Phases and phase transitions

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. 

1 Phases, phase transitions and phase diagrams Phases and phase transitions 

In Chapter 1 we introduced the term phase. A phase is a state that has a particular composition and also definite, characteristic physical and chemical properties. We may have several different phases that are identical in composition but different in physical properties. A phase can be in the solid, liquid or gas state. In addition, there may exist more than one distinct crystalline phase. This is termed polymorphism, and each crystalline phase represents a distinct polymorph of the substance. 

A transition between two phases of the same substance at equilibrium is called a first-order phase transition. At the equilibrium phase transition temperature the equilibrium condition eq. (1.84) yields 

Chemical Thermodynamics of Materials by Svein St0len and Tor Grande 2004 John Wiley Sons, Ltd ISBN 0 471 492320 2 

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Litster J D and Birgeneau R J 1982 Phases and phase transitions Phys. Today 35 26-33... 

Fundamental membrane research has benefited greatly from the study of monolayers. One of the most important discoveries from this sort of research is the very existence of two-dimensional phases and phase transitions. Generally, studies of the sort that can be carried out with monolayers and bilayers cannot be directly extended to living cells, but some exceptional cases have shown that the extrapolation is valid. For example, it is known from monolayer studies that the presence of unsaturated hydrocarbon chains in lipid monolayers prevents some phase transitions from occurring as the temperature is lowered. Certain mutants of Escherichia coli are unable to synthesize fatty acids and hence can be manipulated through the compounds they are provided as nutrients. Abnormal levels of saturated hydrocarbon can... 

Numerous studies about phases and phase transitions detected by optical investigations of f elements have been published by Haire, Peterson, and co-workers. In many cases they used the Eu3+ ion to correlate the luminescence properties with structural changes. The Eu3+ ion exhibits a variety of characteristic transitions serving as a fingerprint for the structure (Chen et al., 1992e). However, in view of the problematic situation with respect to the local symmetry in the case of doped ions mentioned above, there has been some discussion on whether the Eu3+ ion or f elements in general can be used as indicators of the actual host structure or not (Tanner and Rudowicz, 1993 Stump et al., 1993). In summary, it must be concluded that the spectral/structural correlation has limitations especially in the case of doped ions where deviations between local and real site symmetry may readily occur. 

Koynova R, Caffrey M. Phases and phase transitions of the phosphatidylcholines. Biochim. Biophys. Acta-Rev. Biomembranes 54. 1998 1376 91-145. 

Pabst G, Amenitsch H, Kharakoz DP, Laggner P, Rappolt M. Structure and fluctuations of phosphatidylcholines in the vicinity of the main phase transition. Phys. Rev. E 2004 70 021908. Koynova R, Caffrey M. Phases and phase-transitions of the hydrated phosphatidylethanolamines. Chem. Phys. Lipids 1994 69 1-34. 

Yamanaka T, Fukumori Y (1995) Molecular aspects of the electron transfer system which participates in the oxidation of iron by Thiobacillus ferrooxidans. FEMS Microbiol Rev 17 401-413 Yanagisawa K, Ovenstone J (1999) Crystallization of anatase from amorphous titania using the hydrothermal technique Effects of starting material and temperature. J Phys Chem B 103 7781-87 Yang J, Mei S, Ferreira IMF (2000) Hydrothermal synthesis of nanosized titania powders lirfluence of peptization and peptizing agents on the crystalline phases and phase transition. J Am Ceram Soc 83 1361-1368... 

This opens the possibility to tailor block copolymers with a wide variety of LC phases and phase transition temperatures. A interesting possibility is the preparation of thermoplastic LC elastomers of the ABA-type with amorphous A-blocks having a high Tg and an elastomeric LC B-block with low Tg. An uniform director orientation can be achieved in these systems by stress as shown recently for chemically crosslinked elastomers (12). Various applications of these systems in which optical uniaxiality and transparency are induced by strain can be envisaged. 

New phases and phase transitions observed in over-charged states of LiCo02-based cathode materials. J. Power Sources 2001, 274, 97-98. 

Adlayer Phases and Phase Transitions on fee (111) Surfaees The structure of adsorbed monolayers, in particular the registry between the adlayer and the substrate, is affected by the symmetry of the substrate, the adsorbate-adsorbate interactions, and the corrugations in the adsorbate-substrate interaction potential [259]. The later is rather weak on the (111) faces of fee metals, and of comparable magnitude to the lateral interactions between the haKde adsorbates in high-density adlayers. If the average lattice constants of adlayer and... 

Adlayer Phases and Phase Transitions on fee (100) Surfaees With the exception of Au(lOO) the only stable low-order commensurate phase studied on (100) metal surfaces is the c(2 x 2) structure [53, 55, 268-270, 278]. Although the commensurate c(2 X 2) phase, where all adsorbates... 

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