|M.Sc Student||Reis Jochanan|
|Subject||Thermodynamic and Kinetic Models of Micelle Formation - A|
Self Assembly Case Study
|Department||Department of Chemical Engineering||Supervisor||Professor Emeritus Abraham Marmur|
|Full Thesis text|
The term "Self-Assembly" describes processes in which the components of a system spontaneously form well defined or desirable hierarchical structures. The term usually refers to systems where the interaction forces between the self-assembling components are physical, rather than chemical. In terms of size scales, self-assembly typically refers to processes in the nanometer scale. Such processes are prevalent in complex fluids, nano-technology, and biological systems. The understanding of self-assembly is therefore paramount to the progress of many scientific and engineering endeavors.
It is the aim of this research to obtain an initial understanding of the theory of self-assembly.
For this purpose, a well-studied and relatively simple self-assembly system was chosen for a theoretical study - dilute aqueous solutions of simple surfactant molecules. The surfactant molecules in this type of solution form spherical or near spherical aggregates due to the amphiphilic nature of the surfactant molecules, at concentration higher than a critical concentration which is called the Critical Micelle Concentration (CMC). Such micellar solutions are considered to easily and quickly achieve a state of thermodynamic equilibrium, and as such they are uniquely suitable for the study of thermodynamic and kinetic theory. Building on these qualities of micellar solutions, the target of the study was to construct a theoretical model for the self-assembly of micelles, which will provide a good basis of understanding for the further study of self-assembly systems.
The literature on the theory of micelle formation is reviewed.
A "Multiple Components" and a "Multiple Phases" thermodynamic formalism for micelle formation are derived from general basic thermodynamic theory. The derivation facilitates a substantial understanding of the assumptions and limitations of the "Multiple Chemical Equilibrium" and "Pseudo-Phase Separation" formalisms so prevalent in the literature. The multiple components formalism is shown to be principally generally applicable to self-assembly systems.
A model for the standard chemical potential of micelle formation is chosen from the literature, implemented, and applied to the multiple components formalism. The model predicts the CMC, the micelles shapes, and the micelles size distribution, as a function of the surfactant molecular properties (hydrocarbon chain length and head group dimensions) and the solution conditions (the temperature, the salt concentration, and the surfactant concentration).
A kinetic model of slow reversible coagulation is proposed as a method for calculating the rates of micelle formation, giving the rate of change of the concentrations of all of the micelle sizes in the system.
The van-der Waals and electrostatic inter-micellar interaction potentials are calculated using known approximate expressions for colloidal spheres, and the energy barrier to association of all possible micelle pairs is estimated from the inter-micellar interaction potential.
The energy barrier to micelle dissociation into all possible micelle pairs is estimated from the standard chemical potential of micelle formation.
Micelle formation is found to be dominated by the mechanism of step-wise association/dissociation, as is accepted in the literature to be the case for low concentration surfactant solutions.
The methods employed in this work for the thermodynamics and kinetics of micelle formation are theoretically applicable to other self-assembly systems.