, tetradecanol, n-hexadecanol, oleyl alcohol, n-octadecanol, isopropanol, isobutanol, tert-butanol, 2-ethylbutanol, 2-ethylhexanol, 3-heptanol, 3,5,5-trimethylhexanol, 3,7-dimethyloctanol, cyclohexanol, cyclopentanol, cyclopentanomethanol, cyclohexylmethanol, 4-cyclohexyl-1-butanol, 4-ethylcyclohexanol, cycloheptanol, phenol, ortho-cresol, 2-ethylphenol, 2-propylphenol, 4-ethylphenol, octylphenol, nonylphenol, dodecylphenol, di- and tristyrylphenols, benzyl alcohol, 2-phenylethanol, 1-naphthol, 2-naphthol, 2-phenylphenol, 4-phenylphenol, polyisobutylenephenol, sec-phenethyl alcohol, 4-ethylbenzyl alcohol, alcohol 4-butylbenzyl, 2naphthalenemethanol, 3-phenyl-1-propanol, 4-phenyl-1-butanol, cinnamyl alcohol and 4propoxyphenol, 2-dimethylaminoethanol,2-diethylaminoethanol, 2-dibutylaminoethanol, 2-propen-1-ol, allyl alcohol, 4-penten-1-ol, 2-hexen-1-ol, 3-nonen-1-ol, 7-dodecen-1-ol, 2-allyloxyethanol, 2-allylphenol, 2-vinyloxyethanol, 2-hydroxyethyl methacrylate, hydroxypropyl methacrylate, hydroxybutyl methacrylate, saturated linear alcohols commercially available under the trade name Unilin (available from Baker Hughes) and saturated branched alcohols, such as the Guerbet alcohols which are commercially available under the trade name Isofol (available from Sasol GmbH) which includes mixtures thereof. Specific examples of commercially available Guerbet alcohols are Isofol 12, 14T, 16, 18T, 18E, 20, 24, 28, 32, 32T, and 36. Useful amines include, but are not limited to, primary amines: methylamine, ethylamine, propylamine, butylamine, amylamine, hexylamine, heptylamine, octylamine, nonylamine, decylamine, undecylamine, dodecylamine, tridecylamine, 1-tetradecylamine, R LfrQ / n / Lznz / q / ΥΙΛΙ pentadecylamine, 1-hexadecylamine, octadecylamine, isopropylamine, sec-butylamine, isobutylamine, terc-butylamine, 1-methylbutylamine, 1,3-dimethylbutylamine, 3,3dimethylbutylamine, 2-ethylhexylamine, 3-dimethylaminopropylamine, N-methylethylenediamine, Ν,Ν'-dimethylethylenediamine, cyclopentylamine, cyclohexylamine, cyclohexanomethylamine, cycloheptylamine, alylamine and oleylamine, aniline, 2-ethylaniline, 4-butylaniline, 4cyclohexylaniline, 4-aminobiphenyl, 1-aminonaphthalene, 2-aminonaphthalene, bencylamine, phenethylamine, 3-phenyl-1-propylamidine, 3-aminopropylimidazole, 4-phenylbutylamine, m-anisidine and p-phenethidine;and secondary amines: dimethylamine, N-ethylmethylamine, diethylamine, dipropylamine, diisopropylamine, N-methylbutylamine, N-methyl-tert-butylamine, dibutylamine, dihexylamine, di-(2-ethylhexyl)amine, diisobutylamine, dinonylamine, dipentylamine, didodecylamine, dioctylamine, didodecylamine, N-methyloctadecylamine, N-methylcyclohexylamine, N-ethylcyclohexylamine, dicyclohexylamine, bis-(2-methoxyethyl)amine, N-methylallylamine, diallylamine, N-methylaniline, N-ethylaniline, N-butylaniline, diphenylamine, N-ethyl-1-naphthylamine, N-benzylmethylamine, dibenzylamine, N-ethylbenzylamine and N-methylphenylamine, which includes mixtures thereof. When X is a cyclic amine, it is derived from cyclic secondary amines. Useful cyclic secondary amines include, but are not limited to, piperidine, morpholine, 4-methylpiperidine, 4-phenylpiperidine, thiomorpholine, azetidine, 1-methylpiperazine, 2-methylpiperazine, and pyrrolidine, which includes mixtures thereof. In the present invention, the dispersing molecule of Formula I may contain polyether chains, polyester chains, polyesteramide chains, or combinations of each type of chain, such as polyether-co-polyester, polyether-co-polyesteramide, polyether-co-polyester-co-polyesteramide, or polyester-co-polyesteramide chains thereof. Therefore, in one embodiment, the sum of the variables, m + n, in the present invention is at least 3. For example, m + n can be from 3 to 65, for example, from 5 to 50. In one embodiment of the invention, n can be any integer from 0 to 65. In another embodiment, n is any integer from 1 to 65, for example, at least 2, 3, 4, or more, for example, from 5 to 50. In yet another embodiment, n is 0. The variable m can be any integer from 0 to 35. In one embodiment, m can be any integer from 1 to 35, for example, at least 2, 3, 4, or more, for example, from 5 to 16. In another embodiment, m is 0. In Formula I forms containing a polyether segment (i.e., where n is 1 or more), R1 can be H, methyl, or ethyl groups. The polyether segment is R LfrQ / n / Lznz / q / YILI is derived from the ring-opening reaction of alkylene oxides, such as ethylene oxide, propylene oxide, butylene oxide, or mixtures thereof. In one embodiment of the invention, n can be any integer from 0 to 65. In another embodiment, n is any integer from 1 to 65, for example, at least 2, 3, 4, or more, for example, from 5 to 30. In yet another embodiment, n is 0. The polyether segment can be synthesized by any method known to those skilled in the art, including, but not limited to, the polymerization of alkylene oxides in the presence of monoalcohols or secondary amines to initiate polyether chain extension. Polymerization can be conveniently carried out in the presence of basic catalysts, such as sodium or potassium hydroxide, at a temperature of 50 °C to 150 °C or 70 °C to 140 °C, preferably under pressure to avoid the loss of volatile alkylene oxides.In one embodiment, monoalcohol polyether compounds of Formula II, where n is 3 or more and y and m are both zero, are commercially available. Examples include, but are not limited to, polypropylene glycol monobutyl ethers, poly(ethylene glycol-ran-propylene glycol) monobutyl ethers, or polyethylene glycol monomethyl ethers of various molecular weights from Aldrich, or under the trade names Synalox from Dow or Polyglykol from Clariant. Specific examples of Synalox™ are 100-D20, 100-40B, 100-50B, 100-D95, and 100-150B. Specific examples of Polyglykol™ are B01 / 20, B01 / 40, B01 / 80, B01 / 120, and B01 / 240. Polypropylene glycol monoisotridecyl ether is available under the trade name PolyglykolTM from Clariant; a specific example is T01 / 35. Other monosubstituted polyethylene oxide alkenyl ethers, cycloalkyl ethers, or aryl ethers are also available from a variety of sources, such as Sigma-Aldrich, Croda, Clariant, BASF, Dow, and Ineos. In embodiments of Formula I, the variable b is either 0 or 1, with the condition that b can only be 1 when both n and m are at least 1. In one embodiment, b is 1 and the sum of the variables, m + n, is at least 4. R5 represents a linear or branched hydrocarbon chain containing up to 3 carbon atoms, and R6 represents hydrogen (H), a hydrocarbyl group having from 1 to 22 carbon atoms, which may optionally contain ether, ester, tertiary amino, or amide functional groups. In one embodiment, R6 can be derived from alkyl (meth)acrylate or (meth)acrylamide. In another embodiment, R6 comprises the residue of an alkyl (meth)acrylate or mixtures thereof. In one embodiment, R6 is an alkyl acrylate, and in another embodiment, R6 is an alkyl methacrylate. In one embodiment, R6 is an alkyl acrylamide, and in another embodiment R6 is an alkyl methacrylamide. In one embodiment, R6 is H.Suitable examples of an alkyl (meth)acrylate or (meth)acrylamide include those (meth)acrylate or (meth)acrylamide compounds in which the alkyl group is methyl, ethyl, propyl, isopropyl, butyl, pentyl, hexyl, heptyl, octyl, 2-ethylhexyl, nonyl, decyl, dodecyl, tetradecyl, hexadecyl, octadecyl, eicosyl, 2-dimethylaminoethyl, 3-dimethylaminopropyl, or mixtures thereof. As used herein, the term (meth)acrylate or (meth)acrylamide includes acrylate or methacrylate or mixtures thereof, or acrylamide or methacrylamide or mixtures thereof. In some embodiments of Formula I containing both a polyether segment (i.e., where n is 1 or more) and a polyester or polyesteramide segment or a mixture thereof (i.e., where m is 1 or more) and b is 0, the polyether segment can be derived from the ring-opening reaction of alkylene oxides in the presence of monoalcohols or secondary amines to initiate chain extension from the polyether or from the commercially available polyether monoalcohols described above. In other embodiments of Formula I containing both a polyether segment (i.e., where n is 1 or more) and a polyester or polyesteramide segment or a mixture thereof (i.e., where m is 1 or more) and b is 1, the polymer residue of Formula II, namely X-(CH2CHR1-O)n-[R5-N(R6)]b- may comprise a polyetheramine, for example, poly(alkylene oxide)monoalkyl or aryl ether monoamine.This polyetheramine can be synthesized by any method known to those skilled in the art, including, but not limited to, the ring-opening reaction of alkylene oxides, such as ethylene oxide, propylene oxide, or butylene oxide, or mixtures thereof, in the presence of a monoalcohol initiator to form an alcohol-terminated polyether chain, followed by the conversion of the alcohol-terminated polyether chain to an amine by using known amination reaction conditions, such as ammonia in the presence of a metal catalyst, such as those described in US Patents 3,654,370, 4,618,717, 4,960,942, and 5,457,147. In one embodiment, polyetheramine can be obtained by alkoxylation of amino alcohols as described in US document 5,879,445 (in particular, the description in column 2, line 50 to column 7, line 50).In another embodiment, polyetheramine can be obtained by the base-catalyzed addition of an alcohol-terminated polyether chain to acrylonitrile, followed by hydrogenation to give an amine-terminated polyether chain. Polyetheramines are commercially available under the trade names Jeffamine™ M series or Surfonamine™ B and L series monoamines from Huntsman Corporation. Specific examples of Jeffamine™ amines are M-600 (9,1,600), M-1000 (3,19,1000), M-2005 (29,6,2000), M-2095 (4,41,2000), and M-2070 (10,31,2000). Specific examples of Surfonamine™ amines are B-60 (9,1,600), L-100 (3,19,1000), B-200 (29,6,2000), B100 (12,5,0,1000), L200 (4,41,2000), L207 (10,31,2000), and L300 (8,58,3000). The figures in parentheses are approximate repeating units of propylene oxide, ethylene oxide, and number-average molecular weight, respectively.Commercially available polyetheramines, such as those listed herein, may be incorporated into the Formula II alcohol-terminated polymer by means known to those skilled in the art. In Formula I embodiments containing a polyester segment (i.e., where m is 1 or more), R2 may be a branched or linear, saturated or unsaturated hydrocarbon chain containing from 1 to 10 carbon atoms, for example, from 2 to 7 carbon atoms, or -R8(C=O)YR9- where Y is oxygen, and R8 is a branched or linear, saturated or unsaturated hydrocarbon chain containing from 1 to 10 carbon atoms and R9 is a branched or linear, saturated or unsaturated hydrocarbon chain containing from 2 to 10 carbon atoms, and which may also include heteroatoms, such as oxygen present as ether groups. The variable m can be any integer from 0 to 35. In one modality, m can be any integer from 1 to 35, for example, at least 2, 3, 4, or more, for example, from 5 to 16. In another modality, m is 0.The polyester segment can be synthesized by any method known to those skilled in the art, including, but not limited to, (i) polymerization of lactones and / or hydroxycarboxylic acids in the presence of monoalcohols or amines to initiate polyester chain extension, or (ii) polymerization reaction of a diol with a dibasic acid or derivatives thereof, such as acid chlorides, anhydrides, or dialkyl esters, in the presence of a stoichiometric amount of monoalcohols or amines to control molecular weight and suppress the formation of dicarboxylic polyesters. This can be conveniently carried out at a temperature of 50°C to 250°C or 70°C to 200°C, optionally in the presence of an esterification catalyst and in an inert atmosphere. The inert atmosphere can be provided by any inert gas from the Periodic Table, but preferably by nitrogen.The catalyst for «i hq / n / 1 znz / q / υιλι esterification can be any previously known in the art and includes, but is not limited to, tetraalkyl titanate, for example, tetrabutyl titanate, zinc salt of an organic acid, for example, zinc acetate, zirconium salt of an aliphatic alcohol, for example, zirconium isopropoxide or zirconium butoxide, methanesulfonic acid, toluenesulfonic acid, phosphoric acid, diphenyl phosphate, or a strong organic acid such as trifluoroacetic acid. In another embodiment, the synthesis of the polyester segment can be achieved by any method now known or hereafter developed without departing from the scope of the invention. For example, the polyester segment can be synthesized by polymerizing hydroxycarboxylic acids and / or lactones in the presence of monoalcohols or amines to initiate polyester chain extension. The raw materials used can also include those now known or hereafter developed. Specific examples of suitable hydroxycarboxylic acids are glycolic acid and lactic acid, including their cyclic dimers glycolide and lactide, 6-hydroxycaproic acid, 5-hydroxyvaleric acid, 5-hydroxydecanoic acid, 10-hydroxyundecanoic acid, and 4-hydroxydecanoic acid, or mixtures thereof.Examples of lactones include ε-caprolactone substituted with a C1-4 alkyl or optionally δ-valerolactone substituted with a C1-4 alkyl and β-propiolactone, or mixtures thereof. The alkyl substituent in ε-caprolactone and δ-valerolactone can be a C1-4 alkyl and can be linear or branched. Suitable examples of lactones are ε-caprolactone and its analogues 7-methyl-, 2-methyl-, 3-methyl-, 5-methyl-, 6-methyl-, 4-methyl-, 5-tert-butyl-, 4,4,6-trimethyl-, and 4,6,6-trimethyl-, and δ-valerolactone and its analogue p-methyl-6-valerolactone. In another embodiment, the polyester segment can be synthesized by the polymerization reaction of a diol with a dibasic acid or its derivatives, such as acid chlorides, anhydrides, or dialkyl esters, in the presence of a stoichiometric amount of monoalcohols or amines to control the molecular weight and suppress the formation of dicarboxylic polyesters. Specific examples of suitable diols that result in the R9 hydrocarbon chain described above include alkylene glycols, such as ethylene glycol, propylene glycol, neopentyl glycol, 1,4-butanediol, 1,6-hexanediol, cis- and trans-1,2- and 1,4-cyclohexanedimethanol; diols with ether linkages, such as diethylene glycol, dipropylene glycol, tripropylene glycol, and triethylene glycol; and polyalkylene glycols, such as polyethylene glycols, polypropylene glycols, and polybutylene glycols. AI frQ / ni Lznz / q / YILI mixed and random block copolymers of polyethylene glycol and polypropylene glycol (Pluronic™ and reverse Pluronic™ ex BASF) with a number-average molecular weight (MW) of less than 1000. Specific examples of suitable dibasic acids, diesters, and anhydrides that result in the R8 hydrocarbon chain described above include maleic anhydride, succinic anhydride, glutaric acid, fumaric acid, malonic acid, adipic acid, sebacic acid, italic anhydride, pimelic acid, fatty acid dimers and their hydrogenated versions, and cyclohexane dicarboxylic anhydride. Specific examples of alcohols and amines used to initiate polymerization of the polyester segment were described above. In Formula I embodiments containing a polyesteramide segment (i.e., where m is 1 or more), R2 may be a hydrocarbon chain containing 2 to 15 carbon atoms that includes an amide functional group -N(R11)-(C=O)- where R11 is H or a hydrocarbon chain containing 1 to 4 carbon atoms, or R2 may be -R8(C=O)YR9- where Y is nitrogen, and R8 is a branched or linear, saturated or unsaturated hydrocarbon chain containing 1 to 10 carbon atoms and R9 is a branched or linear, saturated or unsaturated hydrocarbon chain containing 2 to 10 carbon atoms, and which may also include heteroatoms, such as oxygen present as ether groups. The variable m can be any integer from 0 to 35. In one modality, m can be any integer from 1 to 35, for example, at least 2, 3, 4, or more, for example, from 5 to 16. In another modality, m is 0.The polyesteramide segment can be synthesized by any method known to those skilled in the art, including, but not limited to, (i) polymerization of lactones with aminocarboxylic acids in the presence of monoalcohols or amines to initiate polyesteramide chain extension or (ii) polymerization reaction of an aminoalcohol with a dibasic acid or derivatives thereof, such as acid chlorides, anhydrides or dialkyl esters in the presence of a stoichiometric amount of monoalcohols or amines to control molecular weight and suppress the formation of dicarboxylic polyesters. In another embodiment, the synthesis of the polyesteramide segment can be achieved by any method known or subsequently developed without departing from the scope of the invention. For example, the polyesteramide segment can be synthesized by polymerizing lactones with aminocarboxylic acids in the presence of monoalcohols or amines to initiate chain extension. AI HQ / ni Lznz / q / YILI polyesteramide and can be conveniently carried out at a temperature of 50 °C to 250 °C or 70 °C to 200 °C, optionally in the presence of an esterification catalyst and in an inert atmosphere. The inert atmosphere and the esterification catalyst can be any of those known prior to the art and include, but are not limited to, those described above. The raw materials used can also include those now known or subsequently developed. Specific examples of suitable aminocarboxylic acids (or amino acids) include 11-aminoundecanoic acid, 12-aminododecanoic acid, 6-aminocaproic acid, 4-aminobutyric acid, β-alanine, glycine, and sarcosine. Mixtures of aminocarboxylic acids can be used. Specific examples of suitable lactones, alcohols, and amines were described above. In another embodiment, the synthesis of the polyesteramide segment can be achieved by the polymerization reaction of an amino alcohol with a dibasic acid or its derivatives, such as acid chlorides, anhydrides, or dialkyl esters, in the presence of a stoichiometric amount of monoalcohols or amines to control the molecular weight and suppress the formation of dicarboxylic polyesters. The amino alcohol can be a C2-10 amino alcohol and may also include heteroatoms, such as oxygen present as ether groups. Specific examples of suitable amino alcohols include ethanolamine, 3-amino-1-propanol, 4-aminobutanol, 2-aminobutanol, 2-amino-2-methyl-1-propanol, 5-amino-1-pentanol, 5-amino-2-pentanol, 2-amino-3-methyl-1-butanol, 6-amino-1-hexanol, 2-amino-1-hexanol, serine, 4-aminocyclohexanol, 2-(2-aminoethoxy)ethanol, or mixtures thereof. Specific examples of suitable dibasic acids, diesters and anhydrides, alcohols, and amines were described above. In Formula I, R3 comprises a branched or linear, saturated or unsaturated hydrocarbon chain containing from 2 to 80 carbon atoms. In one embodiment, R3 is a linear saturated carbon chain containing 20 carbons. In another embodiment, R3 is derived from a cyclic anhydride. In Formula I, the variables q and t are each at least 1, so that each dispersing molecule contains a mixture of both salt and amide bonds. In one embodiment, q + t is any integer from 2 to 200, for example, from 2 to 150, where q is greater than or equal to t. A LfrQ / Π / Lznz / q / YILI In Formula I, MA represents a multiamine species. In one embodiment, the multiamine species used in the present invention may have a number-average molecular weight (MW), measured by ebullioscopic analysis, of between 300 and 20,000 g / mol, for example, from 300 to 10,000 g / mol. In another embodiment, MA comprises at least four amines. In one embodiment, MA is a polyamine and is selected from polyethyleneimine, modified polyethyleneimine, polyallylamine, modified polyallylamine, polyvinylamine, modified polyvinylamine, or mixtures thereof. In one embodiment, at least 70, 80, 90, or 95 percent by weight of the multiamine species is polyethyleneimine. The MA can be linear or branched. Linear polyethyleneimines can be prepared by the hydrolysis of poly(N-acyl)alkylenimines, as described, for example, by Takeo Saegusa et al. in Macromolecules, 1972, Vol. 5, page 4470. Branched polyethyleneimines of different molecular weights are commercially available from BASF and Nihon Shokubai. Polyallylamine and poly(N-alkyl)allylamines of different molecular weights are commercially available from Nitto Boseki. Polyvinylamine of different molecular weights is available from Mitsubishi Kasai. Poly(propyleneimine) dendrimers are commercially available from DSM Fine Chemicals and poly(amidoamine) dendrimers are available as Starburst dendrimers from Aldrich Chemical Co. In one embodiment, the MA is C2-6 poly(alkyleneimine) and / or polyethyleneimine. In another embodiment, the MA can be modified by reacting a portion of its primary and / or secondary amino groups with esters, such as ethyl or butyl acetate, isocyanates, such as phenyl isocyanate, lactones, such as ε-caprolactone and δvalerolactone, anhydrides, such as succinic, maleic, italic, isatoic, 1,2-naphthalic anhydride, 1,8-naphthalic anhydride, or 1,2,4-benzencentric carboxylic acid anhydride, cyclic carbonates, such as ethylene carbonate, (meth)acrylates, such as ethyl acrylate or 2-hydroxyethyl acrylate, or epoxides, such as phenylglycidyl ether, while ensuring that there are still primary and / or secondary amino groups of the modified polyamine that are unmodified and, therefore, still in the form of amine. In another embodiment, the MA can be polyethyleneimine. Polyethyleneimine can be modified by replacing one or more protons of the NH units with a C2-4 alkyleneoxy unit. Polyethyleneimine can be modified by alkoxylation using a C2-4 alkylene oxide, such as ethylene oxide, propylene oxide, butylene oxide, or mixtures thereof. Examples of alkoxylated polyethyleneimines are commercially available from BASF and Nihon Shokubai. In this embodiment, the modified MA will still contain primary and / or secondary amino groups that are unmodified and still in the amine form to form the dispersing polymers described herein. The modification of the MA can be carried out under reaction conditions commonly understood by those skilled in the art, whether such conditions exist now or are subsequently developed. It is understood that the modification of the MA prior to the addition of the chains to create the dispersant can be performed under reaction conditions (such as higher temperature) that may not be viable after the dispersant molecule is formed. In Formula I, H+ represents a proton species generated when anhydrides react with the multiamine MA to form an amide bond and a salt bridge. The H+ species bonds to one of the nitrogen atoms of an amine group of MA to generate an ammonium cation. In one embodiment, the number of H+ species equals the sum of q + p, so that, in general, the dispersing molecule of Formula I is uncharged. In Formula I, the variables p and z can be 0, 1, or more. In one form, p + z is any integer from 1 to 200. In another form, p + z is any integer from 2 to 200. In Formula I, R4 can be a linear or branched saturated carbon chain containing from 1 to 4 carbon atoms, for example, 1 or 2. In one embodiment, R4 is derived from a non-cyclic anhydride. The dispersant of the present invention (e.g., Formula I) is made by using a novel process comprising the following steps: (a) providing an alcohol-terminated polymer of the formula X-(CH2CHR1-O)n-[R5-N(R6)]b-[(C=O)R2-O]mH (Formula II), (b) reacting the alcohol-terminated polymer with a cyclic anhydride to provide an acid-terminated polymer, (c) reacting the acid-terminated polymer with a non-cyclic anhydride to provide a mixture of anhydrides, and (d) reacting the mixture of anhydrides with a multiamine species, wherein the multiamine species has a number-average molecular weight of 300 to 20,000, to form a dispersant molecule, wherein q and t are each at least one such that the dispersant contains both amide and AI t?Q / ni Lznz / q / YILI salines. In Formula II, X represents either RQ or a cyclic secondary amine. When X is RQ, R is a branched or linear, saturated or unsaturated, or cyclic hydrocarbon chain containing from 1 to 50 carbon atoms, Q is O, or NR7 or NH, with the condition that Q can only be NH when n is 0 and b is 0, and R7 is a linear or branched, saturated or unsaturated hydrocarbon chain containing from 1 to 18 carbon atoms, which may optionally contain ether, ester, or amide functional groups or a halide substituent. X may also be a cyclic amine structure derived from one or more cyclic secondary amines. In Formula II, R1 is H, methyl or ethyl, R5 is a linear or branched hydrocarbon chain containing up to 3 carbon atoms; R6 is hydrogen, a hydrocarbyl group containing from 1 to 22 carbon atoms, or the residue of an alkyl (meth)acrylate or (meth)acrylamide.The variable b is 0 or 1, with the condition that b can only be 1 when both n and m are both at least 1. R2 is a linear or branched, saturated or unsaturated hydrocarbon chain containing from 1 to 15 carbon atoms or -R8(C=O)YR9-, where Y is O or NH or NR10, R8 is a hydrocarbon chain containing from 1 to 10 carbon atoms, R9 is a hydrocarbon chain containing from 1 to 10 carbon atoms and R10 is a hydrocarbon chain containing from 1 to 20 carbon atoms, which may include an ester, ether or amide group.When R2 is a hydrocarbon chain containing 1 to 15 carbon atoms, R2 can be, in one embodiment, a linear or branched, saturated or unsaturated hydrocarbon chain containing 1 to 10 carbon atoms, for example, 2 to 7, and in another embodiment, R2 can be a hydrocarbon chain containing 2 to 15 carbon atoms which includes an amide functional group having the formula -N(R11)-(C=O)-, where R11 is H, or a hydrocarbon chain containing 1 to 4 carbon atoms. In Formula II, n is any integer from 0 to 65 and m is any integer from 0 to 35, with the condition that m + n is at least 3. In one embodiment, the alcohol-terminated polymer has a number-average molecular weight of 300 to 5000 g / mol, for example, 500 to 3000 g / mol. In one embodiment, the alcohol-terminated polymer and the cyclic anhydride are combined in a molar ratio of approximately 1:1 and reacted at a temperature high enough to solubilize the cyclic anhydride. For example, in one embodiment, temperatures of approximately 130 °C may be suitable. In one embodiment, the reaction can take place over a period of 2 to 48 hours and can be conveniently carried out at a temperature of 50 to 150 °C or 70 to 140 °C under a controlled atmosphere. A LfrQ / Π / Lznz / q / YILI inert, optionally in the presence of a catalyst, such as phosphoric acid. Examples of suitable cyclic anhydrides include, for example, glutaric anhydride, 1,2-cyclohexanedicarboxylic anhydride, homophthalic anhydride, succinic anhydride, diglycol anhydride, polyisobutylenesuccinic anhydride, 2-phenylsuccinic anhydride, or alkylsuccinic anhydride. The acid-terminated polymer is then reacted with a non-cyclic anhydride. Suitable non-cyclic anhydrides include butyric anhydride, isobutyric anhydride, propionic anhydride, and acetic anhydride, or mixtures thereof. In one embodiment, this reaction yields a mixture of hetero- and homoanhydride products, where heteroanhydrides are anhydrides composed of either the polymer or the non-cyclic anhydride, and homoanhydrides are anhydrides composed of either the polymer or the residual non-cyclic anhydride. In one embodiment, the acid-terminated polymer and the non-cyclic anhydride are combined in a molar ratio between 1:0.5 and 1:2. The preceding reaction step is carried out using a setup that allows excess anhydride and acid byproduct to be removed from the reaction vessel. In one embodiment, this reaction is carried out for 2 to 10 hours at a reaction temperature above the boiling point of the acid being generated but below the boiling point of the non-cyclic anhydride. For example, when using acetic anhydride, a temperature of approximately 120 °C is suitable. The reaction temperature is then increased to a temperature above the boiling point of the non-cyclic anhydride (for example, approximately 150 °C when using acetic anhydride), and the reaction is carried out for a further 1 to 72 hours. The reactions described here can be performed at atmospheric pressure.Experts in the technique should understand that the reaction can be carried out at reduced pressure, such as in a vacuum, which could reduce both the reaction temperature and the reaction time. The resulting mixture of anhydrides is then reacted with a multiamine species as described herein. The anhydride mixture and the multiamine component are combined in a weight ratio of 1:1 to 25:1, for example, 3:1 to 18:1. This reaction is carried out at a temperature below 100 °C, preferably below 80 °C, for 1 to 6 hours under an inert atmosphere. R LfrQ / n / Lznz / q / YILI of a hydrocarbon containing from 1 to 20 carbon atoms, which may include an ester, ether, or amide group. When R2 is a hydrocarbon chain containing from 1 to 15 carbon atoms, R2 may be, in one embodiment, a linear or branched, saturated or unsaturated hydrocarbon chain containing from 1 to 10 carbon atoms, and in another embodiment, R2 may be a hydrocarbon chain containing from 2 to 15 carbon atoms which includes an amide functional group having the formula -N(R11)-(C=O)-, where R11 is H, or a hydrocarbon chain containing from 1 to 4 carbon atoms. The variable n is any integer from 0 to 65 and the variable m is any integer from 0 to 35, with the condition that m + n is at least 3. R3 is a linear or branched, saturated or unsaturated hydrocarbon containing between 2 and 80 carbons. The variables q and t are each at least 1, while q + t can be any integer from 2 to 150.MA is a type of multiamine with a number-average molecular weight of 300 to 20,000 g / mol. p + z can be 0, or any integer from 1 or 2 to 200; R4 is a linear or branched saturated carbon chain containing between 1 and 4 carbon atoms, preferably between 1 and 3. In one embodiment, in Formula I, n is 0. In another embodiment, in Formula I, n is any integer from 3 to 65 and m is 0. In yet another embodiment, in Formula I, m is 0. In another embodiment, in Formula I, m is any integer from 3 to 35, for example, from 5 to 16, and n is 0. In another embodiment, in Formula I, both n and m are positive integers and n + m is from 3 to 65, for example, from 5 to 30. In one embodiment, the process of preparing a dispersant as described above results in a dispersant of Formula I where n is 0 and m is at least 3. In another embodiment, the process of preparing a dispersant as described above results in a dispersant of Formula I where m is 0 and n is at least 3. In another embodiment, the process of preparing a dispersant as described above results in a dispersant of Formula I where either m is 0, but m + n is at least 3. In another embodiment, the process of preparing a dispersant as described above results in a dispersant of Formula I where m + n is any integer from 3 to 65, for example, from 5 to 30. In one embodiment, the dispersant of the present invention can be further functionalized to tailor its properties and application performance to specific requirements. These modification reactions, described below, can be between the various reagents listed below and the amines of the polyamine species that have not yet reacted with the polyether, polyester, and / or polyesteramide groups detailed above. The modification of any remaining amino groups can be carried out in any manner known to a person skilled in the art. Such modifications are desirable when, for example, the amino groups react with a binding system in which a pigment dispersion or paste is incorporated and cause flocculation. Such modifications can be performed under reaction conditions commonly understood by those skilled in the art, whether existing now or developed in the future.For modifications to the amine that are made after the multiamine (MA) species has been incorporated into the dispersing molecule as described herein, it should be understood that such modifications may be required to be made under controlled temperatures, e.g., 100°C or lower. The modifications indicated are advantageous embodiments of the present invention and can be implemented by: a) reaction of one or more of the remaining free primary and secondary amino groups of the polyamine species with isocyanates, lactones, anhydrides, epoxides, cyclic carbonates, or (meth)acrylates. Specific examples of suitable isocyanates include phenyl isocyanate. Specific examples of suitable lactones include caprolactone and valerolactone. The reaction of one or more of the remaining free primary and secondary amino groups of the polyamine species with anhydrides is described in US Patents 6,878,799 and 7,767,750. Specific examples of suitable anhydrides include maleic anhydride, succinic anhydride, italic anhydride, tetrahydrophthalic anhydride, methyltetrahydrophthalic anhydride, hexahydrophthalic anhydride, methylhexahydrophthalic anhydride, 1,8-naphthalic anhydride, optionally substituted with nitro or halogen substituents such as Cl and Br, isatoic anhydride, trimellitic anhydride, alkenyl and alkyl succinic anhydrides of Ci-20.The reaction of one or more of the remaining free primary and secondary amino groups of the polyamine species with epoxides is described in JP4031471. Specific examples of suitable epoxides include styrene oxide, propylene oxide, and ethylene oxide. Specific examples of suitable cyclic carbonates include ethylene carbonate and 2,2-dimethyltrimethylene carbonate. Specific examples of suitable (meth)acrylates include ethyl acrylate and 2-hydroxyethyl acrylate. RI FQ / ni Lznz / q / YILI (b) Salification and / or reaction of one or more of the remaining free primary, secondary, or tertiary amino groups of the polyamine species with mono- or polycarboxylic acids, mineral acids, phosphorus, and acids containing polyoxometalate or strong acids. Suitable reagents for this purpose include hydrochloric acid, acetic acid, sulfuric acid, alkylsulfonic acids, alkyl hydrogen sulfates, or arylsulfonic acids. The salification and / or reaction of one or more of the remaining free amino groups of the amine polyamine species with mono- or polycarboxylic acids or phosphorus-containing acids is described in documents JP9157374, US 2010 / 0017973, and US 2013 / 0126804.Specific examples of suitable monocarboxylic acids include optionally substituted C1-50 aliphatic monocarboxylic acids such as acetic acid, propionic acid, caproic acid, caprylic acid, 2-ethylhexanoic acid, nonanoic acid, decanoic acid, lauric acid, myristic acid, palmitic acid, oleic acid, linoleic acid, stearic acid, arachidic acid, erucic acid, behenic acid, methoxyacetic acid, mixtures of fatty acids derived from oils of natural sources such as sunflower oil, rapeseed oil, castor oil, and olive oil, branched alkylcarboxylic acids available under the trademark Isocarb™ (formerly Sasol), Unicid™ acids which are synthetic linear C25-50 primary acids commercially available from Baker Hughes, and aromatic carboxylic acids such as benzoic acid, salicylic acid, and naphthoic acid.Specific examples of suitable polycarboxylic acids include succinic acid, malonic acid, adipic acid, sebacic acid, malic acid, fumaric acid, citric acid, and tartaric acid. Specific examples of suitable phosphorus-containing acids include phosphoric acid and phosphorous acid. Specific examples of suitable polyoxometalate-containing acids include phosphomolybdic acid, phosphotungstic acid, and silicomolybdic acid. c) oxidation of one or more of the remaining free primary, secondary or tertiary amino groups of the polyamine species to nitrogen oxides; d) Quaternization of one or more of the remaining free tertiary amino groups of the polyamine species. This can be achieved by using alkyl sulfates, alkyl or aralkyl halides, halocarboxylic esters, alkyl oxalates, or epoxides. Suitable reagents for this purpose include dimethyl sulfate, benzyl chloride, methyl halides such as chlorine, bromine, and iodine, dimethyl oxalate, ethylene oxide, propylene oxide, and styrene oxide in the presence of acids, and propane (or butane) sultone; and e) reaction of one or more of the remaining free primary, secondary or tertiary amino groups of the polyamine species with one or more polymer(s) terminated in reactive monoamino groups of MW 150 - 3000. Suitable examples of carboxylic acid-terminated polyester, polyesteramide and polyamide polymers are described in US documents 4,224,212, 4,861,380, 5,700,395, 5,760,257, 6,197,877, 8,202,935, JP4866255, JP8010601, JP9157361, WO 2006 / 113258 and WO 2007 / 039605. Suitable examples of carboxylic acid-terminated polyether polymers are described in documents JP4248207, US 7,767,750, 7,671,119, 7,872,070, 8,076,409 and 8,168,713. Suitable examples of phosphate-, sulfate-, and sulfonate-terminated polyester polymers are described in documents US 4,861,380 and 6,197,877.Suitable examples of polyester, polyesteramide, and polyamide polymers terminated in (meth)acrylate are described in documents EP713894, JP3488001, JP2010-222522, and US 8,202,935. Suitable examples of polyether polymers terminated in (meth)acrylate are described in documents US 7,923,474 and JP2010-222522. Suitable examples of polyether, polyether / polyester, polyether / polyurethane, and polyether / polyester / polyurethane polymers terminated in phosphate, sulfate, and sulfonate are described in documents US 5,130,463, 5,151,218, 6,111,054, 6,310,123, 7,595,416, and 8,202,935. Suitable examples of isocyanate-terminated polyester and polyether polymers are described in documents JP4031471, JP7149855 and WO 2007 / 039605. Suitable examples of epoxide-, acetoacetoxy-, or cyclocarbonate-terminated polyacrylate polymers are described in document US 5,100,969. An objective of the present invention is to provide compounds capable of enhancing color intensity or other dyeing properties, increasing particulate solids content, and / or forming improved dispersions, resulting in an enhanced brightness in the final composition. This is achieved while also producing a composition with reduced viscosity, good dispersion stability, reduced particle size and particle size distribution, reduced turbidity, improved brightness, and increased darkness (especially when the composition is black). The composition(s) of the present invention may also be stable under storage at room temperature and under high-temperature storage conditions. R LfrQ / Π / Lznz / q / YILI temperature and can also provide reduced discoloration / yellowing of the final coatings. The polymer of the present invention is useful as a dispersant for various small particle dispersions, such as suspended pigments and particles in various polar and nonpolar media. Compositions of these particles, the dispersant, and a continuous phase are useful as inks, coatings, paints, and base mixtures for coloring inks, coatings, and paints. Industrial application The particulate solid present in the composition may be any organic or inorganic solid material that is substantially insoluble in the organic medium at the temperature in question and which is desirable to stabilize in a finely divided form. The particulate solids may be in the form of granular material, a fiber, a platelet, or in the form of a powder, often a blown powder. In one embodiment, the particulate solid is a pigment. The particulate solid (typically a pigment or filler) can have an average particle size that is measured by light scattering measurements of 10 nanometers to 10 microns, or from 10 nanometers to 1, 2, 3 or 5 microns, or from 20 nanometers to 1, 2, 3 or 5 microns in diameter. Examples of suitable solids include pigments for solvent-based inks; pigments, thinners, fillers, foaming agents, and flame retardants for paints and plastic materials; dyes, especially disperse dyes; optical brightening agents and textile auxiliaries for solvent-based dye baths; pigments for inks, toners, and other solvent-based application systems; solids for oil-based and invert emulsion drilling muds; powders and solid particles in dry cleaning fluids; rails; particulate ceramic materials and magnetic materials for ceramics, piezoceramic printing, refractories, abrasives, foundries, capacitors, fuel cells, ferrofluids, conductive inks, magnetic recording media, water treatment, and hydrocarbon soil remediation; organic and inorganic monodisperse solids;metal, metal oxides and carbon for electrodes in batteries, fibers such as wood, paper, glass, steel, carbon and boron for composite materials; and biocides, agrochemicals and pharmaceuticals which are applied as dispersions in organic media. In one modality, the solid is an organic pigment of any of the recognized classes of pigments described, for example, in the Third Edition of the Colour Index (1971) and subsequent revisions of, and supplements thereof, under the chapter entitled “Pigments”. Examples of organic pigments include azo, disazo, trisazo, condensed azo pigments, azo lakes, naphthol, anthantrone, anthrapyrimidine, anthraquinone, benzimidazolone, carbazole, diketopyrrolopyrrole, flavantrone, indigoid pigments, indanthrone, isodibenzantrone, isoindanthrone, isoindolinone, isoindoline, isoviolantrone, metal complex pigments, oxazine, perylene, perinone, pyrantrone, pyrazoloquinazolone, quinacridone, quinophthalone, thioindigo, triarylcarbonium pigments, triphenodioxazine, xanthene, and phthalocyanine series, especially copper phthalocyanine and its halogenated nuclear derivatives, and also acid, basic, and mordant dye lakes.Carbon black, although strictly inorganic, behaves more like an organic pigment in its dispersing properties. In one form, organic pigments include phthalocyanines, especially copper phthalocyanines, monoazos, disazos, indanthrones, anthranthrones, quinacridones, diketopyrrolopyrrole, perylenes, and carbon blacks. Examples of inorganic pigments include metal oxides, such as titanium dioxide, rutile titanium dioxide, and surface-coated titanium dioxide; titanium oxides of different colors, such as yellow and black; iron oxides of different colors, such as yellow, red, brown, and black; zinc oxide; zirconium oxides; aluminum oxide; oxymetallic compounds, such as bismuth vanadate, cobalt aluminate, cobalt stannate, cobalt zincate, zinc chromate; and mixed metal oxides of two or more of manganese, nickel, titanium, chromium, antimony, magnesium, praseodymium, cobalt, iron, or aluminum; Prussian blue; vermilion; ultramarine; zinc phosphate; zinc sulfide; calcium and zinc molybdates and chromates; metallic effect pigments, such as aluminum, copper, and copper / zinc alloy flakes; and pearlescent flakes, such as lead carbonate and lead oxychloride. bismuth. Inorganic solids include thinners and fillers, such as crushed and precipitated calcium carbonate, calcium sulfate, calcium oxide, calcium oxalate, calcium phosphate, calcium phosphonate, barium sulfate, barium carbonate, magnesium oxide, magnesium hydroxide, natural magnesium hydroxide or brucite, precipitated magnesium hydroxide, magnesium carbonate, dolomite, aluminum trihydroxide, aluminum hydroperoxide or boehmite, calcium and magnesium silicates, and aluminosilicates, including A LfrQ / Π / Lznz / q / YILI nanoclays, kaolin, montmorillonites including bentonites, hectorites and saponites, ball clays including natural, synthetic and expandable, mica, talc including muscovite, phlogopite, lepidolite and chlorite, chalk, synthetic and precipitated silica, fumed silica, metallic fibers and powders, zinc, aluminum, glass fibers, refractory fibers, carbon black including single and multi-walled carbon nanotubes, reinforcing and non-reinforcing carbon black, graphite, buckminsterfullerene, asphaltene, graphene, diamond, alumina, quartz, perlite, pegmatite, silica gel, wood flour, wood flakes including softwoods and hardwoods, sawdust, paper / fiber powder, cellulosic fibers such as kenaf, hemp, sisal, flax, cotton, cotton linters, jute, ramie, rice hulls, raffia, cattail, coconut fiber, coir, oil palm fiber, ceiba, banana leaf, caro, curaua, henequen leaf, harakeke leaf,abaca, sugarcane bagasse, straw, bamboo strips, wheat flour, MDF and the like, vermiculite, zeolites, hydrotalcites, power plant fly ash, incinerated sewage sludge ash, pozzolans, blast furnace slag, asbestos, chrysotile, anthophyllite, crocidolite, wollastonite, attapulgite and the like, particulate ceramic materials such as alumina, zirconia, titania, ceria, silicon nitride, aluminum nitride, boron nitride, silicon carbide, boron carbide, mixed silicon-aluminum nitrides and metal titanates; particulate magnetic materials such as magnetic oxides of transition metals, often iron and chromium, for example, gammaFe2Os, Fe3U4, and cobalt-doped iron oxides, ferrites, for example, barium ferrites; and metallic particles, for example, aluminum, iron, nickel, cobalt, copper, silver, gold, palladium, and platinum metals and alloys thereof. Other useful solid materials include flame retardants, such as pentabromodiphenyl ether, octabromodiphenyl ether, decabromodiphenyl ether, hexabromocyclododecane, ammonium polyphosphate, melamine, melamine cyanurate, antimony oxide, and borates; biocides or industrial microbial agents, such as those listed in Tables 2, 3, 4, 5, 6, 7, 8, and 9 of the chapter entitled “Industrial Microbial Agents” in Kirk-Othmer's Encyclopedia of Chemical Technology, Vol. 13, 1981, 3rd Edition; and agrochemicals, such as the fungicides flutriafen, carbendazim, chlorothalonil, and mancozeb. The organic medium present in the composition of the invention is, in one embodiment, a plastic material and, in another embodiment, an organic liquid. The organic liquid may be polar or non-polar. By the term “polar,” we mean in relation to the liquid AI t?Q / ni Lznz / q / YILI organic, it is understood that an organic liquid is capable of forming moderate to strong bonds as described in the article entitled “A Three Dimensional Approach to Solubility” by Crowley et al. in Journal of Paint Technology, Vol. 38, 1966, page 269. Such organic liquids generally have a number of hydrogen bonds of 5 or more as defined in the aforementioned article. Suitable examples of polar organic liquids include amines, ethers, especially lower alkyl ethers, organic acids, esters, ketones, glycols, glycol ethers, glycol esters, alcohols, and amides. In Ibert Mellan's book, "Compatibility and Solubility" (published in 1968 by Noyes Development Corporation), Table 2.14 on pages 39-40 provides numerous specific examples of such liquids with moderately strong hydrogen bonding, and all of these liquids fall within the scope of the term "polar organic liquid" as used herein. In one embodiment, polar organic liquids are dialkyl ketones, alkyl esters of alkane carboxylic acids, and alkanols, especially such liquids containing up to, and including, a total of 6 carbon atoms.Examples of polar organic liquids include dialkyl and cycloalkyl ketones, such as acetone, methyl ethyl ketone, diethyl ketone, diisopropyl ketone, methyl isobutyl ketone, diisobutyl ketone, methyl isoamyl ketone, methyl n-amyl ketone, and cyclohexanone; alkyl esters, such as methyl acetate, ethyl acetate, isopropyl acetate, butyl acetate, ethyl formate, methyl propionate, methoxypropyl acetate, and ethyl butyrate; glycols and glycol esters and ethers, such as ethylene glycol, 2-ethoxyethanol, 3-methoxypropylpropanol, 3-ethoxypropylpropanol, 2-butoxyethyl acetate, 3-methoxypropyl acetate, 3-ethoxypropyl acetate, and 2-ethoxyethyl acetate; alkanols, such as methanol, ethanol, n-propanol, isopropanol, butanol and isobutanol (also known as 2-methylpropanol), terpineol and dialkyl and cyclic ethers, such as diethyl ether and tetrahydrofuran.In one embodiment, the solvents are alkanols, alkanecarboxylic acids, and alkanecarboxylic acid esters. In another embodiment, the present invention is suitable for organic liquids that are substantially insoluble in an aqueous medium. Furthermore, a person skilled in the art will appreciate that small amounts of an aqueous medium (such as glycols, glycol ethers, glycol esters, and alcohols) may be present in the organic liquids, provided that the overall organic liquid is substantially insoluble in an aqueous medium. R LfrQ / Π / Lznz / q / YILI Examples of organic liquids that can be used as polar organic liquids include film-forming resins, such as those suitable for preparing inks, paints, and chips for use in various applications. Examples of such resins include polyamides, such as Versamid™ and Wolfamid™, and cellulose ethers, such as ethylcellulose and ethylhydroxyethylcellulose, nitrocellulose, and cellulose acetate butyrate resins, including mixtures thereof. Examples of paint resins include short alkyd oil / melamine-formaldehyde, polyester / melamine-formaldehyde, thermosetting acrylic / melamine-formaldehyde, long alkyd oil, medium alkyd oil, short alkyd oil, polyether polyols, and multi-media resins, such as acrylics and urea / aldehyde. The organic liquid can be a polyol, that is, an organic liquid with two or more hydroxyl groups. In one form, polyols include alpha-omega diols or alpha-omega diol ethoxylates. In one sense, nonpolar organic liquids are compounds containing aliphatic groups, aromatic groups, or mixtures thereof. Nonpolar organic liquids include nonhalogenated aromatic hydrocarbons (e.g., toluene and xylene), halogenated aromatic hydrocarbons (e.g., chlorobenzene, dichlorobenzene, chlorotoluene), nonhalogenated aliphatic hydrocarbons (e.g., linear and branched aliphatic hydrocarbons containing six or more carbon atoms, both fully and partially saturated), halogenated aliphatic hydrocarbons (e.g., dichloromethane, carbon tetrachloride, chloroform, trichloroethane), and naturally occurring nonpolar organic products (e.g., vegetable oil, sunflower oil, rapeseed oil, linseed oil, terpenes, and glycerides). In one embodiment, the organic liquid comprises at least 0.1% by weight, or 1% by weight or more of a polar organic liquid based on the total organic liquid. In one embodiment, the organic liquid is water-free. The plastic material may be a thermosetting resin. Thermosetting resins useful in this invention include resins that undergo a chemical reaction when heated, catalyzed, or subjected to ultraviolet, laser, infrared, cationic, electron beam, or microwave radiation and become relatively infusible. Typical reactions in thermosetting resins include the oxidation of unsaturated double bonds, reactions involving epoxy / amine, R LfrQ / Π / 1 znz / q / YILI epoxy / carbonyl, epoxy / hydroxyl, reaction of epoxy with a Lewis acid or Lewis base, polyisocyanate / hydroxy, amino resin / hydroxy moieties, free radical or polyacrylate reactions, cationic polymerization of epoxy resins and vinyl ether, and silanol condensation. Examples of unsaturated resins include polyester resins made by the reaction of one or more diacids or anhydrides with one or more diols. Such resins are commonly supplied as a mixture with a reactive monomer, such as styrene or vinyltoluene, and are often referred to as orthophthalic and isophthalic resins. Additional examples include resins that use dicyclopentadiene (DCPD) as a co-reactant in the polyester chain.Additional examples also include the reaction products of bisphenol A diglycidyl ether with unsaturated carboxylic acids, such as methacrylic acid, subsequently supplied as a solution in styrene, commonly referred to as vinyl ester resins. In one form, the thermosetting composite material or thermosetting plastic can be a polyester, a polyvinyl acetate, a polyester resin in styrene, a polystyrene, or mixtures thereof. Polymers with hydroxy functionality (frequently polyols) are widely used in thermosetting systems for crosslinking with amino resins or polyisocyanates. Polyols include acrylic polyols, alkyd polyols, polyester polyols, polyether polyols, and polyurethane polyols. Typical amino resins include melamine-formaldehyde resins, benzoguanamine-formaldehyde resins, urea-formaldehyde resins, and glycoluryl-formaldehyde resins. Polyisocyanates are resins with two or more isocyanate groups, including both monomeric aliphatic and monomeric aromatic diisocyanates and their polymers. Typical aliphatic diisocyanates include hexamethylene diisocyanate, isophorone diisocyanate, and hydrogenated diphenylmethane diisocyanate. Typical aromatic isocyanates include toluene diisocyanates and diphenylmethane diisocyanates. If desired, the compositions of the present invention may contain other ingredients, for example resins (where these do not already constitute the organic medium), binders, co-solvents, crosslinking agents, fluidizing agents, wetting agents, anti-sedimentation agents, plasticizers, surfactants, dispersants other than the compound of the present invention, humectants, antifoaming agents, anti-cratering agents, rheology modifiers, heat stabilizers, light stabilizers, AI HQ / ni Lznz / q / YILI UV absorbers, antioxidants, leveling agents, gloss modifiers, biocides and preservatives. The compositions typically contain from 1 to 95% by weight of the particulate solid; the precise amount depends on the nature of the solid and the relative densities of the solid and the polar organic liquid. For example, a composition in which the solid is an organic material, such as an organic pigment, may contain from 15 to 60% by weight of the solid, while a composition in which the solid is an inorganic material, such as an inorganic pigment, filler, or diluent, may contain from 40 to 90% by weight of the solid, based on the total weight of the composition. Compositions containing an organic liquid can be prepared using any of the conventional methods known for preparing dispersions. The solid, the organic medium, and the dispersant can be mixed in any order. The mixture is then subjected to mechanical treatment to reduce the solid particles to an appropriate size, for example, by high-speed mixing, ball milling, basket milling, bead milling, gravel milling, sand crushing, attrition crushing, two- or three-roll milling, or plastic milling, until the dispersion is formed. Alternatively, the solid can be treated to reduce its particle size independently or in mixture with either the organic medium or the dispersant. The other ingredient(s) are then added, and the mixture is stirred to produce the desired composition.The composition can also be made by crushing or grinding the dry solid with the dispersant and then adding the liquid medium or mixing the solid with the dispersant in a liquid medium in a pigment washing process. The composition of the present invention is particularly suitable for liquid dispersions. In one embodiment, such dispersion compositions comprise: a) from 0.5 to 80 parts of a particulate solid; b) from 0.1 to 79.6 parts of a Formula I polymer / dispersant; and c) from 19.9 to 99.4 parts of an organic liquid. where all relative parts are by weight and the quantities (a) + (b) + (c) = 100. In one embodiment, component a) comprises from 0.5 to 30 parts of a pigment and such dispersions are useful as (liquid) inks, paints and base mixtures. If a composition comprising a particulate solid and a Formula 1 dispersant in dry form is required, the organic liquid is typically volatile so that it can be readily removed from the particulate solid by a simple separation method such as evaporation. In one embodiment, the composition comprises the organic liquid. If the dry composition consists essentially of the dispersant of formula (1) and the particulate solid, it typically contains at least 0.2%, at least 0.5%, or at least 1.0% of dispersant of Formula 1 based on the weight of the particulate solid. In one embodiment, the dry composition contains no more than 100%, no more than 50%, no more than 20%, or no more than 10% by weight of dispersant of Formula 1 based on the weight of the particulate solid. As described herein, the compositions of the invention are suitable for preparing base mixtures wherein the particulate solid is ground into an organic liquid in the presence of a compound of Formula 1. Therefore, in accordance with yet another additional aspect of the invention, a base mixture is provided comprising a particulate solid, an organic liquid, and a polymer of formula (1). Typically, the base mix contains 20 to 70% by weight of particulate solids based on the total weight of the base mix. In one embodiment, the particulate solids are not less than 10 or not less than 20% by weight of the base mix. Such base mixes may optionally contain a binder that is added either before or after milling. In one modality, the binder is a polymeric material capable of binding the composition together by volatilizing the organic liquid. Binders are polymeric materials that include both natural and synthetic materials. In one embodiment, binders include poly(meth)acrylates, polystyrenes, polyesters, polyurethanes, alkyds, polysaccharides such as cellulose and nitrocellulose, and natural proteins such as casein. The binder may be nitrocellulose. In one embodiment, the binder is present in the composition at more than 100% based on the amount of particulate solids, more than 200%, more than 300%, or more than 400%. The amount of optional binder in the base mix can vary widely, but is typically not less than 10% and often not less than 20% by weight of the continuous / liquid phase of the base mix. In one embodiment, the amount of RI frQ / ni Lznz / q / YILI binder is not more than 50% nor more than 40% by weight of the continuous / liquid phase of the base mixture. The amount of dispersant in the base mixture depends on the amount of particulate solids but is typically 0.5 to 5% by weight of the base mixture. The dispersions and base mixtures made from the composition of the invention are particularly suitable for use in non-aqueous, solvent-free formulations employing energy-curable systems (ultraviolet, laser, infrared, cationic, electron beam, microwave) with monomers, oligomers, etc., or a combination thereof, present in the formulation. They are particularly suitable for use in coatings such as paints, varnishes, inks, other coating materials, and plastics. Suitable examples include their use in low-, medium-, and high-solids paints; general industrial paints, including baking paints, two-component paints, and metal coatings such as coil and can coatings, powder coatings, UV-curable coatings, and wood varnishes; and inks such as flexographic, gravure, offset, lithographic, letterpress, or embossing inks.Screen printing and printing inks for packaging printing, non-impact inks such as inkjet inks including continuous injection and drop-on-demand injection, including thermal, piezo, and electrostatic phase-change inks and hot-melt wax inks, inks for inkjet printers and printing varnishes such as overprint varnishes; polyol and plastisol dispersions; non-aqueous ceramic processes, especially processes of the ribbon casting, gel casting, doctor blade, extrusion, and injection molding type, an additional example being the preparation of dry ceramic powders for isostatic pressing; compounds such as sheet molding and bulk molding compounds, resin transfer molding, pultrusion, hand-placement and spray-placement processes, matched-die molding; construction materials such as casting resins, cosmetics, personal care such as nail coatings,Sunscreens, adhesives, toners such as liquid toners, plastic materials, and electronic materials such as coating formulations for color filter systems in displays, including organic light-emitting diode (OLED) devices, liquid crystal displays, and electrophoretic displays; glass coatings, including fiber optic coatings, reflective coatings, and antireflective coatings; and conductive and magnetic inks and coatings. They are useful in modifying the surface of pigments and fillers to improve the dispersibility of the dry powders used in the previous applications. Further examples of coating materials are given in Bodo Muller, Ulrich Poth, Lackformulierung und Lackrezeptur, Lehrbuch fr Ausbildung und Praxis, Vincentz Verlag, Hanover (2003) and in PGGarrat, Strahlenhartung, Vincentz Verlag.Hanover (1996). Examples of printing ink formulations are given in EWFlick, Printing Ink and Overprint Varnish Formulations - Recent Developments, Noyes Publications, Park Ridge NJ, (1990) and later editions. In one embodiment, the composition of the invention further includes one or more additional known dispersants. The following examples provide illustrations of the invention. These examples are not exhaustive and are not intended to limit the scope of the invention. Reagents Used 1-Dodecanol - from Sigma Aldrich lsofol™-36 - from Condea Chemie GmbH ε-Caprolactone - from Perstorp Diphenyl phosphate - from Sigma Aldrich 1-Butanol - from Fisher Scientific, PM 750 - poly(ethylene glycol) methyl ether - from Sigma Aldrich, PM 750 Zirconium (IV) butoxide solution - from Sigma Aldrich, 80 wt% in 1-butanol mPEG 500 - poly(ethylene glycol) methyl ether - from Sigma Aldrich, MW 500 δ-Valerolactone - from BASF BuO PPG 1000 - poly(propylene glycol) butyl ether - from Sigma Aldrich, PM 1000 L-Lactide - Puralact B3 grade - from Corbion Surfonamine™ B60 - by Huntsman Surfonamine L100 - from Huntsman Succinic anhydride - from Sigma Aldrich Glutaric anhydride - from TCI Hexadecenylsuccinic anhydride - from Vertellus Octadecenylsuccinic anhydride - from Vertellus Homophthalic Anhydride - from Acros Organics Toluene - from Fisher Scientific mPEG 1000 - poly(ethylene glycol) methyl ether - from Ineos, PM 1000 mPEG350 - poly(ethylene glycol) methyl ether - from Sigma Aldrich PM 350 Synalox™ 50-30B - poly(ethylene glycol-ran-propylene glycol) monobutyl ether MW 1000 - from Dow, Orthophosphoric Acid Solution - from Sigma Aldrich, 85% wt in water Propoxylated Alcohol 1-24 molar equivalents of propylene oxide initiated with a C12-C15 alcohol, MW 1600 from Lubrizol Butoxylated alcohol 1-20 molar equivalents of butylene oxide starting with a C12-C15 alcohol, MW 1700 from Lubrizol Acetic anhydride - from Sigma Aldrich Epomin™ SP200 Polyethyleneimine - from Nippon Shokubai, PM 10,000 Epomin™ SP018 Polyethyleneimine - from Nippon Shokubai, PM 1800 Epomin™ SP006 Polyethyleneimine - from Nippon Shokubai, PM 600 Adipic acid - from Sigma Aldrich 1,4-butanediol - from Sigma Aldrich 6-Aminohexanoic acid - from Sigma Aldrich Orthophosphoric acid - from Sigma Aldrich Dimethyl sulfate - from Sigma Aldrich Polyisobutenylsuccinic anhydride 550 - from Lubrizol PM550 Step 1 - synthesis of alcohol-terminated polymers Alcohol-terminated polymer 1: 1-Dodecanol (100.85 parts) and εcaprolactone (802.98 parts) were loaded into a reaction vessel and heated to 70 °C under nitrogen. Once at temperature, diphenyl phosphate (2.71 parts) was added. After 4 hours, the reaction was stopped to produce a white, waxy solid. This is the alcohol-terminated polymer 1. Alcohol-terminated polymer 2: ε-caprolactone (410.01 parts) was loaded into a reaction vessel and heated to 110 °C under nitrogen. After 1 hour, the temperature was reduced to 70 °C. Once at this temperature, 1-butanol (88.75 parts) and diphenyl phosphate (1.50 parts) were added. After 3 hours, the reaction was stopped to produce a clear, colorless liquid. This is the alcohol-terminated polymer 2. Alcohol-terminated polymer 3: mPEG 750 (111.80 parts) and εcaprolactone (141.23 parts) were loaded into a reaction vessel and heated to 120 °C under nitrogen. After 10 hours, a zirconium butoxide solution (0.95 parts) was added, and the temperature was increased to 180 °C. After 20 hours, the reaction was stopped, producing a yellow paste. This is the alcohol-terminated polymer 3. ri no / nor ιτιαη / υιλι Alcohol-terminated polymer 4: mPEG 500 (60.00 parts), εcaprolactone (46.62 parts), δ-valerolactone (48.10 parts), and L-lactide (51.89 parts) were loaded into a reaction vessel and heated to 120 °C under nitrogen. After 1.5 hours, a zirconium butoxide solution (0.77 parts) was added, and the temperature was increased to 180 °C. After 19 hours, the reaction was stopped, producing a clear brown liquid. This is the alcohol-terminated polymer 4. Alcohol-terminated polymer 5: BuO PPG 1000 (431.04 parts) and L-lactide (310.63 parts) were loaded into a reaction vessel and heated to 120 °C under nitrogen. After 1.7 hours, a zirconium butoxide solution (2.23 parts) was added, and the temperature was increased to 180 °C. After 19 hours, the reaction was stopped, producing a brown paste. This is the alcohol-terminated polymer 5. Alcohol-terminated polymer 6: mPEG 500 (65.02 parts), εcaprolactone (81.61 parts), and δ-valerolactone (78.10 parts) were loaded into a reaction vessel and heated to 70 °C under nitrogen. Orthophosphoric acid solution (0.68 parts) was added, and the temperature was increased to 120 °C. After 8 hours, the reaction stopped, producing a clear, colorless liquid. This is the alcohol-terminated polymer 6. Alcohol-terminated polymer 7: 1-Dodecanol (25.41 parts), εcaprolactone (70.00 parts), δ-valerolactone (68.22 parts), and L-lactide (68.75 parts) were charged into a reaction vessel and heated to 120 °C under nitrogen. After 17 hours, a zirconium butoxide solution (0.87 parts) was charged, and the temperature was increased to 180 °C. After 8 hours, the reaction was stopped, producing a cloudy yellow liquid. This is the alcohol-terminated polymer 7. Alcohol-terminated polymer 8: Isofol™-36 (70.04 parts) and εcaprolactone (152.81 parts) were loaded into a reaction vessel and heated to 70 °C under nitrogen. When the reaction temperature reached 70 °C, orthophosphoric acid (0.72 parts) was added and the temperature was increased to 120 °C. After 8 hours, the reaction stopped, producing a whitish solid at room temperature. This is the alcohol-terminated polymer 8. Alcohol-terminated polymer 9: Surfonamine™ B60 (60 parts), ε-caprolactone (99.4 parts), and orthophosphoric acid (0.1 g) were added to a reaction vessel and stirred at 120 °C for several hours under a nitrogen atmosphere. A pale yellow liquid (157 parts) was obtained. This is the alcohol-terminated polymer 9. AI frQ / ni Lznz / q / YILI Alcohol-terminated polymer 10: Surfonamine™ L100 (60 parts) and εcaprolactone (12.8 parts) were loaded into a reaction vessel and heated to 120 °C with stirring under nitrogen. o-Phosphoric acid (0.1 parts) was added and stirred at 120 °C for 8 hours. The reaction was stopped to produce a pale yellow paste. This is the alcohol-terminated polymer 10. Alcohol-terminated polymer 11: mPEG350 (100 parts), εcaprolactone (63.6 parts), δ-valerolactone (38.6 parts), and o-phosphoric acid (0.2 parts) were loaded into a reaction vessel and heated to 120 °C with stirring under a nitrogen atmosphere for 16 hours. The reaction was stopped to produce a colorless liquid. This is the alcohol-terminated polymer 11. Alcohol-terminated polymer 12: The procedure of Agent J in US Patent 4,518,435 was repeated to make a polyether adduct prepared by the condensation of 2-diethylaminoethanol with 10 moles of ethylene oxide followed by 20 moles of propylene oxide. This is the alcohol-terminated polymer 12. Alcohol-terminated polymer 13: Adipic acid (81.09 parts), decanol (12.56 parts), and 1,4-butanediol (150.15 parts) were loaded into a reaction vessel and heated to 130 °C with stirring under nitrogen. o-Phosphoric acid (0.42 parts) was added, and the mixture was stirred at 130 °C for 49.5 hours. The reaction was stopped to produce a white solid. This is the alcohol-terminated polymer 13. Alcohol-terminated polymer 14: Octylamine (11.32 parts) and εcaprolactone (140 parts) were loaded into a reaction vessel and heated to 90 °C with stirring under nitrogen. After 3.5 hours, the temperature was increased to 120 °C, and stirring continued for 30 minutes. Zirconium butoxide (0.46 parts) was then added, and the temperature was increased to 180 °C. The reaction was stirred at 180 °C for 18 hours. The reaction was stopped to produce a white solid. This is the alcohol-terminated polymer 14. Alcohol-terminated polymer 15: A 2-naphthol polyether form and 10 moles of ethylene oxide (69.42 parts) and ε-caprolactone (134.75 parts) were loaded into a reaction vessel and heated to 70 °C with stirring under nitrogen. o-Phosphoric acid (0.61 parts) was added, and the temperature was increased to 120 °C. The reaction was stirred at 120 °C for 18.5 hours. The reaction was stopped to produce a cream-colored, waxy solid. This is the alcohol-terminated polymer 15. Alcohol-terminated polymer 16: 6-Aminohexanoic acid (70.13 parts) and ε-caprolactone (127.02 parts) were loaded into a reaction vessel and heated to 180 °C with stirring under nitrogen for 1.5 hours. After this time, the temperature was reduced to 120 °C for 0.75 hours. Then, decanol (20.77 parts) was added, and after 5 minutes, zirconium butoxide (0.43 parts) was added. The temperature was increased to 180 °C and stirred for 17.5 hours at this temperature. The reaction was stopped to produce a beige solid. This is the alcohol-terminated polymer 16. Step 2 - reaction of the alcohol-terminated polymer with the cyclic anhydride to generate the acid-terminated polymer Acid-terminated polymer 1: The alcohol-terminated polymer 1 (843.81 parts) was loaded into a reaction vessel and heated to 70 °C under nitrogen. Once at temperature, succinic anhydride (50.53 parts) was added and the temperature was increased to 130 °C. After 20 hours, the reaction was stopped to produce a white, waxy solid with an acidity value of 34 mg KOH / g. This is acid-terminated polymer 1. Acid-terminated polymer 2: The alcohol-terminated polymer 2 (450.00 parts) and toluene (22.37 parts) were loaded into a reaction vessel equipped with a condenser and heated to 70 °C under nitrogen. At this temperature, succinic anhydride (108.13 parts) was added, and the temperature was increased to 130 °C. After 18 hours, the reaction was stopped, and the mixture was cooled to 60 °C. The toluene was removed using a rotary evaporator to produce a slightly cloudy, pale yellow liquid with an acidity value of 116 mg KOH / g. This is the acid-terminated polymer 2. Acid-terminated polymer 3: The alcohol-terminated polymer 3 (211.77 parts) was loaded into a reaction vessel and heated to 70 °C under nitrogen. At this temperature, succinic anhydride (12.46 parts) was added and the temperature was increased to 130 °C. After 71 hours, the reaction was stopped to produce a pale yellow paste with an acidity value of 34 mg KOH / g. This is the acid-terminated polymer 3. Acid-terminated polymer 4: The alcohol-terminated polymer 4 (180.00 parts) was loaded into a reaction vessel and heated to 70 °C under nitrogen. At this temperature, succinic anhydride (10.44 parts) was added, and the temperature was increased to 130 °C. After 121 hours, the reaction was stopped to produce a clear brown liquid with an acidity value of 44 mg KOH / g. This is the acid-terminated polymer 4. Acid-terminated polymer 5: The alcohol-terminated polymer 5 (180.00 parts) was loaded into a reaction vessel and heated to 70 °C under nitrogen. At this temperature, succinic anhydride (10.52 parts) was added, and the temperature was increased to 130 °C. After 31 hours, the reaction was stopped to produce a viscous amber liquid with an acidity value of 34 mg KOH / g. This is the acid-terminated polymer 5. Acid-terminated polymer 6: mPEG 1000 (300.00 parts) was loaded into a reaction vessel and heated to 70 °C under nitrogen. Once at temperature, succinic anhydride (30.01 parts) was added and the temperature was increased to 130 °C. After 5 hours, the reaction was stopped to produce a white waxy paste with an acidity value of 54 mg KOH / g. This is the acid-terminated polymer 6. Acid-terminated polymer 7: BuO PPG 1000 (100.00 parts) was loaded into a reaction vessel and heated to 70 °C under nitrogen. When at temperature, succinic anhydride (10.04 parts) was added and the temperature was increased to 130 °C. After 18 hours, the reaction was stopped to produce a clear, colorless liquid with an acidity value of 45 mg KOH / g. This is the acid-terminated polymer 7. Acid-terminated polymer 8: Synalox™ 30-50B (245.03 parts) and an orthophosphoric acid solution (0.97 parts) were loaded into a reaction vessel and heated to 70 °C under nitrogen. Once at temperature, succinic anhydride (24.52 parts) was added and the temperature was increased to 130 °C. After 9 hours, the reaction was stopped to produce a clear, colorless liquid with an acidity value of 61 mg KOH / g. This is Acid-terminated Polymer 8. Acid-terminated polymer 9: Propoxylated alcohol 1 (300.00 parts) was charged into a reaction vessel and heated to 70 °C under nitrogen. When at temperature, succinic anhydride (18.76 parts) was charged and the temperature was increased to 130 °C. After 26 hours, the reaction was stopped to produce a clear yellow liquid with an acidity value of 36 mg KOH / g. This is acid-terminated polymer 9. Acid-terminated polymer 10: The alcohol-terminated polymer 6 (200.00 parts) was loaded into a reaction vessel and heated to 70 °C under nitrogen. When at temperature, succinic anhydride (11.57 parts) was added and the temperature was increased to 130 °C. After 41 hours, the reaction was stopped to produce a RI FQ / ni Lznz / q / YILI colorless transparent liquid with an acidity value of 42 mg KOH / g. This is the Acid Terminated Polymer 10. Acid-terminated polymer 11: Alcohol-terminated polymer 7 (200.00 parts) was loaded into a reaction vessel and heated to 70 °C under nitrogen. When at temperature, succinic anhydride (11.74 parts) was added and the temperature was increased to 130 °C. After 16 hours, the reaction was stopped to produce a cloudy yellow liquid with an acidity value of 41 mg KOH / g. This is acid-terminated polymer 11. Acid-terminated polymer 12: The alcohol-terminated polymer 8 (188.10 parts) was loaded into a reaction vessel and heated to 70 °C under nitrogen. When at temperature, succinic anhydride (11.40 parts) was added and the temperature was increased to 130 °C. After 8.5 hours, the reaction was stopped to produce a whitish solid at room temperature with an acidity value of 40 mg KOH / g. This is the acid-terminated polymer 12. Acid-terminated polymer 13: Alcohol-terminated propoxylated alcohol 1 (140.60 parts) was loaded into a reaction vessel and heated to 70 °C under nitrogen. When at temperature, glutaric anhydride (9.40 parts) was added and the temperature was increased to 130 °C. After 18 hours, the reaction was stopped to produce a clear liquid at room temperature with an acidity value of 36.10 mg KOH / g. This is acid-terminated polymer 13. Acid-terminated polymer 14: Alcohol-terminated propoxylated alcohol 1 (150.08 parts) was loaded into a reaction vessel and heated to 70 °C under nitrogen. When at temperature, a mixture of hexadecenylsuccinic anhydride and octadecenylsuccinic anhydride in equal weights (30.54 parts) was charged, and the temperature was increased to 130 °C. After 21.5 hours, the reaction was stopped to produce a clear, pale yellow liquid at room temperature with an acidity value of 41.09 mg KOH / g. This is acid-terminated polymer 14. Acid-terminated polymer 15: Alcohol-terminated propoxylated alcohol 1 (119.98 parts) was loaded into a reaction vessel and heated to 70 °C under nitrogen. When at temperature, homophthalic anhydride (10.79 parts) was added and the temperature was increased to 130 °C. After 23 hours, the reaction was stopped to produce a clear liquid at room temperature with an acidity value of 39.88 mg KOH / g. This is acid-terminated polymer 15. RI frQ / ni Lznz / q / YILI Acid-terminated polymer 16: Alcohol-terminated polymer 9 (150.06 parts) was loaded into a reaction vessel and heated to 70 °C under nitrogen. When at temperature, succinic anhydride (9.12 parts) was added and the temperature was increased to 130 °C. After 4.5 hours, the reaction was stopped to produce a whitish wax at room temperature with an acidity value of 46.45 mg KOH / g. This is acid-terminated polymer 16. Acid-terminated polymer 17: Butoxylated alcohol 1 (283 parts) was loaded into a reaction vessel and heated to 70 °C with stirring under a nitrogen atmosphere. When at temperature, succinic anhydride (13.4 parts) was added and the temperature was increased to 120 °C. After 20 hours, the reaction was stopped to produce a colorless liquid with an acidity value of 25.3 mg KOH / g. This is acid-terminated polymer 17. Acid-terminated polymer 18: The alcohol-terminated polymer 10 (72.8 parts) was loaded into a reaction vessel and heated to 80 °C under a nitrogen atmosphere. When at temperature, succinic anhydride (5.6 parts) was added and the temperature was increased to 120 °C. After 8 hours, the reaction was stopped to produce a pale yellow waxy solid with an acid value of 46.1 mg KOH / g. This is the acid-terminated polymer 18. Acid-terminated polymer 19: Alcohol-terminated polymer 11 (202.2 parts) was loaded into a reaction vessel and heated to 80 °C under a nitrogen atmosphere. When at temperature, succinic anhydride (28.5 parts) was added and stirred at 80 °C for 12 hours. The reaction was stopped to produce a pale yellow liquid with an acidity value of 72.3 mg KOH / g. This is acid-terminated polymer 19. Acid-terminated polymer 20: Propoxylated alcohol 1 (200 parts) was loaded into a reaction vessel and heated to 70 °C under nitrogen. When at temperature, succinic anhydride (11.1 parts) was added and the temperature was increased to 120 °C. After 20 hours, the reaction was stopped to produce a colorless liquid with an acidity value of 34 mg KOH / g. This is acid-terminated polymer 20. Acid-terminated polymer 21: The alcohol-terminated polymer 12 (153 parts) was loaded into a reaction vessel and heated to 70 °C under nitrogen. When at temperature, succinic anhydride (8.7 parts) was added and the temperature was increased to 120 °C. After 10 hours, the reaction was stopped to produce a A LfrQ / Π / Lznz / q / YILI pale yellow turbid liquid with an acidity value of 31.9 mg KOH / g. This is the acid-terminated polymer 21. Acid-terminated polymer 22: Propoxylated alcohol 1 (59.5 parts) and polyisobutenylsuccinic anhydride 550 (36.06 parts) were loaded into a reaction vessel and heated to 70 °C under nitrogen. When at temperature, o-phosphoric acid (0.84 parts) was added and the temperature was increased to 130 °C. After 50 hours, the reaction was stopped to produce a clear yellow liquid at room temperature with an acidity value of 31.25 mg KOH / g. This is acid-terminated polymer 22. Acid-terminated polymer 23: Alcohol-terminated polymer 13 (55.1 parts) was loaded into a reaction vessel and heated to 70 °C under nitrogen. When at temperature, succinic anhydride (3.1 parts) was added and the temperature was increased to 130 °C. After 4.5 hours, the reaction was stopped to produce a white solid at room temperature with an acidity value of 38.38 mg KOH / g. This is acid-terminated polymer 23. Acid-terminated polymer 24: Alcohol-terminated polymer 14 (140.13 parts) was loaded into a reaction vessel and heated to 70 °C under nitrogen. When at temperature, succinic anhydride (8.11 parts) was added and the temperature was increased to 130 °C. After 2.5 hours, the reaction was stopped to produce a clear liquid at room temperature with an acidity value of 32.58 mg KOH / g. This is acid-terminated polymer 24. Acid-terminated polymer 25: Alcohol-terminated polymer 15 (185.04 parts) was loaded into a reaction vessel and heated to 70 °C under nitrogen. When at temperature, succinic anhydride (10.80 parts) was added and the temperature was increased to 130 °C. After 20 hours, the reaction was stopped to produce a cream-colored solid at room temperature with an acidity value of 35.74 mg KOH / g. This is acid-terminated polymer 25. Acid-terminated polymer 26: Alcohol-terminated polymer 16 (115.26 parts) was loaded into a reaction vessel and heated to 70 °C under nitrogen. When at temperature, succinic anhydride (7.04 parts) was added and the temperature was increased to 130 °C. After 3.75 hours, the reaction was stopped to produce a cream-colored solid at room temperature with an acidity value of 35.15 mg KOH / g. This is acid-terminated polymer 26. The temperature was set to 150 °C. After an additional 17 hours, the Dean Stark trap was removed, leaving one port open. After another hour, the reaction was stopped, producing a dark brown, waxy solid. This is Polymeric Anhydride 6. Polymeric Anhydride 7: The finished Polymer 7 (40.00 parts) and acetic anhydride (3.94 parts) were loaded into a reaction vessel fitted with a Dean-Stark trap and heated to 120 °C under nitrogen. After 6 hours, the temperature was increased to 150 °C. After an additional 16 hours, the Dean-Stark trap was removed, leaving one port open. After an additional 1 hour, the reaction was stopped to produce a clear, pale yellow liquid. This is Polymeric Anhydride 7. Polymeric Anhydride 8: The finished Polymer 8 (150.00 parts) and acetic anhydride (16.71 parts) were loaded into a reaction vessel fitted with a Dean-Stark trap and heated to 120 °C under nitrogen. After 6 hours, the temperature was increased to 150 °C. After an additional 16 hours, the Dean-Stark trap was removed, leaving one port open. After an additional 1 hour, the reaction was stopped, producing a dark brown liquid. This is Polymeric Anhydride 8. Polymeric Anhydride 9: The finished Polymer 9 (90.00 parts) and acetic anhydride (6.49 parts) were loaded into a reaction vessel fitted with a Dean-Stark trap and heated to 120 °C under nitrogen. After 6 hours, the temperature was increased to 150 °C. After an additional 17 hours, the Dean-Stark trap was removed, leaving one port open. After an additional 1 hour, the reaction was stopped, producing a clear brown liquid. This is Polymeric Anhydride 9. Polymeric Anhydride 10: The finished Polymer 10 (120.00 parts) and acetic anhydride (8.03 parts) were loaded into a reaction vessel equipped with a Dean-Stark trap and heated to 120 °C under nitrogen. After 6 hours, the temperature was increased to 150 °C. After an additional 23 hours, the reaction was stopped to produce a dark brown, clear liquid. This is Polymeric Anhydride 10. Polymeric Anhydride 11: The finished Polymer 11 (120.01 parts) and acetic anhydride (8.15 parts) were loaded into a reaction vessel fitted with a Dean-Stark trap and heated to 120 °C under nitrogen. After 6 hours, the temperature was increased to 150 °C. After an additional 20 hours, the Dean-Stark trap was removed, leaving one port open. After another hour, the reaction was stopped to produce a clear orange liquid. This is Polymeric Anhydride 11. R LfrQ / Π / Lznz / q / YILI Polymeric Anhydride 12: The finished Polymer 12 (100.18 parts) and acetic anhydride (6.96 parts) were loaded into a reaction vessel fitted with a Dean-Stark trap and heated to 120 °C under nitrogen. After 6 hours, the temperature was increased to 150 °C. After an additional 9 hours, the Dean-Stark trap was removed, leaving one port open. After an additional 1 hour, the reaction was stopped to produce a light brown solid at room temperature. This is Polymeric Anhydride 12. Polymeric Anhydride 13: The finished Polymer 13 (69.98 parts) and acetic anhydride (4.73 parts) were loaded into a reaction vessel fitted with a Dean-Stark trap and heated to 120 °C under nitrogen. After 6 hours, the temperature was increased to 150 °C. After an additional 12.75 hours, the Dean-Stark trap was removed, leaving one port open. After an additional 1 hour, the reaction was stopped, yielding a clear liquid at room temperature. This is Polymeric Anhydride 13. Polymer Anhydride 14: The finished polymer was loaded into a reaction vessel fitted with a Dean-Stark trap and heated to 120 °C under nitrogen. After 6 hours, the temperature was increased to 150 °C. After an additional 16 hours, the Dean-Stark trap was removed, leaving one port open. After another 1 hour, the reaction was stopped, producing a pale yellow, clear liquid at room temperature. This is Polymer Anhydride 14. Polymeric Anhydride 15: The finished Polymer 15 (65.01 parts) and acetic anhydride (4.02 parts) were loaded into a reaction vessel fitted with a Dean-Stark trap and heated to 120 °C under nitrogen. After 6 hours, the temperature was increased to 150 °C. After an additional 16.5 hours, the Dean-Stark trap was removed, leaving one port open. After an additional 1 hour, the reaction was stopped, producing a clear, yellow liquid at room temperature. This is Polymeric Anhydride 15. Polymeric anhydride 16: The finished polymer 16 (60.00 parts) and acetic anhydride (4.26 parts) were loaded into a reaction vessel fitted with a Dean-Stark trap and heated to 120 °C under nitrogen. After 6 hours, the temperature was increased to 150 °C. After an additional 15 hours, the Dean-Stark trap was removed, leaving one port open. After an additional 1 hour, the reaction was A LfrQ / Π / Lznz / q / YILI stopped to produce a clear golden liquid at room temperature. This is Polymeric Anhydride 16. Polymeric Anhydride 17: The finished Polymer 17 (102 parts) and acetic anhydride (12 parts) were loaded into a reaction vessel equipped with a Dean-Stark trap and heated to 120 °C with stirring under a nitrogen atmosphere. After 10 hours, the temperature was increased to 150 °C. After an additional 4 hours, the reaction was stopped to produce a pale yellow liquid. This is Polymeric Anhydride 17. Polymer Anhydride 18: The finished Polymer 18 (78 parts) and acetic anhydride (10 parts) were loaded into a reaction vessel equipped with a Dean Stark trap and heated to 120 °C under a nitrogen atmosphere. After 6 hours, the temperature was increased to 150 °C to remove excess acetic anhydride and residual acetic acid. After an additional 4 hours, the reaction was stopped to produce a pale amber waxy solid. This is Polymer Anhydride 18. Polymeric Anhydride 19: The finished Polymer 18 (230 parts) and acetic anhydride (35 parts) were loaded into a reaction vessel fitted with a Dean Stark trap and heated to 120 °C under a nitrogen atmosphere. After 6 hours, the temperature was increased to 150 °C to remove excess acetic anhydride and residual acetic acid. After an additional 4 hours, the reaction was stopped to produce a pale yellow liquid. This is Polymeric Anhydride 19. Polymer Anhydride 20: The finished Polymer 20 (101 parts) and acetic anhydride (10 parts) were loaded into a reaction vessel equipped with a Dean-Stark trap and heated to 120 °C under a nitrogen atmosphere. After 10 hours, the temperature was increased to 150 °C. After a further 10 hours, the reaction was stopped to produce a pale yellow liquid. This is Polymer Anhydride 20. Polymeric Anhydride 21: The finished Polymer 21 (52 parts) and acetic anhydride (6 parts) were loaded into a reaction vessel equipped with a Dean Stark trap and heated to 120 °C under a nitrogen atmosphere. After 6 hours, the temperature was increased to 150 °C to remove excess acetic anhydride and residual acetic acid. After an additional 4 hours, the reaction was stopped to produce a dark amber liquid. This is Polymeric Anhydride 21. Polymeric anhydride 22: The finished polymer was loaded into a reaction vessel equipped with acid 22 (85.04 parts) and acetic anhydride (3.87 parts). R LfrQ / Π / Lznz / q / YILI was placed in a Dean Stark trap and heated to 120 °C under a nitrogen atmosphere. After 6 hours, the temperature was increased to 150 °C. After a further 7 hours, the reaction was stopped to produce a viscous brown liquid. This is Polymeric Anhydride 22. Polymeric Anhydride 23: The finished Polymer 23 (50.03 parts) and acetic anhydride (3.2 parts) were loaded into a reaction vessel equipped with a Dean-Stark trap and heated to 120 °C under a nitrogen atmosphere. After 6 hours, the temperature was increased to 150 °C. After an additional 13.25 hours, the reaction was stopped to produce a brown solid. This is Polymeric Anhydride 23. Polymeric Anhydride 24: The finished Polymer 24 (130.05 parts) and acetic anhydride (8.72 parts) were loaded into a reaction vessel equipped with a Dean-Stark trap and heated to 120 °C under a nitrogen atmosphere. After 6 hours, the temperature was increased to 150 °C. After an additional 12.75 hours, the reaction was stopped to produce a pale cream-colored solid. This is Polymeric Anhydride 24. Polymer Anhydride 25: The finished Polymer 25 was loaded into a reaction vessel equipped with a Dean-Stark trap (60.04 parts acid) and acetic anhydride (4.04 parts) and heated to 120 °C under a nitrogen atmosphere. After 6 hours, the temperature was increased to 150 °C. After an additional 9 hours, the reaction was stopped to produce a cream-colored wax solid. This is Polymer Anhydride 25. Polymeric Anhydride 26: The finished Polymer 26 (60.08 parts) and acetic anhydride (4.33 parts) were loaded into a reaction vessel equipped with a Dean-Stark trap and heated to 120 °C under a nitrogen atmosphere. After 6 hours, the temperature was increased to 150 °C. After an additional 26.5 hours, the reaction was stopped to produce a brown solid. This is Polymeric Anhydride 26. Step 4 - reaction of the polymeric anhydride with the multiamine to generate the dispersant. Dispersant 1: Polymeric Anhydride 1 (50.01 parts) was loaded into a reaction vessel and heated to 70 °C, then Epomin™ SP018 (3.86 parts, which had been preheated to 70 °C) was added. After 1 hour, the reaction was stopped to produce a pale yellow waxy solid with an acid value of 44 mg KOH / g and a base equivalence of 1060. This is Dispersant 1. Dispersant 2: Polymeric Anhydride 1 (45.01 parts) and Polymeric Anhydride 2 (15.03 parts) were loaded into a reaction vessel and heated to 70 °C. Then, Epomin™ SP018 (4.61 parts, which had been preheated to 70 °C) was added. After 1 hour, the reaction was stopped to produce a brownish-yellow waxy solid with an acid value of 56 mg KOH / g and a base equivalence of 1221. This is Dispersant 2. Dispersant 3: Polymeric Anhydride 3 (129.75 parts) was loaded into a reaction vessel and heated to 70 °C, then Epomin™ SP018 (10.00 parts, which had been preheated to 70 °C) was added. After 1 hour, the reaction was stopped to produce a brown paste with an acidity value of 16 mg KOH / g and a base equivalence of 1053. This is Dispersant 3. Dispersant 4: Polymeric Anhydride 4 (40.02 parts) was loaded into a reaction vessel and heated to 70 °C, then Epomin™ SP018 (3.08 parts, which had been preheated to 70 °C) was added. After 1 hour, the reaction was stopped to produce a dark brown, cloudy liquid with an acidity value of 27 mg KOH / g and a base equivalence of 1246. This is Dispersant 4. Dispersant 5: Polymeric Anhydride 5 (40.00 parts) was loaded into a reaction vessel and heated to 70 °C, then Epomin™ SP018 (3.09 parts, which had been preheated to 70 °C) was added. After 1 hour, the reaction was stopped to produce a pale brown viscous, cloudy liquid with an acidity value of 14 mg KOH / g and a base equivalence of 1228. This is Dispersant 5. Dispersant 6: Polymeric Anhydride 6 (50.01 parts) was loaded into a reaction vessel and heated to 70 °C, then Epomin™ SP018 (3.86 parts, which had been preheated to 70 °C) was added. After 1 hour, the reaction was stopped to produce a dark brown waxy solid with an acid value of 26 mg KOH / g and a base equivalence of 993. This is Dispersant 6. Dispersant 7: Polymeric Anhydride 7 (34.98 parts) was loaded into a reaction vessel and heated to 70 °C, then Epomin™ SP018 (2.69 parts, which had been preheated to 70 °C) was added. After 1 hour, the reaction was stopped to produce a pale yellow, clear liquid with an acidity value of 18 mg KOH / g and a base equivalence of 958. This is Dispersant 7. Dispersant 8: Polymeric Anhydride 8 (130.01 parts) was loaded into a reaction vessel and heated to 70 °C, then Epomin™ SP018 (10.01 parts) was loaded, which AI t?Q / ni Lznz / q / YILI had been preheated to 70 °C). After 1 hour, the reaction stopped to produce a dark brown liquid with an acidity value of 32 mg KOH / g and a base equivalence of 1008. This is Dispersant 8. Dispersant 9: Polymeric Anhydride 9 (50.00 parts) was loaded into a reaction vessel and heated to 70 °C, then Epomin™ SP018 (3.85 parts, which had been preheated to 70 °C) was added. After 1 hour, the reaction was stopped to produce a clear brown liquid with an acidity value of 16 mg KOH / g and a base equivalence of 1071. This is Dispersant 9. Dispersant 10: Polymeric Anhydride 1 (70.04 parts) was loaded into a reaction vessel and heated to 70 °C, then Epomin™ SP018 (3.93 parts, which had been preheated to 70 °C) was added. After 1 hour, the reaction was stopped to produce a brownish-yellow waxy solid with an acid value of 49 mg KOH / g and a base equivalence of 1946. This is Dispersant 10. Dispersant 11: Polymeric Anhydride 1 (50.00 parts) was loaded into a reaction vessel and heated to 70 °C, then Epomin™ SP018 (5.56 parts, which had been preheated to 70 °C) was added. After 1 hour, the reaction was stopped to produce a pale yellow waxy solid with an acid value of 50 mg KOH / g and a base equivalence of 634. This is Dispersant 11. Dispersant 12: Polymeric Anhydride 1 (60.00 parts) was loaded into a reaction vessel and heated to 70 °C, then Epomin™ SP006 (4.61 parts, which had been preheated to 70 °C) was added. After 1 hour, the reaction was stopped to produce a pale yellow solid with an acidity value of 43 mg KOH / g and a base equivalence of 1145. This is Dispersant 12. Dispersant 13: Polymeric Anhydride 10 (60.00 parts) was loaded into a reaction vessel and heated to 70 °C, then Epomin™ SP018 (4.62 parts, which had been preheated to 70 °C) was added. After 1 hour, the reaction was stopped to produce a clear, dark brown, viscous liquid with an acidity value of 28 mg KOH / g and a base equivalence of 1119. This is Dispersant 13. Dispersant 14: Polymeric Anhydride 11 (60.01 parts) was loaded into a reaction vessel and heated to 70 °C, then Epomin™ SP018 (4.63 parts, which had been preheated to 70 °C) was added. After 1 hour, the reaction was stopped to produce a cloudy, viscous brown liquid with an acidity value of 19 mg KOH / g and a base equivalence of 1221. This is Dispersant 14. RI frQ / ni Lznz / q / YILI Dispersant 15: Polymeric Anhydride 9 (60.00 parts) was loaded into a reaction vessel and heated to 70 °C. Then, succinic anhydride (0.94 parts) and Epomin™ SP018 (4.62 parts, which had been preheated to 70 °C) were added. After 1 hour, the reaction was stopped to produce a cloudy brown liquid with an acidity value of 24 mg KOH / g and a base equivalence of 1104. This is Dispersant 15. Dispersant 16: Polymeric Anhydride 12 (70.01 parts) was loaded into a reaction vessel and heated to 70 °C, then Epomin™ SP018 (5.37 parts, which had been preheated to 70 °C) was added. After 1 hour, the reaction was stopped to produce a dark brown solid at room temperature with an acidity value of 32 mg KOH / g and a base equivalence of 910. This is Dispersant 16. Dispersant 17: Polymeric Anhydride 13 (50.02 parts) was loaded into a reaction vessel and heated to 70 °C, then Epomin™ SP018 (3.83 parts, which had been preheated to 70 °C) was added. After 1 hour, the reaction was stopped to produce a cloudy yellow liquid at room temperature with an acidity value of 18.25 mg KOH / g and a base equivalence of 1152.11. This is Dispersant 17. Dispersant 18: Polymeric Anhydride 14 (70.05 parts) was loaded into a reaction vessel and heated to 70 °C, then Epomin™ SP018 (5.37 parts, which had been preheated to 70 °C) was added. After 1 hour, the reaction was stopped to produce a golden liquid at room temperature with an acidity value of 28.27 mg KOH / g and a base equivalence of 1013.35. This is Dispersant 18. Dispersant 19: Polymeric Anhydride 15 (43.98 parts) was loaded into a reaction vessel and heated to 70 °C, then Epomin™ SP018 (3.38 parts, which had been preheated to 70 °C) was added. After 1 hour, the reaction was stopped to produce a brown liquid at room temperature with an acidity value of 29.89 mg KOH / g and a base equivalence of 1068.52. This is Dispersant 19. Dispersant 20: Polymeric Anhydride 16 (49.99 parts) was loaded into a reaction vessel and heated to 70 °C, then Epomin™ SP018 (3.84 parts, which had been preheated to 70 °C) was added. After 1 hour, the reaction was stopped to produce a clear, viscous, orange liquid at room temperature with an acidity value of 30.64 mg KOH / g and a base equivalence of 1158.4. This is Dispersant 20. Dispersant 21: Polymeric Anhydride 17 (51 parts) was loaded into a reaction vessel and heated to 70 °C with stirring under a nitrogen atmosphere, then Epomin™ SP018 (3 parts, which had been preheated to 70 °C) was loaded. After R LfrQ / Π / 1 znz / q / YILI hour, the reaction was stopped to produce a pale yellow liquid with an acidity value of 12.6 mg KOH / g and a base equivalence of 1516. This is Dispersant 21. Dispersant 22: Polymeric Anhydride 18 (75 parts) was loaded into a reaction vessel and heated to 70 °C, then Epomin™ SP018 (6.5 parts, which had been preheated to 70 °C) was added. After 1 hour, the reaction was stopped to produce a light brown waxy solid with an acid value of 22.7 mg KOH / g and a base equivalence of 1083. This is Dispersant 22. Dispersant 23: Polymer Anhydride 19 (50 parts) was loaded into a reaction vessel and heated to 70 °C, then Epomin SP200 (5 parts, which had been preheated to 70 °C) was added. After 1 hour, the reaction was stopped to produce an amber liquid with an acidity value of 44.5 mg KOH / g and a base equivalent of 930. This is Dispersant 23. Dispersant 24: Polymer Anhydride 19 (50 parts) was loaded into a reaction vessel and heated to 70 °C, then Epomin™ SP018 (5 parts, which had been preheated to 70 °C) was added. After 1 hour, the reaction was stopped to produce an amber liquid with an acidity value of 43.1 mg KOH / g and a base equivalence of 962. This is Dispersant 24. Dispersant 25: Polymer Anhydride 20 (51 parts) was loaded into a reaction vessel and heated to 70 °C, then Epomin™ SP200 (4 parts, which had been preheated to 70 °C) was added. After 1 hour, the reaction was stopped to produce a pale amber liquid with an acidity value of 19.2 mg KOH / g and a base equivalence of 1203. This is Dispersant 25. Dispersant 26: Polymer Anhydride 20 (45 parts) was loaded into a reaction vessel and heated to 70 °C, then Epomin™ SP200 (5 parts, which had been preheated to 70 °C) was added. After 1 hour, the reaction was stopped to produce a pale amber liquid with an acidity value of 25 mg KOH / g and a base equivalence of 753. This is Dispersant 26. Dispersant 27: Dispersant 18 (39.99 parts) was loaded into a reaction vessel and heated to 70 °C under nitrogen, then caprolactone (0.81 parts) was added. After one hour, the reaction was stopped to produce a viscous liquid / paste with an acidity value of 27.45 mg KOH / g and a base equivalent of 1257.93. This is Dispersant 27. AI HQ / ni Lznz / q / YILI Dispersant 28: Dispersant 16 (40.17 parts) was loaded into a reaction vessel and heated to 70 °C under nitrogen. Orthophosphoric acid (85% w / w, 0.82 parts) and toluene (40.96 parts) were then added. After one hour, the reaction was stopped to produce a viscous liquid / paste with an acidity value of 24.13 mg KOH / g and a base equivalent of 1174.43. This is Dispersant 28. Dispersant 29: Dispersant 19 (30.24 parts) was loaded into a reaction vessel and heated to 70 °C under nitrogen, then butyl acrylate (0.57 parts) was added. After one hour, the reaction was stopped to produce a viscous liquid / paste with an acidity value of 25.79 mg KOH / g and a base equivalent of 1384.03. This is Dispersant 29. Dispersant 30: Dispersant 1 (35.09 parts) was loaded into a reaction vessel and heated to 70 °C under nitrogen, then dimethyl sulfate (0.7 parts) was added. After one hour, the reaction was stopped to produce a viscous liquid / paste with an acidity value of 49.56 mg KOH / g and a base equivalent of 1535.18. This is Dispersant 30. Dispersant 31: Dispersant 3 (50.03 parts) was loaded into a reaction vessel and heated to 70 °C under nitrogen. Then, Example 198 from US Patent 6197877 (1.00 part), which had been preheated to 70 °C, was added. After one hour, the reaction was stopped to produce a viscous liquid / paste with an acidity value of 16.13 mg KOH / g and a base equivalent of 1240.25. This is Dispersant 31. Dispersant 32: Polymer Anhydride 21 (52 parts) was loaded into a reaction vessel and heated to 70 °C, then Epomin™ SP018 (3.8 parts, which had been preheated to 70 °C) was added. After 1 hour, the reaction was stopped to produce a dark amber liquid with an acidity value of 15.9 mg KOH / g and a base equivalence of 679. This is Dispersant 32. Dispersant 33: Polymer Anhydride 22 (70.02 parts) was loaded into a reaction vessel and heated to 70 °C, then Epomin™ SP018 (5.42 parts, which had been preheated to 70 °C) was added. After 1 hour, the reaction was stopped to produce a brown viscous liquid at room temperature with an acidity value of 25.23 mg KOH / g and a base equivalence of 1025.32. This is Dispersant 33. Dispersant 34: Polymeric Anhydride 23 (40.03 parts) was loaded into a reaction vessel and heated to 70 °C, then Epomin™ SP018 (3.08 parts, which had been preheated to 70 °C) was added. After 1 hour, the reaction was stopped to produce a brown solid at room temperature with an acidity value of 24.95 mg KOH / g and a base equivalence of 990.76. This is Dispersant 34. Dispersant 35: Polymeric Anhydride 24 (100.14 parts) was loaded into a reaction vessel and heated to 70 °C, then Epomin™ SP018 (7.66 parts, which had been preheated to 70 °C) was added. After 1 hour, the reaction was stopped to produce a cream-colored solid at room temperature with an acidity value of 18.85 mg KOH / g and a base equivalence of 1184.82. This is Dispersant 35. Dispersant 36: Polymeric Anhydride 25 (50.03 parts) was loaded into a reaction vessel and heated to 70 °C, then Epomin™ SP018 (3.87 parts, which had been preheated to 70 °C) was added. After 1 hour, the reaction was stopped to produce a beige solid at room temperature with an acidity value of 22.75 mg KOH / g and a base equivalence of 1123.03. This is Dispersant 36. Dispersant 37: Polymeric Anhydride 26 (40.01 parts) was loaded into a reaction vessel and heated to 70 °C, then Epomin SP018 (3.11 parts, which had been preheated to 70 °C) was added. After 1 hour, the reaction was stopped to produce a brown solid at room temperature with an acidity value of 22.58 mg KOH / g and a base equivalence of 899.5. This is Dispersant 37. Dispersant 38: Polymer Anhydride 9 (47.09 parts) and Polymer Anhydride 1 (47 parts) were loaded into a reaction vessel and heated to 70 °C. Then, Epomin™ SP018 (7.27 parts, which had been preheated to 70 °C) was added. After 1 hour, the reaction was stopped to produce a brown liquid at room temperature with an acidity value of 46.21 mg KOH / g and a base equivalence of 1064.50. This is Dispersant 38. COMPARATIVE EXAMPLES The examples below are based on the teaching from the literature that acid-terminated polymers can readily react with multifunctional polyamines (especially PEI), and therefore in each comparative example we have taken the same acid-terminated polymer that was used as an intermediate to create in each case the closest possible comparative example. The reaction conditions used were the stirring of the acid-finished polymer with the multifunctional polyamine (especially PEI) at 120 °C for 6 hours, as these are the reaction conditions used in dispersants 1 through 28 of US patent 7,767,750 (WO2005 / 010109 A2), where the polyester-based PEI dispersants were made. Comparative Example 1: Acid-terminated Polymer 1 (30.05 parts) was loaded into a reaction vessel and heated to 70 °C. Then, Epomin™ SP018 (2.31 parts, which had been preheated to 70 °C) was loaded, and the temperature was increased to 120 °C. After 6 hours, the reaction was stopped to produce a brownish-orange waxy solid with an acid value of 26 mg KOH / g and a base equivalence of 1392. This is Comparative Example 1. Comparative Example 2: Acid-terminated Polymer 3 (60.01 parts) was loaded into a reaction vessel and heated to 70 °C. Then, Epomin™ SP018 (4.62 parts, which had been preheated to 70 °C) was loaded, and the temperature was increased to 120 °C. After 6 hours, the reaction was stopped to produce a brown paste with an acidity value of 19 mg KOH / g and a base equivalence of 1505. This is Comparative Example 2. Comparative Example 3: Acid-terminated Polymer 4 (60.02 parts) was loaded into a reaction vessel and heated to 70 °C. Then, Epomin™ SP018 (4.62 parts, which had been preheated to 70 °C) was loaded, and the temperature was increased to 120 °C. After 6 hours, the reaction was stopped to produce a dark brown, cloudy liquid with an acidity value of 31 mg KOH / g and a base equivalence of 1882. This is Comparative Example 3. Comparative Example 4: Acid-terminated Polymer 5 (60.01 parts) was loaded into a reaction vessel and heated to 70 °C. Then, Epomin™ SP018 (4.64 parts, which had been preheated to 70 °C) was loaded, and the temperature was increased to 120 °C. After 6 hours, the reaction was stopped to produce a cloudy, viscous, pale brown liquid with an acidity value of 30 mg KOH / g and a base equivalence of 1791. This is Comparative Example 4. Comparative Example 5: Acid-terminated Polymer 6 (50.00 parts) was loaded into a reaction vessel and heated to 70°C. Then, Epomin™ SP018 (3.87 parts, which had been preheated to 70°C) was loaded and the temperature was increased to 120°C. After 6 hours, the reaction was stopped to produce a non-homogeneous mixture of R LfrQ / Π / Lznz / q / YILI solid and turbid liquid with an acidity value of 20 mg KOH / g and a base equivalence of 1745. This is Comparative Example 5. Comparative Example 6: Acid-terminated Polymer 7 (50.02 parts) was loaded into a reaction vessel and heated to 70 °C. Then, Epomin™ SP018 (3.85 parts, which had been preheated to 70 °C) was loaded, and the temperature was increased to 120 °C. After 6 hours, the reaction was stopped to produce a cloudy brown liquid with an acidity value of 26 mg KOH / g and a base equivalence of 1369. This is Comparative Example 6. Comparative Example 7: Acid-terminated Polymer 8 (80.00 parts) was loaded into a reaction vessel and heated to 70 °C. Then, Epomin™ SP018 (6.15 parts, which had been preheated to 70 °C) was loaded, and the temperature was increased to 120 °C. After 6 hours, the reaction was stopped to produce a milky yellow liquid with an acidity value of 35 mg KOH / g and a base equivalence of 1502. This is Comparative Example 7. Comparative Example 8: Acid-terminated Polymer 9 (50.01 parts) was loaded into a reaction vessel and heated to 70 °C. Then, Epomin™ SP018 (3.85 parts, which had been preheated to 70 °C) was loaded, and the temperature was increased to 120 °C. After 6 hours, the reaction was stopped to produce a clear orange liquid with an acidity value of 15 mg KOH / g and a base equivalence of 1452. This is Comparative Example 8. Comparative Example 9: Acid-terminated Polymer 10 (60.01 parts) was loaded into a reaction vessel and heated to 70 °C. Then, Epomin™ SP018 (4.62 parts, which had been preheated to 70 °C) was loaded, and the temperature was increased to 120 °C. After 6 hours, the reaction was stopped to produce a clear orange liquid with an acidity value of 25 mg KOH / g and a base equivalence of 1558. This is Comparative Example 9. Comparative Example 10: Acid-terminated Polymer 11 (60.00 parts) was loaded into a reaction vessel and heated to 70 °C. Then, Epomin™ SP018 (4.64 parts, which had been preheated to 70 °C) was loaded, and the temperature was increased to 120 °C. After 6 hours, the reaction was stopped to produce a viscous brown liquid with an acidity value of 30 mg KOH / g and a base equivalence of 1900. This is Comparative Example 10. AI frQ / ni Lznz / q / YILI Comparative Example 11: Acid-terminated Polymer 12 (50.00 parts) was loaded into a reaction vessel and heated to 70 °C. Then, Epomin™ SP018 (3.87 parts, which had been preheated to 70 °C) was loaded and the temperature was increased to 120 °C. After 6 hours, the reaction was stopped to produce a yellow solid at room temperature with an acidity value of 24 mg KOH / g and a base equivalence of 1409. This is Comparative Example 11. Comparative Example 12: Acid-terminated Polymer 13 (50.51 parts) was loaded into a reaction vessel and heated to 70 °C. Then, Epomin™ SP018 (3.98 parts, which had been preheated to 70 °C) was loaded, and the temperature was increased to 120 °C. After 6 hours, the reaction was stopped to produce a cloudy, orange, viscous liquid at room temperature with an acidity value of 27.01 mg KOH / g and a base equivalence of 1298.10. This is Comparative Example 12. Comparative Example 13: Acid-terminated Polymer 14 (65.98 parts) was loaded into a reaction vessel and heated to 70 °C. Then, Epomin™ SP018 (5.06 parts, which had been preheated to 70 °C) was loaded, and the temperature was increased to 120 °C. After 6 hours, the reaction was stopped to produce a clear brown liquid at room temperature with an acidity value of 20.89 mg KOH / g and a base equivalence of 1131.20. This is Comparative Example 13. Comparative Example 14: Acid-terminated Polymer 15 (45.13 parts) was loaded into a reaction vessel and heated to 70 °C. Then, Epomin™ SP018 (3.59 parts, which had been preheated to 70 °C) was loaded, and the temperature was increased to 120 °C. After 6 hours, the reaction was stopped to produce a light brown, opaque liquid at room temperature with an acidity value of 18.71 mg KOH / g and a base equivalence of 2690.50. This is Comparative Example 14. Comparative Example 15: Acid-terminated Polymer 17 (51 parts) was loaded into a reaction vessel and heated to 70 °C with stirring under a nitrogen atmosphere. Then, Epomin™ SP018 (3 parts, which had been preheated to 70 °C) was loaded and heated to 120 °C with stirring under a nitrogen atmosphere. After 10 hours, the reaction was stopped to produce a pale yellow, cloudy liquid with an acidity value of 9.2 mg KOH / g and a base equivalence of 1998. This is Comparative Example 15. Comparative Example 16: Acid-terminated Polymer 20 (39 parts) was loaded into a reaction vessel and heated to 70 °C with stirring under a nitrogen atmosphere. Then, Epomin™ SP200 (3 parts, which had been preheated to 70 °C) was loaded. It was heated to 120 °C with stirring under a nitrogen atmosphere. After 6 hours, the reaction was stopped to produce a dark amber liquid with an acidity value of 9.8 mg KOH / g and a base equivalence of 1586. This is Comparative Example 16. Comparative Example 17: Acid-terminated Polymer 21 (52 parts) was loaded into a reaction vessel and heated to 70 °C with stirring under a nitrogen atmosphere. Then, Epomin™ SP018 (4 parts, which had been preheated to 70 °C) was loaded and heated to 120 °C with stirring under a nitrogen atmosphere. After 6 hours, the reaction was stopped to produce a yellow liquid with an acidity value of 12.3 mg KOH / g and a base equivalence of 789. This is Comparative Example 17. APPLICATION TESTS Application Testing Reagents Dowanol MPA - from Sigma Aldrich Toluene - from Fisher Scientific Ethanol - from Fisher Scientific Ethyl Acetate - from Fisher Scientific Exxol D140 - From ExxonMobil Heliogen Blue L7101F - from BASF Irgalite Rubine D4240 - from BASF Symular Carmine 6B400s - Sun Chemicals Bayferrox 130M - by Lanxess 3mm Glass Beads - by Sigmund Lindner Application Results Each Dispersant (0.25 parts) listed in Tables 2-5 below was added to an 8-drachm vial, and solvent (8.25 parts) was added. The dispersant was then dissolved by shaking and heating as needed. Once dissolved, 3 mm glass beads (17 parts) were added, followed by Heliogen Blue L7101F (1.50 parts). The vials were then sealed and shaken on a horizontal shaker for 16 hours. The flowability of the resulting dispersion was then evaluated using a visual characterization scale from A to E (from fluid to viscous): A - free movement of glass beads (fluid) RI FQ / ni Lznz / q / YILI B - movement 1 minute after agitation C - movement 10 seconds after agitation D - movement during agitation E - no movement (gelled) RI frQ / ni Lznz / q / YILI Table 1. Pigment dispersion results. Solvent: Dowanol MPA Dispersant Flow Rate Dispersant Flow Rate Comparative Example 6 D Dispersant 7 B Comparative Example 7 D Dispersant 8 C / B RI frQ / ni 1707 / 3 / YILI Table 2. Pigment dispersion results. Solvent: Toluene Dispersant Flow Rate Dispersant Flow Rate Comparative Example 1 C / D Dispersant 1 B / A Dispersant 2 B / A Dispersant 10 B Dispersant 11 B / A Dispersant 12 B / A Dispersant 38 A Comparative Example 2 C Dispersant 3 B / A Comparative Example 3 D / C Dispersant 4 C / B Comparative Example 4 D / C Dispersant 5 C / D Comparative Example 5 C Dispersant 6 B / A Comparative Example 6 C Dispersant 7 A / B Comparative Example 8 D / C Dispersant 9 B / A Comparative Example 9 B Dispersant 13 B / A Comparative Example 11 C Dispersant 16 B Dispersant 28 C / B Table 3. Pigment dispersion results. Solvent: ethanol / ethyl acetate Dispersant Flow Rate Dispersant Flow Rate Comparative Example 5 D Dispersant 6 A Comparative Example 8 D Dispersant 9 A Table 4. Pigment dispersion results. Solvent: ethanol / ethyl acetate 4:1 Dispersant Flow Rate Dispersant Flow Rate Comparative Example 5 D Dispersant 6 A Comparative Example 8 D Dispersant 9 A Each Dispersant (0.40 parts) listed in Tables 6 to 9 below was added to an 8-drachm vial, and solvent (7.60 parts) was added. The dispersant was then dissolved by shaking and heating as needed. Once dissolved, 3 mm glass beads (17 parts) were added, followed by Irgalite Rubine D4240 (2.00 parts). The vials were then sealed and shaken on a horizontal shaker for 16 hours. The flowability of the resulting dispersion was then assessed using a visual characterization scale from A to E (from fluid to viscous): A - free movement of glass beads (fluid); B - movement 1 minute after shaking; C - movement 10 seconds after shaking; D - movement during shaking; E - no movement (gelled). R LfrQ / Π / Lznz / q / YILI Table 5. Pigment dispersion results. Solvent: Ethanol Dispersant Flow Rate Dispersant Flow Rate Comparative Example 6 D / C Dispersant 7 A Comparative Example 8 D Dispersant 9 B / A Dispersant 15 B / A Comparative Example 13 D Dispersant 18 C Table 6. Pigment dispersion results. Solvent: Toluene Dispersant Flow Rate Dispersant Flow Rate Comparative Example 3 C Dispersant 4 B / A Comparative Example 8 D Dispersant 9 B / A Comparative Example 9 C Dispersant 13 A Table 7. Pigment dispersion results. Solvent: Exxol D140 Dispersant Flow Rate Dispersant Flow Rate Comparative Example 13 B / C Dispersant 18 A / B Dispersant 27 B Dispersant 33 A Table 8. Pigment dispersion results. Solvent: Xylene / Butanol 2.5:1 Dispersant Flow Rate Dispersant Flow Rate Comparative Example 1 D / E Dispersant 34 A Comparative Example 11 D Dispersant 35 A Each Dispersant (0.40 parts) listed in Table 10 below was added to an 8-drachm vial, and solvent (7.60 parts) was added. The dispersant was then dissolved by shaking and heating as needed. Once dissolved, 3 mm glass beads (17 parts) were added, followed by Symuler Carmine 6B400s (2.00 parts). The vials were then sealed and shaken on a horizontal shaker for 16 hours. The flowability of the resulting dispersion was then assessed using a visual characterization scale from A to E (from fluid to viscous): A - free movement of glass beads (fluid); B - movement 1 minute after shaking; C - movement 10 seconds after shaking; D - movement during shaking; E - no movement (gelled). Table 9. Pigment dispersion results. Solvent: Ethanol / Ethyl Acetate A LfrQ / Π / Lznz / q / YILI Dispersant Flow Rate Dispersant Flow Rate Comparative Example 14 D / C Dispersant 19 A / B Dispersant 29 A Each Dispersant (0.40 parts) listed in Table 11 below was added to an 8-drachm vial, and solvent (7.60 parts) was added. The dispersant was then dissolved by shaking and heating as needed. Once dissolved, 3 mm glass beads (17 parts) were added, followed by Irgalite Rubine (2.00 parts). The vials were then sealed and shaken on a horizontal shaker for 16 hours. The flowability of the resulting dispersion was then assessed using a visual characterization scale from A to E (from fluid to viscous). A - free movement of the glass beads (fluid) B - movement 1 minute after agitation C - movement 10 seconds after agitation D - movement during agitation E - no movement (gelled) Table 10: Pigment dispersion results. Solvent: Ethanol / Ethyl Acetate Dispersant Flow Rate Dispersant Flow Rate Comparative Example 12 C Dispersant 17 A Each dispersant (0.10 parts) listed in Table 12 below was added to an 8-drachm vial, and solvent (4.90 parts) was added. The dispersant was then dissolved by shaking and heating as needed. Once dissolved, 3 mm glass beads (17 parts) were added, followed by Bayferrox 130M (5.00 parts). The vials were then sealed and shaken on a horizontal shaker for 16 hours. The flowability of the resulting dispersion was then assessed using a visual characterization scale from A to E (from fluid to viscous). A - free movement of the glass beads (fluid) B - movement 1 minute after agitation C - movement 10 seconds after agitation D - movement during agitation E - no movement (gelled) Table 11. Pigment dispersion results. Solvent: Toluene R LfrQ / Π / Lznz / q / YILI Dispersant Flow Rate Dispersant Flow Rate Comparative Example 1 D / C Dispersant 1 C / B Comparative Example 3 D / C Dispersant 4 B / C Comparative Example 6 C Dispersant 7 A Comparative Example 8 D Dispersant 9 A / B Dispersant 36 A The dispersions were prepared by dissolving each of the Dispersant Examples 21 and 25 and Comparative Examples 16 and 17 (0.4 parts) in ethanol:ethyl acetate 4:1 (v:v) (7.6 parts). Then, 3 mm glass beads (17 parts) and Irgalite Rubine D4240 pigment (2.0 parts, Pigment Red 57.1 exBASF) were added to each solution, and the contents were milled in a horizontal shaker for 16 hours. Viscosity was assessed by determining the freedom of movement of the glass beads across the base of the mill. In all cases, except where no agent was present, the pigment was wetted, and a homogeneous dispersion was formed. The viscosity of the resulting dispersion was evaluated using a visual characterization scale from A to E (good to poor). The results are given below, which clearly illustrate that the dispersant of the invention produces superior, more fluid dispersions.Particle sizes for each dispersion were obtained by taking a sample of the milling dispersion (0.04 parts) and diluting it in ethyl ethaneacetate 4:1 (v:v) (8 parts) and measuring the particle size on a Nanotrac DLS particle size analyzer. The results obtained are: R LfrQ / Π / Lznz / q / YILI Table 12. Results of the scattering in Irgalite Rubine Example Viscosity Classification Particle Size nm D50 / D90 Control (Without dispersant) E Gelled Comparative Example 15 D 497 / 1351 Dispersant Example 21 B 308 / 419 Comparative Example 16 D 329 / 451 Dispersant Example 25 B 213 / 345 Comparative Example 17 D 330 / 582 Dispersant Example 32 A 163 / 289 Particle size analysis: The dispersions selected from Tables 2-12 above were diluted in the appropriate solvent (approximately 1:50 by volume). Particle size analysis was performed for each dispersion as indicated in Tables 9-10 below. D50 and D90 values ​​were obtained from intensity-based distributions. Table 13. Results of particle size analysis. Pigment: Heliogen Blue L7101F. Solvent: Toluene Dispersant D50 / nm D90 / nm Dispersant D50 / nm D90 / nm Comparative Example 3 1732 2470 Dispersant 4 908 1357 Comparative Example 10 1578; 1065 2690; 3930 Dispersant 14 685; 643 1059; 1078 Comparative Example 11 4130 5520 Dispersant 16 1047 1618 Table 14. Results of particle size analysis. Pigment: Irgalite Rubine D4240. Solvent: Toluene Dispersant D50 / nm D90 / nm Dispersant D50 / nm D90 / nm Comparative Example 3 1578; 2307 2049; 3530 Dispersant 4 561; 643 1264; 1168 Comparative Example 9 445 761 Dispersant 13 225 348 Table 15. Results of particle size analysis. Pigment: Irgalite Rubine D4240. Solvent: Ethanol Dispersant D50 / nm D90 / nm Dispersant D50 / nm D90 / nm Comparative Example 13 479 706 Dispersant 18 304 498 Table 16. Results of particle size analysis. Pigment: Irgalite Rubine D4240. Solvent: Exxol D140 Dispersant D50 / nm D90 / nm Dispersant D50 / nm D90 / nm Comparative Example 13 372 533 Dispersant 18 284 444 Dispersant 27 262.2 509.0 Dispersant 33 195 367 Table 17. Results of particle size analysis. Pigment: Irgalite Rubine D4240. Solvent: Ethanol:Ethyl acetate 1:1 Dispersant D50 / nm D90 / nm Dispersant D50 / nm D90 / nm Comparative Example 12 331 557 Dispersant 17 242 327 Table 18. Results of particle size analysis. Pigment: Irgalite Rubine D4240. Solvent: Xylene / Butanol 2.5:1 RI frQ / ni Lznz / q / YILI Dispersant D50 / nm D90 / nm Dispersant D50 / nm D90 / nm Comparative Example 11 1278 2654 Dispersant 34 321 512 Dispersant 35 249 375 Viscosity Measurements: Viscosity was measured using a rheometer for the dispersions selected from Tables 2-12 above. Two shear rates were selected for data comparison: 40 s⁻¹ and 100 s⁻¹. Table 19. Viscosity Data. Pigment: Heliogen Blue L7101F. Solvent: Toluene Dispersant Viscosity at 40 s¹ / Pa-s Viscosity at 100 s¹ / Fas Dispersant Viscosity at 40 s¹ / Pa-s Viscosity at 100 s¹ / Pa-s Comparative Example 1 0.638 0.285 Dispersant 1 0.421 0.198 Comparative Example 3 0.763 0.376 Dispersant 4 0.605 0.283 Table 20. Viscosity data. Pigment: Irgalite Rubine D4240. Solvent: Toluene Dispersant Viscosity at 40 s' 1 / Pa-s Viscosity at 100 s' 1 / Pa-s Dispersant Viscosity at 40 s' 1 / Pa-s Viscosity at 100 s' 1 / Pa-s Comparative Example 9 0.391 0.171 Dispersant 13 0.00835 0.00784 As used in this description, the transitional term “comprising,” which is synonymous with “including,” “containing,” or “characterized by,” is inclusive or open-ended and does not exclude additional unmentioned method elements or steps. However, in each instance of “comprising” in this description, the term is also intended to encompass, as alternative modalities, the phrases “essentially consisting of” and “consisting of,” where “consisting of” excludes any unspecified element or step, and “essentially consisting of” permits the inclusion of additional unmentioned elements or steps that do not materially affect the basic and novel characteristics of the composition or method under consideration. Although the invention has been explained in relation to its preferred embodiments, it should be understood that the various modifications thereof will become apparent to those skilled in the art upon reading the description. Therefore, it should be understood that the invention described herein is intended to cover such modifications that fall within the scope of the appended claims.

Claims

CLAIMS 1. A dispersant of the following structure: {x-(CH2CHR1-o)n-[R'-x(R<5)]b-[(c=o)R;-o]m-(c=o)-R!-(c=o)o >q [o-(c=o)-r4]p MA (HJq-p Formula 1 ¡X-(CH:CHR1-O)n-[R--N(Ró)]b-[(C=O)R;-O]m-(C=O)-R-'-(C=O)]t ' [(C=O)-R4]: wherein X is RQ or a cyclic secondary amine, wherein when X is RQ, R is a hydrocarbon chain containing from 1 to 50 carbon atoms and Q is oxygen, or NR7 or NH, with the condition that Q can only be NH when n is 0 and b Let n be 0, and R7 is a hydrocarbon chain containing from 1 to 18 carbon atoms; R1 is H, methyl or ethyl; R5 is a hydrocarbon chain containing up to 3 carbon atoms; R6 is hydrogen, a hydrocarbyl group containing from 1 to 22 carbon atoms, or the residue of an alkyl (meth)acrylate or (meth)acrylamide; b is 0 or 1, with the condition that b can only be 1 when both n and m are both at least 1;R2 is a hydrocarbon chain containing from 1 to 15 carbon atoms or R8(C=O)YR9-, where Y is O or NH or NR10, R8 is a hydrocarbon chain containing from 1 to 10 carbon atoms, R9 is a hydrocarbon chain containing from 2 to 10 carbon atoms and R10 is a hydrocarbon chain containing from 1 to 20 carbon atoms; n is any integer from 0 to 65 and m is any integer from 0 to 35, with the condition that m + n is at least 3; R3 is a hydrocarbon containing from 2 to 80 carbon atoms; q and t are each at least 1; MA is a multiamine species having a number-average molecular weight of 300 to 20,000 g / mol; R4 is a carbon chain containing between 1 and 4 carbons, preferably between 1 and 2; and ρ + z is 0 or any integer from 1 to 200.; 2. The dispersant of claim 1, wherein X is RQ and Q is oxygen.

3. The dispersant of claim 1, wherein X is RQ and Q is NR7.

4. The dispersant of claim 1, wherein X is RQ and Q is NH and n is 0 and b is 0.

5. The dispersant of claim 1, wherein X is a cyclic secondary amine, selected from piperidine, morpholine, 4-methylpiperidine, 4-phenylpiperidine, thiomorpholine, azetidine, 1-methylpiperazine, 2-methylpiperazine, and pyrrolidine and mixtures thereof.

6. The dispersant of any of claims 1 to 5, wherein R is a hydrocarbon chain containing from 1 to 30 carbon atoms.

7. The dispersant of any of claims 1 to 6, wherein R is a branched or linear, saturated or unsaturated alkyl, aryl, aralkyl or alkylaryl hydrocarbon chain.

8. The dispersant of any of claims 1 to 7, wherein R further contains a halogen group.

9. The dispersant of any of claims 1 to 7, wherein R contains a heteroatom selected from N or O.

10. The dispersant of any of claims 1 to 7, wherein R7 contains a functional group selected from groups consisting of ether, ester, or amides.

11. The dispersant of any of claims 1 to 10, wherein R6 is H.

12. The dispersant of any of claims 1 to 10, wherein R6 is a hydrocarbon chain containing from 1 to 22 carbon atoms.

13. The dispersant of any of claims 1 to 10, wherein R6 is the residue of an alkyl (meth)acrylate or (meth)acrylamide.

14. The dispersant of any of claims 1 to 13, wherein R2 is R8(C=O)YR9-.

15. The dispersant of claim 14, wherein Y is NH.

16. The dispersant of claim 14, wherein Y is NR10 where R10 is a hydrocarbon chain containing from 1 to 20 carbon atoms.

17. The dispersant of claim 16, wherein R10 includes an ester, ether, or amide group.

18. The dispersant of any of claims 1 to 13, wherein R2 is a linear or branched, saturated or unsaturated hydrocarbon chain containing from 1 to 10 carbon atoms.

19. The dispersant of claim 18, wherein R2 is a hydrocarbon chain containing from 2 to 7 carbon atoms.

20. The dispersant of any of claims 1 to 13, wherein R2 is a hydrocarbon chain containing from 2 to 15 carbon atoms and includes an amide functional group having the formula -N(R11)-(C=O)-, where R11 is H or a hydrocarbon chain containing from 1 to 4 carbon atoms.

21. The dispersant of any of claims 1 to 20, wherein R3 is a branched or linear, saturated or unsaturated hydrocarbon chain containing from 2 to 20 carbon atoms.

22. The dispersant of any of claims 1 to 21, wherein the MA has a number average molecular weight of 600 to 10,000 g / mol.

23. The dispersant of any of claims 1 to 22, wherein the MA has at least 4 amine groups.

24. The dispersant of any of claims 1 to 23, wherein the MA comprises polyethyleneimine or modified polyethyleneimine.

25. The dispersant of claim 24, wherein the dispersant is modified by reacting the dispersant with (a) an isocyanate, lactone, epoxy, anhydride, cyclic carbonate, (meth)acrylate via the Michael addition reaction and / or a polymeric species having a group that reacts with a primary or secondary amine to form a salt or covalent bond, (b) an oxidizing species that could convert the amino group into a nitric oxide, (c) a salting agent, or (d) a tertiary amino group of said multiamine species or the dispersant containing the multiamine species is reacted with a quaternizing agent to form a quaternized amino group.

26. The dispersant of any of claims 1 to 25, wherein R4 contains 1 or 2 carbon atoms.

27. The dispersant of any of claims 1 to 26, wherein q + t is any integer from 2 to 200.

28. The dispersant of claim 27, wherein q + t is any integer from 2 to 150. AI t?Q / ni Lznz / q / YILI 29. The dispersant of any of claims 1 to 28, wherein q is greater than or equal to t.

30. The dispersant of any of claims 1 to 29, wherein p + z is 0.

31. The dispersant of any of claims 1 to 29, wherein p + z is any integer from 1 to 200.

32. The dispersant of any of claim 31, wherein p + z is any integer from 2 to 200.

33. The dispersant of any of claims 1 to 32, wherein n is any integer from 1 to 65.

34. The dispersant of any of claims 1 to 32, wherein n is 0.

35. The dispersant of any of claims 1 to 34, wherein m is any integer from 1 to 35.

36. The dispersant of any of claims 1 to 33, wherein m is 0.

37. The dispersant of claim 35, wherein m is from 5 to 16.

38. The dispersant of any of claims 1 to 37, wherein m + n is from 3 to 65.

39. The dispersant of any of claims 1 to 37, wherein m + n is from 5 to 30.

40. The dispersant of any of claims 1 to 32, wherein b is 1 and m + n is at least 4.

41. A method for preparing a dispersant, wherein the method comprises the steps of: (a) providing an alcohol-terminated polymer of the formula: X-(CH2CHR1-O)n[R5-N(R6)]b-[(C=O)R2-O]mH, wherein X is RQ or a cyclic amine, wherein R is a hydrocarbon chain containing from 1 to 50 carbon atoms and Q is O, or NR7 or NH, provided that X is only NH when n is 0 and b is 0, R7 is a hydrocarbon chain containing from 1 to 18 carbon atoms; R1 is H, methyl or ethyl, R5 is a hydrocarbon chain containing up to 3 carbon atoms; R6 is hydrogen, a hydrocarbyl group containing from 1 to 22 carbon atoms, or the residue of an alkyl (meth)acrylate or (meth)acnamide; b is 0 or 1, with the condition that b can only be 1 when both n and m are both at least 1;R2 is a hydrocarbon chain containing from 1 to 15 carbon atoms or -R8(C=O)YR9-, where Y is O or NH or NR10, R8 is a hydrocarbon chain containing from 1 to 10 carbon atoms, R9 is a hydrocarbon chain containing from 1 to 10 carbon atoms and R10 is a hydrocarbon chain containing from 1 to 20 carbon atoms, n is any integer from 0 to 65 and m is any integer from 0 to 35, with the condition that m + n is at least 3; (b) reacting the alcohol-terminated polymer with a cyclic anhydride to provide an acid-terminated polymer; (c) reacting the acid-terminated polymer with a non-cyclic anhydride to provide a mixture of anhydrides; (d) reacting the mixture of anhydrides with a multiamine species, wherein the multiamine species has a number-average molecular weight of 300 to 20,000, to form a dispersing molecule.

42. The dispersant of claim 41, wherein X is RQ and Q is oxygen.

43. The dispersant of claim 41, wherein X is RQ and Q is NR7.

44. The dispersant of claim 41, wherein X is RQ and Q is NH and n is 0 and b is 0.

45. The dispersant of claim 41, wherein X is a cyclic secondary amine, selected from piperidine, morpholine, 4-methylpiperidine, 4-phenylpiperidine, thiomorpholine, azetidine, 1-methylpiperazine, 2-methylpiperazine, and pyrrolidine and mixtures thereof. R LfrQ / Π / Lznz / q / YILI 46. ​​The dispersant of any of claims 41 to 45, wherein R is a hydrocarbon chain containing from 1 to 30 carbon atoms.

47. The dispersant of any of claims 41 to 46, wherein R is a branched or linear, saturated or unsaturated hydrocarbon chain of alkyl, aryl, aralkyl or alkylaryl.

48. The dispersant of any of claims 41 to 47, wherein R further contains a halogen group.

49. The dispersant of any of claims 41 to 47, wherein R contains a heteroatom selected from N or O.

50. The dispersant of any of claims 41 to 47, wherein R7 contains a functional group selected from groups consisting of ether, ester, or amides.

51. The dispersant of any of claims 41 to 50, wherein R6 is H.

52. The dispersant of any of claims 41 to 50, wherein R6 is a hydrocarbon chain containing from 1 to 22 carbon atoms.

53. The dispersant of any of claims 41 to 50, wherein R6 is the residue of an alkyl (meth)acrylate or (meth)acrylamide.

54. The dispersant of any of claims 41 to 53, wherein R2 is R8(C=O)YR9-.

55. The dispersant of claim 54, wherein Y is NH.

56. The dispersant of claim 54, wherein Y is NR10 where R10 is a hydrocarbon chain containing from 1 to 20 carbon atoms.

57. The dispersant of claim 56, wherein R10 includes an ester, ether, or amide group.

58. The dispersant of any of claims 41 to 53, wherein R2 is a linear or branched, saturated or unsaturated hydrocarbon chain containing from 1 to 10 carbon atoms.

59. The dispersant of claim 58, wherein R2 is a hydrocarbon chain containing from 2 to 7 carbon atoms.

60. The dispersant of any of claims 1 to 53, wherein R2 is a hydrocarbon chain containing from 2 to 15 carbon atoms and includes an amide functional group having the formula, -N(R11)-(C=O)-, wherein R11 is H or a hydrocarbon chain containing from 1 to 4 carbon atoms.

61. The method of any one of claims 41 to 60, wherein the cyclic anhydride is selected from the group consisting of glutaric anhydride, 1,2-cyclohexanedicarboxylic anhydride, homophthalic anhydride, diglycol anhydride, succinic anhydride, polyisobutylenesuccinic anhydride, 2-phenylsuccinic anhydride, alkylsuccinic anhydride, or mixtures thereof.

62. The method of claim 61, wherein the cyclic anhydride comprises succinic anhydride.

63. The method of claim 61, wherein the cyclic anhydride comprises glutaric anhydride.

64. The method of any of claims 41 to 63, wherein the non-cyclic anhydride comprises propionic anhydride.

65. The method of any of claims 41 to 64, wherein the non-cyclic anhydride comprises acetic anhydride.

66. The method of any of claims 41 to 65, wherein the mixture of anhydrides and the multiamine species are reacted in a weight ratio of between 1:1 and 25:

1.

67. The method of any of claims 41 to 66, further comprising step (e): reacting the dispersing molecule with (a) an isocyanate, lactone, epoxy, anhydride, cyclic carbonate, (meth)acrylate by Michael addition reaction and / or a polymeric species having a group that reacts with a primary or secondary amine to form a salt or covalent bond, (b) an oxidizing species that could convert the amine group into a nitric oxide, (c) a salting agent, or (d) a tertiary amino group of said multiamine species or the dispersant containing the multiamine species is reacted with a quaternizing agent to form a quaternized amino group.