Phase Diagram Of Solutions Research Articles

The Influence of Ion Pair Formation on the Phase Behavior of Polyelectrolyte Solutions

In this paper we calculate the phase diagrams of polyelectrolyte solutions taking into account the possibility of ion pair formation between counterions and ions on polymer chains with their subsequent aggregation in multiplets. Multiplets play a role of reversible physical crosslinks between different polymer chains. Furthermore, we assume that the dielectric constant, and hence the binding energy of ion pairs and multiplets, depends on the volume fraction of polymer in the solution. We have shown that ion pairing and multiplet formation leads to instability of the homogeneous phase, so that at some conditions the phase separation can proceed even in doog solvent. Another qualitatively new feature of the behavior of polyelectrolyte solutions is the emergence of a triple point on the phase diagram. The effect of the solvent polarity and the polarity of the dry polymer on the general form of the phase diagram is studied in detail.

Crystal-chemical effect of the thermodynamic history on the composition-temperature phase diagrams of (Na,Li)NbO3 and (Na,K)NbO3 solid solutions

Composition (x)-temperature (T) phase diagrams obtained for the first time for single-crystalline (Na,Li)NbO3 (system I) and (Na,K)NbO3 (system II) niobates are compared with the known phase diagrams for ferroelectric niobate ceramics prepared by various techniques (standard firing and hot pressing). In system I, the thermodynamic history (process conditions) is shown to have a pronounced effect on the diagrams throughout the range of perovskite stability, while in system II, the effect is the most significant at low potassium concentration (x≲0.15). These data are associated with a small value of the tolerance factor t of the solid solutions, whose properties are sensitive to the thermodynamic history. Small (≲0.9–0.93) values of t indicate the “porosity” of the structure of solid solutions I and II in the above concentration ranges. Under these condi-tions, polarization-and rotation-related structure instabilities compete on equal terms and substitutional and interstitial solid solutions may coexist.

Phase Diagram of Diblock Polyampholyte Solutions

We discuss in this paper the phase diagram of a diblock polyampholyte solution in the limit of high ionic strength as a function of concentration and charge asymmetry. This system is shown to be very similar to solutions of so-called charged-neutral diblock copolymers: at zero charge asymmetry the solution phase separates into a polyelectrolyte complex and almost pure solvent. Above a charge asymmetry threshold, the copolymers are soluble as finite size aggregates. Scaling laws of the aggregates radius as a function of pH of the solution are in qualitative agreement with experiments.

The phase diagram and properties of solid solutions of the ternary sodium-lithium-potassium niobate system

A phase diagram of the (Na,Li,K)NbO3 ternary system in the NaNbO3 region was constructed using the experimental X-ray diffraction data. Various physical properties of solid solutions were studied in a broad range of component concentrations. Promising compositions for the high-and medium-frequency piezotransducers are determined.

New data on the polymorphous transformations and T-x phase diagrams of Na1-x Li x NbO3 and Na1—x K x NbO3 solid solutions

Na1-x Li x NbO3 (0 x 0.006) and Na1—x K x NbO3 (0 x 0.10) solid solution crystals have been grown from the flux. Dielectric, X-ray and optical studies of the crystals revealed the presence of new phase transitions in the temperature range from—50C to 200C. The results obtained imply the necessity of substantial correction of the known T-x phase diagrams of NaNbO3-based solid solutions in the compositional range adjacent to pure NaNbO3 Thus the dielectric, optical, and structural studies and the analysis of the corresponding published data indicate that, in addition to the six well-known phase transitions in NaNbO3 one more phase transition occurs in the vicinity o150C which is close to a second-order phase transition and is assumed to take place between two antiferroelectric orthorhombic phases. Phase transition in the 150-200 temperature range occurs in NLN and NKN crystals as well. In the antiferroelectric-ferroelectric crossover compositional range one more first-order phase transition is observed at 30-100C both in NLN and NKN crystals. The existence of the phase transitions in NaNbO3 and NaNbO3-based solid solutions in the 30-200C temperature range (which falls within the working interval of numerous NaNbO3-based materials) can produce a considerable effect on the temperature and time stability of various characteristics of these materials. This fact should necessarily be taken into account in designing new NaNbO3-based materials for various purposes. In particular, it is important to refine the corresponding temperature-composition phase diagrams of NaNbO3-based solid solutions and the theoretical models which describe the sequence ot phase transitions in NaNbO3

Phase diagrams of monomer and uv-cured difunctional-acrylate-nematic-liquid-crystal systems.

This paper deals with the thermal properties of systems made of the difunctional monomer 1,6-hexanedioldiacrylate (HDDA) and the low-molecular-weight liquid crystal E7. Experimental phase diagrams of uv-cured and uncured solutions of HDDA/E7 systems are established with a polarized optical microscope and a differential scanning calorimeter and the data analyzed within a theoretical formalism that combines the Flory-Huggins model of isotropic mixing and the Maier-Saupe model of nematic order. Ultraviolet-curing samples with a difunctional monomer such as HDDA leads to a crosslinked polymer network and consequently an elastic contribution to the free energy is introduced according to the Flory-Rehner theory of rubber elasticity. The amount of liquid crystal segregated is evaluated to assess the efficiency of the phase separation mechanism.

Hydration and Phase Behavior of Poly(N-vinylcaprolactam) and Poly(N-vinylpyrrolidone) in Water

Phase transitions of poly(N-vinylcaprolactam) (PVCL) and poly(N-vinylpyrrolidone) (PVPy) in H2O and D2O were investigated by turbidimetry, differential scanning calorimetry (DSC), and Fourier transform infrared (FTIR) spectroscopy. The phase diagram of PVCL solution is binodal with a lower critical solution temperature (LCST) of 32.5 °C and a critical concentration of about 5 wt %. PVPy also undergoes a phase separation around 30 °C in aqueous 1.5 M KF solution. The IR spectra of PVCL and PVPy in water critically change at the phase transition temperature (Tp). Above Tp the C−H stretching and the C−H bending bands shift to lower wavenumbers. The amide I band of PVCL is divided into four components, and the intensities of the 1565, 1588, and 1625 cm-1 components increase and that of the 1610 cm-1 component decreases while the phase transition proceeds. Addition of KCl and KF lower Tp of PVCL, whereas KI and KBr raise Tp. Addition of methanol gradually raises Tp up to ca. 40 vol % and steeply raises Tp at >...

Phase diagram of dilute lattice surfactant solution

We have studied the temperature–composition phase diagram for a dilute surfactant model solution on the square lattice through Monte Carlo simulations. A micellar region and a solubility line were identified from the measurement of different properties, among which the volume fraction of aggregate, specific heat, and convergence of relaxation from different initial conditions. We have compared properties of the above system with those of a symmetric lattice solution in the dilute regime. Comparison of data allow an interpretation of the micellar phase as a transition region between a microscopically homogeneous phase and a solid phase.

Improved phase diagram of polyelectrolyte solutions

A previously reported phase diagram of polyelectrolyte solutions as functions of degree of polymerization and the concentration is improved. The new phase diagram is also intended for salt-free solutions of polyelectrolytes with the constitutional repeating unit -C-CX-, X being a charged group. The main improved point is the crossover concentrations between the dilute and semidilute regimes in the low concentration range of less than 10−2 mol/l, which is based on the recent most reliable experimental data on the persistence length of flexible polyion chains. This phase diagram as well introduces both the concentrated regime, which has been not only theoretically predicted but also experimentally confirmed, and the experimentally newly found swollen regime. Furthermore, it is proposed that the dilute regime is separated into four regions, gaslike, poor order, liquidlike order and crystal. The degrees of orderliness in these regions have been assumed to depend on the ratio δ/ξcent of the amplitude of thermal fluctuations to the mean intermolecular distance. Typically, δ/ξcent=1/5 as the critical Lindemann ratio of melting is assigned for the crossover between the liquidlike order and crystal regions. Interestingly, the most probable region for the formation of a 3-D lattice is located within the experimental approach.

Compatibility of gelatin and dextran in aqueous solution.

The temperature-composition phase diagrams of aqueous solutions of gelatin and dextran, which show liquid/liquid phase segregation, were explored at temperatures above the gelation temperature of gelatin. The compositions of the coexisting phases were found to show practically no dependence on temperature between 40 and 80 degrees C. Also, the total polymer concentration at which phase separation occurred was found to be nearly independent of temperature. These observations suggest an entropy-driven phase separation. An explanation in terms of depletion, reversible clustering, and subsequent transient network formation of gelatin at temperatures well above the temperature of gelation is suggested. Phase separation is found to be accompanied by strong fractionation of the molar mass distribution in the two phases.

Description of ferroelectric phase transitions in solid solutions of relaxors in the framework of the random-field theory

A model based on the random-field theory is proposed for calculating the properties of solid solutions of ferroelectric relaxors. The electric dipoles randomly distributed in the system are treated as sources of random fields. The random field distribution function is calculated taking into account the contribution of nonlinear and correlation effects and the differences in the dipole orientations for different solid solution components. The dependence of the phase transition temperature Tc on the concentration of solid solution components is analyzed. Numerical calculations are performed for the lead scandoniobate and lead scandotantalate solid solutions (PbSc1/2Nb1/2O3)1−x(PbSc1/2Ta1/2O3)x with different degrees of ordering and the lead magnoniobate and lead titanate solid solution (PbMg1/3Nb2/3O3)1−x(PbTiO3)x. It is shown that the higher transition temperature for more disordered solid solutions of the composition (PbSc1/2Nb1/2O3)1−x(PbSc1/2Ta1/2O3)x in the range 0≤x<0.5 is associated with the larger nonlinearity coefficient for PbSc1/2Nb1/2O3 as compared to that for PbSc1/2Ta1/2O3. The theory provides a means for calculating the region of the coexistence of the phases with different symmetry groups in the temperature-composition phase diagram of the (PbMg1/3Nb2/3O3)1−x(PbTiO3) solid solution. Numerical calculations with the use of the fitting parameters obtained from the known transition temperatures Tc for the solid solution components adequately describe the experimental phase diagrams for the aforementioned solid solutions of ferroelectric relaxors.

Effects of PEG on detergent micelles: implications for the crystallization of integral membrane proteins.

The solubilization of integral membrane proteins with detergents produces protein-detergent complexes (PDCs). Interactions between the detergent moieties of PDCs contribute significantly to their behavior. The effects of the precipitating agent polyethylene glycol (PEG) upon these detergent-detergent interactions have been examined, focusing on the detergent system used to crystallize the bacterial outer membrane protein OmpF porin. Static and dynamic light scattering were used to assess the effects of temperature and concentration upon the hydrodynamic size distribution and the aggregation state of detergent micelles and a phase diagram for micellar solutions was mapped. Estimates of the second osmotic virial coefficient obtained from static light-scattering measurements on micelles were shown to accurately reflect the thermodynamic quality of the solvent. Solvent quality decreases as the consolute boundary is approached, suggesting micelle-micelle attractive forces help to organize PDCs into crystalline aggregates near the cloud point. An apparent increase in micelle mass is observed as the solution approaches the cloud point. These results raise the possibility that the detergent-mediated aggregation of PDCs and/or slight changes in micelle geometry may prove to be important in the nucleation of membrane protein crystals.

Phase Behavior of Solutions of Polymers with Multiply Aggregating Groups

We have theoretically investigated phase diagrams of solutions of aggregating polymers. In our model all polymer chains in the solution carry a certain number of aggregating groups (“stickers”), capable of the formation of thermoreversible aggregates, each assumed to consist of exactly m stickers. The treatment of aggregation corresponds to the Flory-like theory of gelation. We have studied the dependence of the phase diagram on the parameters of aggregation, such as its strength (fraction of monomeric units carrying stickers and aggregation constant) and cooperativity (aggregation number). In the considered system of homopolymer chains the stickers have been found to always promote phase separation. The value of aggregation number m is crucial for the topology of the phase diagram: for m ≥ 5 the triple point may appear in the phase diagram. Conditions on the properties of the system ensuring the appearance of this feature have been obtained. The interrelation between gelation and phase separation for different values of parameters is elucidated.

Calculation of phase diagrams for solid solutions of ferroelectrics

The integral equations for calculating ferroelectric and antiferroelectric phase transition temperatures, order parameters, and critical concentrations of solid solution components are derived. The electric dipoles randomly distributed in the system are treated as sources of random fields. The random field distribution function is constructed taking into account the contribution of nonlinear effects and the differences in the dipole orientations for different solid solution components. The dependence of the phase transition temperature on the composition of a binary solid solution in the ferroelectric-antiferroelectric and ferroelectric-paraelectric systems is calculated. Numerical calculations are carried out for the PbTixZr1−x O3 and BaZrxTi1−x O3 solid solutions. The results obtained are in good agreement with the experimental phase diagrams of these systems. Analysis of the results indicates that any solid solution containing ferroelectric (antiferroelectric) and paraelectric components transforms into a relaxor state at sufficiently high concentrations of the paraelectric component.

Formation of junction zones in thermoreversible methylcellulose gels

AbstractTo analyze the structure of junction zones formed in methylcellulose (MC) gel, the modified Eldridge–Ferry method was applied to phase diagrams for aqueous solutions of different molecular weight MCs derived from micro‐DSC, small‐angle X‐ray scattering, and visual inspection. The results suggested that junctions in MC gels took thin, rodlike fringed‐micellar crystallites. The junction multiplicity s decreased from 4.3 for low‐temperature melting gels to 2.0 for high‐temperature melting gels. With increasing molecular weight, the number ζ of statistical units in a junction along a single chain increased from 27 to 54. Because the number depends sensitively on the enthalpy of bonding per mole of the repeat units of MC, our estimate is considered to give an upper bound to the junction length. © 2001 John Wiley &amp; Sons, Inc. J Polym Sci B: Polym Phys 39: 943–946, 2001

Characterization of molecular alignment in aqueous suspensions of Pf1 bacteriophage.

The phase diagram of Pf1 solutions has been studied indirectly by observation of 2H quadrupole splittings of the solvent signal and measurement of dipolar couplings in solute macromolecules. At low volume fractions of Pf1 and at high ionic strength, alignment of both the phage and the solute depends strongly on the strength of the magnetic field. Both the theoretical and experimentally determined phase diagram of Pf1 show that at low concentrations and high ionic strengths the solution becomes isotropic. However, just below the nematic phase boundary the behavior of the system is paranematic, with cooperative alignment which depends on the strength of the applied magnetic field. Above 16 mg/ml Pf1 is fully nematic up to 600 mM NaCl. Alignment of proteins with a significant electric dipole moment, which tends to be strong in Pf1, can be reduced by either high ionic strength or low phage concentration. Because ionic strength modulates both the orientation and magnitude of the alignment tensor in Pf1 medium, measurement at two ionic strengths can yield linearly independent alignment tensors.

Polydisperse star polymer solutions

We analyze the effect of polydispersity in the arm number on the effective interactions, structural correlations, and phase behavior of star polymers in a good solvent. The effective interaction potential between two star polymers with different arm numbers is derived using scaling theory. The resulting expression is tested against monomer-resolved molecular dynamics simulations. We find that the theoretical pair potential is in agreement with the simulation data in a much wider polydispersity range than other proposed potentials. We then use this pair potential as an input in a many-body theory to investigate polydispersity effects on the structural correlations and the phase diagram of dense star polymer solutions. In particular, we find that a polydispersity of 10%, which is typical in experimental samples, does not significantly alter previous findings for the phase diagram of monodisperse solutions.

Phase Diagrams of Salt-Free Polyelectrolyte Semidilute Solutions

We analyze the phase behavior of polyelectrolyte salt-free solutions using the random phase approximation (RPA). Within this approximation, the phase diagrams of salt-free polyelectrolyte solutions show phase separation even without including short-range attractions or ion condensation. We find that the phase behavior of large chains resembles the phase diagram of polymer network solutions. That is, the equilibrium is established between a swollen network phase and a chain-free phase. Even though RPA is capable of reproducing certain aspects of the phase diagram, the model has to be modified to include ion condensation self-consistently in the analysis.

Phase diagram of aqueous solution at high pressure and low temperature

This paper presents a constant mass high pressure isothermal calorimeter and describes the range of applications that this type of equipment can deal with. As an example, the thermophysical properties of an aqueous solution of MgSO4 at low temperature and at high pressure have been investigated. The main results showed that the phase change heat of the solution decreased with increasing pressure and the phase change temperature of the eutectic concentration was depressed under high pressure. Those changes could be related to the MgSO4 solubility and to water latent heat changes.

Thermoreversible gelation and phase separation in aqueous methyl cellulose solutions

We derived typical phase diagrams for aqueous solutions of methyl cellulose (MC) of different molecular weights via micro-differential scanning calorimetry, small-angle X-ray scattering, and visual inspection. The phase diagrams showed the cooccurrence of gelation and phase separation and qualitatively agreed with the theoretically calculated diagrams. The sol–gel transition line and phase separation line of a lower critical solution point type shifted toward lower temperatures and lower concentrations with an increase in the MC molecular weight. The sol–gel transition line intersected at a temperature higher than the critical point of the phase separation; therefore, both sol–gel phase separation and gel–gel phase separation were possible, depending on the temperature. Specifically, through visual inspection of a high molecular weight MC sample in the critical temperature region, we observed phase separation into two coexisting gels with different polymer concentrations. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 91–100, 2001