Abstract This thesis studies the effect of the molar fraction of mixture of ionic liquids on the capacitance of an electric double super capacitor using classical density functional theory. We have modeled a super capacitor with porous electrodes containing spherical pores where its electrolyte consisting of a mixture of two ionic liquids with a common cation in a form of a dimer and monomeric anions of different sizes. The effect of various factors such as molar fraction, dielectric constant, ion size and pore size of the porous electrodes on ion adsorption and capacitance of electric double layer super capacitors have been studied. Also, the effect of the mentioned factors on the supercapacitor operating potential window and potential of zero charge (PZC) have been studied. Although pure ionic liquids with small ions in our study had wider theoretical potential window than ionic liquids mixture but the mixtures recommended for increasing the capacitance of the supercapacitors. In fact, at specific mole fraction of the mixture of ionic liquids, for which PZC is close to zero, we have a wider operating potential window with respect to pure one which causes a maximum capacitance. our results for nanopores with a reduced radius of 5.83 and a relative dielectric constant of 5 showed maximum capacitance for a mixture with molar fraction of 0.22 of an ionic liquid with a smaller anion. In this mole fraction, the amount of capacitance showed an increase of 35% compared to pure ionic liquid with larger ions and an increase of 5% compared to pure ionic liquid with smaller ions. In order to investigate the effect of dielectric constant, the capacitance of super capacitors in two different values of the dielectric constant was eva‎luated. The results show that increase in dielectric constant, causes to more capacitance. Also, we observed that at sufficiently large radii of pores the capacitance value would not be affected by the PZC value and the selectivity of the ions by nanopores plays an important role. Keywords: Classical density functional theory, Ionic liquid mixture, Operating potential window, potential of zero charge, Electrical double layer supercapacitors, Integral specific capacitance.

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حسين فرخ پور , كيومرث اسكندري