Phase Separation In Binary Mixtures Research Articles

Control of structure formation in phase-separating systems

In this paper, we study the evolution of phase-separating binary mixtures which are subjected to alternate cooling and heating cycles. An initially homogeneous mixture is rapidly quenched to a temperature T(1)<T(c), where T(c) is the critical temperature. The mixture undergoes phase separation for a while and is then suddenly heated to a temperature T(2)>T(c). These cycles are repeated to create a domain morphology with multiple length scales, i.e., the structure factor is characterized by multiple peaks. For phase separation in d = 2 systems, we present numerical and analytical results for the emergence and growth of this multiple-scale morphology.

Self-assembly of double hydrophilic block copolymers in concentrated aqueous solution

We report the unusual aqueous (micro)phase separation of binary mixtures of two biocompatible, hydrophilic homopolymers and the corresponding double-hydrophilic diblock copolymers of poly(ethylene oxide) (PEO) and poly[2-(methacryloyloxy)ethyl phosphorylcholine) (PMPC). SAXS analysis of these double hydrophilic block copolymers in concentrated aqueous solution shows highly hydrated nano-structures and a hydration mechanism is proposed based on these data.

Effects of elastic interactions on the aggregation of nanostructures

Externally imposed fields can directly affect microstructural evolution arising from diffusional phase separation in binary mixtures and potentially can be utilized to form highly ordered nanostructures. The effects of elastic fields on phase separation and coarsening are investigated in this paper using a Cahn–Hilliard-type phase-field model. Periodic traction distributions are shown to lead to patterned microstructures. The kinetics and morphology of aggregation are found to depend significantly on the transformation strain, contrast in moduli between phases and the magnitude of externally applied tractions (mechanical fields). The trends observed in simulations are analyzed in detail in terms of Eshelby-type estimates for elastic interaction energies, and the correlations are shown to be remarkably accurate. Predictions based solely upon interaction energies can provide very useful guidelines to develop strategies to control the morphology of aggregation.

Natural element analysis of the Cahn–Hilliard phase-field model

We present a natural element method to treat higher-order spatial derivatives in the Cahn–Hilliard equation. The Cahn–Hilliard equation is a fourth-order nonlinear partial differential equation that allows to model phase separation in binary mixtures. Standard classical \({{\mathcal{C}}^0}\)-continuous finite element solutions are not suitable because primal variational formulations of fourth-order operators are well-defined and integrable only if the finite element basis functions are piecewise smooth and globally \({{\mathcal{C}}^1}\)-continuous. To ensure \({{\mathcal{C}}^1}\)-continuity, we develop a natural-element-based spatial discretization scheme. The \({{\mathcal{C}}^1}\)-continuous natural element shape functions are achieved by a transformation of the classical Farin interpolant, which is basically obtained by embedding Sibsons natural element coordinates in a Bernstein–Bezier surface representation of a cubic simplex. For the temporal discretization, we apply the (second-order accurate) trapezoidal time integration scheme supplemented with an adaptively adjustable time step size. Numerical examples are presented to demonstrate the efficiency of the computational algorithm in two dimensions. Both periodic Dirichlet and homogeneous Neumann boundary conditions are applied. Also constant and degenerate mobilities are considered. We demonstrate that the use of \({{\mathcal{C}}^1}\)-continuous natural element shape functions enables the computation of topologically correct solutions on arbitrarily shaped domains.

Phase Separation in Binary Mixtures of Bipolar and Monopolar Lipid Dispersions Revealed by 2H NMR Spectroscopy, Small Angle X-Ray Scattering, and Molecular Theory

Binary mixtures of C20BAS and POPC membranes were studied by solid-state 2H NMR spectroscopy and small angle x-ray scattering (SAXS) over a wide range of concentrations and at different temperatures. Three specifically deuterated C20BAS derivatives—[1′,1′,20′,20′-2H4]C20BAS, [2′,2′,19′,19′-2H4]C20BAS, and [10′,11′-2H2]C20BAS—combined with protiated 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), as well as membranes containing POPC-d31 and fully protiated bolalipid, were used in NMR experiments to obtain structural information for the mixtures. The 2H NMR spectra of [10′,11′-2H2]C20BAS/POPC membrane dispersions reveal that the bolalipid is predominantly in the transmembrane conformation at high bolalipid concentrations (100, 90, and 70 mol %). At ≤50 mol % C20BAS, smaller quadrupolar couplings appear in the spectra, indicating the presence of U-shaped conformers. The proportion of U-shaped bolalipids increases as the amount of POPC in the membrane increases; however, the transmembrane component remains the dominant bolalipid conformation in the membrane even at 45°C and 10 mol % C20BAS, where it accounts for ∼50% of the bolalipid population. The large fraction of C20BAS transmembrane conformers, regardless of the C20BAS/POPC ratio, together with the findings from molecular mean-field theory calculations, suggests the coexistence of phase-separated bolalipid-rich domains and POPC-rich domains. A single lamellar repeat distance was observed in SAXS experiments corresponding to the average repeat spacing expected for C20BAS- and POPC-rich domains. These observations are consistent with the presence of microphase-separated domains in the mixed membrane samples that arise from POPC-C20BAS hydrophobic mismatch.

Self-Assembly of Ligated Gold Nanoparticles: Phenomenological Modeling and Computer Simulations

We study the assembly of ligated gold nanoparticles by both phenomenological modeling and computer simulations for various ligand chain lengths. First, we develop an effective nanoparticle-nanoparticle pair potential by treating the ligands as flexible polymer chains. Besides van der Waals interactions, we incorporate both the free energy of mixing and elastic contributions from compression of the ligands in our effective pair potentials. The separation of the nanoparticles at the potential minimum compares well with experimental results of gold nanoparticle superlattice constants for various ligand lengths. Next, we use the calculated pair potentials as input to Brownian dynamics simulations for studying the formation of nanoparticle assembly in three dimensions. For dodecanethiol ligated nanoparticles in toluene, our model gives a relatively shallower well depth and the clusters formed after a temperature quench are compact in morphology. Simulation results for the kinetics of cluster growth in this case are compared with phase separations in binary mixtures. For decanethiol ligated nanoparticles, the model well depth is found to be deeper, and simulations show hybrid, fractal-like morphology for the clusters. Cluster morphology in this case shows a compact structure at short length scales and a fractal structure at large length scales. Growth kinetics for this deeper potential depth is compared with the diffusion-limited cluster-cluster aggregation (DLCA) model.

Phase Separation in Binary Mixtures of Bipolar and Monopolar Lipid Dispersions Revealed by Solid-State 2H NMR Spectroscopy and Small Angle X-ray Scattering

Binary mixtures of C20BAS and POPC membranes have been studied by 2H NMR spectroscopy and small angle X-ray scattering (SAXS) over a wide range of concentrations and at different temperatures. Experiments tested the possibility of formation of phase-separated lipid domains predicted by the mean field theory [1]. Membranes composed of three specifically deuterated C20BAS derivatives [1,1,20,20-2H4]C20BAS, [2,2,19,19-2H4] C20BAS, and [10,11-2H2] C20BAS with protiated POPC and with membranes containing POPC-d31 and fully protiated bolalipid were used in NMR experiments to obtain structural information for the mixture. The 2H NMR spectra of 10,11-2H2-C20BAS:POPC membrane dispersion reveal that the bolalipid is predominantly in the transmembrane conformation at high bolalipid concentrations. At 50 mole percent C20BAS and lower, components appear in the spectra with smaller quadrupolar couplings, most likely indicating the presence of U-shaped conformers. The proportion of U-shaped bolalipids becomes more prominent as the amount of POPC in the membrane increases. However, the transmembrane component is still the dominant bolalipid conformation in the membrane even at 45 °C and 10 mole percent C20BAS, where it accounts for roughly 50% of the bolalipid population. The large fraction of C20BAS transmembrane conformers regardless of the C20BAS:POPC ratio together with POPC-bolalipid hydrophobic mismatch can be explained by co-existence of bolalipid-rich domains separate from the POPC-rich domains. In SAXS experiments only a single distinct lamellar repeat distance was observed, corresponding roughly to the average of bolalipid-rich and POPC-rich domains. These observations are consistent with the presence of microphase-separated domains in the mixed membrane samples. [1] G.S. Longo et al. (2007) Biophys. J. 93, 2609.

Sol-gel synthesis of monolithic silica gels and glasses from phase-separating tetraethoxysilane–water binary system

A facile synthetic route for monolithic silica gels and glasses from a phase-separating binary mixture of tetraalkoxysilane and water, free from alcohols, organic additives, or other third components, has been developed.

Asymmetric oscillations during phase separation under continuous cooling: A simple model

We investigate the phase separation of binary mixtures under continuous cooling using the Cahn-Hilliard equation including the effect of gravity. In our simple model, sedimentation is accounted for by instantaneously "removing" droplets from the supersaturated mixture into the coexisting phase once the droplets have reached a defined maximum size. Our model predicts an oscillatory variation of turbidity. Depending on the composition, either both phases oscillate (symmetric oscillations) or only one of the phases oscillates (asymmetric oscillations). In the asymmetric case, droplet sedimentation from the majority phase into the minority phase reduces supersaturation in the minority phase. This inhibits droplet formation in the minority phase. The cooling rate dependence of the period agrees with experimental results.

Diffusion processes in homogeneous and phase-separated binary fluid mixtures.

Diffusion processes in dynamically asymmetric binary fluid mixtures made of monodisperse polystyrene (PS) and a rodlike nematogen molecule (5CB) are studied by pulsed-field gradient spin echo NMR in the vicinity of the phase-separation/phase-dissolution temperature. The phase-separation process and the loss of mobility of polymer chains at Tg take place simultaneously evidencing the strong effect of elasticity on the sample morphology. Below the instability point of the mixture, two self-diffusion coefficients, named Dfast and Dslow, are observed and assigned to mobile molecules i) dissolved in the polymeric matrix and ii) phase-separated in isolated or interconnected domains, respectively. The temperature dependence of Dfast exhibits an Arrhenius-like behaviour when the mixture is submitted to a slow cooling rate whereas a Vogel-Fulcher-Tamman-Hesse law is obeyed for deep quenches. These results show the dynamic heterogeneities existing in the PS/5CB system below the UCST. Characteristic length scales are estimated from modelling echo attenuation curves exhibiting diffraction-like patterns.

Influence of temperature on microdomain organization of mixed cationic–zwitterionic lipidic monolayers at the air–water interface

The thermodynamic behavior of mixed DOTAP–DPPC monolayers at the air–water interface has been investigated in the temperature range from 15 to 45 °C, covering the temperature interval where the thermotropic phase transition of DPPC, from solid-like to liquid-like, takes place. Based on the regular solution theory, the miscibility of the two lipids in the mixed monolayer was evaluated in terms of the excess Gibbs free energy of mixing Δ G ex , activity coefficients f 1 and f 2 and interaction parameter ω between the two lipids. The mixed DOTAP–DPPC film was found to have positive deviations from ideality at low DOTAP mole fractions, indicating a phase-separated binary mixture. This effect depends on the temperature and is largely conditioned by the structural chain conformation of the DPPC lipid monolayer. The thermodynamic parameters associated to the stability and the miscibility of these two lipids in a monolayer structure have been discussed in the light of the phase diagram of the DOTAP–DPPC aqueous mixtures obtained from differential scanning calorimetry measurements. The correlation between the temperature behavior of DOTAP–DPPC monolayers and their bulk aqueous mixtures has been briefly discussed.

Characterization of Physical Properties of Supported Phospholipid Membranes Using Imaging Ellipsometry at Optical Wavelengths

Subnanometer-scale vertical z-resolution coupled with large lateral area imaging, label-free, noncontact, and in situ advantages make the technique of optical imaging ellipsometry (IE) highly suitable for quantitative characterization of lipid bilayers supported on oxide substrates and submerged in aqueous phases. This article demonstrates the versatility of IE in quantitative characterization of structural and functional properties of supported phospholipid membranes using previously well-characterized examples. These include 1), a single-step determination of bilayer thickness to 0.2 nm accuracy and large-area lateral uniformity using photochemically patterned single 1,2-dimyristoyl- sn-glycero-3-phosphocholine bilayers; 2), hydration-induced spreading kinetics of single-fluid 1-palmitoyl-2-oleoyl- sn-glycero-3-phosphocholine bilayers to illustrate the in situ capability and image acquisition speed; 3), a large-area morphological characterization of phase-separating binary mixtures of 1,2-dilauroyl- sn-glycero-3-phosphocholine and galactosylceramide; and 4), binding of cholera-toxin B subunits to GM 1-incorporating bilayers. Additional insights derived from these ellipsometric measurements are also discussed for each of these applications. Agreement with previous studies confirms that IE provides a simple and convenient tool for a routine, quantitative characterization of these membrane properties. Our results also suggest that IE complements more widely used fluorescence and scanning probe microscopies by combining large-area measurements with high vertical resolution without the use of labeled lipids.

Polymer Modifies the Critical Region of the Coexisting Liquid Phases

Several recent conceptual advances, which take advantage of the polymer conformation in the near critical point of coexisting liquid phases and practical techniques of some unique molecular interactions between polymer chain and the solvent molecules, have been made to allow the investigation of the effect of the well-defined polymer in phase separation of binary mixtures. The behavior of a flexible linear or branched chain polymer (polyethylene oxide, PEO, MW = 9 x 10(5), as an impurity) in the critical binary mixture of isobutyric acid (I) + water (W) was studied by the refractive index (n) measurements using a very accurate and sensitive refractometer. The refractive index in each phase of IW as well as three different PEO concentrations (C = 0.395, 0.796, and 1.605 mg/cm(3)) in the near critical composition of IW have been measured at temperatures below the system's upper critical point. We observed that the polymer was significantly affected in the critical region of IW and these various concentrations of PEO show an important behavior on the critical exponents (beta), the critical temperatures (T(c)), and critical composition (phi(c)), which are depicting the shape of the coexistence curve. The phase-transition region of coexisting phases of IW shifts down with the addition of PEO and T(c) decreases linearly with increasing PEO concentrations. This may indicate that the polymer chain entangles with each phase, thereby the polymer monomers strongly interact with neighbor solvent particles and also intrachain interaction between the polymer segments. At such conditions, the collapse of polymer chain is possible in the vicinity of the critical point. At temperatures T close enough to T(c), the critical exponent beta (defined by the relation (n(1) - n(2)) proportional, variant (T(c) - T)(beta), with n(1) and n(2) being the refractive indices of the coexisting phases) was found to decrease from 0.382 to 0.360 when the PEO concentration changes from 0.395 to 1.605 mg/cm(3). These values are higher than that of 0.326 +/- 0.005 of pure IW, which is compatible with the three-dimensional Ising value beta = 0.325. The observed critical exponents for the PEO in IW are fully renormalized Ising critical exponents. Besides, the phi(c) values decrease with increasing the C values in the mixture of IW. It appears that the shape of the PEO in IW coexistence curves is similar from that of pure IW.

Nanoscale Pattern Formation in Non-Equilibrium Surface Chemical Reactions

Using examples from surface science, we consider in this article problems of nonequilibrium pattern formation in reactive soft matter. An interplay of reaction, diffusion and energetic interactions between adatoms can produce a variety of non-equilibrium nanostructures, both stationary and traveling. These structures are similar to the patterns found in phase-separating binary mixtures under the influence of reactions. Because of their small sizes, such nanostructures are significantly affected by fluctuations. The derivation of mesoscopic stochastic equations for fluctuating concentrations, starting from the microscopic master equation of the lattice approximation, is discussed. Special attention is paid to surface chemical reactions involving a promoter species, where experimental observations are available.

Nematic-nematic phase separation in binary mixtures of thick and thin hard rods: Results from Onsager-like theories

The fundamental nature of the nematic-nematic phase separation in binary mixtures of rigid hard rods is analyzed within the Onsager second-virial theory and the extension of Parsons and Lee which includes a treatment of the higher-body contributions. The particles of each component are modeled as hard spherocylinders of different diameter , but equal length . In the case of a system which is restricted to be fully aligned (parallel rods), we provide an analytical solution for the spinodal boundary for the limit of stability of demixing; only a single region of coexistence bounded at lower pressures (densities) by a critical point is possible for such a system. The full numerical solution with the Parsons-Lee extension also indicates that, depending on the length of the particles, there is a range of values of the diameter ratio where the phase coexistence is closed off by a critical point at lower pressure. A second region of coexistence can be found at even lower pressures for certain values of the parameters; this region is bounded by an "upper" critical point. The two coexistence regions can also merge to give a single region of coexistence extending to very high pressure without a critical point. By including the higher-order contributions to the excluded volume (end effects) in the Onsager theory, we prove analytically that the existence of the lower critical point is a direct consequence of the finite size of the particles. A new analytical equation of state is derived for the nematic phase using the Gaussian approximation. In the case of Onsager limit (infinite aspect ratio), we show that the phase behavior obtained using the Parsons-Lee approach substantially deviates from that with the Onsager theory for the transition due to the nonvanishing third and higher order virial coefficients. We also provide a detailed discussion of the phase behavior of recent experimental results for mixtures of thin and thick rods of the same length, for which the Onsager and Parsons-Lee theories can provide a qualitative description.

Oscillatory instabilities in phase separation of binary mixtures: Fixing the thermodynamic driving

Binary liquid mixtures can show pronounced oscillations in the differential scanning calorimeter signal for the specific heat and in the turbidity when phase separation is induced by continuously ramping the temperature. For a fixed ramp rate, i.e., a linear temporal drift of temperature, only a small number of oscillations have been observed. In the present manuscript we describe an experimental setup where simultaneous video-microscopy and shadow-graph measurements can be performed on mixtures subjected to an arbitrary temporal temperature evolution. In particular, it can be adjusted to fix the thermodynamic driving force, which characterizes the rate of change of the composition of the coexisting phases. With this novel technique both the number of oscillations and the temperature interval where oscillations are observed increase significantly. This technique can easily be applied to a great variety of binary mixtures, permitting detailed investigations of their phase-separation kinetics under slowly ramping temperature.

Local structure of a phase-separating binary mixture in a mesoporous glass matrix studied by small-angle neutron scattering

The mesoscopic structure of the binary system isobutyric acid + heavy water (D(2)O) confined in a porous glass (controlled-pore silica glass, mean pore width ca. 10 nm) was studied by small-angle neutron scattering at off-critical compositions in a temperature range above and below the upper critical solution point. The scattering data were analyzed in terms of a structure factor model similar to that proposed by Formisano and Teixeira [Eur. Phys. J. E 1, 1 (2000)], but allowing for both Ornstein-Zernike-type composition fluctuations and domainlike structures in the microphase-separated state of the pore liquid. The results indicate that the phase separation in the pores is shifted by ca. 10 K and spread out in temperature. Microphase separation is pictured as a transition from partial segregation at high temperature, due to the strong preferential adsorption of water at the pore wall, to a tube or capsule configuration of the two phases at low temperatures, depending on the overall composition of the pore liquid. Results for samples in which the composition of the pore liquid can vary with temperature due to equilibration with extra-pore liquid are consistent with this picture.

Phase Separation in Binary Mixtures Containing Linear Perfluoroalkanes

Mixed systems containing fluorocarbons (FC) phase separate below certain temperatures. The liquid−liquid coexistence curves show upper critical solution temperatures (Tc) that depend on the nature of the components. In this work, we report the phase separation measurements of mixtures obtained from short-chain linear perfluoroalkanes (perfluorohexane, perfluoroheptane, and perfluorooctane) with some n-alkanes, cyclohexane, benzene, ethers, and chlorinated solvents. The results are discussed in terms of the chemical nature and polarizability of the components.

Phase separation in binary mixtures containing polymers: A quantitative comparison of single‐chain‐in‐mean‐field simulations and computer simulations of the corresponding multichain systems

AbstractWe discuss a phenomenological, coarse‐grained simulation scheme, single‐chain‐in‐mean‐field (SCMF) simulation, for investigating the kinetics of phase separation in dense polymer blends and mixtures of polymers and solvents. In the spirit of self‐consistent‐field calculations, we approximate the interacting multichain problem by that of a single chain in an external field, which, in turn, depends on the local densities of the components. To study the time evolution of the mixture, we perform an explicit Monte Carlo (MC) simulation of an ensemble of independent chains in the external field and periodically calculate the average densities and update the external field. Unlike dynamic self‐consistent‐field theory, these SCMF simulations do not assume that the chain conformations relax much more quickly than the density and incorporate the single‐chain dynamics explicitly rather than via an Onsager coefficient. This allows us to study systems with large spatial inhomogeneities and dynamic asymmetries. To assess the accuracy and limitations of the simulation scheme, we compare the results of SCMF simulations using a discretized Edwards Hamiltonian with computer simulations of the corresponding multichain system for (1) the early stages of spinodal decomposition of a symmetric binary polymer blend in response to a quench from χN = 0.314 to χN = 5 (where χ is the Flory–Huggins parameter and N is the number of segments), for which the growth rate of composition fluctuations is compared with MC simulations of the bond fluctuation model and alternative dynamic self‐consistent‐field calculations, and (2) the evaporation of a solvent from a low‐molecular‐weight thin polymer film, for which a comparison is made with molecular dynamics (MD) simulations of a bead‐necklace model with a monomeric solvent. In the latter case, the polymer conformations are extracted from MD simulations and modeled in the SCMF simulations by a discretized Edwards Hamiltonian augmented by a chain‐bending potential. From the MD simulations of thin polymer films in equilibrium with its vapor, phase coexistence has been determined, and the second‐ and third‐order virial coefficients in the SCMF simulations have been adjusted accordingly. Finally, MD simulations of bulk solutions of a polymer and a solvent over a range of compositions, as well as the pure solvent at various densities, have been performed to determine self‐diffusion coefficients that enter the SCMF simulations in the form of density‐dependent segmental mobilities. A comparison of the polymer and solvent profiles in a thin film as a function of time and the fraction of the solvent evaporating from a solvent‐swollen film, as obtained from MD simulations and parameterized SCMF simulations, shows satisfactory agreement for this simple mapping procedure. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 934–958, 2005

Instability of a fluid–fluid interface in driven colloidal mixtures

A Rayleigh–Taylor-like interface instability is studied in a compressible Brownian Yukawafluid mixture on the ‘molecular’ scales of length and time of the individual particles. As amodel, a two-dimensional phase-separated symmetric binary mixture of colloidal particlesof type A and B with a fluid–fluid interface separating an A-rich phase from a B-rich phaseis investigated, by means of Brownian computer simulations, when brought intonon-equilibrium via a constant external driving field which acts differently on the differentparticles and perpendicular to the interface. Two different scenarios are observed whichoccur either for high or for low interfacial free energies as compared to the drivingforce. In the first scenario for high interfacial tension, the critical wavelengthλc of the unstable interface modes is in good agreement with the classical Rayleigh–Taylor formulaprovided that dynamically rescaled values for the interfacial tension are used. The wavelengthλc increases with time, representing an effect of self-healing of the interface due to a localdensity increase near the interface. The Rayleigh–Taylor formula is confirmed even ifλc is of the order of a molecular correlation length. In the second scenario for very largedriving forces as compared to the interfacial line tensions, on the other hand, the particlespenetrate the interface easily due to the driving field and form microscopic lanes with awidth different from the predictions of the classical Rayleigh–Taylor formula. The resultsare of relevance for phase-separating colloidal mixtures in a gravitational or electric field.