Liquid-State Physical Chemistry: Fundamentals, Modeling, and Applications (2013)
1.2. Solids, Gases, and Liquids
In this section, the general structural features of liquids as intermediate between solids and gases, and the associated energetics, are briefly discussed. These considerations will clarify the nature and the complexity of liquids and solutions.
Starting with solids, generally two classes of solids can be distinguished: crystalline and amorphous materials. As is well known, the basic feature of crystalline solids is order. Crystalline solids can further be divided into single-crystalline or polycrystalline materials, in both of which a regularly ordered structure exists at the atomic scale (Figure 1.1). This structure is maintained, at least in principle, throughout the whole material in a single-crystalline material, whereas in a polycrystalline material regions of different crystallographic orientations exist. These regions are referred to as grains, and the boundaries between them as grain boundaries. Studies using X-ray diffraction have clearly revealed the long-range atomic order of these materials. In amorphous solids there is no long-range order (Figure 1.1), although the local coordination of a specific molecule1) in the amorphous state may not be that different from the coordination of the same type of molecule in the corresponding crystalline state (if it exists).
Figure 1.1 Schematics of (a) an amorphous and (b) a crystalline structure.
From the observation that the structure of a solid is, in essence, maintained with increasing temperature up to the melting point2), it already follows that the potential energy Upot is more important than the kinetic energy Ukinbecause a strong energetic interaction more or less immobilizes the molecules in space. Therefore, we have in general
This makes a regular spatial array of molecules the most suitable reference configuration for modeling a crystalline solid. This regularity can be described globally by the concept of lattices (long-range order) and locally by a well-defined coordination number (short-range order). Other aspects such as the kinetic energy of the molecules or defects in the regularity of the structure can be considered to be first order perturbations on this regularity. This implies that relatively simple models of particular features of the solid state – that is, models that ignore many details – can already describe the physical phenomena in solids reasonably well.
For gases, the molecules move through space almost independently of each other, as evidenced by the wide applicability of the ideal gas law PV = nRT, with as usual the pressure P, the volume V, the number of moles n, the gas constant R, and the temperature T. Hence, order is nearly absent and the reference configuration can be described as random. This is exactly the reverse of the situation in a solid. Thus, it can be concluded that the potential energy is small as compared with the kinetic energy and we have:
For gases, the reference configuration is thus a random distribution of molecules in space. In this case the influence of intermolecular interactions can be considered to first order as a perturbation, leading to some coordination of molecules with other molecules. Again, relatively simple models can provide already a good clue for the understanding of gases, as exemplified by the ideal gas model.
Liquids do have some properties akin to those of solids, and some other properties more similar to those of gases. For example, their density ρ, thermal expansion coefficient α and compressibility κ are typically not too different from the corresponding solid. As a rule of thumb, the specific volume increases from 5% to 15% upon melting (water is a well-known exception). On the other hand, liquids and gases have fluidity3) in common, although a liquid has a meniscus while a gas has no such thing and the viscosity η of liquids is higher than those of gases. This indicates that the movement of molecules in fluids is relatively easy when compared to solids. This is also reflected by similar values of the shear modulus G and diffusion coefficient D for liquids and gases. Figure 1.2 shows schematically the structure of solids, liquids and gases. As might be expected, the situation for liquids with respect to energy is somewhere in the middle, and both the potential energy and kinetic energy play important roles. Therefore, we have
Figure 1.2 Schematic of structure and coordination of (a) a solid, (b) a liquid, and (c) a gas. While solids and liquids have comparable values of density ρ, thermal expansion coefficient α and compressibility κ, the liquid and gas have more comparable values of viscosity η, shear modulus G, and diffusion coefficient D.
This implies that neither an ordered nor a fully disordered configuration is present in a liquid. The choice of a reference configuration becomes accordingly (much) more troublesome. Although long-range order is absent, short-range order is present and the concept of coordination number is still valuable for liquids. However, because of the approximately equal importance of kinetic and potential energy, relatively simple models of liquids usually are much less reliable than for either solids or gases. This increased complexity shifts the topic to a more advanced level, implying that in education less attention is given to the subject than it deserves in view of its practical importance.
To summarize, while the dominant feature of a solid is order, and that of a gas is disorder, the liquid is somewhere in between. The static structure of solids, liquids and gases is illustrated in Figure 1.3. This is achieved by using the pair correlation function4) g(r), which describes the probability of finding a molecule at a distance r from a reference molecule at the origin5). From Figure 1.3 it is clear that for crystalline solids only at discrete distances other molecules are present, whereas for gases the probability of finding another molecule rapidly becomes constant with increasing distance. For liquids, the situation is intermediate, as evidenced by some structure in g(r) for small r and the limiting behavior g(r) = 1 for large r. The coordination number, that is, the number of nearest neighbor molecules around a reference molecule, is, however, similar to the coordination number in the corresponding solid.
Figure 1.3 Schematic of the coordination of a solid, a liquid and a gas. (a) A solid with a regular array of molecules leading to long-range order and a well-defined coordination shell; (b) A liquid with similar density as the solid and having a random dense packing of molecules, leading only to short-range order in which the coordination number is of prime relevance; (c) A gas with also a random packing of molecules and ordering, albeit limited, due to the mutual weak attraction of the molecules.