Overlapping regimes

In the spectrum from classical intermetaUics to valence compounds to insulators, a smooth transition in their chemical bonding (metallic to ionic) is observed. At the border between Zind phases and metaUic phases, the typical properties of Zind phases diminish and metallic conductivity appears. However, it is inaccurate to impose and define a sharp boundary between classical Zind phases and the metallic phases (e.g.. Laves and Hume-Rothery phases), and it is in the overlapping regimes where much chemistry stiU remains to be discovered and understood. 

The last approximation in equation (4.1) is only really valid for the small-overlap regime, which this is not, but it serves to remind us of the approximately inverse energy dependence of the stabilization. One may ask how AEhGt would be expected to change in the series C— , C—N, C—O, and C—F or the series H— , H—N, H—O, and... 

Moreover, using the values of this table, we are going to verify that, in good solvent and in the overlap regime, the screening length obeys eqn (15.4.40). We shall observe that below a certain temperature this law ceases to be valid, as predicted from theory. 

To explain the behavior of polymer solutions in the overlapped regime, it is necessary to adopt a picture of the structure of these systems. The chain molecule is represented as a string of m statistical subunits with mean-squared end-to-end vectors R12 The average concentration inside a statistical subunit can be expressed as ... 

We shall now discuss briefly the conformation of one chain in the overlapping regime > i). To simplify the discussion we shall in fact restrict our attention to large concentrations = 1, corresponding to f = a. The reason for this choice is that the most interesting effects occur at scales > D, while < D in the overlapping regime. Even with this simpliflcation, the discussion is rather delicate, and the conclusions reached by the present author in Ref. 14 were incorrect. An improved version has been developed recently, and will be summarized here. 

The faradaic peak current at an NEE operating in the Total Overlap Regime for a reversible redox system obeys the Randles-Sevcik equation (5) ... 

The transition from a non-overlapping regime to an overlapping regime occurs approximately at T p = 1. The analytical expression for the resonance energy corresponds to this transition for a one-dimensional potential with a smooth barrier (within the WKB approximation ), i.e. 

In the non-overlapping regime, the above expression is valid for almost the entire decay process, but in the overlapping regime, it only corresponds to an insignificant initial transient. Eqn (20.65) can be written as ... 

FIG. 15 Concentration profile for a grafted layer immersed in a good solvent in the overlapping regime. 

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