Isopiestic experiments

An apparatus for isopiestic experiments is easy to construct. Solutions of a volatile solvent with different concentrations of a nonvolatile solute are placed in an apparatus looking like a receiver of a distillation equipment as shown in Fig. 6.16. 

As pointed out above, there is another way VPO can be applied to measure activity differences between two polymer solution drops that differ slightly in concentration (in the same solvent, of course). In this case, VPO is quasi an isopiestic experiment and the unknown activity can be determined by using reference solutions with known solvent activity values ... 

Fig. 5.7 The vapour pressure lowerings of trisodium citrate at 25 °C as a function of its molality in aqueous solutions. - [163], - [164], - [157], - [157 ], - [161 ] andB- [165 ]. - from isopiestic experiments in ternary systems...

Vapour pressure depressions of potassium citrates were measured in the 20-40 °C temperature range by Sadeghi and Ziamajidi [156] and Sadeghi and Goodarzi [158, 159] and they are presented in Table 5.11. Their values were determined in isopiestic experiments in the binaiy K3Cit + H2O and KH2Cit + H2O systems, but also in the ternary systems with alanine and polypropylene oxide 400. 

Table 5.12 Relative humidities and vapour pressures of water over diammonium hydrogen citrate solutions as a function of temperature and concentration. ([162] - From isopiestic experiments in binary and ternary systems)...

Because polyelectrolytes are nonvolatile, the most important thermodynamic property for vapor + liquid phase equilibrium considerations is the vapor pressure of water above the aqueous solution. Instead of the vapor pressure, some directly related other properties are used, e.g., the activity of water a, the osmotic pressure 71, and the osmotic coefficient < . These properties are defined and discussed in Sect. 4. Membrane osmometry, vapor pressure osmometry, and isopiestic experiments are common methods for measuring the osmotic pressure and/or the osmotic coefficient. A few authors also reported experimental results for the activity coefficient y i of the counterions (usually determined using ion-selective electrodes) and for the freezing-point depression of water AT p. The activity coefficient is the ratio of activity to COTicentration ... 

Tables 3 6 give a survey of literature data for the vapor-liquid equilibrium of aqueous solutions of a single polyelectrolyte with various counterions. Abbreviations (shown in Table 2) are used to characterize the polyelectrolyte and the experimental procedures (MO membrane osmometry DMO differential membrane osmometry VO vapor pressure osmometry ISO isopiestic experiments EMF electromotive force measurements including also measurements with ion-selective electrodes as well as titration FPD freezing point depression GDM gel deswelling investigations). Table 3 gives a survey for aqueous solutions of poly(styrene sulfonic acid).

The activity of a volatile solvent in a solution that contains a nonvolatile solute can be obtained from an experimental technique known as the isopiestic method .19 An apparatus is constructed similar to that shown in Figure 6.17. The mixture in container A is a solution of a nonvolatile solute in a solvent in which A], the activity of the solvent, has been accurately determined in other experiments as a function of concentration. Containers B and C hold solutions of other nonvolatile solutes in the same solvent. These are the solutions for which the activity of the solvent is to be determined. 

The activity of the solvent often can be obtained by an experimental technique known as the isopiestic method [5]. With this method we compare solutions of two different nonvolatile solutes for one of which, the reference solution, the activity of the solvent has been determined previously with high precision. If both solutions are placed in an evacuated container, solvent will evaporate from the solution with higher vapor pressure and condense into the solution with lower vapor pressure until equilibrium is attained. The solute concentration for each solution then is determined by analysis. Once the molality of the reference solution is known, the activity of the solvent in the reference solution can be read from records of previous experiments with reference solutions. As the standard state of the solvent is the same for all solutes, the activity of the solvent is the same in both solutions at equUibrium. Once the activity of the solvent is known as a function of m2 for the new solution, the activity of the new solute can be calculated by the methods discussed previously in this section. 

This simple relationship was derived before as equation 5.24, and was first used by Bauman and Eichorn in 1947 to predict selectivity sequences for simple monovalent cations from mean ionic activity coefficient data for pure aqueous electrolyte solutions containing a common anion. The inaccessibility of resin phase activity coefficients to direct measurement always remains a problem with thermodynamic equilibrium treatments. Therefore Glueckauf and others developed weight swelling and isopiestic water vapour sorption techniques to determine osmotic coefficients of pure salt forms of a resin, from which the mean ionic activity coefficients of mixed resinates could be computed using a modified form of Harned s Rule. Such studies predicted selectivity coefficient values which were in fair agreement with experiment and also demonstrated the fixed ion of the resin to be osmotically inactive. 

Since the polymer solution remains quasi unehanged in eoneenlration, this modified VPO-method is faster than isopiestic isothermal distillation experiments with organic solvents and polymer solutions. Difficulties with the increasing viscosity of concentrated polymer solutions set limits to its applicability, because solutions should flow easily to form drops. 

In summary, die decision for a special equipment depends to some extend on concentration, temperature and pressure ranges one is interested in. From the experience of the author, the combination of isopiestic vapor pressure/vapor sorption measurements for the determination of solvent activities with infinite dilution IGC for the determination of Henry s constants provides good experimental data and covers a temperature range that is broad enough to have a sufficient data basis for thermodynamic modeling. If one is interested in both solvent solubiUty and diffusion data, finite concentration IGC or piezoelectric sorption techniques should be applied. 

Equation-of-state approaches are preferred concepts for a quantitative representation of polymer solution properties. They are able to correlate experimental VLE data over wide ranges of pressure and temperature and allow for physically meaningful extrapolation of experimental data into unmeasured regions of interest for application. Based on the experience of the author about the application of the COR equation-of-state model to many polymer-solvent systems, it is possible, for example, to measure some vapor pressures at temperatures between 50 and 100 C and concentrations between 50 and 80 wt% polymer by isopiestic sorption together with some infinite dilution data (limiting activity coefficients, Henry s constants) at temperatures between 100 and 200 C by IGC and then to calculate the complete vapor-liquid equilibrium region between room temperature and about 350 C, pressures between 0.1 mbar and 10 bar, and solvent concentration between the common polymer solution of about 75-95 wt% solvent and the ppm-region where the final solvent and/or monomer devolatilization process takes place. Equivalent results can be obtained with any other comparable equation of state model like PHC, SAFT, PHSC, etc. 

Isopiestic measurements. High-temperature isopiestic method could be considered as an instrumental method among other methods of sampling without temperature and pressure drops to study hquid-gas equilibrium (Tsopiesf in Table 1.1). One of the electrolyte solutions present in the isopiestic vessel is a reference since its vapor pressure is known imder the conditions of the experiment. The compositions of the solutions placed in the same vessel change during equilibration due to a redistribution of water between liquid solutions to reach the common vapor pressure at the constant temperature. The equilibrium composition of the isopiestic solutions could be measured at the experimental or at the room temperature if the samples of isopiestic solutions carefidly preserved and analyzed in order to determine the concentration (isopiestic molality) at the equilibrium, isopiestic vapor pressures and activity coefficients for the electrolytes. 

Isopiestic [33] experiments also offer access to chemical potentials. This method monitors the conditions under which the vapor pressures above different solutions of nonvolatile solutes (like polymers or salts) in the same solvent become identical, where one of these solutions is a standard for which the thermodynamic data are known. These experiments can be considered to be a special form of differential osmometry (cf. Sect. 3.2) where the semi-permeable membrane, separating two solutions of different composition, consists of the gas phase. 

Ever since Franklin and Gosling [1] examined the first fibers of DNA it has been known that DNA occurs in vivo in hydrated form. Experiments involving sedimentation equilibrium studies [2-4], isopiestic measurements [5], gravimetric [6], X-ray fiber diffraction, infrared [7-9] and NMR spectroscopic investigations [10-12] lead to the conclusion that DNA is heavily hydrated. The hydration is not homogeneous around the DNA and can be described in the terms of two discrete lays representing primary and secondary hydration shells. 

---