EOF vector

A negative power supply (-10 kV) is used for anion separations. The BGE typically contains 0.05 % to 0.30 % PDDAC, up to 150 mM sodium chloride or lithium sulfate, and a 20 mM borate buffer. The EOF vector and the electrophoretic vectors of the sample anions are both in the anodic direction. The fraction of each sample anion that is attached to exchange sites in the PDDAC has a cathodic electrophoretic vector, although this is believed to be weak. The net electrophoretic vector for any given anion... 

Reproducible migration times require a stable EOF. The magnitude of the EOF vector is influenced by the extent to which silica silanol groups are ionized to give a negative charge, and this varies considerably with pH. Thus, a stable EOF requires a thorough equilibration of the capillary surface with a pH buffer and finally with the buffered capillary electrolyte. 

Figure 3 The mobilities of cations and anions are illustrated using vectors, as is the effect of EOF on the total mobility.

The electrophoretic separation principle is based on the velocity differences of charged solute species moving in an applied electric field. The direction and velocity of that movement are determined by the sum of two vector components, the migration and the electroosmotic flow (EOF). The solute velocity v is represented as the product of the electric field strength E and the sum of ionic mobility uUm and EOF coefficient /a OF ... 

In the presence of EOF, the observed velocity is due to the contribution of electrophoretic and electroosmotic migration, which can be represented by vectors directed either in the same or in opposite direction, depending on the sign of the charge of the analytes and on the direction of EOF, which depends on the sign of the zeta potential at the plane of share between the immobilized and the diffuse region of the electric double layer at the interface between the capillary wall and the electrolyte solution. Consequently, is expressed as... 

Fig. 9 Climatic current vector fields in the Black Sea at a depth of a 0 m, b 300 m in September from adaptation modeling. Inset in Fig. 9a climatic water salinity anomaly (negative shaded and dotted) relative sum of annual mean and 1-st EOF at a depth of 100 m in September...

The EOF brings an additional, unspecific velocity vector to the electrophoretic migration of the separands. The total migration velocity of the analyte, i, is then... 

For a complete treatment of a laser-driven molecule, one must solve the many-body, multidimensional time-dependent Schrodinger equation (TDSE). This represents a tremendous task and direct wavepacket simulations of nuclear and electronic motions under an intense laser pulse is presently restricted to a few bodies (at most three or four) and/or to a model of low dimensionality [27]. For a more general treatment, an approximate separation of variables between electrons (fast subsystem) and nuclei (slow subsystem) is customarily made, in the spirit of the BO approximation. To lay out the ideas underlying this approximation as adapted to field-driven molecular dynamics, we will consider from now on a molecule consisting of Nn nuclei (labeled a, p,...) and Ne electrons (labeled /, j,...), with position vectors Ro, and r respectively, defined in the center of mass (rotating) body-fixed coordinate system, in a classical field E(f) of the form Eof t) cos cot). The full semiclassical length gauge Hamiltonian is written, for a system of electrons and nuclei, as [4]... 

With EOF, the overall migration mobility of ions is the resulting vector sum of the Hep and Heo-The velocity of ions is expressed as Eq. (9) ... 

Combined Pressure-Driven Fiow and Eiectroosmotic Fiow, Fig. 1 Simulation results of the velocity vector of EOF in a T-shaped microgeometry of uniform zeta potential. The parameters used in computation are cross section dimensions of the microchannels 100 X 100 pm, concentration of NaHCOs electrolyte 1 mM, zeta potential 70 mV, and applied electric field strength 120 V/cm... 

Combined Pressure-Driven Flow and Electroosmotic Flow, Fig. 3 Simulation results of the velocity vector and streamline of EOF in the microchannel shown in Fig. 2... 

The distribution of the velocity of the EOF across the radius of the channel or column is an important issue. In the normal laminar flow that is raised by a difference in pressure, the radial profile of the velocity vector has a parabolic shape it is zero at the inner wall and maximum in the channel axis. The radial profile of the EOF is quite different it is also zero at the wall but in a very short distance, which is approximately equal to the thickness of the diffusion layer, it attains a certain value, which is constant across the rest of radius. The radial profile of the EOF is plug-like . This is a very beneficial feature of this type of flow, as it does not cause axial dispersion of the separand. 

Here, pi is the absolute mobility, that of the ion at infinite dilution, / is the correction factor that takes into account the deviation from ideal behavior. It can be seen that an additional parameter occurs in this equation the mobility of the electro-osmotic flow (EOF), Peof> which occurs in many cases in the separation systems and leads to an additional velocity vector of the solutes. 

The movement of charged analytes is now considered as a consequence of the combination of their own individual electrophoretic mobilities (Equation [3.61]) and their participation in the bulk electro-osmotic flow (EOF). The net speed of motion of an analyte ion in the field direction (along the length of the capillary) is the vector sum of its electrophoretic velocity (Equation [3.61])... 

Figure 11.17 shows the separation of eleven inorganic and organic anions with a PDDAC-coated capillary and a 100-mM aqueous solution of tetrabutylammoni-um acetate at pH 6.0. A negative power supply was used with co-migration of the EOF and electrophoretic vectors. 

The principal component analysis technique provides a set of M-dimensional vectors ii,..., ek,..., k < M, called EOFs that are linear combinations of the original variables. The first principal component accounts for as much as the variance of the original variables as possible. The second one explains as much of the remaining variance and so on. Therefore, retaining the first p components, it is possible to account for most of the variation of the original variables in such a way that Y = yi, , can be estimated by a linear combination of these vectors,... 

EOF is generated by applying external electrical potentials to the liquid in a microchannel. Therefore, the applied electrical potential field must be known in order to solve the flow field. When an electric field is applied along a microchannel, the current is setup along the channel. For most microfluidic applications where electrically neutral dilute solutions are often used, the local electric current vector is given by. 

Figs.7b and 8b. Note that for the local modes of Figs.6b,7b,8 b it is assumed that on the plane EOF there is 0=y, the vector Vyz is parallel to y-z plane and... 

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