Electrophoretic mobility, polyelectrolyte

Gorin has extended this analysis to include (1) the effects of the finite size of the counterions in the double layer of spherical particles [137], and (2) the effects of geometry, i.e. for cylindrical particles [2]. The former is known as the Debye-Huckel-Henry-Gorin (DHHG) model. Stigter and coworkers [348,369-374] considered the electrophoretic mobility of polyelectrolytes with applications to the determination of the mobility of nucleic acids. 

Muthukumar, M, Theory of Electrophoretic Mobility of Polyelectrolyte Chains, Macromolec-ular Theory and Simulations 3, 61, 1994. 

The electrophoretic mobility p of a polyelectrolyte chain in an infinitely dilute solution containing an added salt at concentration c under a constant external electric field E, as defined through... 

In this section we consider the motion of a uniformly charged flexible polyelectrolyte in an infinitely dilute solution under an externally imposed uniform electric field E. The objective is to calculate the electrophoretic mobility p defined by... 

Summarizing, the electrophoretic mobility of a flexible polyelectrolyte chain in infinitely dilute solutions is given by Eq. (156) ... 

The Dependencies of Radius of Gyration Rg, Static Correlation Length Hydrodynamic Screening Length Viscosity r, Self-Translational Diffusion Coefficient D, Cooperative Diffusion Coefficient Dc, Coupled Diffusion Coefficient Df, and Electrophoretic Mobility p on c and N for Various Regimes of Polyelectrolyte and Salt Concentrations... 

Although the theory of polyelectrolyte dynamics reviewed here provides approximate crossover formulas for the experimentally measured diffusion coefficients, electrophoretic mobility, and viscosity, the validity of the formulas remains to be established. In spite of the success of one unifying conceptual framework to provide valid asymptotic results, in qualitative agreement with experimental facts, it is desirable to establish quantitative validity. This requires (a) gathering of experimental data on well-characterized polyelectrolyte solutions and (b) obtaining the relationships between the various transport coefficients. Such data are not currently available, and experiments of this type are out of fashion. In addition to these experimental challenges, there are many theoretical issues that need further elaboration. A few of these are the following ... 

In the model, Xp is determined by a temperature dependent electrophoretic mobility factor [123] which contains the viscosity of the solvent as well as its relative permittivity, Xc °, the radius of the polymer chain and the Debye screening length 1D. The following equation holds for the case that electrolyte and polyelectrolyte are in the same concentration range ... 

For quite some time, there have been indications for a phase-separation in the shell of polyelectrolyte block copolymer micelles. Electrophoretic mobility measurements on PS-PMAc [50] indicated that a part of the shell exhibits a considerable higher ionic strength than the surrounding medium. This had been corroborated by fluorescence studies on PS-PMAc [51-53] and PS-P2VP-heteroarm star polymers [54]. According to the steady-state fluorescence and anisotropy decays of fluorophores attached to the ends of the PMAc-blocks, a certain fraction of the fluorophores (probably those on the blocks that were folded back to the core/shell interface) monitored a lower polarity of the environment. Their mobility was substantially restricted. It thus seemed as if the polyelectrolyte corona was phase separated into a dense interior part and a dilute outer part. Further experimental evidence for the existence of a dense interior corona domain has been found in an NMR/SANS-study on poly(methylmethacrylate-fr-acrylic acid) (PMMA-PAAc) micelles [55]. 

We derive an approximate expression for the electrophoretic mobility of spherical polyelectrolytes for the case of low potentials. In this case, the equilibrium potential i/ ° (r) is given by... 

Electrokinetic equations describing the electrical conductivity of a suspension of colloidal particles are the same as those for the electrophoretic mobility of colloidal particles and thus conductivity measurements can provide us with essentially the same information as that from electrophoretic mobihty measurements. Several theoretical studies have been made on dilute suspensions of hard particles [1-3], mercury drops [4], and spherical polyelectrolytes (charged porous spheres) [5], and on concentrated suspensions of hard spherical particles [6] and mercury drops [7] on the basis of Kuwabara s cell model [8], which was originally applied to electrophoresis problem [9,10]. In this chapter, we develop a theory of conductivity of a concentrated suspension of soft particles [11]. The results cover those for the dilute case in the limit of very low particle volume fractions. We confine ourselves to the case where the overlapping of the electrical double layers of adjacent particles is negligible. 

Here Vp has been replaced with the pressure difference between the two points is AP, K°, and K are, respectively, the usual conductivity and the complex conductivity of the electrolyte solution in the absence of the particles, (f> is the particle volume fraction, (j)c is the volume fraction of the particle core, Vc is the volume of the particle core, volume fraction of the polyelectrolyte segments, I4 is the total volume of the polyelectrolyte segments coating one particle, and po, are respectively, the mass density of the particle core and that of the electrolyte solution, and ps is the mass density of the polyelectrolyte segment, V is the suspension volume, and p(cai) is the dynamic electrophoretic mobility of the particles. Equation (26.4) is an Onsager relation between CVP and pirn), which takes a similar form for an Onsager relation between sedimentation potential and static electrophoretic mobility (Chapter 24). 

The intrinsic electrophoretic mobility of polyelectrolytes is directly linked to the charge-to-surface ratio of the solvated molecule. Therefore CZE can quickly deliver valuable results on charge distribution. By using many chemically different types of polyelectrolytes, the influence of polyelectrolyte structure and of the type, pH, ionic strength and temperature of the background electrolyte can be investigated systematically. 

The electrophoretic mobility of particles having a cylindrical or ellipsoidal shape was studied theoretically by Stigter, " van der Drift et al., " and Ohshima. The polyelectrolytes and the spherical particles covered by a layer of polymer " - (or of polyelectrolyte) are two other types of systems that have been matters of great interest. In a recent series of papers Ohshima and... 

Some of the relevant questions primarily motivated by scientific interest are the following. How is the size of a polyelectrolyte affected by molecular weight, intrinsic stiffness, solvent quality, or ionic strength Which observables are well characterized by coarse-grained quantities such as a linear charge density, and which depend on chemical details How are dynamic quantities like viscosity or electrophoretic mobility related to static properties of poly electrolytes ... 

Manning GS. Limiting laws and counterion condensation in polyelectrolyte solutions. 7. Electrophoretic mobility and conductance. J Phys Chem 1981 85 1506-1515. 

In Figure 2 are represented the electro-optical effect a, the electrophoretic mobility Ue, and the relaxation time r of the particle disorientation after the switching off of the electric field as a function of the initial polyelectrolyte concentration. One observes that the a and r variations correspond to the variation of f/e, i.e., the electrostatic attraction of the polyelectrolyte to the oppositely charged surface, which is the main driving force for the adsorption, governs the electro-optical behavior and stability of the suspension containing this polyelectrolyte. 

FIG. 3 Top Turbidity difference between polyelectrolyte-free SDS solutions and solutions containing 20 ppm polyelectrolyte as a function of SDS concentration. Data are presented for PCMA, 100% charged ( ), AM-MAPTAC-30, 30% charged ( ), AM-MAPTAC-10, 10% charged (o), and AM-MAPTAC-1, 1% charged (A). Bottom Electrophoretic mobility of polyelectrolyte-SDS aggregates. 

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