Short-range periodicity

As an example, it has been pointed out that the Hamaker and Lifshitz theories assume (exphcitly and implicitly, respectively) that intensive physical properties of the media involved such as density, and dielectric constant, remain unchanged throughout the phase—that is, right up to the interface between phases. We know, however, that at the atomic or molecular level solids and liquids (and gases under certain circumstances) exhibit short-range periodic fluctuations they are damped oscillating functions. Conceptually, if one visualizes a hquid in contact with a flat solid surface (Fig. 4.8a), one can see that the molecules (assumed to be approximately spherical, in this case) trapped between the surface and the bulk of the liquid will have less translational freedom relative to the bulk and therefore be more structured. That structure will (or may) result in changes in effective intensive properties near the surface. 

Focal-conic textures are patterns that are usually observed for smectic phases where the layers are allowed to form curved structures. Such mesophases must therefore have only short-range periodic order, as long-range ordering serves to destabilize curved structures. Typically, focal-conic domains... 

Thus, the structure factor of the liquid with a short-range periodicity is the two Lorentzians centered Aq = q =2% a and q = -qo, Fig. 5.19b. Their positions are a measure of the molecular size a and their widths are a measure of the characteristic distance for the short range molecular correlations. The total intensity of scattering for positive q is shown in Fig. 5.20a. Note that the curve for the total intensity is slightly asymmetric because this function is a product of the form factor and the structure factor according to Eq. 5.25. 

The secondary protein structure refers to certain short-range periodic or repeating patterns often foimd along protein chains. Secondary structure is maintained by interactions between amino acids that are fairly close together in the linear sequence of the protein chain or adjacent to each other on neighboring chains. The most common of these patterns is called the alpha (a)-helix, shown in Figure 19.9. hi the a-hehx structure, the amino acid chain is wrapped into a tight coil in which the side chains extend outward from the coil. The structure is... 

As noted in the introductory section, disordered crystals have long-range positional order whereas liquid crystals have short-range periodic order. The extent of the bond orientational order differentiates the hexatic and non-hexatic liquid crystal phases [41-43], The positional order can be described in terms of an ideal average lattice structure... 

The major role of TOF-SARS and SARIS is as surface structure analysis teclmiques which are capable of probing the positions of all elements with an accuracy of <0.1 A. They are sensitive to short-range order, i.e. individual interatomic spacings that are <10 A. They provide a direct measure of the interatomic distances in the first and subsurface layers and a measure of surface periodicity in real space. One of its most important applications is the direct determination of hydrogen adsorption sites by recoiling spectrometry [12, 4T ]. Most other surface structure teclmiques do not detect hydrogen, with the possible exception of He atom scattering and vibrational spectroscopy. 

The short-range order in a material is important in determining optoelectronic properties. For instance, x-ray and electron diffraction experiments performed on amorphous siHcon (i -Si) and germanium (a-Ge) have revealed that the nearest neighbor environments are approximately the same as those found in their crystalline counterparts (6) photoemission experiments performed on i -Si show that the DOS in valence and conduction bands are virtually identical to the corresponding crystal with the exception that the singularities (associated with periodicity) present in the latter are smeared out in the former. 

Kinetic studies involving enzymes can principally be classified into steady and transient state kinetics. In tlie former, tlie enzyme concentration is much lower tlian that of tlie substrate in tlie latter much higher enzyme concentration is used to allow detection of reaction intennediates. In steady state kinetics, the high efficiency of enzymes as a catalyst implies that very low concentrations are adequate to enable reactions to proceed at measurable rates (i.e., reaction times of a few seconds or more). Typical enzyme concentrations are in the range of 10 M to 10 ], while substrate concentrations usually exceed lO M. Consequently, tlie concentrations of enzyme-substrate intermediates are low witli respect to tlie total substrate (reactant) concentrations, even when tlie enzyme is fully saturated. The reaction is considered to be in a steady state after a very short induction period, which greatly simplifies the rate laws. 

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