Polymer fluid-solid equilibrium

A semi-grand canonical treatment for the phase behaviour of colloidal spheres plus non-adsorbing polymers was proposed by Lekkerkerker [141], who developed free volume theory (also called osmotic equilibrium theory ), see Chap. 3. The main difference with TPT [115] is that free volume theory (FVT) accounts for polymer partitioning between the phases and corrects for multiple overlap of depletion layers, hence avoids the assumption of pair-wise additivity which becomes inaccurate for relatively thick depletion layers. These effects are incorporated through scaled particle theory (see for instance [136] and references therein). The resulting free volume theory (FVT) phase diagrams calculated by Lekkerkerker et al. [142] revealed that for <0.3 coexisting fluid-solid phases are predicted, whereas at low colloid volume fractions a gas-hquid coexistence is found for q > 0.3, as was predicted by TPT. 

Fig. 4.20 Schematic equilibrium phase diagram of a colloid-polymer mixture for small q. Full curve is the fluid-solid coexistence curve, dashed curve is the metastable gas-liquid coexistence region...

Eli Ruckenstein How useful is thermodynamics in the treatment of the kind of problem described by Anthony Pearson Is the solid polymeric material in an equilibrium state or in a metastable state My personal experience with polymeric surfaces is that their characteristics depend upon the environmental fluid. In a hydrophilic environment, the polymers tend to expose their hydrophilic moieties to the environment, while in a hydrophobic one they will expose their hydrophobic moieties. A polymeric material equilibrated first in a hydrophobic medium and introduced later in a hydrophilic medium will undergo changes in its surface. These rearrangements are in some case rapid, but in others, very slow. 

Several authors [3-9] studied the solubility of polymers in supercritical fluids due to research on fractionation of polymers. For solubility of SCF in polymers only limited number of experimental data are available till now [e.g. 4,5,10-12], Few data (for PEG S with molar mass up to 1000 g/mol) are available on the vapour-liquid phase equilibrium PEG -CO2 [13]. No data can be found on phase equilibrium solid-liquid for the binary PEG S -CO2. Experimental equipment and procedure for determination of phase equilibrium (vapour -liquid and solid -liquid) in the binary system PEG s -C02 are presented in [14]. It was found that the solubility of C02 in PEG is practically independent from the molecular mass of PEG and is influenced only by pressure and temperature of the system. 

For the calculations, different EoS have been used the lattice fluid (LF) model developed by Sanchez and Lacombet , as well as two recently developed equations of state - the statistical-associating-fluid theory (SAFT)f l and the perturbed-hard-spheres-chain (PHSC) theoryt ° . Such models have been considered due to their solid physical background and to their ability to represent the equilibrium properties of pure substances and fluid mixfures. As will be shown, fhey are also able to describe, if not to predict completely, the solubility isotherms of gases and vapors in polymeric phases, by using their original equilibrium version for rubbery mixtures, and their respective extensions to non-equilibrium phases (NELF, NE-SAFT, NE-PHSC) for glassy polymers. 

In recent years, supercritical technology, especially supercritical carbon dioxide (scCCb), has been widely applied in the processing of polymer nanocomposites. A supercritical fluid is defined as "any substance, the temperature and pressure of which are higher than their critical values, and which has a density close to, or higher than, its critical density" (Darr Poliakoff, 1999). Fig. 3 shows a schematic representation of the density and organization of molecules of a pure fluid in solid state, gas state, liquid state and the supercritical domain. No phase separation occurs for any substance at pressures or temperatures above its critical values. In other words, the critical point represents the highest temperature and pressure at which gas and liquid can coexist in equilibrium. 

Because the measurement of a contact angle must involve some movement of the wetting line, it is possible, or even probable, that the act of spreading of the hquid will displace certain surface equilibria that will not be reestablished over the time frame of the experiment. For example, the displacement of a second fluid may result in the estabhshment of a nonequilibrium situation in terms of the adsorption of the various components at the solid-liquid, solid-fluid 2, and liquid-fluid 2 interfaces. Time will be required for adsorption equilibrium to be attained, and it may not be attained during the time of the contact angle measurement if the transport and adsorption-desorption phenomena involved are slow. The kinetic effect may be especially significant for solutions containing surfactants, polymers, or other dissolved adsorbates. 

Over the p t several years we and our collaborators have pursued a continuous space liquid state approach to developing a computationally convenient microscopic theory of the equilibrium properties of polymeric systems. Integral equations method [5-7], now widely employed to understand structure, thermodynamics and phase transitions in atomic, colloidal, and small molecule fluids, have been generalized to treat macromolecular materials. The purpose of this paper is to provide the first comprehensive review of this work referred to collectively as Polymer Reference Interaction Site Model (PRISM) theory. A few new results on polymer alloys are also presented. Besides providing a unified description of the equilibrium properties of the polymer liquid phase, the integral equation approach can be combined with density functional and/or other methods to treat a variety of inhomogeneous fluid and solid problems. 

Some transitions that are only known for macromolecules, however, will not be mentioned at all since they are covered elsewhere in this Encyclopedia (see, eg. Gel Point). Also we shall not be concerned here with the transformations from the molten state to the solid state of polymeric materials, since this is the subject of separate treatments (see Crystallization Kinetics Glass Transition Viscoelasticity). Unlike other materials, polymers in the solid state rarely reach full thermal equilibrium. Of course, all amorphous materials can be considered as frozen fluids (see Glass Transition) Rather perfect crystals exist for metals, oxides, semiconductors etc, whereas polymers typically are semicrystalline, where amorphous regions alternate with crystalline lamellae, and the detailed structure and properties are history-dependent (see Semicrystalline Polymers). Such out-of-equilibrium aspects are out of the scope of the present article, which rather emphasizes general facts of the statistical thermodynamics (qv) of phase transitions and their applications to polymers in fluid phases. 

The difference between a rubber network and a polymer melt is that in the former type of material the chains are permanently interconnected to form a three-dimensional network, whereas in the latter they are not As a consequence, crossiinked rubbers must be considered as solids with an equilibrium modulus, whereas polymer melts are basically fluids, which only behave as networks under special conditions ... 

Isobaric-isothermal methods are often also called dynamic methods. One or more fluid streams are pumped continuoirsly into a thermostated equilibriirm cell. The pressure is kept constant during the experiment by controlling an effluent stream, irsually of the vapor phase. One can distinguish between continuorrs-flow methods and semi-flow methods. In continuous-flow methods, both phases flow throrrgh the eqrrihbrirrm 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 pure-gas circulation methods and can be used to measure gas solubilities in liquids and melts or solubilities of liquid or solid substances in supercritical fluids. 

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