Isopiestic vapor

Rard (1992) reported the results of isopiestic vapor-pressure measurements for the aqueous solution of high-purity NiCl2 solution form 1.4382 to 5.7199 mol/kg at 298.1510.005 K. Based on these measurements he calculated the osmotic coefficient of aqueous NiCb solutions. He also evaluated other data from the literature and finally presented a set of smoothed osmotic coefficient and activity of water data (see Table IV in original reference). 

As a means of verifying the model parameters of Table II, the osmotic coefficient was calculated from isopiestic vapor pressure measurement data (17) for the KCl-KBr-H20 system at 25°C (Table III). 

The experimental basis of sorption studies includes structural data (SANS, SAXS, USAXS), isopiestic vapor sorption isotherms,i and capillary isotherms, measured by the method of standard porosimetry. i 2-i44 Thermodynamic models for water uptake by vapor-equilibrated PEMs have been suggested by various groupThe models account for interfacial energies, elastic energies, and entropic contributions. They usually treat rate constants of interfacial water exchange and of bulk transport of water by diffusion and hydraulic permeation as empirical functions of temperature. 

Gibbs free energies of water sorption, AG "(/l), can be extracted from isopiestic vapor sorption isotherms this analysis shows that AG (T) < AG", where AG" = -44.7 kj moH is the Gibbs free energy for vapor sorption at a free water surface at ambient condihons. Water absorbed by the membrane is therefore more strongly bound than water at a free bulk water surface this affirms the hydrophilic nature of water sorption in PEMs. 

To begin, it is essential to rationalize the equilibration of water within the membrane at AP = 0, APs = 0, j = 0, and = 0. The suggested scenario of membrane swelling is based on the interplay of capillary forces and polymer elasticity. In order to justify a scenario based on capillary condensation, isopiestic vapor sorption isotherms for Nafioni in Figure 6.9(a) are compared with data on pore size distributions in Figure 6.9(b) obtained by standard porosimetry.i In Figure 6.9(a), a simple fit function. 

Thus, in small-angle x-ray scattering, measurement of the molecular weight of a macromolecule in concentrated solvent requires knowledge of the preferential interaction parameter. This can be measured by techniques such as differential refractometry, densimetry, and isopiestic vapor phase equilibrium measurements. For densimetry,... 

Cryoscopy. Souchay (40) has summarized the application of fused salt cryoscopy to ionic solutes. Obviously two limitations are inherent in this method. Under ordinary pressures, measurements are possible at only one temperature—namely that of the transition point (e.g., ca. 32.38°C. in the case of Na2S04 10 H20). Secondly, the solute is being examined in solutions of high ionic strength only. Isopiestic vapor pressure measurements have been used as a variation, which, in principle, eliminate both limitations. However, it does not appear that it is as yet possible to analyze such data to yield equilibrium constants (33). Furthermore, Tobias has cast doubt upon the inherent accuracy of the method when the polyions contain more than 3 or 4 metal ions (41). 

The use of the infinitely dilute solution as the reference state of a volatile component is not convenient for the experimental study of isopiestic vapor-liquid equilibria. Equation (10.79) may be written as... 

Figure 4.4.7a. Isopiestic vapor-sorption apparatus using a quartz spring 1 - connection to the vacuum line, 2 - connection to the thermostating unit which realizes the constant measuring temperature T2 (the correct value of T2 is obtained by a Pt-100 resistance thermometer within the cell that is not shown), 3 - closing plug, 4 - quartz spring (reading of its extension is made by a cathetometer), 5 - sample pan with the polymer solution, 6 -pure solvent reservoir at temperature T[. [Reprinted with permission from Ref 82, Copyright 1982, Wiley-VCH].

Figure 4.4.8. Isopiestic vapor-sorption apparatus with built-in manometer using a quartz spring 1 - connection to the vacuum, 2-9 -stop corks, 10, 11, 12 - connections to nitrogen, 13 - degassing flask for the pure solvent, 14, 18 - buffers, 15 - cold trap, 16,19 - Hg-ma-nometers, 17,20 - mercury float valves, 21 -pure solvent reservoir at temperature Ti provided by 22 - thermostat, 23 - temperature controlled air box, 24 - measuring cell, 25 - quartz spring (four quartz springs can be inserted into the equilibrium cell, only one is shown), 26 - pan with the polymer solution, 27 - closing plug sealed with epoxy resin, 28 - heating to avoid solvent condensation.

Figure 4.4.9. Schematic diagram of an isopiestic vapor sorption apparatus using an electronic microbalance PC - personal computer, MB - microbalance, WBl-3 - water bath thermostats with T3>T2>Ti, Vl-3 - valves, WM - W-tube mercury manometer, S - polymer sample/solution, SV - solvent reservoir, MS -magnetic stirrer, CT - cold trap, VP - vacuum pump. [Reprinted with permissitm from Ref. 92, Copyright 1998, American Chemical Society].

Figure 4.4.10. Schematic diagram of an isopiestic vapor sorption apparatus using a piezoelectric crystal detector. [Reprinted with permission from Ref 101, Copyright 1995, American Chemical Society].

Figure 4.4.15. Experimental data of the system toluene + polystyrene, = 1380 g/mol, at 323.15K, isopiestic vapor pressure/sorption measurement (fiill circles), VPO at higher concentrations (gray circles), data from authors own work.

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. 

Figure 4.4.7b. Dynamic isopiestic vapor-sorption apparatus using a quartz spring (drawing provided by G. Sadowski) a) evaporator, b) superheater, c) measuring cell, d) condenser, e) quartz spring, f) polymer sam-ple/solution, g) Pt-100 resistance thermometer. [Reprinted with permission from Ref. 87, Copyright 1995, Wiley-VCH].

Robinson, R.A. J.M. Wilson R.H. Stokes, "The activity coefficients of lithium, sodium and potassium sulfate and sodium thiosulfate at 25° from isopiestic vapor pressure measurements", JACS, v63, pplOll (1941)... 

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. 

The isopiestic vapor pressure technique is one of the most useful methods for deter-... 

Benzene and 1-octanol are two hquids that mix in aU proportions. Benzene has a measurable vapor pressure, whereas 1-octanol is practically nonvolatile. The data in Table 9.8 on the next page were obtained by Platford using the isopiestic vapor pressure method. 

By means of the isopiestic vapor pressure technique, the osmotic coefficients of aqueous solutions of urea at 25 °C have been measured at molalities up to the saturation limit of about 20molkg . The experimental values are closely approximated by the function... 

Sections 12.2.1 and 12.2.2 will describe freezing-point and osmotic-pressure measurements, two much-used methods for evaluating - /ta in a binary solution at a given T and p. The isopiestic vapor-pressure method was described in Sec. 9.6.4. The freezing-point and isopiestic vapor-pressure methods are often used for electrolyte solutions, and osmotic pressure is especially useful for solutions of macromolecules. 

The experimental basis of sorption studies includes isopiestic vapor sorption isotherms (Morris and Sun, 1993 Pushpaet al., 1988 Rivin et al., 2001 Zawodzinski et al., 1993c) and capillary isotherms, measured by standard porosimetry (Divisek et al., 1998 Vol fkovich and Bagotsky, 1994 Vol fkovich et al., 1980). A number of thermodynamic models of water uptake by vapor-equilibrated PEMs have been... 

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