Field dependence of mobility

The dependence of drift mobility on the external field must be interpreted by a theoretical model, and as such it can elucidate the transport mechanism in a given case. In this section, we will only describe the phenomenological and experimental aspects. Their theoretical significance will be taken up in Sect. 10.2. 

FIGURE 10.1 (a) Electron drift velocity versus external electric field in methane, NP, and TMS showing sublinear dependence. See text for details, (b) Electron drift velocity versus external electric field in neohexane, ethane, 2,2,2,4-TMP, and butane at the indicated temperatures. Generally, the field dependence is supralinear, whereas for neohexane, linear variation has been seen up to 140 kV/cm. See text for details. Reproduced from Schmidt (1977), with permission of National Research Council of Canada . 

TABLE 10.2 Critical Field E and Nature of Field Dependence of Mobility in Various Nonpolar Liquids 

TABLE 10.3 Saturation Drift Velocity in High-Mobility Liquids 

In certain liquids, the electron drift velocity shows peculiar behavior under special circumstances, some of which will now be described. 

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There is abundant evidence that the above formalism provides a framework for explaining the majority of experimental facts including the temperature and field dependence of mobility albeit not in the entire field regime, notably (i) the temperature dependence of the slope parameter of lnxF172 plots, (ii) the prefaetor mobility, (iii) the influence of randomly positional dipoles on the width of the... 

Table 10.2 lists the critical field Ec in various nonpolar liquids along with the approximate nature of field dependence of mobility when E > Eq. It is remarkable that the higher the zero-field mobility is, the smaller is the value of Ec, indicating the role of field-induced heating. Also note that in the sublinear case, Ec is larger in the case of molecular liquids than for liquefied rare gases,... 

Dunlap DH, Parris PE, Kenkre VM (1996) Charge-dipole model for the universal field dependence of mobilities in molecularly doped polymers. Phys Rev Lett 77 542... 

Figure 3. Field dependence of mobility (9). Key X, sweepout expansion and...

In the early to mid 1980s, the characterization of ions with field dependence of mobility was treated theoretically [36] and was based on the following concept if ions had the same mobility but differing dependence of mobility with E/N, then the characteristic differences in mobility could be a basis for ion separation. Thus, a complete expression of mobility is shown in Eq. 3, where the mobility coefficient contains a non-linear... 

Fig. 6. Schematic of a differential mobility spectrometer showing the principles of ion separation in a differential mobility spectrometry (DMS) drift tube. Ion paths are governed by both the asymmetric electric field and field dependence of mobility for an ion. The inset displays the asymmetric waveform of separation electric field used in the DMS drift tube. The waveforms shown are theoretical (top part) and actual or experimental (bottom part) used in these experiments.

Figure 93 Transient photocurrent signals (i) for 8 pm thick Alq3 layers sandwiched between the ITO anode and A1 cathode. Light pulses entered the samples through the ITO anode. The change from the dispersive transport for Alq3 as-received from the supplier (circles) to the non-dispersive transport with purified (squares) Alq3 samples. It can be seen in both linear (a) and double logarithmic (b) plots. In the inset of part (a) electric field dependence of mobility is shown, in part (b) the TOF transient for as-received Alq3 exposed to ambient is added (diamonds). After Ref. 423. Copyright 2003 American Institute of Physics, with permission.

Figure 8 The field dependencies of mobilities of a series of TPM derivatives doped into PS.

The field dependence of mobility is observed to be Poole-Frenkel-like over a wide range of applied voltage. This has been observed both for pure polymers, e.g. PVK, and molecularly loaded polymers, e.g. DEH and TAPC in polycarbonate. Data for loaded systems are shown in Fig. 8.29. The fit to the DEH data is obtained using the full analytical expression derived by Dunlap et al. (1996). 

As can be seen in the table, the mobility is reasonably constant as a function of voltage for the undoped paper and the paper doped with NaCl. Some variability can be noted in the conductive base sheet paper however this is more likely to be due to sample variability than intrinsic electric field dependence of mobility, since as previously noted, every electric field measurement in that case was performed on a fresh sample. 

Krylov, E. Nazarov, E.G. Miller, R.A. Tadjikov, B. Eiceman, G.A., Field dependence of mobilities for gas-phase-protonated monomers and proton-bound dimers of ketones by planar field asymmetric waveform ion mobility spectrometer (PFAIMS), J. Phys. Chem. A 2002, 106, 5437-5444. 

Krylova, N. Krylov, E. Eiceman, G.A. Stone, J.A., Effect of moisture on the field dependence of mobility for gas-phase ions of organophosphorus compounds at atmospheric pressure with field asymmetric ion mobility spectrometry, J. Phys. Chem. A 2003, 107, 3648-3654. 

Paranjape, B.V., Field dependence of mobility in gases, Phys. Rev. 1980, A21, 405M07. 

FIGURE 11.6 Plot of alpha values for protonated monomers of organophosphate compounds obtained at two fields of 80 (bottom) and 140 (top) Td as a function of moisture. DMMP, dimethyl-methylphosphonate TMP, trimethyl-phosphate DEMP, diethyl-methyl-phosphonate DEEP, diethyl-ethylphosphonate DIMP, di-iso-prophyl-methylphosphonate DEIP, diethyl-iso-prophylphosphonate TEP, triethyl phosphate TPP, tripropyl phosphate DBBP, dibutyl-butylphosphonate TBP, tri-n-butylphosphate. (From Krylova et al., Effect of moisture on high field dependence of mobility for gas phase ions at atmospheric pressure organophosphorus compounds, J. Phys. Chem. 2003. With permission.)... 

This comparison showed that the TOF and CELIV yields mutually consistent picture of mobility in the studied P3HT samples. Importantly, the negative electric field dependence of mobility [91] at higher temperatures is observed using both experimental techniques, which confirms that it is not an artifact of the TOF technique, but rather an intrinsic property of the materials studied. 

Fieure 8.66. Plots of various mobilities as a function of F /kT. The arrays of circles viewed along thick short arrows indicate the temperature dependence of mobility at fixed fields the data taken at constant source-drain voltages of — 10, —20, and —30 V are shown with filled circles for the sake of clear visualization. The arrays of circles viewed along the thin long arrows indicate the field dependence of mobility at fixed temperatures. Only four arrays are labeled for simplicity. Reprinted with permission from Reference 209. Copyright 1995 The American Physical Society. 

The exp( F ) form of the mobility in combination with the above temperature dependence allows us to express the temperature and field dependence of mobility as the following empirical equation ... 

Polaron theory, on the other hand, predicts the following field dependence of mobility for a polaronic system without disorder [271,272] ... 

Fig.3. Electric field dependence of mobility in PDBG. The slope varies with temperature an becomes negative at T=To as indicated in the insert.

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