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We discuss extensive sets of experimental data including static and dynamic light scattering, ultrasonic velocity measurements and high and low frequency dielectric relaxation, taken in the vicinity the critical point of a ternary microemulsion system. Upon approaching the critical point we observed a slowing down of the dielectric relaxation time and of the first cumulant of the time-dependent droplet density correlation function C2(t) which shows a non-exponential behavior at long time. These features can be well acccounted for by assuming that the microemulsion system is made of polydispersed transient fractal aggregates having a fractal dimension df=2.5 and a polydispersity index τ=2.2.

We discuss the static and dynamic critical behavior of binary solutions of water with some alkyl-oxyethylene-glycol monoether (CiEj) and of di 2 ethylhexyl sodium sulfosuccinate (AOT)-water-decane ternary microemulsion systems. Extensive sets of measurements of the scattered light intensity, of the order-parameter fluctuations time correlation function, and of the shear viscosity, have been performed for different systems. In most of the cases our data sets show systematic deviations from the behavior usually observed for molecular binary fluids. We show that generalized hydrodynamics cannot account for these deviations. A modified version of the Sorensen et al. (1976) dynamical droplet model has been worked out. This model which assumes that the physical clusters formed close to the critical point can be treated like percolating aggregates, and which includes the finite size of the monomers, very well accounts for all our experimental results.

The three-component ionic microemulsion system consisting of AOT/water/ decane shows an interesting phase behavior in the vicinity of room temperature. The phase diagram in the temperature-volume fraction (of the dispersed phase) plane exhibits a lower consolute critical point at about 40°C and 8% volume fraction. A percolation line, starting from the vicinity of the critical point, cuts across the plane, extending to the high-volume fraction side at progressively lower temperatures. This phase behavior can be understood in terms of a system of polydispersed spherical water droplets, each coated by a monolayer of AOT, dispersed in a continuum of oil. These droplets interact with each other via a hard-core plus a short-range attractive interaction, the strength of which increases with temperature. We show that Baxter's sticky-sphere model can account quantitatively for the phase behavior, including the percolation line, provided that the stickiness parameter is a suitable function of temperature. We use the structure factors measured by small-angle neutron scattering below the critical temperature to determine this functional dependence. We also investigate the dynamics of droplets, below and approaching the critical and percolation points, by dynamic light scattering. Both theQ dependence of the first cumulant and the time evolution of the droplet density correlation function can be quantitatively calculated by assuming the existence of polydispersed fractal clusters formed by the microemulsion droplets due to attraction.

We report precise measurements of the time correlation function in a pseudo two-component water-in-oil microemulsion system made of surfactant AOT, water, and decane close to its consolute critical point and percolation threshold. Systematic studies of the intensity correlation functions using a correlator with a logarithmic sampling time show sizable deviations from a single exponential decay. It is shown that an extension of the dynamic droplet model is able to account for the nonexponential behavior at intermediate and long times. The linewidth is in satisfactory agreement with the model, which also takes into account the finite size of the microemulsion droplets

The three-component ionic microemulsion system consisting of AOT/water/decane shows an interesting phase behavior in the vicinity of room temperature. The phase diagram in the temperature-volume fraction (of the dispersed phase) plane exhibits a lower consolute critical point around 10% volume fraction and a percolation line, cutting across the plane starting from the vicinity of the critical point, extends to high volume fraction side, at progressively lower temperatures. This phase behavior can be understood in terms of a system of polydispersed spherical water droplets, each coated by a monolayer of AOT, dispersed in a continuum of oil. These droplets interact with each other via a hard-core plus a short-range attractive interaction, the strength of which increases with temperature. We show that Baxter's sticky sphere mode1 can account for the phase behavior including the percolation line, quantitatively, provided that the stickiness parameter is a suitable function of temperature. We use the structure factors measured by small angle neutron scattering below the critical temperature to determine this functional dependence. We also investigate the dynamics of droplets below and approaching the percolation line by dynamic light scattering. Both the first cumulant and the droplet density time correlation function can be quantitatively calculated by assuming the existence of polydispersed fractal clusters form by the microemulsion droplets due to the attraction. Analysis of SANS data indicates that above the percolation line, the clustered droplets structure gradually transforms into an ordered bicontinuous structure.

The electrical conductivity of a three-component ionic microemulsion has been measured in the phase diagram region where the lamellar phase, made up of repeated layers of water, surfactant and oil, exists. The data have been analyzed on the basis of an effective medium theory expression, taking into account the ion distribution within the water layer according to the Poisson-Boltzmann equation. — PACS numbers: 64.60. Cn, 05.40. + j, 82.70. Dd

The authors have performed an extensive series of dynamic light scattering measurements of a three-component water-in-oil microemulsion system, consisting of AOT/water/decane, throughout the isotropic one-phase region at water to AOT molar ratio X=40.8, covering wide ranges of volume fraction phi and temperature T above and below the percolation threshold. The droplet density correlation function at long time has a nonexponential form for phi >0.4 and below the percolation threshold. When fitted to a stretched exponential function the apparent exponent beta , starting at about 0.7 at the lowest temperatures, increases continuously and approaches unity at the percolation temperature and above. The initial and the average decay rates of the correlation function, as a function of temperature, show an abrupt change of slope at the percolation threshold.

An extensive set of measurements of low-frequency conductivity \ensuremath{\sigma} of a three-component microemulsion system, sodium-di-2-ethyl-hexylsulfosuccinate (AOT)-water-decane, as a function of temperature (T from 10 to 50 \ifmmode^\circ\else\textdegree\fi{}C) and volume fraction of the dispersed phase (\ensuremath{\varphi} from 0.098 to 0.65) has been made. The measurements were made at a fixed value of the water-to-surfactant molar ratio equal to 40.8, where the microemulsion consists of AOT-coated water droplets, 85 \AA{} in radius, dispersed in oil. \ensuremath{\sigma} can be quantitatively calculated at low \ensuremath{\varphi} by means of a charge fluctuation model of Eicke et al., while it can be interpreted for higher vlaues of \ensuremath{\varphi} in terms of power-law behavior with indices related to the dynamic percolation picture below the threshold and the static one above it. The percolation locus in \ensuremath{\varphi}-T plane has been determined starting from the vicinity of the lower consolute point up to \ensuremath{\varphi}=0.65. This line can be successfully interpreted in terms of a modified version of the analytical theory of percolation given by Xu and Stell.

The low-frequency electrical conductivity of water-in-oil microemulsions in presence of NaCl electrolyte solution has been measured in the temperature range from −15 to 60°C, for different volume fractions of the surfactant + water phase, in the interval from Φ = 0.1 to Φ = 0.8. The effects induced by the presence of the added salt, concerning the phase diagram in the (Φ − T) plane and the conductivity regimes far and close to the percolation, are discussed on the basis of the Eicke-Hall theory and a new approach to the conductometric behavior of microemulsions recently developed, which gives a more detailed and accurate description of the percolation characteristics.

The high-frequency dielectric relaxations of highly concentrated water-in-oil microemulsions have been investigated in the frequency range from 1 MHz to 1 GHz, at different temperatures, in the interval from 5 °C to 60 °C. In the region of the phase diagram studied, the system undergoes a progressive change of its structure, passing from water droplets dispersed in an oil matrix below percolation to two bicontinuous regions separated by a lamellar phase, above percolation. We have focused our attention on these two bicontinuous regions, where well-pronounced dielectric dispersions appear. An analysis in terms of scaling laws indicates a static percolation process above the percolation threshold and close to it and a process characterized by a very small value of the critical index, at higher temperatures, close to the phase transition.

18 pages, 9 figures, 3 tables.-- Printed version published Dec 1, 2003., Miniemulsions have been formed in quaternary systems water/hexanol/sodium dodecyl sulfate/decane by dilution of a microemulsion with an excess of water. We have investigated systematically the effect of composition variables in the droplet size and Ostwald Ripening rate. This droplet size has been investigated by using dynamic light scattering of samples submitted to further dilution in water. According to the dynamic light scattering results, the initial droplet size depends on the initial microemulsion water content, the larger the initial water concentration, the smaller the initial droplet size. This is probably related to the structure of the initial phase. The rate of Ostwald Ripening depends on the final surfactant concentration as expected for differences in interfacial tension. At high surfactant and dispersed phase contents, instability due to flocculation has been observed. Other experiments in which a fifth component (a more hydrophobic oil) was added to slow down Ostwald Ripening showed an initial droplet size increasing comparable to the systems without additive but after a relatively long time of approximately 2 h, a decrease was observed., Financial support from CIRIT (Generalitat de Catalunya) projects PIC 99-15 and ITT-CTP98-13 and MCYT MAT2001-1188-CO2-02.

The behavior of frequency-dependent electrical conductivity and permittivity close to the percolation threshold of a two-component system is interpreted in terms of formation of polydispersed fractal clusters. We derive an explicit form of the scaling function for the complex conductivity and its limit of validity. The measurements performed on two water-in-oil microemulsion systems are very well accounted for and show the expected scaling behavior. Stretched exponential behavior of the polarization correlation function is also obtained.

The three-component ionic microemulsion system consisting of AOT/water/decane shows an unusual phase behaviour in the vicinity of room temperature. The phase diagram in the temperature-volume-fraction (of the dispersed phase) plant: exhibits a lower consolute critical point at about 40 degrees C and 10% volume fraction. A percolation line, starting from the vicinity of the critical point, cuts across the plane, extending to the high-volume-fraction side at progressively lower temperatures. This phase behaviour can be understood in terms of a system of polydispersed spherical water droplets, each coated by a monolayer of AOT, dispersed in a continuum of oil. These droplets interact with each other via a hard-core plus a short-range attractive interaction, the strength of which increases with temperature. We show that Baxter's sticky-sphere model can account for the phase behaviour, including the percolation line, quantitatively provided that the stickiness parameter is a suitable function of temperature. We use the structure factors measured by small-angle neutron scattering (SANS) below the critical temperature to determine this functional dependence. We also investigate the dynamics of droplets, below and approaching the critical and percolation points, by dynamic light scattering. The first cumulant and time evolution of the droplet density correlation function can be quantitatively calculated by assuming the existence of polydispersed fractal clusters formed by the microemulsion droplets due to attraction. The relaxation phenomena observed in an extensive set of measurements of electrical conductivity and permittivity close to percolation can also be interpreted through the same cluster-forming mechanism, which reproduces the most relevant features of the frequency-dependent complex dielectric constant of this system.

The three-component ionic microemulsion system consisting of AOT/water/decane shows an unusual phase behavior in the vicinity of room temperature. The phase diagram in the temperature-volume fraction (of the dispersed phase) plane exhibits a lower consolute critical point at about 40 degrees centigrades and 10% volume fraction. A percolation line, starting from the vicinity of the critical point, cuts across the plane, extending to high volume fraction side at progressively lower temperatures. In this paper we review the evidence that allows to interpret the phase behavior of our system in terms of interacting spherical droplets. We also investigate the dynamics of droplets, below and approaching the critical point by dynamic light scattering. The first cumulant and time evolution of the droplet density correlation function can be quantitatively calculated by assuming the existence of polydispersed fractal clusters formed by the microemulsion droplets due to attraction. The relaxation phenomena observed in an extensive set of measurements of electrical conductivity and permittivity close to percolation is also reviewed and interpreted through the same cluster-forming mechanism, which reproduces the most relevant features of the frequency-dependent complex dielectric constant of this system.

An extended phase diagram for an ionic microemulsion system made of water, n-decane, and the ionic surfactant sodium-di-2 ethyl-hexyl sulfosuccinate is deduced from a very extensive set of electrical-conductivity and neutron-scattering measurements. This diagram shows high-temperature phase transitions that explain some original features previously not reported. Furthermore we propose a phenomenological model based on the solution of a Poisson-Boltzmann equation which accounts well for electrical conductivity data we obtain in the lamellar phase.

We report on the extension of the droplet model to account for static and dynamic light scattering studies of a ternary water-in-oil microemulsion close to its critical point. This model, which assumes that the critical microemulsion droplets are forming transient polydisperse fractal aggregates, reproduces well the usual features of critical phenomena and is also able to account, in a very natural way, for the dynamical background effects evidenced experimentaly.

We study static electrical conductivity of water-in-oil microemulsions in the single-phase region. Below the percolation threshold, the data can be interpreted in terms of a fluctuating-charge model. Above the percolation threshold, in the lamellar region, the conductivity is consistent with randomly oriented water layers separated by surfactant sheets. The loci of the percolation thresholds are measured for different values of water to surfactant molar ratio and explained in terms of a continuum percolation model

We study the static electrical conductivity of microemulsions in the single-phase region below the percolation threshold, where the data are interpreted in terms of a fluctuating charge model, and in the lamellar phase above percolation, where conductivity is due to randomly oriented water layers.

We review a series of investigations of the static and dynamic properties of a three‐component water‐in‐oil microemulsion system in which the molar ratio of water to surfactant is kept constant. This system behaves effectively like a two‐domponent macromolecular fluid in which there are spherical, surfactant coated water droplets of macroscopic dimensions dispersed in a continuum of oil. The properties investigated include electrical conductivity, dielectric relaxation, shear viscosity and viscoelastic relaxation, static neutron and light scattering and dynamic light scattering. We focus mainly on the phenomena of the dynamic slowing‐down of the dielectric relaxation and the droplet density fluctuations as the system approaches the percolation threshold from below, both in temperature and in volume fraction. A theory of static and dynamic light scattering, formulated along the lines of scattering from a system of polydisperse fractal clusters, quantitatively accounts for the dynamic slowing‐down phenomenon and the non‐exponential decay of the time correlation function.

The dynamic slowing down of the first cumulant and the stretched exponential decay of the droplet density-time correlation function at long time, previously observed for the one-phase sodium-di-2-ethylhexylsulfosuccinate (AOT)-water-decane microemulsion system, are attributed to the approach to a percolation threshold as the volume fraction of the microemulsion is increased at constant temperature. A model for dynamic light scattering, formulated along the line of the scattering from a system of transient polydispersed fractal clusters, quantitatively accounts for all the light-scattering data reported so far and also for some additional results

We report on critical phenomena in multicomponent fluids consisting of three‐component Water/Oil/Surfactant microemulsions and on nonionic surfactant/water/binary mixtures. Due to the existence of aggregates of quasi‐macroscopic sizes, static and dynamic background effects become important. A method of analysis of experimental data, involving both mode coupling equations and the linear model equation of states, is developed. All the available experimental results can be very well explained by the mode‐coupling theory involving 3‐d Ising critical exponents.

We report experimental and theoretical results on extensive static and dynamic light scattering studies of a ternary water-in-oil one phase microemulsion formed in a AOT/Water/Decane mixture. Close to the percolation threshold, all the experimental data obtained by different authors can be very well accounted for by a theoretical model extending previous works of Chen and Teixeira and Martin et al. on colloidal aggregates and sol-gel transition. This model which assumes that the microemulsion droplets are forming transient polydispersed fractal aggregates, shows that like critical phenomena, percolation can be described by universal scaling laws involving universal indices.

We report in this lecture critical phenomena in multicomponent fluids consisting of solutions of supramolecular aggregates such as three-component Water/Oil/Surfactant microemulsions or micellar systems formed from mixtures of water and a non-ionic surfactant. Due to the existence of aggregates of quasi-macroscopic sizes, static and dynamic background effects become important. A comprehensive method of analysis of experimental data, involving both mode coupling equations and the linear model equation of states, is developed. This method allows us to compare data obtained by different authors for the solutions along critical and of-critical isochores. All the available experimental results can be very well explained by the mode-coupling theory involving 3-d Ising critical exponents, provided that the static and dynamic background effects are properly taken into account.

Three-component mixtures of sodium di-2-ethyl-hexylsulfosuccinate (AOT), water and decane, having a fixed molar ratio of water to AOT equal to 40 but with different amount of decane, form one-phase microemulsions in the vicinity of room temperature. The microemulsion consists of spherical droplets of water, coated by mono-layers of AOT, dispersed in continuous medium of decane. The average radius of the droplets is about 85 A with a polydispersity of 25%. By varying the relative amount of decane, the volume fraction of the doplets can be varied continuously from 10 to 70%, simulating gas and liquid phases of simple fluids. The phase diagram of this model microemulsion system, in the temperature-volume fraction ( T − φ )-plane, shows a lower miscibility gap at low φ with a lower consolute temperature of 40°C at a critical volume fraction of 10%. For φ > 40%, the isotropic, disordered microemulsions undergo a first order phase transformation to a lamellar structure upon heating to sufficiently high T . In addition, there is a percolation line cutting the one-phase region from low to high volume fractions starting near the consolute point. Extensive dynamic light scattering measurements have been used to study time-dependent droplet density correlation functions below and above the percolation temperatures, in both dilute and dense microemulsions. Evolution of the time correlation functions from an exponential to a stretched exponential decay, as the volume fraction and temperature are varied, is discussed in the light of the critical phenomenon, the percolation transition and a glass-like transition at volume fraction of 60%.

Extensive light scattering measurements, including the intensity, turbidity, and linewidth, on a three‐component microemulsion system consisting of mixtures of water, decane, and a surfactant sodium di‐2 ethylhexylsulfosuccinate (AOT) (WDA), have been made. The critical and several off‐critical mixtures have been studied along constant microemulsion droplet volume fraction lines in the one‐phase region over a very large temperature range. In the vicinity of the lower phase separation temperature Tp the intensity data are very well accounted for by the standard theory of critical binary fluids using a single value for the short range correlation length ξ0=(13.5±1.5) A. By combining a mode‐coupling theory including the background effects and a linear model equation of state applicable in the critical region, we have been able to fit the dynamic light scattering data using a Debye cutoff length q−1D which is equal to the constant average diameter of microemulsion droplets. Furthermore, we find clear evidence...

Light beating spectroscopy experiments were performed on concentrated W/O microemulsions located in the vicinity of the gel phase on the phase diagram. New results are reported: the most interesting feature is the non-exponential behaviour of the self-correlation function g (1)(K, τ) of the scattered field. The initial decay rate of g (1)(K, τ) is not directly proportional to K 2; whereas the long time decay is found fairly exponential.

An extensive static and dynamic light-scattering experiment on a water-in-oil microemulsion system (water/n-decane/AOT) showed that the critical dynamics of this three-component microemulsion is completely governed by a Debye cut-off wavenumber qD, which is equal to the inverse diameter of the microemulsion droplet. Furthermore, the authors found occurrence of a crossover phenomenon for the statics and dynamics, at a correlation length xi c such that qD xi c=1, the crossover temperature being at about 10 degrees C below the critical temperature.