Particles weakly charged

The Hamiltonian considered above, which connmites with E, involves the electromagnetic forces between the nuclei and electrons. However, there is another force between particles, the weak interaction force, that is not invariant to inversion. The weak charged current mteraction force is responsible for the beta decay of nuclei, and the related weak neutral current interaction force has an effect in atomic and molecular systems. If we include this force between the nuclei and electrons in the molecular Hamiltonian (as we should because of electroweak unification) then the Hamiltonian will not conuuiite with , and states of opposite parity will be mixed. However, the effect of the weak neutral current interaction force is mcredibly small (and it is a very short range force), although its effect has been detected in extremely precise experiments on atoms (see, for... 

Strong acids (those that ionize completely in solution) are more likely to dissolve solids because charged particles such as hydrogen ions will interact more strongly with solids than will neutral particles. Weak acids do not readily donate hydrogen ions and consequently remain mostly in the neutral form. As a result, weak acids do not dissolve solids as readily as strong acids. 

Analyses of the hadronic peak cross section data obtained at LEP1 [20] implies a small amount of missing invisible width in Z decays. These data imply an effective number of massless neutrinos, N = 2.985 0.008, which is below the prediction of 3 standard neutrinos by the standard model of electroweak interactions. The weak charge Qw in atomic parity violation can be interpreted as a measurement of the 5 parameter. This indicates a new Qw = —72.06 0.44 is found to be above the standard model prediction. This effect is interpreted as due to the occurrence of the Z particle, which will be refered to as the ZY particle. 

When either ion-hydration interaction or ion-dispersion forces were included in the treatment, the results were qualitatively identical to the traditional DLVO theory, which roughly predicts that strongly charged colloidal particles are stable, and weakly charged particles coagulate. Significant quantitative differences, which can account for specific ion effects, could he introduced by either mechanism, when suitable interaction parameters were selected. 

Fig. 7,2. Influence of colloidal sol stability on the porous structure of gel layers (a) stable sol with non-aggregated particles (b) partially aggregated sol with weakly charged particles.

In Eq. (1), So is the permittivity of free space (8.8 X 10 F/m), E is the maximum electric field before breakdown of air occurs (3 x lO V/m), a is the particle radius in m, and Sr is the relative dielectric constant of a powder particle. This equation shows that the maximum charge that can be acquired is proportional to the electric field and the square of the particle radius. It is also weakly dependent on the relative dielectric constant of the particle. The charge-to-mass ratio takes into account the mass of the particle and is determined by dividing Eq. (1) by the mass of a spherical particle, (4/3) na p, where p is the density of the... 

With high particle charges and low ionic concentrations, electrostatic repulsion (39,4C) alone should be capable of stabilizing, the colloid. This Typically occurs when surface potentials are around lOOmV. Steric stabilization (41,42) in nonaq-ueous media is important to achieve stability in weakly charged systems. Direct experimental measurements of particle-particle forces or potentials in nonaqueous media are not yet available. 

Copper phthalocyanine (CuPc) is one of the most important blue organic pigments that are widely used in the varnish-, paint- and printing industries. Its surface is hydrophobic and weakly charged. The particles of CuPc during contact with water without a stabilizer are not wetted and float on the water surface. 

P.Debye and E. Httckel offered an approximate solution of the above equation for the system consisting of weakly charged spherical particles of radius r, when ze% / k T< 1, and sinh (zePoisson-Boltzmann equation, written in spherical coordinates, in this case appears as ... 

In the other limiting case of weakly charged colloidal particles y zeq>0 / 4kT (see Chapter III,3). In this case the critical coagulation concentration of electrolyte is a weaker function of counter-ion charge, given by the equation originally derived by Derjaguin ... 

To what extent this happens depends on the type of polymers, contact time, and properties of the surface of the particles to be flocculated. Suitable polymers are weakly charged or nonionic, that is, high molecular-mass polyacrylamide and polyethylene oxide. Floes made by bridging are large but fairly easily broken by shearing, which may tear the bridging polymers and retard the process of re-flocculation. 

Borsali et al. [1992] note that the formulation of Cohen et al. [1988] above is strictly valid only for point-charged particles and have presented a more physically realistic treatment developed within the framework of the Rouse dynamical model, and valid for weakly charged polyions. They find that Eqs. (1.139) to (1.142) reduce to [Borsali et al., 1992]... 

Lagueerr, A. and Stoll, S. (2005). Adsorption of a weakly charged polymer on an oppositely charged colloidal particle Monte Carlo simulations investigation. Polymer, 46, 1359-1372. 

M. Watzlawek, G. Nagele, Sedimentation of strongly and weakly charged colloidal particles Prediction of fractional density dependence. J. Colloid Interface Sci. 214(2), 170-179 (1999). doi 10.1006/jcis. 1999.6181... 

The applicability of Eq. (5.24) breaks down for weakly charged particles kflT 1) because the free energy of the EDL is then strongly related to the (apparent) surface potential y/Q. For spherical particles with a thin double layer ku 1) of Gouy-Chapman type, Deijaguin (1940) derived a criterion for the suspension stability that can be expressed as ... 

---