Macroscopic objects

In this section we consider electromagnetic dispersion forces between macroscopic objects. There are two approaches to this problem in the first, microscopic model, one assumes pairwise additivity of the dispersion attraction between molecules from Eq. VI-15. This is best for surfaces that are near one another. The macroscopic approach considers the objects as continuous media having a dielectric response to electromagnetic radiation that can be measured through spectroscopic evaluation of the material. In this analysis, the retardation of the electromagnetic response from surfaces that are not in close proximity can be addressed. A more detailed derivation of these expressions is given in references such as the treatise by Russel et al. [3] here we limit ourselves to a brief physical description of the phenomenon. 

In general, a point group synnnetry operation is defined as a rotation or reflection of a macroscopic object such that, after the operation has been carried out, the object looks the same as it did originally. The macroscopic objects we consider here are models of molecules in their equilibrium configuration we could also consider idealized objects such as cubes, pyramids, spheres, cones, tetraliedra etc. in order to define the various possible point groups. 

If the concentration of junction points is high enough, even branches will contain branches. Eventually a point is reached at which the amount of branching is so extensive that the polymer molecule becomes a giant three-dimensional network. When this condition is achieved, the molecule is said to be cross-linked. In this case, an entire macroscopic object may be considered to consist of essentially one molecule. The forces which give cohesiveness to such a body are covalent bonds, not intermolecular forces. Accordingly, the mechanical behavior of cross-linked bodies is much different from those without cross-linking. 

How is physics, as it is currently practiced, deficient in its description of nature Certainly, as popularizations of physics frequently reniiiid us, theories such as Quantum Electrodynamics are successful to a reinarkiible degree in predicting the results of experiments. However, any reasonable measure of success requires that wc add the caveat, ...in the domain (or domains) for which the theory was developed. For example, classical Newtonian physics is perfectly correct in its description of slow-moving, macroscopic objects, but is fundamentally incorrect in its description of quantum and/or relativistic systems. 

The uncertainty principle has negligible practical consequences for macroscopic objects, but it is of profound importance for subatomic particles such as the electrons in atoms and for a scientific understanding of the nature of the world. 

The uncertainty principle is negligible for macroscopic objects. Electronic devices, however, are being manufactured on a smaller and smaller scale, and the properties of nanoparticles, particles with sizes that range from a few to several hundred nanometers, may be different from those of larger particles as a result of quantum mechanical phenomena, (a) Calculate the minimum uncertainty in the speed of an electron confined in a nanoparticle of diameter 200. nm and compare that uncertainty with the uncertainty in speed of an electron confined to a wire of length 1.00 mm. (b) Calculate the minimum uncertainty in the speed of a I.i+ ion confined in a nanoparticle that has a diameter of 200. nm and is composed of a lithium compound through which the lithium ions can move at elevated temperatures (ionic conductor), (c) Which could be measured more accurately in a nanoparticle, the speed of an electron or the speed of a Li+ ion ... 

Fedichev, P. O., Men shikov, L. 1., Long-range order and interactions of macroscopic objects in polar liquids. ArXiv Condensed Matter e-prints 0601129, 2006. 

In the 1920s it was found that electrons do not behave like macroscopic objects that are governed by Newton s laws of motion rather, they obey the laws of quantum mechanics. The application of these laws to atoms and molecules gave rise to orbital-based models of chemical bonding. In Chapter 3 we discuss some of the basic ideas of quantum mechanics, particularly the Pauli principle, the Heisenberg uncertainty principle, and the concept of electronic charge distribution, and we give a brief review of orbital-based models and modem ab initio calculations based on them. 

When Dirac completed work on his theory in 1928, it was a notable success. Among other things, it explained electron spin, which turned out to be a relativistic effect, rather than something analogous to the spin of a macroscopic object like a top. But the theory also made what seemed to be a very strange prediction. If Dirac s theory was correct, then there had to exist particles that had properties like the electron, but that carried a positive rather than a negative charge. At the time, such particles, called positrons, had never been observed. 

Fluorescence scanners resolve fluorescence as a function of spatial coordinates in two dimensions for macroscopic objects such as electrophoresis gels, blots and chromatograms... 

Consider, for example, colloidal particles, i.e., particles that are too small to display the properties of macroscopic objects, say, <0.01 mm, and too large to behave like atoms and small molecules, approximately >10,000 pm. These colloidal particles move under electric fields, and if they are pigments, electric fields can be used to guide the colloidal particles to deposit upon metals and color them. The hues formed in this way may be more permanent than paint. But why do the particles move The... 

One of the most important things to bear in mind in studying van der Waals forces is that this topic has ramifications that extend far beyond our discussion here. Van der Waals interactions, for example, contribute to the nonideality of gases and, closer to home, gas adsorption. We also see how these forces are related to surface tension, thereby connecting this material with the contents of Chapter 6 (see Vignette X below). These connections also imply that certain macroscopic properties and measurements can be used to determine the strength of van der Waals forces between macroscopic objects. We elaborate on these ideas through illustrative examples in this chapter. 

More often than not one deals with colloidal objects immersed in a liquid or other such media, and therefore interactions between similar or dissimilar materials in an arbitrary medium are of importance in colloid science. Moreover, it is very useful to relate such dissimilar interactions to those between identical particles in vacuum. In the last section (Section 10.8) we present what are known as combining relations for accomplishing this. The van der Waals forces between macroscopic objects are usually attractive, but under certain circumstances they (and, as a consequence, the Hamaker constant) can be negative, as noted in Vignette X. A brief discussion of this completes Section 10.8. 

Preliminaries. In this chapter we shall address the simplest nonequilibrium situation—one-dimensional locally electro-neutral electrodiffusion of ions in the absence of an electric current. We shall deal with macroscopic objects, such as solution layers, ion-exchangers, ion-exchange membranes with a minimum linear size of the order of tens of microns. 

The SMA effect can be traced to properties of two crystalline phases, called martensite and austenite, that undergo facile solid-solid phase transition at temperature Tm (dependent on P and x). The low-temperature martensite form is of body-centered cubic crystalline symmetry, soft and easily deformable, whereas the high-temperature austenite form is of face-centered cubic symmetry, hard and immalleable. Despite their dissimilar mechanical properties, the two crystalline forms are of nearly equal density, so that passage from austenite to a twinned form of martensite occurs without perceptible change of shape or size in the macroscopic object. 

Why do halite crystals have such a distinct shape As we explore in this chapter, the macroscopic properties of any substance can be traced to how its submicroscopic parts are held together. The sodium and chloride ions in a halite crystal, for example, are held together in a cubic orientation, and as a result the macroscopic object we know as a halite crystal is also cubic. 

Strategy In each case, we use the de Broglie relation. The mass of a proton is given in Table B.l, and the speed of light is given inside the back cover. Expect the macroscopic object, the marble, to have a very short wavelength. Remember to express all quantities in kilograms, meters, and seconds, and use 1 J = 1 kg-m2-s-2. 

The symbol h, which is read h bar, means h/ln, a useful combination that occurs widely in quantum mechanics. From inside the back cover, we see that ti = 1.054 X 10-34 J-s. Equation 6 tells us that if the uncertainty in position is very small (Ax very small), then the uncertainty in linear momentum must be large, and vice versa (Fig. 1.11). The uncertainty principle has negligible practical consequences for macroscopic objects, but it is of profound importance for electrons in atoms and for a scientific understanding of the nature of the world. 

The uncertainty principle is negligible for. macroscopic objects. Electronic devices, however, are being manufactured on a smaller and smaller scale so that the properties of nanoparticles, particles whose sizes range from a few to several hundred nanometers, may be different from those of larger particles due to quantum mechanical phenomena, (a) Calculate the minimum uncertainty in the speed of an electron confined in a nanoparticle with a diameter of... 

Forces between macroscopic objects result from a complex interplay of the interaction between molecules in the two objects and the medium separating them. The basis for an understanding of intermolecular forces is the Coulomb1 force. The Coulomb force is the electrostatic force between two charges Qi and Q-2-... 

For macroscopic objects the adhesion force is often small compared to the load. For microscopic bodies this can be different. The reason is simple the weight of an object sliding over a surface usually decreases with the third power of its diameter (or another length characterizing its size). The decrease of the actual contact area and hence the adhesion force follows a weaker dependence. For this reason, friction between microbodies is often dominated by adhesion while in the macroscopic world we can often neglect adhesion. 

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