Polyelectrolytes apparent molal volume

The apparent molal volume belongs, from a formal point of view, to the same group of thermodynamic properties as the enthalpy of dilution. The expression for the concentration dependence of the apparent molal volume of a polyelectrolyte can be derived from the electrostatic free enthalpy in a way similar to that shown above. In the final expression, which is analogous to Equation (24), the derivative dA/dT is replaced by d2/dP. Recently, Skerjanc [28] has studied the apparent molal volume of solutions of polystyrenesulphonates and shown that the cell model is applicable within a wide concentration range. 

On the other hand t and A r contain the rate constants of the equilibrium under study and, for bimolecular reactions, the concentrations of the species involved in the reaction [4b, 8]. Had counter-ion site binding been a one step process the determination of t would have provided a direct estimation of the lifetime of the bound counter-ions and, therefore, of the exchange rate between bound and free counterions. On the other hand the study of as a function of concentration would have permitted to obtain informations on the distribution of bound counterions between those bound with and without dehydration. Unfortunately, as will be shown in Section 4, site binding is a multistep process involving at least two equilibria. All of the unknown quantities involved in such a process (four rate constants, two volume changes and the concentrations of the species) cannot be obtained from ultrasonic absorption data alone. Independent measurements become necessary. For this purpose we have measured the density d of the polyelectrolyte solutions from which can be obtained the apparent molal volume FcP of the polyelectrolyte CP (C counterion, P polyion) according to ... 

As said in the introduction and in Section 2 ultrasonic data alone (A, N2,Ai and A 2) do not permit to obtain all of the unknown quantities associated with the process represented by Equation (5) (the rate constants k, k2 and the volume changes and AV22 and the concentration [PCJ, [PC2] and [PC3]). Independent measurements become necessary. For this purpose apparent molal volumes of polyelectrolytes have been determined. 

Apparent Molal Volumes of Polyelectrolytes and Their Use for the Determination of the Volume Change Upon Counter-ion Site Binding... 

Table II gives the values of the apparent molal volumes at infinite dilution F p (see Section 2) for a series of polyelectrolytes. Using the values of the apparent molal volumes of the counter-ions [17] Vq, which are also listed in Table II, one can obtain the apparent molal volume of the polyion, (Fp )c, by making use of the equation...

Equation (6) has been verified to a high degree of accuracy for simple electrolytes. It assumes a complete ionization of the salt at infinite dilution. An examination of Table II reveals that for each of the polyelectrolytes studied in this work the values of (Fp )c depend on the counter-ion. This result means that the additivity law does not hold for polyelectrolyte solutions. A simple explanation for this behaviour is provided by Manning s theory which states that even at infinite dilution part of the counter-ions remain condensed on the polyions. On the other hand, dilatometry [2], refractometry [3] and ultrasonic absorption [9, 10] have shown that part of the condensed counterions and of the sites on which they are bound are dehydrated. Therefore, the value ()c of the apparent molal volume of the polyion P, as obtained from Equation (6) >vill include the volume change dVc associated with the binding of C. This is why the subscript C was placed on the apparent molal volume of the polyion P in Equation (6). If we call (Fp )true> the true apparent molal volume of the polyion P it may be assumed that (Fp )true (Fp)tma since there are numerous evidences [9,10, 18, 4c] that a negligible volume change is associated with the condensation of TMA" ion (this ion... 

Apparent molal volumes of polyelectrolytes and volume changes upon counter-ion binding... 

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