Phase diagrams of two-component systems

Surfactant Aggregation at High Concentrations. Phase Diagrams of Two-Component Systems... 

The phase diagrams of two-component systems are represented in the two-dimensional space, where the composition is shown on the x axis (in molar or in mass fractions) in agreement with the lever rule, and the temperature is given on the y axis (in °C or in Kelvin). They are the so-called isobaric diagrams, since the constant pressure, mostly the atmospheric one, is assumed. The Gibbs phase law attains thus the form... 

Fig. 1 Phase diagram of two-component system. Left panel system with UCST right panel system with LCST. Interior curves spinodal exteric curves binodal.

Figure 6.1. Phase diagrams of two-component systems. Left system with UCST. Right system with LCST. Interior curves spinodal. Ej -rior curves binodal.

Flalf a century later Van Konynenburg and Scott (1970, 1980) [3] used the van der Waals equation to derive detailed phase diagrams for two-component systems with various parameters. Unlike van Laar they did not restrict their treatment to the geometric mean for a g, and for the special case of b = hgg = h g (equalsized molecules), they defined two reduced variables. 

In phase diagrams for two-component systems the composition is plotted vs. one of the variables of state (pressure or temperature), the other one having a constant value. Most common are plots of the composition vs. temperature at ambient pressure. Such phase diagrams differ depending on whether the components form solid solutions with each other or not or whether they combine to form compounds. 

The phase diagrams of two-component surfactant-water systems are typically quite different for nonionic and ionic compounds. As exemplified in Fig. 2.22 there are at low temperatures different liquid crystalline phases while at intermediate temperatures there may be a total mutual solubility of surfactant and water98. At higher temperatures, there is, as already noted, a separation into two phases with a very large two-phase region. One of the phases contains very little surfactant, while the other contains appreciable amounts of both components. The cloud-point curve can be described as a liquid-liquid solubility curve with a lower consolute tempera-... 

In conclusion, we have demonstrated that linear A-B-C block copolymers can form the double-diamond morphology, but not gyroid. It is evident that the simulation method is useful for investigating morphologies of block copolymer systems. Future studies should include the phase diagram of two-component block copolymers. 

To determine the complete phase diagram of a ternary system as a function of temperature, at least a three-dimension diagram is necessary. Such diagrams are unfortunately quite difficult to visualize and it is often preferable to reduce the diagrams to two dimensions by keeping the concentration of some of the components constant. Some results for the BE-H2O phase diagram as a function of temperature for fixed quantities of DEC are shown in Fig. 4. In this diagram the mole fraction of BE refers to the binary system... 

The phase diagram of such a system has four planes. The plane pc(A) is the vertical projection of the plane of primary crystallization of the compound A, plane pc(B) represents the plane of primary crystallization of the component B, and the plane pc(C) refers to the primary crystallization of compound C. Finally, the plane pc(AB) is the projection of the plane of primary crystallization of compound AB. In the case of the congruently melting compound AB its figurative point lies inside the plane of the primary crystallization of this compound. In comparison with the simple eutectic ternary system a new boundary line, Ctj - Ct2, which represents the common crystallization of compounds C and AB, will arise. The joint AB-C divides the ternary system A-B-C into two simple... 

Setting aside any consideration of solvate species or considerations of chemical reaction, systems of polymorphic interest consist of only one component. The complete phase diagram of a polymorphic system would provide the boundary conditions for the vapor state, the liquid phase, and for each and every true polymorph possible. From the phase rule, it is concluded that the maximum amount of variance (two degrees of freedom) is only possible when the component is present in a single phase. All systems of one component can therefore be perfectly defined by assigning values to a maximum of two variable factors. However, this bivariant system is not of interest to our discussion. 

When a single component is in equilibrium between two phases, the phase rule predicts that it must be a univariant system exhibiting only one degree of freedom. It is worthwhile to consider several univariant possibilities, since the most complicated phase diagram of a polymorphic system can be broken down into its component univariant systems. The phase rule applies equally to all of these systems, and all need to be understood for the entire phase diagram to be most useful. 

In a one-component, or unary, system, only one chemical component is required to describe the phase relationships, for example, iron (Fe), water (H2O) or methane (CH4). There are many one-component systems, including all of the pure elements and compounds. The phases that can exist in a one-component system are limited to vapour, liquid and solid. Phase diagrams for one-component systems are specified in terms of two variables, temperature, normally specified in degrees centigrade,... 

Table SI. 4 A comparison of phase diagrams of one-component and two-component systems...

Four different types of two-component system will now be considered. Detailed attention is paid to the first type solely to illustrate the information that can be deduced from a phase diagram. It will be noted that the concentration of a solution on a phase diagram is normally given as a mass fraction or mass percentage and not as mass of solute per unit mass of solvent , as recommended for the solubility diagram (section 3.3). Mole fractions and mole percentages are also suitable concentration units for use in phase diagrams. 

Some comments must be made about phase diagrams, abounding in the literature, which show areas of stability of the different phases / phase assemblages. A phase diagram for two-component to higher-component systems is a compositional map showing areas or volumes (called primary phase fields ) within... 

Fig 1 Diagrams of basic types of two-component system where vapor and one liquid phase are in equilibrium. 

Examples of phase diagrams (a) one-component system (water), (b) two-component system (naphtalene/benzene). 

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