Theoretical investigation of the phase behaviour of model ternary mixtures containing n-alkanes,perfluoro-n-alkanes,and perfluoroalkylalkane diblock surfactants

We have used the hetero-SAFT-VR approach developed by McCabe and collaborators [Mol. Phys. 104, 571 (2006)] to investigate the phase equilibria of a number of binary and ternary mixtures of n-alkanes, perfluoro-n-alkanes, and perfluoroalkylalkane diblock surfactants. We focused our work on the understanding of the microscopic conditions that control the phase behaviour of these mixtures, with a particular emphasis of the effect on the liquid–liquid separation and the stabilisation of n-alkane + perfluoro-n-alkane mixtures when a diblock surfactant is added. We used very simple molecular models for n-alkanes, and perfluoro-n-alkanes that describe the molecules as chains with tangentially bonded segments with molecular parameters taken from the literature. In the particular case of semifluorinated alkanes or SFA surfactants, we used an hetero-segmented diblock chain model where the parameters for the alkyl and perfluoroalkyl segments taken from the corresponding linear alkanes and perfluoroalkanes, as shown in our previous work [J. Phys. Chem. B 111, 2856 (2007)]. Our goal was to identify the main effects on the phase behaviour when different perfluoroalkylalkane surfactants are added to mixtures of n-alkanes and perfluoro-n-alkanes. We selected the n-heptane + perfluoromethane binary mixture, and studied the changes on the phase behaviour when a symmetric (same number of alkyl and perfluoroalkyl chemical groups) or an asymmetric (different number of alkyl and perfluoroalkyl chemical groups) diblock surfactants is added to the binary mixture. We have obtained the phase diagrams of a wide range of binary and ternary mixtures at different thermodynamic conditions. We have found a variety of interesting behaviours as we modify the alkyl or/and the perfluoroalkyl chain-length of the diblock surfactants: the usual changes in the vapour–liquid phase separation, changes in the type of phase diagrams (typically from type I to type V phase behaviour according to the Scott and Konynenburg classification), azeotropy, and Bancroft points. We noted that the main effect of adding a symmetric or an asymmetric surfactant to the n-heptane + perfluoromethane mixture is to stabilise the system, i.e. to decrease the two-phase (liquid–liquid) immiscibility region of the ternary diagram as the surfactant concentration is increased. This effect becomes larger as the chain length of the surfactant is increased, which is consistent with a higher number of alkyl–alkyl and perfluoroalkyl–perfluoroalkyl favourable interactions in the mixture.     

Critical properties of nitrobenzene + n-alkanes solutions

Coexistence curves and critical parameters are given for solutions of nitrobenzene with a series of n-alkanes from n-pentane to n-eicosane. By mixing suitable n-alkanes, a pseudosolvent was obtained and the critical properties of the nitrobenzene + pseudo-n-alkane solution were compared with those of the corresponding binary solution.     

Excess properties of Lennard-Jones binary mixtures from computer simulation and theory

Monte Carlo simulation and theory are used to calculate the excess thermodynamic properties of binary mixtures of spherical Lennard-Jones molecules. We study the excess functions of three binary mixtures characterized by the following size and dispersive energy ratios: (1) (σ₂₂/σ₁₁)³ = 2 and ?₂₂/?₁₁ = 2; (2) (σ₂₂/σ₁₁)³ = 1 and ?₂₂/?₁₁ = 1/2 and (3) (σ₂₂/σ₁₁)³ = 1/2 and ?₂₂/?₁₁ = 2. In all cases, the unlike size parameter, σ₁₂, is kept constant and equal to the value given by the Lorentz combining rule (σ₁₂ = (σ₁₁ + σ₂₂)/2). However, different unlike dispersive energy parameter values are considered through the following combining rules: (a) ?₁₂ = (?₁₁?₂₂)^1/2 (Berthelot rule); (b) ?₁₂ = ?₁₁ (association); and (c) ?₁₂ = ?₂₂ (solvation). The pressure and temperature dependence of the excess volume and excess enthalpy is studied using the NpT Monte Carlo simulation technique for all the systems considered. Additionally, the simplest conformal solution theory is used to check the adequacy of this approach in predicting the excess properties in a wide range of thermodynamic conditions and variety of binary mixtures. In particular, we have applied the van der Waals one-fluid theory to describe Lennard-Jones binary mixtures through the use of the Johnson et al. [1993, Molec. Phys., 78, 591] Helmholtz free energy. Agreement between simulation results and theoretical predictions is excellent in all cases and thermodynamic conditions considered. This work confirms the applicability of the van der Waals one-fluid theory in predicting excess thermodynamic properties of mixtures of spherical molecules. Furthermore, since binary mixtures of spherical Lennard-Jones molecules constitute the reference fluid to be used in perturbation theories for complex fluids, such as the statistical association fluid theory (SAFT), this work shows clearly the applicability of the conformal solution theory within the framework of SAFT for predicting excess functions.     

Molecular simulation of adsorption and transport diffusion of model fluids in carbon nanotubes

Grand canonical Monte Carlo (GCMC) and dual-control-volume grand canonical molecular dynamics (DCV-GCMD) simulations were carried out with Lennard-Jones model fluids in carbon nanotubes, with the objective of investigating the effect of varying molecular properties on adsorption and diffusion. The influence of the molecular weight, and the Lennard Jones parameters σ (a measure of the molecule size) and ? (a measure of the interaction strength) on adsorption isotherms, fluxes, and transport diffusivities was studied. For these simulations, the properties of component 1 in the mixture were held constant and one of the properties of component 2 was changed systematically. Furthermore, the validity of Graham's law, which relates the fluxes of two counter diffusing species to their molecular weight, was investigated on a molecular level. Graham's law is fulfilled for the whole range of molecular weights and Lennard-Jones parameters σ investigated. However, large deviations were observed for large values of ?₂. Here, the interaction of the two components in the mixture becomes so strong that component 1 is dragged along by component 2.     

The non-Fermi-liquid nature of the metallic states of the Hubbard Hamiltonian

It has long since been argued that the metallic states of the single-band Hubbard Hamiltonian ? in two spatial dimensions (i.e. for d = 2) should be non-Fermi liquid, a possibility that would lead to the understanding of the observed anomalous behaviour of the doped copper-oxide-based superconducting compounds in their normal metallic states. Here we present a formalism which enables us to express, for arbitrary d, the behaviour of the momentum-distribution function nσ(k) pertaining to uniform metallic ground states of ? close to S _F; σ (the Fermi surface of the fermions with spin index σ, σ = ↑, ↓) in terms of a small number of constant parameters which are bound to satisfy certain inequalities implied by the requirement of the stability of the ground state of the system. These inequalities restrict the range of variation in nσ(k) for k infinitesimally inside and outside the Fermi sea pertaining to fermions with spin index σ and consequently the range of variation in the zero-temperature limit of nσ(k) for k on S _F; σ On the basis of some available accurate numerical results for nσ(k) pertaining to the Hubbard and the t-J Hamiltonian, we conclude that, at least in the strong-coupling regime, the metallic ground states of ? for d = 2 cannot be Fermi-liquid nor can they in general be purely Luttinger or marginal Fermi liquids. We further rigorously identify the pseudogap phenomenon, or 'truncation' of the Fermi surface, clearly observed in the normal states of underdoped copper-oxide-based superconductors, as corresponding to a line of resonance energies (i.e. these energies strictly do not relate to quasiparticles) located below the Fermi energy, with a concomitant suppression to zero of the jump in nσ(k) over the 'truncated' parts of the Fermi surface. Our analyses make explicit the singular significance of the non-interacting energy dispersion ε _k underlying ? in determining the low-energy spectral and transport properties of the metallic ground states of ?.     

Assessment of body composition and total energy expenditure in humans using stable isotope techniques; IAEA Human Health Series No. 3

During the last decade compound-specific deuterium (²H) analysis of plant leaf wax-derived n-alkanes has become a promising and popular tool in paleoclimate research. This is based on the widely accepted assumption that n-alkanes in soils and sediments generally reflect δ²H of precipitation (δ²H_prec). Recently, several authors suggested that δ²H of n-alkanes (δ²H_n-alkanes) can also be used as a proxy in paleoaltimetry studies. Here, we present results from a δ²H transect study (～1500 to 4000 m above sea level [a.s.l.]) carried out on precipitation and soil samples taken from the humid southern slopes of Mt. Kilimanjaro. Contrary to earlier suggestions, a distinct altitude effect in δ²H_prec is present above ～2000 m a.s.l., that is, δ²H_prec values become more negative with increasing altitude. The compound-specific δ²H values of nC₂₇ and nC₂₉ do not confirm this altitudinal trend, but rather become more positive both in the O-layers (organic layers) and the A_h-horizons (mineral topsoils). Although our δ²H_n-alkane results are in agreement with previously published results from the southern slopes of Mt. Kilimanjaro [Peterse F, van der Meer M, Schouten S, Jia G, Ossebaar J, Blokker J, Sinninghe Damsté J. Assessment of soil n-alkane δD and branched tetraether membrane lipid distributions as tools for paleoelevation reconstruction. Biogeosciences. 2009;6:2799–2807], a re-interpretation is required given that the δ²H_n-alkane results do not reflect the δ²H_prec results. The theoretical framework for this re-interpretation is based on the evaporative isotopic enrichment of leaf water associated with the transpiration process. Modelling results show that relative humidity, decreasing considerably along the southern slopes of Mt. Kilimanjaro (from 78?% in ～2000 m a.s.l. to 51?% in 4000 m a.s.l.), strongly controls δ²H_{leaf water}. The modelled ²H leaf water enrichment along the altitudinal transect matches well the measured ²H leaf water enrichment as assessed by using the δ²H_prec and δ²H_n-alkane results and biosynthetic fractionation during n-alkane biosynthesis in leaves. Given that our results clearly demonstrate that n-alkanes in soils do not simply reflect δ²H_prec but rather δ²H_{leaf water}, we conclude that care has to be taken not to over-interpret δ²H_n-alkane records from soils and sediments when reconstructing δ²H of paleoprecipitation. Both in paleoaltimetry and in paleoclimate studies changes in relative humidity and consequently in δ²H_n-alkane values can completely mask altitudinally or climatically controlled changes in δ²H_prec.     

Size-dependent diffusion in cycloalkanes

The translational diffusion constants, D, of biphenyl, trans-stilbene, 1,4-diphenyl-1,3-butadiene, 1,1,4,4-tetraphenyl-1,3-butadiene, 1,6-diphenyl-1,3,5-hexatriene, tetraphenylethylene, 9,10-diphenylanthracene, bibenzyl, triptycene, perylene and 2,3-benzanthracene (tetracene) have been measured in combinations of the cycloalkanes cyclohexane, methylcyclohexane, n-butylcyclohexane, cis-decalin and trans-decalin using capillary flow techniques. Tetracene and chrycene have been studied in a series of n-alkanes. Deviations from the Stokes–Einstein (SE) relation (D?=?k _B T/6πηr) were found. For a given solute, the hydrodynamic radius r decreases as both the viscosity?η?and the solvent/solute size ratio increase; the data were fitted to D/T?=?A/η ^?p with p<1 (p?=?1 for the SE relation). The p values in the cycloalkanes increase as the solute size increases, are compared to the values in the n-alkanes and are discussed in terms of the properties of the two types of solvent. The experimental D values also are compared to the predictions of the Wilke–Chang equation and a free volume model which includes both the masses and sizes of the solution components.     

Analytical representation of the density derivative of the Percus–Yevick hard-sphere radial distribution function

ABSTRACT

Explicit analytical expressions are presented for the density derivative, ?g_HS(R; ρ)/?ρ, of the Percus–Yevick approximation to the hard-sphere radial distribution function for R ≤ 6σ, where σ is the hard-sphere diameter and ρ = (N/V)σ³ is the reduced density, where N is the number of particles and V is the volume. A FORTRAN program is provided for the implementation of these for R ≤ 6σ, which includes code for the calculation of g_HS(R; ρ) itself over this range. We also present and incorporate within the program code convenient analytical expressions for the numerical extrapolation of both quantities past R = 6σ. Our expressions are numerically tested against exact results.     

On the difference between a point multipole and an equivalent linear arrangement of point charges in force field models for vapour–liquid equilibria; partial charge based models for 59 real fluids

The replacement of a point dipole and a point quadrupole by a corresponding linear arrangement of two point charges (+q, ?q) and accordingly three point charges (+q, ?2q, +q) is studied with respect to vapour–liquid equilibria. The dependence of saturated liquid density, vapour pressure and heat of vaporization on the choice of the distance d between the charges in the point charge arrangement is analysed. For the studied dipolar two-centre Lennard-Jones (2CLJD) and quadrupolar two-centre Lennard-Jones (2CLJQ) models, d/σ between 1/15 and 1/20 is a reasonable compromise between numerical and physical accuracy, where σ is the Lennard-Jones size parameter. The results are used to derive validated partial charge based models of 59 real fluids from previously published point dipole and point quadrupole based models.     

A new method for deriving atomic charges and dipoles for n, -alkanes: investigation of transferability and geometry dependence

Atomic charge models are known to be unsatisfactory for representing the ab initio electrostatic potential (ESP) of n, -alkanes. A new method for deriving atomic charges and dipoles is proposed and applied to n-alkanes ranging from C₄ to C₁₀. Electrostatic parameters found by this method reproduce accurately the ab initio ESP. The issues of transferability and conformational dependence are also addressed by introducing charges and dipoles taken from a truncated distributed multipole analysis, in the same spirit as the restrained electrostatic potential method. A transferable model is proposed for larger alkanes (>C₁₀). We also estimate the error made when using a set of Boltzmann-weighted electrostatic parameters for all conformers. The reduced number of electrostatic sites considered in our model makes it suitable for computer simulation of liquid n-alkanes.     

Proton conductivity and ferroelectric phase transition in hydrogen-bonded ferroelectric NH4IO3

We report on the ac dielectric permittivity (ε) and the electric conductivity (σ_ω), as function of the temperature 300?K?T4IO₃. The main feature of our measured parameters is that, the compound undergoes a ferroelectric phase transition of an improper character, at (368?±?1)K from a high temperature paraelectric phase I (Pm2₁ b) to a low temperature ferroelectric phase II (Pc21n). The electric conduction seems to be protonic. The frequency dependent conductivity has a linear response following the universal power law (σ_{( ω )}?=?A(T)ω ^{s (T)}). The temperature dependence of the frequency exponent s suggests the existence of two types of conduction mechanisms.     

Phase transformations in calcite from electrical impedance measurements

The phase transformation in calcite I-IV-V and calcite ? aragonite have been characterized by electrical impedance measurements at temperatures 600–1200°C and pressures 0.5–2.5?GPa in a piston cylinder apparatus. The bulk conductivity σ has been measured from Argand plots in the frequency range 10⁵–10^?2?Hz in an electric cell representing a coaxial cylindrical capacitor. The synthetic polycrystalline powder of CaCO₃ and natural crystals of calcite were used as starting materials. The transformation temperature T_c was identified from resistivity-temperature curves as a kink point of the activation energy. At pressure above 2?GPa in ordered phase calcite I, the activation energy E _σ is c. 1.05?eV, and in disordered phase calcite V E _σ is c. 0.75?eV. The pressure dependence of T_c for the rotational order–disorder transformation in calcite is positive for pressures <1?GPa and negative for pressures >1?GPa. The transformation boundary of calcite 1–IV is observed only during first heating in samples after a long annealing at low temperatures. The activation energy of calcite I???IV decreases gradually from 1.8 to 1.05?eV with the pressure increase from 0.5 to 2?GPa. The kinetics of calcite ? aragonite transformation has been monitored by measuring a time-variation of the electrical resistance of a calcite sample at 10³?Hz in the stability P-T field of aragonite. The variation of the impedance correlates with the degree of phase transformation, estimated from X-ray powder diffraction studies on quenched products of experiments. The kinetics of calcite ? aragonite transformation may be fitted to the Avrami kinetics with the exponent m???1–1.5.     

Ab initio potential energy surface for the nitrogen molecule pair and thermophysical properties of nitrogen gas

A four-dimensional potential energy hypersurface (PES) for the interaction of two rigid nitrogen molecules was determined from high-level quantum-chemical ab initio computations. A total of 408 points for 26 distinct angular configurations were calculated utilizing the counterpoise-corrected supermolecular approach at the CCSD(T) level of theory and basis sets up to aug-cc-pV5Z supplemented with bond functions. The calculated interaction energies were extrapolated to the complete basis set limit and complemented by corrections for core–core and core–valence correlations, relativistic effects and higher coupled-cluster levels up to CCSDT(Q). An analytical site–site potential function with five sites per nitrogen molecule was fitted to the interaction energies. The PES was validated by computing second and third pressure virial coefficients as well as shear viscosity and thermal conductivity in the dilute-gas limit. An improved PES was obtained by scaling the CCSDT(Q) corrections for all 408 points by a constant factor, leading to quantitative agreement with the most accurate experimental values of the second virial coefficient over a wide temperature range. The comparison with the best experimental data for shear viscosity shows that the values computed with the improved PES are too low by about 0.3% between 300 and 700?K. For thermal conductivity large systematic deviations are found above 500?K between the calculated values and most of the experimental data.     

Exact short time dynamics for steeply repulsive potentials

The autocorrelation functions for the force on a particle, the velocity of a particle and the transverse momentum flux are studied for the power law potential v(r)=ε(σr)^ν (soft spheres). The latter two correlation functions characterize the Green–Kubo expressions for the self-diffusion coefficient and shear viscosity. The short-time dynamics is calculated exactly as a function of ν. The dynamics is characterized by a universal scaling function S(τ), where τ=t/τ_ν and τ_ν is the mean time to traverse the core of the potential divided by ν. In the limit of asymptotically large ν this scaling function leads to delta function in time contributions in the correlation functions for the force and momentum flux. It is shown that this singular limit agrees with the special Green–Kubo representation for hard-sphere transport coefficients. The domain of the scaling law is investigated by comparison with recent results from molecular dynamics simulation for this potential.     

Prediction of vicinal proton–proton coupling constants 3 J HH from density functional theory calculations

Vicinal coupling constants ³ J _HH have been calculated at the optimized geometries for a series of selected molecules with the aim of developing a practical procedure for predicting this kind of coupling. Calculations of couplings and optimizations of molecular geometries have been carried out at the DFT/B3LYP level using a moderate sized basis set. When the Fermi contact contributions to ³ J _HH calculated for 25 mono- and 23 1,1-di-substituted ethanes are multiplied by a factor of 0.904, the corresponding predicted couplings J ^pre are in good agreement with the experimental J ^exp couplings, with standard deviation σ of 0.10?Hz. When such a comparison is carried out for the remaining sets of molecules the σ deviation increases to 0.26?Hz for a dataset of 21 couplings from 11 monosubstituted cyclohexanes, to 0.19?Hz for a dataset of 40 couplings from 6 norbornane type molecules and to 0.25?Hz for a dataset of 54 couplings from 14 three-membered rings. For the complete dataset of 163 couplings the?σ?deviation amounts to 0.20?Hz. This figure is further reduced to 0.17?Hz by adding to the J ^pre coupling a small correction given by the term ?0.15cos?, depending on the dihedral angle ? between the coupled protons. A larger σ deviation of 0.31?Hz was reported for the best empirically parameterized extended Karplus equation. DFT J ^pre values could be further improved by more accurate calculations for the pertinent substituted ethane constituents of the molecule in question by applying a substituent effect model.     

Simple pair potential model for real fluids. II. Transport properties of dilute gases

The collision integrals required for evaluating the dilute gas transport properties have been computed for the hybrid pair potential of Nezbeda. Calculations of viscosity and self-diffusion coefficients of Ar, Kr, Xe, and CH₄ have been made and the results compared with those based on the Lennard-Jones potential. It is found that (i) the potential parameters determined from the viscosity give the attractive force constant,C ₆, in good agreement with experimental data, (ii) the accuracy of calculated viscosity is reasonable even at low temperatures, and (iii) the hybrid model gives in all cases much better results than the Lennard-Jones potential.     

Scaling laws of aquatic locomotion

In recent years studies of aquatic locomotion have provided some remarkable insights into the many features of fish swimming performances. This paper derives a scaling relation of aquatic locomotion CD(Re)~2 =(Sw)~2 and its corresponding log law and power law. For power scaling law,(Sw)~2 = β_nRe~((2-1)/n), which is valid within the full spectrum of the Reynolds number Re=UL/v from low up to high, can simply be expressed as the power law of the Reynolds number Re and the swimming number Sw=ωAL/v as Re ∝ (Sw)~σ,with σ=2 for creeping flows,σ=4/3 for laminar flows, σ=10/9 and σ=14/13 for turbulent flows. For log law this paper has derived the scaling law as Sw ∝ Re=(lnRe+1.287), which is even valid for a much wider range of the Reynolds number Re. Both power and log scaling relationships link the locomotory input variables that describe the swimmer's gait A;ω via the swimming number Sw to the locomotory output velocity U via the longitudinal Reynolds number Re, and reveal the secret input-output relationship of aquatic locomotion at different scales of the Reynolds number.     

Characterization of organic–inorganic hybrid layered perovskite and intercalated compound (n-C12H25NH3)2ZnCl4

We report on some electrical properties and solid–solid phase transitions of organic–inorganic hybrid layered halide perovskite and intercalated compound (n-C₁₂H₂₅NH₃)₂ZnCl₄ which is one member of the long-chain compounds of the series (n-C_nH_2n+1NH₃)_2,(n = 8–18). The complex dielectric permittivity ?*(ω,T) and the ac conductivity σ (ω,T) were measured as functions of temperature 100 K < T < 390 K and frequency 5 kHz < f < 100 kHz. Moreover, the differential scanning calorimetery and the differential thermal analysis thermograms were performed. The analysis of our data confirms the existence of a structural phase transition at T ≈ (362?±?2) K, where the compound changes its state from intercalation to non-intercalation with a drastic increase in the c-axis by about 16.4%.

The behavior of the frequency-dependent conductivity follows the Jonscher universal power law: σ (ω, T) α?^s(?,T). The mechanism of electrical conduction in the low-temperature phase (phase II) can be described as quantum mechanical tunneling model.