Colloidal particles dielectric

Colloidal particles can be seen as large, model atoms . In what follows we assume that particles with a typical radius <3 = lOO nm are studied, about lO times as large as atoms. Usually, the solvent is considered to be a homogeneous medium, characterized by bulk properties such as the density p and dielectric constant t. A full statistical mechanical description of the system would involve all colloid and solvent degrees of freedom, which tend to be intractable. Instead, the potential of mean force, V, is used, in which the interactions between colloidal particles are averaged over... 

Two uncharged dielectric materials ( 1 and 2 ) are dispersed as equal-sized, spherical colloidal particles in a dielectric medium, 3 . (see Figure 7.14) If the refractive indices at visible frequencies follow the series > 3 > tii, determine the relative strengths (and sign, i.e. whether repulsive or attractive) of the three possible interactions. Explain your reasoning. 

Equations for calculating van der Waals interaction forces/energies between macromolecules or colloidal particles are quite well established (Israelachvili, 1992 Dickinson and McClements, 1995 McClements, 2005). (For example, see equations (3.35) and (3.36) in chapter 3). The interactions between nanoparticles are potentially more complicated, however, because the nanoparticle size and interparticle separation are comparable in magnitude, precluding the use of the asymptotic forms of the equations also nanoparticles are commonly anisotropic, and their dielectric properties are often not known (Min et al., 2008). 

Schwarz, G. (1962) A theory of the low-frequency dielectric dispersion of spherical colloidal particles in electrolyte solution, Journal of Physical Chemistry 66, 2636-2642... 

In an attempt to overcome the low infusible character and low solubility of aniline, dispersion polymerization of aniline was conducted in water-dispersible colloidal particles that can be cast as films or blended with other materials to prepare composites. HRP mediated polymerization of aniline in a mixture of phosphate buffer and organic solvent resulted in polyaniline composed of ortho-directed units and para-directed units. Increasing the pH or adopting an organic solvent with a high dielectric constant, enhanced the production of ortho-directed units [54]. These ortho-directed polyanilines were more thermally flexible and electrically conductive. 

When working with colloidal dispersions, we mostly deal with aqueous solutions, in which colloidal particles are immersed. From this point of view, all colloidal material can be separated into the two categories—dielectrics, with d <5C ew (fid and w are dielectric constants of a dielectric and water, respectively), and conductors, with c > w (sc is the dielectric permittivity of a conductor). 

HLC have suggested that the solvent dipoles near the colloidal particles are preferentially aligned. This effect is well known in theories of the electrical double layer. One simple way of accounting for this effect is through the use of a Stern layer of low dielectric constant near the colloidal particles. It is difficult to calculate this correction for spherical particles. As a result, HLC considered a hard sphere fluid between two hard walls and with a region of low dielectric constant near the walls. They found that Eq. (62) should be generalized to... 

Electrophoresis — Movement of charged particles (e.g., ions, colloidal particles, dispersions of suspended solid particles, emulsions of suspended immiscible liquid droplets) in an electric field. The speed depends on the size of the particle, as well as the -> viscosity, -> dielectric permittivity, and the -> ionic strength of the solution, and it is directly proportional to the applied electric field. In analytical as well as in synthetic chemistry electrophoresis has been employed to separate species based on different speeds attained in an experimental setup. In a typical setup the sample is put onto a mobile phase (dilute electrolyte solution) filled, e.g., into a capillary or soaked into a paper strip. At the ends of the strip connectors to an electrical power supply (providing voltages up to several hundred volts) are placed. Depending on their polarity and mobility the charged particles move to one of the electrodes, according to the attained speed they are sorted and separated. (See also - Tiselius, - electrophoretic effect, - zetapotential). 

Another model of experimental interest concerns the case of a highly conductive shell around practically non-conductive material. It may be applied to macromolecules or colloidal particles in electrolyte solution which usually have counterion atmospheres so that the field may displace freely movable ionic charges on their surfaces. The resulting dielectric effect turns out to be equivalent to a simple Maxwell-Wagner dispersion of particles having an apparent bulk conductivity of... 

Casimir and Polder also showed that retardation effects weaken the dispersion force at separations of the order of the wavelength of the electronic absorption bands of the interacting molecules, which is typically 10 m. The retarded dispersion energy varies as R at large R and is determined by the static polarizabilities of the interacting molecules. At very large separations the forces between molecules are weak but for colloidal particles and macroscopic objects they may add and their effects are measurable. Fluctuations in particle position occur more slowly for nuclei than for electrons, so the intermolecular forces that are due to nuclear motion are effectively unretarded. A general theory of the interaction of macroscopic bodies in terms of the bulk static and dynamic dielectric properties... 

According to Deijaguin-Landau-Verwey-Overbeek (DLVO) theory, a cornerstone of modem colloid science, two types of forces exist between colloidal particles suspended in a dielectric medium electrostatic forces, which result from an unscreened surface charge on the particle, and London-van der Waals attractive forces, which are universal in nature. The colloidal stability and rheology of oxide suspensions, in the absence of steric additives, can be largely understood by combining these two forces (assumption of additivity). 

A dielectric sphere of dielectric coefficient e embedded in an infinite dielectric of permittivity 82 is an important case from many points of view. The idea of a cavity formed in a dielectric is routinely used in the classical theories of the dielectric constant [67-69], Such cavities are used in the studies of solvation of molecules in the framework of PCM [1-7] although the shape of the cavities mimic that of the molecule and are usually not spherical. Dielectric spheres are important in models of colloid particles, electrorheological fluids, and macromolecules just to mention a few. Of course, the ICC method is not restricted to a spherical sample, but, for this study, the main advantage of this geometry lies just in its spherical symmetry. This is one of the simplest examples where the dielectric boundary is curved and an analytic solution is available for this geometry in the form of Legendre polynomials [60], In the previous subsection, we showed an example where the SC approximation is important while the boundaries are not curved. As mentioned before, using the SC approximation is especially important if we consider curved dielectric boundaries. The dielectric sphere is an excellent example to demonstrate the importance of curvature corrections . 

Earlier experiments [400,401] (see also Refs. 402 and 403) showed that hydrated colloidal particles are characterized by polarization whose nature is determined by spontaneous orientation of the polar molecules of water on the surface of particles leading to formation of the giant momentum P. The energy advantage of formation of P is shown in Ref. 404, which is in agreement with a detailed study of the dielectric anomalies in thin water layers conducted in Ref. 405. Spontaneous polarization of the monolayers of polar molecules is theoretically substantiated in Refs. [406,407]. 

X-B. Wang, Y. Huang, R. Holzel, J. P. H. Bnrt and R. Pethig, Theoretical and experimental investigations of the interdependence of the dielectric, Dielectrophoretic and electrorotational behavionr of colloidal particles, J. Phys. D Appl Phys.,26, 312-322 (1993). 

Impedance is the ratio of the voltage across a system to the current passing through the system. It measures the dielectric properties (permittivity and conductivity) of the system. The dielectric behavior of colloidal particles in suspension is generally described by Maxwell s mixture theory [26]. This relates the complex permittivity of the suspension to the complex permittivity of the particle, the suspending medium and the volume fraction. Based-on Maxwell s mixture theory, shelled-models have been widely used to model the dielectric properties of particles in suspension [35-40]. A single shelled spherical model is shown in Fig. la. 

This treatment is no longer valid in the case of electrophoresis of small particles surrounded by a thick diffuse layer of counterions, i.e. when r/8 l. In this situation colloidal particle becomes similar to a large polyvalent ion in a dielectric medium. If such an ion is regarded as spherical capacitor, its charge, q", is related to its surface potential by a relationship well known from electrostatics, i.e. ... 

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