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Then, for the consideration of the excluded volume eect of the species, athree-component symmetric lattice gas was chosen as a reference system, for which the mentioneddependence is well-known. Then, varying the functional (8) over the potential ψ , and using theexpressions for the chemical potentials of the lattice gas species and equation of state of the latticegas, the following self-consistent eld equation with accounting for the polarizability of the co-solventmolecules, their excluded volume and excluded volume of ions has been obtained:∇((r)∇ψ(r)) = −4π ρ̄c (r),(9)where the equilibrium charge densities are introducedρ̄c (r) = ρext (r) + q+ c̄+ (r) + q− c̄− (r),(10)local ions concentrationsc̄± (r) =1 + v c+,bc±,b exp [−βq± ψ(r)] βγc2e−βq+ ψ(r) − 1 + c−,b e−βq− ψ(r) − 1 + c0,b e 2 (∇ψ(r)) − 1and local dielectric permittivity(11)(12)(r) = ε + 4πγc c̄0 (r),wherec̄0 (r) =c0,b exphβγc (∇ψ(r))22i βγc21 + v c+,b e−βq+ ψ(r) − 1 + c−,b e−βq− ψ(r) − 1 + c0,b e 2 (∇ψ(r)) − 1(13)is the local concentration of the co-solvent molecules and c±,b and c0,b are the concentrations of ionsand co-solvent molecules in the bulk solution, respectively, v is a volume of the lattice gas cell.9(a)0.25(b)γ˜c = 0.005γ˜c = 0.02γ˜c = 0.040.20.3γ˜c = 0.1γ˜c = 0.2γ˜c = 0.30.20.15C̃C̃0.10.10.05000246810120142468101214u0u0Figure 2: Dierential electric capacitance at dierent polarizabilities: (a) γ̃c = 0.005, 0.02, 0.04and (b) γ̃c = 0.1, 0.2, 0.3.

The data is shown for c̃ = 1.63 × 10−3 , c̃0,b = 0.5, ξ = 2.32.Then, much as in the rst part of the Chapter 1, a theory of the at EDL at the metal/electrolytesolution interface was constructed. As in the previous part an 1:1 electrolyte was considered, i.e.q+ = −q− = e. As in the rst part, using the rst integral of the self-consistent eld equationand the boundary condition, relating the induction on the electrode and its surface charge density,an analytical expression for the DC has been obtained, taking into account eects of the excludedvolume of the solution particles, and, in addition, the polarizabiblity of the co-solventC=e (c̄+,s − c̄−,s )el ,4πσ(14)where c̄±,s = c̄± (0) is the local concentrations of the ions on the electrode;el = ε + 4πγc c̄0,s(15)is local dielectric permittivity on the electrode, c̄0,s = c̄0 (0) is the local co-solvent concentration onthe electrode.Turning to the numerical results, the following dimensionless parameters were introduced: c̃0,b =c0,b v , c̃ = cv , γ̃c = γc /vε, Ẽ = βev 1/3 E , u = βeψ , z̃ = z/v 1/3 , σ̃ = σβev 1/3 /ε, ξ = lB /v 1/3(lB = e2 /εkB T is the Bjerrum length).

Eective linear size v 1/3 of the lattice gas cell has beenchosen as a length scale. To perform the numerical calculations, following values of the physicalparameters were taken ε = 80, T = 300 K , c = 0.1 mol/L, v 1/3 = 0.3 nm, which result in thefollowing dimensionless parameters: c̃ = 1.63 × 10−3 , ξ = 2.32.During the analysis of the DC behavior it was determined that increase in the co-solventmolecules polarizability leads to the increase in the DC in the region of the potentials, which valuesare lower than certain threshold value, close to the ”saturation” potential usat (potential, at whichthe maximum of DC is realised). However, if the potential on the electrode exceeds that thresholdvalue, then the increase in the polarizability, oppositely, causes a decrease in the DC (g. 2a).On the contrary, when the polarizability becomes big enough, its increase leads to the continuousgrowth of the DC for all values of the electrode potential (g.

2b). Such a behavior of the DC isdetermined by the fact that at the small values of the polarizability γ̃c , the increase in the electrodepotential results in expelling the co-solvent molecules from the double layer by the ions, which areattracted from the bulk solution. However, when the polarizability is large enough, the co-solventmolecules start to compete with the ions for the ”space” in the vicinity of the electrode, so thereis an excess of the co-solvent molecules in the double layer in comparison to the bulk solution. Inaddition, it is worth noting, that attraction of the co-solvent molecules, possessing induced dipolemoments, from the bulk solution to the charged electrode happens due to the presence of the electric eld gradient, which, in turn, appears due to the electrode charge screening by the oppositelycharged ions.

Analysis showed that increase in the bulk co-solvent concentration may lead to the10(a)0.3(b)c̃0,b = 0c̃0,b = 10−4c̃0,b = 10−30.20.3c̃0,b = 0.01c̃0,b = 0.05c̃0,b = 0.10.2C̃C̃0.10.100024681012140u02468101214u0Figure 3: Dierential electric capacitance C̃ = C̃(u0 ) at dierent co-solvent concentrations inthe bulk phase: (a) c̃0,b = 0, 10−4 , 10−3 and (b) c̃0,b = 0.01, 0.05, 0.1. The data is shown forc̃ = 1.63 × 10−3 , ξ = 2.32, γ̃c = 0.3.shift of the saturation potential in two dierent ways. Namely, when the bulk co-solvent concentration is small enough, its increase leads to the shift of the maximum of C̃ = C̃(u0 ) to the regionof larger values of the electrode potential (g.

3a). That means, that additive of the small amountof the polarizable co-solvent prevents DC from saturation. In the case of large enough co-solventconcentrations maximum of the DC prole shifts, alternatively, to the region of smaller potentialvalues (g. 3b). Then, the dependence of the saturation potential on the co-solvent concentrationat the dierent polarizabilities has been studied. It was established, that non-monotonic behaviorof the saturation potential with the co-solvent concentration in the bulk solution appears only whenthe polarizability is big enough.

However, additive of the co-solvent with rather small polarizabilityleads to the monotonic decrease in the saturation potential.Then, the comparison of the DC behavior, predicted by the theory without account for theexcluded volume eect (formulated in the rst part of the Chapter 1) and theory, based on thelattice gas model, was made. It was shown, that account for the excluded volume leads to theappearance of the maximum in the DC dependance on the electrode potential, which is in agreementwith the Kornyshev theory [Kornyshev, J. Phys. Chem. B, 2007].Finally, it was discussed how the additive of the polarizable co-solvent molecules and changeof their polarizability aects on the prole of the electrostatic potential u(z̃).

It was shown, thatincrease in the co-solvent polarizability leads to the slowdown of the decrement of the electrostaticpotential. As in the theory without accounting for the excluded volume eect, this behavior couldbe explained by the continuous increase of the local dielectric permittivity on the electrode and,as follows, weakening of the screening eect of the electrode charge by the oppositely chargedions.

Nevertheless, the increase of the co-solvent concentration could lead to the distinction in thebehavior of the electrostatic potential prole from that obtained by the theory without excludedvolume eect. That is, a small additive of the co-solvent to the bulk solution leads to the slowdown ofthe electrostatic potential decrease.

However, if the co-solvent concentration is bigger than certainthreshold value, then its further increase will lead to the decrease in the electrostatic potential,starting from a certain distance from the electrode. It was noted, that non-monotonic behavior ofthe potential prole with increase in the co-solvent concentration has a clear physical interpretation.Indeed, when the co-solvent concentration is small, its increase leads to the continuous growth of thelocal co-solvent concentration in the EDL, and, as a consequence, to the reduction of the electrodecharge screening by the ions.

However, at the big enough bulk co-solvent concentrations, from thecertain distance from the electrode, attractive force between the electrode and polarizable moleculesbecomes smaller than repulsion force between these molecules and ions due to the excluded volumeeect that leads to the decrease in the electrostatic potential values. Note that existence of the nonmonotonic behavior of the potential prole with the co-solvent concentration is a new observation11as against to the simplied theory without account for the excluded volume eect (where themonotonic increase in the potential with the increase in the co-solvent concentration is realized),and is determined, as is easily seen, by the competition between the polarizability and the excludedvolume eect.In the conclusion of the Chapter 1 restrictions of the oered EDL models and their potentialimprovements are discussed, and also possible physical-chemical systems, which one can apply thesemodels to, are mentioned.

It was pointed out that the predicted eects of the co-solvent electronicpolarizability are waiting for their experimental conrmation. In addition, it is noted that theproposed theory can be used as a theoretical framework for the modelling of the solubilizationof the aromatic compounds (for instance, benzene) in aqueous solution by the charged micellaraggregates, formed by the ions of the amphiphilic imidasole ionic liquids.Chapter 2The situation with the liquid electrolytes ionic liquids (IL) with a small addition of polar solventmolecules is of a great interest for the modern electrochemical applications. The importance of thisproblem determines by the fact, that IL, which in their pure state represent liquid electrolyteswithout solvent, are universal absorbents of the small molecules of any compounds.

Addition ofthe small amount of polar organic solvent in IL is a conventional procedure, leading to the increaseof the ionic mobility, increasing electric conductivity. On the other side, IL themselves can easilysorb dierent molecules from atmosphere, rst of all, water molecules from the air. For chemicalengineers the eect of the water absorbtion from the atmosphere is highly unfavorable, as it leads tothe uncontrolled physical-chemical properties of IL, associated with the air humidity uctuations.This problem is the most important for the electrochemistry. Indeed, one of the IL advantages isconnected with the wide electrochemical window (range of the electrode potential values, where thesolvent molecules are stable).

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