Use of normal boiling point correlations for predicting critical parameters of paraffins for vapour–liquid equilibrium calculations with the SRK equation of state

Correlations between normal boiling points and critical parameters (critical temperatures and critical pressures) and between normal boiling points and acentric factors of normal and branched paraffins in the range from C₇ to C₁₀₀ have been developed. These correlations can be used to quickly and easily compute critical properties that allow to reproduce closely, by means of the Soave–Redlich–Kwong (SRK) equation of state (EoS), the vapour pressure of pure compounds. In the range of 0.5–5 mmHg the values of vapour pressure calculated by means of the SRK EoS become less accurate and they can be improved using a different equation for the temperature-depending attractive parameter (i.e., the Mathias–Copeman alpha function) instead of the classical Soave function.     

The Soave,Twu and Boston–Mathias alpha functions in cubic equations of state. Part II. Modeling of thermodynamic properties of pure compounds

Cubic equations of state (EoS) are commonly used for industrial applications, due to their simplicity in predicting pure compound and mixture thermodynamic properties in vapor and liquid phases. The accuracy of their predictions mainly depends on the choice of the attractive term a(T) and numerous models were developed in literature for this purpose. Among them, the Soave and the Twu models have acquired a wide popularity, as well as the Boston–Mathias model commonly used for supercritical applications. However, most of the works concerned with the comparison of literature attractive terms only focuses on the representation of pure component saturation properties. In particular, the analysis of the respective influence of the EoS and the first and second derivatives of the alpha function on the modeling of enthalpies and heat capacities with respect to temperature and pressure, especially in the supercritical range, was never reported in literature. This is precisely the purpose of the present study.     

The Cubic-Two-State Equation of State: Cross-associating mixtures and Monte Carlo study of self-associating prototypes

A new equation of state for associating fluids has recently been presented by Medeiros and Tellez-Arredondo, the Cubic-Two-State Equation of State (CTS EoS) [Ind. Eng. Chem. Res. 47 (2008) 5723]. This equation arises from the coupling of the Soave–Redlich–Kwong EoS (SRK) with an association term from a two-state association model. The CTS EoS is polynomial in volume and it is able to describe vapor pressures and molar volume of associating fluids such as water, alcohol and phenol, among others. The equation is also able to describe the liquid–vapor equilibria of their mixtures with alkanes. In this paper, the physical and thermodynamic foundations of the CTS EoS are further investigated. In order to verify its applicability for cross-associating systems, the equation was employed in the prediction of phase equilibria behavior of binary alcohol–alcohol and water–alcohol mixtures. Very good agreement between predictions and experimental phase equilibria data was obtained with very simple combining rules and only one adjustable binary parameter. No additional parameters were necessary to describe ternary systems. With the purpose of checking the model's hypothesis and limitations, the two-state association term was coupled with the hard sphere Carnahan–Starling EoS, forming the CS-TS equation and the association characteristic parameters were determined theoretically for prototype association fluids. Monte Carlo NPT simulations of such fluids were performed and the results were compared with the equation's predictions. The CS-TS was able to describe qualitatively the pvT$pvT$ behavior of the prototype; nevertheless, it is not as accurate as those predictions obtained from the combination CS with Wertheim's association term. It seems that, when adjusting parameters of the CTS EoS to real substances, the discrepancies between the predicted and the real association contribution are dissipated among other adjustable parameters, specially on the dispersive term of the SRK equation. Finally, it is shown that CTS EoS isotherms can only have one or three real bigger roots than the co-volume for positive pressures, similar to cubic equations of state, and then it has the desirable form to describe vapor–liquid phase equilibria of associating compounds mixtures.     

Modeling of thermodynamic behavior of PVT properties and cloud point temperatures of polymer blends and polymer blend + carbon dioxide systems using non-cubic equations of state

In recent years, many factors influencing phase behavior of polymer blends have been studied because of their widely technological importance, as a simple method of formulating new materials with tailored properties which make them suitable for a variety of applications. This work has three main goals which were reached by using the Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT) and the Sanchez–Lacombe (SL) non-cubic equations of state (EoS), which in previous works have shown their ability to handle long chain and associating interactions. First, both equations of state were tested with the correlation of the specific volumes of pure blends (PBD/PS, PPO/PS, PVME/PS, PEO/PES) and the prediction of the specific volumes for blends; second, the modeling of blend miscibilities in the liquid–liquid equilibria (LLE) of PBD/PS, PPG/PEGE, PVME/PS, PEO/PES, and PnPMA/PS blends; third, the modeling of the phase behavior of PS/PVME blends at various compositions in the presence of CO₂. PC-SAFT and SL pure-component parameters were regressed by fitting pure-component data of real substances (liquid pressure–volume–temperature, PVT, data for polymers and vapor pressure and saturated liquid molar volume for CO₂) and the fluid phase behavior of blend systems were simulated fitting one binary interaction parameter (k_ij) by regression of experimental data using the modified likelihood maximum method. Results were compared with experimental data obtained from literature and an excellent agreement was obtained with both EoS, which were also capable of predicting the fluid phase behavior corresponding to the critical solution temperatures (LCST: lower critical solution temperature, UCST: upper critical solution temperature) of blends.     

A modification to the Peng–Robinson-fitted equation of state for pure substances

In this work we present two modifications to the Peng–Robinson-Fitted equation of state where pure component parameters are regressed to vapor pressure and saturated liquid density data. The first modification (PR-f-mod) is a method that enhances the equation of state pure component property predictions through simple temperature dependent pure component parameters. In the second modification (PR-f-prop) we propose a temperature dependency for co-volume b in the repulsive parameter of the EoS, and revise the temperature function in the attractive term. The agreement with experimental data for 72 pure substances, including highly polar compounds, is remarkably good. We obtain average absolute deviations in saturated liquid density of less than 1% for all substances studied.     

High-pressure vapor–liquid equilibria of systems containing ethylene glycol,water and methane: Experimental measurements and modeling

This work presents new experimental phase equilibrium measurements of the binary MEG–methane and the ternary MEG–water–methane system at low temperatures and high pressures which are of interest to applications related to natural gas processing. Emphasis is given to MEG and water solubility measurements in the gas phase. The CPA and SRK EoS, the latter using either conventional or EoS/G^E mixing rules are used to predict the solubility of the heavy components in the gas phase. It is concluded that CPA and SRK using the Huron–Vidal mixing rule perform equally satisfactory, while CPA requires fewer interaction parameters.     

Molecular dynamics simulations of monoclinic calcium apatites: A universal equation of state

Molecular dynamics simulations of monoclinic (P2₁/b) hydroxy- and chlorapatite were undertaken in the range 498 K < T < 1298 K, and for pressures up to 7.5 GPa. The all-atom Born–Huggins–Mayer force field, that had been previously used to successfully describe the room temperature isotherms of both compounds, was also used in this work. The isothermal sets of p–V data generated by simulation were each fitted to the three-parameter form of the isothermal Parsafar and Mason equation of state (EoS) with an accuracy better than 0.07%. Taking the temperature dependence of the coefficients into account, it was found that the MD data are satisfactorily reproduced by the universal EoS. The isothermal compressibility coefficient dependence with pressure can be described by a linear relation.     

Multiparameter equations of state for siloxanes: [(CH3)3-Si-O1/2]2-[O-Si-(CH3)2]i=1,…,3, and [O-Si-(CH3)2]6

This article presents the continuation of the work on the development of technical equations of state for linear and cyclic siloxanes already documented in this journal. The fluids considered herewith are octamethyltrisiloxane (MDM, C₈H₂₄Si₃O₂), decamethyltetrasiloxane (MD₂M, C₁₀H₃₀Si₄O₃), dodecamethylpentasiloxane (MD₃M, C₁₂H₃₆Si₅O₄), dodecamethylcyclohexasiloxane (D₆, C₁₂H₃₆Si₆O₆). The 12-parameter functional form proposed by Span and Wagner has been selected because of its positive characteristics. Siloxanes are produced in bulk quantities and are mostly utilized in the cosmetics industry and, mixed, as high-temperature heat transfer fluids. Furthermore, they are used as working fluids in high-temperature organic Rankine cycle power plants. The available property measurements are carefully evaluated and selected for the optimization of equation of state parameters. For some of the fluids, experimental values are scarce, therefore ad hoc estimation methods have been used to supply more information to the procedure for the optimization of the parameters of the equation of state. In addition, saturated liquid density and vapor pressure measurements are correlated with the equations proposed by Daubert and Wagner–Ambrose, respectively, to provide short, simple, and accurate equations for the computation of these properties. The recently developed isobaric ideal-gas heat capacity correlation for the selected siloxanes is included in the thermodynamic models. The performance of the newly developed equations of state is tested by comparison with experimental data and also with predictions calculated with the Peng–Robinson–Stryjek–Vera cubic EoS, as this model was adopted in previous technical studies. The new thermodynamic models perform significantly better than cubic equations of state. T–s and P  – v$v$ diagrams for all the substances are also reported.     

A novel and easy two-step,microwave-assisted method for the synthesis of halophenyl pyrrolo[2,3-b]quinoxalines via their pyrrolo precursors. Evaluation of their bioactivity

A novel, two-step, facile route for the synthesis of pyrrolo[2,3-b]quinoxalines via 2,3-dioxopyrroles, enhanced by microwave irradiation, is presented. The newly synthesized 2,3-dioxo-5-halophenyl pyrrolo precursors 4a–c as well as the non-aromatized ethyl 2-(4-halophenyl)-1-methyl-2,4-dihydro-1H-pyrrolo[2,3-b]quinoxaline-3-carboxylates 6a–c and the aromatized ethyl 2-(4-halophenyl)-1-methyl-1H-pyrrolo[2,3-b]quinoxaline-3-carboxylates 7a–c were evaluated for their antioxidant, cytostatic, and antiviral properties. Most of them proved to be potent hydroxyl radical scavengers and inhibited in vitro lipid peroxidation. The compounds showed moderate antiproliferative activity, while 6a inhibited vaccinia virus at an EC₅₀ value of 2 μM, and 4c and 6c inhibited Sindbis virus at EC₅₀ values of 4 μM.     

Conversion of novel palladacycles into oxopyrrolo[3,4-b]quinolines

The quinolinylcyclopalladated complexes 3a–b were synthesised in good yields (81% and 77%) by the insertion reaction of the prepared dinuclear palladium complexes [Pd(C,N-2-C₉H₄N-CHO-3-R-6)Cl(PPh₃)]₂ [(R = H (2a), R = OMe (2b)] with isonitrile XyNC (Xy = 2,6-Me₂C₆H₃). The cyclopalladated complexes 3a–b were also obtained in low yields (39% and 33.5%) via a one pot oxidative addition reaction of quinoline chloride 1a–b with isonitrile XyNC:Pd(dba)₂ (4:1). The reactions of 3a–b with Tl(TfO) (TfO = triflate, CF₃SO₃) in the presence of H₂O or EtOH causes depalladation reactions of the complexes to provide the corresponding organic compounds 4a–b, 5a–b and 6a–b in yields (41%, 27% and 18–19%). The products were characterized by satisfactory elemental analyses and spectral studies (IR, ¹H, ¹³C and ³¹P NMR). The crystal structures of 2a, 3a and 3b were determined by X-ray diffraction studies.     

Unsymmetric 1,3,4-oxa(thia)diazoles of quinoxaline–naphthalene conjugates

Two new series of unsymmetric 1,3,4-oxa(thia)diazoles 1a,b containing both quinoxaline and naphthalene moieties were prepared and their mesomorphic properties were investigated. The mesomorphic behavior of compounds 1a,b and 2 was studied by DSC analysis and polarized optical microscopy. All compounds 1a and 2 exhibited hexagonal columnar phases (Col_h), which were also confirmed by powder XRD diffractometer. N_cell and R_ar values equal to 5.23 and 22.73 Å² within a slice of 9.0 Å thick were also obtained for 1a (n=16), indicating that a more disc-like structure constructed by two molecules lying side-by-side was correlated in Col_h phases. In contrast, all compounds 1b were not mesogenic, and the lack of mesomorphic properties in 1b might be due to their unfavorable conformations. The PL spectra of all compounds 1a,b showed one intense peak at λ_max=509–512 nm, and these photoluminescent emissions originated from quinoxaline moiety.     

Synthesis,structure and spectroelectrochemical property of (2,2′-bipyridine)–metal (M = Pt,Pd) dichloride with 4,4′-bis(fluorous-ponytail) on bipyridine

The 4,4′-bis(R_fCH₂OCH₂)-2,2′-bpy ligands [R_f = n-C₃F₇ (1a), HCF₂(CF₂)₃ (1b)] were prepared and then treated with [MCl₂(CH₃CN)₂] (M = Pt or Pd) to result in the corresponding metal complexes, [MCl₂(4,4′-bis(R_fCH₂OCH₂)-2,2′-bpy)] (M = Pt 2a–b; Pd 3a–b). Both ligands and metal complexes were fully characterized by multi-nuclei NMR (¹H, ¹⁹F and ¹³C), FTIR, and mass (GC/MS or HR-FAB) methods. The X-ray structures of 2a–b and 3a–b were studied. With terminal CF₃, the structures of 2a and 3a exhibit disordered polyfluorinated regions in solid state. With terminal HCF₂, the structures of 2b and 3b show a π–π stacking of the bpy planes, five-membered C–H···O hydrogen bond and an unusual intramolecular blue-shifting C–H···F–C hydrogen bond system, whereas without terminal HCF₂, the structures of 2a and 3a show the similar π–π stacking, five-membered C–H···O hydrogen bond and typical orientation of polyfluorinated ponytails, but not the C–H···F–C hydrogen bond system. The CV and UV/Vis studies were also carried out.     

Synthesis,crystal structure and spectroscopic characterization of new neutral and cationic (η-p-cymene)–ruthenium(II) complexes with phosphine–amide ligands

The dimeric starting material [Ru(η⁶-p-cymene)(μ-Cl)Cl]₂ reacts with the phosphino-amides o-Ph₂P–C₆H₄CO–NH–R [R = ⁱPr (a), Ph (b), 4-MeC₆H₄ (c), 4-FC₆H₄ (d)] to give the mononuclear compounds 1a–d [RuCl(η⁶-p-cymene)(o-Ph₂P–C₆H₄–CO–NH–R)]Cl. The subsequent reaction of these complexes with KPF₆ produced the cationic species 2a–d [RuCl(η⁶-p-cymene)(o-Ph₂P–C₆H₄–CO–NH–R)][PF₆] in which phosphino-amides also act as rigid P,O-chelating ligands. The molecular structures of 2b–d were determined crystallographically. Amide deprotonation is achieved when complexes 2a–d were made react with 1 M aqueous solution of KOH, affording the corresponding neutral species 3a–d [RuCl(η⁶-p-cymene)(o-Ph₂P–C₆H₄–CO–N–R)] in which a P,N-coordination mode is suggested.     

A new formulation of the predictive NRTL-PR model in terms of kij mixing rules. Extension of the group contributions for the modeling of hydrocarbons in the presence of associating compounds

A generalized NRTL model was previously proposed for the modeling of non ideal systems and was extended to the prediction of phase equilibria under pressure according to the cubic NRTL-PR EoS. In this work, the model is reformulated with a predictive k_ij temperature and composition dependent mixing rule and new interaction parameters are proposed between permanent gases, ethane and nitrogen with hydrocarbons, ethane with water and ethylene glycol. Results obtained for excess enthalpies, liquid-vapor and liquid-liquid equilibria are compared with those provided by the literature models, such as VTPR, PPR78, CPA and SRKm. A wide variety of mixtures formed by very asymmetric compounds, such as hydrocarbons, water and ethylene glycols are considered and special attention is paid to the evolution of k_ij with respect to mole fractions and temperature.     

Phosphorus–nitrogen compounds: Part 19. Syntheses,structural and electrochemical investigations,biological activities,and DNA interactions of new spirocyclic monoferrocenylcyclotriphosphazenes

The reactions of hexachlorocyclotriphosphazatriene, N₃P₃Cl₆, with N-alkyl-N-ferrocenylmethylethylene diamines, FcCH₂NH(CH₂)₂NHR₁ [R₁ = Me (1) and Et (2)], and sodium [3-(N-ferrocenylmethylamino)-1-propanoxide] (3) produce spirocyclic monoferrocenyl tetrachlorophosphazenes (1a–3a). The tetrapyrrolidinophosphazenes (1b–3b) are prepared from the reactions of corresponding phosphazenes (1a–3a) with excess pyrrolidine. The reaction of 1a with excess morpholine affords geminal-morpholino phosphazene (1c), whilst the reactions of 2a and 3a give diethylaminotrimorpholino (2c) and fully substituted morpholino products (3c), respectively. The structural investigations of the compounds are examined by Fourier transform IR, MS, ¹H, ¹³C, ³¹P NMR, DEPT, HETCOR, and HMBC techniques. The crystal structures of 3b and 3c are determined using X-ray crystallography. Cyclic voltammetric and chronoamperometric data show that compounds 1a–3a, 1b–3b, and 1c–3c exhibit electrochemically reversible one-electron oxidation of Fc redox centers which are hardly affected by the substituents on the phosphazene ring. The compounds 1b, 2b, 3b, and 3c are screened for antibacterial activities against Gram-positive and Gram-negative bacteria and for antifungal activities against yeast strains. In addition, the antituberculosis activities (in vitro) of these compounds are evaluated against INH-susceptible reference strain M. tuberculosis H37Rv, and six multi-drug resistant clinical M. tuberculosis isolates. Compound 2b is found to be the most active against the susceptible the reference strain. In addition, 1b, 2b, and 3c are active against all the multidrug-resistant clinical isolates at the highest concentrations. Gel electrophoresis data indicate that the compounds promote the formation of strand breaks in plasmid DNA. Almost all the concentrations lost of supercoiled DNA suggests that the compound 3b is very efficient plasmid-modifier. The compounds inhibit BamHI cleavage of pUC18 DNA while restricting HindIII.     

Vapor–liquid equilibrium in the n-butane + methanol system,measurement and modeling from 323.2 to 443.2 K

New experimental vapor–liquid equilibrium (VLE) data for the n-butane + methanol binary system are reported over a wide temperature range from 323.2 to 443.2 K and pressures up to 5.4 MPa. A static–analytic apparatus, taking advantage of two pneumatic capillary samplers, was used. The phase equilibrium data generated in this work are in relatively good agreement with previous data reported in the literature. Three different thermodynamic models have been used to represent the new experimental data. The first model is the cubic-based Peng–Robinson equation of state (EoS) combined with the Wong–Sandler mixing rules. The two other models are the non-cubic SAFT-VR and PC-SAFT equations of state. Temperature-dependent binary interaction parameters have been adjusted to the new data. The three models accurately represent the new experimental data, but deviations are seen to increase at low temperature. A similar evolution of the binary parameters with respect to temperature is observed for the three models. In particular a discontinuity is observed for the k_ij values at temperatures close to the critical point of butane, indicating the effects of fluctuations on the phase equilibria close to critical points.     

Columnar catenar bisoxazoles and bisthiazoles

Three new series of catenar liquid crystals 1a–c derived from heterocyclic bisoxazoles and bisthiazoles exhibiting columnar phases were reported. All compounds 1a–c exhibited hexagonal columnar phases, which were confirmed by powder XRD diffractometer. Compounds 1a have a slightly wider temperature range of columnar phases than that of compounds 1b, which might be attributed to higher dipole polarized in 1a. A N_cell and R_ar value equal to 2.54–2.76 and 19.99–20.45 Å² within a slice of 9.0 Å thick were obtained for three derivatives 1a–c (all ns=12), indicating that a single molecule was packed within columns in Col_h phases. All derivatives showed good stabilities at temperature below T=408 °C on TGA. The PL spectra of all compounds 1a–c showed one intense peak at λ_max=505–510 nm, and these photoluminescent emissions originated from quinoxaline moiety.     

Polarization effects in mesogenic isoxazoles and 1,3,4-oxadiazoles

Four new series of unsymmetric isoxazoles and 1,3,4-oxadiazoles were prepared, characterized and their mesomorphic properties investigated. Isoxazoles were obtained by condensation–cyclization of β-diketones with hydroxylamine hydrochloride in refluxing THF, while 1,3,4-oxadiazoles were obtained from hydrazine-carboxylate in refluxing POCl₃. Two single crystallographic structures were determined by X-ray crystallographic analysis. A correlated dimeric structure was formed by H-bonds in isoxazoles 1a (n=6), leading to a more elongated structure required for the formation of mesophases. All compounds 1a–c formed N, SmA or/and SmC phases. In contrast, compounds 1d exhibited columnar phases, and an N_cell=14.6 obtained from powder XRD data indicated that a correlated structure formed by four molecules was probably induced in Col_h phases. The better mesomorphic behavior formed in 1a than 1b might be attributed to stronger intermolecular interactions and higher polarization induced in isoxazoles 1a.     

The Soave,Twu and Boston–Mathias alpha functions in cubic equations of state: Part I. Theoretical analysis of their variations according to temperature

A theoretical analysis of the strengths and weaknesses of the Soave, Twu and Boston–Mathias attractive terms was performed with the Redlich–Kwong EoS. Special attention was paid to the variations of the alpha functions and their first and second derivatives with respect to temperature. Contrary to the Soave function, abnormal behaviors of the derived Twu and Boston–Mathias functions were evidenced in the temperature range commonly covered by industrial applications. The unsuccessful variations of the derived alpha functions observed with these two last models strengthen the interest of the Soave equation for the modeling of derived thermodynamic properties. The accuracy of pure component data modeling by means of the cubic equation of state is discussed in a second part.