Full-time kinetics of self-assembly and disassembly in micellar solution via the generalized Smoluchowski equation with fusion and fission of surfactant aggregates

Micelle kinetics of photoswitchable surfactants: Self-assembly pathways and relaxation mechanisms

HYPOTHESIS

A key question in the kinetics of surfactant self-assembly is whether exchange of unimers or fusion/fission of entire micelles is the dominant pathway. In this study, an isomerizable surfactant is used to explore fundamental out-of-equilibrium kinetics and mechanisms for growth and dissolution of micelles.

EXPERIMENTS

The kinetics of cationic surfactant 4-butyl-4'-(3-trimethylammoniumpropoxy)-phenylazobenzene was studied using molecular dynamics simulations. The fusion and exchange processes were investigated using umbrella sampling. Equilibrium states were validated by comparison with small-angle X-ray scattering data. The photo-isomerization event was simulated by modifying the torsion potential of the photo-responsive group to emulate the trans-to-cis transition.

FINDINGS

Micelle growth is dominated by unimer exchange processes, whereas, depending on the conditions, dissolution can occur both through fission and unimer expulsion. Fusion barriers increase steeply with the aggregation number making this an unlikely pathway to equilibrium for micelles of sizes that fit with the experimental data. The barriers for unimer expulsion remain constant and are much lower for unimer insertion, making exchange more likely at high aggregation. When simulating photo-conversion events, both fission and a large degree of unimer expulsion can occur depending on the extent of the out-of-equilibrium stress that is put on the system.

Nonlinear dynamics in micellar surfactant solutions. I. Kinetics

This is the first of a pair of articles that present the theory of kinetic and transport phenomena in micelle-forming surfactant solutions in a form that facilitates discussion of large deviations from equilibrium. Our goal is to construct approximate but robust reduced models for both homogeneous and inhomogeneous systems as differential equations for unimer concentration c_{1}, micelle number concentration c_{m}, average micelle aggregation number q and (optionally) aggregation number variance σ_{m}^{2}. This first article discusses kinetics in homogeneous solutions. We focus particularly on developing models that can describe both weakly perturbed states and states in which c_{1} is suppressed significantly below the critical micelle concentration, which leads to rapid shrinkage and dissociation of any remaining micelles. This focus is motivated by the strong local suppression of c_{1} that is predicted to occur near interfaces during some adsorption processes that are considered in the second article. Toward this end, we develop a general nonlinear theory of fast stepwise processes for systems that may be subjected to large changes in q and c_{1}. This is combined with the existing nonlinear theory of slow association and dissociation processes to construct a general model for systems governed by stepwise reaction kinetics. We also consider situations in which the slow process of micelle creation and destruction instead occurs primarily by micelle fission and fusion, and analyze the dependencies of micelle lifetime and the slow relaxation time upon surfactant concentration in systems controlled by either association-dissociation or fission-fusion mechanisms.

Structural Insights into Self-Assembled Aerosol-OT Aggregates in Aqueous Media Using Atomistic Molecular Dynamics

In water, the surfactant dioctyl sulfosuccinate (Aerosol-OT or AOT) exhibits diverse aggregate structures, ranging from micelles to lamella. An atomic-level understanding, however, of the formation and structure of these aggregates is lacking. Herein, using atomistic molecular dynamics (MD) with microsecond-long simulations, self-assembly of AOT in water is studied for concentrations of 1, 7.2, and 20 wt % at 293 K and for 7.2 wt % at 353 K. Assembly proceeds through stepwise association and dissociation of single AOT molecules, and the fusion and fission of AOT clusters. At 293 K, AOT self-assembles into either (i) spherical micelles (1 wt %), (ii) biphasic systems consisting of rod-like and prolate spheroidal micelles (7.2 wt %), or (iii) bilayers (20 wt %). We hypothesize that the observed rod-like structure is a precursor to lamellar microdomains found experimentally in biphasic dispersions. Increasing temperature to 353 K at 7.2 wt % results in a system consisting of prolate micelles but no rod-like micelles. Simulated phase behavior agrees with previously published experimental observations. Individual aggregates formed during self-assembly are identified using graph theory. Structural metrics of these aggregates like the radius of gyration, shape anisotropy, and prolateness are presented. Trends in structural metrics quantitatively reflect how shapes and sizes of AOT aggregates vary with surfactant concentration and temperature. These simulations provide deeper insight into open questions in the scientific community and demonstrate a method to generate physics-based micelle structures that can be used to rationalize experimental observations.

Surfactant desorption and scission free energies for cylindrical and spherical micelles from umbrella-sampling molecular dynamics simulations

HYPOTHESIS

The free energies associated with adsorption/desorption of individual surfactants from micelles and the fusion/scission of long micelles can be used to estimate the rate constants for micellar kinetics as functions of surfactant and salt concentration.

EXPERIMENTS

We compute the escape free energies △G_esc of surfactant from micelles and the scission free energies △G_sciss of long micelles from coarse-grained molecular dynamics simulations coupled with umbrella sampling, for micelles of both sodium dodecylsulfate (SDS) in sodium chloride (NaCl) and cetyltrimethylammonium chloride (CTAC) in sodium salicylate (NaSal).

FINDINGS

For spherical micelles, △G_esc values have maxima at certain aggregation numbers, and at salt-to-surfactant molar concentration ratios R near unity, consistent with experiments. For cylindrical micelles, SDS/NaCl shows a minimum, and CTAC/NaSal a maximum in △G_esc, both at R ~ 0.7, while △G_sciss of CTAC micelles also peaks at around R ~ 0.7 and that of SDS micelles increases monotonically with R. We explain the non-monotonic dependence of escape and scission free energies on R by a combination of electrostatic screening and the decrease of micelle radius with increasing R. Transitions from predominantly spherical to cylindrical micelles, and between adsorption/desorption and fusion/scission kinetics with changing salt concentration can be inferred from the free energies for CTAC/NaSal.

The effect of a finite number of monomers available for aggregation at nucleation and micellization in a fixed volume

The expressions for the minimal work of aggregate formation as a function of the aggregation number and monomer concentration for a system with a limited number of monomers and a fixed volume have additional terms in comparison with a bulk metastable phase. The role of these terms has been analyzed in the case of droplet homogeneous nucleation and micellization in a nonionic surfactant solution. The appearance of the potential well and direct and reversal aggregation barriers in such systems and their dependence on the system parameters and monomer concentration have been considered and compared.

Mechanism of Micelle Birth and Death

In micellar surfactant solutions, changes in the total number of micelles are rare events that can occur by either of two mechanisms-by stepwise association and dissociation via insertion and expulsion of individual molecules or by fission and fusion of entire micelles. Molecular dynamics simulations are used here to estimate rates of these competing mechanisms in a simple model of block copolymer micelles in homopolymer solvent. This model exhibits a crossover with increasing degree of repulsion between solvent and micelle core components, from a regime dominated by association and dissociation to a regime dominated by fission and fusion.

Simulation of diblock copolymer surfactants. II. Micelle kinetics

Molecular dynamics (MD) simulations are used to measure dynamical properties of a simple bead-spring model of A-B diblock copolymer molecules, and to characterize rates and mechanisms of several dynamical processes. Dynamical properties are analyzed within the context of a kinetic population model that allows for both stepwise insertion and expulsion of individual free molecules and occasional fission and fusion of micelles. Kinetic coefficients for stepwise processes and micelle fission have been extracted from MD simulations of individual micelles. Insertion of a free surfactant molecule into a preexisting micelle is shown to be a completely diffusion-controlled process for the model studied here. Estimates are given for rates of rare events that create and destroy entire micelles by competing mechanisms involving stepwise association and dissociation or fission and fusion. Both mechanisms are shown to be relevant over the range of parameters studied here, with association and dissociation dominating in systems with more soluble surfactants and fission and fusion dominating in systems with less soluble surfactants.

Engineering approaches in siRNA delivery

siRNAs are very potent drug molecules, able to silence genes involved in pathologies development. siRNAs have virtually an unlimited therapeutic potential, particularly for the treatment of inflammatory diseases. However, their use in clinical practice is limited because of their unfavorable properties to interact and not to degrade in physiological environments. In particular they are large macromolecules, negatively charged, which undergo rapid degradation by plasmatic enzymes, are subject to fast renal clearance/hepatic sequestration, and can hardly cross cellular membranes. These aspects seriously impair siRNAs as therapeutics. As in all the other fields of science, siRNAs management can be advantaged by physical-mathematical descriptions (modeling) in order to clarify the involved phenomena from the preparative step of dosage systems to the description of drug-body interactions, which allows improving the design of delivery systems/processes/therapies. This review analyzes a few mathematical modeling approaches currently adopted to describe the siRNAs delivery, the main procedures in siRNAs vectors' production processes and siRNAs vectors' release from hydrogels, and the modeling of pharmacokinetics of siRNAs vectors. Furthermore, the use of physical models to study the siRNAs vectors' fate in blood stream and in the tissues is presented. The general view depicts a framework maybe not yet usable in therapeutics, but with promising possibilities for forthcoming applications.

Polylogarithmic equilibrium treatment of molecular aggregation and critical concentrations

A new modeling approach to molecular aggregation is proposed under the condition of generalized microreversibility.