Energy double-layer

Using the conditions of the Langmuir approximation for the double-layer repulsion, calculate for what size particles in water at 25°C the double-layer repulsion energy should equal kT if the particles are 40 A apart. 

Often the van der Waals attraction is balanced by electric double-layer repulsion. An important example occurs in the flocculation of aqueous colloids. A suspension of charged particles experiences both the double-layer repulsion and dispersion attraction, and the balance between these determines the ease and hence the rate with which particles aggregate. Verwey and Overbeek [44, 45] considered the case of two colloidal spheres and calculated the net potential energy versus distance curves of the type illustrated in Fig. VI-5 for the case of 0 = 25.6 mV (i.e., 0 = k.T/e at 25°C). At low ionic strength, as measured by K (see Section V-2), the double-layer repulsion is overwhelming except at very small separations, but as k is increased, a net attraction at all distances... 

Much use has been made of micellar systems in the study of photophysical processes, such as in excited-state quenching by energy transfer or electron transfer (see Refs. 214-218 for examples). In the latter case, ions are involved, and their selective exclusion from the Stem and electrical double layer of charged micelles (see Ref. 219) can have dramatic effects, and ones of potential imfKntance in solar energy conversion systems. 

Referring to Section V-2, the double-layer system associated with a surface whose potential is some value j/o requires for its formation a free energy per unit area or a t of... 

The necessity to calculate the electrostatic contribution to both the ion-electrode attraction and the ion-ion repulsion energies, bearing in mind that there are at least two dielectric ftmction discontinuities hr the simple double-layer model above. 

Within this framework, by considering the physical situation of the electrode double layer, the free energy of activation of an electron transfer reaction can be identified with the reorganization energy of the solvation sheath around the ion. This idea will be carried through in detail for the simple case of the strongly solvated... 

For many practically relevant material/environment combinations, thennodynamic stability is not provided, since E > E. Hence, a key consideration is how fast the corrosion reaction proceeds. As for other electrochemical reactions, a variety of factors can influence the rate detennining step. In the most straightforward case the reaction is activation energy controlled i.e. the ion transfer tlrrough the surface Helmholtz double layer involving migration and the adjustment of the hydration sphere to electron uptake or donation is rate detennining. The transition state is... 

When two conducting phases come into contact with each other, a redistribution of charge occurs as a result of any electron energy level difference between the phases. If the two phases are metals, electrons flow from one metal to the other until the electron levels equiUbrate. When an electrode, ie, electronic conductor, is immersed in an electrolyte, ie, ionic conductor, an electrical double layer forms at the electrode—solution interface resulting from the unequal tendency for distribution of electrical charges in the two phases. Because overall electrical neutrality must be maintained, this separation of charge between the electrode and solution gives rise to a potential difference between the two phases, equal to that needed to ensure equiUbrium. 

Fig. 1. Potential energies of interaction between two coUoidal particles as a function of their surface-surface separation, for electrical double layers due...

Electrostatic Repulsive Forces. As the distance between two approaching particles decreases, their electrical double layers begin to overlap. As a first approximation, the potential energy of the two overlapping double layers is additive, which is a repulsive term since the process increases total energy. Electrostatic repulsion can also be considered as an osmotic force, due to the compression of ions between particles and the tendency of water to flow in to counteract the increased ion concentration. 

Fig. 20.17 Potential energy-distance curves for a cathodic reaction showing how the potential energy barrier is lowered by when E < p,z.c. The barrier is assumed to be symmetrical so that /S => yi, where 5 is the distance of the O.H.P. from the surface of the electrode. Full curve—no field across double layer dashed curve-potential diflcrence is E and is negative...

Activation Overpotential that part of an overpotential (polarisation) that exists across the electrical double layer at an electrode/solution interface and thus directly influences the rate of the electrode process by altering its activation energy. 

The electrical double layer at Hg, Tl(Ga), In(Ga), and Ga/aliphatic alcohol (MeOH, EtOH) interfaces has been studied by impedance and streaming electrode methods.360,361 In both solvents the value ofis, was independent of cei (0.01 < cucio4 <0.25 M)and v. The Parsons-Zobel plots were linear, with /pz very close to unity. The differential capacity at metal nature, but at a = 0,C,-rises in the order Tl(Ga) < In(Ga) < Ga. Thus, as for other solvents,120 343 the interaction energy of MeOH and EtOH molecules with the surface increases in the given order of metals. The distance of closest approach of solvent molecules and other fundamental characteristics of Ga, In(Ga), Tl(Ga)/MeOH interfaces have been obtained by Emets etal.m... 

Two hundred years were required before the molecular structure of the double layer could be included in electrochemical models. The time spent to include the surface structure or the structure of three-dimensional electrodes at a molecular level should be shortened in order to transform electrochemistry into a more predictive science that is able to solve the important technological or biological problems we have, such as the storage and transformation of energy and the operation of the nervous system, that in a large part can be addressed by our work as electrochemists. 

Figure 5.7. Schematic representation of the definitions of work function O, chemical potential of electrons i, electrochemical potential of electrons or Fermi level p = EF, surface potential %, Galvani (or inner) potential

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