Macroscopic samples

In Chapter 2, a brief discussion of statistical mechanics was presented. Statistical mechanics provides, in theory, a means for determining physical properties that are associated with not one molecule at one geometry, but rather, a macroscopic sample of the bulk liquid, solid, and so on. This is the net result of the properties of many molecules in many conformations, energy states, and the like. In practice, the difficult part of this process is not the statistical mechanics, but obtaining all the information about possible energy levels, conformations, and so on. Molecular dynamics (MD) and Monte Carlo (MC) simulations are two methods for obtaining this information... 

We hope that macroscopic samples of quasi-spherical onion-like particles will soon become available, and then we will be able to characterize these systems in detail. Probably a new generation of carbon materi-aks can be generated by the three-dimensional packing of quasi-spherical multi-shell fullerenes. 

Molecules do not consist of rigid arrays of point charges, and on application of an external electrostatic field the electrons and protons will rearrange themselves until the interaction energy is a minimum. In classical electrostatics, where we deal with macroscopic samples, the phenomenon is referred to as the induced polarization. I dealt with this in Chapter 15, when we discussed the Onsager model of solvation. The nuclei and the electrons will tend to move in opposite directions when a field is applied, and so the electric dipole moment will change. Again, in classical electrostatics we study the induced dipole moment per unit volume. 

Calculating ensemble or time averages over a relatively small number of points (perhaps a few million) and a limited number of particles (perhaps a few hundred), instead of something which approaches a macroscopic sample of perhaps 10 ° molecules/configurations. 

Fluctuations are larger in networks of low functionality and they are unaffected by sample deformation. The mean squared chain dimensions in the principal directions are less anisotropic than in the macroscopic sample. This is the phantom network model. 

The parameters of neutron scattering theory of polymer networks are A, the macroscopic stretching of the sample, or linear degree of swelling, f, the network functionality, K. which accounts for restricted junction fluctuations and a, a measure of the degree to which chain extension parallels the macroscopic sample deformation. The functionality is known from knowledge of the chemistry of network formation, and A is measured. Both K and a must be extracted from experiments. 

The monomeric unit is chiral, each individual polymer molecule consists of isochiral monomers, but the macroscopic sample is a racemate. Chains... 

In a macroscopic sample the molecules are arranged inside the boundary line... 

The arrangement of moments in a typical antiferromagnetic is shown in Fig. 3.1. Moments on adjacent atoms are, in the simplest cases such as MnO or NiO, coupled so that they are antiparallel. Then at low temperatures the susceptibility depends on whether the field is parallel or perpendicular to the moments. If it is parallel, the susceptibility X goes to zero as T->0. This is because the coupling prevents any spins from turning over, and no spin waves are excited. On the other hand, if the field is perpendicular to the moments, they will be oriented by the field as shown in Fig. 3.2 and x is independent of temperature. The susceptibilities in the two directions are shown in Fig. 3.3. In practice, a macroscopic sample will usually contain numerous domains, and then the average susceptibility is... 

Schematic illustrations of these processes are shown in Figure 6.8. Two things must be remembered about these sketches One unit of surface is affected by the processes, and the shape of the affected area is immaterial. It is understood that these are elements of volume and area that are portions of macroscopic samples. Our interest is in the free energy change accompanying each process.

Each listed type of randomization (orientional, hydrogen-bonding network, nuclear spin statistics, isotopes, impurities, defects, and others that could be cited) makes independent contributions to S0 0. Hence, it seems safe to conclude that no macroscopic sample of real substance that ever appeared on Earth satisfies S0 = 0, i.e., that every real substance represents an imperfect exception to the third law as commonly stated. 

Our world can be studied at different levels of magnification. At the macroscopic level, matter is large enough to be seen, measured, and handled. A handful of sand and a glass of water are macroscopic samples of matter. At the micro-scopic level, physical structure is so fine that it can be seen only with a microscope. A biological cell is microscopic, as is the detail on a dragonfly s wing. Beyond the microscopic level is the submicroscopic—the realm of atoms and molecules and an important focus of chemistry. 

Why is it not practical to have a macroscopic sample that is 100 percent pure ... 

Name ten elements you have access to macroscopic samples of as a consumer here on Earth. 

Electron microscopy (59, 60) is not as generally applicable because sample preparation is sometimes difficult. For the butadiene-styrene copolymers used here, contrasting of the butadiene phase with 0s04 is particularly suitable (41). Thin films, several tenths of a micron thick, are cast from dilute solutions and placed in the vapor of an aqueous 0s04 solution. A similar process is followed for thin sections of macroscopic samples. If the morphological structure of these films in planes normal to the film surface is of interest, such films must be embedded before cutting in a material of similar hardness which does not swell or dissolve the sample to be investigated. 

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