«A. Belkadi1,2, F. Llovell3, V. Gerbaud1*, L. F. Vega2,3*,+ 1 Université de Toulouse, LGC (Laboratoire de Génie Chimique), CNRS, INP, UPS, 5 rue ...»
MODELING THE VAPOR – LIQUID EQUILIBRIUM AND
ASSOCIATION OF NITROGEN DIOXIDE / DINITROGEN
TETROXIDE AND ITS MIXTURES WITH CARBON
A. Belkadi1,2, F. Llovell3, V. Gerbaud1*, L. F. Vega2,3*,+
Université de Toulouse, LGC (Laboratoire de Génie Chimique), CNRS, INP, UPS, 5
rue Paulin Talabot, F-31106 Toulouse Cedex 01 – France 2 MATGAS Research Center, Campus UAB. 08193 Bellaterra, Barcelona Spain 3 Institut de Ciència de Materials de Barcelona, (ICMAB-CSIC), Consejo Superior de Investigaciones Científicas, Campus de la UAB, 08193 Bellaterra, Barcelona, Spain * Corresponding authors: Vincent.Gerbaud@ensiacet.fr, firstname.lastname@example.org.
+ Present address: Carburos Metálicos-Grup Air Products. C/ Aragón 300. 08009 Barcelona. Spain.
1 Abstract We have used in this work the crossover soft-SAFT equation of state to model nitrogen dioxide/dinitrogen tetraoxide (NO2/N2O4), carbon dioxide (CO2) and their mixtures. The prediction of the vapor – liquid equilibrium of this mixture is of utmost importance to correctly assess the NO2 monomer amount that is the oxidizing agent of vegetal macromolecules in the CO2 + NO2 / N2O4 reacting medium under supercritical conditions. The quadrupolar effect was explicitly considered when modeling carbon dioxide, enabling to obtain an excellent description of the vapor-liquid equilibria diagrams. NO2 was modeled as a self associating molecule with a single association site to account for the strong associating character of the NO2 molecule. Again, the vapor- liquid equilibrium of NO2 was correctly modeled. The molecular parameters were tested by accurately predicting the very few available experimental data outside the phase equilibrium. Soft-SAFT was also able to predict the degree of dimerization of NO2 (mimicking the real NO2/N2O4 situation), in good agreement with experimental data.
Finally, CO2 and NO2 pure compound parameters were used to predict the vapor – liquid coexistence of the CO2 + NO2 / N2O4 mixture at different temperatures.
Experimental pressure – CO2 mass fraction isotherms recently measured were well described using a unique binary parameter, independent of the temperature, proving that the soft-SAFT model is able to capture the non-ideal behavior of the mixture.
Keywords: soft-SAFT, crossover, reacting systems, CO2, NO2 / N2O4 2
1. Introduction Accurate thermodynamic properties of pure compounds and mixtures, in particular phase equilibrium properties, are needed over a wide range of temperatures and pressures for the optimization of existing and the design of new process and/or materials in chemical industry. Even though experimental data is always preferred, this information is often scarce and it does not cover all mixtures and operating conditions, thus inducing a persistent effort to derive accurate thermodynamic models.
From the modeling of hydrocarbon or organic compound properties needed in the petrochemical industry, and because of the advent of novel industrial technologies, a shift in modeling has occurred, focusing on uncommon fluids (ionic liquids, biomolecules, etc.) or on common fluids under severe temperature and pressure conditions, like the supercritical ones. In a comprehensive paper, Prausnitz and Tavares  recalled 50 years of thermodynamic models focused on vapor – liquid equilibrium.
Hydrocarbons and other non polar fluid vapor – liquid equilibrium properties can be satisfactorily modeled using a symmetric approach to model both, the vapor and the liquid phase fugacity with the use of a van der Waals type equation model [2,3], the Soave – Redlich – Kwong or Peng – Robinson equations being the most popular ones.
When polar fluids are involved at moderate pressures, activity coefficient models are more suitable for modeling the liquid phase. When a higher pressure range is also a concern, a symmetric equation of state approach with complex mixing rules including an excess Gibbs energy term from an activity coefficient model can provide good results. Unfortunately, even those approaches show limitations for complex fluids and can drastically fail near the critical region, unless an specific treatment is included [4,5].
secondary amines, practical thermodynamic modeling has suggested the description of the dimer – monomer association equilibrium in the relevant phase in order to correct the monomer composition participating into the vapor – liquid phase equilibrium. This is the case for acetic acid, a molecule that dimerizes mostly in the vapor phase [6,7].
Self-associating fluids in the liquid phase are not so frequent but do exist, like NO2, which forms N2O4 dimers in the liquid phase .
In the recent decades, progress in computer science has enabled molecular simulations to solve real problems, like the prediction of vapor – liquid equilibrium of highly non ideal complex mixtures, by the use of statistical mechanic principles, developing efficient bias to sample fluid configurations [9,10]. However, although the large computational time of the molecular simulation is not prohibitory to obtain thermodynamic properties that are hardly measurable, it still prevents its use in practical and fast chemical engineering calculations.
Molecular based equations of state also routed in statistical mechanics, are a very attractive alternative. They retain their interest in chemical engineering calculations as they apply to a wide spectrum of thermodynamic conditions and compounds, being computationally much less demanding than molecular simulations.
Among them, the Statistical Associating Fluid Theory equation of state (SAFT) has become very popular because of its capability of predicting thermodynamics properties of several complex fluids, including chain, aromatic and chlorinated hydrocarbons, esters alkanols, carboxylic acids, etc . SAFT was envisioned as an application of Wertheim’s theory of association [12-14] through the use of a first order thermodynamic perturbation theory (TPT) to formulate a physically based EoS [11, 15
promoted the development of different versions that tried to overcome the limitations of the original one [18,19].
The objective of this paper is to check the accuracy of one of these approaches for describing the vapor-liquid equilibrium diagrams and association of the CO2 + NO2 / N2O4 mixture. The prediction of the vapor – liquid equilibrium of this mixture is of utmost importance to correctly assess the NO2 monomer amount that is the oxidizing agent of vegetal macromolecules in the CO2 + NO2 / N2O4 reacting medium. Such a mixture is the reacting media in a novel process where body-degradable polymers readily usable for inside body surgery treatment are produced through the oxidation of polysaccharides and cellulose macromolecules by NO2/N2O4 in a reactor where CO2 is present in excess under supercritical conditions . Currently, the oxidizing agent is suspected to be NO2 monomers but a real assessment of its exact quantity in the reacting medium is missing to further optimize the process conditions.
Supercritical CO2 is now well established as a solvent for use in extractions. The modeling of CO2 is routinely done using cubic equation of state. However, CO2 bears a quadrupole that, if not considered in the modeling, provides inaccurate mixture predictions that have to be corrected by the use of binary interaction parameters . A recent modeling of CO2 – perfluoroalkanes vapor – liquid equilibrium mixtures using the soft-SAFT equation of state showed that no binary interaction parameters are required when the quadrupolar moment on carbon dioxide is explicitly included and molecules do not greatly differ in size. In that case, the quadrupolar effect on the phase
increasing the model extrapolation capability .
The oxides of nitrogen are of main interest, notably for their occurrence in biological and environmental chemistry. Nitrogen dioxide (NO2) is notoriously known to self associate in the liquid phase to produce dinitrogen tetroxide (N2O4) according to Equation 1 . In the liquid phase, N2O4 can also additionally isomerizes . In the vapor phase, it was shown that dimerization also occurs, while the formation of trimers, tetramers or sequential indefinite self-association hypothesis can be discarded . In this work NO2 is modeled as a self associating molecule with a single association site to account for the strong associating character of the NO2 molecule. Assuming that the self associating compound NO2 is a mixture of monomers NO2 and dimers N2O4, the
dissociation reaction to be considered is:
According to interpretation of Raman and X-ray spectra  and the most recent computational chemistry study , it has been confirmed that the NO2 association takes place along the NN bond line. Both NO2 and N2O4 molecules are fairly rigid.
Hence, in spite of its importance and given the non-ideal behavior of the components, the CO2 + NO2 / N2O4 mixture is a challenging mixture to model. The approach we have taken here is to use the soft-SAFT equation of state [26,27], as it explicitly builds on the association and the quadrupolar interactions. Therefore, the equation is able to provide insights on the mixture behavior, as for instance, the degree of aggregation of associating molecules in each phase in equilibrium . Like most
relating the model to the experimental system. An advantage of SAFT-type equations versus other approaches is that, as they are based on statistical mechanics, parameters have a clear physical meaning; when carefully fitted they can be used with predictive power to explore other regions of the phase diagram far from the data and operating conditions used in the parameter regression, performing better than other models for interacting compounds like activity coefficient models . Modeling predictions are compared to very recent experimental measurements of NO2 – CO2 equilibrium isotherms .
The paper is organized as it follows: first, the crossover soft-SAFT equation of state is shortly described, including the molecular model used for CO2 and NO2. In the results section, the soft-SAFT equation results are presented and discussed, as compared to available experimental data, phase envelopes of the pure compounds, additional thermodynamic data of NO2 (used to validate the pure component parameters), degree of dimerization for the NO2/N2O4 system, and the mixture CO2 + NO2 / N2O4. Some concluding remarks are provided in the last section.
2. The crossover soft-SAFT equation of state The soft-SAFT EoS  is a modification of the original SAFT equation [15based on Wertheim’s TPT [12-14]. Since the SAFT equation and its modifications have been extensively revised , only the main features of the equation are retained here. SAFT-type equations of state are written in terms of the residual Helmholtz
where a and aid are the total Helmholtz energy density and the ideal gas Helmholtz energy density at the same temperature and density, respectively. aref is the contribution to the Helmholtz energy of the spheres term composing the molecules; achain, the chain contribution term and aassoc, the association term, both come from Wertheim’s theory.
Finally, apolar takes into account the polar contribution to the Helmholtz energy. In essence, in the SAFT approach the total Helmholtz energy is the sum of different microscopic contributions, all of which can be taken into account in a systematic manner.
The main difference between the soft-SAFT equation and the original SAFT equation [15-17] is the use of the Lennard–Jones (LJ) intermolecular potential for the reference fluid in the soft-SAFT equation, with dispersive and repulsive forces into the same term, instead of the perturbation scheme based on a hard-sphere reference fluid plus dispersive contributions to it. This difference also appears in the chain and association term, since they both use the radial distribution function of the reference fluid, and it has turned out to be relevant for some applications of the equation.
Hence, the reference term in the soft-SAFT EOS is a LJ spherical fluid, which represents the units making up the chains. Following our previous work, we have used the accurate EoS of Johnson et al. . The chain term in the equation comes from Wertheim’s theory, and it is formally identical in the different versions of SAFT. It is
where ρ is the molecular density of the fluid, T is the temperature and kB is the Boltzmann constant. In the soft-SAFT case, it is applied to tangent LJ spheres of chain length m that are computed following a pair correlation function g LJ, evaluated at the bond length σ.
The association term comes from the first-order Wertheim’s TPT for associating fluids, The Helmholtz energy density change due to association is calculated from the equation
where Mi is the number of associating sites of component i and X iα the mole fraction of component i not bonded at site α which accounts for the contributions of all associating
sites in each species:
The term ∆αiβj is related to the strength of the association bond between site α in molecule i and site β in molecule j, from which two additional molecular parameters,
for details) The extension of the equation to polar systems is done by adding a new contribution that consists in a perturbed polar term proposed by Gubbins and Twu .
derived for an arbitrary intermolecular reference potential and can be found in the original papers [32-33]. These expressions include the polar moment of the molecule (Q for the quadrupole case, which is the one evaluated in this work ), whose value is taken from experimental measurements.