Movement in an Electric Field

Modes of Operation There is a close analogy between sedimentation of particles or macromolecules in a gravitational field and their elec trophoretic movement in an electric field. Both types of separation have proved valuable not only for analysis of colloids but also for preparative work, at least in the laboratoiy. Electrophoresis is applicable also for separating mixtures of simple cations or anions in certain cases in which other separating methods are ineffectual. 

Reliable, though relative, information about the size of ions in aqueous media can be obtained from data on the electrophoretic mobility of these ions [160], as the velocity of their movement in an electric field is direcdy proportional to their charge and inversely proportional to their hydrodynamic radius. According to these estimations (Table 12.3), the size of hydrated cations and anions decreases according to the following series ... 

Compare the observations of Frumkin, /. Colloid Science 1 (1946), who describes completely similar movements in an electric field in the case of mercury drops in water. 

The vesicle wall is however very thin and not or hardly visible but its presence is betrayed by the flattening on one side of the coacervate drop. These coacervate drops can while lying on a surface also carry out creep movements in an electric field in the direction of the arrow below the figures. Compare with Fig. 20 (p. 452). 

Electrically assisted transdermal dmg deflvery, ie, electrotransport or iontophoresis, involves the three key transport processes of passive diffusion, electromigration, and electro osmosis. In passive diffusion, which plays a relatively small role in the transport of ionic compounds, the permeation rate of a compound is deterrnined by its diffusion coefficient and the concentration gradient. Electromigration is the transport of electrically charged ions in an electrical field, that is, the movement of anions and cations toward the anode and cathode, respectively. Electro osmosis is the volume flow of solvent through an electrically charged membrane or tissue in the presence of an appHed electrical field. As the solvent moves, it carries dissolved solutes. 

Electrophoretic techniques are based on the movement of ions in an electrical field. An ion of charge q experiences a force F given by T = Eq/d, where E is the voltage (or electrical potential) and dis the distance between the electrodes. In a vacuum, T would cause the molecule to accelerate. In solution, the molecule experiences frictional drag, iy, due to the solvent ... 

The influence of interionic fores on ion mobilities is twofold. The electrophoretic effect (occurring also in the case of the electrophoretic motion of charged colloidal particles in an electric field, cf. p. 242) is caused by the simultaneous movement of the ion in the direction of the applied... 

An ionophoretic method was described by Tewari [41] for the study of equilibria in a mixed ligand complex system in solution. This method is based on the movement of a spot of metal ion in an electric field with the complexants added in the background electrolyte at pH 8.5. The concentration of the primary ligand (nitrilo-triacetate) was kept constant, while that of the secondary ligand (penicillamine) was varied. The stability constants of the metal nitrilotriacetate-penicillamine complexes have been found to be 6.26 0.09 and 6.68 0.13 (log K values) for the Al(III) and Th(IV) complexes, respectively, at 35 °C and an ionic strength of 0.1 M. 

There are, in principle, three ways in which material may be transported to the electrode surface diffusion, convection and migration. Of these, perhaps the most straightforward is migration, which simply consists of the movement of a charged particle under the influence of an electric field. Experimentally, it is well established that after an extremely short time an ion in solution in an electric field will behave as if it had acquired a steady velocity in the direction of the field. The reason why a steady velocity is established rather... 

When applied to the motion of ions in a crystal, the term drift applies to motion of ions under the influence of an electric field. Although movement of electrons in conduction bands determines conductivity in metals, in ionic compounds it is the motion of ions that determines the electrical condu-ctivity. There are no free or mobile electrons in ionic crystals. The mobility of an ion, ji, is defined as the velocity of the ion in an electric field of unit strength. Intuitively, it seems that the mobility of the ion in a crystal should be related to the diffusion coefficient. This is, in fact, the case, and the relationship is... 

The physical approach uses alternating current (ac-) dielectrophoresis to separate metallic and semiconducting SWCNTs in a single step without the need for chemical modifications [101]. The difference in dielectric constant between the two types of SWCNTs results in an opposite movement along an electric field gradient between two electrodes. This leads to the deposition of metallic nanotubes on the microelectrode array, while semiconducting CNTs remain in the solution and are flushed out of the system. Drawbacks of this separation technique are the formation of mixed bundles of CNTs due to insufficient dispersion and difficulties in up-scaling the process [102]. 

Classical Free-Electron Theory, Classical free-electron theory assumes the valence electrons to be virtually free everywhere in the metal. The periodic lattice field of the positively charged ions is evened out into a uniform potential inside the metal. The major assumptions of this model are that (1) an electron can pass from one atom to another, and (2) in the absence of an electric field, electrons move randomly in all directions and their movements obey the laws of classical mechanics and the kinetic theory of gases. In an electric field, electrons drift toward the positive direction of the field, producing an electric current in the metal. The two main successes of classical free-electron theory are that (1) it provides an explanation of the high electronic and thermal conductivities of metals in terms of the ease with which the free electrons could move, and (2) it provides an explanation of the Wiedemann-Franz law, which states that at a given temperature T, the ratio of the electrical (cr) to the thermal (k) conductivities should be the same for all metals, in near agreement with experiment ... 

The most commonly used procedure for checking the purity of proteins is sodium do-decyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE). In electrophoresis, molecules move in an electrical field (see p.276). Normally, the speed of their movement depends on three factors—their size, their shape, and their electrical charge. 

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