The intramicellar fluorescence quenching in cylindrical micelles. II

Diffusion-Controlled Reactions in Micellar Systems

Reaction kinetics in micellar solutions are studied theoretically with an emphasis on diffusioncontrolled luminescence quenching. Different spatial arrangements of reactants within individual micelles are analyzed and a general method for treating diffusion-controlled reactions in a finite volume employing an effective potential approximation is developed. Several models are considered for the exchange of reactants between micelles including migration mediated by the bulk phase and successive multiparticle hopping through transient channels connecting micelles during their sticky collisions. These results are combined in a general stochastic theory of reaction kinetics in micellar solutions with exchange. The theory is further extended to reactions in clusters of micelles using a continuous time random walk approach. Once the principal features of micellar kinetics are understood, one can extract important structural and dynamic information on the aggregates and their guest molecules by analyzing suitably designed experiments.

Compartmental analysis in photophysics: Kinetics and identifiability of models for quenching of fluorescent probes in micelles

The parameters describing the kinetics of excited-state processes can possibly be recovered by analysis of the fluorescence decay surface measured as a function of the experimental variables. The identifiability analysis of a photophysical model assuming errorless time-resolved fluorescence data can verify whether the model parameters can be determined. In this work, we have used the methods of similarity transformation and Taylor series to investigate the identifiability of two models utilized to describe the time-resolved fluorescence quenching of stationary probes in micelles. The first model assumes that exchange of the quencher between micelles is much slower than the fluorescence decay of the unquenched probe (the 'immobile' quencher model). The second model assumes that quenchers exchange between the aqueous and micellar phases (the 'mobile' quencher model). For the 'immobile' quencher model, the rate constants for deactivation (k(0)) and quenching (k(q)) of the excited probe are uniquely identified together with the average number of quencher molecules per micelle. For the 'mobile' quencher model, the rate constants k(0) and k(q) are uniquely identified, as are the rate constants for entry (k(+)) and exit (k(-)) of one quencher molecule into and from a micelle, and the micellar aggregation number. The concomitant rate equations describing the time-resolved fluorescence are solved using z-transforms.

Identifiability of Models for Fluorescence Quenching in Aqueous Micellar Systems

The first deterministic identifiability analysis is presented for four commonly used kinetic models of fluorescence quenching of an excited probe in aqueous micelles: A) model with immobile quenchers, B) model with mobile quenchers, C) an extension of model B in which exchange of quenchers both via the aqueous phase and during micelle collisions is taken into account, and D) model with probe migration. It is shown that these specific models for fluorescence decay of an excited probe solubilized in a micelle and quenched by molecules or ions that are Poisson-distributed over the micelles, resulting in the generalized four-parameter equation f(t)=A(1) exp{-A(2)t-A(3)[1-A(4)t]}, are uniquely identifiable in terms of four descriptive A parameters. Moreover, each model also can be uniquely identified in terms of the underlying rate constants and micellar concentration or mean micellar aggregation number. This means that these parameters can be extracted in a unique way from time-resolved fluorescence quenching experiments on a probe in micelles. For each model the recommended analysis approach is given.

Mixed Micellization of Dimeric (Gemini) Surfactants and Conventional Surfactants

The aqueous solutions of mixtures of various conventional surfactants and dimeric anionic and cationic surfactants have been investigated by electrical conductivity, spectrofluorometry, and time-resolved fluorescence quenching to determine the critical micelle concentrations and the micelle aggregation numbers in these mixtures. The following systems have been investigated: 12-2-12/DTAB, 12-2-12/C(12)E(6), 12-2-12/C(12)E(8), 12-3-12/C(12)E(8), Dim3/C(12)E(8), and Dim4/C(12)E(8) (12-2-12 and 12-3-12=dimethylene-1,2- and trimethylene-1,3-bis(dodecyldimethylammonium bromide), respectively; C(12)E(6) and C(12)E(8)=hexa- and octaethyleneglycol monododecylethers, respectively; Dim3 and Dim4=anionic dimeric surfactants of the disodium sulfonate type, Scheme 1; DTAB=dodecyltrimethylammonium bromide). For the sake of comparison the conventional surfactant mixtures DTAB/C(12)E(8) and SDS/C(12)E(8) (SDS=sodium dodecylsulfate) have also been investigated (reference systems). Synergism in micelle formation (presence of a minimum in the cmc vs composition plot) has been observed for the Dim4/C(12)E(8) mixture but not for other dimeric surfactant/nonionic surfactant mixtures investigated. The aggregation numbers of the mixed reference systems DTAB/C(12)E(8) and SDS/C(12)E(8) vary monotonously with composition from the value of the aggregation number of the pure C(12)E(8) to that of the pure ionic component. In contrast, the aggregation number of the dimeric surfactant/C(12)E(8) mixtures goes through a minimum at a low value of the dimeric surfactant mole fraction. This minimum does not appear to be correlated to the existence of synergism in micelle formation. The initial decrease of the aggregation number of the nonionic surfactant upon addition of ionic surfactant, up to a mole fraction of ionic surfactant of about 0.2 (in equivalent per total equivalent), depends little on the nature the surfactant, whether conventional or dimeric. The results also show that the microviscosity of the systems containing dimeric surfactants is larger than that of the reference systems. Copyright 2001 Academic Press.

Kinetics of diffusion-assisted reactions in microheterogeneous systems

This review is focused on the basic theory of diffusion-assisted reactions in microheterogeneous systems, from porous solids to self-organized colloids and biomolecules. Rich kinetic behaviors observed experimentally are explained in a unified fashion using simple concepts of competing distance and time scales of the reaction and the embedding structure. We mainly consider pseudo-first-order reactions, such as luminescence quenching, described by the Smoluchowski type of equation for the reactant pair distribution function with a sink term defined by the reaction mechanism. Microheterogeneity can affect the microscopic rate constant. It also enters the evolution equation through various spatial constraints leading to complicated boundary conditions and, possibly, to the reduction of dimensionality of the diffusion space. The reaction coordinate and diffusive motion along this coordinate are understood in a general way, depending on the problem at hand. Thus, the evolution operator can describe translational and rotational diffusion of molecules in a usual sense, it can be a discrete random walk operator when dealing with hopping of adsorbates in solids, or it can correspond to conformational fluctuations in proteins. Mathematical formulation is universal but physical consequences can be different. Understanding the principal features of reaction kinetics in microheterogeneous systems enables one to extract important structural and dynamical information about the host environments by analyzing suitably designed experiments, it helps building effective strategies for computer simulations, and ultimately opens possibilities for designing systems with controllable reactivity properties.