An apparent critical point in binary mixtures: experimental and simulation study

We report the experimental and simulation studies for the system of nitrobenzene-cyclododecane, showing an apparent critical point, which lies in their metastable, experimentally inaccessible state, below their melting point, affecting physical and chemical properties of this system in the stable liquid phase. The nonlinear dielectric effect (NDE) was measured in the mixture of nitrobenzene with cyclododecane. The mixture has been found to show an apparent critical point which lies below the melting point, manifested as anomalous NDE behavior in the vicinity of the critical concentrations in the stable liquid phase. The melting temperature of this system was estimated using the differential scanning calorimetry method. For such a system, we also performed Monte Carlo (MC) simulations that aimed to analyze the kinds of phase transitions observed and the conditions of their occurrence in Lennard-Jones mixture. The enthalpy, configurational energy, and radial distribution function have been estimated by the MC simulation method in the N-P-T system. Immiscibility conditions according to the approach by Schoen and Hoheisel [Mol. Phys. 57, 65 (1986)] are also discussed.     

Electric permittivity near the critical point of binary mixtures

Electric permittivity for binary solutions of nitrobenzene in 2,2,4-trimethyl pentane, hexane, cyclohexane and cycloheptane was measured versus temperature for critical concentrations. The critical temperatures were determined. It was observed that the derivative d?/dT decreased with decreasing temperature when the system passed from a single phase to a two-phase state.     

Variation of polymer chain dimensions with temperature below the theta point

The temperature dependence of the intrinsic viscosity [η] for the system polystyrene-cyclohexane in the interval ?20 < (T ? ψ) ≤ 0 near the ideal temperature ψ has been investigated. The observed diminution in size of the molecular coil with decreasing temperature is attributable to attractive net polymer-solvent interactions, denoted by negative values for the excluded volume parameter z. The data thus comprise an interesting selection for comparison with the predictions of various excluded volume theories. Among the approximate, closed-form expressions the functional relationship of Flory (x⁵ ? α³ ～ z) appears to describe best the variation of [η] with temperature in the region examined. The behavior of the Huggins constant k′ derived from the intrinsic viscosity plots is also examined, in accordance with the Peterson-Fixman model, suitably extended to the temperature region below ψ.     

A perturbed hard-sphere-chain equation of state for mixtures: Prediction from critical point constants

A modified perturbed hard-sphere-chain equation of state by Eslami [H. Eslami, Fluid Phase Equilibr. 216 (2004) 21-26], is extended to mixtures. The resulting equation of state for mixtures consists of two temperature-dependent parameters as well as an additional parameter, reflecting the segment size for pure components. The temperature-dependent parameters of the equation of state are correlated as universal functions of the reduced temperature. It is shown that knowing just the critical constants of pure components is sufficient to calculate the temperature-dependent parameters. The equation of state for mixtures is checked against the experimental pressure-volume-temperature data for a large number of mixtures, having varieties of molecular sizes and shapes. It is shown that no interaction parameter is needed to describe the behavior of fluid mixtures. Among about 3500 data points for mixtures, the average absolute deviation, compared to the experimental data, is about 0.93%.     

Nonlinear dielectric effect near the critical point of binary mixtures

The nonlinear dielectric effect (NDE) was measured in two binary systems near the critical point. The effect of independent of specific dipole-dipole interactions in contrast with previous conceptions. Its singular part is proportional to (T ? T_c)^{?$\text{1}\text{2}$} in agreement with Snider's theory as applied to NDE.     

Dynamics of phase separation and critical phenomena in polymer mixtures

The phenomenological mean-field theory for statics and dynamics of polymer mixtures is described, generalizing the approaches of Flory-Huggins, Cahn-Hilliard and de Gennes. Predictions are made for critical behavior, spinodal decomposition and homogeneous nucleation. The validity of the mean-field approximations is discussed with Ginzburg criteria. The results of the theory are compared to computer simulations and recent experiments.Invited talk delivered at the Tagung der Deutschen Physikalischen Gesellschaft, Fachausschu\ Polymerphysik, Kaiserslautern, 12–14 March 1986, and at the Gordon Research Conference on Polymer Physics, Andover, New Hampshire, 14–18 July 1986.The author is grateful to Dieter W. Heermann, Alla Sariban, Harry L. Frisch, Josef JÄckie and Thomas Schichtel for their fruitful collaboration on this research described in this review. He thanks them and Arthur BaumgÄrtner for allowing to present partially unpublished material, and for stimulating discussions. Furthermore the author has benefitted from discussions with P. G. de Gennes, P. Pincus, H. Sillescu and G. R. Strobl. This research is supported in part by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 41.     

Universality in eight-arm star polystyrene and methylcyclohexane mixtures near the critical point

Measurements of the coexistence curve and turbidity were made on different molecular mass samples of the branched polymer-solvent system eight-arm star polystyrene in methylcyclohexane near its critical point. We confirmed that these systems belong in the Ising universality class. The location of the critical temperature and composition as well as the correlation length, susceptibility, and coexistence curve amplitudes were found to depend on molecular mass and the degree of branching. The coexistence curve diameter had an asymmetry that followed a "complete scaling" approach. All the coexistence curve data could be scaled onto a common curve with one adjustable parameter. We found the coexistence curve amplitude to be about 12% larger for branched than linear polystyrenes of the same molecular mass in either solvent cyclohexane or methylcyclohexane. The two-scale-factor universality ratio R was found to be independent of molecular mass or degree of branching.     

Positron annihilation in the vicinity of the critical solution point of methanol-cyclohexane mixtures

The positron annihilation method was used to investigate critical phenomena in liquid mixtures of methanol and cyclohexane. Anomalies in the annihilation parameters near the critical solution temperature were found.     

A vibrational sum frequency spectroscopy study of the liquid-gas interface of acetic acid-water mixtures: 2. Orientation analysis

Vibrational sum frequency spectroscopy has been used to investigate the surface of aqueous acetic acid solutions. By studying the methyl and carbonyl vibrations with different polarization combinations, an orientation analysis of the acetic acid molecules has been performed in the concentration range 0-100%. The surface tension of acetic acid solutions was also measured in order to obtain the surface concentration. The orientation of the interfacial acetic acid molecules was found to remain essentially constant in an upright position with the methyl group directed toward the gas phase in the whole concentration range. The tilt angle (theta(CH)3) of the symmetry axis of the methyl group with respect to the surface normal was found to be lower than 15 degrees when considering a delta distribution of angles or as narrow as 0 +/- 11 degrees when assuming a Gaussian distribution. Further investigations showed that the C=O bond tilt (theta(C)(=)(O)) of the acetic acid hydrated monomer was constant and close to 55 degrees in the concentration range where it was detected. Finally, the orientation information is discussed in terms of different species of acetic acid, where the formation of a surface layer of acetic acid cyclic dimers is proposed at high acid concentrations.     

A critical analysis of the statistical effect in metal-complex formation

Evaluation of the statistical factor for formation of a metal-ligand complex requires explicit formulation of a detailed chemical model for the formation reaction. It is thus not possible in general to separate independent statistical effects from the other factors involved in determining the value of the equilibrium constants.     

Single reaction interface in flow analysis

The dual or multiple reaction interface concept, commonly associated to the distinct flow techniques, was replaced by a single interface concept, which do not no rely on the utilisation of a well-defined and compelling sample volume but only on mutual penetration of sample and reagent zones at a single reaction interface where both sample and reagent met together prior to detection. In the proposed approach basic principles of flow analysis, such as controlled dispersion and reaction zone formation, are not influenced by sample and reagent volumes but determined exclusively by the extension of the overlap of two adjoining quasi-infinite zones enhanced by multiple flow reversals and the pulsed nature of the flowing streams.The detector is positioned at the core of the flow manifold (not in the conventional terminal position), and repetitive flow reversals enable interface manipulations, including multi-detection of the entire reaction interface or the monitoring of the evolution of a pre-selected interface zone by using suitable reversal cycle times.The implementation of the developed approach was facilitated due to the configuration simplicity and operational versatility of multi-pumping flow systems. Its performance was evaluated by monitoring processes involving two or four-solution reaction interfaces.     

Liquid-vapor interface of methanol-water mixtures: a molecular dynamics study

Molecular dynamics simulations were carried out to investigate the structural and thermodynamic properties and variations in the dipole moments of the liquid-vapor interfaces of methanol-water mixtures. Various methanol-water compositions were simulated at room temperature. We found that methanol tends to concentrate at the interface, and the computed surface tension shows a composition dependence that is consistent with experimental measurements. The methanol molecule shows preferred orientation near the interface with the methyl group pointing into the vapor phase. The methanol in the mixture is found to have larger dipole moments than that of pure liquid methanol. The strong local field induced by the surrounding water molecules is partly the reason for this difference. The dependence of hydrogen-bonding patterns between methanol and water on the interface and the composition of the mixture is also discussed in the paper.     

Polysorbate20 adsorption layers below and above the critical micelle concentration over aluminum; cloud point and inhibitory role investigations at the solid/liquid interface

Non‐ionic polysorbate20 surfactant was used to produce adsorption protective layers below and above its critical micelle concentration (CMC) at the liquid/solid interface. The well‐ordered accumulation of surfactant molecules on the metal surface below the CMC led to the formation of oriented surfactant monolayers. On the other hand, as the surfactant concentration increased above the CMC, the monodisperse micelles, free surfactant molecules and oriented surfactant monolayers undergo aggregate formation and produce a turbid solution. The gradual increase in the number and size of aggregates leads to phase separation and hence disassembled protective layers that allow easier penetration of corrosive HCl at a metal surface. This was demonstrated by inhibition efficiency, activation energy, enthalpy and entropy of activation values. Two‐dimensional irregular crystalline sheets accumulated at the surface of aluminum, as shown by scanning electron micrographs. Adsorption of polysorbate20 at the aluminum surface exhibited a Temkin isotherm fit. Larger desorption processes at the cloud point demonstrate aggregate formation and phase separation, and hence poorer adsorption layers at the metal surface. Copyright © 2012 John Wiley & Sons, Ltd.     

Activities and thermodynamic excess properties of aqueous 2,5-dimethylpyridine mixtures near the critical demixing point: Comparison with 2,6-dimethylpyridine-water mixtures

Activities of 2,5-dimethylpyridine in aqueous solution have been measured at eleven temperatures, two below and nine above the lower critical temperature of the mixture, by the dynamic method of Randall and Weber. Gibbs free energy, enthalpy and entropy are derived to obtain excess quantities and all the results are discussed in connection with the liquid-liquid phase separation, the critical situation and the association properties of the molecules. A comparison is also made with the aqueous 2,6-dimethylpyridine system. A new version of the phase diagram is proposed.     

Static and dynamic light scattering studies of the critical behaviour of polymer mixtures

Critical fluctuations were studied in polymer mixtures of poly(dimethylsiloxane) and poly(ethylmethylsiloxane), which exhibit an upper critical temperature at T_c ⋍ 57 °C. The measurements were performed in a broad temperature range at three compositions in the miscible region close to the coexistence line. The temperature dependence of the static structure factor S(q=0) can be described by a mean field behaviour except for temperatures in the range of 6 K above T_c. There, a turnover to an Ising behaviour is observed according to a modified Landau-Ginzburg criterion. The mean field spinodal temperature T_s was determined by extrapolation of S(0)⁻¹ to zero. From the Ornstein-Zernike representation of the angular dependence of S(q), the correlation length ζ of the concentration fluctuations can be determined and leads to a critical amplitude ζ₀ = lim ζ(T→∞) = 20.5 Å. The interdiffusion dynamics described by the mutual diffusion constant D has been measured by quasielastic light scattering. It shows for the critical composition ϕ_c a critical slowing down as T approaches the critical temperature T_c. Furthermore, the q² scaling of the relaxation rate of the interdiffusion dynamics changes to q³ behaviour close to T_c according to the mode coupling theory by Kawasaki.     

Self-bonding in an amorphous polymer below the glass transition: A T-peel test investigation

Films of amorphous polystyrene (PS) with a weight-average molecular weight (M_w) of 225 × 10³ g/mol were bonded in a T-peel test geometry, and the fracture energy (G) of a PS/PS interface was measured at the ambient temperature as a function of the healing time (t_h) and healing temperature (T_h). G was found to develop with (t_h)^1/2 at T_h = T_g-bulk − 33 °C (where T_g-bulk is the glass-transition temperature of the bulk sample), and log G was found to develop with 1/T_h at T_g-bulk − 43 °C ≤ T_h ≤ T_g-bulk − 23 °C. The smallest measured value of G = 1.4 J/m² was at least one order of magnitude larger than the work of adhesion required to reversibly separate the PS surfaces. These three observations indicated that the development of G at the PS/PS interface in the temperature range investigated (<T_g-bulk) was controlled by the diffusion of chain segments feasible above the glass-transition temperature of the interfacial layer, in agreement with our previous findings for fracture stress development at several polymer/polymer interfaces well below T_g-bulk. Close values of G = 8–9 J/m² were measured for the symmetric interfaces of polydisperse PS [M_w = 225 × 10³, weight-average molecular weight/number-average molecular weight (M_w/M_n) = 3] and monodisperse PS (M_w = 200 × 10³, M_w/M_n = 1.04) after healing at T_h = T_g-bulk − 33 °C for 24 h. This implies that the self-bonding of high-molecular-weight PS at such relatively low temperatures is not governed by polydispersity. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1861–1867, 2004     

Graphical analysis of the formation function-II: the pseudo cross-over point

In a further attempt to enhance the possibility of interpreting the formation function, a number of special shapes of the formation function are discussed, which give rise to a pseudo cross-over point. It is shown that under certain conditions a pseudo cross-over point can be found in the following cases: (1) two series of homonuclear complexes, (2) a mixture of a series of homonuclear and polymeric complexes, (3) a series of mononuclear complexes and two polynuclear complexes with nearly the same composition, (4) a system which gives a real cross-over point, and one or more polynuclear complexes, (5) a system of two polynuclear complexes. The conditions are mainly discussed in terms of the composition of the complexes. Calculated curves illustrate the different possibilities.