Rigid entities

One of the most important phenomena in material science is the reinforcement of mbber by rigid entities, such as carbon black, clays, silicates, calcium carbonate, zinc oxide, MH, and metal oxide [45 7]. Thus, these fillers or reinforcement aids are added to mbber formulations to optimize properties that meet a given service application or sets of performance parameters [48-53]. Although the original purpose is to lower the cost of the molding compounds, prime importance is now attached to the selective active fillers and their quantity that produce specific improvements in mbber physical properties. 

Protein structures obtained by X-ray crystallography convey the impression of proteins as rigid entities with the positions of atoms fixed with respect to each other. This has led to the comparison of protein-protein and... 

The early work considered water molecules as rigid entities. Both the attractive and repulsive parts of a core potential are needed and these were constructed in two principal ways. In the first approach the components are obtained by ab-initio quantum mechanical calculations for the ground state energy of the water dimer (e.g. MCY at Hartree-Fock level [4]). The analytical form of these potentials was fitted to the calculated energy surfaces (details of these potentials are given in ref [8]). This resulted in unusually long 0-0... 

Figure 4.4 Mixed matrix membranes (MMM) with covalent linking of rigid entities like buckyballs into polymers.

The helices formed by double-stranded nucleic acids are not rigid entities, but display flexibility chracterized by numerous thermal motions of phosphate units. These motions have been measured by P-NMR and are very fast. Relaxation times occur in the nanosecond time range (Bolton and James, 1980). The local motions are, however, not strongly coupled to the conformation of the nucleic acid, and intercalated dyes are reoriented on a slower time scale. 

So far we have considered the bidentate ligands as rigid entities with nearly constant donor-donor distances in all... 

W. Saenger We see no obvious changes in the glucose geometry from one cyclodextrin adduct to the next - the glucoses behave as fairly rigid entities. 

Of course when dealing with flexible molecules it is necessary to include further degrees of freedom. There are different approaches that can be taken to treat flexible molecules. Some methods treat a representative of each conformation of the molecule as a rigid entity. The search becomes more complex because many molecules may be needed to represent the molecular flexibility. Other methods treat the torsion angles which can give rise to the different conformations as additional degrees of freedom. 

To build the necessary compounds such as proteins and DNAs, you have to combine smaller units by condensation reactions. Condensation reactions are typically accompanied by positive free energy changes, though of relatively small magnitudes. Condensation is opposite of the hydrolysis above and is accompanied by the formation of a more rigid entity and hence by the decrease in randomness (entropy). That means that such a reaction would not proceed without an added (negative) energy. 

We will find that the potential energy is important and stabilizing the bond. The fault lies in the use of the AOs to construct MOs. We have treated these as rigid entities with a radial decay set for the atomic state, but this is not appropriate to the molecular environment. 

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