Solids, Liquids, and Phase Transitions

Solid iodine is converted directly to a vapor (sublimes) when warmed. Here, purple iodine vapor is redeposited as a solid on the cooler upper surfaces of the vessel. 

1 Bulk Properties of Gases, Liquids, and Solids Molecular Interpretation 

Interpreting bulk properties qualitatively on the basis of microscopic properties requires only consideration of the long-range attractive forces and short-range repulsive forces between molecules it is not necessary to take into account the details of molecular shapes. We have already shown one kind of potential that describes these intermolecular forces, the Lennard-Jones 6-12 potential used in Section 9.7 to obtain corrections to the ideal gas law. In Section 10.2, we discuss a variety of intermolecular forces, most of which are derived from electrostatic (Coulomb) interactions, but which are expressed as a hierarchy of approximations to exact electrostatic calculations for these complex systems. 

FIGURE 10.1 Intermolecular forces create structure in liquids and solids. If a single atom is removed from a snapshot of the atomic arrangement in a solid (a), it is easy to figure out exactly where to put it back in. For a liquid (b), the choices are limited. If a single atom is removed from a gas (c), no clue remains to tell where it came from. 

The much greater separation between molecules in the gas phase than in the condensed phases dramatically influences the effect of intermolecular forces. The repulsive force, although very strong, is very short-ranged and becomes 

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Since an analyte and interferent are usually in the same phase, a separation often can be effected by inducing a change in one of their physical or chemical states. Changes in physical state that have been exploited for the purpose of a separation include liquid-to-gas and solid-to-gas phase transitions. Changes in chemical state involve one or more chemical reactions. 

As we saw in Section 5.1, a single substance can exist in different phases, or physical forms. The phases of a substance include its solid, liquid, and gaseous forms and its different solid forms, such as the diamond and graphite phases of carbon. In one case—helium—two liquid phases are known to exist. The conversion of a substance from one phase into another, such as the melting of ice, the vaporization of water, and the conversion of graphite into diamond, is called a phase transition (recall Section 6.11). 

In the studies that attribute the boundary friction to confined liquid, on the other hand, the interests are mostly in understanding the role of the spatial arrangement of lubricant molecules, e.g., the molecular ordering and transitions among solid, liquid, and amorphous states. It has been proposed in the models of confined liquid, for example, that a periodic phase transition of lubricant between frozen and melting states, which can be detected in the process of sliding, is responsible for the occurrence of the stick-slip motions, but this model is unable to explain how the chemical natures of lubricant molecules would change the performance of boundary lubrication. 

With the critical exponent being positive, it follows that large shifts of the critical temperature are expected when the fluid is confined in a narrow space. Evans et al. computed the shift of the critical temperature for a liquid/vapor phase transition in a parallel-plates geometry [67]. They considered a maximum width of the slit of 20 times the range of the interaction potential between the fluid and the solid wall. For this case, a shift in critical temperature of 5% compared with the free-space phase transition was found. From theoretical considerations of critical phenomena... 

Sample. This source places no restrictions on target material. Clusters of metals, produced. For example, polyethylene and alumina have been studied as well as refractory metals like tungsten and niobium. Molecular solids, liquids, and solutions could also be used. However the complexity of the vaporization process and plasma chemistry makes for even more complex mixtures in the gas phase. To date the transition metals(1-3) and early members of group 13 (IIIA) and 14 (IVA)( 11-16) have been the most actively studied. 

The triple point is the location at which all three phases boundaries intersect. At the triple point (and only at the triple point), all three phases (solid, liquid, and gas) coexist in dynamic equilibrium. Below the triple point, the solid and gas phases are next-door neighbors, and the solid-to-gas phase transition occurs directly. 

The temperature at which a phase transition occurs is dependent on pressure (Figure 7). At atmospheric pressure (1 atm) the solid-to-liquid phase transition occurs at 0 °C and the liquid-to-gas phase transition occurs at 100 °C. If we increase the pressure, say to 100 atm, the solid-to-liquid phase transition occurs at a temperature slightly less than 0°C (—0.74°C) however, the liquid-to-gas phase transition occurs at a much greater temperature (312°C). If we decrease the pressure, say to 0.1 atm, the solid-to-liquid phase transition occurs at a temperature slightly greater than 0°C (0.004 °C) and the liquid-to-gas phase transition occurs at a lower temperature (46 °C). If we decrease the pressure further to below the triple point, there is no solid-to-liquid phase transition rather, the solid-to-gas phase transition occurs directly. At a pressure of 0.001 atm, the sublimation temperature is — 20.16°C. 

Truhlar, D. G. Variational transition state theory and multidimensional tunneling for simple and complex reactions in the gas phase, solids, liquids, and enzymes, in Kohen, A. and Limbach, H. H., Eds. Isotope Effects in Chemistry and Biology. CRC Press/Taylor Francis, Boca Raton, FL (2006), pp. 579-619. 

Look back at the large phase diagram (Figure 7-1) and notice the intersection of the three lines at 0.01° and 6 X 10 atm. Only at this triple point can the solid, liquid, and vapor states of FljO all coexist. Now find the point at 374° C and 218 atm where the liquid/gas boundary terminates. This critical point is the highest temperature and highest pressure at which there is a difference between liquid and gas states. At either a temperature or a pressure over the critical point, only a single fluid state exists, and there is a smooth transition from a dense, liquid-like fluid to a tenuous, gas-like fluid. 

The phase changes of water result in the transitions between the solid, liquid, and gas states ... 

In the Chapter 7, formation of monolayers in air-liquid interfaces and the resulting film pressure and phase transitions are discussed. This chapter also includes a brief discussion of adsorption on solid surfaces from solutions. 

The order of a transition can be illustrated for a fixed-stoichiometry system with the familiar P-T diagram for solid, liquid, and vapor phases in Fig. 17.2. The curves in Fig. 17.2 are sets of P and T at which the molar volume, V, has two distinct equilibrium values—the discontinuous change in molar volume as the system s equilibrium environment crosses a curve indicates that the phase transition is first order. Critical points where the change in the order parameter goes to zero (e.g., at the end of the vapor-liquid coexistence curve) are second-order transitions. 

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