Universal Quasichemical Functional Group Activity Coefficient Research Articles

Flexible heuristic algorithm for automatic molecule fragmentation: application to the UNIFAC group contribution model

A priori calculation of thermophysical properties and predictive thermodynamic models can be very helpful for developing new industrial processes. Group contribution methods link the target property to contributions based on chemical groups or other molecular subunits of a given molecule. However, the fragmentation of the molecule into its subunits is usually done manually impeding the fast testing and development of new group contribution methods based on large databases of molecules. The aim of this work is to develop strategies to overcome the challenges that arise when attempting to fragment molecules automatically while keeping the definition of the groups as simple as possible. Furthermore, these strategies are implemented in two fragmentation algorithms. The first algorithm finds only one solution while the second algorithm finds all possible fragmentations. Both algorithms are tested to fragment a database of 20,000+ molecules for use with the group contribution model Universal Quasichemical Functional Group Activity Coefficients (UNIFAC). Comparison of the results with a reference database shows that both algorithms are capable of successfully fragmenting all the molecules automatically. Furthermore, when applying them on a larger database it is shown, that the newly developed algorithms are capable of fragmenting structures previously thought not possible to fragment.

Thermodynamic Stability Conditions of Clathrate Hydrates in Methane/Carbon Dioxide + Tetrahydrofuran + Cyclopentane + Water Systems: Experimental Measurement and Modeling

In this communication, experimental hydrate dissociation data for methane + tetrahydrofuran (THF) (0.03 and 0.0555 mole fractions in aqueous solution) + cyclopentane (CP) + water systems are reported in the temperature range from 294.8 to 301.3 K and pressure range from 1.91 to 4.95 MPa, which are measured using an isochoric pressure-search method. Other experimental data were collected from the literature. Then a thermodynamic model for four-phase equilibria, hydrate (H)–aqueous liquid (Lw)–organic liquid (La)–vapor/gas (V), systems composed of water, methane (CH4), carbon dioxide (CO2), and/or CP was developed. The thermodynamic model is based on the solid solution theory of van der Waals–Platteeuw (vdW-P) for the hydrate phase and Peng–Robinson equation of state (P-R EOS) for vapor/gas phase. For calculating the activity coefficient of water and THF in the aqueous phase, the universal quasichemical (UNIQUAC) functional-group activity coefficient (UNIFAC) model is also used. The Langmuir constants of TH...

Mechanistic investigations in ultrasound-assisted extraction of astaxanthin from Phaffia rhodozyma MTCC 7536

This study has dealt with physical mechanism of ultrasound-assisted astaxanthin extraction from dry cell mass (DCM) of Phaffia rhodozyma. Preliminary experiments for screening of extraction solvent revealed highest extraction yield for acetone. Further experiments were performed using mixtures of DMSO and acetone with varying compositions as extraction solvent. The results were analyzed in concurrence with prediction of astaxanthin solubility using UNIFAC (Universal Quasi-Chemical Functional-Group Activity Coefficients) method and simulations of cavitation bubble dynamics. The highest astaxanthin yield of 1536 ± 3 μg/g DCM was obtained for solvent comprising 33% v/v DMSO + 67% v/v acetone. UNIFAC predicted astaxanthin solubility (1.57 g/L) was also highest for this composition, although the convection intensity predicted by bubble dynamics simulations was relatively low. Astaxanthin yield reduced with further increase in DMSO volume fraction in solvent. This result has pointed towards dominant role of solubility of solute rather than intensity of convection in extraction mixture in the extraction yield of astaxanthin.

The impacts of the activity coefficient on heating and evaporation of ethanol/gasoline fuel blends

The evolutions of droplet radii and temperatures for ethanol and gasoline fuels and their blends are investigated using a modified version of the Discrete Component (DC) model, taking into account the effect of the activity coefficient (AC). The universal quasi-chemical functional–group AC (UNIFAC) model is used to predict the ACs of the blended ethanol and gasoline fuels approximated by 21 components. In contrast to previous studies, it is shown that droplet lifetimes predicted for pure gasoline are not always shorter than those predicted for ethanol/gasoline blends. They depend on the total vapour pressure of the mixture. It is shown that the original DC model predicts ethanol/gasoline fuel droplet lifetimes with errors up to 5.7% compared to those predicted using the same model but with the ACs obtained from the UNIFAC model.

Solvent screening and liquid-liquid measurement for extraction of phenols from aromatic hydrocarbon mixtures

The separation of phenolic compounds from low temperature coal tar has great significance for further application of the coal tar. In this paper, the separation of special phenolic compounds from model coal tar (phenols + toluene) was studied. The universal quasi chemical functional group activity coefficient (UNIFAC) and conductor-like screening model COSMO-SAC (segment activity coefficient) was carried out to screen suitable solvent. Ethylene glycol was selected as the potential solvent to extract the phenols from aromatic hydrocarbon, evaluated by area of two-phase region and the criterion of solvent power (SPi∞), selectivity (S∞) and performance index (PI). Liquid-liquid equilibria of the ethylene glycol + phenols + toluene ternary systems were measured in the temperature range (303.15–323.15) K under 101.3 kPa, and the results showed that ethylene glycol has a high extraction efficiency with distribution coefficient (between 2 and 12) and selectivity (between 7 and 255). Moreover, the NRTL and UNIQUAC models were successfully applied to correlate the experimental LLE data with RMSD less than 1.85%, indicating that both models can accurately describe LLE behaviour of this system. Thus, the corresponding binary interaction parameters would be helpful for separation process designing or optimizing.

Liquid phase equilibrium of phenol extraction from bio-oil produced by biomass pyrolysis using thermodynamic models

Abstract Utilization of biomass as a new and renewable energy source is being actively conducted by various parties. One of the technologies for utilizing or converting biomass as an energy source is pyrolysis, to convert biomass into a more valuable product which is bio-oil. Bio-oil is a condensed liquid from the vapor phase of biomass pyrolysis such as coconut shells and coffee shells. Biomass composition consisting of hemicellulose, cellulose, and lignin will oxidize to phenol which is the main content in bio-oil. The total phenolic compounds contained in bio-oil are 47.03% (coconut shell) and 45% (coffee shell). The content of phenol compounds in corrosive bio-oils still quite high, the use of this bio-oil directly will cause various difficulties in the combustion system due to high viscosity, low calorific value, corrosivity, and instability. Phenol compounds have some benefits as one of the compounds for floor cleaners and disinfectants which are contained in bio-oil. The correlation between experimental data and calculations shows that the UNIQUAC Functional-group Activity Coefficients (UNIFAC) equilibrium model can be used to predict the liquid–liquid equilibrium in the phenol extraction process of the coconut shell pyrolysis bio-oil. While the Non-Random Two Liquid (NRTL) equilibrium model can be used to predict liquid–liquid equilibrium in the extraction process of phenol from bio-oil pyrolysis of coffee shells.

CO2 capture by methanol, ionic liquid, and their binary mixtures: Experiments, modeling, and process simulation

The CO2 solubility data in the ionic liquid (IL) 1‐allyl‐3‐methylimidazolium bis(trifluoromethyl sulfonyl)imide, methanol (MeOH), and their mixture with different combinations at temperatures of 313.2, 333.2, and 353.2 K and pressures up to 6.50 MPa were measured experimentally. New group binary interaction parameters of the predictive universal quasichemical functional‐group activity coefficient (UNIFAC)‐Lei model, which has been continually advanced by our group, were introduced by correlating the experimental data of this work and the literature. The consistency between experimental data and predicted results proves the reliability of UNIFAC‐Lei model for CO2‐IL‐organic solvent systems. The newly obtained parameters were incorporated into the UNIFAC property model of Aspen Plus software to optimize a conceptual process developed for the purification of a CO2‐containing gas stream. The simulation results indicate that the use of IL either mixed with MeOH or purely considerably lowers the process power consumption and improves the process performance in terms of CO2 capture rate and solvent loss. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2168–2180, 2018

Screening Monoethanolamine As Solvent to Extract Phenols from Alkane

Coal tar is a byproduct of low temperature coal carbonization. The separation of the compounds has great significance since its main component is the mixture of phenols and hydrocarbons. In this paper, the separation of specific phenolic compounds from model coal tar (phenols + hexane) was studied. The solvent was screened by empirical analysis, the universal quasichemical functional group activity coefficient (UNIFAC), and conductor-like screening model COSMO-SAC (segment activity coefficient). COSMO-SAC was used to calculate the capacity, selectivity, and performance index of solvents. Finally, the monoethanolamine (MEA) was selected as the solvent to extract the phenols. The liquid–liquid equilibrium for the ternary mixture of phenols + hexane + MEA was measured at 303.15 K and 323.15 K under atmospheric pressure, and the results showed that MEA provided a high distribution coefficient, efficiency, and selectivity for phenols. Meanwhile, the extraction process of phenols was simulated based on the nonrandom two-liquid (NRTL) model, for which binary interaction parameters were obtained through calculations of phase equilibrium. The results showed that the purity of phenols can achieve more than 99.5 wt % using MEA as a solvent.

Measurement and Correlation of Liquid–Liquid Equilibria for the Ternary Systems of Water + d-Fructose + 1-Butanol, Water + d-Glucose + 1-Butanol, and Water + d-Galactose + 1-Butanol at (288.2, 303.2 and 318.2) K

The liquid–liquid equilibrium (LLE) data of ternary systems of water + d-fructose + 1-butanol, water + d-glucose + 1-butanol, and water + d-galactose + 1-butanol were determined at three temperatures (288.2, 303.2, and 318.2 K) and atmospheric condition. The distribution coefficients of the monosaccharides were lower than 0.05. For all the three saccharides, their content in the organic-rich phase increased as their content in the aqueous phase increased. The experimental tie-line data were fitted using the Othmer–Tobias equation. The saccharide universal quasichemical functional-group activity coefficient (S-UNIFAC) model was used to predict the LLE data with all the average absolute deviations (AAD) values higher than 0.013. The modified universal quasichemical model was then used to correlate the LLE data. The correlation results agreed better with experimental data than the prediction results obtained with S-UNIFAC. In the production of traditional Chinese medicines, 1-butanol is a promising extractan...

Measurements and Modeling of VLE Data for Butyl Acetate with 2-Propanol or 2-Butanol. Binary Systems at 0.15 and 0.6 MPa

Isobaric vapor–liquid equilibrium is measured at 0.15 and 0.6 MPa for binary mixtures of butyl acetate with 2-propanol and 2-butanol. The experimental data are reported and the thermodynamic consistency is verified by using the point-to-point test. Prediction of these binary systems was obtained by employing the analytical solutions of groups (ASOG) and the different versions of UNIQUAC functional-group activity coefficients (UNIFAC) group contribution models. The perturbed chain-statistical associating fluid theory (PC-SAFT) equation of state has been used to reproduce experimental data.

Predicting Solid–Liquid Equilibrium of Fatty Acid Methyl Ester and Monoglyceride Mixtures as Biodiesel Model Fuels

AbstractFatty acid methyl esters from plant oils are the main component of biodiesel and used as a substitute for petroleum diesel. Biodiesel generally contains a small amount of monoglycerides as intermediate compounds, which have high melting points and often solidify and clog fuel filters. The prediction of the cold‐flow property of biodiesel is of great importance for practical application. In this study, a thermodynamic study was conducted for mixtures of monoglycerides and fatty acid methyl esters. Temperatures of the solid–liquid equilibrium for the mixtures were measured by differential scanning calorimetry and visual observation, while the theoretical values were calculated using the modified Universal Quasi‐chemical Functional‐group Activity Coefficients (UNIFAC) model (Dortmund). The theoretical and experimental results were in good agreement, especially for binary mixtures of monoglycerides and methyl esters. The importance of monoglycerides on the cold‐flow properties of biodiesel was determined, and the effects could be well described by the modified UNIFAC model (Dortmund).

Thermodynamics of enzyme-catalyzed esterifications: I. Succinic acid esterification with ethanol.

Succinic acid (SA) was esterified with ethanol using Candida antarctica lipase B immobilized on acrylic resin at 40 and 50°C. Enzyme activity in the reaction medium was assured prior to reaction experiments. Reaction-equilibrium experiments were performed for varying initial molalities of SA and water in the reaction mixtures. This allowed calculating the molality-based apparent equilibrium constant K m as function of concentration and temperature. K m was shown to depend strongly on the molality of water and SA as well as on temperature. It could be concluded that increasing the molality of SA shifted the reaction equilibrium towards the products. Water had a strong effect on the activity of the enzyme and on K m . The concentration dependence of K m values was explained by the activity coefficients of the reacting agents. These were predicted with the thermodynamic models Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT), NRTL, and Universal Quasichemical Functional Group Activity Coefficients (UNIFAC), yielding the ratio of activity coefficients of products and reactants K γ . All model parameters were taken from literature. The models yielded K γ values between 25 and 115. Thus, activity coefficients have a huge impact on the consistent determination of the thermodynamic equilibrium constants K th. Combining K m and PC-SAFT-predicted K γ allowed determining K th and the standard Gibbs energy of reaction as function of temperature. This value was shown to be in very good agreement with results obtained from group contribution methods for Gibbs energy of formation. In contrast, inconsistencies were observed for K th using K γ values from the classical gE-models UNIFAC and NRTL. The importance of activity coefficients opens the door for an optimized reaction setup for enzymatic esterifications.

Influence of organic compound functionality on aerosol hygroscopicity: dicarboxylic acids, alkyl-substituents, sugars and amino acids

Abstract. Hygroscopicity data for 36 organic compounds, including amino acids, organic acids, alcohols and sugars, are determined using a comparative kinetics electrodynamic balance (CK-EDB). The CK-EDB applies an electric field to trap-charged aqueous droplets in a chamber with controlled temperature and relative humidity (RH). The dual micro dispenser set-up allows for sequential trapping of probe and sample droplets for accurate determination of droplet water activities from 0.45 to > 0.99. Here, we validate and benchmark the CK-EDB for the homologous series of straight-chain dicarboxylic acids (oxalic–pimelic) with measurements in better agreement with Universal Quasichemical Functional Group Activity Coefficients (UNIFAC) predictions than the original data used to parametrise UNIFAC. Furthermore, a series of increasingly complex organic compounds, with subtle changes to molecular structure and branching, are used to rigorously assess the accuracy of predictions by UNIFAC, which does not explicitly account for molecular structure. We show that the changes in hygroscopicity that result from increased branching and chain length are poorly represented by UNIFAC, with UNIFAC under-predicting hygroscopicity. Similarly, amino acid hygroscopicity is under-predicted by UNIFAC predictions, a consequence of the original data used in the parametrisation of the molecular subgroups. New hygroscopicity data are also reported for a selection of alcohols and sugars and they show variable levels of agreement with predictions.

Solubility of water and acetone in hypromellose acetate succinate, HPMCAS-L

Thermodynamic properties of a hypromellose acetate succinate (HPMCAS-L)-acetone-water system at temperatures below the glass transition temperature of HPMCAS-L were investigated. The solubility of water and acetone in HPMCAS-L is important for the optimization of spray-drying processes used in pharmaceutical manufacturing of solid dispersion formulations. Finite concentration data of each component were obtained separately using gravimetric sorption, differential pressure decay, and capillary column inverse gas chromatography. Results of thermodynamic properties were compared with prediction models based on the UNIQUAC functional-group activity coefficients (UNIFAC) method as well as the correlation model of Flory-Huggins. UNIFAC interaction parameters, modified to account for the interactions of water with the monosaccharide type groups in HPMCAS-L, had to be used in order to generate reasonable predictions. Overall, the Flory-Huggins model provided the best representation for both binary systems.

Cutinase from Fusarium oxysporum catalyzes the acylation of tyrosol in an aqueous medium: Optimization and thermodynamic study of the reaction

Recently, tyrosol has gained attention as a result of its many pharmacological properties and due to the fact that it can be isolated from cheap and abundant resources. Lipophilic tyrosyl esters, which are scarce in nature, have proven in certain cases to acquire improved biological activity compared to tyrosol itself, increasing their potential use in the food and cosmeceutical industries. The enzymatic approach for the synthesis of such esters has prevailed, as it is “green”, compared to chemical practices. We hereby report the enzymatic synthesis of tyrosyl esters of various aliphatic fatty acids performed by a recombinant cutinase from Fusarium oxysporum (FoCut5a). The reaction system used consists of an aqueous phase saturated with the corresponding fatty-acid vinyl ester, which played the role of the acyl donor. We also proceeded to the study of several parameters on the yield of the tyrosyl butyrate ester synthesis. The maximum yield achieved was 60.7% after 4h at 20°C, in pH 7.0, with initial tyrosol concentration of 12.5mM and using 5μg FoCut5a mL−1 reaction as catalyst. The optimum reaction conditions can be considered mild, highlighting the environmentally friendly nature of this reaction, along with the fact that there are not any harmful reagents involved. Additionally, the use of two thermodynamic models, Conductor-like Screening Model for Real Solvents (COSMO-RS) and UNIquac Functional-group Activity Coefficients (UNIFAC), were employed for the prediction of reactants’ and products’ solubilities and their distribution in the reaction biphasic system, aiming to correlate the reaction yields with these important thermodynamic quantities and understand the ability of this enzymatic reaction in synthesizing tyrosyl esters.

Hygroscopic behavior of multicomponent organic aerosols and their internal mixtures with ammonium sulfate

Abstract. Water-soluble organic compounds (WSOCs) are important components of organics in the atmospheric fine particulate matter. Although WSOCs play an important role in the hygroscopicity of aerosols, knowledge on the water uptake behavior of internally mixed WSOC aerosols remains limited. Here, the hygroscopic properties of single components such as levoglucosan, oxalic acid, malonic acid, succinic acid, phthalic acid, and multicomponent WSOC aerosols mainly involving oxalic acid are investigated with the hygroscopicity tandem differential mobility analyzer (HTDMA). The coexisting hygroscopic species including levoglucosan, malonic acid, and phthalic acid have a strong influence on the hygroscopic growth and phase behavior of oxalic acid, even suppressing its crystallization completely during the drying process. The phase behaviors of oxalic acid/levoglucosan mixed particles are confirmed by infrared spectra. The discrepancies between measured growth factors and predictions from Extended Aerosol Inorganics Model (E-AIM) with the Universal Quasi-Chemical Functional Group Activity Coefficient (UNIFAC) method and Zdanovskii–Stokes–Robinson (ZSR) approach increase at medium and high relative humidity (RH) assuming oxalic acid in a crystalline solid state. For the internal mixture of oxalic acid with levoglucosan or succinic acid, there is enhanced water uptake at high RH compared to the model predictions based on reasonable oxalic acid phase assumption. Organic mixture has more complex effects on the hygroscopicity of ammonium sulfate than single species. Although hygroscopic species such as levoglucosan account for a small fraction in the multicomponent aerosols, they may still strongly influence the hygroscopic behavior of ammonium sulfate by changing the phase state of oxalic acid which plays the role of "intermediate" species. Considering the abundance of oxalic acid in the atmospheric aerosols, its mixtures with hygroscopic species may significantly promote water uptake under high RH conditions and thus affect the cloud condensation nuclei (CCN) activity, optical properties, and chemical reactivity of atmospheric particles.

Estimation of Equilibrated Vapor Concentrations Using the UNIFAC Model for the Tetrachloroethylene-Chlorobenzene System.

Equilibrated vapor concentrations at 25°C of the tetrachloroethylene-chlorobenzene system were obtained in the presence of air to establish a method for estimating vapor concentrations in work environments where multicomponent organic solvents are used. The experimental data were correlated by introducing activity coefficients calculated by the UNIFAC (Universal Quasichemical Functional Group Activity Coefficient) model. There were four interaction parameters between groups in this solution system, and three had already been determined.However, the fourth parameter--the interaction parameter between ACCl and Cl-(C=C) groups--remains unknown. Therefore, this parameter was determined by a nonlinear least-squares method to obtain the best fit for the experimental data. The calculated values were found to be in good agreement with the experimental values.

Improved AIOMFAC model parameterisation of the temperature dependence of activity coefficients for aqueous organic mixtures

Abstract. This study presents a new, improved parameterisation of the temperature dependence of activity coefficients in the AIOMFAC (Aerosol Inorganic–Organic Mixtures Functional groups Activity Coefficients) model applicable for aqueous as well as water-free organic solutions. For electrolyte-free organic and organic–water mixtures the AIOMFAC model uses a group-contribution approach based on UNIFAC (UNIversal quasi-chemical Functional-group Activity Coefficients). This group-contribution approach explicitly accounts for interactions among organic functional groups and between organic functional groups and water. The previous AIOMFAC version uses a simple parameterisation of the temperature dependence of activity coefficients, aimed to be applicable in the temperature range from ~ 275 to ~ 400 K. With the goal to improve the description of a wide variety of organic compounds found in atmospheric aerosols, we extend the AIOMFAC parameterisation for the functional groups carboxyl, hydroxyl, ketone, aldehyde, ether, ester, alkyl, aromatic carbon-alcohol, and aromatic hydrocarbon to atmospherically relevant low temperatures. To this end we introduce a new parameterisation for the temperature dependence. The improved temperature dependence parameterisation is derived from classical thermodynamic theory by describing effects from changes in molar enthalpy and heat capacity of a multi-component system. Thermodynamic equilibrium data of aqueous organic and water-free organic mixtures from the literature are carefully assessed and complemented with new measurements to establish a comprehensive database, covering a wide temperature range (~ 190 to ~ 440 K) for many of the functional group combinations considered. Different experimental data types and their processing for the estimation of AIOMFAC model parameters are discussed. The new AIOMFAC parameterisation for the temperature dependence of activity coefficients from low to high temperatures shows an overall improvement of 28% in comparison to the previous model version, when both versions are compared to our database of experimentally determined activity coefficients and related thermodynamic data. When comparing the previous and new AIOMFAC model parameterisations to the subsets of experimental data with all temperatures below 274 K or all temperatures above 322 K (i.e. outside a 25 K margin of the reference temperature of 298 K), applying the new parameterisation leads to 37% improvement in each of the two temperature ranges considered. The new parameterisation of AIOMFAC agrees well with a large number of experimental data sets. Larger model–measurement discrepancies were found particularly for some of the systems containing multi-functional organic compounds. The affected systems were typically also poorly represented at room temperature and further improvements will be necessary to achieve better performance of AIOMFAC in these cases (assuming the experimental data are reliable). The performance of the AIOMFAC parameterisation is typically better for systems containing relatively small organic compounds and larger deviations may occur in mixtures where molecules of high structural complexity such as highly oxygenated compounds or molecules of high molecular mass (e.g. oligomers) prevail. Nevertheless, the new parameterisation enables the calculation of activity coefficients for a wide variety of different aqueous/water-free organic solutions down to the low temperatures present in the upper troposphere.

UNIFAC model for ionic liquid‐CO (H2) systems: An experimental and modeling study on gas solubility

The universal quasichemical functional‐group activity coefficients (UNIFAC) model for ionic liquids (ILs) has become notably popular because of its simplicity and availability via modern process simulation softwares. In this work, new group binary interaction parameters (αmn and αnm) between CO (H2) and IL groups were obtained by correlating the solubility data in pure ILs at high temperatures (above 273.2 K) collected from the literature. the solubility of CO in [BMIM]+[BF4]−, [OMIM]+[BF4]−, [OMIM]+[Tf2N]−, and their mixtures, as well as that of H2 in [EMIM]+[BF4]−, [BMIM]+[BF4]−, [OMIM]+[Tf2N]−, and their mixtures, at temperatures from 243.2 to 333.2 K and pressures up to 6.0 MPa were measured. The UNIFAC model was observed to well predict the solubility in pure and mixed ILs at both high (above 273.2 K) and low (below 273.2 K) temperatures. Moreover, the selectivity of CO (or H2) to CO2 in ILs increases with decreasing temperature, indicating that low temperatures favor for gas separation. © 2014 American Institute of Chemical Engineers AIChE J 60: 4222–4231, 2014

Isobaric Vapor–Liquid Equilibria of Binary Systems (Propyl Acetate + 2-Methylbutan-1-ol), (Propyl Acetate + Hexan-1-ol), and (Propyl Acetate + Heptan-1-ol) at 101.3 kPa

Isobaric vapor–liquid equilibrium (VLE) data for the binary systems formed by (propyl acetate +2-methylbutan-1-ol), (propyl acetate + hexan-1-ol), and (propyl acetate + heptan-1-ol) have been determined at the pressure of 101.3 kPa using an equilibrium still. The experimental data were checked through the semiempirical methods of Herington, and the thermodynamic consistency was satisfactory. The activity coefficients were correlated with the nonrandom two liquid (NRTL), Wilson, and universal quasichemical (UNIQUAC) models. In addition, the UNIQUAC functional-group activity coefficients (Do) model was used to correlate the VLE data. The NRTL model shows slightly better results compared with other three models among all three binary systems.