Kinetics of Surfactant Micellization: a Free Energy Approach

We present a new theoretical approach to the kinetics of micelle formation in surfactant solutions, in which the various stages of aggregation are treated as constrained paths on a single free-energy landscape. Three stages of well-separated time scales are distinguished. The first and longest stage involves homogeneous nucleation of micelles, for which we derive the size of the critical nuclei, their concentration, and the nucleation rate. Subsequently, a much faster growth stage takes place, which is found to be diffusion-limited for surfactant concentrations slightly above the critical micellar concentration ({\it cmc}), and either diffusion-limited or kinetically limited for higher concentrations. The time evolution of the growth is derived for both cases. At the end of the growth stage the micelle size may be either larger or smaller than its equilibrium value, depending on concentration. A final stage of equilibration follows, during which the micelles relax to their equilibrium size through fission or fusion. Both cases of fixed surfactant concentration (closed system) and contact with a reservoir of surfactant monomers (open system) are addressed and found to exhibit very different kinetics. In particular, we find that micelle formation in an open system should be kinetically suppressed over macroscopic times and involve two stages of micelle nucleation rather than one.Comment: 24 pages, 14 figure

Thermodynamics of micellization of oppositely charged polymers

The complexation of oppositely charged colloidal objects is considered in this paper as a thermodynamic micellization process where each kind of object needs the others to micellize. This requirement gives rise to quantitatively different behaviors than the so-called mixed-micellization where each specie can micellize separately. A simple model of the grand potential for micelles is proposed to corroborate the predictions of this general approach.Comment: 7 pages, 2 figures. Accepted for publication in Europhysics Letter

Micellization of Sliding Polymer Surfactants

Following up a recent paper on grafted sliding polymer layers (Macromolecules 2005, 38, 1434-1441), we investigated the influence of the sliding degree of freedom on the self-assembly of sliding polymeric surfactants that can be obtained by complexation of polymers with cyclodextrins. In contrast to the micelles of quenched block copolymer surfactants, the free energy of micelles of sliding surfactants can have two minima: the first corresponding to small micelles with symmetric arm lengths, and the second corresponding to large micelles with asymmetric arm lengths. The relative sizes and concentrations of small and large micelles in the solution depend on the molecular parameters of the system. The appearance of small micelles drastically reduces the kinetic barrier signifying the fast formation of equilibrium micelles.Comment: Submitted to Macromolecule

Self-consistent field theory for obligatory coassembly

We present a first-order model for obligatory coassembly of block copolymers via an associative driving force in a nonselective solvent, making use of the classical self-consistent field (SCF) theory. The key idea is to use a generic associative driving force to bring two polymer blocks together into the core of the micelle and to employ one block of the copolymer(s) to provide a classical stopping mechanism for micelle formation. The driving force is generated by assuming a negative value for the relevant short-range Flory-Huggins interaction parameter. Hence, the model may be adopted to study micellization via H bonding, acceptor-donor interactions, and electrostatic interactions. Here, we limit ourselves to systems that resemble experimental ones where the mechanism of coassembly is electrostatic attraction leading to charge compensation. The resulting micelles are termed complex coacervate core micelles (CCCMs). We show that the predictions are qualitatively consistent with a wide variety of experimentally observed phenomena, even though the model does not yet account for the charges explicitly. For example, it successfully mimics the effect of salt on CCCMs. In the absence of salt CCCMs are far more stable than in excess salt, where the driving force for self-assembly is screened. The main limitations of the SCF model are related to the occurrence of soluble complexes, i.e., soluble, charged particles that coexist with the CCCM

Multi-scale coarse-graining of diblock copolymer self-assembly: from monomers to ordered micelles

Starting from a microscopic lattice model, we investigate clustering, micellization and micelle ordering in semi-dilute solutions of AB diblock copolymers in a selective solvent. To bridge the gap in length scales, from monomers to ordered micellar structures, we implement a two-step coarse graining strategy, whereby the AB copolymers are mapped onto ``ultrasoft'' dumbells with monomer-averaged effective interactions between the centres of mass of the blocks. Monte Carlo simulations of this coarse-grained model yield clear-cut evidence for self-assembly into micelles with a mean aggregation number n of roughly 100 beyond a critical concentration. At a slightly higher concentration the micelles spontaneously undergo a disorder-order transition to a cubic phase. We determine the effective potential between these micelles from first principles.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Lett

Voltammetric determination of the critical micellar concentration of surfactants by using a boron doped diamond anode

The electrochemistry of three surfactants has been studied by voltammetry at boron doped diamond (BDD) electrode in sodium sulphate solutions. The electrochemical behaviour of these surfactants is characterized by an oxidation signal (peak or wave) situated before the electrolyte oxidation. The anodic current is found to follow a linear relation with the concentration of the surfactants; the slope decreases abruptly above the critical micellar concentration (CMC) of the surfactants. The CMC values obtained for an anionic (sodium dodecylbenzenesulfonate, SDBS), a cationic (polyoxyethylene-23-dodecyl ether, BRIJ 35) and a neutral (1-(hexadecyl)trimethylammonium bromide, CTAB) surfactant are found in good agreement with those measured by the classical technique of surface tension. This voltammetric method has the advantage not to require the use of a redox active electrochemical probe

Ultrasonic and Densitometric Characterization of Hyaluronan and its Interaction with Surfactant

This disertation thesis is focused on the study of physico-chemical interactions of hyaluronan (with molecular weights from 10 to 1750 kDa) with cationic surfactants measured using uncommon technique named high resolution ultrasonic spectroscopy. Densitometer was also used for the study of these interactions, in measuring of density and ultrasonic velocity of hyaluronan with different molecular weight in dependence on elevated temperature (25 50 °C). The aim is the determination of critical micelle concentration (CMC) and critical aggregation concentration (CAC) of the suractants in the absence and in the presence of hyaluronan with various molecular weights. Interactions in this system are important for the design of the systems for the targeted delivery, especially for the drugs. The experiments were made in water and sodium chloride solution. The significant breakpoint in the ultrasonic velocity showed changes in the system hyaluronan-surfactant.Tato disertační práce se zaměřuje na fyzikálně-chemické interakce hyaluronanu (molekulové hmotností od 10 do 1750 kDa) s kationickými tenzidy. Pro zkoumání a měření vzájemného působení byla použita technika s názvem ultrazvuková spektroskopie s vysokým rozlišením (HR-US). Při zkoumání interakcí byl též použit denzitometr, a to při měření hustoty a uktrazvukové rychlosti hyaluronanu o různé molekulové hmotnosti v závislosti na vybrané teplotě (25-50 °C). Práce se zaměřuje se na studium kritické micelární (CMC) a agregační (CAC) koncentrace tenzidů v přítomnosti a nepřítomnosti hyaluronanu o různé molekulové hmotnosti. Interakce hyaluronanu s kationickými tenzidy jsou důležité pro systémy s cíleným transportem, zejména léčiv. Měření interakcí bylo prováděno ve vodě a v roztoku chloridu sodného. V získaných datech lze pozorovat významné zlomy v ultrazvukové rychlosti, které nám ukazují změny v systému hyaluronan-tenzid.