Application of nature‐inspired algorithms with generalized Pitzer‐Debye‐Hückel (PDH) refinement for liquid liquid equilibria (LLE) correlation in cyclic di‐ether systems

Abstract

Metaheuristic algorithms such as the genetic algorithm (GA) and cuckoo search (CS) algorithms have been widely used for phase equilibria computation. In the present work, correlation of the liquid-liquid splitting of 1,3-dioxolane + water and 1,4-dioxane + water mixtures using the buffers 3-n-morpholino-propanesulfonic acidacid (HEPPS), and the ionic-liquid (IL) tetra-methyl-ammonium 3-[4-(2-hydroxymethyl)-1-piperazinyl]propanesulfonate [TMA][EPPS] is performed by the GA-NRTL, CS-NRTL, GA-UNI-QUAC, and CS-UNIQUAC methods. Thermodynamically consistent binary interaction parameters are obtained after a rigorous investigation of the dimensionless excess Gibbs free energy of mixing G M (L)/RT topology thereby satisfying the Gibbs minor common tangent phase stability test. The results indicate that the GA-UNIQUAC method performs the best for correlating the biphasic regions with very high quantitative accuracies and well-resolved G M (L)/RT surface description. Furthermore, the UNIQUAC model is significantly enhanced by incorporating a thermodynamically consistent extended Pitzer-Debye-Hückel* (PDH*) contribution term considering weak electrostatic long-range interactions within the IL-rich phases.

Impact of extended long-range electrostatics on the correlation of liquid-liquid equilibria in aqueous ionic liquid systems

“…In contrast, the E-PDH and ME-PDH equations allow a better representation of the phase equilibria. These results support the conclusions of Chang and Lin [31], Ganguly et al [41] and González de Castilla et al [55] regarding superior thermodynamic modeling performance when consistently including concentration dependent properties within long-range electrostatics.…”

“…As experiments may be time-consuming and costly, one proper tool to evaluate properties of different compounds in mixtures is predictive thermodynamic modeling. When considering IL-based systems, their behavior has been accurately modeled using equations of state (EoS) [12][13][14][15][16][17][18][19][20], such as the Perturbed Chain based on Statistical Associating Fluid Theory (PC-SAFT) and Cubic Plus Association (CPA), or excess Gibbs free energy (G E ) models [21][22][23][24][25][26][27][28][29][30][31][32][33][34], such as the Non-Random Two-Liquid (NRTL) [31,[35][36][37][38], UNIversal QUAsi-Chemical (UNIQUAC) and UNIversal Function group Activity Coefficient (UNIFAC) [24,26,[39][40][41][42][43][44] or even the predictive Conductor-like Screening Model for Realistic Solvents (COSMO-RS) [29][30][31][32][33][45][46][47]…”

“…Shilov and Lyashchenko [58,60,63] developed an extended Debye-Hückel theory, while Büllow et al [18] coupled a similar term with the ePC-SAFT EoS. A widely explored alternative is the extended PDH term, occasionally present in literature as ext-PDH [41]. This extension of the conventional PDH equation has been combined with other short-ranged interaction models by several authors.…”

“…Chang and Lin [31,32] presented its full derivation and coupled it with the COSMO-SAC model tailoring the long-range term to fit ILs in organic solvents. This approach was afterwards tested by Ganguly et al [41] with an eUNIQUAC model. In these cases, concentration dependent properties are employed in ext-PDH and its use outperforms the conventional PDH, especially at high IL concentrations.…”

On the analogy between the restricted primitive model and capacitor circuits. Part II: A generalized Gibbs-Duhem consistent extension of the Pitzer-Debye-Hückel term with corrections for low and variable relative permittivity

“…[15][16][17][18][19][20] All of which require a complement for long-ranged coulombic interactions between charged species, commonly given by Debye-Hückel theory, 21 the Mean Spherical Approximation (MSA) 22,23 or the Pitzer-Debye-Hückel term 24,25 and in many cases benefit from the use of a Born term. 17,26 The Pitzer-Debye-Hückel term and its extensions are most commonly applied to g E -models like the electrolyte NRTL, [27][28][29] UNIFAC/UNIQUAC based electrolyte models 5,6, [30][31][32][33] and COSMO-RS based electrolyte models. [8][9][10][11][12][34][35][36][37] The thermodynamically consistent introduction of the dielectric constant in these electrolyte theories regained particular focus in the recent literature.…”