Described herein is a poly-lysine derivative obtained by a process including heating an aqueous lysine solution to boiling, increasing a temperature of the aqueous lysine solution to a reaction temperature in the range of about 105° C. to about 180° C., and keeping the reaction temperature in the range of about 105° C. to about 180° C. until (i) a melt viscosity of the reaction mixture is in the range of about 350 mPa*s to about 6,500 mPa*s, and (ii) an amine number in the range of about 100 mg KOH/g to about 500 mg KOH/g is achieved. The process also includes adding alkyl-carboxylic acid or alkenyl-carboxylic acid in amounts of 2.5 mol % to 10 mol %, and increasing or keeping the reaction temperature in the range of about 105° C. to about 180° C. until number of free alkyl-carboxylic acid or alkenyl-carboxylic acid is ≤9% by weight.