Volume Fraction Of Micelles Research Articles

Investigating the effect of dipropylene glycol and mixed-surfactant concentrations on perfume release

HypothesisThe solubilization and release of perfume from aqueous micellar solutions are to a large extent dependent on the geometric, surface and electrostatic properties of the micelle. These properties are influenced by the molecular structure of the surfactant, the solvent properties, and additives (hydrotropes). Both surfactant and co-solvent are expected to affect solvent polarity, hence addition of a co-solvent of lower polarity than water should reduce the size of micelles, whereas addition of surfactant should increase the size of micelles. ExperimentThe effect of dipropylene glycol and surfactant concentration on micelle size and perfume release were systematically studied on (a) branched-chain sodium trideceth-2 sulfate (ST2S)/cocamidopropyl betaine (CAPB), and (b) linear-chain sodium laureth-1 sulfate (SLE1S)/CAPB mixed-surfactant systems. Combined small-angle neutron scattering (SANS) and GC-MS studies were conducted to elucidate the impact of co-solvent and surfactant on fractional charge/size of micelle and perfume release from formulations. Principal component analysis (PCA) was done to determine if the 12-PRM perfume accord could be simplified into smaller groups of PRMs. Statistical analysis was performed to determine if perfume release was significantly correlated to any aspects of the colloidal domain as a function of DPG or surfactant concentration. FindingsThe micelles shrank, aggregation numbers decreased, and fractional charges increased with increasing DPG concentration, whereas the opposite occurred with increasing surfactant concentrations. These trends were largely consistent for both mixed-micelle systems. GC-MS headspace concentration results further demonstrated that although the perfume headspace concentrations typically follow certain trends, performance is largely dependent on surfactant and DPG concentration. PCA showed that the 12-PRM accord could be treated as two components of perfume molecules, with florol strongly contributing to the second component. Statistical analysis showed that the first component significantly correlated to the micelle size and volume fraction as a function of DPG and surfactant concentration in both mixed-surfactant systems. This is the first time the release of a multi-component perfume accord was systematically studied as a function of DPG and surfactant concentration, and how DPG and surfactant variation affect the colloidal domain in the presence of a multi-component perfume accord.

Rheological signatures of gel–glass transition and a revised phase diagram of an aqueous triblock copolymer solution of Pluronic F127

In this work, we study temperature-induced state change of an aqueous solution of triblock copolymer composed of poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide), PEO-PPO-PEO (Pluronic F127), at different concentrations using rheology. While this temperature-dependent state change visually appears like a liquid–soft solid transition, and the soft solid state has been termed as a gel in the literature, there is a debate regarding the precise microstructure of the soft solid state. We observe that over a concentration domain of interest, an aqueous solution of F127 overwhelmingly demonstrates all the characteristic rheological features of not just a sol–gel–glass transition at low temperatures and glass–liquid transition at high temperatures, but also that associated with the individual states, such as sol, post-gel, and glass. The temperature at which the gel–glass transition is observed decreases while the temperature associated with glass–liquid transition increases with an increase in the concentration of F127. Based on the observed behavior, we propose a mechanism that considers the change in micelle volume fraction and alteration of the hydrophilicity of PEO corona as a function of temperature. Finally, we construct a phase diagram and discuss the similarities and differences with respect to various phase diagrams of F127 solution available in the literature.

Diafiltration affects the gelation properties of concentrated casein micelle suspensions obtained by filtration.

Using membrane filtration it is possible to selectively concentrate proteins and, in the case of microfiltration, concentrate casein micelles. During filtration, water is often added and this practice, called diafiltration, causes further release of permeable components and maintains filtration efficiency. Filtration causes changes in composition of the protein as well as the soluble phase, including soluble calcium, which is a critical factor controlling the gelation properties of the casein micelles in milk. It was hypothesized that concentrates obtained using membrane filtration with or without diafiltration would have different gelation behavior. To test this hypothesis, two concentrates of similar casein micelle volume fraction were prepared, using spiral wound polymeric microfiltration membranes with a 800 kDa molecular weight cutoff, with or without diafiltration. The concentrates showed a gelation behavior comparable to that of skim milk, with a similar gelation time and with a higher firmness, due to the higher number of protein linkages in the network. In contrast, the hydrolysis of κ-casein by chymosin and casein aggregation were inhibited in diafiltered casein micelle suspensions. When the concentrates were recombined with the original skim milk to a final concentration of 5% protein, which re-established a similar soluble phase composition, differences in gelation behavior were no longer observed: both treatments showed similar gelation time and gel firmness. These results confirmed that membrane filtration can result in concentrates with different functionality, and that ionic environmental conditions are critical to the aggregation behavior of casein micelles. This is of particular significance in industrial settings where these fractions are used as a way to standardize proteins in cheese making.

Comicellization of Binary PEO–PPO–PEO Triblock Copolymer Mixtures in Ethylammonium Nitrate

The micellization of dilute solutions of Pluronic block copolymers P123 (EO20–PO70–EO20) and F127 (EO106–PO70–EO106) and comicellization of binary mixtures in partially deuterated ethylammonium nitrate (d3EAN, a protic ionic liquid) are studied by small-angle neutron scattering. The average Pluronics composition in micelles shows a linear dependence on the bulk Pluronic composition. The mole ratio between P123 molecules in the micelles to those existing as unimers in solvent increases with temperature and P123 concentration. At a fixed F127/P123 ratio, the micelle core radius, the micelle corona thickness, and the aggregation number decrease with increasing temperature, while the total micelle volume fraction increases. At a fixed temperature, increasing P123 content in the binary mixtures leads to a weak minimum in micelle core size and aggregation number and a weak maximum in micelle corona thickness and total volume fraction of micelles. The comicellization behavior in d3EAN resembles that in aqueous s...

Influence of cleavage of photosensitive group on thermally induced micellization and gelation of a doubly responsive diblock copolymer in aqueous solutions: A SANS study

In the present study, small-angle neutron scattering (SANS) was used to investigate the temperature and concentration dependence of micelle formation and growth of a thermo- and light-responsive hydrophilic block copolymer and the influence of removing photosensitive group. The water-soluble polymer poly(ethylene oxide)- b -poly(ethoxytri(ethylene glycol) acrylate- co - o -nitrobenzyl acrylate) (PEO- b -P(TEGEA- co -NBA) underwent sol-gel/gel-sol transitions in response to temperature changes in the range of 15–55 °C in a 25 wt% aqueous solution. The SANS data showed that individual chains existed at low temperatures and dilute solutions. Spherical micelles formed and packed into an ordered structure at elevated temperatures and high concentrations. Data fitting revealed that the micelle growth followed both micelle fusion and unimer insertion mechanisms after the critical micelle temperature was reached in moderately concentrated solutions whereas the fusion mechanism was dominant at higher temperatures. The UV exposure led to a 22% expansion in chain dimension at the unimer stage due to repulsive interactions between the ionized segments after the removal of the light sensitive group. The higher onset temperature of sol-gel transition after irradiation was mainly ascribed to the higher lower critical solution temperature (LCST). On the other hand, the lower gel-sol transition temperature upon UV exposure was due to the reduction in micelle volume fraction after the cleavage of o -nitrobenzyl group. These results correlated well with the dynamic rheological data. • SANS reveals the molecular mechanisms of polymer micellization and gelation. • The unimers stretch upon the removal of the light sensitive group. • The cleavage of the light sensitive group leads to a narrower gel zone. • The scattering data uncovers material distributions in micelles. • Micelle growth follows both micelle fusion and unimer insertion mechanisms.

Dielectric Analysis for the Spherical and Rodlike Micelle Aggregates Formed from a Gemini Surfactant: Driving Forces of Micellization and Stability of Micelles.

The self-aggregation behavior of Gemini surfactant 12-2-12 (ethanediyl-1,2-bis(dimethyldodecylammonium bromide)) in water was investigated by dielectric relaxation spectroscopy (DRS) over a frequency range from 40 Hz to 110 MHz. Dielectric determination shows that well-defined spherical micelles formed when the concentration of the surfactant was above a critical micelle concentration CMC1 of 3 mM and rodlike micelles formed above CMC2, 16 mM. The formation mechanism of the spherical micelles and their transition mechanism to clubbed micelles were proposed by calculating the degree of counterion binding of the micelles. The interactions between the head groups and the hydrophobic chains of the surfactant led to the formation of the micelles, whereas the transition is mainly attributed to the interaction among the hydrophobic chains. By analyzing the dielectric relaxation observed at about 10(7) Hz based on the interface polarization theory, the permittivity and conductivity of micelle aggregates (spherical and clubbed) and volume fraction of micelles were calculated theoretically as well as the electrical properties of the solution medium. Furthermore, we also calculated the electrokinetic parameters of the micelle particle surface, surface conductivity, surface charge density, and zeta potential, using the relaxation parameters and phase parameters. On the basis of these results, the balance of forces controlling morphological transitions, interfacial electrokinetic properties, and the stability of the micelle aggregates was discussed.

Poly(3‐hexyl thiophene)‐b‐poly(N‐isopropyl acrylamide): Synthesis and its composition dependent structural, solubility, thermoresponsive, electrochemical, and electronic properties

ABSTRACTConjugated block copolymers consisting of poly(3‐hexyl thiophene) (P3HT) and a thermoresponsive polymer poly(N‐isopropyl acrylamide) (PNIPAM) with varying composition have been synthesized by facile click reaction between alkyne terminated P3HT and azide terminated PNIPAM. The composition‐dependent solubility, thermoresponsive property in water, phase behavior, electrochemical, optical, and electronic properties of the block copolymers were systematically investigated. The block copolymers with higher volume fraction of PNIPAM form thermoresponsive spherical micelles with P3HT‐rich crystalline cores and PNIPAM coronas. Both X‐ray and atomic force microscopic studies indicated that the blocks copolymers showed well‐defined microphase separated nanostructures and the structure depended on the composition of the blocks. The electrochemical study of the block copolymers clearly demonstrated that the extent of charge transport through the block copolymer thin film was similar to P3HT homopolymer without any significant change in the band gap. The block copolymers showed improved or similar charge carrier mobility compared with the pure P3HT depending on the composition of the block copolymer. These P3HT‐b‐PNIPAM copolymers were interesting for fabrication of optoelectronic devices capable of thermal and moisture sensing as well as for studying the thermoresponsive colloidal structures of semiconductor amphiphilic systems. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016, 54, 1785–1794

Aggregation behavior and electrical properties of amphiphilic pyrrole-tailed ionic liquids in water, from the viewpoint of dielectric relaxation spectroscopy

The self-aggregation behavior of amphiphilic pyrrole-tailed imidazolium ionic liquids (Py(CH₂)₁₂mim⁺Br⁻: Py = pyrrole, mim = methylimidazolium) in water is investigated by dielectric spectroscopy from 40 Hz to 110 MHz. Dielectric determination shows that the critical micelle concentration (CMC) is 8.5 mM, which is lower than that for traditional ionic surfactants. The thermodynamic parameter of the micellization, the Gibbs free energy ΔG, was calculated for Py(CH₂)₁₂mim⁺Br⁻ and compared to those of the corresponding C(n)mim⁺Br⁻ (n = 12, 14). It was found that the main driven forces of the Py(CH₂)₁₂mim⁺Br⁻ aggregation were hydrophobic interaction and π-π interactions among the adjacent Py groups. Further, the structure of aggregation was speculated theoretically that Py groups partially insert into the alkyl chains and the staggered arrangement in micelles is formed. When the concentration of Py(CH₂)₁₂mim⁺Br⁻ is higher than CMC, two remarkable relaxations which originated from diffusion of counterions and interfacial polarization between the micelles and solution, were observed at about 1.3 MHz and 55 MHz. The relaxation parameters representing the real properties of the whole system were obtained by fitting the experimental data with Cole-Cole equation. A dielectric model characterizing the structure and electrical properties of spherical micelles was proposed by which the conductivity, permittivity and the volume fraction of micelles as well as electrical properties of solution were calculated from the relaxation parameters. An intriguingly high permittivity of about 150 for the micelle was found to be a direct consequence of the strong orientational order of water molecules inside the core of micelle, and essentially is attributed to the special structure of the micelle. Furthermore, the calculation of the interfacial electrokinetic parameters of the micelles, i.e., the surface conductivity, surface charge density and zeta potential, were also achieved based on the relaxation parameters and phase parameters from higher frequency relaxation. On the basis of the results obtained, the aggregation behaviours and interfacial electrokinetic properties of the special micelles are discussed.

Temperature Effect on the Nanostructure of SDS Micelles in Water.

Sodium dodecyl sulfate (SDS) surfactants form micelles when dissolved in water. These are formed of a hydrocarbon core and hydrophilic ionic surface. The small-angle neutron scattering (SANS) technique was used with deuterated water (D2O) in order to characterize the micelle structure. Micelles were found to be slightly compressed (oblate ellipsoids) and their sizes shrink with increasing temperature. Fits of SANS data to the Mean Spherical Approximation (MSA) model yielded a calculated micelle volume fraction which was lower than the SDS surfactant (sample mixing) volume fraction; this suggests that part of the SDS molecules do not participate in micelle formation and remain homogeneously mixed in the solvent. A set of material balance equations allowed the estimation of the SDS fraction in the micelles. This fraction was found to be high (close to one) except for samples around 1 % SDS fraction. The micelle aggregation number was found to decrease with increasing temperature and/or decreasing SDS fraction.

Pressure Jump Kinetics of Disorder to BCC Ordering in Diblock Copolymer Micelles in a Selective Solvent

We present time-resolved small-angle X-ray scattering (SAXS) measurements of the kinetics of a barotropic disorder–order transition in polystyrene–polyisoprene (SI) diblock micelles in diethyl phthalate (DEP), a styrene selective solvent. Because of the fast equilibration in a pressure jump we were able to observe the initial induction stage during which the short-range order of the micellar fluid increases, followed by a sharp first-order nucleation and growth of the BCC phase and eventual late stage coarsening. The time evolution of intensity from individual diffraction spots of a crystallite was obtained from the analysis of 2-dimensional SAXS patterns and shows late stage power-law growth. The time evolution of the SAXS intensity profiles was analyzed by fitting the contribution to the scattering from the ordered Bragg peaks by Gaussians and analyzing the contribution to the scattering from the disordered micellar liquid in terms of the Percus–Yevick interacting hard-sphere model. The time evolution of the micellar structural parameters obtained from this analysis reveals that the disorder to order transition occurs when the volume fraction of micelles reaches 0.53, and the effective hard sphere radius and volume fraction of micelles increases upon ordering while the core radius is unaffected. In both the ordered and disordered states the hard sphere radius and volume fraction of micelles increase with increasing pressure indicating increased swelling of the micellar corona. In the ordered state there is considerable penetration of the corona chains from neighboring micelles.

Phase behaviour of casein micelles and barley beta-glucan polymer molecules in dietary fibre-enriched dairy systems

Enrichment of colloidal dairy systems with dietary fibre frequently causes quality defects because of phase separation. We investigate phase separation in skimmed milk enriched with Glucagel (a commercial product made from barley that is predominantly comprised of the polysaccharide β-glucan). The driving force for phase separation was depletion flocculation of casein micelles in the presence of molecules of the polysaccharide. Depending on the volume fraction of casein micelles and the concentration of Glucagel, the stable system phase separated either as a transient gel or as a sedimented system. The rate at which phase separation progressed also depended on the volume fraction of casein micelles and the concentration of Glucagel. To confirm the role of depletion flocculation in the phase separation process, enzymatic reduction in the molecular weight of β-glucan was shown to limit the range of attraction between micelles and allow the stable phase to exist at a higher β-glucan concentration for any given volume fraction of casein micelles. These phase diagrams will be useful to dairy product manufacturers striving to improve the nutrient profile of their products while avoiding product quality impairment.

Changes in the calcium cluster distribution of ultrafiltered and diafiltered fresh skim milk as observed by Small Angle Neutron Scattering

The effect of ultrafiltration and diafiltration on the distribution of the calcium phosphate clusters of the casein micelle was investigated using Small Angle Neutron Scattering (SANS). In the case of ultrafiltration, fresh skim milk was subjected to concentration using membrane filtration up to 5× its original volume, the retentate was rediluted with its corresponding serum and subsequently dialyzed against reconstituted milk powder dispersed in D2O/H2O (UF 5×(D)). In the case of diafiltered samples, the samples were concentrated adding water (diafiltration) at two different levels (DF 2·5× or DF 5×) and then redispersed with D2O/H2O. In the DF 5× case, the serum components were diluted to less than 1% of their original concentration. For analysis, all samples had the same volume fraction of dispersed casein micelles (φ=0·1), which is that of the control, unprocessed skim milk. A peak in the SANS data was observed in fresh skim milk at a scattering vector, qo, of 0·034 Å-1 (directly proportional to the reciprocal characteristic length), in agreement with previous literature results. Neutron data on the ultrafiltered, UF 5×(D) and diafiltered, DF 2·5× and DF 5× milk samples showed a progressive decrease in the intensity of the peak but invariance in qo. These results, combined with the determination of soluble and insoluble calcium in the samples, suggest a progressive and irreversible removal of calcium from within the micelle during membrane filtration of milk. Using SANS it was possible to clearly show changes in the micellar calcium clusters that may not otherwise be fully determined by only measuring the amount of total and insoluble calcium in milk.

Coagulation properties of ultrafiltered milk retentates measured using rheology and diffusing wave spectroscopy

The effect of concentration of milk by ultrafiltration on renneting has been widely studied as it is of great interest in dairy technology. Although a number of reports are available on the texture and microstructure of the milk gels formed at various concentrations, very little is understood on the effect of concentration on the stages preceding aggregation, or how concentration may affect the interactions between micelles. This study aims to investigate the renneting behavior of milk concentrated by ultrafiltration (without diafiltration) to 3× and 5× (v/v) and compare it to that of skim milk. The scattering properties of the casein micelles under quiescent conditions suggest that they deviate from hard-sphere behavior at 5× concentration (micelle volume fraction, ϕ = 0.5). The release of the caseinomacropeptide during renneting was not significantly different amongst the three different casein concentrations tested (1×, 3×, and 5×). No significant differences were also noted in the rennet coagulation time as detected by both diffusing wave spectroscopy and rheology. Concentrated milk samples formed significantly (p-value < 0.05) stiffer gels than regular milk due to an increased number of bonds in the network. The level of milk concentration also accelerated a change in the spatial distribution and rate of change of turbidity of the micelles because of a decrease in the overall inter-particle distance and increased collision frequencies. This in situ investigation of concentrated milk samples suggested that the changes in rennet coagulation with concentration are merely a cause of crowding effects.

Gelation of casein micelles in β-casein reduced milk prepared using membrane filtration

Pasteurized skim milk was subjected to membrane filtration using a molecular weight cut-off of 80 kDa and a plate and frame pilot scale system at temperatures below 10 °C. Via this process, transmission of whey proteins and β-casein through the membrane was achieved. The milk was concentrated to two times (based on volume reduction), and whey protein-free permeate was added to return to the original volume fraction of casein micelles in milk. This diafiltration process was carried out four times, and the retentate obtained was nearly free of whey proteins and with approximately 20% of β-casein removed. The same membrane filtration was also carried out at 25 °C to achieve transmission of whey protein but not of β-casein, and to obtain whey protein-depleted milk without depletion of β-casein. The gelling behaviour of these samples, reconstituted to the original casein volume fraction, was examined using rheology and diffusing wave spectroscopy. When compared to the original skim milk it was found that there were no statistically significant differences in gelation behaviour during acidification, but differences were noted in gelation time and final stiffness modulus for samples undergoing renneting. These differences were attributed mostly to the changes in ionic composition, as when the serum composition of the retentates was re-equilibrated against the original skim milk by dialysis; the gelation behaviour of the samples was comparable to that of skim milk. The results clearly indicate the importance of the milk's overall ionic balance in the early stages of aggregation of rennet-induced gelation of milk.

Slow dynamics of wormlike micelles

We present an extensive rheology study of the wormlike micelle system lecithin-water-cyclohexane. In this system the micelles are really wormlike, meaning that there are no signs of micellar branching, as it has previously been demonstrated by NMR self-diffusion experiments (R. Angelico, U. Olsson, G. Palazzo and A. Ceglie, Phys. Rev. Lett., 1998, 81, 2823). Wormlike micelles break and recombine, processes that are important for the stress relaxation. When branching is highly unfavorable, micelle recombination reactions only involve micelle ends, the concentration of which are very low when the micelles are very long. Hence, the break and recombination kinetics is very slow for true wormlike micelles. In the present system, the stress relaxation times are of the order of an hour. This is about three to four orders of magnitude longer than what commonly is observed in systems claimed to contain wormlike micelles. We conclude that systems with true wormlike micelles are very rare. An exponential stress relaxation is observed except at lower concentrations, where the micellar breaking time appears to exceed the reptation time. Because of the slow dynamics, the linear elastic modulus can be obtained from small rapid shear deformations, for which the system obeys Hooke's law. Larger deformations result in a fracture of the micellar network at a critical strain γ* ∼ ϕ−1, where ϕ is the micelle volume fraction. For γ < γ* we may still obtain fracture, although with a lag time, τ*, that decreases with increasing γ, and vanishes when γ = γ*. Extrapolating τ* to zero deformation we obtain the estimate ≈250 s at the highest concentration ϕ = 0.29. We interpret this time as the equilibrium micellar breaking time at rest, a quantity not previously measured.

Micelle Morphology and Mechanical Response of Triblock Gels

The effect of polymer concentration on mechanical response and micelle morphology of ABA and AB copolymers in B-selective solvents has been systematically studied. Micelle morphology was determined using a combination of small-angle X-ray scattering, shear, and birefringence while mechanical response at low and high strains was determined using indentation techniques. Self-consistent field theory calculations were used to determine micelle volume fraction profiles and to construct an equilibrium phase map. The transition from spherical to cylindrical micelles increases the triblock gel modulus and energy dissipation. Combining knowledge of gel relaxation time, which determines the rate at which the gel can equilibrate its micelle structure, with the equilibrium phase map allows estimation of the experimental temperatures and time scales over which kinetic trapping will arrest micelle structure evolution. Kinetic trapping enables cylindrical morphologies to be obtained at significantly lower polymer fractions than is possible in equilibrated systems.

On the concentration-induced growth of nonionic wormlike micelles

We present a comprehensive study of the concentration-induced growth of nonionic wormlike micelles in dilute solutions, below the overlap concentration, where we combine static and dynamic light scattering and NMR self-diffusion. The data are analyzed in detail in terms of the number-averaged contour length, assuming an exponential size distribution, as predicted by theory, and that the micellar flexibility can be described by the wormlike chain model with a certain persistence length. A very good agreement between the different experimental methods is obtained. The number-averaged contour length increases with increasing micelle volume fraction. The data are consistent with a power law, where the power law exponent is in the range 0.5-0.8, depending on the system. The result is in reasonable agreement with the theory of living polymers.

The impedance of solutions of AOT/water micelles in hexane

Broadband dielectric spectroscopy was used to study the electric properties of solutions of reverse AOT/water micelles in hexane. An analysis of the frequency dependences of the complex electric modulus allowed us to find the region of frequencies in which dc-conductivity was observed and exclude the region of electrode effects. At frequencies f of ∼ 104Hz, the field dependences of dc-conductivity changed from linear (the Ohm law) to quadratic (the Mott law) as the volume fraction of micelles increased. This was evidence of a strengthening of the effect of current limitation by a volume charge. The upper and lower limits of the drift mobility of carriers μ responsible for dc-conductivity were estimated as 0.1 cm−2 V−1 s−1 < μ < 0.3 cm−2 V−1 s−1, which was close to the mobility of electrons in hexane. This allowed us to relate the nature of current carriers to that of free electrons; the activation energy of electron creation was found to be Ea ≈ 0.41 eV. The electron lifetime up to its trapping by acceptors was estimated. The results obtained and the literature data on the rate constants of such reactions led us to conclude that micelles were capable of absorbing acceptor impurities from solvents (additional solvent purification).

The colloid structural forces as a tool for particle characterization and control of dispersion stability

Knowing the size and interactions of colloid particles, one can predict the stepwise thickness transitions and the contact angles of particle-containing liquid films. Here, we consider the inverse problem, viz. how to determine the particle properties by measurements with liquid films. We carried out experiments with films formed from aqueous solutions of two nonionic surfactants, Brij 35 and Tween 20, which contain spherical micelles of diameters in the range 7-9 nm. From the measured contact angles, we determined the micelle aggregation number and volume fraction. In addition, from the measured disjoining-pressure isotherms we determined the micelle diameter. In other words, the liquid-film measurements give information about the micelles, which is analogous to that obtainable by dynamic and static light scattering. Furthermore, we investigate the predictions of different quantitative criteria for stability-instability transitions, having in mind that the oscillatory forces exhibit both maxima, which play the role of barriers to coagulation, and minima that could produce flocculation or coalescence in colloidal dispersions (emulsions, foams, suspensions). The interplay of the oscillatory force with the van der Waals surface force is taken into account. Two different kinetic criteria are considered, which give similar and physically reasonable results about the stability-instability transitions. Diagrams are constructed, which show the values of the micelle volume fraction, for which the oscillatory barriers can prevent the particles from coming into close contact, or for which a strong flocculation in the depletion minimum or a weak flocculation in the first oscillatory minimum could be observed.

Micelle formation in statistical copolymers

Formation of microdomain structures in concentrated systems of irregular (stochastic) copolymers with weak composition asymmetry (epsilon>>1) is considered theoretically. The study is focused on the weak segregation regime for infinitely long copolymer chains near the disorder-to-order transition. It is shown that the transition occurs below the spinodal (at chi(0)< chi*) and that it results in the formation of micelles rather than in a superposition pattern of a few harmonic composition waves. The micelle size is inversely proportional to Delta(chi=chi)-(chi0). For small Delta(chi) the micelles are like large nearly uniform droplets with "reflected" composition, -epsilon. As Delta(chi) increases the micelle composition profile develops oscillations. A first-order transition from spherical-wave micelles to micelles with internal bcc structure is predicted at chi/chi*-1 proportional to epsilon(2). Interaction of micelles is also considered. It is shown that micelles always tend to form a fcc superlattice. The micellization in the weak segregation regime is controlled by the so-called nonlocal free energy. The classical fourth order (in composition parameter A) approximation for this energy is significantly generalized in the regime of low volume fraction of micelles. It is shown that the nonlocal energy strongly (exponentially) increases with A near and above a certain critical value A approximately equal to A*.