Surface charge density proton

Of the various inorganic soil constituents, smectites (montmorillonite clays) have the greatest potential for sorption of pesticides on account of their large surface area and abundance in soils. Weak base pesticides, both protonated and neutral species, have been shown to be sorbed as interlayer complexes. Sorption of atrazine on smectites ranges from 0 to 100% of added atrazine, depending on the surface charge density of the smectite (36). 

Thus, the net surface charge of a hydrous oxide is determined by the proton transfer and reactions with other cations or anions. In general, the net surface charge density of a hydrous oxide is given by... 

Relationship between pH, surface potential, xp or Coulombic term, log P, or Coulombic free energy, AGcoui), and surface charge density, a (or surface protonation) for various ionic strengths of a 1 1 electrolyte for a hydrous ferric oxide surface (P = exp(-Fi //RT). 

If the surface is populated with these amphoteric groups at N sites/unit area, the surface charge density of the surface is (e = protonic charge)... 

M2+ is not adsorbed at the 0-plane of adsorbed counterions but at the surface plane of adsorbed protons. The surface potential ij o and surface charge density are defined by... 

This hydrodynamic contribution to n is determined by the dielectric constant (e) and the viscosity of water (u), the surface charge density of the pore (Z), the pore radius (rp), and the proton conductivity of the pore (cTpore)- The hydrodynamic electro-osmotic coefficient for a typical pore with Tp = 1 nm is found in the range of [i.e., n ydr -1-10]. 

Intrinsic surface charge density, defined by the number of Coulombs per square meter bound by surface functional groups, either because of isomorphic substitutions, or because of dissociation/protonation reactions. 

Proton surface charge density, defined as the difference between the number of moles of complexed proton charges and of complexed hydroxyl charges per unit mass of colloids. 

Acid/hase potentiometry enables the surface charge density to be measured. This involves comparison of the titration curves obtained for the suspension of oxide at several different ionic strengths (10 10" M) with that of the electrolyte alone, followed by calculation of the net consumption of protons or hydroxyl ions (mol g ) at each pH. The data is presented as a plot of excess of acid or base (Fh - Toh ) mol g or mol m ) vs pH (adsorption isotherm) or as a plot of surface charge, cr, (coulombs m ) vs pH (charging curve) (Figure 10.5). 

In the above expressions, n is the concentration of the 1 1 electrolyte, k = (2e2n/eeokT)y2 is the reciprocal Debye length, e is the protonic charge, e0 is the permittivity constant, e is the dielectric constant, and ty o is the surface potential when the plates are infinitely far apart, which is related to the surface charge density via the expression oe = (4ne/ic) sinh(e o/2 T). 

A more complex, and perhaps more realistic, approach is to use a mass action expression for the surface charge. For example, if the surface charge is produced by the loss of protons from the surface, then some of these protons may reabsorb if the pH of the solution is lowered enough. In that case, the surface charge density might be controlled by a surface reaction such as... 

Figure 9.20. Relationship between pH, surface potential, (or Coulombic term, log P, or Coulombic free energy, AGcoui) and surface charge density, o (or surface protonation), for various ionic strengths of a 1 1 electrolyte for a hydrous ferric oxide surface [P = exp(--Fi/ // 7 )]. (a) Dependence of the Coulombic term and surface potential on solution pH note the near-Nemstian behavior at low ionic strength, (b) xp versus or these curves correspond to the Gouy-Chapman theory, (c) o versus pH these are the curves obtained experimentally. (From Dzombak and Morel, 1990.)...

The net proton surface charge density, oh, can be determined from alkali-metric/acidimetric titration, as described in Example 9.2. 

In case of materials showing some degree of solubility the problem how to subtract the blank" is not trivial. Schulthess and Sparks proposed a back titration method to determine the surface charge density of such materials [45]. In this method a series of solutions of different pH is prepared and the solid is added to each solution. After certain time necessary to reach equilibrium a sample of supernatant is taken from each suspension and it is titrated back to the original pH value (before addition of solid). This method was designed to distinguish between surface charging and uptake/release of protons by soluble species. The volume of titrant is then substituted to Eq. (3.1) to obtain (Tq as discussed above for the pH and cip results, and the results obtained by back titration method are listed as pH and cip in Table 3.1. 

In view of experimental difficulties in determination of surface charge density at extreme pH values by potentiomentric titration, other arguments must be considered to resolve the problem of the possibility to charge the silica surface positively. For example a molecular dynamic study led to conclusion that silica surface is not protonated [20]. On the other hand, according to Seidel et al. [21] protonated monosilicic acid is the most abundant silicon species in solution at pH <4.5. (Attention Fig. 3 in Ref. 21 which shows this result has an erroneous legend. Actually the protonated species is represented by the. .. line.) Assuming that the silica surface behaves similarly as monosilicic acid in solution, this result is in favor of protonation of silica at low pH. 

The apparent (in C/m ) is obtained from Equation 2.10 or 2.11. The surface charge density can also be expressed as charge per unit mass (in C/g) [523,524], especially when A is not available. The two representations (charge per unit mass or per unit surface area) produce different numerical values of charge density but the same PZC. In [525] and other papers from the same research group, the surface charge density is expressed as Z, the number of protons reacted per surface site. Z = 0 in their terminology is not necessarily the PZC [75]. Such results can be obtained when the number of surface sites per unit mass or per unit surface area is known. 

Lucas, LT. et al., Surface charge density of maghemite nanoparticles Role of electrostatics in the proton exchange, J. Phys. Chem. C. Ill, 18568, 2007. 

The surface charge density can thus be related to the pK/ values for the surface protons in the same way as done in solutions. According to the Nemst eqnation, the surface potential can be related to the pHp c as... 

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