Effect short-range

The expansion of a covalently bonded polymer chain will be restricted by the valence angles between each chain atom. In grareral, this angle is 0 for a homoatomic chain, and Equation 10.4 can be modified to allow for these short-range interactions. 

For the simplest case of an all-carbon backbone chain such as polyethylene, 6 = 109° and cos 6 = - so that Equation 10.5 reduces to 

This indicates that the polyethylene chain is twice as extended as the freely jointed chain model when short-range interactions are considered. 

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As with SCRF-PCM only macroscopic electrostatic contribntions to the Gibbs free energy of solvation are taken into account, short-range effects which are limited predominantly to the first solvation shell have to be considered by adding additional tenns. These correct for the neglect of effects caused by solnte-solvent electron correlation inclnding dispersion forces, hydrophobic interactions, dielectric saturation in the case of... 

This closure property is also inherent to a set of differential equations for arbitrary sequences Uk in macromolecules of linear copolymers as well as for analogous fragments in branched polymers. Hence, in principle, the kinetic method enables the determination of statistical characteristics of the chemical structure of noncyclic polymers, provided the Flory principle holds for all the chemical reactions involved in their synthesis. It is essential here that the Flory principle is meant not in its original version but in the extended one [2]. Hence under mathematical modeling the employment of the kinetic models of macro-molecular reactions where the violation of ideality is connected only with the short-range effects will not create new fundamental problems as compared with ideal models. 

We summarize this section by emphasizing that we have identified a host of effects, and we have seen that they are mainly short-range effects that are primarily associated with the first solvation shell. A reasonable way to model these effects quantitatively is to assume they are proportional to the number of solvent molecules in the first hydration shell with environment-dependent proportionality constants. 

In the absence of charges and dipoles, short-range effects such as hydrogen bonding and hydrophobic hydration become important. The complex solute-solvent interactions in such cases, however, are not well understood. In addition there is the possibility of ion or ion-pair catalysis. Especially in cases with solvents of low dielectric constant, it has been observed that k3 rather than log k3 becomes linear in cs... 

Consideration of short-range effects, in which the repulsive terms which lead to the hump in the energy curve are called into play, is an extremely... 

The inductive effect is a rather short-range effect, and its influence decreases rapidly as the... 

We suggest that these highly contaminated sediments are then slowly transported by resuspension and currents to sea-ward locations where the sediments accumulate in basins or the deep o-cean. The rapid decrease in PAH to a level of 160 ppb within 94 km of Boston (see Figure 4) Indicates that this transport mode is a rather short range effect (10). 

When a molecule is placed in a solvent, the interaction between the molecule (the solute) and the solvent can, roughly, be divided into long-range effects and short-range effects, that is, effects related to the first few solvation shells . 

Among the first of them are the so-called substitution effects due to steric, induction, catalytic, or some other types of influence of the reacted active centers on the reactivity of neighboring unreacted centers. In order to take account of such short-range effects it has been suggested (Kuchanov, 1978) to use under mathematical modeling an extended Flory principle. In line with this principle, the reactivity of any active center of a molecule is supposed to be controlled exclusively by local chemical structure of the... 

The above-described "labeling-erasing" procedure is in common use in statistical chemistry of polymers (Kuchanov, 2000). It gives a chance to obtain a number of important theoretical results under kinetic modeling of polymerization and polycondensation processes, where the deviation from their description in terms of the ideal kinetic model is due to the short-range effects. 

The allowance for the short-range effects has been carried out in two types of kinetic models (Kuchanov, 1992). In the first of them, the reactivity of a macroradical is presumed to be dependent on the types of n monomeric units preceding the terminal one. Here the mathematical formalism differs from that used in the case of the ideal model only in one point. The states of the Markov chain are associated in the framework of these models with monomeric units, each supplied by the label specifying the type of sequence U, of units acting upon the reactivity of the active center. 

It is also possible to combine the supermolecule and continuum approaches by using specific solvent molecules to capture the short-range effects (i.e., those involving specific noncovalent interactions between solute and solvent) and a reaction field to treat longer range effects.33-35 Alternatively, structures along the gas phase reaction coordinate can be immersed in a box of hundreds (or more) of explicit solvent molecules that are treated using force field approaches.36,37 Each type of method - the SCRF, solvent box, and supermolecule approaches - tests the importance of particular features of the solvent on the reactivity of the solute dielectric constant, multiple specific classical electrostatic interactions, and specific local directional noncovalent interactions, respectively. 

The so-called polarizable continuum model (PCM) offers a unified and well sound framework for the evaluation of all these contributions both for isotropic and anisotropic solutions. In PCM, the solute molecule (possibly supplemented by some strongly bound solvent molecules, to include short-range effects such as hydrogen bonds) is embedded in a cavity formed by the envelope of spheres centered on the solute atoms. The procedures to assign the atomic radii and to form the cavity have been described in detail together with effective classical approaches for evaluating K vand ,... 

Specific Hormones (Not listed are the numerous cytokines. diverse hormones that have only a short range effect)... 

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