### Abstract

To improve and expand kinetic analysis of fast relaxation (via attachments and detachments of surfactant molecules) in an ensemble of spherical micelles in surfactant solutions, a general scheme for reducing the linearized difference Becker-Doring equations to the differential equation of an arbitrary order with respect to the aggregation number is proposed. A perturbation theory is formulated for any model of spherical micelles, where the main approximation corresponds to the kinetic Aniansson equation for the case of a symmetrical potential well of the aggregation work and the perturbation operator is written in the Hermitian form. The latter allows one to use standard perturbation techniques to find the fast relaxation times with the help of extended differential kinetic equation. The calculations were carried out in the second order of the perturbation theory, and the longest fast relaxation times were found as a function of the surfactant concentration for the droplet and the quasi-droplet models of direct spherical micelles and the star model of diblock polymeric spherical micelles. In the case of the droplet model, inclusion of corrections gives the concentration dependence of the longest fast relaxation time that virtually coincides with results of numerical solution of the system of linearized Becker-Doring difference equations. For the quasi-droplet model, the fast relaxation time found in the main approximation considerably deviate from the numerical result (up to 50%). Addition of corrections allows us to reduce these deviations to a considerably smaller value (to 10%). For the star micelle model, a fine agreement between the analytical and numerical solutions is obtained. (C) 2019 Elsevier B.V. All rights reserved.

Original language | English |
---|---|

Pages (from-to) | 725-734 |

Number of pages | 10 |

Journal | Journal of Molecular Liquids |

Volume | 284 |

DOIs | |

Publication status | Published - 15 Jun 2019 |

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### Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics
- Materials Chemistry
- Atomic and Molecular Physics, and Optics
- Spectroscopy
- Physical and Theoretical Chemistry

### Cite this

*Journal of Molecular Liquids*,

*284*, 725-734. https://doi.org/10.1016/j.molliq.2019.03.160

}

*Journal of Molecular Liquids*, vol. 284, pp. 725-734. https://doi.org/10.1016/j.molliq.2019.03.160

**Analytical description of molecular mechanism of fast relaxation of spherical micelles with the extended Becker-Doring differential equation.** / Adzhemyan, Loran Ts; Eroshkin, Yury A.; Babintsev, Ilya A.; Shchekin, Alexander K.

Research output

TY - JOUR

T1 - Analytical description of molecular mechanism of fast relaxation of spherical micelles with the extended Becker-Doring differential equation

AU - Adzhemyan, Loran Ts

AU - Eroshkin, Yury A.

AU - Babintsev, Ilya A.

AU - Shchekin, Alexander K.

PY - 2019/6/15

Y1 - 2019/6/15

N2 - To improve and expand kinetic analysis of fast relaxation (via attachments and detachments of surfactant molecules) in an ensemble of spherical micelles in surfactant solutions, a general scheme for reducing the linearized difference Becker-Doring equations to the differential equation of an arbitrary order with respect to the aggregation number is proposed. A perturbation theory is formulated for any model of spherical micelles, where the main approximation corresponds to the kinetic Aniansson equation for the case of a symmetrical potential well of the aggregation work and the perturbation operator is written in the Hermitian form. The latter allows one to use standard perturbation techniques to find the fast relaxation times with the help of extended differential kinetic equation. The calculations were carried out in the second order of the perturbation theory, and the longest fast relaxation times were found as a function of the surfactant concentration for the droplet and the quasi-droplet models of direct spherical micelles and the star model of diblock polymeric spherical micelles. In the case of the droplet model, inclusion of corrections gives the concentration dependence of the longest fast relaxation time that virtually coincides with results of numerical solution of the system of linearized Becker-Doring difference equations. For the quasi-droplet model, the fast relaxation time found in the main approximation considerably deviate from the numerical result (up to 50%). Addition of corrections allows us to reduce these deviations to a considerably smaller value (to 10%). For the star micelle model, a fine agreement between the analytical and numerical solutions is obtained. (C) 2019 Elsevier B.V. All rights reserved.

AB - To improve and expand kinetic analysis of fast relaxation (via attachments and detachments of surfactant molecules) in an ensemble of spherical micelles in surfactant solutions, a general scheme for reducing the linearized difference Becker-Doring equations to the differential equation of an arbitrary order with respect to the aggregation number is proposed. A perturbation theory is formulated for any model of spherical micelles, where the main approximation corresponds to the kinetic Aniansson equation for the case of a symmetrical potential well of the aggregation work and the perturbation operator is written in the Hermitian form. The latter allows one to use standard perturbation techniques to find the fast relaxation times with the help of extended differential kinetic equation. The calculations were carried out in the second order of the perturbation theory, and the longest fast relaxation times were found as a function of the surfactant concentration for the droplet and the quasi-droplet models of direct spherical micelles and the star model of diblock polymeric spherical micelles. In the case of the droplet model, inclusion of corrections gives the concentration dependence of the longest fast relaxation time that virtually coincides with results of numerical solution of the system of linearized Becker-Doring difference equations. For the quasi-droplet model, the fast relaxation time found in the main approximation considerably deviate from the numerical result (up to 50%). Addition of corrections allows us to reduce these deviations to a considerably smaller value (to 10%). For the star micelle model, a fine agreement between the analytical and numerical solutions is obtained. (C) 2019 Elsevier B.V. All rights reserved.

KW - Aggregation

KW - Fast relaxation

KW - Kinetics

KW - Micelles

KW - Self-assembly and disassembly

KW - The Becker–Döring equation

KW - The Becker-Doring equation

KW - THERMODYNAMIC CHARACTERISTICS

KW - MICELLIZATION

KW - MODELS

KW - KINETICS

KW - CYLINDRICAL MICELLES

KW - EQUILIBRIUM

KW - AGGREGATION

KW - DROPLET

UR - http://www.scopus.com/inward/record.url?scp=85064314983&partnerID=8YFLogxK

U2 - 10.1016/j.molliq.2019.03.160

DO - 10.1016/j.molliq.2019.03.160

M3 - Article

AN - SCOPUS:85064314983

VL - 284

SP - 725

EP - 734

JO - Journal of Molecular Liquids

JF - Journal of Molecular Liquids

SN - 0167-7322

ER -