Polymer-vapor equilibrium relations

Because of the highly nonideal behavior of polymer-solvent solutions, polymer-vapor equilibrium relations account for the third major difference found in stripping operations with polymeric solutions. The appro-... 

One of the most common techniques for determining x parameters for polymer-solvent systems is the vapor pressure method.(10) In this approach, the uncrosslinked polymer is exposed to solvent vapor of known pressure, p. The polymer absorbs solvent until equilibrium is established, x is related to p and V2, the volume fraction of polymer at equilibrium, by the Flory-Huggins equation (ll)... 

Vapor-liquid equilibrium data form the basic information for chemical engineering calculations, in particular the design and operation of distillation plants in the chemical, pharmaceutical, polymer, petrochemical and related industries. The data are also important for understanding molecular interactions and developing theories of pure liquids and liquid mixtures because they are related to the structure and the energy of interaction of the molecules. 

Here, the transport rates depend on the partition coefficient Kfp only. The solute concentration in the membrane can often be related to the gas phase partial pressure using Henry s law or a similar equilibrium relationship. At higher pressures, vapor-liquid equilibrium or gas-polymer absorption data are necessary to determine the concentration gradient in the membrane. 

The most important type of phase equilibrium in (nonpolymer related) industry is, for many applications, the vapor-liquid equilibria (VLE). For the polymer industry, liquid-liquid, and liquid-solid equilibria are equally important. 

Studies of various kinds of equilibria provide a wealth of information about polymer systems. Classical thermodynamics, which is concerned with the macroscopic properties of a system and the relations that hold between them at equilibrium, form a sufficient basis for description of these equilibria in polymer systems. We shall consider in a major part of this chapter methods of study of polymer solutions that deal with equilibria and can be fully described by thermodynamic relations. These include vapor pressure, osmotic pressure, and phase separation in polymer-solvent systems. 

Since then. Dr. Woldfarth s main researeh has been related to polymer systems. Currently, his research topics are molecular thermodynamics, continuous thermodynamics, phase equilibria in polymer mixtures and solutions, polymers in supercritical fluids, PVT behavior and equations of state, and sorption properties of polymers, about which he has published approximately 100 original papers. He has written the following books Vapor-Liquid Equilibria of Binary Polymer Solutions, CRC Handbook of Thermodynamic Data of Copolymer Solutions, CRC Handbook of Thermodynamic Data of Aqueous Polymer Solutions, CRC Handbook of Thermodynamic Data of Polymer Solutions at Elevated Pressures, CRC Handbook of Enthalpy Data of Polymer-Solvent Systems, and CRC Handbook of Liquid-Liquid Equilibrium Data of 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). 

The data reduction of vapor-pressure osmometry (VPO) follows to some extent the same relations as outlined above. However, from its basic principles, it is not an equilibrium method, since one measures the (very) small difference between the boiling point temperatures of the pure solvent drop and the polymer solution drop in a dynamic regime. This temperature difference is the starting point for determining solvent activities. There is an analogy to the boiling point elevation in thermodynamic equilibrium. Therefore, in the steady state period of the experiment, the following relation can be applied if one assumes that the steady state is sufficiently near the vapor-liquid equilibrium and linear non-equilibrium thermodynamics is valid ... 

MAU Maurer, G., Lammertz, S., and Schafer, L.N., Aqueous solutions of polyelectrolytes Vapor-hquid equilibrium and some related properties, Adv. Polym. Sci., 238, 67, 2011. 

Vapor-liquid equilibrium data of polyesteramide in water and ethanol Data extract from Landolt-Bornstein VIII/6D3 Polymers, Polymer Solutions, Physical Properties and their Relations I (Thermodynamic Properties Equilibria of Ternary Polymer Solutions) ... 

The pressure of VC monomer, the equilibrium VC monomer concentration in the PVC particles, the VC monomer concentration in water, the swelling factor of polymer particles related to variations of radius of particles, pressure of saturated vapors. 

A related colligative technique is vapor-pressure osmometry. Two thermistors are placed in a carefully thermostatted chamber that contains a pure-solvent reservoir so that the atmosphere is saturated with solvent vapor. A drop of solvent is placed on one thermistor and a drop of polymer solution is placed on the other. Because of the solvent s lower chemical potential in the solution, solvent vapor condenses on the solution drop, giving up its heat of condensation, warming the solution drop relative to the pure solvent drop. In principle, the equilibrium AT is thermodynamically related to the molar solution concentration, thereby allowing calculation of M . In practice, heat losses (mainly along the thermistor leads) require that the instrument be calibrated for precise results, really making it a relative technique (as opposed to absolute). On a routine basis, commercial instruments are probably limited to maximum M values of 40,000-50,000 [4]. 

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