Thermodynamics of the sorption of organic vapors in a carbosilane dendrimer and a hyperbranched polymer

Fluorinated derivatives of the carbosilane G6 dendrimer and the hyperbranched polymer of the same chemical structure are synthesized and characterized via the method of inverse gas chromatography. For various organic compounds (n-alkanes, aromatic hydrocarbons, partially fluorinated and perfluorinated organic compounds), the following thermodynamic parameters of their interaction with the above polymers are defined: solubility coefficient S, the sorption enthalpy, the partial molar enthalpy of mixing, the Flory-Huggins parameter, and the solubility parameter. The thermodynamic behavior of vapors in the dendrimer is similar to that in the hyperbranched polymer. For a dendrimer and a hyperbranched polymer, a linear correlation between the logarithm of S and T _cr ² is established, where T _cr is the critical temperature of a probe. For both polymers, the partial enthalpy of mixing of n-alkanes is shown to be independent of the dimensions of the probe molecules. This behavior is typical of the vapor sorption in linear polymers at temperatures above the glass transition temperature.     

Transport and physicochemical parameters of polypentenamer

Physicochemical properties of a cis-polypentenamer—a hydrocarbon polymer with a low glass transition temperature (T _g = 168.8 K)—have been studied. Measurements of permeability coefficients P in rubbery material for a wide range of gases (He, H₂, O₂, N₂, CO₂, CH₄, C₂H₆, C₃H₈, and n-C₄H₁₀) indicate a high permeability of this polymer for which the values of P are only slightly lower than those of the most permeable rubber—poly(dimethylsiloxane). The method of inverse gas chromatography has been employed to estimate solubility coefficients S for n alkanes C₃–C₁₀ and cycloalkanes in cis-polypentenamer in the range from 25 to 150°C. It has been shown that the solubility coefficients linearly increase in lnS-T _cr ² coordinates, where T _cr is the critical temperature of a solute. In terms of the above correlation, the solubility coefficients of light gases have been estimated and the diffusion coefficients D of gases in the same polymer have been calculated via the formula P=DS. The free volume in cis-polypentenamer has been studied by positron annihilation lifetime spectroscopy. The temperature dependence of the positronium lifetime τ ₃ that characterizes the size of the free volume element in a polymer demonstrates saturation at temperatures above 250 K. This effect is probably related to a rapid migration of fluctuation holes in the rubbery polymer at temperatures remote enough from its glass transition temperature.     

Potential functions of internal rotation in <Emphasis Type="Italic">n</Emphasis>-alkanes and its contribution to thermodynamic properties

The potential functions of braked internal rotation V(?) in n-alkanes (ethane, propane, butane, n-pentane, n-hexane, n-heptane) were calculated by ab initio and DFT methods with the 6-311++G(3df,3pd) basis set. The functions were approximated as a series of six cosines. The dependences of V(?) on the length of the hydrocarbon chain in n-alkanes were analyzed. The heights of the trans-cis and trans-gauche barriers and the differences between the energies of the trans and gauche conformers were calculated and compared with the experimental data. From the calculated geometric parameters and V(?), the contributions of the braked internal rotation to the enthalpy, entropy, heat capacity, and Gibbs free energy at 298 K were determined. The contributions of internal rotations are transferable within the framework of additive approaches. The generalized function V _av(?) for n-alkanes and averaged contributions of internal rotation of the C-C bonds and CH₃- and -CH₂- tops to the thermodynamic properties were suggested.     

Comparison of Gasoline-Ranged <Emphasis Type="Italic">n</Emphasis>-Alkanes Conversions Using Dielectric Barrier Discharge: A Kinetic Study

Here, we compared the conversion of gasoline-ranged n-alkanes (C₆–C₉) using dielectric barrier discharge. For an energy density of ~68 J/L and an initial n-alkane concentration of ~230 ppm, when carbon number increased from 6 to 9, the energy efficiency of n-alkane conversion increased from 117 to 240 mmol/kWh, CO _x selectivity decreased from 46 to 20%, and ozone concentration increased from 216 to 240 ppm. The effect of energy density and initial n-alkane concentration were also investigated. The understanding of initial step of conversion was greatly aided by a proposed kinetic model. The pathways of consecutive reactions from the initiation to products were also discussed.     

Calculating excess volumes of binary solutions with allowance for structural differences between mixed components

Analytical dependences of a volume’s properties on the differences between the geometric structures of initial monosystems are obtained for binary systems simulated by a grain medium. The effect of microstructural parameter k (the ratio of volumes of molecules of mixed components) on the concentration behavior of the relative excess molar volume of different types of real binary solutions is analyzed. It is established that the contribution due to differences between the volumes of molecules and coefficients of the packing density of mixed components is ~80–100% for mutual solutions of n-alkanes and ~55–80% of the experimental value of the relative excess molar volume for water solutions of n-alcohols.     

The equilibrium structures of the Li[C<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>]<Subscript>1</Subscript> (<Emphasis Type="Italic">n</Emphasis> = 7–12) complexes and their alternation depending on <Emphasis Type="Italic">n</Emphasis>

The equilibrium geometric configurations of the Li[C _n ]₁ (n = 7–12) complexes, where [C _n ]₁ is a cylindrical hydrocarbon containing the simplest zigzag nanotube fragment, were determined by the density functional theory method with the PBE0 exchange-correlation functional. Analytic molecular orbital (MO) estimates were obtained for isolated [C _n ]₁ hydrocarbons in the Hückel approximation. The appearance of nonbonding MOs for hydrocarbons with even n was demonstrated. Equilibrium structure types were found to alternate as n increased. This alternation correlated with the behavior of the frontier orbitals of the [C _n ]₁ hydrocarbon. At odd n, the Li atom was situated near the boundary of the π electron density of the bracelet, and the complex had C _s symmetry. Complexes with even n had the C _2v point group, and lithium was situated in the inner cylinder cavity above the center of one of benzene rings.     

Adsorption properties of γ-Al<Subscript>2</Subscript>O<Subscript>3</Subscript> as measured by gas chromatography

The adsorption properties of γ-Al₂O₃ were studied using gas chromatography. Isotherms of adsorption of n-alkanes (C₆–C₉), hex-1-ene, benzene, and isobutanol were measured within 70–100°C. The isosteric heats of adsorption and contributions to them from dispersion (Δq _dis) and specific (Δq _sp) interactions were determined for hex-1-ene, benzene, and isobutanol. Under the conditions covered, hex-1-ene molecules are adsorbed mainly on account of dispersion interactions. For the adsorption of benzene, Δq _dis is nearly twice as large as Δq _sp, while for the adsorption of isobutanol, Δq _sp is nearly twice as large as Δq _dis. At 100°C, isobutyl alcohol is chemisorbed.     

The thermodynamic parameters of sorption and enantioselectivity of the chiral smectic liquid crystal 2-methylbutyl ester of 4-(4-decyloxybenzylideneamino)-cinnamic acid

The thermodynamic characteristics of sorption of n-alkanes, arenes, aldehydes, monoatomic alcohols, and optical isomers of camphene and butanediol-2,3 by a chiral smectic liquid crystal, 2-methylbutyl ester of 4-(4-decyloxybenzylideneamino)-cinnamic acid, from the gas phase were studied over the temperature range including the S*_C and S*_A mesophases and isotropic phase. The standard and excess thermodynamic functions of sorption were determined for 26 sorbates of the classes of substances specified. The S*_C and S*_A mesophases exhibited selectivity with respect to the separation of para and meta xylenes (α _p/m = 1.06–1.07, 90–108°C) and pronounced enantioselectivity (α_R/S = 1.05–1.09, 87–108°C). The helically twisted structure of the smectic liquid crystal was shown to play an important role in the mechanism of the chiral recognition of optical isomers of polar and low-polarity compounds under gas-liquid chromatography conditions.     

Phase Equilibrium States in the <Emphasis Type="Italic">n</Emphasis>-Dodecane–<Emphasis Type="Italic">n</Emphasis>-Hexadecane–Cyclododecane System

A three-component system comprising cyclododecane and n-alkanes is studied by means of differential thermal analysis on a differential scanning microcalorimeter. It is concluded that the investigated system is of the eutectic type and the n-dodecane–n-hexadecane–cyclododecane eutectic mixture system is 73.0 wt % n-С₁₂Н₂₆, 9.0 wt % n-С₁₆Н₃₄, and 18.0 wt % С₁₂Н₂₄. Its melting point is found to be ?17.7°C.     

First principle study of magnetic and electronic properties of single X (X = Al,Si) atom added to small carbon clusters (C<Subscript> <Emphasis Type="Italic">n</Emphasis> </Subscript>X, <Emphasis Type="Italic">n</Emphasis> = 2–10)

In this paper, the magnetic and electronic properties of single aluminum and silicon atom added to small carbon clusters (C_nX; X = Al, Si; n = 2–10) are studied in the framework of generalized-gradient approximation using density functional theory. The calculations were performed for linear, two dimensional and three dimensional clusters based on full-potential local-orbital (FPLO) method. The total energies, HOMO–LUMO energy gap and total magnetic moments of the most stable structures are presented in this work. The calculations show that C_nSi clusters have more stability compared to C_nAl clusters. In addition, our magnetic calculations were shown that the C_nAl isomers are magnetic objects whereas C_nSi clusters are nonmagnetic objects.     

Compositions of nanoparticles of hexagonal symmetry

The formulas for calculation of the number of atoms in nanoparticles with symmetry group D _6h are reported. The numbers of atoms are determined by six structurally invariant numbers and the “quantum number” of the group order n. Eight classes of nanostructures with symmetry group D _6h are revealed: C _{? + 12z} , where z = 0, 1, 2, …, and C _? is C ₂, C ₆, C ₈, or C ₁₄. The sum rule for the coordination numbers of all atoms of subshells related to symmetry elements is established. Two-dimensional nanoparticles are considered.     

Copolymers of Maleic Anhydride and Methylene Alkanes: Synthesis,Modification, and Pour Point Depressant Properties

Copolymers with the equimolar composition and presumably alternating microstructure are synthesized by the radical copolymerization of methylene alkanes, the products of dimerization of α-olefins with the general formula RCH₂CH₂C(=CH₂)R (R = n-C₄H₇, n-C₆H₁₃, n-C₈H₁₇, n-C₁₀H₂₁, n-C₁₂H₂₅), with maleic anhydride. The products of reactions between the obtained copolymers and 1-octadecanamine or 1-octadecanol are isolated and spectrally characterized. The depressor efficiency of the copolymers with respect to the solutions of paraffins in n-alkanes is studied. Qualitative differences between the copolymers of maleic anhydride with methylene alkanes and reference copolymers based on 1-octadecene are estimated using vibrational viscometry combined with analysis of the size and morphology of paraffin crystals. It is shown that the copolymers with methylene alkanes more effectively decrease the cold filter plugging point (CFPP) of paraffin solutions in n-decane.     

Identification of endogenous and anthropogenic hydrocarbons in bottom deposits of peat lakes and evaluation of their contribution to the “hydrocarbon index”

Gas chromatography with mass spectrometric detection was used to analyze bitumens isolated from bottom sediments of peat lakes contaminated with petroleum products. Endogenous hydrocarbons are characterized by the presence of n-alkanes with an odd number of carbon atoms in the molecule in the characteristic region of C₂₃–C₃₃, the absence of a “hump” characteristic of oil products in the chromatogram, and the presence of light hydrocarbons, eluting in the initial part of the chromatogram (light hydrocarbons are usually lost when the sample is dried). The distribution profile of odd n-alkanes is used to assess the contribution of endogenous hydrocarbons to the “hydrocarbon index” with the help of the pattern recognition method. The concentration of light hydrocarbons is from 50 and 300–400 to 3500–5000 mg/kg for a number of samples and even up to 26000 mg/kg in some samples. The concentration of petroleum hydrocarbons and heteroatomic compounds varies from the lowest values of 30–80 mg/kg up to 20000 mg/kg and higher.     

The inductive effect of a radical center and transferability of the properties of functional groups in <Emphasis Type="Italic">n</Emphasis>-alkyl radicals

Electron density distribution in n-alkyl radicals (from ethyl to n-octyl) was studied by the B3LYP/6-311++G(3df,3pd) DFT method. The theory of atoms in molecules was used to show that the inductive effect of a free valence extends to two neighboring CH₂ groups. The electronegativities χ(C^?H₂) > χ(CH₃) > χ(CH₂) of groups and χ(C^?) > χ(H) > χ(C) atoms were qualitatively determined. The group method for calculating the enthalpies of formation of n-alkyl radicals Δ_f H°(n-C _n H_{2n+ 1}, n > 5) was substantiated.     

Measurement and Modeling the Excess Molar Volumes and Refractive Index Deviations of Binary Mixtures of 2-Propanol, 2-Butanol and 2-Pentanol with <Emphasis Type="Italic">N</Emphasis>-Propylamine

The densities, ρ, and refractive indices, n _D, of 2-alkanols (C₃–C₅) with N-propylamine have been measured for the whole range of composition at temperatures from (298.15–328.15) K at 10 K intervals and ambient pressure of 81.5 kPa, using an Anton Paar DMA 4500 oscillating tube densimeter and an Anton Paar Abbemat 500 automatic refractometer. From the experimental data, excess molar volumes \( V_{\text{m}}^{\text{E}} \) partial molar volumes \( \bar{V}_{i} \) apparent molar volumes V _?i and refractive index deviations Δn _D the binary systems consisting of N-propylamine + 2-alkanols (2-propanol, 2-butanol, 2-pentanol) were calculated and \( V_{\text{m}}^{\text{E}} \) and Δn _D values were correlated with the Redlich–Kister polynomial. The effect of temperature and the chain length of the alcohol on the excess molar volumes and refractive index deviations are discussed in terms of molecular interaction between unlike molecules. The excess molar volumes are negative and refractive index deviations are positive over the entire composition range, which indicates strong hydrogen bonding between molecules of the mixtures. A comparative study has been made of the refractive indices obtained experimentally and those calculated by means of the Lorentz–Lorenz, Weiner and Arago–Biot relations. The perturbed chain statistical associating fluid theory (PC-SAFT), simplified PC-SAFT and Prigogine–Flory–Patterson theory were also applied to correlate and predict the density and excess molar volumes of the mixtures.     

Heat capacities and thermal diffusivities of <Emphasis Type="Italic">n</Emphasis>-alkane acid ethyl esters—biodiesel fuel components

The heat capacities and thermal diffusivities of ethyl esters of liquid n-alkane acids C _n H_2n–1O₂C₂H₅ with the number of carbon atoms in the parent acid n = 10, 11, 12, 14, and 16 are measured. The heat capacities are measured using a DSC 204 F1 Phoenix heat flux differential scanning calorimeter (Netzsch, Germany) in the temperature range of 305–375 K. Thermal diffusivities are measured by means of laser flash method on an LFA-457 instrument (Netzsch, Germany) at temperatures of 305–400 K. An equation is derived for the dependence of the molar heat capacities of the investigated esters on temperature. It is shown that the dependence of molar heat capacity C _p,m (298.15 K) on n (n = 1–6) is close to linear. The dependence of thermal diffusivity on temperature in the investigated temperature range is described by a first-degree polynomial, but thermal diffusivity a (298.15 K) as a function of n has a minimum at n = 5.     

Exact treatment of generalized modifications of finite-dimensional systems by the LRM approach

LRM (Low Rank Modification) is a mathematical method that produces eigenvalues and eigenstates of generalized eigenvalue equations. It is similar to the perturbation expansion in that it assumes the knowledge of the eigenvalues and eigenstates of some related (unperturbed) system. However, unlike perturbation expansion, LRM produces correct results however large the modification of the original system. LRM of finite-dimensional systems is here generalized to the combined (external and internal) modifications. Parent n-dimensional system A _n containing n eigenvalues λ _i and n eigenstates \({| {\Phi_i}\rangle}\) is described by the generalized n × n eigenvalue equation. In an external modification system A _n interacts with another ρ-dimensional system B _ρ which is situated outside the system A _n . In an internal modification relatively small σ-dimensional subsystem of the parent system A _n is modified. Modified system C _n+ρ that contains external as well as internal modifications is described by the generalized (n + ρ) × (n + ρ) eigenvalue equation. This system has (n + ρ) eigenvalues \({\varepsilon_s}\) and (n + ρ) corresponding eigenstates \({| {\Psi_s}\rangle}\) . In LRM this generalized (ρ + n) × (ρ + n) eigenvalue equation is replaced with a (nonlinear) (ρ + σ) × (ρ + σ) equation which produces all eigenvalues \({\varepsilon_s \notin \left\{ {\lambda_i}\right\}}\) and all the corresponding eigenstates \({| {\Psi_s}\rangle }\) of C _{n + ρ}. Another equation produces remaining solutions (if any) that satisfy \({\varepsilon_s \in \left\{ {\lambda_i}\right\}}\) . Those two equations produce exact solution of the modified system C _{n + ρ}. If (ρ + σ) is small with respect to n, this approach is numerically much more efficient than a standard diagonalization of the original generalized eigenvalue equation. Unlike perturbation expansion, LRM produces exact results, however large modification of the parent system A _n .     

Phase transitions in paraffins, <Emphasis Type="Italic">n</Emphasis>-alkane alcohols,and <Emphasis Type="Italic">α,ω</Emphasis>-alkane diols with different chain lengths

A comparative analysis of phase transitions in paraffins (C _n H_2n+2), n-alkane alcohols (C _n H_2n+1OH), and α,ω-alkane diols ?ubC _n H_2n (OH)₂?ub; has been performed via differential scanning calorimetry. The elimination of methodical errors makes it possible to calculate the true values of thermodynamic parameters of phase transitions and to gain insight into their nature. Methods of finding true heat capacity jumps in the region of low-temperature solid-phase transitions of the first order and high-temperature order-disorder transitions of the second-order have been proposed. The quantitative analysis of heat capacity jump profiles has been performed within the framework of the first-order diffuse transition theory and Landau’s theory of order-disorder transitions.     

Processes of hydrogenation of trifluoromethylfullerenes in the mass spectrometer ion source

The processes of hydrogenation of a mixture of trifluoromethylfullerenes was studied in situ by means of positive-and negative-ion mass spectrometry. The effective addition of 1, 5, and 11 hydrogen atoms was revealed. The appearance energies of positive trifluoromethylfullerene ions C ₆₀ (CF₃) _n ⁺ (n = 1–8) and C₆₀(CF₃) _n H⁺ (n = 1, 3, 5, 7) were determined.     

A Systematic Search for Structures and Stabilities of Asymmetric Clusters (HfInN<Subscript>3</Subscript>)<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 1-6)

In order to find single source precursors (SSP), the structures, relative stabilities, and IR spectra of small asymmetric clusters (HFInN₃) _n (n = 1–6) are systematically investigated by means of the density functional theory at the B3LYP level. The obtained geometries show that the frameworks of clusters (HFInN₃) _n (n = 2–6) prefer to be 2n-membered ring with alternating indium and α-nitrogen atoms. The averaged binding energies reveal that all of asymmetric clusters (HFInN₃) _n (n = 1–6) can continue to gain energy as the cluster size n increasing. The second-order difference of energy (Δ₂E) and the HOMO-LUMO energy gap (E_gap) as a function of the cluster size n both exhibit a pronounced even-odd alternation phenomenon. The influences of cluster size n and temperature T on the thermodynamic properties of clusters are discussed. Judged by enthalpies and Gibbs free energies, the formations of the most stable clusters (HFInN₃) _n (n = 2–6) from the monomer are thermodynamically favorable in the range of 200–800 K.