Packing considerations

Apart from these simple silanes, derivatives witli aromatic groups at different places in tire chain have also been investigated [136, 137], It was found tliat tire average tilt angle of tliese molecules depends on tire specific functional entities contained in tire chains. It is likely tliat apart from packing considerations—important for bulky groups, for example—otlier factors also influence tire resulting tilt. 

The twist of these aggregates determines the resulting structure. When ribbons stack into fibrils, and fibrils into fibres, packing considerations cause these twisted aggregates to bend and modify their twist with an elastic energy penalty8eiast- For fibrils, it can be shown that the afibrii per peptide in a fibril is ... 

An alternative possibility is a vertical stacking structure where the p-strands are arranged on top of each other, again satisfying electrostatic and hydrophobic packing considerations (Fig. 20). Whichever is more likely, this is still far from a complete picture because the exact arrangement of the two disulphide-linked peptide chains is not yet known. 

In cubic closest-packing, consideration of the face-centered unit cell is a convenient way to get an impression of the arrangement of the interstices. The octahedral interstices are situated in the center of the unit cell and in the middle of each of its edges [Fig. 17.3(a)], The octahedra share vertices in the three directions parallel to the unit cell edges. They share edges in the directions diagonal to the unit cell faces. There are no face-sharing octahedra. 

Our prejudices favor either crystal packing considerations or, more likely, the fact that X-A19 has fewer desirable locations for bridge hydrogen placement (i.e., locations adjacent to the positively charged LB BH group are shunned). 

Not all structures are based on close packed lattices. Ions that are large and soft often adopt structures based on a primitive or body centred cubic lattice as found in CsCl (22173) and a-AgI (200108). Others, such as perovskite, ABO3 (Fig. 10.4), are based on close packed lattices that comprise both anions and large cations. The larger and softer the ions, the more variations appear, but the lattice packing principle can still be used. Santoro et al. (1999,2000) have shown how close-packing considerations combined with the use of bond valences can give a quantitative prediction of the structure of BaRuOs (10253). 

Most commonly, metal ions M2+ and M3+ (M = a first transition series metal), Li+, Na+, Mg2+, Al3+, Ga3+, In3+, Tl3+, and Sn2+ form octahedral six-coordinate complexes. Linear two coordination is associated with univalent ions of the coinage metal (Cu, Ag, Au), as in Ag(NH3)2+ or AuCL Three and five coordination are not frequently encountered, since close-packing considerations tell us that tetrahedral or octahedral complex formation will normally be favored over five coordination, while three coordination requires an extraordinarily small radius ratio (Section 4.5). Coordination numbers higher than six are found among the larger transition metal ions [i.e., those at the left of the second and third transition series, as exemplified by TaFy2- and Mo(CN)g4 ] and in the lanthanides and actinides [e.g., Nd(H20)93+ as well as UC Fs3- which contains the linear uranyl unit 0=U=02+ and five fluoride ligands coordinated around the uranium(VI) in an equatorial plane]. For most of the metal complexes discussed in this book a coordination number of six may be assumed. 

MOLECULAR ARCHITECTURE OF SURFACTANTS, PACKING CONSIDERATIONS, AND SHAPES OF MICELLES... 

Lindman 1979 and Chapter 17 of Israelachvili 1991). In what follows we restrict ourselves to the features essential for illustrating how packing considerations influence the resulting shapes of the surfactant aggregates and ignore the presence of water inside the Stern layer. 

We first define the basic geometric parameters of the surfactants and follow this up with an illustration and a discussion of packing considerations that allow us to predict the shapes of the aggregates. 

Once the estimates for ah, v and (c t are available, one can determine the preferred shapes of the surfactant aggregates using geometric packing considerations, as discussed in the following subsection and illustrated in Example 8.3. 

What is meant by the optimal head group area of a surfactant What is the packing parameter (P Explain how packing considerations can be used to determine the possible shapes of the micellar aggregates. 

Sections 10.2 and 9.1, respectively). Hence, the observed generation of a concentrated gas-in-liquid (macro)emulsion which interacts readily with simultaneously formed large (rodlike) micelles, using the above surfactant mixtures, is to be expected from and confirms such molecular packing considerations. 

When the packing considerations are taken into account, this model practically predicts that amphiphiles with a single alkyl chain are will form micelles or bilayers, those with two alkyl chains bilayers, and those with three alkyl chains inverted hexagonal phases.[0]... 

On the basis of this argument and the known crystal structures of parents and oxidized products, Ni(dpg)2I and Pd(dpg)2I are metal oxidized while Ni(bqd)2I0.52 is ligand oxidized. Clearly, this argument ignores crystal packing considerations and may well be incorrect. 

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