Small-angle light scattering studies of dense AOT-water-decane microemulsions

Summary We have performed extensive studies of a three-component microemulsion system composed of AOT-water-decane (AOT=sodium-bis-ethylhexyl-sulfosuccinate is an ionic surfactant) using small-angle light scattering (SALS). The small-angle scattering intensities are measured in the angular interval 0.001–0.1 radians, corresponding to a Bragg wave number range of 0.14 μm⁻¹<Q<<1.4 μm⁻¹. The measurements were made by changing temperature and volume fraction ϕ of the dispersed phase (water + AOT) in the range 0.05<ϕ<0.75. All samples have a fixed water-to-AOT molar ratio,w=[water]/[AOT]=40.8, in order to keep the same average droplet size in the stable one-phase region. With the SALS technique, we have been able to observe all the phase boundaries of a very complex phase diagram with a percolation line and many structural organizations within it. We observe at the percolation transition threshold, a scaling behavior of the intensity data. This behavior is a consequence of a clustering among microemulsion droplets near the percolation threshold. In addition, we describe in detail a structural transition from a droplet microemulsion to a bicontinuous one as suggested by a recent small-angle neutron scattering experiment. The loci of this transition are located several degrees above the percolation temperatures and are coincident with the maxima previously observed in shear viscosity. From the data analysis, we show that both the percolation phenomenon and this novel structural transition are derived from a large-scale aggregation between microemulsion droplets.     

A study of the properties of mixed nonionic surfactants microemulsions by NMR, SAXS, viscosity and conductivity

The pseudoternary phase behavior of the water/sucrose laurate/ethoxylated mono-di-glyceride/R (+)-limonene systems was investigated for different surfactants mixing ratios (w/w) at 25 °C. The microemulsion boundaries were determined and the surfactants content at the interface of water- R (+)-limonene was estimated. For surfactants mixing ratio (w/w) equals unity, the area of the one phase microemulsion region reaches its maximum. The system with the maximum microemulsion area was investigated using electrical conductivity, dynamic viscosity, small angle X-ray scattering, and nuclear magnetic resonance. Electrical conductivity increases as the water volume fraction increases and a percolation threshold was observed. Dynamic Viscosity varies as function of the water volume fraction in a non-monotonic way giving two-peaked plot. The characteristics of the domain size of the microemulsions called periodicity measured by small angle X-ray scattering increases with the increase in the water volume fraction. The correlation length of the domain size reaches a maximum when plotted against the water volume fraction in the microemulsions. Relative diffusion coefficients of water increase and those of oil decrease with increasing the water volume fractions in the microemulsions indicating structural transitions.     

Small-angle light scattering in dense microemulsions,transition from droplet to bicontinuous phase

Summary We have performed extensive small-angle light scattering (SALS) measurements on a three-component microemulsion (AOT/decane/water) as a function of the dispersed phase concentration and the temperature. All samples have a water/AOT molar fractionw=40.8. Such a system presents a very complex phase diagram with many structural configurations. With the SALS technique, we have been able to observe all the phase separation lines. In particular we give details on the system structure on the percolation phenomenon and on the bicontinuous phase recently observed. In particular we show that the percolation is driven by a long-scale aggregation between microemulsion droplets. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Quantum critical end point for the Kondo volume collapse model

The Kondo volume collapse describes valence transitions in f-electron metals and is characterized by a line of first order transitions in the pressure-temperature phase plane terminated at critical end points. We analyze the quantum critical end point, when the lower end point is tuned to T=0, and determine the specific heat, thermal expansion, and compressibility. We find that the inclusion of quantum critical fluctuations leads to a novel bifurcation of the first order phase line. Finally, we show that critical strain fluctuations can cause both, superconductivity and non-Fermi liquid behavior near the critical point.     

Direct experimental verification of the isomorphism hypothesis for critical phenomena

The heat capacity at constant volume of a mixture of methane and 0.0345 mole fractions of heptane is experimentally studied over a wide range of densities and temperatures. In the case when the transition from a three-phase state takes place in the presence of a noncritical liquid phase, it is found that the behavior of the heat capacity in the vicinity of the upper end critical point is fully isomorphic with the behavior of the heat capacity in the vicinity of the liquid-vapor critical point of one-component fluid. It is shown that the measured quantity in this experiment is the heat capacity at constant volume and constant chemical potential μ of the heavy impurity component C _{v, μ}. Thus, it has been confirmed by direct measurements that the anomaly of this heat capacity completely coincides in character with the anomaly of the heat capacity at constant volume in the vicinity of the liquid-vapor critical point of one-component fluids.     

Renormalization group approach to the surface and defect critical behavior in the potts model

A simple real-space renormalization group method with two-terminal clusters is used to treat the critical behavior of Potts ferromagnet with free surface and defect plane on the same footing both for square and cubic lattices. For a square lattice, quite different critical behaviors are found for the cases of line defect and free surface. Whenq is larger than three, like the case ofa line type defect in ‘diamond’ hierarchical lattice, the order parameter on a defect line increases discontinuously at the bulk critical point if the defect interaction is sufficiently strong. This behavior, on the contrary, does not occur on the surface of a semi-infinite plane. For a cubic lattice, the phase diagram and renormalization group flow properties are obtained explicitly for bothq=1 (bond percolation) andq=2 (Ising model). In both cases, our calculations whow that the critical behavior on the surface of a semi-infinite system belongs to a different universality class from the critical behavior on the defect plane of a bulk system.     

Percolation phenomenon of calcium bis(2-ethylhexyl) sulfosuccinate water-in-oil microemulsions by conductivity and dielectric spectroscopy measurements

The sodium counterion (Na+) of the sodium bis(2-ethylhexyl) sulfosuccinate (AOT) surfactant was exchanged with calcium Ca2+ to investigate the counterion charge effect on the structure of water in normal decane microemulsions. Ohmic conductivity and dielectric permittivity measurements were performed on samples at constant water to surfactant mole ratio [water]/[Ca(AOT)(2)]=26.6. Increasing the volume fraction of the dispersed phase phi, a percolation phenomenon was observed at the constant temperature of 25 degrees C. The percolation threshold was found at phi approximately 15% by Ohmic conductivity and static dielectric permittivity studied as a function of phi, and by the frequency dependence of the complex permittivity. Critical exponents typical of the static percolation mechanism (formation of bicontinuous microemulsions) were found below and above threshold. The comparison of these results obtained for the two different counterions, Ca2+ and Na+, in AOT surfactant water in normal decane microemulsions allows detection of an important difference. The percolation below threshold is dynamic for the sodium-based microemulsions, accounting for the formation of clusters of droplets, whereas calcium-based microemulsions show a static percolation. For this system, the coalescence of droplets begins to occur below threshold at phi approximately 12%.     

Thermodynamic Derivation of Scaling at the Liquid–Vapor Critical Point

With the use of thermodynamics and general equilibrium conditions only, we study the entropy of a fluid in the vicinity of the critical point of the liquid–vapor phase transition. By assuming a general form for the coexistence curve in the vicinity of the critical point, we show that the functional dependence of the entropy as a function of energy and particle densities necessarily obeys the scaling form hypothesized by Widom. Our analysis allows for a discussion of the properties of the corresponding scaling function, with the interesting prediction that the critical isotherm has the same functional dependence, between the energy and the number of particles densities, as the coexistence curve. In addition to the derivation of the expected equalities of the critical exponents, the conditions that lead to scaling also imply that, while the specific heat at constant volume can diverge at the critical point, the isothermal compressibility must do so.     

A self-consistent Ornstein-Zernike approximation for the site-diluted Ising model

We propose a theory for the site-diluted Ising model which is an extension to disordered systems of the self-consistent Ornstein-Zernike approximation of Hoye and Stell. By using the replica method in the context of liquid-state theory, we treat the concentration of impurities as an ordinary thermodynamic variable. This approach is not limited to the weak-disorder regime or to the vicinity of the percolation point. A preliminary analysis using series expansion shows that it can predict accurately the dependence of the critical temperature on dilution and can reproduce the nonuniversal behavior of the effective exponents. The theory also gives a reasonable estimate of the percolation threshold.     

The stochastic geometry of invasion percolation

Invasion percolation, a recently introduced stochastic growth model, is analyzed and compared to the critical behavior of standardd-dimensional Bernoulli percolation. Various functions which measure the distribution of values accepted into the dynamically growing invaded region are studied. The empirical distribution of values accepted is shown to be asymptotically unity above the half-space threshold and linear below the point at which the expected cluster size diverges for the associated Bernoulli problem. An acceptance profile is defined and shown to have corresponding behavior. Quantities related to the geometry of the invaded region are studied, including the surface to volume ratio and the volume fraction. The former is shown to have upper and lower bounds in terms of the above defined critical points, and the latter is bounded above by the probability of connection to infinity at the half-space threshold. Provided that the critical regimes of Bernoulli percolation possess their anticipated properties, as is known to be the case in two dimensions, these results verify numerical predictions on the acceptance profile, establish the existence of a sharp surface to volume ratio and show that the invaded region has zero volume fraction. Large-time asymptotics are analyzed in terms of the probability that the invaded region accepts a value greater thanx at timen. This quantity is shown to be bounded below byh(x)exp[–c(x)n ^(d-1)/d ] forx above threshold, and to have an upper bound of the same form forx larger than a particular value (which coincides with the threshold ind=2). For two dimensions, it is also established that the infinite-time invaded region is essentially independent of initial conditions.National Science Foundation Postdoctoral Research Fellows. Work supported in part by the National Science Foundation under Grant No. PHY-82-03669John S. Guggenheim Memorial Fellow. Work supported in part by the National Science Foundation under Grant No. MCS-80-19384     

Monte Carlo study of the triangular XY vector Blume-Emery-Griffiths model

The vectorial generalization of the Blume-Emery-Griffiths model, proposed by Berker and Nelson to describe the behavior of films of ³He-⁴He mixtures, is studied by Monte Carlo simulations on the triangular lattice. The temperature versus chemical potential plane phase diagram, for a biquadratic coupling constant equal to the bilinear coupling constant, presents a Berezinzkii-Kosterlitz-Thouless transition line that ends in a first-order transition line at a critical end point. This first-order transition line, on the other hand, terminates at a single critical point. No tricritical point has been detected. The critical exponent η as a function of temperature is independent of the chemical potential.     

Electrical and optical properties of indium tin oxide/epoxy composite film

The electrical and optical properties of the indium tin oxide(ITO)/epoxy composite exhibit dramatic variations as functions of the ITO composition and ITO particle size. Sharp increases in the conductivity in the vicinity of a critical volume fraction have been found within the framework of percolation theory. A conductive and insulating transition model is extracted by the ITO particle network in the SEM image, and verified by the resistivity dependence on the temperature.The dependence of the optical transmittance on the particle size was studied. Further decreasing the ITO particle size could further improve the percolation threshold and light transparency of the composite film.     

Entropic phase separation in polymer-microemulsion networks

We study theoretically a model system of a transient network of microemulsion droplets connected by telechelic polymers and explain recent experimental findings. Despite the absence of any specific interactions between either the droplets or polymer chains, we predict that as the number of polymers per drop is increased, the system undergoes a first-order phase separation into a dense, highly connected phase, in equilibrium with dilute droplets, decorated by polymer loops. The phase transition is purely entropic and is driven by the interplay between the translational entropy of the drops and the configurational entropy of the polymer connections between them. Because it is dominated by entropic effects, the phase behavior of the system is extremely robust and is independent of the detailed properties of either polymers or drops.     

The singular points and phase diagram of the supercritical region of a substance

This paper suggests using the supercritical point and the maximum fluctuation point on the supercritical isotherm for the analysis of the behavior of various substances in the vicinity of the critical point. These three points lie at the vertices of a triangle that is formed by the supercritical isotherm, the line of the local minima of stability, and the line of maxima of fluctuations. In this triangle, which is called supercritical, the fluctuations and instability behave such that this part of the phase surface is most interesting from the viewpoint of performing various chemical reactions. Here, large fluctuations and the stability of the system rapidly decrease with increasing volume. This region is studied in the approximation of the van der Waals and Van Laar equations.     

Conserved Manna model on Barabasi–Albert scale-free network

In this paper, a conserved Manna model is constructed and studied on Barabasi–Albert scale-free network with degree exponent γ = 3. Numerically I show that the system undergoes an absorbing state phase transition when the particle density is varied. Such a phase transition is characterized by measuring several critical exponents associated with the critical behaviour of the model. It has been found that the critical exponents exhibit mean field values of directed percolation. At the critical point, the spreading exponents have also been estimated. They satisfy the usual scaling relations. The effect of various initial conditions has been investigated and the result found to be independent of initial conditions, contrary to the fact that critical behaviour of such model highly depends on initial conditions when studied on regular lattice. The study confirms that though the Manna model in the lower dimensions exhibits different critical behavior other than DP, in the scale-free network it exhibits similar mean field result of DP class.     

Continuous spin-reorientation phase transition in the surface region of an inhomogeneous magnetic film

A continuous spin-reorientation transition from a uniform magnetic state with the in-plane orientation of the moments of all atomic layers to a nonuniform canted state in the surface region is considered. This transition was discovered in experiments on the divergence of magnetic susceptibility in a perpendicular magnetic field at a temperature of about 240 K, which is lower than the Curie point of gadolinium, equal to 292.5 K. These experiments were carried out on an ultrathin iron magnetic film deposited on the (0001) surface of a thin gadolinium film. It is shown that, in the vicinity of the spin-reorientation transition, the thermodynamic potential has a form characteristic of the Landau theory of second-order phase transitions. The orientation angle of the moment of the surface atomic layer with respect to the plane of the film, which is chosen as an order parameter, exhibits anomalous behavior and increases with temperature. Expressions are derived for the magnetic susceptibility of each atomic layer. It is shown that, in the vicinity of the transition, the irregular part of the magnetic susceptibility of each atomic layer exhibits behavior characteristic of the susceptibility in the Landau theory: it is less by a factor of two in the low-symmetry phase and diverges at the transition point. The regular part of the magnetic susceptibility of each atomic layer makes an additional contribution to the asymmetry of the total susceptibility in the vicinity of the transition point; this result follows from the fact that the inhomogeneous magnetic system considered is semi-infinite.     

Experimental evidence for crossover to mean-field tricritical behavior in a concentrated salt solution

We have discovered a mean-field multicritical point on the critical locus in an aqueous solution of 3-methylpyridine and sodium bromide. Light-scattering measurements indicate Ising-like asymptotic critical behavior at the lower salt concentrations. However, the temperature range of Ising critical behavior shrinks with increasing salt concentration and the critical behavior becomes mean-field-like at a concentration of about 17% mass fraction of NaBr. Emergence of a new characteristic length scale diverging at this point and a simultaneous pronounced increase in the background scattering suggests mean-field tricritical behavior associated with the formation of a microheterogeneous phase due to clustering of ions and molecules.     

Microscopic description of an Ising spin glass near the percolation threshold

Monte Carlo results using a microscopic model to describe FexZn(1-x)F2 indicate that its spin-glass phase at x=0.25 and zero magnetic field is characterized by the presence of antiferromagnetic fractal domains, separated by random vacancies and strongly correlated in time. The effective local random-field distribution corroborates this glassy behavior, which emerges irrespective of ab initio competing interactions and is a consequence of the fractal domain structure near the percolation threshold, x(p)=0.24. The aging properties of the system are in agreement with predictions of short-range stochastic spin-glass models and with the droplets model for spin glass close to percolation.     

High-field vs. low-field magneto-transport in a percolating medium

Recent theoretical and numerical work on high-field magneto-transport in a percolating medium is described and compared to earlier work on weak-field magneto-transport in such systems. While the weak-field behavior is well described by the simple nodes-links picture, which ignores blobs and loops on a scale smaller than the percolation correlation length ξ_p, the strong-field behavior is extremely sensitive to those features. The critical behavior at strong magnetic fields H near the percolation threshold is governed by competition between the usual H=0 fixed point and a new H=∞ fixed point. Which of those fixed points dominates the behavior is determined by the relative sizes of two characteristic lenghts: the percolation correlation length ξ_p and a new, magnetic field dependent length ξ_H.