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.     

Influence of temperature and alkyl chain length on phase behavior in Langmuir monolayers of some oxyethylenated nonionic surfactants

We study the surface phase behavior in Langmuir monolayers of a series of nonionic surfactants of the general formula CnE1 with n=14, 16, and 18 by film balance and Brewster angle microscopy (BAM) over a wide range of temperatures. A cusp point followed by a pronounced plateau region in the pressure-area (pi-A) isotherms indicates a first-order phase transition in the coexisting state between a lower density liquid expanded (LE) phase and a higher density liquid condensed (LC) phase at the air-water interface. The formation of bright two-dimensional (2D) LC domains in a dark background visualized by BAM further confirms this observation. In addition to the cusp point at the onset of the LE-LC coexistence state, another cusp point followed by a small plateau is observed for the C14E1 and C18E1 monolayers, indicating a second phase transition between two condensed phases of different compressibility and tilt orientation of the molecules. This unusual two-step phase transition is explained by the Ostwald step rule. The C16E1 and C18E1 monolayers show a kink in their respective isotherms, after which the surface pressure increases steeply with only a little decrease in the molecular area, suggesting that the molecules undergo a transition from a tilted to an almost vertical orientation with respect to the water surface. The thermodynamic parameters for the condensation of the molecules in the LE-LC coexistence state were calculated by employing the 2D Clapeyron equation. The temperature coefficient of the critical surface pressure dpi(c)/dT values shows a decreasing trend from C14E1 to C18E1, suggesting that the condensation process becomes less and less prone to thermal perturbation as the chain length increases. For all the amphiphiles, the DeltaH values are found to be negative, suggesting an exothermic nature of condensation. The negative DeltaS values obtained from the relation DeltaH/T probably come from the restriction on the rotational and translational motion of the molecules constrained in a confined area in the LE-LC transition region.     

Monte Carlo simulations of squalane in the Gibbs ensemble

We investigate the liquid–vapour coexistence curve of 2,6,10,15,19,23-hexamethyltetracosane (squalane) near the critical point with a new Lennard–Jones parameter set and compare our results to existing simulation data as well as to recent experimental vapour pressure data. Comparison of the liquid–vapour coexistence curve to previous simulation data reveals that this new force field, which includes tail corrections to the truncation of the non-bonded interactions increases the liquid density. We determine the critical temperature to 829 K and 825 K (with roughly 1% error) for two different system sizes, 72 and 108 molecules, and the critical density to 0.211 g/cm³ and 0.228 g/cm³, respectively. We extrapolate experimental vapour pressure data by use of Antoine's law to the temperature range covered by simulation and yield good agreement between simulation and experiment. We note that the vapour pressure in simulation is essentially governed by the ideal vapour pressure.     

Surface phase behavior in Gibbs monolayers of bis(ethylene glycol) mono-n-tetradecyl ether at the air-water interface

We present the adsorption kinetics and surface morphology of the adsorbed monolayers of bis(ethylene glycol) mono-n-tetradecyl ether (C14E2) by film balance and Brewster angle microscopy. A cusp point followed by a plateau region in the pressure (pi)-time (t) adsorption isotherm indicates a first-order phase transition in the coexistence region between a lower density liquid expanded (LE) phase and a higher density liquid condensed (LC) phase. A variety of condensed phase domains surrounded by the homogeneous LE phase are observed just after the appearance of the phase transition. The domains are of a spiral or striplike structure at lower temperatures. This characteristic shape of the domains is because of strong dipole-dipole repulsion between the molecules. At 18 degrees C, the domains are found to be quadrant structures. A slight increase in subphase temperature (around 1 degrees C) brings about a quadrant-to-circular shape transition in the domains. The circular domains return to quadrant structures as the subphase temperature is lowered. The domains completely disappear when the temperature is increased beyond 19 degrees C, suggesting that the critical temperature for the condensed domain formation is 19 degrees C. Above this temperature, the hypothetical surface pressure necessary for the phase transition exceeds the actual surface pressure attainable from a solution of concentration greater than or equal to the critical micelle concentration. An increase in molecular motion with increasing temperature results in a higher degree of chain flexibility. As a result, the molecules cannot accumulate in the condensed phase form when the subphase temperature is above 19 degrees C.     

Thermodynamics of the liquid expanded to condensed phase transition of poly(L-lactic acid) in Langmuir monolayers

Surface pressure-area per monomer (pi-A) isotherms show that poly(L-lactic acid) (PLLA) Langmuir monolayers exhibit a liquid expanded-to-condensed (LE/LC) phase transition at low surface pressure. Brewster angle microscopy images show circular domains where the LC phase is surrounded by the LE phase during phase coexistence. Morphology studies via atomic force microscopy show that well-ordered patterns are only observed for Langmuir-Blodgett films prepared in the LC phase, while no ordered features are observed in the LE phase. The morphological differences confirm that during the LE/LC phase transition PLLA molecules form well-ordered structures at the air/water interface. Analysis by the two-dimensional Clausius-Clapeyron equation is used to predict the critical parameters (X(c)). Both critical parameters, the critical temperature (T(c)) and the critical pressure (pi(c)), increase with increasing number average molar mass (M(n)) as X(c) = X(c,infinity) - KM(n)(-1), where X(c,infinity) is the value of the critical parameter at infinite molar mass and K is a constant. For PLLA T(c,infinity) = 36.2 +/- 0.3 degrees C and pi(c,infinity) = 4.53 +/- 0.06 mN x m(-1). This study provides a model polymer system for examining critical behavior in two dimensions.     

Phase behavior of lyotropic rigid-chain polymer liquid crystal studied by dissipative particle dynamics

The phase behavior of lyotropic rigid-chain liquid crystal polymer was studied by dissipative particle dynamics (DPD) with variations of the solution concentration and temperature. A chain of fused DPD particles was used to represent each mesogenic polymer backbone surrounded with the strongly interacted solvent molecules. The free solvent molecules were modeled as independent DPD particles, where each particle includes a lump of solvent molecules with the volume roughly equal to the solvated polymer segment. The simulation shows that smectic-B (S(B)), smectic-A (S(A)), nematic (N), and isotropic (I) phases exist within certain regions in the temperature and concentration parameter space. The temperature-dependent S(B)∕S(A), S(A)∕N, and N∕I phase transitions occur in the high concentration range. In the intermediate concentration range, the simulation shows coexistence of the anisotropic phases and isotropic phase, where the anisotropic phases can be the S(B), S(A), or N phases. Mole fraction and compositions of the coexisted phases are determined from the simulation, which indicates that concentration of rigid rods in isotropic phase increases as the temperature increases. By fitting the orientational distribution function of the systems, the biphasic coexistence is further confirmed. From the parameter α obtained for the simulation, the distribution of the rigid rods in the two coexistence phases is quantitatively evaluated. By using model and simulation methods developed in this work, the phase diagrams of the lyotropic rigid-chain polymer liquid crystal are obtained. Incorporating the solvent particles in the DPD simulation is critical to predict the phase coexistence and obtain the phase diagrams.     

Structure and phase behavior of a confined nanodroplet composed of the flexible chain molecules

A polymer density functional theory has been employed for investigating the structure and phase behaviors of the chain polymer, which is modelled as the tangentially connected sphere chain with an attractive interaction, inside the nanosized pores. The excess free energy of the chain polymer has been approximated as the modified fundamental measure-theory for the hard spheres, the Wertheim's first-order perturbation for the chain connectivity, and the mean-field approximation for the van der Waals contribution. For the value of the chemical potential corresponding to a stable liquid phase in the bulk system and a metastable vapor phase, the flexible chain molecules undergo the liquid-vapor transition as the pore size is reduced; the vapor is the stable phase at small volume, whereas the liquid is the stable phase at large volume. The wide liquid-vapor coexistence curve, which explains the wide range of metastable liquid-vapor states, is observed at low temperature. The increase of temperature and decrease of pore size result in a narrowing of liquid-vapor coexistence curves. The increase of chain length leads to a shift of the liquid-vapor coexistence curve towards lower values of chemical potential. The coexistence curves for the confined phase diagram are contained within the corresponding bulk liquid-vapor coexistence curve. The equilibrium capillary phase transition occurs at a higher chemical potential than in the bulk phase.     

Influence of flexible spacers on liquid-crystalline self-assembly of T-shaped bolaamphiphiles

T-shaped bolaamphiphiles composed of a biphenyl rigid core, a semiperfluorinated lateral chain, two polar 1,2-diol groups in the terminal positions and flexible alkyl spacers connecting the polar groups with the biphenyl core have been synthesized and investigated by polarizing microscopy, DSC and X-ray scattering. The influence of spacer length and position of the spacer on the self-assembly in liquid-crystalline phases was studied. A series of four different columnar phases (Col(hex)/p6mm, Col(rec)/p2gg, Col(squ)/p4gm and Col(squ)/p4mm), representing liquid-crystalline honeycomb structures composed of cylinders having hexagonal, pentagonal, and square cross section, were found on increasing the spacer length. It is also shown that introduction of aliphatic spacers in the backbone of the T-shaped bolaamphiphiles replaces the Col(rec)/c2mm phase made up of rhombic cylinders with the Col(squ)/p4mm phase composed of square cylinders. It also causes the 2d lattice of pentagonal cylinders to increase the symmetry from Col(rec)/p2gg to Col(squ)/p4gm. A temperature-dependent second-order phase transition between these two pentagonal cylinder structures was observed for the first time. Beside these effects on cylinder shape and phase symmetry the flexible spacer units also lead to reduced phase transition temperatures and allow adjustment of cylinder side length to envelop a wider range of side-chain sizes. Electron density maps suggest that this may involve sacrificing some of the hydrogen bonds.     

Evaporation of Lennard-Jones fluids

Evaporation and condensation at a liquid/vapor interface are ubiquitous interphase mass and energy transfer phenomena that are still not well understood. We have carried out large scale molecular dynamics simulations of Lennard-Jones (LJ) fluids composed of monomers, dimers, or trimers to investigate these processes with molecular detail. For LJ monomers in contact with a vacuum, the evaporation rate is found to be very high with significant evaporative cooling and an accompanying density gradient in the liquid domain near the liquid/vapor interface. Increasing the chain length to just dimers significantly reduces the evaporation rate. We confirm that mechanical equilibrium plays a key role in determining the evaporation rate and the density and temperature profiles across the liquid/vapor interface. The velocity distributions of evaporated molecules and the evaporation and condensation coefficients are measured and compared to the predictions of an existing model based on kinetic theory of gases. Our results indicate that for both monatomic and polyatomic molecules, the evaporation and condensation coefficients are equal when systems are not far from equilibrium and smaller than one, and decrease with increasing temperature. For the same reduced temperature T/T(c), where T(c) is the critical temperature, these two coefficients are higher for LJ dimers and trimers than for monomers, in contrast to the traditional viewpoint that they are close to unity for monatomic molecules and decrease for polyatomic molecules. Furthermore, data for the two coefficients collapse onto a master curve when plotted against a translational length ratio between the liquid and vapor phase.     

Liquid-liquid phase transitions in supercooled water studied by computer simulations of various water models

Liquid-liquid and liquid-vapor coexistence regions of various water models were determined by Monte Carlo (MC) simulations of isotherms of density fluctuation-restricted systems and by Gibbs ensemble MC simulations. All studied water models show multiple liquid-liquid phase transitions in the supercooled region: we observe two transitions of the TIP4P, TIP5P, and SPCE models and three transitions of the ST2 model. The location of these phase transitions with respect to the liquid-vapor coexistence curve and the glass temperature is highly sensitive to the water model and its implementation. We suggest that the apparent thermodynamic singularity of real liquid water in the supercooled region at about 228 K is caused by an approach to the spinodal of the first (lowest density) liquid-liquid phase transition. The well-known density maximum of liquid water at 277 K is related to the second liquid-liquid phase transition, which is located at positive pressures with a critical point close to the maximum. A possible order parameter and the universality class of liquid-liquid phase transitions in one-component fluids are discussed.     

Effect of polymer chain in coexisting liquid phases by refractive index measurements

The behavior of polyethylene oxide (PEO, molecular weight, M(w) = 9 x 10(5), as an impurity) was studied in the critical binary mixture of nitroethane (NE) + 3-methylpentane (MP) by refractive index measurements. The measurements were performed at three different PEO concentrations (C = 0.373, 0.759, and 1.509 mg/cc) in the near critical composition of NEMP. We observed that the coexisting phase region shifts down with increasing PEO concentration and the critical temperature (T(c)) decreases linearly with C. At temperatures T close enough to T(c), the critical exponent beta [defined by the relation (n1-n2) proportional (T(c)-T)beta, with n1 and n2 being the refractive indices of the coexisting phases] was found to decrease from 0.456 to 0.372 when the PEO concentration changes from 0.373 to 1.509 mg/cc. These values are higher than that of 0.345+/-0.015 of pure NEMP, which is compatible with the three-dimensional Ising value beta = 0.325. It appears that the shape of the PEO in NEMP coexistence curves is similar from that of pure NE + MP.     

Nonasymptotic critical behavior of a ternary ionic system

Refractive indices n and salt concentrations ms of coexisting phases of the ternary system 1,4-dioxane + water + potassium chloride were measured along the liquid-liquid-solid coexistence curve near the liquid-liquid critical end point. Refractive index measurements were carried out in the range 0.689 x 10-3 < t = (T - Tc)/Tc < 0.118 while salt concentrations were determined for the temperature range 1.84 x 10-3 < t < 8.07 x 10-2. From these experimental results, compositions fD (mass fraction of dioxane on a salt-free basis) and densities rho of coexisting phases were obtained. The shape of the coexistence curve was analyzed using alternatively n, ms, fD, and rho as order parameters. In all cases, the obtained coexistence curve displays, asymptotically, Ising behavior. Outside the asymptotic critical domain, n, ms, and rho show significant deviations of the effective critical exponent from its Ising value, while the concentration variable fD requires no corrections to simple scaling. On the basis of the present results, we conclude that this system shows no indication of multicritical behavior.     

Critical Properties of Argon

Abstract

Measurements of P-V-T properties of argon in the critical region are reported. Isothermal compressibilities have been calculated from the data for liquid and vapor along the coexistence curve and for the gas above the critical temperature at the critical density. Densities of the liquid and vapor along the coexistence curve were measured, and the critical temperature, pressure and density of argon were redetermined. These data are compared with those of other workers; in addition critical indices which represent the manner in which these properties vary as one approaches the critical point were determined and compared with the predictions of several theoretical estimates of these quantities.     

Vibrational energy relaxation of high density HCl fluid in the 150–345 K range

The vibrational lifetime of liquid hydrogen chloride alone the liquid—vapor coexistence curve and of high density hydrogen chloride above the critica anti-Stokes Raman scattering technique. The results obtained above the critical temperature show a gas-liKe behaviour with a larger relaxation rate con is consistent with a contribution of van der Waals dimers to vibrational relaxation. The results obtained along the liquid—vapor coexistence curve ar model.     

Hydrogen bonding in liquid and supercritical 1-octanol and 2-octanol assessed by near and midinfrared spectroscopy

The near and midinfrared spectra of 1-octanol (and 2-octanol) have been measured along the liquid-gas coexistence curve from room temperature up to the critical point and in the supercritical domain along the isotherm T=385 degrees C (and T=365 degrees C) above the critical point of both 1-octanol and 2-octanol for pressure ranging from 0.5 up to 15 MPa. The density values of SC 1- and 2-octanol have been estimated by analysing the near infrared (NIR) spectra in the 3nu(a)(CH) region. A quantitative analysis of the absorption band associated with the OH stretching vibration [nu(OH)] and its first and second overtones [2nu(OH) and 3nu(OH)] was carried out in order to estimate the percentage of "free" OH groups in both alcohols in the whole thermodynamic domain investigated here. Very consistent results have been obtained from the independent analysis of these three different absorption bands which gave us a good confidence in the degree of hydrogen bonding reported here for 1- and 2-octanol. Thus, the percentage of free OH groups which is around 5% in liquid 1-octanol under ambient conditions strongly increase up to 70%-80% at a temperature of about 340 degrees C. Then, in the supercritical domain, upon a decrease of the density from 0.4 to 0.1 g cm(-3), the fraction of free hydroxyl groups is nearly constant presenting a plateaulike regime around 80%. As the density decreases again, this plateau regime is followed by a further increase of X(nb) which reaches a value of 96% for the system in the gaseous phase (0.01 g cm(-3); P=0.45 MPa). Finally, it comes out from this study that the percentage of free OH groups is always greater in 2-octanol than in 1-octanol at the same density.     

Octupole-like supramolecular aggregates of conical iron fullerene complexes into a three-dimensional liquid crystalline lattice

The installation of three structural features into a fullerene molecule, a conical shape, a polar iron-ferrocene complex, and long alkyl chains, allowed dipolar molecules 1 and 2 to undergo microphase separation and to form a three-dimensional lattice in a crystalline and a thermotropic liquid crystalline phase. The key feature is a tetrameric octupole-like aggregate, in which four dipoles are arranged supramolecularly to cancel the molecular polarity, forming a sphere. In addition to this lattice formation mechanism, the molecules incorporate noteworthy features, such as redox active C(60)/ferrocene and luminescent cyclophenacene.     

Casimir amplitudes and capillary condensation of near-critical fluids between parallel plates: renormalized local functional theory

We investigate the critical behavior of a near-critical fluid confined between two parallel plates in contact with a reservoir by calculating the order parameter profile and the Casimir amplitudes (for the force density and for the grand potential). Our results are applicable to one-component fluids and binary mixtures. We assume that the walls absorb one of the fluid components selectively for binary mixtures. We propose a renormalized local functional theory accounting for the fluctuation effects. Analysis is performed in the plane of the temperature T and the order parameter in the reservoir ψ(∞). Our theory is universal if the physical quantities are scaled appropriately. If the component favored by the walls is slightly poor in the reservoir, there appears a line of first-order phase transition of capillary condensation outside the bulk coexistence curve. The excess adsorption changes discontinuously between condensed and noncondensed states at the transition. With increasing T, the transition line ends at a capillary critical point T=T(c) (ca) slightly lower than the bulk critical temperature T(c) for the upper critical solution temperature. The Casimir amplitudes are larger than their critical point values by 10-100 times at off-critical compositions near the capillary condensation line.     

Vapor-liquid and vapor-solid phase equilibria for united-atom benzene models near their triple points: the importance of quadrupolar interactions

Gibbs ensemble Monte Carlo simulations were used to calculate the vapor-liquid and vapor-solid coexistence curves for benzene using two simple united-atom models. An extension of the Gibbs ensemble method that makes use of an elongated box containing a slab of the condensed phase with a vapor phase along one axis was employed for the simulations of the vapor-solid equilibria and the vapor-liquid equilibria at very low reduced temperatures. Configurational-bias and aggregation-volume-bias Monte Carlo techniques were applied to improve the sampling of particle transfers between the two simulation boxes and between the vapor and condensed-phase regions of the elongated box. An isotropic united-atom representation with six Lennard-Jones sites at the positions of the carbon atoms was used for both force fields, but one model contained three additional out-of-plane partial charge sites to explicitly represent benzene's quadrupolar interactions. Both models were fitted to reproduce the critical temperature and density of benzene and yield a fair representation of the vapor-liquid coexistence curve. In contrast, differences between the models are very large for the vapor-solid coexistence curve. In particular, the lack of explicit quadrupolar interactions for the 6-site model greatly reduces the energetic differences between liquid and solid phases, and this model yields a triple point temperature that is about a factor of 2 too low. In contrast, the 9-site model predicts a triple point of benzene at T = 253 +/- 6 K and p = 2.3 +/- 0.8 kPa in satisfactory agreement with the experimental data (T = 278.7 K and p = 4.785 kPa).     

A finite-size scaling study of a model of globular proteins

Grand canonical Monte Carlo simulations are used to explore the metastable fluid-fluid coexistence curve of the modified Lennard-Jones model of globular proteins of ten Wolde and Frenkel [Science, 277, 1975 (1997)]. Using both mixed-field finite-size scaling and histogram-reweighting methods, the joint distribution of density and energy fluctuations is analyzed at coexistence to accurately determine the critical-point parameters. The subcritical coexistence region is explored using the recently developed hyper parallel tempering Monte Carlo simulation method along with histogram reweighting to obtain the density distributions. The phase diagram for the metastable fluid-fluid coexistence curve is calculated in close proximity to the critical point, a region previously unattained by simulations.     

Polarization transfer solid-state NMR for studying surfactant phase behavior

The phase behavior of amphiphiles, e.g., lipids and surfactants, at low water content is of great interest for many technical and pharmaceutical applications. When put in contact with air having a moderate relative humidity, amphiphiles often exhibit coexistence between solid and liquid crystalline phases, making their complete characterization difficult. This study describes a (13)C solid-state NMR technique for the investigation of amphiphile phase behavior in the water-poor regime. While the (13)C chemical shift is an indicator of molecular conformation, the (13)C signal intensities obtained with the CP and INEPT polarization transfer schemes yield information on molecular dynamics. A theoretical analysis incorporating the effect of molecular segment reorientation, with the correlation time τ(c) and order parameter S, shows that INEPT is most efficient for mobile segments with τ(c) < 0.01 μs and S < 0.05, while CP yields maximal signal for rigid segments with τ(c) > 10 μs and/or S > 0.5 under typical solid-state NMR experimental conditions. For liquid crystalline phases, where τ(c) < 0.01 μs and 0 < S < 0.3, the observed CP and INEPT intensities serve as a gauge of S. The combination of information on molecular conformation and dynamics permits facile phase diagram determination for systems with solid crystalline, solid amorphous, anisotropic liquid crystalline, and isotropic liquid (crystalline) phases as demonstrated by experiments on a series of reference systems with known phase structure. Three solid phases (anhydrous crystal, dihydrate, gel), two anisotropic liquid crystalline phases (normal hexagonal, lamellar), and two isotropic liquid crystalline phases (micellar cubic, bicontinuous cubic) are identified in the temperature-composition phase diagram of the cetyltrimethylammonium succinate/water system. Replacing the succinate counterion with DNA prevents the formation of phases other than hexagonal and leads to a general increase of τ(c).