Effective mobilities

The mixture of acetonitrile/water (1 1, v/v) was selected as most effective mobile phase. The optimum conditions for chromatography were the velocity of mobile phase utilization - 0,6 ml/min, the wave length in spectrophotometric detector - 254 nm. The linear dependence of the height of peack in chromathography from the TM concentration was observed in the range of 1-12.0 p.g/mL. 

Mobile CA. These arc CA in which some (or all) lattice sites are free to move about the lattice. In effect, mobile CA are primitive models of mobile robots. Typically, their internal state space reflects some features of the local environment within which they are allowed to move and with which they are allowed to interact. An example of mobile CA used to model some aspects of military engagements is discussed in Chapter 12. 

Figure 14-13. Evolution of the field-effect mobility of OFETs for five organic materials polythio-phenc (PT) and its derivatives, qualerthiophcne (4T), scxithio-phenc (6T), dihcxyl-sexithiophene (DH6T). and pcntaecnc.

Another significant feature found recently is that the effect of the chain length on the field-effect mobility is much less pronounced than indicated in earlier reports [68, 74]. The increase from 4T to 6T corresponds to about a factor of ten, while that from 6T to 8T is only two (the low mobility measured for the dihexyl-substituted 8T must be ascribed to the difficulty in synthesizing and purifying this compound 75 J). Representative data arc gathered in Table 14-1. Also note that the effect of alkyl end substitution is reduced by a factor of two to three (as compared to up to 1000 in earlier reports 68 ). 

Table 14-1. Typical field-effect mobility (in cm2 V 1 s ) of unsubsliluled and dialkyl-subsliluled oli-gothiophenes.

Figure 14-21. Varialion of the field-effect mobility as a functior of the conductivity of various) doped polyfdodccyloxy-terlhienyl) (PDOT), a polylhiophene derivative (adapted from Ref. II3 ).

An alternative method to estimate the field-effect mobility consists of using the transconduclanee in the linear regime, given by Eq. (14.32). We noie that the... 

Figure 14-23. Variation of the field-effect mobility, as deduced by differentiating the drain current at Vt,=-i V, as a function of the gale voltage, for the same device as in Figure 14-22.

In a more extensive development of the tortnons-path and barrier theories, Boyack and Giddings [45] considered the transport of solnte in a simple geometrical system similar to that used in the diffnsion analysis of Michaels [241] bnt with added tortuosity effects. The effective mobility in this system was found to be... 

FIG. 26 Effective mobility versus porosity for various length ratios using Eq. (100). (Based on Ref. 45.)... 

Combining hindered diffusion theory with the diffusion/convection problem in the model pore, Trinh et al. [399] showed how the effective transport coefficients depend upon the ratio of the solute to pore size. Figure 28 shows that as the ratio of solute to pore size approaches unity, the effective mobility function becomes very steep, thus indicating that the resolution in the separation will be enhanced for molecules with size close to the size of the pore. Similar results were found for the effective dispersion, and the implications for the separation of various sizes of molecules were discussed by Trinh et al. [399]. 

It can be noted that in general this result predicts that the ratio of the dispersion coefficient to the free-solution diffusion coefficient is different from the ratio of the effective mobility to the free-solution mobility. In the case of gel electrophoresis, where it is expected that the (3 phase is impermeable (i.e., the gel fibers), the medium is isotropic, and the a phase is the space between fibers, the transport coefficients reduce to... 

The standard Rodbard-Ogston-Morris-Killander [326,327] model of electrophoresis which assumes that u alua = D nlDa is obtained only for special circumstances. See also Locke and Trinh [219] for further discussion of this relationship. With low electric fields the effective mobility equals the volume fraction. However, the dispersion coefficient reduces to the effective diffusion coefficient, as determined by Ryan et al. [337], which reduces to the volume fraction at low gel concentration but is not, in general, equal to the porosity for high gel concentrations. If no electrophoresis occurs, i.e., and Mp equal zero, the results reduce to the analysis of Nozad [264]. If the electrophoretic mobility is assumed to be much larger than the diffusion coefficients, the results reduce to that given by Locke and Carbonell [218]. 

FIG. 32 Effective mobility. (Reprinted with permission of the American Institute of Physics and O. Lumpkin from Ref. 223, Copyright 1984, American Institute of Physics.)... 

The form of the effective mobility tensor remains unchanged as in Eq. (125), which imphes that the fluid flow does not affect the mobility terms. This is reasonable for an uncharged medium, where there is no interaction between the electric field and the convective flow field. However, the hydrodynamic term, Eq. (128), is affected by the electric field, since electroconvective flux at the boundary between the two phases causes solute to transport from one phase to the other, which can change the mean effective velocity through the system. One can also note that even if no electric field is applied, the mean velocity is affected by the diffusive transport into the stationary phase. Paine et al. [285] developed expressions to show that reversible adsorption and heterogeneous reaction affected the effective dispersion terms for flow in a capillary tube the present problem shows how partitioning, driven both by electrophoresis and diffusion, into the second phase will affect the overall dispersion and mean velocity terms. 

Water-in-oil macroemulsions have been proposed as a method for producing viscous drive fluids that can maintain effective mobility control while displacing moderately viscous oils. For example, the use of water-in-oil and oil-in-water macroemulsions have been evaluated as drive fluids to improve oil recovery of viscous oils. Such emulsions have been created by addition of sodium hydroxide to acidic crude oils from Canada and Venezuela. In this study, the emulsions were stabilized by soap films created by saponification of acidic hydrocarbon components in the crude oil by sodium hydroxide. These soap films reduced the oil/water interfacial tension, acting as surfactants to stabilize the water-in-oil emulsion. It is well known, therefore, that the stability of such emulsions substantially depends on the use of sodium hydroxide (i.e., caustic) for producing a soap film to reduce the oil/water interfacial tension. 

The major design concept of polymer monoliths for separation media is the realization of the hierarchical porous structure of mesopores (2-50 nm in diameter) and macropores (larger than 50 nm in diameter). The mesopores provide retentive sites and macropores flow-through channels for effective mobile-phase transport and solute transfer between the mobile phase and the stationary phase. Preparation methods of such monolithic polymers with bimodal pore sizes were disclosed in a US patent (Frechet and Svec, 1994). The two modes of pore-size distribution were characterized with the smaller sized pores ranging less than 200 nm and the larger sized pores greater than 600 nm. In the case of silica monoliths, the concept of hierarchy of pore structures is more clearly realized in the preparation by sol-gel processes followed by mesopore formation (Minakuchi et al., 1996). 

Since there are (Tf + Tt) 1 cycles of trapping and detrapping per unit time, the drift velocity is (Ax)/(xf + tt), from which the effective mobility is derived to be... 

Apart from fundamental constants and the liquid temperature, the variable parameters in the effective mobility equation are the quasi-free mobility, the trap density, and the binding energy in the trap. Figure 10.2, shows the variation of prff with e0 at T = 300 K for /tqf = 100 cm3v 1s 1 and nt = 1019cm-3. It is clear that the importance of the ballistic mobility (jl)l increases with the binding... 

In comparing the results of the quasi-ballistic model with experiment, generally pq[ = 100 cn v s-1 has been used (Mozumder, 1995a) except in a case such as isooctane (Itoh et al, 1989) where a lower Hall mobility has been determined when that value is used for the quasi-free mobility. There is no obvious reason that the quasi-free mobility should be the same in all liquids, and in fact values in the range 30-400 cmV -1 have been indicated (Berlin et al, 1978). However, in the indicated range, the computed mobility depends sensitively on the trap density and the binding energy, and not so much on the quasi-free mobility if the effective mobility is less than 10 crr v s-1. A partial theoretical justification of 100 cm2 v 1s 1 for the quasi-free mobility has been advanced by Davis and Brown (1975). Experimentally, it is the measured mobility in TMS, which is considered to be trap-free (vide supra). 

Baird and Rehfeld (1987) have analyzed the thermodynamics of electron transport in the two-state trapping model. According to these authors, the effective mobility, ignoring the mobility in the trapped state, is given by... 

FIGURE 10.6 Comparison of the quasi-ballistic and the usual trapping models with respect to the variation of the free energy change upon trapping with the effective mobility. Reproduced from Mozumder (1996), with the permission of Am. Chem. Soc.O... 

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