Gum Arabic underwent enzymatic modification with curcumin oxidation products, prompting self-assembly in water at lower concentrations than native gum Arabic, which was fully soluble. The resulting particles displayed a narrow size distribution, suggestive of a micellization mechanism akin to Critical Micellization Concentration (CMC) in surfactants or Critical Aggregation Concentration (CAC) in polymers. Accurately determining CAC is vital for utilizing polymers in molecule encapsulation, but precise measurement is challenging, requiring multiple techniques. Initially, CAC was probed via turbidity measurements, dynamic light scattering (DLS), and isothermal calorimetric titration (ITC), yielding a range of 0.0015 to 0.01 %. Micro-scale thermophoresis (MST) was then employed for the first time to define CAC more precisely, facilitated by the intrinsic fluorescence of modified gum Arabic. Using MST, CAC was pinpointed at 0.001 % (w/v), a novel approach. Furthermore, MST revealed a low EC50 value of 0.007 % (w/t) for self-assembly, signifying uniformity among GAC sub-units and assembly stability upon dilution.