Solid macroscopic properties

Macroscopic properties often influence tlie perfoniiance of solid catalysts, which are used in reactors tliat may simply be tubes packed witli catalyst in tlie fonii of particles—chosen because gases or liquids flow tlirough a bed of tliem (usually continuously) witli little resistance (little pressure drop). Catalysts in tlie fonii of honeycombs (monolitlis) are used in automobile exliaust systems so tliat a stream of reactant gases flows witli little resistance tlirough tlie channels and heat from tlie exotlieniiic reactions (e.g., CO oxidation to CO,) is rapidly removed. 

Figure 9-1 shows the addition of solid iodine to a mixture of water and alcohol. At first the liquid is colorless but very quickly a reddish color appears near the solid. Stirring the liquid causes swirls of the reddish color to move out— solid iodine is dissolving to become part of the liquid. Changes are evident the liquid takes on an increasing color and the pieces of solid iodine diminish in size as time passes. Finally, however, the color stops changing (see Figure 9-1). Solid is still present but the pieces of iodine no longer diminish in size. Since we can detect no more evidence of change, we say that the system is at equilibrium. Equilibrium is characterized by constancy of macroscopic properties ...

These include cold drawn, high pressure oriented chain-extended, solid slate extruded, die-drawn, and injection moulded polymers. Correlation of hardness to macroscopic properties is also examined. In summary, microhardness is shown to be a useful complementary technique of polymer characterization providing information on microscopic mechanical properties. 

The group velocity, dco/dq, is constant and independent of the wavelength, as shown in Figure 8.5. The discontinuous nature of matter can be neglected, and for these wavelengths the vibrational characteristics of the material can be described by its macroscopic properties (density and elastic constants). The group velocity is here equal to the speed of sound in the solid. 

The long side chains of a homopolypeptide have remarkable motional freedom about multiple bonds, while the main chain forms the secondary regular conformation such as a-helix, /1-sheet, and turn, which are rigid structures. The macroscopic properties of the rigid a-helical polypeptide, therefore, highly depends on the dynamic structure of the side chains so that a lot of studies on the side chain dynamics of the a-helical polypeptides have been carried out in the solid and solution states.12,14,29 66... 

The macroscopic properties of a material are related intimately to the interactions between its constituent particles, be they atoms, ions, molecules, or colloids suspended in a solvent. Such relationships are fairly well understood for cases where the particles are present in low concentration and interparticle interactions occur primarily in isolated clusters (pairs, triplets, etc.). For example, the pressure of a low-density vapor can be accurately described by the virial expansion,1 whereas its transport coefficients can be estimated from kinetic theory.2,3 On the other hand, using microscopic information to predict the properties, and in particular the dynamics, of condensed phases such as liquids and solids remains a far more challenging task. In these states... 

A phase is defined as a state of matter that is uniform throughout in terms of its chemical composition and physical state in other words, a phase may be considered a pure substance or a mixture of pure substances wherein intensive properties do not vary with position. Accordingly, a gaseous mixture is a single phase, and a mixture of completely miscible liquids yields a single hquid phase in contrast, a mixture of several solids remains as a system with multiple solid phases. A phase rule therefore states that, if a limited number of macroscopic properties is known, it is possible to predict additional properties. 

The macroscopic properties of the three states of matter can be modeled as ensembles of molecules, and their interactions are described by intermolecular potentials or force fields. These theories lead to the understanding of properties such as the thermodynamic and transport properties, vapor pressure, and critical constants. The ideal gas is characterized by a group of molecules that are hard spheres far apart, and they exert forces on each other only during brief periods of collisions. The real gases experience intermolecular forces, such as the van der Waals forces, so that molecules exert forces on each other even when they are not in collision. The liquids and solids are characterized by molecules that are constantly in contact and exerting forces on each other. 

Although it is relatively easy to understand why some of the macroscopic properties of liquids, especially their shape, can depend on surface properties, it is not so obvious for solids. However, the strength of a solid is determined by the ease with which micro-cracks propagate, when placed under stress, and this depends on its surface energy, that is the amount of (surface) work required to continue the crack and hence expose new surface. This has the direct effect that materials are stronger in a vacuum, where their surface energy is not reduced by the adsorption of either gases or liquids, typically available under atmospheric conditions. 

The values obtained in different laboratories for the activity of various electrocatalysts are not directly comparable. The reduction of oxygen — for which data have been published by various groups — proceeds at the three-phase boundary where gas, liquid, and solid meet. This boundary is affected by such macroscopic properties of the catalyst as particle size, density, surface tension, and porosity. 

To understand heterogeneous catalysis it is necessary to characterize the surface of the catalyst, where reactants bond and chemical transformations subsequently take place. The activity of a solid catalyst scales directly with the number of exposed active sites on the surface, and the activity is optimized by dispersing the active material as nanometer-sized particles onto highly porous supports with surface areas often in excess of 500m /g. When the dimensions of the catalytic material become sufficiently small, the properties become size-dependent, and it is often insufficient to model a catalytically active material from its macroscopic properties. The structural complexity of the materials, combined with the high temperatures and pressures of catalysis, may limit the possibilities for detailed structural characterization of real catalysts. 

Some small print should appear here we shall come back to it. The different phases that the system displays will in general be distinguished by the values of some macroscopic property loosely described as an order parameter. Thus, for example, the density serves to distinguish a liquid from a vapor a structure factor distinguishes a liquid from a crystalline solid. A suitable order parameter, M, allows us to associate with each phase, a, a corresponding portion q rj of -space. We write that statement concisely in the form... 

It is a misinterpretation of the concept of a phase to consider these two possible sites for a counterion as separate phases. This confuses a macroscopic property of a well-defined phase (a solid) in equilibrium with another well-defined phase (a homogeneous electrolyte solution) with an internal property of an inhomogeneous single phase, the macroionic (or colloidal or gel) phase. It divides the macroionic phase into two regions that have no physical counterpart. 

This section attempts to relate the micro structural organization of fat crystals to the mechanical properties. The importance of hierarchies in structural organization will again be stressed in this section in an attempt correlate micro structure to macroscopic properties. Figure 17.7 depicts the hierarchies in a fat crystal network structure. Past work has focused on lipid composition, polymorphism and solid fat content to interpret the mechanical strength of the network (Kamphuis and Jongschapp 1985 Papenhuijzen 1971, 1972 Payne 1964). 

The electrical conductivity of a material is a macroscopic solid-state property since even in high molecular-weight polymers there is not just one conjugated chain which spans the distance between two electrodes. Then it is not valid to describe the conductivity by the electronic structure of a single chain only, because intra- and interchain charge transport are important. As with crystalline materials, some basic features of the microscopic charge-transport mechanism can be inferred from conductivity measurements [83]. The specific conductivity a can be measured as the resistance R of a piece of material with length d and cross section F within a closed electrical circuit,... 

Tabor, D. (1981). Solid Surfaces their atomic, electronic and macroscopic properties. Contemp. Phys. 22, 215. 

Other macroscopic properties that in principle can be measured are the excess density and the excess compressibility of the interfacial liquid. These excess quantities can be positive or negative and follow from a comparison of the corresponding quantities in systems with the liquid and solid separated. Alternatively, liquid behaviour in pores can be studied. An example of this kind has been given by Derjaguin ) who claims that water in narrow pores of silica gel or Aerosil does not exhibit the typical thermal expansion minimum at 4 C because of structural changes near the surface. Ldring and Findenegg ) studied surface excesses dilatometrically. 

---