1070-3632/02/7204-0607 $27.00 2002 MAIK Nauka/Interperiodica Russian Journal of General Chemistry, Vol. 72, No. 4, 2002, pp. 607 621. Translated from Zhurnal Obshchei Khimii, Vol. 72, No. 4, 2002, pp. 651 666. Original Russian Text Copyright 2002 by Rusanov, Grinin, Kuni, Shchekin. Nanostructural Models of Micelles and Primicellar Aggregates A. I. Rusanov, A. P. Grinin, F. M. Kuni, and A. K. Shchekin St. Petersburg State University, St. Petersburg, Russia Received October 15, 2001 Abstract For the case of direct spherical micelles, two nanostructural models of molecular aggregates have been discussed: the classical drop model implying flexibility of hydrocarbon chains of molecules and their full immersion into the hydrocarbon core of an aggregate, and a quasi-drop model allowing partial outcropping of the chains in the strainless state from the core. For the sake of simplicity, a solution is assumed to contain only a single surfactant whose molecules possess only one, unbranched hydrocarbon radical. Within the frames of the models, the behavior of the chemical potential of surfactant molecules in a primicellar and micellar molecular aggregate has been analyzed, as well as the work of formation of the molecular aggregate as a function of the aggregation number and the solution concentration. INTRODUCTION The rigorous theory of micellar systems, as well as the theory of molecular aggregative systems at all, is formulated on the basement of the mass action law. The mass action law constant is known to include the Gibbs energy of a single micelle, so that the calcula- tion of this quantity proves to be necessary in the theoretical description of micelles. The general theoretical formalism for the description of a single micelle has been already developed [1, 2], but models are needed for particular estimations. The data on the structure and properties of quite ready stable micelles are accessible from experiment, but the knowledge of the properties of primicellar (molecular or ionic) aggregates is also needed for the creation of the ki- netic theory of micellization. What is especially important for the kinetic theory is the behavior of critical (unstable) micelle embryos whose properties are practically unknown up to the present time. The use of as-plausible-as-possible speculative models of embryos remains the only approach to carrying out necessary calculations. In this presentation, we will confine ourselves with the case of direct spherical micelles. We will consider two nanostructural models for primicellar and micellar molecular aggregates: the classical drop model implying flexibility of hydrocarbon chains of molecules and their full immersion into the hydro- carbon core of an aggregate, and a quasi-drop model allowing partial outcropping of the chains in the strainless state from the core. For the sake of sim- plicity, a solution is assumed to contain only a single surfactant whose molecules possess only one hydro- carbon radical, the hydrocarbon chain having no branches. 1. DROP MODEL OF MOLECULAR AGGREGATE 1.1. Parameters of Hydrocarbon Chain We will use for calculations the following formulas for the length l C and the volume v C of a hydrocarbon chain including n C carbon atoms [3] l C = (1.5 + 1.265n C ) , (1.1.1) v C = (27.4 + 26.9n C ) 3 . (1.1.2) From here the length of a single segment in the middle of the hydrocarbon chain is l 1 = 1.265 and its volume is v 1 = 26.9 3 . Then the cross-section area in the middle of the hydrocarbon chain is a 1 = v 1 /l 1 = 21.265 2 (1.1.3) (if the cross-section is round, its diameter is 5.203 ). On the other side, the average cross-section area for the whole chain a C is a C = v C /l C . (1.1.4) Accounting for (1.1.1) and (1.1.2), it is easy to see that always a C < a 1 (for example, we have a C = 19.638 2 at n C = 1 and a C = 20.995 2 at n C = 12). This gives evidence for the existence of a coning at the chain end. If one simulates the middle part of the chain with a round cylinder, its end can be represented as a