Polymer solution thermodynamics enthalpy

The extent to which permeant molecules are sorbed and their mode of sorption in a polymer depend upon the enthalpy and entropy of permeant/polymer mixing, i.e, upon the activity of the permeant within the polymer at equilibrium. Much information on polymer-solution thermodynamics is given elsewhere in this volume. Here, a brief description is given of the most common types of sorption isotherms which have been utilized to describe permeation in polymers. 

Several recent theories for polymer solution thermodynamics include entropic, enthalpie and free-volume contributions to the free energy of mixing. The free-volume eontributions modify the entropic components, and have the opposite temperature dependence from the combinatorial term, helping to explain the lower critical solution temperature. Since Eq. (B 18) assumes a constant value for the entropic component, it may not be valid over large temperature ranges. However, Eq. (B18) will predict the upper critical solution temperature, and, from this standpoint, is adequate for a number of phase equilibria applications near this condition. 

In Chap. 8 we discuss the thermodynamics of polymer solutions, specifically with respect to phase separation and osmotic pressure. We shall devote considerable attention to statistical models to describe both the entropy and the enthalpy of mixtures. Of particular interest is the idea that the thermodynamic... 

The energy of vaporization is not accessible for polymers, but cohesive energy density of polymers can be determined from PVT-data. However, common ways for determining polymer solubility parameters use thermodynamic properties of polymer solutions and their relations to excess enthalpy or excess Gibbs energy per unit volume. These excess quantities are related to the (square) difference between the solubility parameters of solvents and polymers, i.e. (d -... 

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. 

Some implicit databases are provided within the Polymer Handbook by Schuld and Wolf or by Orwoll and in two papers prepared earlier by Orwoll. These four sources list tables of Flory s x-fiinction and tables where enthalpy, entropy or volume changes, respectively, are given in the literature for a large number of polymer solutions. The tables of second virial coefficients of polymers in solution, which were prepared by Lechner and coworkers (also provided in the Polymer Handbook), are a valuable source for estimating the solvent activity in the dilute polymer solution. Bonner reviewed vapor-hquid equilibria in concentrated polymer solutions and listed tables containing temperature and concentration ranges of a certain number of polymer solutions. Two CRC-handbooks prepared by Barton list a larger number of thermodynamic data of polymer solutions in form of polymer-solvent interaction or solubility parameters." ... 

Microcalorimetry. Skerjanc and Pavlin note the use of standard equimpent to obtain heats of mixing in ionic polymer solutions. Gusenkov and Krestov have considered the interpretation of microcalorimetric data to obtain thermodynamic parameters and illustrated their analysis with results from an aqueous biopolymer solution. Filisko et al. " have studied enthalpy in amorphous liquid polymers from measurements of their heats of solution. 

In the lattice model of polymer solutions, polymer chain is simply represented by a number of consecutively occupied lattice sites, each site corresponding to one chain unit. The rest single sites are assigned to solvents. This simple lattice treatment of polymer solutions allows a very convenient way to calculate thermodynamic properties of flexible and semiflexible polymer solutions from the statistical thermodynamic approach. By the mean-field assumption, the entropy part and the enthalpy part of partition function can be separately calculated. 

The chemical potential i (i.e. the partial molar free energy) is the most fundamental physical quantity to describe the thermodynamic properties of polymer solutions. If p is represented as functions of absolute temperature (7), pressure (7 ) and the composition (for example, the polymer concentration for a binary mixture), one can determine not only the molecular weight, M, of the solute (the polymer), but also many other thermodynamic quantities, such as the partial molar entropy, the partial molar enthalpy and the partial molar volume of each component. 

Enthalpy of dilution of poly(ethylene glycol) in anisole Data extract from Landolt-Bornstein VIII/6D2 Polymers, Polymer Solutions, Physical Properties and their Relations I (Thermodynamic Properties PVT-data and miscellaneous properties of polymer solutions) ... 

A detailed presentation of the thermodynamics of polymer solutions is given in Chapter 4 here only the final Flory-Huggins equation (eq. (3.45)) is presented. The decrease in free energy comes from the mixing enthalpy and entropy and the molar free energy of mixing (AGj J becomes ... 

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