Nonassociative Systems Research Articles

Calculation of azeotropic properties for binary mixtures with the PC-SAFT equation of state

In this work, we present a novel approach to predict the location of azeotropes for binary mixtures using the perturbed-chain statistical associating fluid theory equation of state (PC-SAFT).The proposed method requires as input the pure-component parameters of the PC-SAFT equation: the segment number (m), the hard-core segment diameter (σ), and the segment-segment interaction energy parameter (ε/k) for every pure non-associating fluid. By using these parameters, PC-SAFT estimates with accuracy the azeotropes properties of binary mixtures as well as the successful prediction of vapour-liquid equilibria for many non-associating binary systems. In order to improve the predictive ability of the PC-SAFT equation, the interaction parameters of 8 binary systems containing novel refrigeration fluid, were estimated from binary vapour–liquid equilibrium data. For comparison, the data were also modelled using the (PR-MC-WS-NRTL) thermodynamic model. Good agreements are found between the calculated results and reference data and the relative error does not exceed 3.69% and 0.97% for the molar fraction and the pressure respectively.

A Theoretical Model for the Charging Dynamics of Associating Ionic Liquids

Association between cations and anions plays an important role in the interfacial structure of room-temperature ionic liquids (ILs) and their electrochemical performance. Whereas great efforts have been devoted to investigating the association effect on the equilibrium properties of ILs, a molecular-level understanding of the charging dynamics is yet to be established. Here, we propose a theoretical procedure combining reaction kinetics and the modified Poisson-Nernst-Planck (MPNP) equations to study the influences of ionic association on the dynamics of electrical double layer (EDL) in response to an applied voltage. The ionic association introduces a new decay length λS and relaxation time scale τRC=λSL/D, where L is the system size and D is ion diffusivity, that are distinctively different those corresponding to non-associative systems. Analytical expressions have been obtained to reveal the quantitative relations between the dynamic timescales and the association strength.

New modified PC-SAFT pure component parameters for accurate VLE and critical phenomena description

The theory of Perturbed Chain Statistical Associating Fluid (PC-SAFT) is largely applied in many industrial fields. It requires three parameters: the segment number (m), the hard-core segment diameter (σ), and the segment-segment interaction energy parameter (ε/k) for every pure non-associating fluid. By convention, they are determined by fitting vapor pressure and liquid density data. However, the shortage behind these parameters adopted by their respective authors is that they give excessive values of critical temperatures and critical pressures, which are crucial to forecasting vapor-liquid critical pressure and composition of the mixture at high pressures and temperatures.In this paper, a new approach is proposed to evaluate PC-SAFT parameters of different substances from diverse chemical families. Good fits of saturation pressure and vapor densities values of 94 pure substances are obtained, with an overall AARD of 0.89% and 1.50% respectively.The proposed method requires as input the critical pressure (Pc), the critical temperature (Tc), and the acentric factor (ω). By using these parameters, PC-SAFT estimates with accuracy the critical properties of pure compounds as well as the successful prediction of vapor-liquid equilibria for many non-associating binary systems at critical regions including mixtures containing ammonia, comparing with other literature values. But the limitation of this method is reflected in underestimated liquid densities.

One-Sided Sequent Systems for Nonassociative Bilinear Logic: Cut Elimination and Complexity

Bilinear Logic of Lambek amounts to Noncommutative MALL of Abrusci. Lambek proves the cut–elimination theorem for a one-sided (in fact, left-sided) sequent system for this logic. Here we prove an analogous result for the nonassociative version of this logic. Like Lambek, we consider a left-sided system, but the result also holds for its right-sided version, by a natural symmetry. The treatment of nonassociative sequent systems involves some subtleties, not appearing in associative logics. We also prove the PTime complexity of the multiplicative fragment of NBL.

Gelfand–Dorfman algebras, derived identities, and the Manin product of operads

Gelfand–Dorfman bialgebras (GD-algebras) are nonassociative systems with two bilinear operations satisfying a series of identities that express Hamiltonian property of an operator in the formal calculus of variations. The paper is devoted to the study of GD-algebras related with differential Poisson algebras. As a byproduct, we obtain a general description of identities that hold for operations a≻b=d(a)b and a≺b=ad(b) on a (non-associative) differential algebra with a derivation d.

Nonexistence of Idempotent Means on Free Binary Systems

AbstractFree binary systems are shown not to admit idempotent means. This refutes a conjecture of the author. It is also shown that the extension of Hindman’s theorem to nonassociative binary systems formulated and conjectured by the author is false.

CONIC REGULAR FUNCTIONS OF CONIC QUATERNION VARIABLES IN THE SENSE OF CLIFFORD ANALYSIS

Abstract. The aim of this paper is to research certain properties ofconic regular functions of conic quaternion variables in C 2 . We generalizethe properties of conic regular functions and the Cauchy theorem of conicregular functions in conic quaternion analysis. 1. IntroductionWe introduce the four dimensional commutative conic quaternions, not quater-nions, and its associated function theory and analysis. Conic quaternions havethe following advantages: It is a classical four dimensional function theory andhas something that is impossible with quaternions and other non-commutativeor non-associative systems. Muses [11, 12] discussed speci c examples andtheorems, specially, the relation of hypernumbers to time, developed in termsof hypernumber computation. Davenport [1] worked with numbers that havefour distinct components and constructed a formal algebra formed upon a ba-sis commutative ring and a consistent de nition of multiplication and someoperators. Kajiwara etal: [2, 3] obtained mathematical results of quaternionalgebra, properties of several operators in quaternions and regenerations forthe inhomogeneous Cauchy Riemann system of quaternion and Cli ord anal-ysis. Koriyama etal: [8] gave some de nitions and properties of regularities ofquaternionic functions with regular mappings in a domain in C

Modeling adsorption in binary associating solvents using the extended MPTA model

Application of the MPTA model has been extended to associative liquid adsorption. The MPTA model describes fluid–fluid interactions using an equation of state (EoS) term, and fluid–solid interactions using a potential equation. In order to extend the application to associative liquid adsorption, an association term has been considered for fluid–fluid interactions. Sixteen binary mixtures containing associating and non-associating components in equilibrium with various adsorbents have been studied; fluid–fluid interactions have been modeled using the Peng–Robinson, Soave–Redlich–Kwong, volume-translated SRK and CPA equations of state, while the effects of fluid–solid interactions have been taken into account using Dubinin–Radushkevich–Astakhov (DRA) and Steele potential functions. The model parameters have been obtained by fitting the model to experimental data on surface excess. For the studied systems, the accuracy of fitted isotherms has been found to be more dependent on the fluid–solid potential equation rather than the applied EoS. Calculations show that the SRK equation is a suitable choice for non-associating systems, while the CPA equation is found to be more appropriate for associating systems, as would be expected. The results also show that the Steele potential function is in better agreement with experimental data than the DRA potential function.

Universal Associative Envelopes of Nonassociative Triple Systems

We construct universal associative envelopes for the nonassociative triple systems arising from the trilinear operations of Bremner and Peresi applied to the 2-dimensional simple associative triple system. We use noncommutative Gröbner bases to determine monomial bases, structure constants, and centers of the universal envelopes. We show that the infinite dimensional envelopes are closely related to the down-up algebras of Benkart and Roby. For the finite dimensional envelopes, we determine the Wedderburn decompositions and classify the irreducible representations.

Jordan triple disystems

We take an algorithmic and computational approach to a basic problem in abstract algebra: determining the correct generalization to dialgebras of a given variety of nonassociative algebras. We give a simplified statement of the KP algorithm introduced by Kolesnikov and Pozhidaev for extending polynomial identities for algebras to corresponding identities for dialgebras. We apply the KP algorithm to the defining identities for Jordan triple systems to obtain a new variety of nonassociative triple systems, called Jordan triple disystems. We give a generalized statement of the BSO algorithm introduced by Bremner and Sánchez-Ortega for extending multilinear operations in an associative algebra to corresponding operations in an associative dialgebra. We apply the BSO algorithm to the Jordan triple product and use computer algebra to verify that the polynomial identities satisfied by the resulting operations coincide with the results of the KP algorithm; this provides a large class of examples of Jordan triple disystems. We formulate a general conjecture expressed by a commutative diagram relating the output of the KP and BSO algorithms. We conclude by generalizing the Jordan triple product in a Jordan algebra to operations in a Jordan dialgebra; we use computer algebra to verify that resulting structures provide further examples of Jordan triple disystems. For this last result, we also provide an independent theoretical proof using Jordan structure theory.

Irreducible Lie–Yamaguti algebras of generic type

Lie–Yamaguti algebras (or generalized Lie triple systems) are binary–ternary algebras intimately related to reductive homogeneous spaces. The Lie–Yamaguti algebras which are irreducible as modules over their inner derivation algebras are the algebraic counterparts of the isotropy irreducible homogeneous spaces. These systems splits into three disjoint types: adjoint type, non-simple type and generic type. The systems of the first two types were classified in a previous paper through a generalized Tits Construction of Lie algebras. In this paper, the Lie–Yamaguti algebras of generic type are classified by relating them to several other nonassociative algebraic systems: Lie and Jordan algebras and triple systems, Jordan pairs or Freudenthal triple systems.

Lie algebras with S3- or S4-action and generalized Malcev algebras

Lie algebras endowed with an action by automorphisms of any of the symmetric groups S3 or S4 are considered, and their decomposition into a direct sum of irreducible modules for the given action is studied. In the case of S3-symmetry, the Lie algebras are coordinatized by some non-associative systems, which are termed generalized Malcev algebras, as they extend the classical Malcev algebras. These systems are endowed with a binary and a ternary product, and include both the Malcev algebras and the Jordan triple systems.

Models of some simple modular Lie superalgebras

We provide models of the exceptional simple modular Lie superalgebras in characteristic p = 3 that appeared in the 2007 classification by Bouarroudj, Grozman and Leites of Lie superalgebras with indecomposable symmetrizable Cartan matrices. The models relate these exceptional Lie superalgebras to some low-dimensional nonassociative algebraic systems.

Calculations of the enthalpy of solution of nonelectrolytes in mixed solvents within the framework of molecular association theory

The enthalpies of solution of nonelectrolytes in mixed solvents were calculated using the Associated Solution + Lattice thermodynamic model, whose parameters are equilibrium constants, the enthalpies of formation of associates, and the energy of mutual exchange of mixed solvent components. The method of calculations used provided close agreement between calculation results and experimental data on nonassociated solutions and systems with a complex molecular association character.

Equation of State Coupled with Scaled Particle Theory for Surface Tensions of Liquid Mixtures

A new statistical mechanics model is developed to calculate the surface tensions of liquid mixtures, based on an equation of state for chain fluids and the scaled particle theory. Transferrable molecular parameters fitted to experimental phase equilibrium properties are used in this model. The feasibility of the model has been systematically tested in the correlations of 62 binary mixtures and in the predictions of 7 binary and 5 ternary mixtures, including nonassociating, self-associating, and cross-associating systems with overall average absolute relative deviations of 0.31%, 0.86%, and 0.92%, respectively. The accuracy of the new model makes it particularly well-suited in the calculation of surface tensions for a wide range of complex liquid mixtures.

Applications of Associating Martin−Hou Equation of State to Vapor−Liquid Equilibria in the Critical Region or the Near-Critical Region

The associating Martin−Hou equation of state (AMH EOS) has been extended to high-pressure vapor−liquid equilibria calculations of alcohol-containing systems in the critical or near-critical region. The old mixing rules used in previous studies have been revised. The high-pressure vapor−liquid equilibria of some alcohol + hydrocarbon systems can be represented satisfactorily by the AMH EOS with the old mixing rules. However, the high-pressure vapor−liquid equilibria of alcohol + carbon dioxide systems and some other alcohol + hydrocarbon systems should be correlated well by the AMH EOS with the revised mixing rules. High-pressure vapor−liquid equilibria of two ternary systems that contain two alcohols and two nonassociating ternary systems are predicted from binary data.

Applications of the simplified perturbed-chain SAFT equation of state using an extended parameter table

An equation of state based on perturbation theory, the simplified perturbed-chain statistical associating fluid theory (PC-SAFT) is applied to binary systems that include an extensive number of non-associating compounds. Pure-component parameters of different compounds that are not available in the literature are estimated by correlating vapour-pressure and liquid-density data and by using an interpolation method. PC-SAFT parameters for 200 new compounds are estimated for different families of nonassociating compounds (alkanes, alkenes, alkynes, cycloalkenes, nitroalkanes, polynuclear aromatics, ketones, esters, sulphides, siloxanes, plasticizers, cyclo- and fluorinated-hydrocarbons, etc.). For many different families of compounds, the segment diameter and interaction energy are found to be constant with increasing molar mass, while the segment number increases linearly with molar mass. Using these parameters, simplified PC-SAFT is shown to predict vapour–liquid equilibria successfully for many nonassociating systems and also correlates liquid–liquid equilibria for perfluorohexane- n-alkane systems. In a few cases, a small binary interaction parameter k ij is needed for the satisfactory correlation of the experimental data.

Associative polymer/particle dispersion phase diagrams III: Pigments

The colloidal interactions of both HEUR and HASE associative polymers with pigments in the presence of dispersant are complicated and subject to a number of variables. The objective of this work was to clarify the conditions needed to achieve good pigment dispersion in associative thickener systems by characterizing particle dispersion behavior. This had previously been done for latex particles, but not for pigments such as TiO2. Good dispersion leads to optical properties, such as gloss and hiding, that are superior to nonassociative thicknener systems. Pigment dispersion phase diagrams represent a good way to visualize the complex interactions among pigments, dispersant, and thickener. The two most important variables were found to be pigment type (i.e., surface composition) and dispersant composition. Associative thickners can yield good pigment dispersion or flocculation, depending on the correct matching of dispersants and pigment type. Because of the hydrophobic functional groups governing associative thickner behavior, dispersants having some hydrophobic character yielded the best pigment dipersions and optical properties because they could couple the pigment particles with the associative thickener network. Interior-grade TiO2 tended to yield better dispersions and optical properties than exterior-grade TiO2. Optimized associative thickner systems generally had improved optical properties over comparable nonassociative systems. Optical properties correlated well with particle dispersion behavior as displayed by the dispersion phase diagrams.

Prediction of Binary VLE for Imidazolium Based Ionic Liquid Systems Using COSMO-RS

A novel method based on unimolecular quantum mechanical calculation has been used to predict the binary vapor−liquid equilibria (VLE) of ionic liquids (ILs).The recently developed conductor-like screening model (COSMO), along with the most common quantum chemical package of GAUSSIAN 03, has been used in this work. These conductor-like screening model calculations combined with exact statistical thermodynamics provide the information necessary for the evaluation of molecular interactions in liquids. An effective parametrization has been done using 10 associated and 22 binary nonassociated systems; these 32 systems are all non-ILs. The effective contact surface area aeff and the hydrogen-bonding coefficient chb have been estimated using a sequential scheme. The root-mean-square error obtained for excess Gibb's free energy is ∼0.1 for aeff and chb. Values for α‘ (misfit constant), σhb (cutoff surface charge density for hydrogen bonding), and cavity radii (ri) as given in the literature have been used as defa...

An accurate density functional theory for the vapor-liquid interface of associating chain molecules based on the statistical associating fluid theory for potentials of variable range

A Helmholtz free energy density functional is developed to describe the vapor-liquid interface of associating chain molecules. The functional is based on the statistical associating fluid theory with attractive potentials of variable range (SAFT-VR) for the homogenous fluid [A. Gil-Villegas, A. Galindo, P. J. Whitehead, S. J. Mills, G. Jackson, and A. N. Burgess, J. Chem. Phys. 106, 4168 (1997)]. A standard perturbative density functional theory (DFT) is constructed by partitioning the free energy density into a reference term (which incorporates all of the short-range interactions, and is treated locally) and an attractive perturbation (which incorporates the long-range dispersion interactions). In our previous work [F. J. Blas, E. Martin del Rio, E. de Miguel, and G. Jackson, Mol. Phys. 99, 1851 (2001); G. J. Gloor, F. J. Blas, E. Martin del Rio, E. de Miguel, and G. Jackson, Fluid Phase Equil. 194, 521 (2002)] we used a mean-field version of the theory (SAFT-HS) in which the pair correlations were neglected in the attractive term. This provides only a qualitative description of the vapor-liquid interface, due to the inadequate mean-field treatment of the vapor-liquid equilibria. Two different approaches are used to include the correlations in the attractive term: in the first, the free energy of the homogeneous fluid is partitioned such that the effect of correlations are incorporated in the local reference term; in the second, a density averaged correlation function is incorporated into the perturbative term in a similar way to that proposed by Toxvaerd [S. Toxvaerd, J. Chem. Phys. 64, 2863 (1976)]. The latter is found to provide the most accurate description of the vapor-liquid surface tension on comparison with new simulation data for a square-well fluid of variable range. The SAFT-VR DFT is used to examine the effect of molecular chain length and association on the surface tension. Different association schemes (dimerization, straight and branched chain formation, and network structures) are examined separately. The surface tension of the associating fluid is found to be bounded between the nonassociating and fully associated limits (both of which correspond to equivalent nonassociating systems). The temperature dependence of the surface tension is found to depend strongly on the balance between the strength and range of the association, and on the particular association scheme. In the case of a system with a strong but very localized association interaction, the surface tension exhibits the characteristic "s shaped" behavior with temperature observed in fluids such as water and alkanols. The various types of curves observed in real substances can be reproduced by the theory. It is very gratifying that a DFT based on SAFT-VR free energy can provide an accurate quantitative description of the surface tension of both the model and experimental systems.