Absolute vapor pressure

When cavitation occurs in a pump, its efficiency is reduced. It ean akso cause sudden surges in flow and pressure at the discharge nozzle. The calculation of the NPSITr (the pump s minimum required energy) and the NPSITa (the system s available energy), is based on an understanding of the lic]uid s absolute vapor pressure. 

The work of this laboratory extends the defect treatment to intermetallie compounds. The experiments measure simultaneously both the cadmium vapor pressure and the composition at equilibrium for a series of only slightly different alloy compositions. The precision and the relative accuracy of the measurements are high the absolute values suffer from any starting composition uncertainty and from errors in the absolute vapor pressure of cadmium as determined by other techniques. The experimental method is described elsewhere in this symposium (6). It has proved possible to infer the concentration and identity of lattice defects by analyzing the experimental data following the analytical techniques described below. 

The absolute vapor pressure of cadmium is not as well known as the relative values. 

Absolute vapor pressure measurement may be considered to be the classical technique for our purposes, because one measures directly the vapor pressure above a solution of known polymer concentration. Refs. 56-65 provide a view of the variety of absolute vapor pressure apparatuses developed and used by different authors. The common principle of an absolute vapor pressure apparatus is shown in Figure 4.4.2. 

Figure 4.4.2. Schematic of the common principle of an absolute vapor pressure apparatus 1 - polymer solution, 2 - connection to the manometer, 3 - Hg-manometer, 4 -heating coils. The whole construction is thermostatedat the measuring temperature, the connection to the manometer is kept slightly above the measuring temperature to avoid condensation.

Figure 4.4.3. Schematic diagram of a modem absolute vapor pressure apparatus T - temperature meter, P - vapor-pressure meter, V - vacuum meter, Z - measuring cell, M - magnetic stirrer, GI and Gil - degassing units for the solvent and for the polymer. ptq)rinted with permission from Ref 58, Copyright 1990,Wiley-VCH].

The measurement of polymer solutions with lower polymer concentrations requires very precise pressure instruments, beeause the difference in the pure solvent vapor pressure becomes very small with deereasing amount of polymer. At least, no one can really answer the question if real thermodynamie equilibrium is obtained or only a frozen non-equilibrium state. Non-equilibrium data ean be deteeted from unusual shifts of the %-function with some experience. Also, some kind of hysteresis in experimental data seems to point to non-equilibrium results. A eommon eonsisteney test on the basis of the integrated Gibbs-Duhem equation does not work for vapor pressure data of binary polymer solutions because the vapor phase is pure solvent vapor. Thus, absolute vapor pressure measurements need very careful handling, plenty of time, and an experienced experimentator. They are not the method of choiee for high-viseous polymer solutions. 

Problems caused by the determination of the unoccupied vapor space were avoided by Haynes et al., since they measure the pressure difference as well as the absolute vapor pressure. Also, the concentration is determined independently by using a differential refractometer and a normalized relation between eoneentration and refractive index. Degassing of the liquids remains a necessity. Time for establishing thermodynamic equilibrium could be somewhat shortened by intensive stirring (slight problems with increasing polymer concentration and solution viscosity were reported). 

In comparison to absolute vapor-pressure measurements, differential vapor-pressure measurements with a high resolution for the pressure difference can be applied even for dilute polymer solutions where the solvent activity is very near to 1. They need more time than VPO-measurements, however. 

From the absolute vapor pressures reported by Pogrebnoi et al. (1997). 

For the reasons outlined above, alternative methods were developed that avoid the measurement of absolute vapor pressures. One procedure combines head space sampling with conventional gas chromatography (HS-GC) [31] and yields relative vapor pressures, normalized to the vapor pressure of the pure solvent. A well-defined volume of the equilibrium gas phase is taken out from a thermostated vial... 

Another possibility for avoiding the measurement of absolute vapor pressures is provided by sorption methods. In most cases, the polymer is positioned on a quartz balance and the amount of solvent it takes up via the vapor phase is weighted. The so-called flow-through variant [32] works with an open system in contrast to the previous method. 

The systems n-butane/l,4-polybutadiene (98% cis) [ -C4/l,4-PB] and w-butane/ 1,2-polybutadiene [n-Cq/l, 2-PB] are the next examples for the modeling of Hory-Huggins interaction parameters [50]. In this case, it appeared particularly interesting to understand why 1,2-PB is totally miscible with n- C4 but 1,4-PB is not. In these experiments we measured the absolute vapor pressures (i.e., not using... 

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