Charged adsorbates

TABLE 6.1 Zero point, thermal and entropic corrections to DFT energies of adsorbates on Pd(lll). Standard state values are referenced to 1 atm pressure 

One can therefore calculate the energy of the neutral adsorbate-slab complex and separately account for the energy of the transferred electron. For the same reasons outlined earlier, a supercell cannot be used to calculate the energy of an excess electron in a metal slab. Alternatively, the energy of the electron can be related to an appropriate reference electrochemical reaction, assumed to be equilibrated in the system of interest, for instance the hydrogen electrode  

This method was popularized by Nprskov and coworkers and has been used widely to simulate ion adsorption [59-62]. In units of eV, the free energy G(e ) of the electron in an electrode is the negative of the absolute potential U in volts  

Experimental values for the potential of the electron in the standard hydrogen electrode have been reported in the range 4.4-4.8eV, so that the free energy of the electron in the standard hydrogen electrode is -4.6 0.2eV [63-65]. The free energy of the electron at nonstandard conditions is then given by the Nemst Equation  

Armed with this bit of thermodynamics, we can now calculate the free energy of adsorption of an anion, reaction 5 as  

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Figure 4.3 Two alternative ways of viewing the charge distribution in an adsorption bond. The upper part of this figure shows the dipole moment the lower part shows a partially charged adsorbate and its image charge. The dipole moments of the surrounding solvent molecules are oriented in the direction opposite to the adsorbate dipole.

If a surface precipitate of metal hydroxy-polymer has formed on an adsorbent, the -pH relationship for the coated adsorbent should resemble closely that observed for particles consisting purely of the hydroxy-polymer or the hydrous oxide of the metal (15). This kind of evidence for Co(ll), La(lII), and Th(lV) precipitation on silica colloids was cited by James and Healy (15). It should be noted, however, that the increase in C toward a maximum value often occurs at pH values well below that required thermodynamically to induce bulk-solution homogeneous precipitation of a metal hydrous oxide (15, 16). If surface precipitation is in the incipient stage under these conditions, it must be a nucleation phenomenon. James and Healy (15) argue that the microscopic electric field at the surface of a charged adsorbent is sufficiently strong to lower the vicinal water activity and induce precipitation at pH values below that required for bulk-solution precipitation of a metal hydrous oxide. 

Adsorbed organic compounds do not necessarily occupy surface sites in a random fashion. Favorable hydrophobic interactions, for example, may cause some organic compounds to adsorb in groups, enhancing overall surface coverage. Electrostatic repulsion between charged adsorbate molecules, in contrast, may space molecules on the surface apart from one another. 

Ligand exchange with small charged adsorbants, e.g., 3-mercaptopropionic acid (MPA) [34]... 

We treat the free electrons or positive holes on the surface as one of the reactants or products and propose that a surface reaction between charged adsorbed particles, both reactants and products, is the essential... 

For instance, the Frumkin s adsorption isotherm for a charged adsorbed species establishes that... 

Finally, the term g(x) represents the potential energy of interaction between the electron at x and the net charge adsorbed at the electrode/electrolyte interface. In the following treatment we will assume that under the illumination conditions em- + ployed in the experiments reviewed above, only the interfacial H concentration is appreciably altered by changes in the illumination level, iJj. Thus we neglect the photo-adsorption/desorption of other ionic species. 

The observed equilibrium thickness represents the film dimensions where the attractive and repulsive forces within the film are balanced. This parameter is very dependent upon the ionic composition of the solution as a major stabilizing force arizes from the ionic double layer interactions between any charged adsorbed layers confining the film. Increasing the ionic strength can reduce the repulsion between layers and at a critical concentration can induce a transition from the primary or common black film to a secondary or Newton black film. These latter films are very thin and contain little or no free interlamellar liquid. Such a transition is observed with SDS films in 0.5 M NaCl and results in a film that is only 5 nm thick. The drainage properties of these films follows that described above but the first black spot spreads instantly and almost explosively to occupy the whole film. This latter process occurs in the millisecond timescale. 

Fig. 6.23 Dependence of the Nemst potential on the density of the proton-binding sites and on adsorption. Upper curves within the bracketed sets correspond to the absence of adsorption. The lower curves show the effect of 100 mM charged adsorbate (adapted from Sandifer 1998)...

The key point of interest in electrosorption (which the above cited arguments do not take into account) is whether—because such a double layer is formed even when an electric field is not applied—the application of an electric field can enhance or reverse the double-layer-controlled interactions between the charged adsorbent and the adsorbate ions in solution (see Figure 5.6). Therefore, the key issue is whether the following arguments are really applicable when it comes to determining the total capacity of electrosorption [148] ... 

Charge neutralization. Polyelectrolytes of opposite charge adsorb electrostatically, thereby neutralizing the surface charge and permitting dispersion forces to drive flocculation. Then the conditions for optimum flocculation should correlate with the point of zero charge for the particles. 

Figure C3-5 Counter charges adsorb on a charged matrix...

The facts described above pave the way toward the concept ofpoint of zero charge. This corresponds to the point where the net, total charge adsorbed at the surface of the particle (including all the cations and anions) is zero. The pH of the suspension that corresponds to the point of zero charge is known as the pHpzc, or simply, pzc. At this pH, the charge balance on the surface of the colloid is zero. As a result, the pH of the solution defines the type of exchange that predominates in the particle ... 

A Donnan effect that prevents self-repulsion of the similarly charged adsorbed IPR ions at higher ionic strength, the higher surface concentration of the IPR ( LH in Equation 3.5) partially compensates for the decreased magnitude of the electrostatic surface potential due to the increased Scoi in Equation 3.5. 

While previous work has often been conducted under conditions where only trace quantities of lead or other heavy metals have been placed in contact with an adsorbent, very few of these approaches have dealt with the problems faced as the adsorbent sites begin to be filled. The usefulness of the VSC-VSP model in taking this into account is illustrated here by demonstration of the effect of charged adsorbed species on the electrostatic potential which acts on the adsorbing ions. When a given number of equivalents of adsorbent are placed in contact with a comparatively large number of moles of cations, some of which will attach to the adsorbent, adsorption will be further opposed in two ways. First, of course, the process of adsorption will reduce the number of sites available for further adsorption. Second, the Gouy potential is said by Bowden ad. (7) to decrease from the... 

In the low-temperature oxidation of LCO in a liquid phase by permanganate [263, 264] or hypobromite [265] the characteristic times of doping prove to be close to those known for electrochemical experiments. This observation probably indicates that mobile oxygen species are identical in these cases. The formation of a charged adsorbate in the gas phase is clearly unlikely. 

In another study that underestimates the importance of carbon surface chemistry, Helmy et al. [709] set out to provide a pH/pK, relationship [that] permits the individual isotherms to be obtained for the charged and neutral sorbate species. They studied the uptakes of quinoline (pK = 4.9) and 8-hydroxyquinoline (pKa = 5.0) on a commercial charcoal the former reached a plateau as pH increased from 2 to 7, while the latter exhibited a maximum at pH = 6 and decreased thereafter. The authors theory led them to conclude that the surface of charcoal prefers the neutral over the charged molecule, which was confirmed by noting that their respective isotherms were of type I and type III. Intriguingly, the reasons for this preference were discussed only in terms of the repulsion between charged adsorbate species, while the electrostatic adsorbate-adsorbent interactions were ignored. Not surprisingly, the work of Muller and coworkers [523-525] is not cited. 

At pH levels above 2, endotoxin aggregates are negatively charged and behave as anions. This property accounts for the attraction that endotoxin aggregates have for divalent cations in solutions. It is also the characteristic that provides the mechanism of action for endotoxin removal by cationically charged adsorbents. 

The addition of the ECPs to the cluster results in a better representation of the electrostatic potential and hence of the electrostatic contribution to the surface bonding. Still missing from this simplified approach is the polarization of the host crystal induced by an adsorbed species. This effect can be particularly important for charged adsorbates. 

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