Interaction competing

Other single-crystal x-ray diffraction studies of transition element dopants in jS-rh boron are based on the results of a refinement of the /3-rh boron structure that establishes the occurrence of four new low-occupancy (3.7, 6.6, 6.8 and 8.5%) B positions in addition to the earlier known ones. The dopant elements studied, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zr, Nb, Hf and Ta, do not enter B positions in the framework, but they enter the Al, A2, D and E positions. In some cases the doping elements have been studied at several concentrations for each element and for different cooling rates. The percentage occupancies of certain positions are eorrelated with the atomie sizes of the dopants. The bond distances between the polyhedra are shorter than those within the polyhedra. The mechanism of doping for some cases is denoted displacive, rather than interstitial or substitutional, because of competing interactions between the six different partially occupied B positions and dopant atoms. 

For example, see, Vedmedenko, E. Y. (2007) Competing Interactions and Pattern Formation in Nanoworld, Wiley-VCH, Weinheim. 

A number of specialised stationary phases have been developed for the separation of chiral compounds. They are known as chiral stationary phases (CSPs) and consist of chiral molecules, usually bonded to microparticulate silica. The mechanism by which such CSPs discriminate between enantiomers (their chiral recognition, or enantioselectivity) is a matter of some debate, but it is known that a number of competing interactions can be involved. Columns packed with CSPs have recently become available commercially. They are some three to five times more expensive than conventional hplc columns, and some types can be used only with a restricted range of mobile phases. Some examples of CSPs are given below ... 

Perhaps the common characteristic of all contributions to this volume is the permanent concern about the intimate relationships between the structural and electronic properties. Indeed, the careful design of increasingly complex molecular and supramolecular architectures allows us now to anticipate many molecular and solid state properties, but the final solid state structures are always the results of many competing interactions. The resulting electronic properties of these radical assemblies, whether conductivity or magnetism, are always very sensitive to minute modifications of their solid state structures and one of the main difficulties through... 

Calculations with one isolated molecule in vacuum often result in overestimation of intramolecular contacts, however, because competing interactions are absent. We started our investigation with the semi-rigid guanidinothiazole ICI27032, a potent competitive H2-antagonist which adopts solely extended conformations, because of its aromatic ring system (Fig. 9.8). 

Reduction of phenyl trifluoromethyl ketone by 119 generally leads to the (S)-carbinol (Table 15, entry 28). One would expect that conformational changes in the favored transition states would occur. However, the degree of asymmetric induction in these cases is quite low, and the (/ )-carbinol was in fact formed in toluene at 110°C (Table 15, entry 29), suggesting a rather delicate balance of competing interactions. 

The essential properties of incommensurate modulated structures can be studied within a simple one-dimensional model, the well-known Frenkel-Kontorova model . The competing interactions between the substrate potential and the lateral adatom interactions are modeled by a chain of adatoms, coupled with harmonic springs of force constant K, placed in a cosine substrate potential of amplitude V and periodicity b (see Fig. 27). The microscopic energy of this model is ... 

Kornyshev-LeiMn (KL) and Tombolato—Ferrarini (TF) models [14, 19] introduced above as the result of competing interactions. 

Example 13.3 demonstrates that phospholipids can form domains of distinct two-dimensional shapes on liquid surfaces. It has been found that the domain shape mainly depends on the chemical composition of the monolayer and the conditions such as temperature, pH, and ionic concentration. Domain structures can usually be understood by taking two competing interactions into account an attractive dispersive van der Waals force and a repulsive dipole-dipole... 

Heteropolymers can self-assemble into highly ordered patterns of microstructures, both in solution and in bulk. This subject has been reviewed extensively [1,123-127]. The driving force for structure formation in such systems is competing interactions, i.e., the attraction between one of the monomer species and the repulsion between the others, on the one hand, and covalent bonding of units within the same macromolecule, on the other hand. The latter factor prevents the separation of the system into homogeneous macroscopic phases, which can, under specific conditions, stabilize some types of microdomain structures. Usually, such a phenomenon is treated as microphase separation transition, MIST, or order-disorder transition, ODT. 

Figure 9. Model for understanding the commensurate-incommensurate phase transition. The Cu(A) system is ordered. The Cu(B) system is disordered because of the frustration caused by the geometrically competing interaction. The molecular field from the Cu(B) system disturbs the order in the Cu(A) system.

Matsushita Y, Creation of hierarchically ordered nanophase structures in block polymers having various competing interactions, Macromolecules, 2007, 40, 771-776. 

One of these models is the spin- ladder with competing interactions of the ferro- and antiferromagnetic types at the F-AF transition line. The exact singlet ground-state wave function on this line is found in the special form expressed in terms of auxiliary Bose-operators. The spin correlators in the singlet state show double-spiral ordering with the period of spirals equal to the system size. 

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