Electrophoretic mobility dynamic

The dynamic electrophoretic mobility of colloidal particles in an applied oscillating electric field plays an essential role in analyzing the results of electroacoustic measurements of colloidal dispersions, that is, colloid vibration potential (CVP) and electrokinetic sonic amplitude (ESA) measurements [1-20]. This is because CVP and ESA are proportional to the dynamic electrophoretic mobility of colloidal particles. In this chapter, we develop a theory of the dynamic electrophoretic mobility of soft particles in dilute suspensions [21]. 

Consider a spherical soft particle moving with a velocity Uexp(—icot) in a liquid containing a general electrolyte in an applied oscillating electric field E exp(—icot), where co is the angular frequency (2n times frequency) and t is time (Fig. 25.1). The dynamic electrophoretic mobility /i(co), which is a function of co, of the particle is defined by... 

The dynamic electrophoretic mobility p(co) of a soft particle can be obtained by solving Eqs. (25.19) and (25.20) with the result that... 

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). 

For a spherical soft particle, an approximate expression for p(co) for the dynamic electrophoretic mobility is given by Eq. (25.45), which is a good approximation when the following conditions are satisfied ... 

According to O Brien [36,37], in dilute dispersion the CVP is related to the dynamic electrophoretic mobility, pdyn, as... 

The dynamic electrophoretic mobility is a useful system characteristic. For instance, it provides a means for determining the isoelectric point from electroacoustic measurements. Other properties of colloidal dispersions, namely -potential and particle size, can also be obtained from measurements of dynamic electrophoretic mobility. For a dilute dispersion (less then a few weight percent) of spherical particles, the dynamic electrophoretic mobility is given by a Smoluchowski-type relationship [37,38] ... 

Both G and/are complex functions, so the dynamic electrophoretic mobility is a complex function as well, i.e. one can write that... 

Similarly to the reciprocity that exists between electroosmosis and streaming potential (See Chapter V,5), there is a reciprocity between the ultrasonic waves and the alternating electric field generated by them. That is, the application of the alternating electric field to disperse systems results in the generation of an ultrasound signal, referred to as the electrosonic amplitude (ESA). The ESA is related to the dynamic electrophoretic mobility via a relationship similar to eq. (V.6), namely... 

O Brien [81,82] introduced the concept of dynamic electrophoretic mobility of the particles, u, as a basic quantity for the electroacoustic description of dispersed systems. The macroscopic (average) current, J, and particle velocity, Vp, are related to the pressure gradient Vp and external... 

Ohshima, H., Dynamic electrophoretic mobility of a soft particle, J. Colloid Interface Sci., 233, 142,... 

Dukhin, A.S., Shilov, V.N., Ohshima, H., and Goetz, P.J., Dynamic electrophoretic mobility in concentrated disperse systems cell model, Langmuir, 15, 3445, 1999. 

Booth and Enderby 1952 Yeager et al. 1953). The discovery of the elec-trokinetic sonic amphtude (ESA) occurred comparatively late, in the 1980s (Oja et al. 1985), yet this effect was soon employed in commercial instruments for zeta-potential measurements. Subsequent theoretical treatments showed that both signals can be traced back to the dynamic electrophoretic mobility and that they form a reciprocal couple of the Onsager type (O Brien 1988 O Brien et al. 1994). 

The zeta potential is the parameter used to characterize a nanostructure s surface charge. Although zeta potential is not measurable directly, it can be calculated using theoretical models applied to the data provided by experimentally determined electrophoretic mobility or dynamic electrophoretic mobility, electrokinetic phenomena and electroacoustic phenomena being the usual sources of data for the calculation of zeta potential. Keeping the zeta potential far from a neutral value is important in order to avoid stability problems in systems once electrostatic repulsion is favored. Indeed, zeta potentials close to neutral result in a tendency to aggregate, and a high zeta potential (in module) is usually associated with stable systems. 

AhuaUi, S., Delgado, A.V, Miklavcic S.J., and White, L.R. 2006. Dynamic electrophoretic mobility of concentrated dispersions of spherical coUoidal particles. On the consistent use of the cell model. Langmuir 22 7041-7051. 

Rawjee, Y. Y and Vigh, Gy., Efficiency optimization in capillary electrophoretic chiral separations using dynamic mobility matching, Anal. Chem., 66,3777,1994. 

In order to influence a migration it is obvious that one can alter the charge of the compounds, the viscosity of the medium and the dynamic radius of the compounds. According to Eq. 17.5, the electrophoretic mobility is the proportionality factor in the linear relationship of the migration velocity and the electric field strength... 

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