Phase Diagram Of Solutions Research Articles

Structure formation in films of weakly charged block polyelectrolyte solutions

A mean-field dynamic density functional theory is used to describe a phase diagram of concentrated solutions of weakly charged flexible block polyelectrolytes in a film. Electrostatics is taken into account by applying the local electroneutrality constraint (the Donnan membrane equilibrium approach). In the Donnan limit it is assumed that a salt added to the solution perfectly screens long-range electrostatic interactions. The phase diagram of a solution of a triblock polyelectrolyte in a film as a function of the solvent concentration and the charge of the polyelectrolyte (solvophilic) block is calculated for a given film thickness. The phase behavior of the block polyelectrolyte film arises from the interplay between surface-induced alignment and the electrostatically-driven structure formation. The observed mesoscopic structures (lamellar, perforated lamellar, cylindrical, micellar, and mixed phases) are oriented parallel to the surfaces for the considered case of morphologies unfrustrated by the film thickness. Structures with connections between parallel layers (bicontinuous, etc.) are not formed. As a result of surface-induced ordering, the region of ordered phases in a film is wider than in bulk and the phase boundary between ordered and disordered phases is more diffuse. As in the case of unconfined block polyelectrolyte solution, the solution in a film does not follow the lyotropic sequence of phases of such a block copolymer upon increase in the charge of the polyelectrolyte block. Upon changing the charge of the solvophilic copolymer block, transformations of copolymer morphology take place via change in curvature of polymeric domains. Due to confinement of a polyelectrolyte film, no swelling of solvophilic domains is observed.

Dielectric study of the phase diagram of the poly(γ‐benzyl‐L‐glutamate)/dimethylformamide system

AbstractThe phase diagram for solutions of poly(γ‐benzyl‐L‐glutamate) in dimethylformamide has been investigated over the entire composition and temperature ranges with dielectric spectroscopy. The dielectric response in this system is dominated by ionic mobility, and phase transitions have been detected as changes in the ionic conductivity. The phase boundaries, determined by dielectric spectroscopy, are consistent with earlier published results obtained by a combination of optical microscopy observations and nuclear magnetic resonance and differential scanning calorimetry studies. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3943–3952, 2004

Ultrasonic studies on the phase transition from the dilute‐good to the theta regimes in polymer solution

AbstractThe phase transition from the dilute‐good solvent (I) to the theta (I′) regimes, which does not exist in the earlier phase diagram presented by Flory and has not been detected by common methods such as intrinsic viscosity, was observed clearly by measurements of ultrasonic velocity in the MHz range. Furthermore, ultrasonic absorption measurements revealed that the thermal relaxation, due to local segmental motions, observed in phase I disappeared in phase I′. Ultrasonic methods allow us to ascertain the existence of a second‐order phase transition from phase I to phase I′ above the theta temperature in the phase diagram of polymer solutions. Copyright © 2004 Society of Chemical Industry

Microscopic Determination of the Phase Diagrams of Lysozyme and γ-Crystallin Solutions

We determine the phase diagrams of two widely studied protein solutions, namely, lysozyme and γ-crystallin in water and added salt, within a short-range, pair-potential representation of macroparticle interactions. A one-parameter fit of the model is performed on the basis of static or dynamic light scattering and self-interaction chromatography data. Demixing and crystallization curves, as calculated through numerical approaches, turn out to be in good agreement with experimental protein-rich−protein-poor and solubility envelopes. Our findings highlight the minimal assumptions about the nature of the microscopic potential allowing a satisfactory reproduction of the phase-diagram topology of globular protein solutions.

Phase behavior of aqueous solutions containing dipolar proteins from second-order perturbation theory.

Due to the interplay of Coulombic repulsion and attractive dipolar and van der Waals interactions, solutions of globular proteins display a rich variety of phase behavior featuring fluid-fluid and fluid-solid transitions that strongly depend on solution pH and salt concentration. Using a simple model for charge, dispersion and dipole-related contributions to the interprotein potential, we calculate phase diagrams for protein solutions within the framework of second-order perturbation theory. For each phase, we determine the Helmholtz energy as the sum of a hard-sphere reference term and a perturbation term that reflects both the electrostatic and dispersion interactions. Dipolar effects can induce fluid-fluid phase separation or crystallization even in the absence of any significant dispersion attraction. Because dissolved electrolytes screen the charge-charge repulsion more strongly than the dipolar attraction, the ionic strength dependence of the potential of mean force can feature a minimum at intermediate ionic strengths offering an explanation for the observed nonmonotonic dependence of the phase behavior on salt concentration. Inclusion of correlations between charge-dipole and dipole-dipole interactions is essential for a reliable calculation of phase diagrams for systems containing charged dipolar proteins and colloids.

Synthesis and micellar characterization of short block length methoxy poly(ethylene glycol)-block-poly(caprolactone) diblock copolymers

A series of short block length methoxy poly(ethylene glycol)-block-poly(caprolactone) diblock copolymers was synthesized and characterized in order to assess the potential of these copolymers as a micellar drug-delivery system. Varying the caprolactone:MePEG weight ratio in the reaction mixture allowed the synthesis of diblock copolymers with a MePEG molecular weight of 750 g/mol and PCL block lengths of 2, 5 or 10 repeat units. Phase diagrams of aqueous solutions of the copolymers were constructed which displayed characteristic cloud points and Krafft points. As the degree of polymerization of PCL increased, critical micelle concentration (CMC) values decreased from 6.97×10 −1 to 3.38×10 −3 g/l, partition equilibrium coefficients ( K v) increased from 1.09×10 4 to 22.2×10 4, and hydrodynamic diameters increased from 12.2 to 19.5 nm. The micelle morphology was determined to be spherical by transmission electron microscopy.

Phase Diagram of Solutions of Associative Polymers

An analytical expression for the free energy of solutions of associative polymers is obtained in the entire polymer concentration-temperature range. This expression is derived under assumption that both local intrachain loops as well as interchain associations contribute to combinatorial part of the system free energy. In a good solvent regime, theory takes into account the swelling of polymer chains and suppression of pairwise associations due to strong monomer-monomer repulsive interactions. Analysis of the general expression of the system free energy shows that associations between functional groups can lead to a collapse of a chain and phase separation even under good solvent conditions for polymer backbone. In a good solvent, changing the fraction of associative groups per chain can trigger a phase separation.

SANS Study on Pressure-Induced Phase Separation of Poly(N-isopropylacrylamide) Aqueous Solutions and Gels

Pressure-induced phase separation of poly(N-isopropylacrylamide) (PNIPA) aqueous solutions and gels were investigated by small-angle neutron scattering (SANS). The cloud point curves were constructed on the pressure−temperature (P−T) plane by visual observation for both the solutions and gels. As observed in the phase diagram of aqueous solutions of proteins, the cloud point temperatures (Tcloud) were a function of the pressure, P, and had maxima at P0 = 51.7 MPa and P0 = 93.2 MPa respectively for the solution and gel in H2O. The difference in Tcloud indicates that the effect of cross-linking is significant, and it leads to an increase of the miscible region. The SANS intensity function for the solution was well represented by a Lorentz function, i.e., an Ornstein−Zernike (OZ) function, from which the correlation length, ξ, and the susceptibility, I(0), were evaluated as a function of pressure. The critical exponents were obtained to be 1.1 ≤ γp ≤ 1.23 and 0.5 ≤ νp ≤ 0.6, for the solution, similar to the ...

Analytic calculation of phase diagrams for solutions containing colloids or globular proteins

Second-order Barker–Henderson perturbation theory gives phase diagrams for colloid and protein solutions that include stable and metastable fluid–fluid, solid–fluid, and solid–solid phases. The potential of mean force is described by a hard-sphere interacting with a Yukawa potential. Calculations for different ranges of attraction show that, as expected, fluid–fluid coexistence becomes metastable when the potential becomes short-ranged. For a very short-ranged Yukawa potential, the phase diagram shows isostructural solid–solid equilibria with a critical point. To test more simplified models, phase diagrams from second-order Barker–Henderson perturbation theory are compared with those from the random-phase approximation for the fluid phase and the van der Waals theory for the solid phase; this comparison shows significantly different phase diagrams. Moreover, with a potential of mean force with primary and secondary minima, calculations using second-order perturbation theory identify conditions where colloidal and protein solutions can present two fluid–fluid regions, each with a critical point; however, the higher-density fluid–fluid region is likely to be metastable. The analytic calculations described here may be useful for interpretation of experimental phase diagrams and for guiding design of separation processes.

A Modified Random Phase Approximation of Polyelectrolyte Solutions

We compute the phase diagrams of salt-free polyelectrolyte solutions, using a modified Debye−Hückel approach. We introduce the chain connectivity via the random phase approximation with three modifications. First, we modify the electrostatic potential at short distances to include a boundary on the electrostatic attractions at the distance of closest approach between charges, which is important in semidilute solutions. This modification is shown to act as a hard core contribution in solutions of simple electrolytes. Second, we introduce a cutoff on the integration of the modes of wavelength smaller than the size over which the electrostatic attractions cannot be linearized and strongly perturbed chain are expected. A concentration-dependent cutoff is shown to be essential to predict physically reasonable phase diagrams. Third, ion condensation is included self-consistently. The modification does not give correct phase diagrams without the concentration-dependent cutoff. The combined modifications give phase diagrams in agreement with Monte Carlo simulations.

Study on the Effects of Nonelectrolyte Additives on the Phase, Thermodynamics, and Structural Changes in Micelles of Silicone Surfactants in Aqueous Solutions from Surface Activity, Small Angle Neutron Scattering, and Viscosity Measurements

Association properties of two silicone surfactants based on poly(dimethylsiloxane)-graft-polyethers in aqueous solutions of 2-butoxyethanol, poly(ethylene glycol), and glucose were determined using various techniques such as surface tension, small-angle neutron scattering, and viscosity. Dilute solution phase diagrams were also constructed, and cloud points were measured for different concentrations of both the surfactants in additive aqueous solutions. The thermodynamic parameters for the micellization were obtained from the temperature-dependent data on critical micelle concentration. The influence of given additive on the micellization of silicone surfactants was monitored from the changes in the free energy of micellization values for the surfactant solutions in water and water + additives. The cloud points and the critical micelle concentration values for the surfactant solutions were found to be decreased in the presence of the selected three additives. The analysis of the changes in the relative permittivities and partial molar volumes for the surfactant solutions in the presence of water and water + additives suggests that the solvent environment around the surfactant solute molecules is different in mixed solvent systems vis-a-vis water and the micellization and surface activity of silicone surfactants were dictated predominantly by the preferential hydration of cosolute additives. The analysis of small angle neutron scattering curves for the surfactant aqueous solutions in the presence of additives showed that the micelles formed have oblate ellipsoidal shape at 30 °C with, however, increased characteristic axial ratios than those in pure water. The increase in the concentration of additives has also increased the size of the micelles. The increase in temperatures corresponding to the values close to the turbid boundaries in the phase diagrams caused a transition from the oblate to the disklike micellar shape. The changes in the hydration values of the micellar associates were monitored from the dilute solution viscosity measurements. The dehydration of the micelles in the presence of additives at 30 °C and also at elevated temperatures occur from the interior to the fringe of the core−outer shell parts and to the outer shell successively.

Existence domains for invariant reactions in binary regular solution phase diagrams exhibiting two phases

The thermodynamic origin of various types of phase diagrams in simple binary systems exhibiting two phases (e.g. a liquid and a solid phase) has been examined using the regular solution model. The necessary conditions for the occurrence of each of these types are identified in terms of the appropriate intersections of the miscibility gap boundaries (in solid/liquid phases) and the liquidus/solidus/iso-G curves. Thus, the regions of occurrence of the different types of possible phase diagrams in the space of the regular solution interchange energy parameters (W α,W β) are clearly delineated. This analysis makes it easier to make intelligent initial selections of model (energy) parameters for their optimization in the calculation of phase diagrams using thermodynamic models such as CALPHAD/CVM.

Phase diagram of solutions of stiff-chain macromolecules: A Monte Carlo simulation

The phase diagram of solutions of semiflexible macromolecules consisting of N=20 effective monomer units has been studied by means of grand canonical Monte Carlo computer simulation using the bond fluctuation model and the configurational bias scheme. Two different types of interactions were taken into account: an intramolecular potential controlling the chain stiffness and an attractive interaction between effective monomer units to model variable solvent quality. A very broad region of density from dilute solution to melt has been covered in the simulation. The phase diagram shows a strong increase of the density difference between isotropic dilute and nematic dense phases upon increasing attraction between monomer units (i.e., decreasing the temperature). We discuss methods of locating the isotropic–nematic transition point and the effects of the vicinity of the polymer–solvent critical point on the properties of the liquid crystalline transition.

Periodic solutions in a porous catalyst pellet—homoclinic orbits

The analysis performed as well as extensive numerical simulations have revealed the possibility of the generation of homoclinic orbits as a result of homoclinic bifurcation in the model which describes transport phenomena and chemical reaction in a porous catalyst pellet. A method has been proposed for the development of a special type of diagrams—the so-called bifurcation diagrams. These diagrams comprise the locus of homoclinic orbits together with the lines of limit points bounding the region of multiple steady states as well as the locus of the points of Hopf bifurcation. Thus, they define a set of parameters for which homoclinic bifurcation can take place. They also make it possible to determine conditions under which homoclinic orbits are generated. Two kinds of homoclinic orbits have been observed, namely semistable and unstable orbits. It is found that the character of the homoclinic orbit depends on the stability features of the limit cycle which is linked with the saddle point. Very interesting dynamic phenomena are associated with the two kinds of homoclinic orbits; these phenomena have been illustrated in the solution diagrams and phase diagrams.

Surface Active and Association Behavior of Oxybutylene−Oxyethylene and Oxyethylene−Oxybutylene−Oxyethylene Copolymers in Aqueous Solutions

The surface active and association properties of commercial diblock B9E16 and triblock E43B14E43 copolymers from Dow Chemical Company were measured from surface tension, dynamic light scattering, and viscosity data. The values of critical micelle concentrations, surface active properties, and the micellar size and its temperature dependence have been found to be distinct in both the copolymers which differ in the ratio of hydrophobic to hydrophilic block lengths. The noted increase in the micellar size and distortion in the shape of the micelles of diblock copolymer with temperature rise have been explained considering the dehydration of micelles at elevated temperatures. An attempt has also been made to relate the distinct differences in the dilute solution phase diagrams to the changes in micellar dimensions.

Mechanism of Microparticle Formation in the Compressed Antisolvent Precipitation and Photopolymerization (CAPP) Process

We investigated the mechanism of particle formation in a new process that combines the principles of photopolymerization and compressed antisolvent processing. In this process, photopolymerization occurs when homogeneous solutions of monomer, initiator, and solvent are exposed to initiating light while being simultaneously introduced into a compressed antisolvent, which can result in highly cross-linked microparticles with a spherical morphology. The resulting particles, when examined using aerodynamic particle sizing, exhibit a bimodal particle size distribution. Ternary phase diagrams of antisolvent, monomer, and solvent solutions were measured and used to explain the mechanism(s) of particle formation. Specific concentration paths from the resulting ternary phase diagrams were investigated, and the significance of crossing the binodal, as well as the importance of where the binodal was crossed, was explained. In addition, manipulation of atomization conditions, varying process residence times, and nucleation rate calculations were used to further investigate the means of particle formation.

Size-dependent continuous binary solution phase diagram

Size-dependent solution phase diagrams for binary systems are established basedon models of size-dependent melting temperature and melting enthalpy ofcomponents and a newly developed model for the size-dependent interactionenergy. The results show that as the size of the components decreases, thetemperatures of solidus and liquidus curves drop and the two-phase zone becomessmall. As the size of the components decreases to a critical size, the two-phasezone deteriorates into a curve where the liquid phase and the solid phase areindistinguishable in structure and thus the phase numbers transform from two toone.

Debye–Hückel Theory for Charged Aligned Needles and for Polyelectrolyte Solutions

We consider a simple extension of the familiar Debye–Huckel theory of electrolyte solutions (in which the ions are represented by spheres with embedded point charges) to study the thermodynamic properties and the phase diagram of ionic solutions in which the ions of at least one of the species are deformed into parallel and rigid needle-like ellipsoidal objects that have a continuous line of charge distribution along their axis of revolution. We examine two specific cases: (a) solutions comprising both cationic and anionic needles that are identical in every respect except for the charge sign, and (b) solutions in which only one ionic species is made up of parallel rigid needles while the other species is made up of point ions. The first system is the analog, for ionic needles, of the familiar restricted primitive model of electrolytes, while the second one is a very simple model for a polyelectrolyte solution. For both systems we investigate how the phase diagram is affected by the extent of deformation of the ions, as measured by the spatial spread of their charge distribution.

Phase Diagram of Polyelectrolyte Solutions: Weak Polymer Effect

We present a mean field theory of phase diagram of solutions of flexible polyelectrolytes with neutralizing counterions. We show that the temperature−concentration curve, corresponding to the coexistence of polymer-rich and polymer-poor solutions, is highly asymmetric, and the degree of polymerization of the polymer has only a weak effect. We have addressed the role of added salt in destabilizing the homogeneous phase of polyelectrolyte solutions, within the framework of quasi-two-component description of the multicomponent system.

Possible complete miscibility of(BN)x(C2)1−xalloys

The stabilities of $(BN)_x(C_2)_{1-x}$ alloys and related superlattices are investigated by ab initio pseudopotential calculations. We find that the $(BN)_1/(C_2)_1$ superlattices in (111) orientations have the lowest formation energy among many short-range ordered $BNC_2$ structures due to the smallest number of B-C and C-N bonds. Based on the calculated formation energies at several compositions and for various ordered structures and assuming thermodynamic equilibrium, the solid solution phase diagram of $(BN)_x(C_2)_{1-x}$ alloys is constructed. We find that the complete miscibility of $(BN)_x(C_2)_{1-x}$ alloys is possible, which is in contrast with previous theoretical predictions but in agreement with experimental reports.