Isotropic systems, component behavior

For an isotropic system where there is no preferred direction, the component behavior is given accordingly by... 

Microemulsions are defined as dispersion of either water in oil or oil in water aided by mixed amphiphiles to produce transparent, isotropic, low viscous, thermodynamically stable solution systems. A microheterogeneous system of microemulsion with nanodispersion of one liquid into another must have a very low (about zero) interfacial tension caused by the presence of amphiphiles at the interface. In addition, the interfacial region must be highly flexible, either to permit the curvature required to surround exceedingly small particles or to allow the easy transition from oil-continuous to water-continuous structure, which is an important physicochemical feature of microemulsion. Along with the concept of nanodispersed droplets of either water in oil or oil in water, there is another concept of simultaneous dispersion of both water and oil in a system termed as bicontinuous where both the liquids are dispersed nearly in equal proportions. A microemulsion system can be one of the three types depending on the relative ratios of the constituting components. To achieve formation of any such system, phase behavior of the multicomponent (oil, water, amphiphile) systems is required to be studied, which is complex and has been elaborately... 

The solution behavior of polymers has been intensively investigated in the past. Dilute solutions, where polymer-polymer interactions may be excluded, have become the basis for the characterization of the primary structure of macromolecules and their dimensions in solution. Besides this "classical" aspect of macromolecular science, interest has focussed on systems, where - due to strong polymer/polymer interactions - association of polymers causes supermolecular structures in homogeneous thermo-dynamically-stable isotropic and anisotropic solutions or in phase-separated multi-component systems. The association of polymers in solutions gives rise to unconventional properties, yielding new aspects for applications and multiple theoretical aspects. 

Most micromechanical theories treat composites where the thermoelastic properties of the matrix and of each filler particle are assumed to be homogeneous and isotropic within each phase domain. Under this simplifying assumption, the elastic properties of the matrix phase and of the filler particles are each described by two independent quantities, usually the Young s modulus E and Poisson s ratio v. The thermal expansion behavior of each constituent of the composite is described by its linear thermal expansion coefficient (3. It is far more complicated to treat composites where the properties of some of the individual components (such as high-modulus aromatic polyamide fibers) are themselves inhomogeneous and/or anisotropic within the individual phase domains, at a level of theory that accounts for the internal inhomogeneities and/or anisotropies of these phase domains. Consequently, there are very few analytical models that can treat such very complicated but not uncommon systems truly adequately. 

Much information is available on the deformation and fatigue behavior of simple thick-walled cylinders [10-17], but it must be remembered that most process reactors will not be a simple hollow cylinder. Components such as connectors, threads and sleeves, windows, and removable closures make a complete analytical solution for a high-pressure system design problem quite involved. Useful design criteria for thick-walled vessels can be derived, however, under the assumption that the material of which the vessel is made is isotropic and that the cylinder is long (more than five diameters) and initially free from stress. The radial and tangential stresses in the walls are then only functions of the radius coordinate (r) and the internal pressure. Given the outer-to-inner wall radius ratio as o/i = w, and the yield point (To) of the material, the yield pressure (py) is... 

Surfactant molecules commonly self-assemble in water (or in oil). Even single-surfactant systems can display a quite remarkably rich variety of structures when parameters such as water content or temperature are varied. In dilute solution they form an isotropic solution phase consisting of micellar aggregates. At more concentrated surfactant-solvent systems, several isotropic and anisotropic liquid crystalline phases will be formed [2]. The phase behavior becomes even more intricate if an oil (such as an alkane or fluorinated hydrocarbon) is added to a water-surfactant binary system and the more so if other components (such as another surfactant or an alcohol) are also included [3], In such systems, emulsions, microemulsions, and lyotropic mesophases with different geometries may be formed. Indeed, the ability to form such association colloids is the feature that singles out surfactants within the broader group of amphiphiles [4]. No wonder surfactants phase behavior and microstructures have been the subject of intense and profound investigation over the course of recent decades. 

These experimental findings have given impulse to the study of simple isotropic models that are able to display anomalous behaviors, as a way to understanding the basic mechanisms of such behaviors. These systems can be appropriate generic models for pure metals, metallic mixtures, electrolytes, and colloids, ft has been found that unusual behaviors may arise in systems of spherical particles (simple fluids) where the unbounded repulsive core is softened through the addition of a finite repulsion at intermediate distances, so as to generate two distinct length scales in the system a hard one, related to the inner core, and a soft one, associated with the soft, penetrable, component of the repulsion [57-81]. Due to... 

S. V. Buldyrev, G. Malescio, C. A. Angell, N. Giovambattista, S. Prestipino, and F. Saija, et al. Unusual phase behavior of one-component systems with two-scale isotropic interactions. J. Phys. Condens. Matteril, 504106 (2009). 

Suppose that the piezoelectric thin film is bonded to an isotropic elastic substrate that does not exhibit piezoelectric behavior. If this film-substrate system is exposed to an electric field 8, then the film material will tend to undergo the stress-free strain specified by (3.83). However, the film is constrained from deforming freely by the substrate. As a result, a stress is generated in the film, and this stress may result in a detectable curvature of the substrate. If the X3—axis is normal to the film-substrate interface then the components of mismatch strain in the film are, in reduced notation. 

Table 1 summarizes the classes of phase behavior found for these polar/nonpolar systems, using an argon-krypton reference system, and compares it with the behavior for simple nonpolar Lennard-Jones systems. An important difference between the two types of systems is that the Lennard-Jones mixtures do not form azeotropes, and appear to exhibit class II behavior only when the components have very different vapor pressures and critical temperatures (T j /Ta > 2). In practice, the liquid ranges of the two components would not overlap in such cases, so that liquid-liquid immiscibility (and hence class II behavior) would not be observed in Lennard-Jones mixtures (the only exception to this statement seems to be when the unlike pair Interaction is improbably weak). Thus, the use of theories based on the Lennard-Jones or other Isotropic potential models cannot be expected to give good results for systems of class II, and will probably give poor results for most systems of classes III, IV and V also. 

In order to describe the behavior of an anisotropic material. Hook s law can be written in completely general terms [42]. This requires that six strain components and 36 elastic coefficients be known in order to calculate the stress. S)mmietry considerations are such that even for the least S5Tnmetrical crystal structure, trichnic, the number of independent elastic constants required is reduced to 21. For metals, whose crystal systems all exhibit relatively high degrees of symmetry, the number of constants is further reduced to 12. Anisotropic materials such as magnesium, zinc, and tin require at least five elastic constants. Materials with cubic crystal structures require three independent elastic constants, while a truly isotropic material requires only two elastic constants. 

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