Terms Of Aggregation Number Research Articles

Model of inverse “dry” micelles with coexisting spherical, globular and cylindrical aggregates

A new statistical thermodynamic model of inverse nonionic aggregates of surfactant molecules in nonpolar solvents is considered. This model admits the fluctuation coexistence of inverse spherical, globular, and spherocylindrical aggregates without activation barriers between them. The model is based on the assumption of a uniform bulk density of the number of molecular groups inside the core of an aggregate that can continuously transform into a sphere, a globule, and a spherocylinder. In this model, for any aggregation numbers, the work of aggregation depends not only on the aggregation numbers and the concentration of surfactant monomers, but also on two independent geometric parameters characterizing, at the same aggregation numbers, the deviation from the spherical form of the aggregate towards globular and spherocylindrical forms. Even in the range of small aggregation numbers, this fact leads to a significant difference between the equilibrium distribution function of aggregates, which depends on the aggregation number and two form parameters, and the one-dimensional distribution function in terms of aggregation numbers. It is shown that the optimal values of the form parameters, which minimize the work of aggregation, are in good agreement for spherocylindrical aggregates with the predictions of a purely geometric model of such aggregates under the additional assumption of a uniform surface density of molecular groups at the micelle core. The predictions of a new molecular thermodynamic model for the degrees of surfactant micellization in inverse aggregates of various forms at different surfactant concentrations are considered.

Surfactant micellization and diffusion at moderate concentrations

Since micellization typically occurs at small concentrations, existing theories imply an ideal behavior of micellar systems near the critical micelle concentration (CMC). However, micellization also occurs at not small but rather moderate concentrations, which needs a certain generalization in theory. In this paper, the theory based on the definition of the CMC via the constant of the mass action law is generalized for relatively concentrated systems where a set of micelles and monomers exhibits a nonideal behavior. The theory is restricted by a concentration range above the CMC where aggregation numbers can be considered as constants. Being more complicated, the case of a nonideal micellar system possesses its own simplifications. First, expressing all concentrations in the CMC units, the activity coefficient f is replaced byf/fmwherefmis the f-value at the CMC. This ratio can be almost constant or unity even for a nonideal system. The second simplification is related to forming electroneutral micelles in a concentrated ionic solution. The theory of such systems is developed in detail including explicit expressions for micellar and monomeric concentrations in terms of aggregation numbers. One more simplification was discovered when applying the theory to the diffusion of surfactants in micellar solutions. This is a quasi-ideal behavior of a relatively concentrated ionic micellar system caused by the mutual compensation of the viscosity and nonideality effects in the course of diffusion.

Growth Behavior, Geometrical Shape, and Second CMC of Micelles Formed by Cationic Gemini Esterquat Surfactants.

Micelles formed by novel gemini esterquat surfactants have been investigated with small-angle neutron scattering (SANS). The growth behavior of the micelles is found to differ conspicuously depending on the length of the gemini surfactant spacer group. The gemini surfactant with a long spacer form rather small triaxial ellipsoidal tablet-shaped micelles that grow weakly with surfactant concentration in the entire range of measured concentrations. Geminis with a short spacer, on the other hand, form weakly growing oblates or tablets at low concentrations that start to grow much more strongly into polydisperse rodlike or wormlike micelles at higher concentrations. The latter behavior is consistent with the presence of a second CMC that marks the transition from the weakly to the strongly growing regime. It is found that the growth behavior in terms of aggregation number as a function of surfactant concentration always appear concave in weakly growing regimes, while switching to convex behavior in strongly growing regimes. As a result, we are able to determine the second CMC of the geminis with short spacer by means of suggesting a rather precise definition of it, located at the point of inflection of the growth curve that corresponds to the transition from concave to convex growth behavior. Our SANS results are rationalized by comparison with the recently developed general micelle model. In particular, this theory is able to explain and reproduce the characteristic appearances of the experimental growth curves, including the presence of a second CMC and the convex strongly growing regime beyond. By means of optimizing the agreement between predictions from the general micelle model and results from SANS experiments, we are able to determine the three bending elasticity constants spontaneous curvature, bending rigidity, and saddle-splay constant for each surfactant.

Asymmetrical flow field-flow fractionation analysis of water suspensions of polymer nanofibers synthesized via RAFT-mediated emulsion polymerization

The aim of this work is to present a method based on asymmetric flow-field-flow-fractionation coupled on-line to a static light scattering (AF4-UV-SLS) detector to characterize self-assembled nanofibers (NFs). The method developed herein allows the determination of both the length distribution of the NFs as well as the distribution in terms of aggregation number per unit length (Agg). Given the remaining synthetic challenges of better controlling the structural homogeneity and particle dimensions, the NF length and aggregation number per unit length are becoming essential for the improvement and control of their chemical processes and a better understanding of their properties. The results obtained with this AF4-UV-SLS method indicate that a well-resolved NF length distribution characterization and Agg determination were attained. These results provide critical information concerning the physical properties of the investigated NFs and open the door to the characterization of new self-assembled polymers with various asymmetrical architectures.

Rheology and SANS on PET-b-PLAc-b-P(DMAEMAq) Triblock Copolymers: Impact of the PET and Polyelectrolyte Chain Length

We report on a small angle neutron scattering (SANS) study of self-organization of a novel triblock copolymer containing a crystalline poly(ethylene terephthalate) oligomer, a rubbery poly(lauryl acrylate) midblock, and a polyelectrolyte block (quaternized poly(2-(dimethylamino)ethyl methacrylate)) of various length. The rheology of the solutions showed a transition from Newtonian flow at low concentrations, to shear-thinning at intermediate concentrations, and finally a yield behavior at high concentrations. The microstructure of the samples investigated by SANS was found to evolve strongly with the polyelectrolyte block length. The data were analyzed in terms of aggregation numbers, radius of gyration, and aggregate hydration. Complete modeling of the intensity curves was achieved by an inversion method extracting an average aggregate radial volume fraction profile. In both rheology and microstructure, a surprising strong impact of the small PET block was observed.

Growth and Branching of Charged Wormlike Micelles as Revealed by Dilution Laws

The successive transitions of morphology in aqueous solutions of interacting micelles are directly evidenced by the position q* of the correlation peak of the small angle neutron scattering profiles. As the volume fraction Phi increases, q* successively fits to the dilution laws expected for spheres and cylinders, and eventually gets close to the one expected for sheets when the micelles get branched. Data in between the swelling laws are quantitatively analyzed in terms of aggregation number and junction density. Varying the temperature in the dilute regime yields the end-cap energy which varies with molecular structure and scales as Phi(-1/2). In the semidilute regime, the junction density scales as nu(j) approximately Phi(1.8), close but slightly faster than theoretically expected. The boosting effect of intermicellar repulsion on growth and branching is pointed out by the present results which directly show that both condensation processes keep the micelles further apart.

A model for the cooperative adsorption of surfactant mixtures on solid surfaces

Adsorption of surfactant mixtures on solids is of considerable theoretical and practical importance. In this study, cooperative adsorption of surfactant mixtures of nonyl phenol ethoxylated decyl ether (NP-10) and n-dodecyl- β- D-maltoside (DM) on silica and alumina has been investigated as a function of the distribution of individual surfactants between solution and solid surface. In the mixed adsorption process, DM is identified to be the “active” adsorbing component and NP is the “passive” co-adsorbing one in the process of adsorption on alumina, while their roles are reversed on silica. A modified model has been proposed to quantify the adsorption behavior of surfactant mixtures and to obtain information in terms of aggregation number and standard free energy for surface aggregation. This model is the first model applied to the aggregation of the surfactant mixture at the solid/solution interfaces.

Micellization of Hydrophobically Modified Cyclodextrins: 2. Inclusion of Guest Molecules

The association of guest molecules in aggregates of a modified cyclodextrin, 6I-(cholest-5-en-3α-ylamido)succinylamido-6I-deoxy-per(2,6-di-O-methyl)cyclomaltoheptaose, was investigated for four different sparingly water-soluble molecules and an anionic surfactant (sodium dodecyl sulfate). The binding and spatial proximities were demonstrated for these different guests by NMR (nuclear Overhauser effect pumping). By use of small-angle X-ray and neutron scattering, the microstructure at the supramolecular scale of the modified cyclodextrin micelle, i.e., aggregation number, charge, and volume, in the presence of guest molecules could be defined. From the analysis of the variations in terms of aggregation number and charge induced by the presence of the guest molecule, the cavity of the cyclodextrin was shown to remain available for solubilization and transport. The stability and specificity of the mixed micelle involving target molecules demonstrated here make these hydrophobically modified cyclodextrins goo...

Determination of micelle aggregation numbers and micelle fluidities from time-resolved fluorescence quenching studies

A critical study of the quenching of the fluorescence of tris(2,2′-bipyridyl)ruthenium(II) by 9-methylantracene in sodium dodecyl sulfate micelles at various ionic strength, in microemulsions and in pentanol-swollen micelles is presented. The results are discussed in terms of aggregation numbers and quenching constants obtained from single-photon counting data and steady-state fluorescence measurements. In connection with the analysis of the time-resolved data, an approach to choose correct time zero is outlined. The choice of the time where the excitation profile has its maximum is suggested. Varying the ionic strength in the micelle solutions resulted in an increase of the mean aggregation number from 63 at zero concentration of sodium chloride to 373 at 0.75M of the electrolyte. The first-order rate constant for quenching decreased in these solutions from 2 × 107 to 0.2 × 107 sec−1 in an inverse proportion to the estimated aggregation numbers. The correct values of the aggregation numbers are probably higher than the estimated values, which is shown in computer simulations assuming a distribution of micelle sizes. The necessity of time-resolved experiments to calculate an aggregation number if demonstrated in measurements on a microemulsion (detergent-pentanol-dodecane). The product of the quenching constant, 0.2 × 107 sec−1, and the lifetime, 309 nsec, of the fluorescent molecule is too small to justify the use of steady-state data only. The estimated aggregation number for this solution is 306, a factor of three higher than earlier reported. For pentanol-swollen micelles, data are presented where there is a need for deconvolution, the quenching constant, 6 × 107 sec−1, being too large to ignore the finite width of the excitation pulse. For this system it is better to calculate the aggregation numbers from steady-state data than from single-photon counting data once the magnitude of the quenching constant and the lifetime have been deduced. The fluidity of the micellar aggregates are discussed by defining local second-order rate constant. These were calculated to 0.4 × 109M−1 sec−1 in micelles, to 1.0 × 109M−1 sec−1 in pentanol-swollen micelles, and to 1.5 × 109M−1 sec−1 in microemulsion particles, compared to a measured value of 4.2 × 109M−1 sec−1 in a homogenous ethanol solution.