Single-component systems phase transitions

Many technological applications of liquid crystals, as in electro-optic display devices, are based on multicomponent mixtures. Such systems offer a route to the desired material properties which cannot be achieved simultaneously for single component systems. Mixtures also tend to exhibit a richer phase behaviour than pure systems with features such as re-entrant nematic phases [3] and nematic-nematic transitions possible. In this section, we describe simulations which have been used to study mixtures of thermotropic calamitic mesogens. 

This chapter introduces additional central concepts of thermodynamics and gives an overview of the formal methods that are used to describe single-component systems. The thermodynamic relationships between different phases of a single-component system are described and the basics of phase transitions and phase diagrams are discussed. Formal mathematical descriptions of the properties of ideal and real gases are given in the second part of the chapter, while the last part is devoted to the thermodynamic description of condensed phases. 

Considerable spread is also observed in reported enthalpies of transition in single-component systems. As an example, the reported enthalpy of the first-order transition giving the fast ionic conductor phase of Agl at 420 K are compared in Table 10.5. In general, the agreement between the results obtained by adiabatic or... 

Franzese G., Malescio G., Skibinsky A., Buldyrev S., Stanley H. (2002) Metastable liquid-liquid phase transition in a single-component system with only one crystal phase and no density anomaly, Phys. Rev. A, 66(5), 051206-051220. 

The thermodynamics of the discontinuity surface can be examined by analyzing how the density of free energy f changes upon transition from one phase to another. From thermodynamics one can establish the relationship between the free energy, F, the isobaric-isothermal potential, f/, and the chemical potential, p, for a single component system ... 

In single-component systems (or pure substances), the chemical composition in all phases is the same. In multicomponent systems, the chemical composition of a given phase changes in response to pressure and temperature changes and these compositions are not the same in all phases. For single-component systems, first-order phase transitions occur with a discontinuity in the first derivative of the Gibbs free energy. In the transitions, T and p remain constant. 

Phase diagrams of single-component systems are useful in illustrating a simple idea that answers a common question How many variables must be specified in order to determine the phase(s) of the system when it s at equilibrium These variables are called degrees of freedom. What we need to know is how many degrees of freedom we need to specify in order to characterize the state of the system. This information is more useful than one might think. Because the position of phase transitions (especially transitions that involve the gas phase) can change quickly... 

Consider a closed, single-component system described by the van der Waals (vdW) equation of state, which was introduced in Chapter 8. In Figure 8.4, the pressure is plotted as a function of the molar volume, V = (V/N), at various temperatures. These isotherms describe the fluid states of substances. What is remarkable about the van der Waals equation of state, for which van der Waals was awarded a Nobel prize in 1910, is that although very simple, it describes and predicts a first-order gas-liquid transition. In this section we discuss in detail this phase behavior of simple fluids. 

Phase rule of Defay-Crisp describing the number of degrees of freedom for a system having one single plane surface (monolayer) Multi-component monolayers consisting of immiscible amphiphiles exhibit the same surface pressure for phase transitions and collapse points as the corresponding one-component monolayers, while these surface-pressures are different for mixtures of miscible amphiphiles. 

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