Dissociation degree

This potential reflects itself in the titration curves of weak polyacids such as poly(acrylic acid) and poly(methacrylic acid) [32]. Apparent dissociation constants of such polyacids change with the dissociation degree of the polyacid because the work to remove a proton from the acid site into the bulk water phase depends on the surface potential of the polyelectrolyte. 

The salt effect is very strong in polyconjugated polyelectrolytes. Figure 15 is a graph of the proton dissociation energy vs. the dissociation degree of PPA of different structures. Also, the graphs for poly(methacrylic acid) and a copolymer... 

However, the addition of even small volumes of alkali leads to the screening of these groups, with a subsequent decrease of the proton dissociation energy at low dissociation degrees. This complies with the salt effect (Fig. 15). 

Table 23 shows the dissociation degrees of several alcohol and alcohol ether sulfates. 

The relations described by Eqs. (7.9) to (7.13) became known as Ostwald s dilution law. They reflect the dependence of conductivity on the dissociation degree a, which changes with increasing concentration q. 

Fig. 1.2 Dependence of the dissociation degree a of a week electrolyte on molar concentration c for different values of the apparent dissociation constant K (indicated at each curve)... 

The unavailability of data on dissociation degree and mobility has thus made ion conductivity an alternative metric that has been universally adopted by the battery research and development community to evaluate the transport ability of electrolytes. However, it should always be remembered that such a metric of convenience is based on an unstated assumption that is, the increase in the overall conductivity should originate, at least partially, from the improvement in the cation conductivity. Qualitatively, this assumption holds true, since a correlation does usually exist between ion conductivity and power performance in batteries, although quantitatively the distribution of this increase between anions and cations is unknown. 

The efforts to improve ion conductivity have revolved around eq 1, that is, aiming at increasing either the salt dissociation degree riij or the ionic mobility (mj). Since these two factors are decided simultaneously by the physicochemical natures of the salt and solvents, different approaches involving either of these electrolyte components have been adopted. 

Here E ( y1 ) stands for the single-particle contribution to the total energy, allowing for molecule interaction with the surface <2 is the heat released in adsorption of molecules z on the /Lh site Fj the internal partition function for the z th molecules adsorbed on the /Lh site F j the internal partition function for the zth molecule in the gas phase the dissociation degree of the z th molecule, and zz the Henry local constant for adsorption of the zth molecule on the /Lh site. Lateral interaction is modeled by E2k([ylj ), and gj (r) allows for interaction between the z th and /Lh particles adsorbed on the /th and gth sites spaced r apart. In the lattice gas model, separations are conveniently measured in coordination-sphere numbers, 1 < r < R. For a homogeneous surface, molecular parameters zz and ej(r) are independent of the site nature, while for heterogeneous, they may depend on it. 

In Fig. 7 IR spectra of PEM-5 and PEM-6 of PEI/PAC and of solution cast PECs of PEI/PAC (n—/n+=0.80 and 1.25) prepared at pH=4 (PAC) and 6 (PEI) are shown. Both the spectrum of the polycation terminated PEM-5 and that of PEC-0.8 of PEI/PAC were comparable, since they contain PEI in excess. The PEM-5 spectrum showed only a minor v(C=0) and a major v(COO ) band, since all COOH groups were consumed by the overlaying PEI layer, whereas the PEM-6 spectrum showed a major v(C=0) and minor v(COCT) band. From these two bands the dissociation degree of PAC can be calculated using the relation... 

Table 1 Dissociation degree am of several samples of PEMs and PECs composed of PAC and PEI or PDADMAC deposited or mixed at pH 6 (PEI) and 4 (PAC)...

According to the Arrhenius theory the decrease of A with increasing concentration of the solution with all electrolytes is merely due to the lowering of the dissociation degree as this theory does not take into account the mutual attraction of ions and the lowering of ion mobility in more concentrated solutions, the velocity of the ions in equation (111-25) should be equal both at finite concentrations and infinite dilution, i. e. ( + + v ) = (v + ). As... 

Although Debye and Hiickel worked out their theory to solve the problem of strong, completely dissociated electrolytes, the results may be applied to weak and transition electrolytes as well, if the actual ionic concentration is substituted in the equation for ionic strength. With strong electrolytes, which are completely dissociated, it is possible to substitute in the term directly the analytical concentration of the substance, but with weak electrolytes their dissociation degree a has to be considered. For example with uni-... 

Such a a diagram valid for diluted acetic acid is shown in Fig. 7. The required values of the dissociation degree x were found by measurement of conductivity of solutions with varying molarity c and the apparent dissociation constant K e was computed according to the formula ... 

For a specific reaction terms such as degree of dissociation , degree of ionization , etc. are commonly used. 

Attempts to derive theoretical relations describing various dissociation degrees are based on the contribution of electrostatic forces to the Gibbs energy, enthalpy, and change in dissociation entropy. These contributions can be calculated [68c]... 

Let us consider 1 mol of mixture with the composition xi(=Xw(Na3AIF6) mol Na3AlF6-bx2(=Xw(X)) mol AI2O3, where X2 << xi. Cryolite dissociates according to reaction (3.184) with a dissociation degree a. The dissolution of AI2O3 in cryolite is accompanied by the reaction (3.185). At equilibrium, we get the following amounts of the individual substances... 

The model of electrical conductivity of molten salt mixtures based on incomplete electrolytic dissociation of components was proposed by DanCk (1989). The dissociation degree of a component is affected by the presence of second component. Consequently, the dissociation degree of both components in the system is not constant, but changes with composition, affecting the concentration of the conducting particles in the electrolyte. This effect is caused by interactions of components, given by the nature of the repulsive forces between ions, determining their actual coordination sphere. 

If we denote the dissociation degrees of the components in the mixture by ai and U2, and their molar fractions by x and X2, then in one mole of an arbitrary mixture the following amounts of particles are present... 

Equation (8.30) can be solved either analytically or preferably using the Newton-Raphson s method. As starting values for and 2 it is advantageous to choose the values of the dissociation degrees of pure components q oi and 02- So it is possible to calculate the values of a and 2 for an arbitrary composition of the mixture and for arbitrary values of the dissociation degrees of the pure components. 

From Eq. (8.36) it follows that when the dissociation degree does not change with composition, i.e. a = oi and U2 = aoc, Eq. (8.36) is identical with the parallel model proposed by Fellner (1984). Thus the expression Xi(ailaoi) can be considered as the activity of component in the mixture. 

The calculation procedure is as follows For the chosen values of the dissociation degrees of the pure components oi and ao2, the values of ai and 2 are calculated according to Eqs. (8.29) and (8.30) for each composition of the mixture with a known value of the molar conductivity, A, exp. The theoretical value of the molar conductivity, i, calc is calculated according to Eq. (8.36), in such a way for each couple of oi and 02 that a set of theoretical values of molar conductivities for the given composition is obtained. The criterion for selection of the right values of aoi and ao2 is given by the relation... 

Table 8.1. Calculated values of the dissociation degrees of pure components in binary systems with a common anion...

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