Cationic transport numbers

The ionic conductivity of the MEEP/metal salt systems was improved by adding a-Al203 particles into the complexes. Chen-Yang [603] obtained a conductivity 0=9.7x10" S cm" for the composite polymer complex MEEP/Li-CIO4/2.5 wt% AI2O3. The cation transport number was in this case 0.77. 

TABLE 8.2 Conductivities, o, Cationic Transport Numbers, Molar Conductivities of the Electrolyte (A) and Cation (X+), and Activation Energies of Conduction, A, for a Number of Melts and Aqueous KCl Solution... 

AU these features—low values of a, a strong temperature dependence, and the effect of impurities—are reminiscent of the behavior of p- and n-type semiconductors. By analogy, we can consider these compounds as ionic semiconductors with intrinsic or impurity-type conduction. As a rule (although not always), ionic semiconductors have unipolar conduction, due to ions of one sign. Thus, in compounds AgBr, PbCl2, and others, the cation transport number is close to unity. In the mixed oxide ZrOj-nYjOj, pure 0 anion conduction t = 1) is observed. 

Frenkel defects on the anion sublattice show only anion migration and hence have fa close to 1. The alkali halides NaF, NaCl, NaBr, and KC1 in which Schottky defects prevail and in which the cations and anions are of similar sizes have both cation and anion contributions to ionic conductivity and show intermediate values of both anion and cation transport number. 

Effect of the salt molecular mass (MB) on the cation transport number (C) in the corresponding solution effective solute (tB) and water (%) transport numbers surface resistances (rc, ra) of, and counterion transport numbers (tc+, ta ) in cation- and anion-exchange membranes specific electric energy consumption (e) in the case of 90% salt recovery at 1 A, and maximum solute concentration theoretically achievable in the concentrating stream (CBCmax). Note NaCl, sodium chloride Na-A, acetate Na-P, propionate Na-L, lactate. 

With Eq. (164) follows the contribution to the current that is apportioned to the cations, denoted as cation transport number t+ ... 

The molar conductance of 0.5 M MgCl2 in water is 165.52 cm moC Q at 25°C. The cationic transport number is 0.308 at this concentration. Estimate the molar conductances of the individual ions. Also estimate the ionic mobilities. 

The second important parameter obtained directly from experiment is the transport number for one of the ions of the electrolyte. On the basis of the analysis in section 6.7, the cationic transport number for a 1-1 electrolyte can be written as... 

Fig. 6.8 Plots of the cationic transport number 25°C against the square root of the electrolyte concentration for three strong electrolytes in water.

At low current density the degree of sodium ion hydration is small— about two water molecules for every sodium ion. The ratio /H2o//Na remains steady until about 0.3 amps cm"2 then rises with increasing current density. The dependence of cation transport number (5,6) and electro-osmotic water fluxes (7,8) on current density have been reported previously. In these cases the dependence of fluxes on current density can be explained by solution polarization phenomena alone. 

The last few years have witnessed a high level of activity pertaining to the research and development of all-solid, thin-film polymer electrolyte batteries most of these use lithium as the active anode material, polymer-based matrices as solid electrolytes, and insertion compounds as active cathode materials. High-performance prototypes of such batteries stand currently under research, whose trends are expected to include the development of amorphous polymers with very low glass-transition temperatures, mixed polymer electrolytes, and fast-ion conductors in which the cationic transport number approaches unity. 

In the same table are given values of the cation transport number taken from the measurements of Longsworth (J. Amer. Chem. Soc. 1932, 54, 2741). 

As a rule (though not always), ionic semiconductors have unipolar conduction because of ions of one sign. Thus, in compounds AgBr, PbCl2, and others the cation transport number is close to unity. In the mixed oxide Zr02 nY20 pure anion conduction = 1) is observed. 

Such styrene/divinylbenzene copolymer membranes can be prepared with a wide variation of properties but the best anion exchange membranes give an anionic transport number greater than 0.98 (i.e. less than 2% of the current is carried by cations in the wrong direction) in typical operating conditions (the transport number will have some dependence on the concentrations of salt in the dilute and concentrated streams). The cationic transport number for the corresponding cation membrane is commonly lower, typically 0.90, and this controls the current efficiency of the process. 

PEO can coordinate alkali metal ions strongly and is used as a solid polymer electrolyte [20-22]. However, conventional PEO-Li salt complexes show conductivities of the order of 10 S/cm, which is not sufficient for battery, capacitor and fuel-cell applications. A high crystalline phase concentration limits the conductivity of PEO-based electrolytes. Apart from high crystallinity, PEO-based electrolytes suffer from low cation transport number (t ), ion-pair formation and inferior mechanical properties. Peter and co-workers [23] reported the modification of PEO with phenolic resin for improvement in mechanical properties and conductivity. 

Power density High surface-area-to-volume ratio High cationic transport number (typical number is 0.5) Monolithic low-impedance cell... 

Table 9.2 Average cation transport number, , correlation coefficient (r) for Equation (9.19) or Equation (9.20), effective fixed charge concentration, Xf, and average cation permselectivity, , for composite HR95, polysulfone support PS-Uf, DEAE-dextran fouled PS-Uf and dense regenerated cellulose RgC membrane.

Transport Number The fraction of the total cell current carried by the cation of an electrolyte solution is called the cation transport number. Similarly, the fraction of the total current carried by the anion is referred to as the anion transport number. Also called Transference Number. 

SECM studies of electroosmosis in the persulfonated polymer Nation have been investigated using the single pore membrane shown in Figure 9.13. Cation transport numbers in Nation approach unity,and electroosmotic flow of water readily occurs in this material. The Nation-filled, single pore membrane is referred to hereafter as the mica/Nafion membrane. 

A dynamic method called Hittorf s method allows determining transport numbers under migration, a method comparable with a fuel cell under operation. The two compartments in the cell are separated by an ion exchange membrane and both compartments are filled with the same KOH solution (same concentration). A current is applied between the two electrodes on either side of the compartments. At the cathode, hydrogen and hydroxide are produced, while at the anode hydroxide is consumed and oxygen is produced. To maintain electroneutrality, the cations (K" ) and anions (OH ) present in the solution migrate through the membrane from one compartment to the other. Anionic and cationic transport numbers f and f ) can subsequently be determined [20,205,206] ... 

The ionic conductivity is obtained by combining the conductivity with the transport number (q.v.). The cation transport number of an electrolyte measures the fraction of the current carried by the cation, so the product of this and the molar conductivity of a completely dissociated binary electrolyte gives the molar conductivity of the cation tcA = Ac, and similarly taA = Aa. 

Most of the polymer electrolytes that have been studied are solid solutions of salts in polymers. There is a possibility that both the cation and anion are mobile in such electrolytes. The ionic transport number in polymer electrolytes is a very important parameter in terms of the conduction mechanism of ions in polymers and of their practical application. Cationic transport numbers have been measured in the polymer electrolytes, especially in those of PEO using various methods, including nuclear magnetic resonance (NMR) [49,50], complex impedance measurements [51,52], tracer diffusion... 

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