Abstract
We used dynamic light scattering to study the characteristic droplet size, in dilute single-phase microemulsions near the critical phase transition point. We found that there existed a general power-law dependence of f on point. We found that there existed a general power-law dependence of f on the reduced variable = . Here stands for any thermodynamic and system variables whose critical value is denoted by . The variables of interest in the present work are temperature and alkane carbon number (ACN). It is found that where = . This is observed both in water- and oil-internal microemulsions, independent of the surfactant properties. This behavior, known as the scaling behavior, was analyzed in terms of generalized homogeneous functions with as the degree of homogeneity. It turns out that only one of the reduced variables is an independent variable in these functions, greatly simplifying the description of the properties of microemulsions in the neighborhood of a critical phase boundary.
Introduction
Critical phenomena have been under intensive investigation for the past 20 years by physicists and physical chemists. There are several reasons for this subject to attract so much attention.
SINGULARITIES.
A large number of thermodynamic properties, especially ones related to the second-order derivative of the free energy, become singular (in a mathematical sense) at the critical point.
UNIVERSALITY.
There exists a universal description (scaling laws) of the singular behavior of all the corresponding thermodynamic parameters in a large number of vastly different systems. These range from simple liquid/gas mixtures, liquid crystals, and magnetic alloys to the quantum mechanical superfluids.
NONCLASSICAL BEHAVIOR.
Though critical properties are macroscopic properties pertaining to the bulk phases, classical thermodynamics is properties pertaining to the bulk phases, classical thermodynamics is inadequate to explain quantitatively what happens in the neighborhood of the critical points.
NEW PARAMETERS.
Geometric properties (such as the symmetry group of the so-called "order parameter") and spatial dimensionality of the system are more important than the nature of basic interactions that produce the phase transition. phase transition. Great progress has been achieved, both experimentally (such as dynamic light scattering) and theoretically (such as the powerful scaling laws and renormalization group theories), in the study of critical phenomena. As a result, a vast amount of knowledge has been accumulated on the subject in recent years. Critical phenomena may also play an important role in the understanding of the fundamental mechanism in EOR by microemulsions and micellar solutions. Microemulsions do exhibit unmistakable critical behavior in certain composition and temperature ranges near the cloud point of a homogeneous system. There are many ways to cause a homogeneous microemulsion to split into a multiphase system. When any of the system variables, such as the temperature, salinity, composition of the oil, and concentration of the dispersed phase, are changed in such a manner that the resultant phase transition occurs in the neighborhood of a plait point, which corresponds to a vanishing tie line, then the system will exhibit critical phenomena. All critical transitions are characterized by pronounced thermodynamic fluctuations. These fluctuations are described by a con-elation length that diverges at the critical point, causing a strong scattering of light known as the critical opalescence, a feature that is also observed in microemulsions. By definition, the correlation length diverges at the critical value, Zc, of the corresponding system variable, . Therefore, the reduced variable delta Z = Zc -Z expresses a measure of a "thermodynamic distance" to the critical point. We use the lower-case letter z = delta Z/Zc to denote the dimensionless scaled variables that are important for the description of the universal behavior of a microemulsion near a critical phase boundary. In the neighborhood of the critical point, the physical phase boundary. In the neighborhood of the critical point, the physical properties of the microemulsion systems depend on some universal function properties of the microemulsion systems depend on some universal function of scaled variables only, independent of the chemical makeup of the system. We call this the critical scaling behavior.
Experimental Procedure
MICROEMULSION SYSTEM.
We have chosen two model microemulsions for our study. One is a simple pure three-component oil-continuous system containing pure normal alkanes, distilled water, and a surfactant commonly known as AOT. This surfactant, sodium di-2-ethyl hexylsulfosuccinate, was twice recrystallized from hexane over activated charcoal. The other is a water-continuous system composed of 8% NaCl brine solution, normal alkanes and a combined surfactant (hepta-ethoxylated octadecyl methyl ammonium-i-dodecyl-o-xylene sulfonates).
SPEJ
p. 197
Exploration of Hard to Solve 3-sat Problems
