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Kuni, F. M.; Grinin, A. P.; Щекин, А. К.; Русанов, А. И.

doi:10.1023/a:1016681807561

Cited by 30 publications

(57 citation statements)

References 3 publications

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“…The fact that, with the account of cylindrical micelles, the aggregation work no longer increases monotonously to infinity behind the first potential well, as was suggested in [9], has no importance for fluxes J' (1) and J'' (1) . Using formulas (5.8) and (5.10) of [9], we then obtain [provided that constraints (1.3) and (1.4) are fulfilled] the analytical expressions for quasi-stationary direct and reverse fluxes of molecular aggregates over the first potential barrier of the aggregation work…”

Section: Direct and Reverse Fluxes Of Aggregates Over The First And Smentioning

confidence: 87%

“…(1.6) and (1.7) for total concentrations c M and g of spherical and cylindrical micelles and the total kinetic equation of step-bystep aggregation follow from the definition of J' (1) , J'' (1) , J' (2) , and J'' (2) as quasi-stationary direct and reverse fluxes [9] corresponding to quasi-stationary solutions of the total kinetic equation of aggregation in the vicinity of the first and second potential barriers of the aggregation work. The fact that, with the account of cylindrical micelles, the aggregation work no longer increases monotonously to infinity behind the first potential well, as was suggested in [9], has no importance for fluxes J' (1) and J'' (1) . Using formulas (5.8) and (5.10) of [9], we then obtain [provided that constraints (1.3) and (1.4) are fulfilled] the analytical expressions for quasi-stationary direct and reverse fluxes of molecular aggregates over the first potential barrier of the aggregation work…”

Section: Direct and Reverse Fluxes Of Aggregates Over The First And Smentioning

confidence: 99%

“…Relations (1.9) and (1.8) differ by that the disintegration is prevented by the barrier of the aggregation work with a height of -, and the intensity of disintegration is proportional to concentration c M /π 1/2 ∆ of molecular aggregates with n = . Using the same speculations as in [9], we obtain [with the fulfillment of constraints (1.4) and (1.5)] the analytical expressions for the quasi-stationary direct and reverse fluxes of molecular aggregates over the second potential barrier of the aggregation work …”

Section: Direct and Reverse Fluxes Of Aggregates Over The First And Smentioning

confidence: 99%

“…Thus, one cannot pass in this theory to the situation where cylindrical micelles do not make overwhelming contribution to the total amount of surfactant in solution or, moreover, they are generally absent in a solution. The kinetic theory for the case of the absence of cylindrical micelles was developed earlier in [9,[11][12][13][14].…”

Section: System Of Linearized Relaxation Equations For the Total Concmentioning

confidence: 99%

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System of relaxation equations for materially isolated surfactant solution with spherical and cylindrical micelles

et al. 2005

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Analytical expressions for the direct and reverse fluxes of molecular aggregates over the first and second potential barriers of the aggregation work in the presence of spherical and cylindrical micelles in nonionic surfactant solution were derived. Expressions for the sum (entering into kinetic equations of micellization) of direct and reverse fluxes of molecular aggregates over the first and second potential barriers of the aggregation work in the vicinity of the final equilibrium state of materially isolated surfactant solution were linearized. In the experimentally important range of the values of overall surfactant concentration in solution where the predominant contribution to the total surfactant amount is introduced by cylindrical micelles, we derived a closed system of two linearized relaxation equations determining the buildup (with time) of experimentally observed total concentrations of spherical and cylindrical micelles in the vicinity of the final equilibrium state of materially isolated surfactant solution. The case of the solutions of such surfactants, for which the spherical shape of a micelle appeared to be unrealizable due to the structure and packing conditions of molecules, was considered separately.

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Section: Direct and Reverse Fluxes Of Aggregates Over The First And Smentioning

confidence: 87%

Section: Direct and Reverse Fluxes Of Aggregates Over The First And Smentioning

confidence: 99%

Section: Direct and Reverse Fluxes Of Aggregates Over The First And Smentioning

confidence: 99%

Section: System Of Linearized Relaxation Equations For the Total Concmentioning

confidence: 99%

See 2 more Smart Citations

System of relaxation equations for materially isolated surfactant solution with spherical and cylindrical micelles

et al. 2005

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“…Earlier [1], we developed the theory of nonionic surfactant solutions containing spherical and cylindrical micelles above the second critical micellization concentration (CMC2) in the experimentally significant region of overall surfactant concentrations where the overwhelming part of the total amount of surfactant in solution was accumulated in cylindrical micelles. Although the equilibrium states of surfactant solution were mainly considered in [1], we performed the linearization of the balance equation of the surfactant amount in the vicinity of the final equilibrium state of materially isolated solution where the state of solution is not at equilibrium.…”

Section: Introductionmentioning

confidence: 99%

Kinetic description of the relaxation of surfactant solutions containing spherical and cylindrical micelles

et al. 2005

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Monotonically decaying relaxation of a materially isolated nonionic surfactant solution containing spherical and cylindrical micelles at the arbitrary heights of the first and second potential barriers of aggregation work is kinetically substantiated. The realistic situation, where the height of second potential barrier is at least slightly higher (by the relative value) than that of the first barrier, is studied. Analytical expressions for two relaxation times of materially isolated surfactant solution are calculated. The shortest of these times corresponds to the relatively fast establishment of the mutual quasi-equilibrium of spherical and cylindrical micelles, beginning with relatively small cylindrical micelles. The longest of relaxation times corresponds to the relatively slow establishment of the total equilibrium of surfactant solution. It is shown that this time (the only significant for the establishment of the final equilibrium of materially isolated surfactant solution) is determined by the height of the first potential barrier of aggregation work and is by no means dependent on the height of the second potential barrier about which not much is known. Variations (with time) of the total concentrations of spherical and cylindrical micelles, surfactant monomer concentration, and the total amount of the substance in cylindrical micelles in the approach of solution to the final equilibrium state are described analytically. It is shown that theoretically admitted small relative deviations of the concentrations of spherical and cylindrical micelles from their values in the final equilibrium state are fully measurable in experiment. Calculated relaxation time of surfactant solution can also be measured experimentally together with the aforementioned values. It is elucidated that this time is approximately proportional to the overall solution concentration, if the second critical micellization concentration (CMC2) by the order of magnitude exceeds the first critical micellization concentration (CMC1), and is virtually independent of the overall solution concentration, if the CMC2 exceeds the CMC1 by two orders of magnitude. The characteristic time of the establishment of quasi-equilibrium distribution of cylindrical micelles throughout the region of their sizes is estimated, thus allowing us to establish the lower limit of the height of the first barrier of aggregation work.

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Kinetic description of the relaxation of surfactant solutions in the absence of activation barrier between spherical and cylindrical micelles

et al. 2005

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The realistic situation, where there is no potential barrier of aggregation work between the spherical and cylindrical micelles, is analyzed within the framework of the kinetic description of the relaxation of nonionic surfactant solution containing spherical and cylindrical micelles. The variations in the sum of the total concentrations of spherical and cylindrical micelles caused by the total flux of molecular aggregates over the potential barrier of aggregation work between the monomers and spherical micelles is taken into account; it is also accounted for that, in the absence of the potential barrier of aggregation work between the spherical and cylindrical micelles, they are present in the mutual quasi-equilibrium. The closed linearized relaxation equation determining the variations (with time) in the total concentrations of spherical and cylindrical micelles in a materially isolated surfactant solution is derived and solved. The variations (with time) of the total concentrations of spherical and cylindrical micelles, the concentration of surfactant monomers, as well as the total amount of surfactant in cylindrical micelles, in the process of approach of a materially isolated micellar solution to the final equilibrium state are described analytically. It is disclosed that, at the mutual quasi-equilibrium of spherical and cylindrical micelles, the opposite-sign deviations of the total amount of substance in cylindrical micelles and the total amount of cylindrical micelles from their values in the final equilibrium state of a materially isolated solution is attributed to the relatively large cylindrical micelles. The agreement between the results obtained and analogous results of the description of micellar relaxation in the presence of the potential barrier of aggregation work between spherical and cylindrical micelles whose relative height is at least slightly lower than that between monomers and spherical micelles is demonstrated. Comparison is performed for the cases of the absence of either spherical or cylindrical micelles. Analytical expressions, which are accessible for experimental verification, for the ratios of relaxation times of surfactant solutions containing spherical and cylindrical micelles to those of surfactant solutions containing either spherical or cylindrical micelles alone are derived.

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Cited by 30 publications

References 3 publications

System of relaxation equations for materially isolated surfactant solution with spherical and cylindrical micelles

System of relaxation equations for materially isolated surfactant solution with spherical and cylindrical micelles

Kinetic description of the relaxation of surfactant solutions containing spherical and cylindrical micelles

Kinetic description of the relaxation of surfactant solutions in the absence of activation barrier between spherical and cylindrical micelles

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