Steps interaction between, repulsive

Another effect of elastic deformation is that it causes a long-range interaction between steps. From the continuum elasticity theory, two steps sepa-rated by a distance have a repulsive interaction proportional to l for homo- and to In i for hetero-epitaxial cases, respectively [84]. This interaction plays an important role, for example, in step fluctuations, terrace width distribution, step bunching, and so forth [7,85-88]. 

Fig. 2. Components of Li enthalpies of complexation with methylamines. Successive steps indicate the effect on energy of interaction between Li and the amine of inclusion of additional components of the binding energy. The diagram shows that the permanent dipoles on amines (the charge on the nitrogen of the isolated amine) favor ammonia over trimethylamine complexation, but that polarizability and inductive effects (shift of negative charge onto the nitrogen in the complex) cause a massive turnaround in favor of complexation with trimethylamine rather than ammonia. Of particular importance is the near inversion of order caused by the addition of repulsive van der Waals terms. Modified after Ref. (9).

Transition metal atoms react much more readily with alkenes than with alkanes because the initial interaction between the metal atom and an alkene is much less repulsive than for M+alkanes. To insert into a C-H bond of an alkane, the metal atom has to break a C-H bond and form an M-C and an M-H bond. The first step in a reaction with an alkene, however, is formation of a 7r-complex in which the C=C bond is merely weakened, not broken.119 The availability of the DCD bonding scheme (Sec. 1.1) leads... 

Usually, MD methods are applied to polymer systems in order to obtain short-time properties corresponding to problems where the influence of solvent molecules has to be explicitly included. Then the models are usually atomic representations of both chain and solvent molecules. Realistic potentials for non-bonded interactions between non-bonded atoms should be incorporated. Appropriate methods can be employed to maintain constraints corresponding to fixed bond lengths, bond angles and restricted torsional barriers in the molecules [117]. For atomic models, the simulation time steps are typically of the order of femtoseconds (10 s). However, some simulations have been performed with idealized polymer representations [118], such as Bead and Spring or Bead and Rod models whose units interact through parametric attractive-repulsive potentials. 

In summary, syndioselective initiators exaggerate the inherent tendency toward syndiotactic placement by accentuating the methyl-methyl repulsive interactions between the propagating chain end and incoming monomer. Isotactic placement occurs against this inherent tendency when chiral active sites force monomer to coordinate with the same enantioface at each propagation step. 

To extract a value of the step-mobility h from the grating relaxation experiments [12], we must evaluate the strength of the step-step interaction y. Computational work suggests that ydue to elastic interactions between Si(OOl) steps is 0.2 eV run [29], while, we estimate that the entropic interaction is 10 times larger. (We use a step stiffness P calculated from the geometric mean of P for Sa and Sb steps given in Ref [30] P, 0.03 eV mn-. ) Therefore, entropic repulsion should dominate, and... 

A series or bunch of m initially straight and parallel steps, between heights 0 and m, may be expected to relax with the same asymptotics as a pair of steps. Modifications may occur, already for a pair of steps, when step-step interactions are present in addition to the entropic step repulsion. Here, we merely refer to recent reviews on experiments and theoretical analyses " on the much studied phenomenon of step bunching for vicinal surfaces, which is accompanied by interesting phase transistions. 

To proceed, we must describe the effective driving force and the effective interactions between steps on this mesoscopic scale. We focus here on two cases of recent experimental and theoretical interest current-induced step bunching on Si( 111) surfaces - " and reconstruction-induced faceting as seen a number of systems including the O/Ag(110) and Si(lll) surfaces" In both cases interesting 2D step patterns can arise from the competition between a driving force that promotes step bunching, and the effects of step repulsions, which tend to keep steps uniformly spaced. 

Fig. 2. An additive step-like interfacial interaction between neutral particles and plates. There is no force between plates for d>dt, attraction when (dl/2)

In summary, short-ranged step-like interactions for ions generate only short-range interactions between plates, which are always attractive for (d1/2)[Pg.431]

One interesting possibility emerges from the likelihood that an n-71 interaction between an oxygen lone pair of LBA and jr electrons of the terminal carbon-carbon double bond of the substrates stabilizes the transition state of the cyclization or the initial protonation step. The transition-state assembly proposed on the basis of this assumption and the steric repulsion would clearly lead to predominant approach of (i )-LBA to the si face of the terminal isoprenyl group (Fig. 4). 

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