Field dependence

The amount of processing required in the field depends upon the composition of the gas and the temperature and pressure to which the gas will be exposed during transportation. The process engineer is trying to avoid liquid drop-out during transportation, since this may cause slugging, corrosion and possibly hydrate formation (refer to Section 10.1.3). For dry gases (refer to Section 5.2.2) the produced fluids are... 

Even for a single radical tire spectral resolution can be enlianced for disordered solid samples if the inliomogeneous linewidth is dominated by iimesolved hyperfme interactions. Whereas the hyperfme line broadening is not field dependent, tire anisotropic g-matrix contribution scales linearly with the external field. Thus, if the magnetic field is large enough, i.e. when the condition... 

Figure 6 shows the field dependence of hole mobiUty for TAPC-doped bisphenol A polycarbonate at various temperatures (37). The mobilities decrease with increasing field at low fields. At high fields, a log oc relationship is observed. The experimental results can be reproduced by Monte Carlo simulation, shown by soHd lines in Figure 6. The model predicts that the high field mobiUty follows the following equation (37) where d = a/kT (p is the width of the Gaussian distribution density of states), Z is a parameter that characterizes the degree of positional disorder, E is the electric field, is a prefactor mobihty, and Cis an empirical constant given as 2.9 X lO " (cm/V). ...

Experimental Hole Mobilities. The experimental values of hole mobihties in polymers are tabulated in Tables 1 and 2. The hole mobihty is field dependent. Whenever the experimental data have been fitted with equation 5, the parameters p.Q, O, and O, which give a complete description of the field dependence of the hole mobihty, are Hsted (Table 2). Otherwise, hole mobilities at selected fields are Hsted. All acronyms are defined in Figures 2 and 3. 

The hole mobiUty is field-dependent and only selected low field and high field values are Hsted here. AH data were measured at room temperature unless... 

Fig. 7. The field-dependence of the charge-generation efficiency of a 2.0- lm thick (0) a l.l-).tm thick ( ), and 1.8-).tm thick (A) fuUerene/PMPS film obtained with positive charging and 340-nm irradiation (A). The soHd lines are calculated from the Onsager model. The best-fit curve is obtained with Tq = 2.7 nm and = 0.85. Also plotted is the charge-generation efficiency of a fuUerene/PVK film (+) obtained with positive charging and 340-nm irradiation (B). The soHd lines are calculated from the Onsager model. The best-fit curve is obtained with = 1.9 nm and = 0.9 (13).

In plasma chromatography, molecular ions of the heavy organic material to be analy2ed are produced in an ionizer and pass by means of a shutter electrode into a drift region. The velocity of drift through an inert gas at approximately 101 kPa (1 atm) under the influence of an appHed electric field depends on the molecular weight of the sample. The various sonic species are separated and collected every few milliseconds on an electrode. The technique has been employed for studying upper atmosphere ion molecule reactions and for chemical analysis (100). 

The reaction of bis(benzene)vanadium [12129-72-5] with TCNE affords an insoluble amorphous black soHd that exhibits field-dependent magnetization and hysteresis at room temperature, an organic-based magnet (12). The anion radical is quite stable in the soHd state. It is paramagnetic, and its intense electron paramagnetic resonance (epr) spectmm has nine principal lines with the intensity ratios expected for four equivalent N nuclei (13) and may be used as an internal reference in epr work (see Magnetic spin resonance). 

The first step for any structure elucidation is the assignment of the frequencies (chemical shifts) of the protons and other NMR-active nuclei ( C, N). Although the frequencies of the nuclei in the magnetic field depend on the local electronic environment produced by the three-dimensional structure, a direct correlation to structure is very complicated. The application of chemical shift in structure calculation has been limited to final structure refinements, using empirical relations [14,15] for proton and chemical shifts and ab initio calculation for chemical shifts of certain residues [16]. 

A variety of methodologies have been implemented for the reaction field. The basic equation for the dielectric continuum model is the Poisson-Laplace equation, by which the electrostatic field in a cavity with an arbitrary shape and size is calculated, although some methods do not satisfy the equation. Because the solute s electronic strucmre and the reaction field depend on each other, a nonlinear equation (modified Schrddinger equation) has to be solved in an iterative manner. In practice this is achieved by modifying the electronic Hamiltonian or Fock operator, which is defined through the shape and size of the cavity and the description of the solute s electronic distribution. If one takes a dipole moment approximation for the solute s electronic distribution and a spherical cavity (Onsager s reaction field), the interaction can be derived rather easily and an analytical expression of theFock operator is obtained. However, such an expression is not feasible for an arbitrary electronic distribution in an arbitrary cavity fitted to the molecular shape. In this case the Fock operator is very complicated and has to be prepared by a numerical procedure. 

Fig. 6. The magnetic field dependence of the high- and low-temperature MR, respeetively the solid lines are caleulated. The inset shows a sehematic of the eontact eonfiguration for the transport measurements.

Song et al. [16] reported results relative to a four-point resistivity measurement on a large bundle of carbon nanotubes (60 um diameter and 350 tm in length between the two potential contacts). They explained their resistivity, magnetoresistance, and Hall effect results in terms of a conductor that could be modeled as a semimetal. Figures 4 (a) and (b) show the magnetic field dependence they observed on the high- and low-temperature MR, respectively. 

A second study [33] on samples that contain a mixture of nanotubes, together with several percent buckyonion -type structures, was carried out at temperatures between 4.5 and 300 K, and fields between 0 and 5.5 T. The moment M is plotted as a function of field in Fig. 7, for the low-field range, and in Fig. 8 for the high-field range. The field dependence is clearly non-linear, unlike that of graphite, in which both the basal plane and the c-axis moments are linear in field, except for the pronounced de Flaas-van Alphen oscillations at low temperature. 

Fig. 8. Field dependence of the momenl of carbon nanolubes al ihe temperaiures shown at high magnetic fields (after Here-mans et al.[26]).

Fig. 4. Magnetic-field dependence of the magnetoconductance of an MWCNT at different temperatures [10].

Fig. 13. Electric-field dependence of the emission current obtained for a carefully aligned MWCNT film [38], Inset Fowler-Nordheim plot, where y is the field-enhancement factor.

While LAO/GIAO had been proposed well before the advent of modem computational chemistry, it was only developments in calculating (geometrical) derivatives of the energy (and wave function) that made it practical to use field-dependent orbitals. ... 

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