Activity coefficient of counterions

Both relaxation times are functions of the thermal motion of the molecules, of chemical-exchange relaxations, and other chemical and physical interactions. Therefore, T and Ti measurements may be used to give a relative measure of these interactions in different systems. For example, they may be used to evaluate the change in the activity coefficient of counterions, such as sodium ions, brought about by the presence of humic or fulvic acid polyions in solution. A further discussion of this is beyond the scope of this chapter, but it is mentioned here to emphasize the versatility of NMR in the study of macromolecular interactions. 

In addition, b is directly related to the conformation of the polymer viz. single or double chain helix formation inplies a decrease of the length b. This hehcal conformation, which often exists in stereoregular polysaccharides, is stabilized by an intrachain and interchain H-bond network. Thus, the study of electrostatic properties will help to characterize the conformation of these polymers as a function of the experimental conditions (pH, ionic concentration, tenperature) [8, 9]. One of the most useful expaiments is the determination of the activity coefficient of counterions (y) obtained by potentiometry (or conductimetry). Its theoretical value is directly related to the charge parameter and the valence of the counterion. The main relations, when X. is higher than unity, are ... 

Rochas C., Rinaudo M., Activity coefficients of counterions and conformation in kappa-carrageenan systems. Biopolymers, 19,1980, 1675-1687. 

Fig. 1. Single-ion activity coefficients of counterions in saltfree polystyrenesulphonate solutions as functions of monomolality. (Data from References [12] and [13].)...

No specific ionic selectivity is really admitted in pectins with monovalent counterions due to the relativity low charge parameter a very interesting behaviour is observed when divalent counterions are considered. Specially, it was demonstrated that when DM<50% the activity coefficient of magnesium is much larger than that of calcium. The transport parameters (f) were found following the order [45] ... 

The activity coefficients of the polymers are much lower than those of the monomer. Theories predict, within their limits, a concentration, molar mass, and chemical structure independence of the counterion activity. As seen from Fig. 14, the experimental curvatures differ from the theoretical predictions. The concentration dependence and the absolute values of fa change with the molar mass. Further, the activity coefficient has been found to be reciprocally related to the molar mass [38]. To obtain reliable results a minimization of the salt out-... 

The influence of molar mass, charge density as well as chain branching was also determined in the presence of low molecular mass salt. As seen in Fig. 16, the differences between theory and experiment are more important to low molar masses. In Fig. 16 the concentration dependence of the activity of the low molecular salt has been taken into account when calculating fac=fexp/fo [H4, 126], where fac and fexp are calculated and experimentally determined counterion activity coefficients, respectively f0 is the activity coefficient of the added low molecular salt in aqueous solution without polyelectrolyte. 

It is a serious drawback that it is not possible to determine the transfer activity coefficient of the proton (or of any other single-ion species) directly by thermodynamic methods, because only the values for both the proton and its counterion are obtained. Therefore, approximation methods are used to separate the medium effect on the proton. One is based on the simple sphere-in-continuum model of Born, calculating the electrostatic contribution of the Gibb s free energy of transfer. This approach is clearly too weak, because it does not consider solvation effects. Different ex-trathermodynamic approximation methods, unfortunately, lead not only to different values of the medium effect but also to different signs in some cases. Some examples are given in the following log yH+ for methanol -1-1.7 (standard deviation 0.4) ethanol -1-2.5 (1.8), n-butanol -t-2.3 (2.0), dimethyl sulfoxide -3.6 (2.0), acetonitrile -1-4.3 (1.5), formic acid -1-7.9 (1.7), NH3 -16. From these data, it can be seen that methanol has about the same basicity as water the other alcohols are less basic, as is acetonitrile. Di-... 

We carried out potentiometric investigations with a Cl sensitive electrode [40] to determine the degree of conversion, i.e., the release of the low molecular counterions in the reactions between sodium poly(styrene sulfonate) (NaPSS) and poly(diallyldimethylammonium chloride) (PDADMAC) and its copolymers with acrylamide of various compositions (for synthesis and characterization of the samples see [41]). The basic idea of these studies on PEC formation is the change of the Cl ion activity coefficient due to the release of the counterions. According to Manning s theory [31], the activity coefficient of the counterions of a polyelectrolyte is given by... 

The activity coefficient of Na counterions [ yf la+) for i-carra-geenan, dextran sulfate, and heparin in water at 25 C, as evaluated from our potentlometrlc data, are reported in Fig. 1. 

Figure 1. Activity coefficient of Na counterions (ysa ) of ionic polysaccharides in water (25°C), N is the polyelectrolyte concentration in equivalents/liter (/s) iso-carrageenan (i = 1.2) (-ff) heparin (i = 13) (A.) dextran sulfate. (M = 4 10 ...

On the other hand data reported in Fig. 8 Indicate that the higher charge-density of Xanthan compared to PS-10 shows up in a higher heat of Cu ion binding and in a lower activity coefficient of Na counterions. From the initial slope of the Qg against [Cu2tl /N plots of Fig. 6 one estimates for Xanthan in water a differential enthalpy of Cu2+ binding of about 1 Kcal per mole of copper bound. In conclusion, as found with the sulfated polysaccharides (Fig. 4) as well as with different synthetic poly-carboxylates ( ), chelation of Cu2+ ions by polyanions is a process systematically driven by the entropy. 

In this work, optical rotation in dilute solutions of kappa carrageenans is used to interpret the activity coefficient of potassium counterions and to demonstrate a conformational transition associated with an increase of the charge parameter corresponding to a dimerization. 

Counterion Activity Coefficients of Ionic Dextran Derivatives in Water at 25 C... 

Let Hg and be the molar concentrations of phosphate sites and added salt, respectively. In his model Manning calculated the following expressions for and > Ihe activity coefficients of the counterions and coions... 

The merit of Katchalsky s approach is that it allows us to calculate the salt absoq)tion without knowing the form of the activity coefficient of the free ions in the gel explicitly. But, Katchalsky s theory does not consider counterion condensation. Tlie interactions between various charge species are over-simplified. 

Fig. 1. Activity coefficient of monovalent and divalent counterions on carboxymethylcelluloses. O, experimental values.-----------------Jq, theoretical values from Oosawa and Manning.

The free fraction of counterions has been obtained [3,7] by different techniques the set of results given in Table I is for monovalent counterions and in Tables I and II for divalent counterions. As shown, at equilibrium, the active fraction of counterions is quasi independent of the methods used especially, the osmotic coefficient is very close to the activity coefficient. The value is almost independent of the nature of the counterions nevertheless, it seems that there is a sequence related to the ionic selecti-vity yu < 7Na < Tk < ycs (Table I). 

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