Theoretical Shielding Effectiveness

All homogenous materials are characterized by a quantity known as the intrinsic impedance  

When an EM wave propagates through the material, the wave impedance approaches the intrinsic impedance of the material. For dielectric 

For a conductor used below optical frequencies defined by cos, the intrinsic impedance of Eq. (9.3) can be written as  

It is customary to define propagation constant (7) in the media such that  

The electric and magnetic fields of a plane wave are related by the intrinsic impedance of the medium 

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The properties of the elements of the sixth period are influenced by lanthanide contraction a gradual decrease of the atomic radius with increasing atomic number from La to Lu. The elements of groups 5 to 11 for the fifth and sixth periods have comparable stmctural parameters. For instance, Nb and Ta, as well as the pair Mo and W, have very similar ionic radii, when they have the same oxidation number. As a result, it is very difficult to separate Nb and Ta, and it is also not easy to separate Mo and W. Similarly, Ag and Au have nearly the same atomic radius, 144 pm. Recent studies of the coordination compounds of Ag(I) and Au(I) indicate that the covalent radius of Au is even shorter than that of Ag by about 8 pm. In elementary textbooks the phenomenon of lanthanide contraction is attributed to incomplete shielding of the nucleus by the diffuse 4f inner subshell. Recent theoretical calculations conclude that lanthanide contraction is the result of both the shielding effect of the 4f electrons and relativistic effects, with the latter making about 30% contribution. 

Si NMR chemical shifts were calculated for each molecule relative to the theoretical shielding for tetramethylsilane (TMS), at the HF/6-311+G(2d,p)86 level using the GIAO method,94 as implemented in Gaussian 94 and Gaussian 98. Shifts for gas-phase molecules are reported because the inclusion of solvation via the SCRF method was found to have little effect on the predicted shifts.83 Comparison of calculated shifts with experimental values for compounds with well-known structures yielded an error estimate of about 1 to 8% for quadra-coordinated silicon and 2 to 9% for penta-coordinated silicon. 

In the nmr spectrum of oxirane, the protons 3 to the oxygen display a small chemical shift compared to that of the j3 protons of larger cyclic ethers this can only be explained by the shielding effect of the abnormal electron density, which assumes a low electron density around the oxygen, as suggested earlier on theoretical grounds. The proton chemical shifts for various substituted oxiranes are given in a number of reviews and handbooks. ... 

MP2 method [175b,176]), as is clearly shown by the results in Fig. 5.44. The remarkable shielding effect of a benzene ring in [7]paracyclophane [177] is nicely reproduced. The calculation of NMR spectra has become an important tool in probing the electronic structure of theoretically interesting molecules [178],... 

The wind tunnel is most frequently employed for this purpose. Perfect simulation is impossible, however, and thus the choice of facility is dictated by the importance of closely simulating either the thermal, chemical, or mechanical aspects of the entry environment. Subsequent specialized testing is then carried out to determine the importance of environmental parameters not closely simulated in the previous evaluation work. Finally, the plastic material is flown in the actual service environment to prove its heat shielding effectiveness, confirm previous theoretical prediction of material behavior, and to provide a sound basis for the selection and design of heat shields for operational flight vehicles. 

Figure 9.14 (a) Measured far-field shielding effectiveness of PVC-ICP blend samples (S4, SIO, S7, and S9) of different conductivities (S4 7.45 S/cm, SIO 3.74 S/cm, S7 0.98 S/cm, and S9 0.18 S/cm) compared to stainless steel (SS) filled ABS sample (b) measured far-field shielding results (dots) are compared with the predictions of above samples (solid lines). Reprinted from Ref. [18] with permission from Wiley, (c) Theoretical EMI SE predicted by model and (d) dependence of experimental SE on conductivity and sample thickness. Reprinted from Ref [47] with permission from Elsevier. 

Eq. (3.23) has been applied to calculate shielding effects due to intermolecular as well as intramolecular electric fields. From experimental studies by Raynes, Buckingham, Bernstein, Schaefer, Petra-kis, Laszlo and others as well as from theoretical calculations by Raynes, Buckingham, Musher and Yonemoto [194 195 196 197 198 199 200], it appears that for protons in C-H bonds A 3 B (9 - 18)... 

Figure 2 Shielding effectiveness of 3 mm-thick composites at 1 GHz versus volume resistivity. Solid line is theoretical curve. From Li, L. and Chung, D.D.L. (1994) Composites, 25(3).

Figure 9. A comparison of theoretical PRJSM predictions (curves) for the radial distribution functions with Monte Carlo simulations (points). The simulations were performed on vinyl chain melts of TV = 33 monomers at a packing fraction of 0.35. Note the shielding effects at short distances, (a) The diagonal components AA, BB, and CC of the correlation functions, (b) The off-diagonal components AB, AC, and BC of the correlation functions.

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