Pure substances, phase transitions first order

The melting of a crystalline substance is a first-order transition, accompanied by an isothermal increase in enthalpy, the latent heat of fusion. Due to the impossibility of obtaining a pure crystalline phase in polymers, melting occurs over a range, and the enthalpy-temperature curve is S-shaped rather than discontinuous. To calculate the heat of fusion from calorimetric measurements entails extrapolation of the curve for the crystalline form to the melting point, which reduces the accuracy of the measurement. Since the quantity required is the heat of melting one mole of crystalline units, the calorimetric heat must be corrected for the fraction of amorphous polymer present, and this introduces a further uncertainty in the determination. 

Fig. 4.3 Enthalpy and free enthalpy for a substance undergoing two first order transitions at T12 and T23. The bold lines correspond to the thermodynamic equilibrium of the pure phases. The dotted curve shows the effect of stabilizing phase 2, by doping. If the phases 1, 2 and 3 are identified with solid, Uquid and gaseous phases, the dotted line mirrors the effect of freezing point depression (T, 2 < T12) and boiling point elevation (T23 > T23).

In this volume, we will apply the principles developed in Principles and Applications to the description of topics of interest to chemists, such as effects of surfaces and gravitational and centrifugal fields phase equilibria of pure substances (first order and continuous transitions) (vapor + liquid), (liquid 4-liquid), (solid + liquid), and (fluid -f fluid) phase equilibria of mixtures chemical equilibria and properties of both nonelectrolyte and electrolyte mixtures. But do not expect a detailed survey of these topics. This, of course, would require a volume of immense breadth and depth. Instead, representative examples are presented to develop general principles that can then be applied to a wide variety of systems. 

Chapters 13 and 14 use thermodynamics to describe and predict phase equilibria. Chapter 13 limits the discussion to pure substances. Distinctions are made between first-order and continuous phase transitions, and examples are given of different types of continuous transitions, including the (liquid + gas) critical phase transition, order-disorder transitions involving position disorder, rotational disorder, and magnetic effects the helium normal-superfluid transition and conductor-superconductor transitions. Modem theories of phase transitions are described that show the parallel properties of the different types of continuous transitions, and demonstrate how these properties can be described with a general set of critical exponents. This discussion is an attempt to present to chemists the exciting advances made in the area of theories of phase transitions that is often relegated to physics tests. 

From the ratio AHyu/AHcai, the cooperative unit size (CUS) (in molecules) can be determined. The CUS is a measure of the degree of intermolecular cooperation between phospholipid molecules in a bilayer for a completely cooperative, first-order phase transition of an absolutely pure substance, this ratio should approach infinity, whereas for a completely noncooperative process, this ratio should approach unity. Although the... 

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. 

Primarily, this approach was based on the formal analogy between a first order phase transition and the micellisation. When a new phase of a pure substance is formed the chemical potential of this substance and its concentration in the initial phase do not change with the total content of this substance in the system. A similar situation is observed above the CMC, where the adsorption and the surface tension become approximately constant. In reality variations of these properties are relatively small to be observed by conventional experimental methods. The application of the Gibbs adsorption equation shows that the constancy of the surfactant activity above the CMC follows from the constancy of the surfactant adsorption T2 [13]... 

Typical behavior of heat capacity, volume, and entropy of a pure substance as a function of temperature given that the system undergoes a first-order phase transition (left) versus a second-order phase transition (right) at the temperature T. ... 

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