Zigzag

Figure B3.5.1. Contour line representation of a quadratic surface and part of a steepest descent path zigzagging toward the minimum.

Figure C2.12.7. Channel system of MFI (top) and MEL (bottom). The linear channels are interconnected by zigzag channels in ZSM-5 while exclusively straight miming channels are present in ZSM-11 - larger internal openings are present at the chaimel intersections - the arrows indicate the pathways for molecular transport tlirough the channel system.

Unbranched alkanes are sometimes referred to as straight chain alkanes but as we 11 see m Chapter 3 their chains are not straight but instead tend to adopt the zigzag shape portrayed m the bond line formulas introduced m Section 1 7... 

FIGURE 3 9 Ball and spoke models of pentane and hexane in their all anti (zigzag) conformations... 

We can relate the conformational preference for an equatorial methyl group m methylcyclohexane to the conformation of a noncyclic hydrocarbon we discussed ear her butane The red bonds m the following structural formulas trace paths through four carbons beginning at an equatorial methyl group The zigzag arrangement described by each path mimics the anti conformation of butane... 

Section 3 3 Higher alkanes adopt a zigzag conformation of the carbon chain m which all the bonds are staggered... 

Representation of the polymer chain in an extended zigzag conformation as shown m Figure 7 16 reveals several distinct structural possibilities differing with respect to the relative configurations of the carbons that bear the methyl groups... 

FIGURE 7 16 Poly mers of propene The mam chain IS shown in a zigzag conformation Every other carbon bears a methyl sub stituent and is a chirality center (a) All the methyl groups are on the same side of the carbon chain in isotactic polypropylene (b) Methyl groups alternate from one side to the other in syndiotactic polypropy lene (c) The spatial orienta tion of the methyl groups IS random in atactic polypropylene... 

Isopropyl group (Section 2 13) The group (CH3)2CH— Isotactic polymer (Section 7 15) A stereoregular polymer in which the substituent at each successive chirality center is on the same side of the zigzag carbon chain Isotopic cluster (Section 13 22) In mass spectrometry a group of peaks that differ in m/z because they incorporate differ ent isotopes of their component elements lUPAC nomenclature (Section 2 11) The most widely used method of naming organic compounds It uses a set of rules proposed and periodically revised by the International Union of Pure and Applied Chemistry... 

A fully extended hydrocarbon molecule will have the familiar zigzag profile... 

There is an intimate connection at the molecular level between diffusion and random flight statistics. The diffusing particle, after all, is displaced by random collisions with the surrounding solvent molecules, travels a short distance, experiences another collision which changes its direction, and so on. Such a zigzagged path is called Brownian motion when observed microscopically, describes diffusion when considered in terms of net displacement, and defines a three-dimensional random walk in statistical language. Accordingly, we propose to describe the net displacement of the solute in, say, the x direction as the result of a r -step random walk, in which the number of steps is directly proportional to time ... 

The filter usually has an endless cloth, traveling intermittently between the plates via roUers, to peel off cakes. Unfortunately, if the cloth is damaged anywhere, the whole cloth must be replaced, which is a difficult process. Each time the filter cloth zigzags through the filter, the filtering direction is reversed this tends to keep the cloth clean. Most of these filters incorporate membranes for mechanical expression, and cakes sometimes stick to the membranes and remain in the chamber after discharge. Some vertical filters are available with a separate cloth for each frame. The cloths maybe disposable and such filters are designed to operate with or without filter aids. 

The entropy value of gaseous HCl is a sum of contributions from the various transitions summarized in Table 4. Independent calculations based on the spectroscopic data of H Cl and H Cl separately, show the entropy of HCl at 298 K to be 186.686 and 187.372 J/(mol K) (44.619 and 44.783 cal/(mol K), respectively. The low temperature (rhombic) phase is ferroelectric (6). SoHd hydrogen chloride consists of hydrogen-bonded molecular crystals consisting of zigzag chains having an angle of 93.5° (6). Proton nmr studies at low temperatures have also shown the existence of a dimer (HC1)2 (7). 

The repeat distance along the chain axis (0.468 nm) is significantly less than that calculated for a planar zigzag stmcture. Therefore, the polymer must be in some other conformation (65—67). Based on k and Raman studies of PVDC single crystals and normal vibration analysis, the best conformation appears to be where the skeletal angle, is 120°, and the torsional of opposite sign) is 32.5°. This conformation is in... 

Zirconium tetrachloride is a tetrahedral monomer in the gas phase, but the soHd is a polymer of ZrCl octahedra arranged in zigzag chains in such a way that each zirconium has two pairs of bridging chlorine anions and two terminal or t-chlorine anions. The octahedra are distorted with unequal Zr—Cl bridge bonds of 0.2498 and 0.2655 nm. The physical properties of zirconium tetrachloride are given in Table 7. 

Another catalytically important zeohte is ZSM-5 (81). There is a three-dimensional network of pores in this zeohte, represented in Figure 16. A set of straight parallel pores is intersected by a set of perpendicular zigzag pores. These pores are smaller than those of the faujasites (Fig. 15). ZSM-5 is classified as a medium pore zeohte, the faujasites ate large pore zeohtes, and zeohte A (Table 2) is a small pore zeohte. 

---