Van der Waals model and equation of state of nitrobenzene-alkanes solutions near the critical consolute temperature

On the basis of the fluctuation theory of phase transitions a system close to the critical point is the ideal gas of order parameter fluctuations. An extended equation of state for binary solutions close to the critical consolute temperature has been proposed taking into account the properties of a real Van der Waals gas in this model. This equation has been used to analyze the temperature dependences of the concentrations of a series of nitrobenzene + alkane binary solutions in terms of different order parameters. It has been shown that the molar concentration of the solution should be used as an order parameter of the analyzed systems. It has been determined that the parameters of the extended equation of state are linear functions of (a) the number of carbon atoms in alkanes and (b) the compressibility factor of the solution components.     

Depolarized light scattering from critical polymer blends

Depolarized light scattering of binary polymer blends in disordered state near the demixing critical point is considered both theoretically and experimentally. It is shown that the depolarized scattering in such systems is predominantly due to double scattering processes induced by composition fluctuations. For long enough polymer chains, this scattering is stronger than the contribution from intrinsic anisotropy fluctuations. The general equation for the static and dynamic double scattering function is obtained in terms of the system structure factor. The scattering functions are calculated both analytically and numerically (dynamic part) for polymer blends. We found that the depolarized intensity depends on the polymerization degree N and the relative distance from the critical point τ = 1 – χ*/χ (where χ is the Flory‐Huggins interaction parameter and χ* its critical value) as I_vh ∼︁ N²/τ², which is in good agreement with the experimental data. It is also shown that the dynamic scattering function is decaying non‐exponentially. We calculate the relaxation rate and the non‐exponentiality parameter as functions of the scattering angle and τ. These theoretical predictions are compared with experimental data for three chemically different blends.     

The use of transition-state theory to extrapolate rate coefficients for reactions of H atoms with alkanes

The thermochemical kinetics formulation of conventional transition state theory has been applied to metathesis reactions of H atoms with a series of alkanes in order to provide a sound framework for the intercomparison of experimental data, and also to extrapolate rate coefficients to temperature regimes that may lie beyond the range of experiments. The calculations require a value for the rate coefficient at some temperature, necessitating a discussion of the extant experimental data and their reliability. The procedures are described, the results of the calculations are presented, and their agreement with experimental data (for methane, ethane, propane, butane, pentane, isobutane, cyclopropane, cyclohexane, neopentane, neooctane, and 2,2,3-trimethylbutane) is discussed. A general expression for reactions of H with large (more than 4 carbons) alkanes is proposed: where n_p, n_s, and n_t are the numbers of primary, secondary, and tertiary H atoms available for abstraction.     

Phase transition and elastic constants of 4-n-octyl-4′-cyanobiphenyl (8CB) obtained using the light-scattering anisotropy of turbidity

Abstract

A light-scattering technique was used to study the anisotropy of turbidity and the three elastic constants K ₁, K ₂ and K ₃ of 8CB as a function of temperature and sample thickness. The turbidity was measured in the nematic and schematic A phases at sample thicknesses l of 0.02, 0.04, 0.1 and 0.2 cm. The effect of the smectic-like (cybotactic nematic) order was observed near the smectic A-nematic phase transition. Owing to the surface-enhanced cybotactic order, evaluation of the elastic constants and order parameter was possible only from the turbidity data at l = 0.2 cm. From the divergence of both K ₂ and K ₃ near T_{S A N} we estimated an average critical exponent value v of 0.65, suggesting that S_A-N in 8CB is a second-order phase transition. The magnetic-field quenching of director fluctuations showed observed effects on the order of magnitude of the temperature dependence of the turbidities, elastic constants and order parameter.     

Effect of electrolytes on the critical temperature of separation and physicochemical properties of binary liquid systems

The effect ions have on the equilibrium and kinetic properties of solutions near the critical temperature of separation is studied. From an analysis of the experimental data obtained in the work and from the literature it is shown that adding ions to a solution increases the correlation length of the system and changes the magnitude of the fluctuation part of the thermodynamic potential and the forces of interaction among the order parameter fluctuations in the vicinity of the critical point. This changes the parameters of the extended equation of state, increases the viscosity of substances, and lowers the coefficient of volume expansion of the system.     

Dynamic Odd–Even Effect in Liquid n‐Alkanes near Their Melting Points

n‐Alkanes are the textbook examples of the odd–even effect: The difference in the periodic packing of odd‐ and even‐numbered n‐alkane solids results in odd–even variation of their melting points. However, in the liquid state, in which this packing difference is not obvious, it seems natural to assume that the odd–even effect does not exist, as supported by the monotonic dependence of the boiling points of n‐alkanes on the chain length. Herein, we report a surprising odd–even effect in the translational diffusional dynamic properties of n‐alkanes in their liquid states. To measure the dynamics of the molecules, we performed quasi‐elastic neutron scattering measurements near their melting points. We found that odd‐numbered n‐alkanes exhibit up to 30 times slower dynamics than even‐numbered n‐alkanes near their respective melting points. Our results suggest that, although n‐alkanes are the simplest hydrocarbons, their dynamic properties are extremely sensitive to the number of carbon atoms.     

Comparability graphs and molecular properties III. C9 and C10 alkanes

The graph-theoretical approach recently developed for comparing and ordering isomeric chemical compounds is extended and applied to the calculation of various molecular properties of C₉ and C₁₀ alkanes (critical densities, volumes, and pressures; heats and entropies of vaporization; standard entropies in liquid and gas state). The key to the approach is in specifying subsets of comparable isomers which are located in the same paths in the so-called comparability graphs. Optimized samples for structure-property correlations are thus obtained.     

Size‐Dependent Melting Temperature of Polymers

A general model for all kinds of size‐dependent melting points, free of any adjustable parameter, is extended to illustrate the size‐dependence of the melting temperature of polyethylene (PE). The model prediction for the depression of the melting temperature of PE is consistent with the calorimetric experimental results as shown in the Figure where the melting temperature of lamellae PE crystals as a function of the thickness of the crystals is presented.

The T_m(D) function of PE shown as a solid line in terms of Equation ( 4 ). The necessary parameters for use of Equation ( 4 ) are shown in Table 1 . The symbols ○ and • denote the experimental evidence of T_m(D) of linear alkanes 14 and cyclic alkanes, 14 respectively. The values of D are determined by D = 0.1273n 6 with 0.1273 nm being the orthorhombic C C lattice distance in the c‐direction. 5 The symbol □ denotes the experimental evidence of chain‐extended PE. 6     

On the Gas‐Phase Reactivity of Complexed OH+ with Halogenated Alkanes

OH⁺ is an extraordinarily strong oxidant. Complexed forms (L? OH⁺), such as H₂OOH⁺, H₃NOH⁺, or iron–porphyrin‐OH⁺ are the anticipated oxidants in many chemical reactions. While these molecules are typically not stable in solution, their isolation can be achieved in the gas phase. We report a systematic survey of the influence on L on the reactivity of L? OH⁺ towards alkanes and halogenated alkanes, showing the tremendous influence of L on the reactivity of L? OH⁺. With the help of with quantum chemical calculations, detailed mechanistic insights on these very general reactions are gained. The gas‐phase pseudo‐first‐order reaction rates of H₂OOH⁺, H₃NOH⁺, and protonated 4‐picoline‐N‐oxide towards isobutane and different halogenated alkanes C_nH_2n+1Cl (n=1–4), HCF₃, CF₄, and CF₂Cl₂ have been determined by means of Fourier transform ion cyclotron resonance meaurements. Reaction rates for H₂OOH⁺ are generally fast (7.2×10^?10–3.0×10^?9 cm³ mol^?1 s^?1) and only in the cases HCF₃ and CF₄ no reactivity is observed. In contrast to this H₃NOH⁺ only reacts with tC₄H₉Cl (k_obs=9.2×10^?10), while 4‐CH₃‐C₅H₄N‐OH⁺ is completely unreactive. While H₂OOH⁺ oxidizes alkanes by an initial hydride abstraction upon formation of a carbocation, it reacts with halogenated alkanes at the chlorine atom. Two mechanistic scenarios, namely oxidation at the halogen atom or proton transfer are found. Accurate proton affinities for HOOH, NH₂OH, a series of alkanes C_nH_2n+2 (n=1–4), and halogenated alkanes C_nH_2n+1Cl (n=1–4), HCF₃, CF₄, and CF₂Cl₂, were calculated by using the G3 method and are in excellent agreement with experimental values, where available. The G3 enthalpies of reaction are also consistent with the observed products. The tendency for oxidation of alkanes by hydride abstraction is expressed in terms of G3 hydride affinities of the corresponding cationic products C_nH_2n+1⁺ (n=1–4) and C_nH_2nCl⁺ (n=1–4). The hypersurface for the reaction of H₂OOH⁺ with CH₃Cl and C₂H₅Cl was calculated at the B3 LYP, MP2, and G3_m* level, underlining the three mechanistic scenarios in which the reaction is either induced by oxidation at the hydrogen or the halogen atom, or by proton transfer.     

Equation for the interfacial tension between demixed polymer solutions

The theory of Cahn and Hilliard is used to derive an equation for the interfacial tension (free energy) between some demixed polymer solutions, applying a simple solution model treated by Debye in his theory of light scattering near the critical solution temperature. For a (symmetrical) system containing two polymers in a common solvent it is found that the interfacial tension is given by σ = (l/12^½)Ω_φp ²σ_r, where l is the Debye l parameter for the range of molecular interaction—here equal to (2S² )^½, where (S² )^½ is the radius of gyration of both polymers, Ω is a heat of mixing parameter for polymer-polymer interaction, φ_p is the total volume fraction of polymer and σ_r is a function of the ratio of temperature and critical solution temperature. The equation is in qualitative agreement with experiments of Langhammer and Nestler.     

Pyrolysis gas chromatography/mass spectrometry of polyvinylsilanes. Mass spectrometric characteristics of alkanes and alkenes containing two or more triorganosilyl substituents

Pyrolysis gas chromatography/mass Spectrometry was applied to the investigation of homopolymers obtained from trimethyl-, n-pentyldimethyl-, n-octyldimethyl- and trideuteromethyldimethyl-vinylsilanes. The electron impact-induced fragmentation of alkanes, alkenes and alkadienes containing two or more corresponding silyl substituents and resulting from pyrolysis of polymers was elucidated. The most characteristic fragmentation patterns of trimethylsilyl-substituted compounds are due to the loss of HSi(CH₃)₃ and Si(CH₃)₄ from M^+˙, the order of which depends on the presence or absence of a double bond in hydrocarbon chain. The same structural parameter determines the probability of the characteristic decomposition of n-alkyldimethylsilyl-substituted compounds through the loss of alkene and alkyl groups from the molecular ions.     

Large Volume Injection in Fast Gas Chromatography with On‐Column Injector

In this work a fast gas chromatography set‐up with on‐column injection was optimized and evaluated with a model mixture of C₈–C₂₈ n‐alkanes. Usual injection volumes when using narrow‐bore (e. g., 0.1 mm i.d.) analytical columns are ca. 0.1 μL. The presented configuration allows introduction of 10–30‐fold larger sample volumes without any distortion of peak shapes. In the set‐up a normal‐bore retention gap (1 m×0.32 mm i. d.) was coupled to a narrow‐bore (4.8 m×0.1 mm i. d.×0.4 μm film thickness) analytical column using a low dead volume column connector. The effects of the experimental conditions such as inlet pressure, sample volume, initial injection temperature, and oven temperature on a peak focusing are discussed. H‐u curves for helium and hydrogen are used to compare their suitability for high speed gas chromatography and to show the dependence of separation efficiency on the carrier gas velocity at high inlet pressures. In the fast gas chromatography system a baseline separation of C₁₀–C₂₈ n‐alkanes was achieved in less than 3 minutes.     

The Effect of Conformational Changes on the Catalytic Transformations of n-Alkanes

Temperature induced conformational changes of various alkanes were studied. n-Hexane was studied in order to demonstrate its ability to be involved in C₅ and C₆ ring closure reactions, while long chain alkanes, such as C₈, C₁₆ and C₂₄, were investigated with the aim to calculate their temperature dependent molecular diameter controlling their penetration ability into zeolite channels.     

Vapor–liquid critical properties of multi-component mixtures containing carbon dioxide and n-alkanes

Vapor–liquid critical temperatures, pressures and densities of multi-component mixtures containing CO₂ and n-alkanes (C4–C7) were measured in a high-pressure view cell by direct visual observations. The molar ratio of alkanes was fixed during the experiment while the composition of CO₂ was varied over the whole range. The critical loci show type I fluid phase behavior if the n-alkanes mixture is treated as a pseudo-continuous component, while correspondingly, CO₂ is a discrete component. The critical properties were calculated by Redlich–Kwong–Soave equation of state (SRK) combined with a renormalization group correction (RG). The predictions of critical properties by SRK + RG are in good agreement with the experimental results.     

X-ray study of the nematic and smectic A phases of the cyano-substituted pyridines

We report an X-ray study of lamellar ordering in the nematic and smectic A phases of a homologous series of polar liquid crystals, the 2-(4-alkylphenyl)-5-cyanopyridines (nCP). Experiments were carried out using a diffractometer with a linear position sensitive detector. In the nematic and smectic A phases of the nCP and their mixtures with non-polar 4-n-butyl-4′-methoxyazoxybenzene two types of layering were found. One corresponds to the fluctuations of the smectic density wave with a monolayer wavevector q ₁, and the other is due to the partial bilayer fluctuations with the incommensurate wavevector q ₂ ≠ q ₁/2. The temperature dependences of the X-ray scattering intensity and the longitudinal correlation length for both types of layering in the nematic phase are presented. The critical behaviour in the vicinity of the smectic A-nematic phase transition occurs for a fluctuation mode, either q ₁ or q ₂, depending on the position on the liquid crystal phase diagram. The influence of the molecular structure of cyano-substituted pyridines on the formation of layered structures of different types is also discussed.     

Synthesis and physical properties of high birefringence phenylacetylene liquid crystals containing a cyclohexyl group

We have synthesized new phenylacetylene-based liquid crystals containing a cyclohexyl or cyclohexylethyl group and evaluated their physical properties in order to develop a range of materials having high value of birefringence. The cyclohexyl-containing compounds exhibited nematic behaviour near room temperature and moderate values of δn of around 0.3. The cyclohexylethyl-containing compounds had a very wide nematic range with a high T_NI and very high values of δn of over 0.4. They also exhibited low viscosities. The order parameter was not affected by introducing either a cyclohexyl or a cyclohexylethyl group and the values of δn based on calculated polarizabilities were obtained experimentally.     

A viscosity equation for polyatomic fluids under normal and high pressures

In this work, we relate the self-diffusion coefficient to the residual entropy of the system according to the free volume theory and scaling principle. The viscosity equation for a freely jointed Lennard-Jones chain fluid is then obtained from the expression of self-diffusion coefficient by applying the Stokes–Einstein equation. The real polyatomic compounds are modeled as chains of tangent Lennard-Jones segments. The segment size and energy parameter as well as chain length (expressed by the number of segments) are obtained from the experimental viscosity data. The proposed viscosity equation reproduces the experimental viscosity data with an average absolute deviation of 5.12% for 18 polyatomic compounds (1600 data points) over wide ranges of temperature and pressure. For engineering applications, the generalized model parameters for normal alkanes with the number of carbon atoms n > 3 are proposed. The segment energy parameter is suggested to be evaluated from the critical temperature, and the segment size parameter and chain length are correlated with the number of carbon atoms in an alkane molecule.     

Studies on the Physical Adsorption Equilibria of Gases on Porous Solids over a Wide Temperature Range Spanning the Critical Region—Adsorption on Microporous Activated Carbon

Adsorption equilibria of nitrogen and methane on microporous ( < 2 nm) activated carbon were measured for a wide temperature range (103‐298 K) spanning the critical region. Information relating to Henry constants, the isosteric heat of adsorption, and the amount of limiting adsorption were evaluated. All isotherms show type‐I features for both sub‐ and supercritical temperatures. A new isotherm equation and a consideration for the importance of the effect of the adsorbed phase volume allow this kind of isotherms to be modeled satisfactorily. The model parameter of the saturated amount of absolute adsorption (n⁰_t) equals the limiting adsorption amount (n^itm), leaving the physical meaning of the latter clarified, and the exponent parameter (q) proves to be an appropriate index of surface heterogeneity.