Charge probabilities

The presented mechanisms are not the only ones occurring. Air bubbles or oil drops in water, for instance, are negatively charged, probably due to an adsorption of hydroxyl ions. The process is far from being understood. Many polymer surfaces acquire a negative surface charge in water. This could be due to anions, which are adsorbed due to the van der Waals force. Again, this process is not well understood. 

A wide variety of this group of surfactants is commercially available. They include some of the Tritons (alkyl phenol additives, as far as they are non-ionic). Tweens (sorbitan fatty acid ester polyoxyethylene ethers). Spans (sorbitan fatty acid esters) and alkyl polyoxyethylenes (C Ej, where n and x stand for the number of CH2- or CH3-. and CHjO-groups in the hydrophobic and hydrophilic parts of the molecule, respectively). Given our interest in the fundamentals we shall emphasize only the last-mentioned group, and only when n and x are sharply defined emd the two moieties are either linear or branched in a defined way. Unless specified otherwise, there is an OH-group at the end of the E-chain. Notwithstanding the non-ionic nature of these molecules, micelles sometimes appear to cany a (low) charge probably caused by preferential uptake of ionic species. 

The second category of aqua ions corresponds to a mixture of differing N values (and symmetries) with almost the same free energy, readily modified by changing salt concentration, temperature (and perhaps even hydrostatic pressure). The rather indifferent choice between N = 7, 8, 9 and 10 may be characteristic for calcium(II), the rare earths and probably also for thorium(IV). The third category are cations with so large radii and so low positive charge (probably K+, Rb+, Cs+ and Ba+2, perhaps even Tl+) that the nearest water molecules are so relatively weakly perturbed and oriented by the cation that the situation is similar to the second layer of water molecules around Co(NH3) 3 or Cr(OH2)g 3, or even N(CH3)4. ... 

In conclusion, the TEM and XPS studies indicate that on the Rh/AljOj catalyst, the rhodium particles tend to spread on the alumina platelets and to be positively charged probably because they are interacting with the electron acceptor sites of the oxide support. 

At the same time, the absolute value of the potential of gas bubbles is found to decrease with pH decreases becoming zero for pH close to 3. At very low pH, it has even been claimed that the bubble could be positively charged, probably because of a preferential accumulation of H" ". 

The specific mass effect is due to the interactions (correlations) between the different outer electrons. The mass effect is very prominent for hydrogen/deuterium but is quickly reduced for heavier elements. For such elements the volume effect becomes important. It is particularly prominent when the electron configuration contains unpaired s electrons. The nucleus has a charge density over a finite volume. The s electron with a charge probability distribution p (r) can penetrate the nucleus and is then no longer under the influence of the pure Coulomb field. A nucleus of mass M has a smaller radius r than one with the mass M+AM, and thus the potential begins to deviate from a Coulombic one at smaller values of r. The situation is illustrated in Fig.2.21. There will be an energy shift described by... 

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