Chemical contribution, free energy interface

The structure of this interface determines fhe sfabilify of PEMs, the state of water, the strength of interactions in the polymer/water/ion system, the vibration modes of side chains, and the mobilities of wafer molecules and protons. The charged polymer side chains contribute elastic ("entropic") and electrostatic terms to the free energy. This complicated inferfacial region thereby largely contributes to differences in performance of membranes wifh different chemical architectures. Indeed, the picture of a "polyelectro-lyfe brush" could be more insighttul than the picture of a well-separated hydrophobic or hydrophilic domain structure in order to rationalize such differences. ... 

This transition may j-.e. reducing the specific surface energy, f. The reduction of f to sufficiently small values was accounted for by Ruckenstein (15) in terms of the so called dilution effect". Accumulation of surfactant and cosurfactant at the interface not only causes significant reduction in the interfacial tension, but also results in reduction of the chemical potential of surfactant and cosurfactant in bulk solution. The latter reduction may exceed the positive free energy caused by the total interfacial tension and hence the overall Ag of the system may become negative. Further analysis by Ruckenstein and Krishnan (16) have showed that micelle formation encountered with water soluble surfactants reduces the dilution effect as a result of the association of the the surfactants molecules. However, if a cosurfactant is added, it can reduce the interfacial tension by further adsorption and introduces a dilution effect. The treatment of Ruckenstein and Krishnan (16) also highlighted the role of interfacial tension in the formation of microemulsions. When the contribution of surfactant and cosurfactant adsorption is taken into account, the entropy of the drops becomes negligible and the interfacial tension does not need to attain ultralow values before stable microemulsions form. 

The first term, ADPxh, is the adiabatic deprotonation energy of XH with the point just outside the solution interface as reference, and is again the work function of the aqueous proton. The last term of Equation 13.41 accounts for the translational free energy generated by the dissociation. This contribution has been approximated by the chemical potential of a free gas phase proton at standard concentration (c°). Ajj+ is the thermal wavelength of the proton. This approximation is justihed because of the small mass of the proton compared to the conjugate base X. Under ambient condition, the translational contribution amounts to a correction of B7 1n[c°Ag,] = -0.19eV or-3.2 pK units. 

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