Modeling Electric Field

SIMION 6.0 was used to model the electric field of a pulled capillary, the ESI Chip and a chip without the integrated counter electrode to gain insights into the 

A Silicon-based ESI Chip with Integrated Counter Electrode 55 

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F. Colonna, E. Evleth, and J. G. Angyan, J. Comput. Chem., 13, 1234 (1992). Critical Analysis of Electric Field Modeling Formamide. 

The Onsager Model in the Non-linear Electric Field Effect. The non-linear dectric field theory of Debye disagrees with most of the measurements of Ac in liquids and thdr solutions. To Van Vleck is due the atten t to reduce the discrepandes by applying Onsager s local electric field model in the treatment of the field effect. Aiming at simplidty, he considered only the influence of reorientation of ri d (not polarizable) electric dipoles p,... 

Buckingham and Pople refer to the effect of the electric field as a paramagnetic term, and it has the dependence of the second term in equation (5), Although equation (5) has the virtue of attempting to describe the true electronic environment of the proton, it has the disadvantages of intractability. The electric field perturbation model is mathematically simple but an extreme approximation. Since these two treatments lead to the same functional dependence on p, perhaps the electric field model provides a useful approximation to the more complete description of equation (5), Whether this proves to be true or whether the characteristic arbitrariness of the electrostatic model will deprive the model of more than qualitative predictive value is not yet clear. In any event, the two treatments do concur in shifting attention from the p" term to the p term with its opposite sign. 

Ti The localized (field) electrical effect parameter. It is identical to cq. Though other localized electrical effect parameters such as cr and op have been proposed, there is no advantage to their use. The cr parameter has sometimes been used as a localized electrical effect parameter such use is generally incorrect. The available evidence is strongly in favour of an electric field model for transmission of the effect. 

Figure 3.3 SIMION electric field models for 28 pm diameter sprayers located 4.7 mm from the ion orifice counter electrode and a spray (solution) voltage of 1.6 kV. Equipotential lines are shown every 50 V. Electric field calculated at the tip of the Taylor cone for each model is shown. (B, C) A comparison of the models shows a 50-fold increase in the electric field generated at the tip of the Taylor cone when the silicon underlying a dielectric film is held at ground potential rather than at the spray potential. Electric field shown in (B) is equivalent to that of a 2 pm diameter pulled capillary with a 1.0 kV spray voltage at a distance of 3 mm from a counter electrode.

A detailed study of the N2 emission rates has been carried out by Morrill et al (1998). In this study, the quasistatic electric field model (Pasko et al, 1997) was used to calculate the electric fields, and the solution to Boltzmann s equation was used to calculate the electron energy distribution function as a fimction of altitude. Results for excitation of seven triplet states of N2 are shown in Fig. 12 at A = 65 and 75 km. The temporal diuation of the excitations may be understood in terms of the faster relaxation (higher conductivity see Fig. 9) of the E field at the higher altitude. 

Should the intensity of the uniform electric field modeling the charge/surface repulsion and surrounding solvent effects be known, the total effective potential Veffiz) which is felt by the chemisorbed radical-anion at f > 0 within our one-dimensional model reads ... 

Sevcikova, H. Marek, M. 1986. Chemical Waves in Electric Field—Modelling, Physica D 21, 61 77. 

Sevcikova, H. and Marek, M. (1986) Chemical waves in electric field-modelling. Phys. D, 21, bl-TJ. 

Figure 3.7 Optimized adsorption configurations of sulfate over the Pt(lll) surface using (a) a vacuum model, (b) a partially solvated model used in the electric field model, and (c) a fully solvated model used in double reference method.

Figure 3.8 The adsorption energy of sulfate anion over Pt(lll) at (a) vacuum and (b) partially solvated interfaces. The diamond ( ) with solid line represents results from the linear free energy model (Model 2a. 1), the square with dotted line represents ( ) the linear free energy model with dipole correction (Model 2a.2), and the triangle (a) with dashed line represents the electric field model (Model 2a.3).

The dipole moment (Model 2a.2) or applied electric field (Model 2a.3) corrections made to the adsorption energy for the adsorbate-electrode model may also now be made including the water bilayer. The dipole moment calculated for the A + 8H20 structure is —0.26 e A whereas that for the 9 Fl20 structure is —1.22 e A. The dipole moment difference of 0.96 e A leads to a slope of adsorption free energy versus potential of 1.68 (recall 1.85 at the vacuum interface), suggesting that fewer electrons transfer upon adsorption of sulfate in the solvated environment compared to the vacuum interface. 

A similar expression can be written for an oxidation reaction. The free energy of the adsorbed species may be calculated at a vacuum, micro-solvated, or fully solvated interface. Corrections to the energy difference between the two adsorbed species may be made using the dipole-field correction (Model 2a.2), and applied electric field (Model 2a.3), or the double-reference method (Model 2b. 1). 

This linear free energy, vacuum interface approach is the simplest model for a reaction involving proton-electron transfer. The effect of the electric field can also be estimated with the consideration of the dipole moment change between reactants and products (Model 2a.2) or application of an electric field (Model 2a.3). The dipole moments are 0.10 and —0.04 e A for O2 and OOH, respectively, on a 3x3 Pt(lll) surface. Assuming the double layer thickness is 3 A, the field at a potential of 1 V is 0.33 V A The correction energy due to the electric field is —0.33 (—0.04 — 0.1)= +0.05 eV. This correction term is + 0.09 for OH reduction to H2O (/r = 0.07 and —0.21, respectively). The effect of an applied electric field could be included in the same manner as the ion adsorption example. 

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