Surface modeling as a tool for constructing pseudo ternary diagrams


  • Juliana Verdan Silva Camilo
  • Anna Áurea Gomes Ferreira
  • Josane Assis Costa
  • Claudia Regina Elias Mansur
  • Fernando Gomes de Souza Junior Universidade Federal do Rio de Janeiro



Microemulsions, Phase Diagrams, Mathematical Modeling


Microemulsions have been developed and evaluated for application in various fields. For their development, ternary phase diagrams are initially constructed, obtained by investigating mixtures of the aqueous and oil phases and a surfactant, to determine the regions composed of liquid microemulsions. However, the construction of these diagrams requires many steps, so simplification of this method can be useful for the formulation and application of these microemulsified systems. Therefore, this article proposes a method to obtain these diagrams employing mathematical modeling, by testing systems composed of kerosene (as oil phase), a nonionic surfactant based on ethoxylated nonylphenol (NP80), and salt water. The study aimed to ascertain which models (linear, quadratic or special cubic) were able to describe the empirical observations, i.e., the ternary phase diagram containing 99 points. The results obtained showed that a quadratic model with a smaller sample (31 points) was able to represent these systems with 61% variability of the observed data and a confidence level higher than 99.9%. The smaller sample (31 points) was defined by means extrapolation lines, as described in the standard ISO11358, permitting identifying the liquid microemulsion regions of the system composed of kerosene, NP80 and salt water. This result is very promising since it permits determining the conditions of interest with significantly less experimental work, and commensurate reduction of the final cost of the experiments.

Author Biography

Fernando Gomes de Souza Junior, Universidade Federal do Rio de Janeiro

Associate (III) Prof. Fernando Gomes: Expertise focused in the use of renewable resources and nanocomposites in sensors, drug delivery and environmental recovery. Coordination of more than ten research projects with financial support from Brazilian government sponsoring agencies. Published 160 scientific articles plus 13 accepted for publication during 2021. Published 8 books. Among them,3 chemistry books in Portuguese and 3 books about Biopolymers in English. He has published more than two hundred papers in Conferences and Scientific meetings. Co-convener of the Sixth International Conference on Natural Polymers, Biopolymers and biomaterials: Applications from macro to nanoscale (, Chairman of the Fifth International Conference on Natural Polymers, Biopolymers and biomaterials: Applications from macro to nanoscale ( and Chaiman of the 1st Brazilian Conference on Design of Experiments and Data Analysis ( Supervisor of 128 undergraduate students; 29 M.Sc. students, 14 Ph.D. students and 6 Post Doc. Nowadays I am the supervisor of 11 undergraduate students; 7 M.Sc. students, 10 Ph.D. students and 3 Post Doc. Associate Editor of the MedCrave Online Journal (MOJ) Polymer Science (ISSN: 2574-9773) since 2017. Editor of the Academic Journal of Polymer Science (ISSN: 2641-8282), since 2018. Member of the Editorial Board of Composite Interfaces (ISSN: 0927-6440), since 2021. Member of the editorial board of Current Applied Polymer Science (ISSN 2452-2716) since 2016 and Editor-in-Chief of Current Applied Polymer Science (ISSN 2452-2716) since 2020. Professor Gomes has founded the Brazilian Journal of Experimental Design, Data Analysis and Inferential Statistics in 2021, acting as its 1st Editor-in-Chief. Awardedtwice as Young Scientist of Rio de Janeiro State (FAPERJ 2011 and 2014), Chair Professorship on Nanoscience and Nanotechnology - Mahatma Gandhi University – India (2018), member of Post Graduate Program in Science and Technology of Polymers of the Macromolecules Institute / Federal University of Rio de Janeiro (UFRJ) since 2008, member of Post Graduate Program in Civil Engineering (COPPE/UFRJ) between 2015-2019 and member of Post Graduate Program in Nanotechnology (COPPE/UFRJ) since 2019.