Dataset Information

Platonic Micelles: Monodisperse Micelles with Discrete Aggregation Numbers Corresponding to Regular Polyhedra.

ABSTRACT: The concept of micelles was first proposed in 1913 by McBain and has rationalized numerous experimental results of the self-aggregation of surfactants. It is generally agreed that the aggregation number (N_agg) for spherical micelles has no exact value and a certain distribution. However, our studies of calix[4]arene surfactants showed that they were monodisperse with a defined N_agg whose values are chosen from 6, 8, 12, 20, and 32. Interestingly, some of these numbers coincide with the face numbers of Platonic solids, thus we named them "Platonic micelles". The preferred N_agg values were explained in relation to the mathematical Tammes problem: how to obtain the best coverage of a sphere surface with multiple identical circles. The coverage ratio D(N) can be calculated and produces maxima at N?=?6, 12, 20, and 32, coinciding with the observed N_agg values. We presume that this "Platonic nature" may hold for any spherical micelles when N_agg is sufficiently small.

SUBMITTER: Fujii S

PROVIDER: S-EPMC5349551 | biostudies-literature | 2017 Mar

REPOSITORIES: biostudies-literature

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Platonic Micelles: Monodisperse Micelles with Discrete Aggregation Numbers Corresponding to Regular Polyhedra.

Fujii Shota S Yamada Shimpei S Matsumoto Sakiko S Kubo Genki G Yoshida Kenta K Tabata Eri E Miyake Rika R Sanada Yusuke Y Akiba Isamu I Okobira Tadashi T Yagi Naoto N Mylonas Efstratios E Ohta Noboru N Sekiguchi Hiroshi H Sakurai Kazuo K

Scientific reports 20170314

The concept of micelles was first proposed in 1913 by McBain and has rationalized numerous experimental results of the self-aggregation of surfactants. It is generally agreed that the aggregation number (N<sub>agg</sub>) for spherical micelles has no exact value and a certain distribution. However, our studies of calix[4]arene surfactants showed that they were monodisperse with a defined N<sub>agg</sub> whose values are chosen from 6, 8, 12, 20, and 32. Interestingly, some of these numbers coinc ...[more]

PMID: 28290532

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Project description:Chemical equilibria of multimerizations in systems with small numbers of particles exhibit a behavior seemingly at odds with that observed macroscopically. In this paper, we apply the recently proposed expression of equilibrium constant for binding, which includes cross-correlations in reactants' concentrations, to write an equilibrium constant for the formation of clusters larger than two (e.g., trimer, tetramer, and pentamer) as series of two-body reactions. Results obtained by molecular dynamics simulations demonstrate that the value of this expression is constant for all concentrations and system sizes, as well as at an onset of a phase transition to an aggregated state, where densities in the system change discontinuously. In contrast, the value of the commonly utilized expression of equilibrium constant, which ignores correlations, is not constant and its variations can reach few orders of magnitude. Considering different paths for the same multimer formation, with elementary reactions of any order, yields different expressions for the equilibrium constant, yet, with exactly the same value. This is also true for routes with essentially zero probability to occur. Existence of different expressions for the same equilibrium constant imposes equalities between averages of correlated, along with uncorrelated, concentrations of participating species. Moreover, a relation between an average particle number and relative fluctuations derived for two-body reactions is found to be obeyed here as well despite couplings to additional equilibrium reactions in the system. Analyses of transfer reactions, where association and dissociation events take place on both sides of the chemical equation, further indicate the necessity to include cross-correlations in the expression of the equilibrium constant. However, in this case, the magnitudes of discrepancies of the uncorrelated expression are smaller, likely because of partial cancellation of correlations, which exist on both the reactant and product sides.

Dataset Information

Platonic Micelles: Monodisperse Micelles with Discrete Aggregation Numbers Corresponding to Regular Polyhedra.

Publications

Platonic Micelles: Monodisperse Micelles with Discrete Aggregation Numbers Corresponding to Regular Polyhedra.

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