In this study, the interaction energy between Triton X-114 surfactant + methylene blue or water and methylene blue + water was investigated using Hartree-Fock (HF) theory with 6-31G* basis set. The results of structures and interaction energies show that these complexes have good physical and chemical interactions at atom and molecular levels. However, the Triton X-114 surfactant + methylene blue complex shows stronger molecular interaction compared to other complexes systems. The order of the interaction energy is 4303.472023 (Triton X-114 surfactant + water) > -1222.962 (methylene blue + water) > -3573.28 (Triton X-114 surfactant + methylene blue) kJ·mole−1. Subsequently, the cloud point extraction was carried out for 15 ppm of methylene blue in a mixture at 313.15 and 323.15 K over the surfactant concentration range from 0.01 M to 0.1 M. From the measured data, the excess molar volume was calculated for both phases. The results show a positive deviation in the dilute phase and a negative deviation in the surfactant rich phase. It is confirmed that the interaction between Triton X-114 and methylene blue is stronger than other complex systems due to the presence of chemical and structural orientation. The concentration of dyes and surfactant in the feed mixture and temperature effect in both phases has been studied. In addition, the thermodynamics feasibility and efficiency of the process have also been investigated.

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