Electrophoretic mobility nonlinear

AC electro-osmosis (ACEO) Nonlinear electrophoretic mobility... 

Nonlinear regression analysis of a plot of /x or Y against [L] provides the association constant KA, and the electrophoretic mobility of the pure complex /jbSL from the experimental data. /x5 corresponds to the substrate mobility at [L] = 0. [L] can be approximated as the added ligand concentration only when the ligand concentration is much greater than the solute concentration or when the binding constant is small. 

O Brien s method was extended to study the electrophoresis of a nonuniformly charged sphere with thin but polarized ion cloud in a symmetric electrolyte [32]. The electrophoretic mobility depends on the charge distribution at the particle surface. It is found that the polarization effect of the ion could leads to different electrophoretic mobilities for particles with different zeta potential distributions but having an identical velocity for the limit of infinite Ka. This intriguing result is due to the fact that the theory for undistorted ion cloud is linear in the distribution of zeta potential, whereas the polarization effects are nonlinear. 

Jalali-Heravi and coworkers used the three descriptors of their multivariable model, that is, Offord charge-to-mass parameter, corrected steric constant, and molar refractivity, as the input parameters for generating the network (Fig. 14.2). In fact, they proposed an MLR-ANN model for the prediction of the electrophoretic mobility of peptides. The purpose for choosing the MLR parameters as inputs for the ANN mode was to compare the abilities of linear and nonlinear models in predicting the electrophoretic mobilities of peptides (9). 

Field-dependent electrophoretic mobility Nonlinear electrophoresis... 

In the 1970s, S. S. Dukhin s group was perhaps the first to recognize that the electrophoretic mobility of polarizable particles must generally depend on the electric field [9]. In a series of Russian papers, which have yet to gain widespread attention, they predicted perturbations of the mobility as AZ oc and thus nonlinear electrokinetic motion At/ oc, which they have come to call the Stotz-Wien effect. For the case of a steady weak field applied to an ideally polarizable sphere of radius a, A. S. Dukhin derived an expansion for the mobility ... 

Scharp, K.A. and Brooks, D.E., Calculation of the electrophoretic mobility of a particle bearing bound polyelectrolyte using the nonlinear Poisson-Boltzmann equation, Biophys. J., 47, 563, 1985. 

Fig. 2.21 Nonlinear relationship between zeta-potential and electrophoretic mobility acc. to O Brien and White (1978)...

To point out the relationship between the electrophoretic mobility (i.e., charge density) and the reduction of the particle size, the electrophoretic mobility has been examined as a function of When the linearity (p vs. ri ) is observed, it reflects the homogeneous charge distribution on the microgel surface and constant reduction of the particles size. When the nonlinearity is observed, it may reflect the complexity of the microgel structure and also the charge distribution in the vicinity of the immobile water molecules [13]. 

Since all materials are polarizable to some degree, the surface charge is generally not fixed. This leads to a broad class of nonlinear electrokinetic phenomena, where bulk electric fields interact with induced diffuse charge in solution to produce nonlinear electrophoretic motion, U =f(E). In electrolytes, such effects of induced-charge electrophoresis (ICEP) occur in addition to the purely electrostatic effect of dielectrophoresis (DEP) in low-frequency AC fields (< 100 kHz), where there is enough time for diffuse-charge relaxation around the particle within each period. ICEP is a complex phenomenon, which can lead not only to nonlinear mobility (in the field direction) but also to rotation and motion in arbitrary directions, even in uniform fields. 

The first experiments demonstrating field-dependent electrophoretic mobility of colloids (Stotz-Wien effect) were reported by several groups in the 1970s [14], and the possibility of using this effect for particle separation using unbalanced AC fields has begun to be explored [14]. This work focused on nonlinear corrections to the classical phenomenon of electrophoresis, where a particle moves in the direction of the applied electric field, U = b(E)E, rather than on the associated ICEO flows and more complicated ICEP motion. 

Laurent, et al. examine ten biomacromolecules and colloidal silica in 1.7 MDa hyaluronic acid(5). For all probe particles, s had a stretched-exponential dependence on matrix c, with v = 0.5. 5 was independent of the centrifugal acceleration, i.e., experiments were in a linear domain in which solution viscoelastic properties were not evident. Contrast is to be made with the electrophoretic mobility, as discussed in the next chapter, in which one can enter a nonlinear domain in which particle mobility depends on the applied field E. The constant B was found, to good accuracy, to be linear in the particle radius, except for the very largest spheres. Laurent, et al. also measured the diffusion coefficients D of four smaller probes in the same polymer solutions. Within experimental error, s/D was independent of matrix concentration. 

Heravi et al., therefore, concluded that the linear models are not able to predict the mobility of the peptides with high charges (9). The limited ability of linear models in predicting the electrophoretic mobihty of a more diverse set of peptides persuaded some researchers to apply machine learning (ML) techniques, which are more generic, nonlinear modeling tools. 

The BRM is a natural generalization of the original reptation model where the motion of the primitive chain in its "tube is considered to become biased when an electric field is applied. The electrophoretic properties of the DNA molecules are related in the BRM to the effect of the field on the conformation of the reptation tube since this conformation tends to orient in the field direction when the primitive chain creates new tube sections, the electrophoretic velocity becomes a nonlinear function of the electric field. This tube alignment also reduces the effectiveness of the entanglements in opposing the electrophoretic drift, with the consequence that, except for transient effects or very small molecules, the mobility becomes molecular-size independent in continuous fields. 

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