ABSTRACT

Using the isothermal mode, an equilibrium cell is charged with the system of interest, the mixture is heated to the desired temperature, and this temperature is then kept constant. The pressure is adjusted in the heterogeneous region above or below the desired equilibrium value depending on how the equilibrium will change pressure. After intensive mixing over the time necessary for equilibrating the system, the pressure reaches a plateau value. The equilibration time is the most important point for polymer solutions. Due to their (high) viscosity and slow diffusion, equilibration will often need many hours or even days. The pressure can be readjusted by adding or withdrawing of material or by changing the volume of the cell if necessary. Before analyzing the compositions of the coexisting phases, the mixture is usually given some time for a clear phase separation. Sampling through capillaries can lead to differential vaporization (especially for mixtures containing gases and high-boiling solvents as well) when no precautions have been taken to prevent a pressure drop all along the capillary. This problem can be avoided with an experimental design that ensures that most of the pressure drop occurs at the end of the capillary. Sometimes, one or more phases will be recirculated to reduce sampling problems. The use of physicochemical methods of analysis inside the equilibrium cell, e.g., by a spectrometer, avoids the problems related to sampling. On the other hand, time-consuming calibrations can be necessary. At the end, isothermal methods need relatively simple and inexpensive laboratory equipment. If carried out carefully, they can produce reliable results. Isobaric-isothermal methods are often also called dynamic methods. One or more fluid streams are pumped continuously into a thermostated equilibrium cell. The pressure is kept constant during the experiment by controlling an effluent stream, usually of the vapor phase. One can distinguish between continuous-flow methods and semi-flow methods. In continuous-flow methods, both phases flow through the equilibrium cell. They can be used only for systems where the time needed to attain phase equilibrium is sufficiently short. Therefore, such equipment is usually not applied to polymer solutions. In semi-flow methods, only one phase is flowing while the other stays in the equilibrium phase. They are sometimes called gas-saturation methods or puregas circulation methods and can be used to measure gas solubilities in liquids and melts or solubilities of liquid or solid substances in supercritical fluids. Isobaric methods provide an alternative to direct measurements of pressure-temperature compositions in liquid phase compositions in vapor phase (P-T-wL-wV) data. This is the measurement of (P-T-wL) data followed by a consistent thermodynamic analysis. Such isobaric analytical methods are usually made in dynamic mode, too. The main advantages of the analytical methods are that systems with more than two components can be studied, several isotherms or isobars can be studied with one filling, and the coexistence data are determined directly. The main disadvantage is that the method is not suitable near critical states or for systems where the phases do not separate well. Furthermore, dynamic methods can be difficult in their application to highly viscous media like concentrated polymer solutions where foaming may cause further problems. Synthetic methods In synthetic methods, a mixture of known composition is prepared and the phase equilibrium is observed subsequently in an equilibrium cell (the problem of analyzing fluid mixtures is replaced by the problem of “synthesizing” them). After known amounts of the components have been placed into an equilibrium cell, pressure and temperature are adjusted so that

_______________________________________________________________________________ the mixture is homogeneous. Then temperature or pressure is varied until formation of a new phase is observed. This is the common way to observe cloud points in demixing polymer systems. No sampling is necessary. The experimental equipment is relatively simple and inexpensive. For multicomponent systems, experiments with synthetic methods yield less information than with analytical methods, because the tie lines cannot be determined without additional experiments. This is specially true when fractionation accompanies demixing. The appearance of a new phase is either detected visually or by monitoring physical properties. Visually, the beginning of turbidity in the system or the meniscus in a view cell can be observed. Otherwise, light scattering is the common method to detect the formation of the new phase. Both visual and non-visual synthetic methods are widely used in investigations on polymer systems at elevated pressures. The problem of isorefractive systems (where the coexisting phases have approximately the same refractive index) does not belong to polymer solutions where the usually strong concentration dependence of their refractive index prevents such a behavior. If the total volume of a variable-volume cell can be measured accurately, the appearance of a new phase can be observed from the abrupt change in the slope of a pressure-volume plot. An example is given in Chapter 4. The changes of other physical properties like viscosity, ultrasonic absorption, thermal expansion, dielectric constant, heat capacity, or UV and IR absorption are also applied as non-visual synthetic methods for polymer solutions. A common synthetic method for polymer solutions is the (P-T-wL) experiment. An equilibrium cell is charged with a known amount of polymer, evacuated and thermostated to the measuring temperature. Then the second component (gas, fluid, solvent) is added and the pressure increases. The second component dissolves into the (amorphous or molten) polymer and the pressure in the equilibrium cell decreases. Therefore, this method is sometimes called the pressuredecay method. Pressure and temperature are registered after equilibration. No samples are taken. The composition of the vapor phase is calculated using a phase equilibrium model if two or more gases or solvents are involved. The determination of the volume of gas or solvent vaporized in the unoccupied space of the apparatus is important as it can cause serious errors in the determination of their final concentrations. The composition of the liquid phase is often obtained by weighing and using the material balance. By repeating the addition of the second component into the cell, several points along the vapor/gas-liquid equilibrium line can be measured. This method is usually applied for all gas solubility/vapor sorption/vapor pressure investigations in systems with polymers. The synthetic method is particularly suitable for measurements near critical states. Simultaneous determination of PVT data is possible. Some problems related to systems with polymers Details of experimental equipment can be found in the original papers compiled for this book and will not be presented here. Only some problems should be summarized that have to be obeyed and solved during the experiment. The polymer solution is often of an amount of some cm3 and may contain about 1g of polymer or even more. Therefore, the equilibration of prepared solutions can be difficult and equilibration is usually very time consuming (liquid oligomers do not need so much time, of course). Increasing viscosity makes the preparation of concentrated solutions more and more difficult with further increasing the amount of polymer. Solutions above 50-60 wt% can hardly be prepared (depending on the solvent/polymer pair under investigation).