Spherical colloid

Microscopic analyses of the van der Waals interaction have been made for many geometries, including, a spherical colloid in a cylindrical pore [14] and in a spherical cavity [15] and for flat plates with conical or spherical asperities [16,17]. 

Altliough tire majority of studies on model colloids involve (quasi-) spherical particles, tliere is a growing interest in the properties of non-spherical colloids. These tend to be eitlier rod-like or plate-like. 

The singlet-level theories have also been applied to more sophisticated models of the fluid-solid interactions. In particular, the structure of associating fluids near partially permeable surfaces has been studied in Ref. 70. On the other hand, extensive studies of adsorption of associating fluids in a slit-like [71-74] and in spherical pores [75], as well as on the surface of spherical colloidal particles [29], have been undertaken. We proceed with the application of the theory to more sophisticated impermeable surfaces, such as those of crystalline solids. 

Loeb, AL Overbeek, JTG Wiersema, PH, The Electrical Double Layer Around a Spherical Colloid Particle, Computation of the Potential, Charge Density, and Free Energy of the Electrical Double Layer Around a sperical Colloid Particle M.I.T. Press Cambridge, MA, 1961. Lorentz, HA, Wied, Ann. 11, 70, 1880. 

O Brien, RW White, LR, Electrophoretic Mobility of a Spherical Colloidal Particle, Journal of the Chemical Society, Faraday Transactions 74, 1607, 1978. 

Weirsema, PH Loeb, AL Overbeek, JTG, Calculation of the Electrophoretic Mobility of a Spherical Colloid Paricle, Journal of Colloid and Interface Science 22, 78, 1966. 

If the electric field E is applied to a system of colloidal particles in a closed cuvette where no streaming of the liquid can occur, the particles will move with velocity v. This phenomenon is termed electrophoresis. The force acting on a spherical colloidal particle with radius r in the electric field E is 4jrerE02 (for simplicity, the potential in the diffuse electric layer is identified with the electrokinetic potential). The resistance of the medium is given by the Stokes equation (2.6.2) and equals 6jtr]r. At a steady state of motion these two forces are equal and, to a first approximation, the electrophoretic mobility v/E is... 

Any study of colloidal crystals requires the preparation of monodisperse colloidal particles that are uniform in size, shape, composition, and surface properties. Monodisperse spherical colloids of various sizes, composition, and surface properties have been prepared via numerous synthetic strategies [67]. However, the direct preparation of crystal phases from spherical particles usually leads to a rather limited set of close-packed structures (hexagonal close packed, face-centered cubic, or body-centered cubic structures). Relatively few studies exist on the preparation of monodisperse nonspherical colloids. In general, direct synthetic methods are restricted to particles with simple shapes such as rods, spheroids, or plates [68]. An alternative route for the preparation of uniform particles with a more complex structure might consist of the formation of discrete uniform aggregates of self-organized spherical particles. The use of colloidal clusters with a given number of particles, with controlled shape and dimension, could lead to colloidal crystals with unusual symmetries [69]. 

Y. Lu, Y. Yin, and Y. Xia Three-Dimensional Photonic Crystals with Non-Spherical Colloids as Building Blocks. Adv. Mater. 13, 415 (2001). 

Y. Xia, Y. Yin, Y. Lu, and J. Me Lellan Template-Assisted Self-Assembly of Spherical Colloids into Complex and Controllable Structures. Adv. Funct. Mater. 13, 907 (2003). 

Commercial carbon black is a spherical colloidal form of nearly pure carbon particles and aggregates with trace amounts of organic impurities adsorbed on the surface. Potential health effects usually are attributed to these impurities rather than to the carbon itself. Soots, by contrast, contain mixmres of particulate carbon, resins, tars, and so on, in a nonadsorbed state. ... 

Let us now examine how we can obtain an estimate of /q from the measured electromobility of a colloidal particle. It turns out that we can obtain simple, analytic equations only for the cases of very large and very small particles. Thus, if a is the radius of an assumed spherical colloidal particle, then we can obtain direct relationships between electromobility and the surface potential, if either Kit > 100 or Kd < 0.1, where K" is the Debye length of the electrolyte solution. Let us first look at the case of small spheres (where Kd < 0.1), which leads to the Hiickel equation. 

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. 

The total DLVO interaction energy (Vs) between two spherical colloids (each of radius a and separated by distance H) is given by the following approximate equation ... 

From microelectrophoresis measurements on a spherical colloid particle, the observed elctromobility L7e is directly related to the zeta potential by the equation ... 

Silica gel is synthetic amorphous silica consisting of a compact network of spherical colloidal silica particles. Its surface area is typically between 300 and 850 m2/g. The predominant pore diameters are in the range 22-150 A. Silica gel is produced via the following procedure a sodium silicate solution reacts with a mineral acid, such as sulfuric acid, producing a concentrated dispersion of finely divided particles of hydrated Si02,... 

Evaporative decomposition erf solutions and spary pyrolysis have been found to be useful in the preparation of submicrometer oxide and non-oxide particles, including high temperature superconducting ceramics [819, 820], Allowing uniform aerosol droplets (titanium ethoxide in ethanol, for example) to react with a vapor (water, for example) to produce spherical colloidal particles with controllable sizes and size distributions [821-825] is an alternative vapor phase approach. Chemical vapor deposition techniques (CVD) have also been extended to the formation of ceramic particles [825]. 

Layer Around a Spherical Colloid Particle, Massachusetts Institute of Technology Press, Cambridge, 1961. 

Quantitative evaluation of a force-distance curve in the non-contact range represents a serious experimental problem, since most of the SFM systems give deflection of the cantilever versus the displacement of the sample, while the experimentalists wants to obtain the surface stress (force per unit contact area) versus tip-sample separation. A few prerequisites have to be met in order to convert deflection into stress and displacement into tip-sample separation. First, the point of primary tip-sample contact has to be determined to derive the separation from the measured deflection of the cantilever tip and the displacement of the cantilever base [382]. Second, the deflection can be converted into the force under assumption that the cantilever is a harmonic oscillator with a certain spring constant. Several methods have been developed for calibration of the spring constant [383,384]. Third, the shape of the probe apex as well as its chemical structure has to be characterised. Spherical colloidal particles of known radius (ca. 10 pm) and composition can be used as force probes because they provide more reliable and reproducible data compared to poorly defined SFM tips [385]. 

For spherical colloidal particles undergoing sedimentation, diffusion or electrophoresis, deviations from Stokes law usually amount to much less than 1 per cent and can be neglected. 

Figure 7.13 Electrophoretic mobility and zeta potential for spherical colloidal particles in electrolyte solutions containing polyvalent ions (A+lz+ = A /z = 70 ft cm2 mol -1). Electrolyte type is numbered with counter-ion charge number first ...

Hard-sphere or cylinder models (Avena et al., 1999 Benedetti et al., 1996 Carballeira et al., 1999 De Wit et al., 1993), permeable Donnan gel phases (Ephraim et al., 1986 Marinsky and Ephraim, 1986), and branched (Klein Wolterink et al., 1999) or linear (Gosh and Schnitzer, 1980) polyelectrolyte models were proposed for NOM. Here the various models must be differentiated in detail—that is, impermeable hard spheres, semipermeable spherical colloids (Marinsky and Ephraim, 1986 Kinniburgh et al., 1996), or fully permeable electrolytes. The latest new model applied to NOM (Duval et al., 2005) incorporates an electrokinetic component that allows a soft particle to include a hard (impermeable) core and a permeable diffuse polyelectrolyte layer. This model is the most appropriate for humic substances. 

Ohshima, H. (2002). Electrophoretic mobility of a charged spherical colloidal particle covered with an uncharged polymer layer. Electrophoresis 23,1993-2000. 

Loeb, A. L., Overbeek, J. Th. G., Wiersems, P. H. The electrical double layer around a spherical colloid particle. Cambridge, MA. MIT 1961... 

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