Colloidal charge

Wang, L.K. Determination of Polyelectrolytes and Colloidal Charges, PB86-169307 US Department of Commerce, National Technical Information Service Springfield, VA, 1984 47 p. 

The generation of colloidal charges in water.The theory of the diffuse electrical double-layer. The zeta potential. The flocculation of charged colloids. The interaction between two charged surfaces in water. Laboratory project on the use of microelectrophoresis to measure the zeta potential of a colloid. 

For effective removal of the colloids, as much of alum should be converted to the solid A1(OH)3(j). Also, as much of the concentrations of the complex ions should neutralize the primary charges of the colloids to effect their destabilization. Overall, this means that once the solids have been formed and the complex ions have neutralized the colloid charges, the concentrations of the complex ions standing in solution should be at the minimum. The pH corresponding to this condition is called the optimum pH. 

In most cases colloidal charges cannot be measured directly, but may be calculated knowing the particle size and mobility. Charge/mass, however, which is of technological interest, can be experimentally determined in the electrical plateout(18,19). 

If the DDL contained only those cations necessary to neutralize the colloid charge, the anion concentration would be zero within the DDL. Because diffusion continually drives anions toward the colloid surface, however, the total negative charge within the DDL is that of the anions plus the colloid s charge. Cations within the DDL must neutralize both sources of negative charge. The cations that neutralize... 

In theory, one can calculate the distribution of electric potential within the double layer for any combination of colloid charge, salt concentration, counter-ion valence and interparticle distance. The Boltzmann equation (8.15) can then be used to calculate cation and anion distributions. From such distributions, cation exchange, colloid swelling, and anion repulsion can be inferred but the calculations are complex, tedious, and often only approximate. 

Davis developed an equation similar to the Vanselow equation from statistical thermodynamics. Electrostatic forces between colloid surfaces and adsorbed cations were calculated for various surface configurations of charge sites. These sites were assumed to be neutralized by individual adsorbed ions. Hence, the model resembles most closely the Helmholtz model of the double layer with the charge of cations on the surface assumed to be just equal to the number of colloid charges. The resultant equation is... 

Extreme pH conditions and pre-adsorption of organics onto the particle surface creates very stable systems and the rejection of the colloids is then reduced significantly. Reduced rejection leads to a penetration of the particles into the pores and adsorption on the pore walls. In this case, the flux decEne is dependent on colloid sige, with the si closest to the membrane pore sio e causing the highest flux decline. In the presence of organics, membrane-colloid charge interaction and adsorption are reduced and rejection decreases for stable colloids. 

These effects can be attributed to the adsorption of organics on the colloids, which increases negative colloid charge and depletes organics in the permeate to some extent, as well as the low solubility of HA at this pH and thus the filtration of the aggregates or the precipitate. 

After optimising the controller, the colloidal charge of 1.50 ml after the machine chest is commercially and process-wise the most appropriate level (Fig. 11.6). Fixative additions of 150 g/t and 450 g/t are chosen as minimum and maximum dosages, respectively. If the measured cationic demand keeps below the target value for a longer period, the minimum dosage is added. 

A quantitative analysis of counterion localization in a salt-free solution of star-like PEs is carried out on the basis of an exact numerical solution of the corresponding Poisson-Boltzmann (PB) problem (Sect. 5). Here, the conformational degrees of freedom of the flexible branches are accounted for within the Scheutjens-Fleer self-consistent field (SF-SCF) framework. The latter is used to prove and to quantify the applicability of the concept of colloidal charge renormalization to PE stars, that exemplify soft charged colloidal objects. The predictions of analytical and numerical SCF-PB theories are complemented by results of Monte Carlo (MC) and molecular dynamics (MD) simulations. The available experimental data on solution properties of PE star polymers are discussed in the light of theoretical predictions (Sect. 6). 

Fig. 1 Adsorption of a polyelectrolyte chain onto spherical colloidal particles for various salt concentrations C (from [35]). The ratio ajb between the colloid radius a and monomer bond length b increases from top to bottom. The colloid surface charge density is constant, hence, the colloidal charge increases with a. The adsorption threshold depends on the salt concentration and the size ratio. More details of the underlying Monte Carlo simulations are provided in Ref. [35]...

Experimentally, a large number of similar studies on the influence of chain stiffness, colloid charge density, and salt concentration have been performed [43, 44, 121-138]. Some theoretical trends regarding the effect of surface curvature and salt concentration on critical adsorption and polyelectrolyte-colloid complexation are supported by experimental observations. These studies, however, also revealed a number of discrepancies and additional physical parameters to be taken into account, as compared with the outcomes of theoretical studies and computer simulations. 

The exact solution for the Debye-Hiickel potential predicts a linear dependence of the critical colloid charge density on the inverse Debye screening length for Kfl 1 (Fig. 5). This is different from the predicted dependence IcTcI based on... 

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