Theory of swelling of a crosslinked substance in equilibrium with a pure solvent in various phases. Part II: The variation of the pressure

A theory of swelling is presented which describes the equilibrium swelling of a body in a solvent in its various states. The pressure dependence of the pressure-concentration swelling curves is treated for the swelling agent occurring in the liquid, crystalline or vapor phase. The slopes of the pressureconcentration swelling curves are dependent on the differential volume of dilution of the solvent and, additionally, on the volume changes of vaporization, crystallization, and sublimation of the solvent corresponding to the state of the swelling agent. At the melting and boiling pressure of the swelling agent the swelling curves change their slopes with a discontinuity, which is most distinct at the evaporation transition. By measurements of the slopes of the swelling curves at the transition pressure the derivative ₁/w₁ at constant temperature and pressure, which is the change of the chemical potential of the solvent with its weight fraction, is obtained. Thus, a further equation is given to test statistical theories at the transition pressures. Simultaneous variations of the swelling with changes of temperature are also treated.     

Theory of swelling of a crosslinked substance in equilibrium with a solvent in various phases

In this paper the thermodynamic theory of a body in a liquid, crystalline or vaporized solvent is treated. The equilibrium swelling curves are discussed for the different states of the solvent. The slopes of the swelling curves are dependent on the differential enthalpy of dilution of the solvent and, additionally, on the enthalpies of vaporization, crystallization and sublimation of the solvent related to the state of the swelling agent. The slopes of the swelling curves are determined by the differential heat of vaporization, the differential heat of solution of the solvent or the differential heat of fusion according to the state of the swelling agent. Directly below the melting pointT _m,1, or directly above the boiling pointT _b,1 of the solvent the swelling curves change their slopes with a sharp bend. This phenomenon can be used to determine (₁/w ₁) at constant temperature and pressure, which means the change of the chemical potential ₁, with the change of the weight fractionw ₁ of the solvent. Using a simplified statistical thermodynamic relation it is possible to describe the principal courses of the swelling curves in all states of the solvent.     

Phase equilibria in polymer/solvent systems VII swelling pressure and swelling equilibrium between gaseous or liquid phases and a gel in a multicomponent system

Differential equations for swelling pressure and swelling equilibria in two-phase systems consisting of many components have been derived. The result includes simple equilibria of gaseous or liquid solvent and a gel which are known from the literature.     

Phase equilibria in polymer/solvent systems, 8. Swelling of chemically crosslinked polymers in mesogenic substances in different states

Swelling curves of chain end-linked polyurethane networks in mesogenic swelling agents were determined gravimetrically. Different slopes of the swelling curves are observed above and below the transition temperature of the liquid-crystalline to the isotropic state. From the sign of the slope it can be derived that the swelling agent is not in the liquid-like state in the gel if the pure swelling agent is liquid-crystalline.     

Thermodynamic behavior of adsorption systems with porous adsorbents along the curves describing equilibrium between bulk phases of an adsorptive

The thermodynamic aspects of adsorption equilibrium in systems with crystalline, liquid, and dense gas phases have been considered. The heats of phase transition and corresponding directions of mass transfer from the adsorbed phase into crystalline and liquid phases at different temperatures have been determined. The general equilibrium diagram in the coordinates Inp-T ^–1 has been given with indication of the equilibrium lines of three-phase systems and characteristic points on the isosteres of adsorption,viz., the Gurvitsch and quasicritical points.Deceased.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1480–1485, August, 1995.     

Phase behavior of the polybutadiene–polystyrene diblock copolymer with the addition of the nonselective solvent dichlorobenzene in temperature and pressure fields

Thermal composition fluctuations were measured in a polybutadiene–polystyrene diblock copolymer with small-angle neutron scattering as a function of the temperature, pressure, and solvent content. The solvent was dichlorobenzene. In particular, we determined the phase diagram, the Flory–Huggins parameter, and the Ginzburg parameter. The two latter parameters were determined in terms of a theory by Fredrickson and Helfand from the susceptibility at an elevated temperature in the disordered regime. These parameters showed an overall linear decrease with pressure and a minimum at a 10% solvent content. The ordering temperature could be sufficiently well described by the theory of concentrated solutions. These results were consistent with corresponding experiments on a polybutadiene–polystyrene blend, for which the compensation of the free volume was observed by the solvent molecules. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3179–3190, 2004     

Phase equilibrium in the system Ln-Mn-O: V. Ln=Yb and Dy at 1100°C

Phase equilibrium was established in the Yb-Mn-O and Dy-Mn-O systems at 1100°C by varying the oxygen partial pressure from −log (P_O2/atm)=0-13.00, allowing construction of phase diagrams at 1100°C for the systems Ln₂O₃-MnO-MnO₂. Under experimental conditions, Yb₂O₃, MnO, Mn₃O₄, and YbMnO₃ phases are found to be present in the Yb-Mn-O system, whereas Dy₂O₃, MnO, Mn₃O₄ DyMnO₃, and DyMn₂O₅ phases are present in the Dy-Mn-O system. Ln₂MnO₄, Mn₂O₃, and MnO₂ are not stable in either system. Small nonstoichiometric ranges are found in the LnMnO₃ phase, with the nonstoichiometry represented by the equations, N_O/N_YbMnO3=1.00×10⁻⁴(log P_O2)³+1.30×10⁻³(log P_O2)²+7.20×10⁻³(log P_O2)+5.00×10⁻⁵ and N_O/N_DyMnO3=1.00×10⁻⁴(log P_O2)³+1.80×10⁻³(log P_O2)²+9.30×10⁻³(log P_O2)+1.69×10⁻². Activities of the components in the solid solutions are calculated using these equations. LnMnO₃ may range Ln₂O₃-rich to Ln₂O₃-poor, while MnO is slightly nonstoichiometric to the oxygen-rich side. DyMn₂O₅ also seems to be nonstoichiometric. Lattice constants of LnMnO₃ under different oxygen partial pressures were determined, as well as lattice constants of DyMn₂O₅ quenched in air. The standard Gibbs energy changes of reactions appearing in the phase diagrams were calculated.     

Phase Equilibrium in the System Ln-M-O: III. Ln=Gd at 1100°C

Phase equilibrium in the system Gd-Mn-O has been established at 1100°C while varying the partial pressure of oxygen between 0 and 13.00 in −log (P_O2/atm), and a phase diagram at 1100°C is presented as a Gd₂O₃-MnO-MnO₂ system. Under the experimental conditions, Gd₂O₃, MnO, Mn₃O₄, GdMnO₃, and GdMn₂O₅ phases are present at 1100°C, but Gd₂MnO₄, Mn₂O₃, and MnO₂ are not stable in the system. The substantial difference from the previously studied La-Mn-O and Nd-Mn-O systems lies in the fact that the LnMn₂O₅-type phase is stable under the present experimental conditions. A wide range of nonstoichiometry has been found in the GdMnO₃ phase coexisting with Gd₂O₃. X in GdMnO_3+X ranges from −0.03 at log P_O2=−9.47 to 0.05 at log P_O2=0. Nonstoichiometry is represented by an equation, N_O/N_GdMnO3=3.00×10⁻⁴(log P_O2)³+5.80×10⁻³(log P_O2)²+3.52×10⁻²(log P_O2)+0.0464, and the activities of components in solid solution are calculated from the equation. Similar to the case of LaMnO₃, GdMnO₃ seems to vary in composition between the Gd₂O₃-rich and Gd₂O₃-poor sides. Lattice constants of GdMnO₃ produced under different oxygen partial pressures and those of GdMn₂O₅ prepared in air were determined, along with spacings and relative intensities of GdMn₂O₅. Standard Gibbs energies of reactions shown in the system were calculated and compared with previously reported values.     

Lyotropic mesophases of cellulose in the ammonia/ammonium thiocyanate solvent system: Phase relationships

Mesophase formation of the cellulose/NH₃/NH₄SCN system has been studied as a function of system composition at 25°C. Compositions for incipience of mesophase formation and for wholly anisotropic phase formation have been determined and relevant phase diagrams constructed. The biphasic gap narrowed when the solvent composition approached 75.5 weight percent NH₄SCN and as the cellulose concentration decreased. As solvent composition was changed, the minimum cellulose volume fraction for mesophase formation ranged between 0.02 to 0.045.     

Determination of Polybrominated Diphenyl Ethers in Water Samples Using Effervescent-Assisted Dispersive Liquid-Liquid Icroextraction with Solidification of the Aqueous Phase

An effective and sensitive method is necessary for the determination of polybrominated diphenyl ethers (PBDEs) pollutants in water. In this study, effervescent-assisted dispersive liquid-liquid microextraction with solidification of the aqueous phase (EA-DLLME-SAP), followed by Gas Chromatography-Tandem Mass Spectrometry (GC-MS-MS) quantitative analysis, was established for the preconcentration and determination of PBDEs in real environmental water samples. 1,1,2,2-Tetrachloroethane was used as the extractant and directly dispersed into the water phase of the aqueous samples with the aid of a large number of carbon dioxide bubbles generated via the acid-base reaction of acetic acid and sodium bicarbonate, which did not require the use of a dispersant during the extraction process. The key factors affecting the extraction recovery were optimized, and an internal standard was used for quantitative analysis, which gave good linearity ranges of 1–100 ng·L⁻¹ (BDEs 28, 47, 99, and 100), 2–200 ng·L⁻¹ (BDEs 153, 154, and 183) and 5–500 ng·L⁻¹ (BDE 209) with limits of quantification in the range of 1.0–5.0 ng·L⁻¹. The accuracy was verified with relative standard deviations < 8.5% observed in tap, lake, river and reservoir water samples with relative recoveries ranging from 67.2 to 102.6%. The presented method contributes to the determination of PBDEs in environmental water samples.     

Phase equilibrium in systems with ionic liquids: An example for the downstream process of the Biphasic Acid Scavenging utilizing Ionic Liquids (BASIL) process. Part I: Experimental data

Experimental results are presented for the (liquid + liquid), (solid + liquid) and (solid + liquid + liquid) equilibria occurring in the downstream process of a typical example for the Biphasic Acid Scavenging Utilizing Ionic Liquids (BASIL)-processes. In a BASIL process an organic base is used to catalyze a chemical reaction and, at the same time, to scavenge an acid that is an undesired side product of that reaction. The particular example of a BASIL process treated here is the reaction of 1-butanol and acetylchloride to butylacetate and hydrochloric acid, where the acid is scavenged by the organic base 1-methyl imidazole (1-MIM) resulting in the ionic liquid 1-methyl imidazolium chloride. The reaction results in a two-phase system as butylacetate and the ionic liquid reveal a large liquid–liquid miscibility gap. The organic base has to be recovered. This is commonly achieved by treating the ionic liquid–rich liquid phase with an aqueous solution of sodium hydroxide (i.e., converting the ionic liquid to the organic base) and extracting the organic base by an appropriate organic solvent (e.g., 1-propanol). The work presented here deals in experimental work with the (liquid + liquid), (solid + liquid) and (solid + liquid + liquid) phase equilibria that are encountered in such extraction processes. Experimental results are reported for temperatures between about 298 K and 333 K: for the solubility of NaCl in several solvents (1-propanol, 1-MIM), (water + 1-MIM), (1-propanol + 1-MIM), (water + 1-propanol), and (water + 1-propanol + 1-MIM) and for the (liquid + liquid) equilibrium as well as for the (solid + liquid + liquid) equilibrium of the ternary system (NaCl + water + 1-propanol) and of the quaternary system (NaCl + water + 1-propanol + 1-MIM).     

On the statistical independence of various column contributions to band broadening. Part 1: Second moment contributions from statistically independent,longitudinal diffusion in both phases

The total length-based second moment contribution from longitudinal sample diffusion in both phases on a column, σD , is derived by adding individual partial differential contributions to a partial differential equation accounting for the longitudinal diffusion processes only. Although each diffusion-dispersed sample part is equilibrated between two phases, the resulting σ,D (= 2D _mt _m + 2D _st _s) can be interpreted as the sum of two independent contributions in accordance with the variance addition rule. (D _m and D _s are the mean diffusion coefficients and t _mand t _s the mean residence times of the sample in the mobile and stationary phases, respectively.) The same σD expression is derived from the random walk model of Giddings by treating the diffusional process in each phase as statistically independent of the other processes. Under these conditions the broadening contribution from longitudinal diffusion in the mobile phase is shown to be independent of the velocity profile.     

Modeling phase equilibria for acid gas mixtures using the CPA equation of state. Part II: Binary mixtures with CO2

In Part I of this series of articles, the study of H₂S mixtures has been presented with CPA. In this study the phase behavior of CO₂ containing mixtures is modeled. Binary mixtures with water, alcohols, glycols and hydrocarbons are investigated. Both phase equilibria (vapor-liquid and liquid-liquid) and densities are considered for the mixtures involved. Different approaches for modeling pure CO₂ and mixtures are compared. CO₂ is modeled as non self-associating fluid, or as self-associating component having two, three and four association sites. Moreover, when mixtures of CO₂ with polar compounds (water, alcohols and glycols) are considered, the importance of cross-association is investigated. The cross-association is accounted for either via combining rules or using a cross-solvation energy obtained from experimental spectroscopic or calorimetric data or from ab initio calculations. In both cases two adjustable parameters are used when solvation is explicitly accounted for. The performance of CPA using the various modeling approaches for CO₂ and its interactions is presented and discussed, comparatively to various recent published investigations. It is shown that overall very good correlation is obtained for binary mixtures of CO₂ and water or alcohols when the solvation between CO₂ and the polar compound is explicitly accounted for, whereas the model is less satisfactory when CO₂ is treated as self-associating compound.