Isopiestic process

An isothermal process is one in which the temperature of the system remains uniform and constant. An isobaric or isopiestic process refers to uniform constant pressure, and an isochoric process refers to constant volume. Paths for these processes of an ideal gas are shown in Fig. 2.9. 

Pressure of reaction and isopiestic process 9.1.4.1 Pressure of reaction... 

The term d W is the maximum work done by the surroundings, and thus the negative of the maximum work done by the system, excluding the work of expansion or compression. We emphasize that such an interpretation is valid only for an isothermal and isopiestic reversible process. 

Equation 5.4 is the basis of a more detailed and fundamental study of the swelling process achieved through the study of resin-water vapour sorption isotherms obtained isopiestically i.e. at equal total pressures and equal resin water content). The isopiestic vapour pressure technique takes account of variable activity of the water in the resin (and therefore IT) by allowing the resin to come to equilibrium with water vapour at different partial vapour pressures P. It is assumed that two resins of the same structural type, but with different degrees of crosslinking, have the same water activity at the same equivalent water content. At equilibrium between resin and vapour phases the water activity in resins (1) and (2) are given by ... 

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. 

A measurement of m then permits 0 to be established. The process is repeated for many different mr and m values, so that the corresponding activity of the dissolved unknown species may be found via Eq. (3.6.14). This procedure is known as the isopiestic method. 

Concentration lowering under isothermal conditions is the classical isopiestic technique, sometimes also called isothermal distillation. A number of solutions (two as the minimum) are in contact with each other via their common solvent vapor phase and solvent evaporates and condenses (this is the isothermal distillation process) between them as long as the chemical potential of the solvent is equal in all solutions. At least one solution serves as reference system, i.e., its solvent activity vs. solvent concentration dependence is precisely known. After an exact determination of the solvent concentration in all equilibrated solutions (usually by weighing), the solvent activity in aU measured solutions is known from and equal to the activity of the reference solution. This method is almost exclusively used for aqueous polymer solutions, where salt solutions can be applied as reference systems. It is a standard method for inorganic salt systems. 

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