Near range order

Miller, R. L. On the existence of near-range order in isotactic polypropylenes. Polymer 1, 135 (1960)... 

With a Fourier transformation of (k) in the distance space, one obtains a separation of the contribution of the various coordination shells. This Fourier transform yields the structural parameters Rj, Nj and ah and thus the near range order of the specimen with respect to the absorbing atoms. The EXAFS analysis for the different absorber atoms within the material yields their specific near range order. Thus, one may get the structure seen form several kinds of absorbing atoms. EXAFS does not require highly crystalline materials. It is a suitable method to study disordered, or even amorphous, structures. The a values provide quantitative information about the thermal and structural disorder. 

The reflectivity spectra R(E) and the reflectivity-EXAFS Xr(E) = R(E) — Rq(E)]/R()(E) are similar, but not identical, to the absorption spectra and x(E) obtained in transmission mode. R(E) is related to the complex refraction index n(E) = 1 — 8(E) — ifl(E) and P(E) to the absorption coefficient /i(E) by ji fil/An. P and 8 are related to each other by a Kramers-Kronig transformation, p and 8 may be also separated in an oscillatory (A/ , AS) and non-oscillatory part (P0,80) and may be used to calculate Xr- This is, briefly, how the reflectivity EXAFS may be calculated from n(E). which itself can be obtained by experimental transmission EXAFS of standards, or by calculation with the help of commercial programs such as FEFF [109] with the parameters Rj, Nj and a, which characterize the near range order. The fit of the simulated to measured reflectivity yields then a set of appropriate structure parameters. This method of data evaluation has been developed and has been applied to a few oxide covered metal electrodes [110, 111], Fig. 48 depicts a condensed scheme of the necessary procedures for data evaluation. 

Hie evaluation of the data yields Rjy Nj, and Sjy i.e., the near-range order parameters of the material seen from the absorber atom. XAS permits the evaluation of the near-range order in the vicinity of the atoms of various elements of one specimen if the energies of their absorption edges are different enough and thus are well separated within the spectrum. It should be mentioned that XAS in reflection looks similar to XAS in transmission mode, however it is different and the evaluation of measurements requires the comparison with reflectivity data calculated form transmission EXAFS spectra. These evaluation procedures involving Kramers-Kronig transform are described in the literature [i-v]. 

It thus is seen to express the contribution to the dipolar part of the Kerr constant from ternary correlations. Like the parameter (152) occurring in molar refraction, it is positive or negative according to the model of orientational near-range ordering. 

Typical absorbance spectra of self-assembled silver nanoparticle layers are shown in Fig. 1. They demonstrate high sensitivity of the SPR to the packing density of nanoparticles, which we define in terms of the overlap parameter tj. Fig. 2 represents the red shift of the SPR wavelength for dipole nanoparticles depending on concentration due to an increase in degree of near-range ordering... 

Interestingly, Yaghi and coworkers employed the reversible formation of borox-ines and boronates in the synthesis of 2-D covalent periodic networks (Scheme 28.7) [66]. In this case, monomers were subjected to solution polymerization, and the products obtained as precipitates. Layered bulk structures and in-plane periodicities were supported by powder X-ray diffraction experiments that exhibited a relatively narrow linewidth that was indicative of more than a near-range order. Although the layers may therefore be regarded as latent 2-D polymers, Hke many other layered systems their individual isolation remained undemonstrated and its feasibility uncertain (see Sections 28.3 and 28.5.1). 

Pair distribution function PDF Near range order ... 

XAS is an interesting tool to obtain in situ results on the near range order of passive layers on metals even for highly disordered or amorphous films. Experimental requirements have been shortly described above. From the reflectivity data, one may calculate with the Fresnel equations the absorption spectra x(E) of the film (see Refs. [140,141] for details). The oscillation of p(E) above the absorption edge, the so-called extended absorption fine structure (EXAFS), leads to the EXAFS fimction %(E) = ( X - MoVMo with the background value Po- The Fourier transform of % E) to the real space yields the structural parameters, i.e., the radius of the coordination shells Rj, their coordination numbers Nj, i.e. the number of neighbors for a given coordination shell and the Debye-Waller factor Oj as a measure of the structural (and thermal) disorder. 

Parameters for near range order (first two coordination shells) of anodic oxide layers grown on Ag in IM NaOH in dependence of the electrode potential, E < 0.725 for AgjO, E > 0.725 for AgO. (From Lutzenkirchen-Hecht, D. and Strehblow, H.-H., Surf. Interf Anal., 41,820,2009.)... 

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