Liquid-solid equilibria, polymer solubility

Lyophilic sols are true solutions of large molecules in a solvent, Solutions of starch, proteins, or polyvinyl alcohol in water are representative of numerous examples. Properties of these solutions at equilibrium (for example, density and viscosity) are regular functions of concentration and temperature, independent of the method of preparation. The solvent-macromolecule compound system may consist uf more than one phase, each phase in general containing both components. Thus, if a solid polymer is added to a solvent in an amount exceeding the solubility limit, the system will consist of a liquid phase (solvent with dissolved polymer) and a solid phase (polymer swollen with solvent, i.e., a polymer with dissolved solvent). 

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. 

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. 

Essentially, extraction of an analyte from one phase into a second phase is dependent upon two main factors solubility and equilibrium. The principle by which solvent extraction is successful is that like dissolves like . To identify which solvent performs best in which system, a number of chemical properties must be considered to determine the efficiency and success of an extraction [77]. Separation of a solute from solid, liquid or gaseous sample by using a suitable solvent is reliant upon the relationship described by Nemst s distribution or partition law. The traditional distribution or partition coefficient is defined as Kn = Cs/C, where Cs is the concentration of the solute in the solid and Ci is the species concentration in the liquid. A small Kd value stands for a more powerful solvent which is more likely to accumulate the target analyte. The shape of the partition isotherm can be used to deduce the behaviour of the solute in the extracting solvent. In theory, partitioning of the analyte between polymer and solvent prevents complete extraction. However, as the quantity of extracting solvent is much larger than that of the polymeric material, and the partition coefficients usually favour the solvent, in practice at equilibrium very low levels in the polymer will result. 

Vapour-phase calibration (VPC) is based on the principle that the concentration of the volatile analyte in the gas phase can be determined by external-standard calibration. If the total amount present in the vial is known, the concentration in the sample phase at equilibrium is calculated from the difference. This technique, where the distribution of a volatile compound between two phases in a headspace vial is determined by using a pure vapour as reference, was originally implemented by Kolb using automated head-space equipment to determine distribution coefficients in gas-liquid [77] and gas-solid systems [78], and later by Schoene et al. [79] to determine solubility coefficients in vapours of both solid and liquid polymers. Although these investigations focused on... 

The act or process by which a compound such as oxygen is molecularly mixed with a liquid (such as water) or a solid (such as a polymer) is called dissolution, and the result of the mixing is a solution. If a solution is very dilute, as is commonly found in packaging, it behaves as an ideal solution, and again the activity coefficient is approximately 1, so concentration can be substituted for activity in thermodynamic relationships. In order to describe the solubility of a compound present in a gas phase that is in contact with a solid phase, as may be the case of oxygen in air contacting a polymer, we need a relationship between the concentration in the liquid (or solid) phase and the concentration (or partial pressure) in the gas phase. In other words, we need an expression for the solubility of the substance at equilibrium, as a function of the partial pressure of the gas or vapor in the contacting gas phase. 

A sol is a dispersion of solid particles or polymers in a liquid. It is possible to precipitate particles that are amorphous or crystalline, or to make amorphous particles that become crystalline through dissolution and reprecipitation. The latter process can produce particles that differ little from ordinary ceramic oxides, except that the sol particles are small (submicron). If the solubility of the solid phase in the liquid is limited, monomers may attach irreversibly to a growing cluster, so that rearrangement into the equilibrium structure is impossible. In that case, polymeric clusters appear with fractal structures that are quite different from ceramics they typically have much lower connectivity (i.e., fewer bridging oxygen bonds) and consequently contain many hydroxyl and organic ligands. 

In the framework of the regular solution theory, the solubility of a solid stabilizer into a liquid polymer amorphous phase obeys to a modified Flory-Rehner law [72] describing the equilibrium of free enthalpy of mixing with free enthalpy of stabilizer melting (instead of elastic forces in the classical theory for solvent induced elastomer swelling [73]) ... 

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