Refining of nonionic surfactant micellization theory based on the law of mass action

Two approaches to determining critical micelle concentration (CMC) are assessed, i.e., from the inflection point in the curve for the concentration dependence of the degree of micellization and as K^1/(1–n), where K is the constant of the law of mass action and n is the aggregation number. The latter approach makes the theory simpler, while the former explicitly expresses the critical degree of micellization via the aggregation number. The concentrations of monomers and micelles are analyzed as functions of the overall concentration of a surfactant in a micellar solution. These functions look much simpler in the graphical form as compared with their complex exact analytical representation. This has resulted in derivation of simple analytical approximations for these functions, with these approximations being useful for calculations. The concentration dependence of the surfactant diffusion coefficient has been considered based on these approximations. It turned out that this dependence not only provides the known method for determining the diffusion coefficient of micelles, but also gives the possibility in principle to determine the aggregation number from the slope of the dependence of the diffusion coefficient on the inverse concentration (counted from the CMC in the CMC units). This new method for determining the aggregation number has been tested using the literature data on the diffusion coefficient of penta(ethylene glycol)-1-hexyl ether in an aqueous solution.     

Micellization theory based on the law of mass action with a variable aggregation number

Variations in the aggregation number of spherical micelles are considered within the micellization theory based on the law of mass action. The mechanism of micellization in a polydisperse aggregated system and the transition to a monodisperse model are explained. A relation between aggregation numbers and chemical potentials of molecules or ions is determined using the curve for equilibrium distribution of aggregates over the aggregation numbers. It is shown that the aggregation numbers of nonionic surfactants unambiguously grow with concentration; however, such a conclusion cannot be drawn for ionic surfactants. For the explicit concentration dependence of the aggregation number, two versions of an analog of the Langmuir equation are proposed to be used, i.e., versions comprising the total surfactant concentration and the concentration of monomers. Comparison with experimental data is carried out by the example of conventional surfactants, namely, sodium dodecyl sulfate and hexadecyltrimethylammonium bromide.     

The mass action law theory of micellar solutions

Theories of micellization based on the application of the mass action law to aggregation processes in surfactant solutions are reviewed. The rigorous thermodynamic justification of the approach, explanation of the critical micelle concentration, inter-relations between the main micellization parameters, and an analysis of the surface tension isotherm of a micellar solution are given. Properties of ionic micellar systems, including counterion binding and the behavior of free monomeric ions, are discussed in detail with illustrative estimations for sodium dodecylsulfate and other surfactants.     

Mean spherical approximation-mass action law theory of equilibrium and conductance in ionic solutions

An improved Bjerrum theory obtained by combining the mean spherical approximation with the mass action law (MSA&MAL) is used to calculate the fraction of ions unpaired over the full range of states of a primitive model electrolyte. It is combined with a new theory for the electrical conductance of the primitive model under the MSA to yield the conductance of an electrolyte over a wide range of concentrations and Bjerrum parameters with only two parameters A_o and R, the distance of closest approach, adjusted to fit the conductivity data. The theory fits the data for aqueous alkali halides over a wide concentration range with A_o values in good agreement with those deduced by more conventional theories and with reasonable small ion pairing constants deduced from the data. It fits the data for LiBr in octanol without the need for invoking triple ion formation. It leads to reasonable predictions for the conductance curves for 1:1 electrolytes even up to the molar region for solvents with dielectric constant from 10 to 80.     

Thermodynamics of micellization of ionic surfactant/alkoxyethanol mixed micelles as a function of temperature

Estimates of the thermodynamic parameters of micellization ((_micG°, (_micH°, and (_micS°) have been determined for a series of mixed micelles consisting of ionic surfactants (sodium dodecylsulfate and dodecyltrimethylamonium bromide) and medium chain length alkoxyethanols as the co surfactant. The enthalpies of micellization have been measured directly for the above systems using isoperibol solution calorimetry; the Gibbs energies and entropies of micellization are obtained by application of the mass-action model to the critical micelle concentration values from the calorimetric titration experiments. The thermodynamic properties of mixed micelle formation with alcohol concentration and temperature are in excellent agreement with our previous results. However, there does appear to be some dependence of the thermodynamic properties of mixed micelle formation on the charge of the ionic surfactant. These dependencies are discussed in terms of the manner in which the ethylene oxide group of the alcohol interacts with the ionic head groups and the location of the solubilizates in the micellar interior.     

The effect of surfactant charge on micellization behavior

 The influence of the surfactant charge on micellization was studied on sodium n-dodecane-phosphonates, varying the charge of the surfactant ion from 0 to 2. The effects on the cmc, hydrolysis, micelle composition, and micelle ionization degree were studied. The increase of one e unit in the charge of the surfactant species reduces the cmc by about one order of magnitude. Received: 18 November 1996 Accepted: 5 March 1997     

Molecular-thermodynamic theory of micellization of multicomponent surfactant mixtures: 1. Conventional (pH-Insensitive) surfactants

A molecular-thermodynamic (MT) theory was developed to model the micellization of mixtures containing an arbitrary number of conventional (pH-insensitive) surfactants. The theory was validated by comparing predicted and experimental cmc's of ternary surfactant mixtures, yielding results that were comparable to, and sometimes better than, the cmc's determined using regular solution theory. The theory was also used to model a commercial nonionic surfactant (Genapol UD-079), which was modeled as a mixture of 16 surfactant components. The predicted cmc agreed well with the experimental cmc, and the monomer concentration was predicted to increase significantly above the cmc. In addition, the monomer and the micelle compositions were predicted to vary significantly with surfactant concentration. These composition variations were rationalized in terms of competing steric and entropic effects and a micelle shape transition near the cmc. To understand the packing constraints imposed on ternary surfactant mixtures better, the maximum micelle radius was also examined theoretically. The MT theory presented here represents the first molecular-based theory of the micellization behavior of mixtures of three or more conventional surfactants. In article 2 of this series, the MT theory will be extended to model the micellization of mixtures of conventional and pH-sensitive surfactants.     

Critical evaluation of micellization behavior of nonionic surfactant MEGA 10 in comparison with ionic surfactant tetradecyltriphenylphosphonium bromide studied by microcalorimetric method in aqueous medium

The micellization behavior of MEGA 10 has been studied at nine different temperatures by isothermal titration calorimetry (ITC), and thermodynamics of the process have been evaluated and examined in detail. The aggregation number of the nonionic surfactant has been estimated from the ITC results by a simulation procedure based on the mass action principle of micellization of the surfactant. The cmc of MEGA 10 has shown a minimum in temperature dependence as observed for ionic surfactants. For a comparison, the cmc and related thermodynamic parameters of an ionic surfactant, tetradecyltriphenylphosphonium bromide (C(14)TPB) studied at several temperatures in aqueous medium has been considered. The contributions of the headgroups of both the surfactants to the free energies of their respective micellization have been deciphered and presented.     

Implicit solvent models for micellization of ionic surfactants

We propose a method for parametrization of implicit solvent models for the simulation of the self-assembly of ionic surfactants into micelles. The parametrization is carried out in two steps. The first step involves atomistic molecular dynamics simulations of headgroups and counterions with explicit solvent to determine structural properties. An implicit solvent model of the headgroup/counterion system is obtained by matching structural quantities between explicit solvent and implicit solvent systems. In the second step, we identify the solvophobic attractions between the tail beads. We determine the solvophobic parameters using grand canonical Monte Carlo simulations with histogram reweighting techniques. The matching objective for the identification of solvophobic attractions is the critical micelle concentration (cmc). We choose sodium dodecyl sulfate as the reference system. On the basis of hydrophobic parameters obtained from this particular model, we study specific ion effects (lithium and potassium instead of sodium) as well as the effect of cationic headgroups (dodecyltrimethylammonium bromide/chloride). Furthermore, the chain length dependence of micellization properties is investigated for sodium alkyl sulfate, with alkyl lengths between 6 and 14. All cases considered give results in broad agreement with experimental data, confirming the transferability of parameters and the generality of the approach.     

Temperature-triggered micellization of block copolymers on an ionic liquid surface

In situ neutron reflectivity was used to study thermally induced structural changes of the lamellae-forming polystyrene-block-poly(2-vinylpyridine) (PS-b-P2VP) block copolymer thin films floating on the surface of an ionic liquid (IL). The IL, 1-butyl-3-methylimidazolium trifluoromethanesulfonate, is a nonsolvent for PS and a temperature-tunable solvent for P2VP, and, as such, micellization can be induced at the air-IL interface by changing the temperature. Transmission electron microscopy and scanning force microscopy were used to investigate the resultant morphologies of the micellar films. It was found that highly ordered nanostructures consisting of spherical micelles with a PS core surrounded by a P2VP corona were produced. In addition, bilayer films of PS homopolymer on top of a PS-b-P2VP layer also underwent micellization with increasing temperature but the micellization was strongly dependent on the thickness of the PS and PS-b-P2VP layers.     

Multiple solutions to the equation of the law of mass action

The appearance of multiple solutions to the equation of the law of mass action indicates a chemical instability where a system, as a result of the first order phase transition, breaks down into several phases. In each phase the reactant concentrations are different.     

Mixed micellization of gemini surfactant with nonionic surfactant in aqueous media: a fluorometric study

Herein we report on the study of the interactions between alkanediyl-α,ω-type cationic dimeric (gemini) surfactant and the nonionic Triton X-100 in aqueous medium. The critical micelle concentrations of binary mixtures were determined by fluorometric study. Using the regular solution theory for the analysis of the experimental data, the attractive nature of interactions and synergistic behavior of gemini surfactant and Triton X-100 mixture were demonstrated. The micelle aggregation number was measured using steady state fluorescence quenching method. The micropolarity, binding constant and dielectric constant of mixed systems were determined from the ratio of peak’s intensity (I ₁/I ₃) in the pyrene fluorescence emission spectrum.     

Effect of stiffness on the micellization behavior of model H4T4 surfactant chains

The micellization behavior of a series of model surfactants, all with four head and tail groups (H4T4) but with different degrees of chain stiffness, was studied using grand canonical Monte Carlo simulations on a cubic lattice. The critical micelle concentration, micellar size, and thermodynamics of micellization were examined. In all cases investigated, the critical micelle concentration was found to increase with increasing temperature as observed for nonionic surfactants in apolar or slightly polar solvents. At a fixed reduced temperature and increasing chain stiffness, in agreement with previous observations, it was found that the critical micelle concentration decreased and the average micelle size increased. This behavior is qualitatively consistent with that experimentally observed when comparing hydrogenated and homologous fluorinated surfactants. Thermodynamic considerations based on the analysis of the temperature dependence of the critical micelle concentration indicated that both effects could be interpreted as arising from an increased number of heterocontacts between hydrophobic portions of stiff surfactants and a lower entropic cost on packing rigid chains. Structural analysis that was also based on considering the inner micellar radial dependence of the surfactant head and tail site fraction distributions suggested that, on stiffening the molecular backbone, the resulting micellar aggregates grew, without appreciable deviations from spherical symmetry. Stiffer surfactants led to a slightly denser micellar core because of better packing.     

The effect of electrolyte on ionic surfactant adsorption

For submicellar solutions of ionic surfactants rigorous thermodynamic expressions are presented which show that the surfactant adsorption will not depend on electrolyte concentration c₃ at constant surfactant concentration c₁, if there is no corresponding dependence on c₁ at constant c₃. Results which indicate otherwise are inconsistent with thermodynamics.     

Unique role of ionic liquid [bmin][BF4] during curcumin-surfactant association and micellization of cationic, anionic and non-ionic surfactant solutions

Hydrophilic ionic liquid, 1-butyl-3-methylimidazolium tetrafluoroburate, modified the properties of aqueous surfactant solutions associated with curcumin. Because of potential pharmaceutical applications as an antioxidant, anti-inflammatory and anti-carcinogenic agent, curcumin has received ample attention as potential drug. The interaction of curcumin with various charged aqueous surfactant solutions showed it exists in deprotonated enol form in surfactant solutions. The nitro and hydroxyl groups of o-nitrophenol interact with the carbonyl and hydroxyl groups of the enol form of curcumin by forming ground state complex through hydrogen bonds and offered interesting information about the nature of the interactions between the aqueous surfactant solutions and curcumin depending on charge of head group of the surfactant. IL[bmin][BF4] encouraged early formation of micelle in case of cationic and anionic aqueous surfactant solutions, but slightly prolonged micelle formation in the case of neutral aqueous surfactant solution. However, for curcumin IL [bmin][BF4] favored strong association (7-fold increase) with neutral surfactant solution, marginally supported association with anionic surfactant solution and discouraged (～2-fold decrease) association with cationic surfactant solution.     

Investigating the effects of pH,surfactant and ionic strength on the stability of alumina/water nanofluids using DLVO theory

Journal of Thermal Analysis and Calorimetry - Alumina nanofluids are one of the most useful nanofluids. In order to evaluate the colloidal behavior of nanoparticles in alumina/water nanofluid, the...