Surface charge density particle

The Poisson-Boltzman (P-B) equation commonly serves as the basis from which electrostatic interactions between suspended clay particles in solution are described ([23], see Sec.II. A. 2). In aqueous environments, both inner and outer-sphere complexes may form, and these complexes along with the intrinsic surface charge density are included in the net particle surface charge density (crp, 4). When clay mineral particles are suspended in water, a diffuse double layer (DDL) of ion charge is structured with an associated volumetric charge density (p ) if av 0. Given that the entire system must remain electrically neutral, ap then must equal — f p dx. In its simplest form, the DDL may be described, with the help of the P-B equation, by the traditional Gouy-Chapman [23-27] model, which describes the inner potential variation as a function of distance from the particle surface [23]. 

How do we determine the net particle surface charge density Historically, surface charge has often been inferred from electrophoretic mobility ( ) (see the discussion on zeta potential in Section 9.5). Semiquantitatively, this is very convenient because of the availability of expedient instrumentation. As shown in Figure 14.7, a qualitative connection between u and Op can be inferred from the variation of u and Op with pH. Furthermore, when u = 0, op = 0 and (/ = 0. But the quantitative relationship between u and Op is highly model dependent. 

Simple Charge Neutralization and Charge Patch Neutralization Oppositely charged polyelectrolytes reduce the particle surface charge density such that particles may approach each other sufficiently closely so that the attractive van der Waals force becomes effective. Flocculation caused by this mechanism should not be sensitive to the molecular weight of the polymer. 

The signal determined in arbitrary units is a complex dimension, which cannot be directly quantified to the zeta potential. Its sign is determined by the charge of the cell wall. It summarizes contributions from the cell wall, the piston, and the whole colloidal material. Thus for a quantitative calculation of the particles surface charge density a polyelectrolyte titration has to be carried out. If one knows the specific surface, for zeta potentials <30 mV it can be calculated according to... 

The contributions detailed in the preceding discussion combine to give the resulting particle surface charge density Op. 

The Debye length, at room temperature may be estimated as /Id = 0.308/v nm, where C is the molar concentration of salt (1 M = 10 mol m ). Note that when the volume fraction of colloidal particles (p is not low, the Debye length Id becomes dependent on p, colloidal particle radius, r, and colloidal particle surface charge density, a [11] ... 

Femandez-Barbero A, Cabrerizo-Vilchez M, Martinez-Garcia R, Hidalgo-Alvarez R (1996) Effect of the particle surface charge density on the colloidal aggregation mechanism. Phys Rev E 53 4981 989. doi 10.1103/PhysRevE.53.4981... 

The colloidal properties of latex products are of great importance from both academic and industrial points of view. Some representative charaeteristics include the particle size and particle size distribution, the particle surface charge density (or zeta potential), the particle surface area covered by one stabilizer molecule, the conformation of the hydrophilic polymer physically adsorbed or chemically couplet onto the particle surface, the type and concentration of functional groups on the particle surface, the particle morphology, the optical and rheological properties and the colloidal stability. 

Where d is the particle surface charge density. The effective particle radius should lead to the concepts of the effective particle volume fraction, (t>eff, the effective inter-particle spacing, IPSeff, the effective free volume of... 

The bound suriace charge is obviously related to the applied electric field E. If a particle surface charge density is dq and the static dielectric constant is dq can be expressed as [lOJ ... 

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