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Markov chain model for the critical micelle concentration of surfactant mixtures

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Abstract

An extension of the Markov chain model (MC) for micellization is proposed, which allows the distribution of the surfactants between the monomer solution and the micelles in a mixed surfactant system to be predicted. The dependence of the critical micelle concentration (cmc) on the composition of the solution is investigated. The equilibrium thermodynamic relation between cmc and micelle composition is discussed. The case of ternary mixtures is analyzed, and theoretical triangular diagram is constructed according to MC. Available experimental data for binary and ternary mixtures agree well with the new MC theory. The dependence of MC parameters on the structure of the surfactants is discussed. Comparison of MC with the simple mixture (“regular solution”) model is presented. The parameters of the MC theory are related to the interaction parameter β SM of the simple mixture model.

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Acknowledgments

This work was funded by the Bulgarian National Science Fund Grants DDVU 02/12 and DDVU 02/43. The fruitful discussions of the work with Prof. Emil Manev are gratefully acknowledged. R. Slavchov is grateful to FP7 project BeyondEverest.

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Authors and Affiliations

  1. Department of Physical Chemistry, Sofia University, 1 J. Bourchier Blvd., 1164, Sofia, Bulgaria

    Radomir I. Slavchov

  2. Laboratory of Water-Soluble Polymers, Polyelectrolytes and Biopolymers, Sofia University, Sofia, Bulgaria

    George S. Georgiev

Authors
  1. Radomir I. Slavchov
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  2. George S. Georgiev
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Correspondence to Radomir I. Slavchov.

Electronic supplementary material

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ESM 1

The following supplementary files are available in the online version of this article: (1) Regular vs. simple mixture. (2) Regarding the possibility that the strict Markov chain model result for the micelle composition is valid at equilibrium. (3) A mixture of sodium alkylbenzenesulfonates. (4) Recipe for constructing the triangular diagram for cmc in ternary surfactant mixtures. (5) List of symbols and abbreviations. (DOCX 241 kb)

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Slavchov, R.I., Georgiev, G.S. Markov chain model for the critical micelle concentration of surfactant mixtures. Colloid Polym Sci 292, 2927–2937 (2014). https://doi.org/10.1007/s00396-014-3337-2

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  • DOI: https://doi.org/10.1007/s00396-014-3337-2

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