Ionic conduction free volume effect

It is apparent from the above discussion that ionic mobility is controlled by the free volume of a liquid and the size of the ions. The size of the voids in the liquid and their effect on liquid density can be changed by decreasing the ion-ion interactions. This will manifest itself by a decrease in surface tension and, in general, the liquids with lower surface tensions are more fluid and have higher conductivities. This is the reason why ionic liquids with discrete, highly fluorinated anions such as PF6 and (F3CS02)2N have become popular. 

An amount of LiTFSl equimolar to the imidazolium cation unit was added to PI and P2 in order to study the effect of alkyl spacer on the ionic conductivity. Figure 30.3 shows Arrhenius plots of the ionic conductivity for the copolymers after addition of salt. Within the measured temperature regime, P2 with alkyl spacer had ionic conductivity one order higher than PI without spacer. There are two possible explanations. An increase in the length of the alkyl spacer causes an increase of free volume and maintains the high mobility of the IL domain. Although... 

In general the effect of the added organic plasticizer appears to increase the free volume of the polymer thereby decreasing the Tg [93] and or reducing the content of the crystalline phase in PEO [83] and also to effect the ionic association in the polymer electrolytes [81]. Many of these effects have been studied by use of a variety of experimental methods such as IR spectroscopy, DSC, EXAFS, X-ray diffraction, NMR, conductivity studies, viscosity measurements etc. [81, 90,93-103]. The effects of the plasticizers on the conductivity behavior of PEO polymer electrolytes along with the conductivity data of other PEO-polymer electrolytes discussed above are summarized in Table 2. 

Another effect observed was that the maximum conductivities for each polymer system decreased with an increase in the length of the alkyl group side chain, R. Thus, although the free volume of the polymer perhaps is increased as the chain length in R increases, this also leads to the availability of fewer coordination sites per volume of polymer. Clearly this latter feature is quite important in fine tuning the ionic conductivities. 

The preference of Nafion for up taking methanol over water is certainly an undesirable property for DMFC using this proton conducting membrane. It would be worth to review the effect of inorganic or organic Nafion composite membranes on the sorption of water-methanol from the liquid phase and on the partition constant. The few reported studies include Nafion/sulfonated organosilica [47] and Nafion/zirconium phosphate [78], where a reduction of the total liquid uptake is observed for the composites in methanol solutions up to 10 M, attributed to a reduction of the free volume in the ionic clusters. 

Another positron state is formed when free volume-type crystal defects are present in the metal crystal. The positively charged ionic cores are missing from these defects, so, usually they are effective traps for any positive particle, including the positron in our case. Thus, in most metals, vacancies, vacancy clusters, dislocations, and grain boundaries localize some or all of the free positrons and produce another positron state, the trapped positron. These localized positrons still can meet conducting electrons, but ionic cores are out of their reach. Accordingly, their annihilation characteristics differ from those of free positrons significantly. Different kinds of traps all have their own characteristic annihilation parameters but these parameters are very close to each other. 

The brief discussion above shows that the structure of a polymer electrolyte and the ion conduction mechanism are complex. Furthermore, the polymer is a weak electrolyte, whose ions form ion pairs, triple ions, and multidentate ions after its ionic dissociation. Currently, there are several important models that attempt to describe the ion conduction mechanisms in polymer electrolytes Arrhenius theory, the Vogel-Tammann-Fulcher (VTF) equation, the Williams-Landel-Ferry (WLF) equation, free volume model, dynamic bond percolation model (DBPM), the Meyer-Neldel (MN) law, effective medium theory (EMT), and the Nernst-Einstein equation [1]. 

The free volume model presumes that ion movement needs a free volume that is related to the polymer chain segment and ion types. However, it does not consider microstructure and cannot explain effects of polarization, ion pairs, and solvation degree on ionic conductivity. 

Solid state physicists are familiar with the free- and nearly free-electron models of simple metals [9]. The essence of those models is the fact that the effective potential seen by the conduction electrons in metals like Na, K, etc., is nearly constant through the volume of the metal. This is so because (a) the ion cores occupy only a small fraction of the atomic volume, and (b) the effective ionic potential is weak. Under these circumstances, a constant potential in the interior of the metal is a good approximation—even better if the metal is liquid. However, electrons cannot escape from the metal spontaneously in fact, the energy needed to extract one electron through the surface is called the work function. This means that the potential rises abruptly at the surface of the metal. If the piece of metal has microscopic dimensions and we assume for simplicity its form to be spherical - like a classical liquid drop, then the effective potential confining the valence electrons will be spherically symmetric, with a form intermediate between an isotropic harmonic oscillator and a square well [10]. These simple model potentials can already give an idea of the reason for the magic numbers the formation of electronic shells. 

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