Eyring's Absolute Rate Theory Research Articles

Modeling dynamic viscosities of multi-component aqueous electrolyte solutions containing Li+, Na+, K+, Mg2+, Ca2+, Cl−, SO42− and dissolved CO2 under conditions of CO2 sequestration

Two accurate models were developed by this study for dynamic viscosities of multi-component aqueous electrolyte solutions containing Li+, Na+, K+, Mg2+, Ca2+, Cl−, SO42− and dissolved CO2 under conditions of CO2 sequestration. The first model is constructed by extending the Mao–Duan model for viscosities of binary aqueous solutions (aqueous single electrolyte solutions) of alkali-chloride to binary solutions of alkaline-earth chlorides, common sulfate and CO2 and combining it with Hu's mixing rule to model viscosities of multi-component solutions. The second model is constructed by improving the Goldsack–Franchetto model based on the Eyring's absolute rate theory to account for the effect of temperature on viscosity. The forms of both models are simple.Comparisons of calculations of the two models with experimental viscosity data show that both models can well represent dynamic viscosities of aqueous single electrolyte solutions and aqueous CO2 solutions at temperatures from 273 K to temperatures higher than 473 K, and at pressures from 0.1 MPa to 100 MPa. Furthermore, the two models can predict viscosities of aqueous NaCl solutions with dissolved CO2, brine containing Li+, Na+, K+, Mg2+, Ca2+, Cl−, SO42− and seawater over a wide P-T range. The absolute average deviations of the two models from most of experimental data sets are less than 2%.

A predictive viscosity model for aqueous electrolytes and mixed organic–inorganic aerosol phases

Abstract. Aerosol viscosity is determined by mixture composition and temperature, with a key influence from relative humidity (RH) in modulating aerosol water content. Aerosol particles frequently contain mixtures of water, organic compounds, and inorganic ions, so we have extended the thermodynamics-based group-contribution model AIOMFAC-VISC to predict viscosity for aqueous electrolyte solutions and aqueous organic–inorganic mixtures. For aqueous electrolyte solutions, our new, semi-empirical approach uses a physical expression based on Eyring's absolute rate theory, and we define activation energy for viscous flow as a function of temperature, ion activities, and ionic strength. The AIOMFAC-VISC electrolyte model's ion-specific expressions were simultaneously fitted, which arguably makes this approach more predictive than that of other models. This also enables viscosity calculations for aqueous solutions containing an arbitrary number of cation and anion species, including mixtures that have never been studied experimentally. These predictions achieve an excellent level of accuracy while also providing physically meaningful extrapolations to extremely high electrolyte concentrations, which is essential in the context of microscopic aqueous atmospheric aerosols. For organic–inorganic mixtures, multiple mixing approaches were tested to couple the AIOMFAC-VISC electrolyte model with its existing aqueous organic model. We discuss the best-performing mixing models implemented in AIOMFAC-VISC for reproducing viscosity measurements of aerosol surrogate systems. We present advantages and drawbacks of different model design choices and associated computational costs of these methods, of importance for use of AIOMFAC-VISC in dynamic simulations. Finally, we demonstrate the capabilities of AIOMFAC-VISC predictions for phase-separated organic–inorganic particles equilibrated to observed temperature and relative humidity conditions from atmospheric balloon soundings. The predictions for the studied cases suggest liquid-like viscosities for an aqueous electrolyte-rich particle phase throughout the troposphere, yet a highly viscous or glassy organic-rich phase in the middle and upper troposphere.

The Debye length and anionic transport properties of composite membranes based on supported ionic liquid-like phases (SILLPS).

An analysis of the ionic transport properties of BMIM [NTf2] in supported ionic-liquid-like phase (SILLP)-based membranes has been carried out based on experimental impedance spectroscopy measurements. The direct current (dc)-conductivity was analyzed to determine the temperature and frequency dependence. The fit of the loss tangent curve data with the Cole-Cole approximation of the electrode polarization model provides the conductivity, diffusivity, and density of charge carriers. Among these quantities, a significant increase in conductivity is observed when an ionic liquid is added to the polymeric matrix containing imidazolium fragments. The use of a recent generalization of Eyring's absolute rate theory allowed the elucidation of how the local entropy restrictions, due to the porosity of the polymeric matrix, control the conductive process. The fit of the conductivity data as a function of temperature manifests the behavior of the excess entropy with respect to the temperature. The activation entropy and enthalpy were also determined. Our results correlate the Debye length (LD) with the experimental values of conductivity, electrode polarization relaxation time, and sample relaxation time involved. Our work provides novel insights into the description of ionic transport in membranes as the diffusivity, mobility, and free charge density depend on the LD. Moreover, we discuss the behavior of the polarization relaxation time, the sample relaxation time, and the static permittivity as a function of the temperature.

Simultaneous representation of thermodynamic properties and viscosities of ILs/DESs+co-solvent systems by Eyring-NRTL model

In this work, the nonrandom two-liquid model (NRTL) was coupled with the Eyring's absolute rate theory (the Eyring-NRTL model), to study thermodynamic properties and viscosities simultaneously with one set of parameters, and ten non-aqueous mixtures containing ionic liquids (ILs)/deep eutectic solvents (DESs) were chosen in the study as the first step. In model parameterizing, three strategies were investigated, which were viscosity as the input only, enthalpy with/without vapor pressure as the inputs, and enthalpy and viscosity as inputs, respectively. The investigation shows that it is possible to represent thermodynamic and kinetic properties simultaneously. Furthermore, the viscosity can be predicted using the model with reasonable parameters determined from the excess enthalpy, and incorporating vapor pressures and limited viscosity data in parameterizing can further improve the model performance on the viscosity. For the first time, the thermodynamic model was coupled with the Eyring's theory to study the systems of (IL/DES + molecular solvent), how to obtain the model parameters was clarified, and the possibility and reliability of the used model in representing thermodynamic and kinetic properties were illustrated and discussed.

An experimental investigation and correlation of the viscosity refrigerant/oil solutions

Abstract 2,3,3,3-tetrafluoroprop-1-ene (R1234yf) and trans-1,3,3,3-tetrafluoropropene (R1234ze(E)) as the promising refrigerants have attracted wide attention. To understand better of the refrigeration-cycle performance working with new refrigerants, the thermodynamic properties of refrigerant/oil mixtures should be well known, especially the viscosity of the refrigerant/oil mixture. Using a dual-capillary method, the viscosities were measured for POE75 saturated with R1234yf and R1234ze(E) from 303.15 to 348.15 K. The viscosity trends of R1234yf/POE75 and R1234ze(E)/POE75 mixtures are similar. As rising solubility, a sharp decrease of viscosity appeared firstly, and then it goes to be flat. Results show that the dissolved refrigerant in oil largely reduces the oil viscosity. Comparing to viscosity models including an empirical model (modified Setchenow-type equation) and Eyring's absolute rate theory coupled with three excess Gibbs energy models (Eyring-MTSM model, Eyring-NRTL model, and Eyring-wilson model), the Eyring-MTSM model give better results than the other studied models.

Modeling of the density, viscosity and electrical conductivity of aqueous solutions saturated in boric acid in presence of lithium sulfate or sodium sulfate at 293.15 to 313.15 K

The modeling of the density, viscosity and electrical conductivity of aqueous solutions saturated with boric acid, in the presence of sodium sulfate or lithium sulfate, are presented. The salt concentrations range studied were from (0 to 3.3242) mol·kg−1 for sodium sulfate and from (0 to 2.9336) mol·kg−1 for lithium sulfate at temperatures from (293.15 to 313.15) K and at 1 atm pressure. A model for the density was derived using the Pitzer model. The Eyring's absolute rate theory and the Pitzer model were combined to represent the viscosity. The Casteel-Amis equation was modified to describe the electrical conductivity with temperature and boric acid effects where necessary. The results showed that the models successfully represented the properties studied and are robust for estimation purposes within and beyond the experimental range studied. Also, it was found that short range interactions of boric acid, sulfate, sodium and lithium ions with water molecules are relevant to determine the volumetric and transport properties of these solutions and that the electrical conductivity is determined by charged species (Na+, SO42−, NaSO4−, HSO4− and Li+, SO42−, LiSO4−) and the solution viscosity; that is mainly influenced by these salts concentrations, boric acid solubility behavior with these salts and temperature. This is valuable information to improve the processes of boric acid production.

Modeling the Transport and Volumetric Properties of Solutions Containing Polymer and Electrolyte with New Model

A new theoretical model based on the local composition concept (TNRF-mNRTL model) was proposed to express the short-range contribution of the excess Gibbs energy for the solutions containing polymer and electrolyte. This contribution of interaction along with the long-range contribution of interaction (Pitzer-Debye-Huckel equation), configurational entropy of mixing (Flory-Huggins relation) and Eyring absolute rate theory were used to fit the viscosity values of ternary aqueous solutions of polymer + electrolyte with considering temperature dependency. The local composition models which are available for correlating the thermodynamic properties of ternary polymer + electrolyte solutions (ternary-Wilson, ternary-modified NRTL, and ternary-modified Wilson) with Eyring absolute rate theory were also used for fitting the viscosity values of ternary solutions for the first time. THe fitting quality of Eyring-TNRF-mNRTL model was compared with these models. The equations of apparent molar volume were also derived from TNRF-mNRTL, ternary-Wilson, ternary-modified NRTL, and ternary-modified Wilson models. These equations were used for correlating the apparent molar volume and density values of ternary polymer + electrolyte solutions.

Estimating the viscosity of ionic liquid at high pressure using Eyring's absolute rate theory

A viscosity model for ionic liquids (ILs) at high pressure based on Eyring's absolute rate theory was presented, in which the flow energy was considered as two parts: the activation energy and the vacancy formation energy. A reference state was introduced to simplify the calculation process. Peng-Robinson equation, Soave-Redlich-Kwong equation and group contribution method were chosen to estimate the compressibility factor required in the present model. The experimental viscosity data of 25 ILs at the temperatures from 273.15 K to 433.15 K and pressures up to 300 MPa were used to test the present model. The overall average absolute relative deviation of the present model coupled with the three compressibility factor calculation methods are 2.03%, 2.01% and 1.92%, respectively. The accuracy effect of the compressibility factor calculation method on the performance of the present model was also investigated. Parameters of the present model were generalized in terms of the carbon numbers of the cation alkyl chain for the homologous series of ILs in order to improve the predictive ability.

Viscosity modeling of water + alkanediols mixtures

In this study, both theoretical and empirical viscosity models were evaluated for binary associating liquid mixtures of water+1,2-ethanediol, 1,3-propanediol, 1,4-butanediol, and 1,5-pentanediol. The interaction between molecules in the mixtures was analyzed using the calculation of excess energy of flow obtained from Eyring's absolute rate theory. Free volume (FV) viscosity model was coupled with Peng-Robinson (PR) and perturbed-chain statistical associating fluid theory (PC-SAFT) equation of states (EoS); friction theory (FT) was coupled with PR EoS; no significant difference was observed in the modeling results using different EoS. A new mixing rule was found to improve the modeling results of FT coupled with the PR EoS for the binary mixtures studied. The empirical models correlated viscosity of aqueous diol systems well with average absolute percent deviation (AAD%) <1.

The study on temperature dependence of viscosity and surface tension of several Phosphonium-based deep eutectic solvents

Deep eutectic solvents (DESs) are derived from two or more salts as the hydrogen bond acceptors (HBAs) and hydrogen bond donors (HBDs). In this work, six deep eutectic solvents (DESs) were prepared namely allyltriphenyl phosphonium bromide- diethylene glycol (ATPPB-DEG) and allyltriphenyl phosphonium bromide - triethylene glycol (ATPPB-TEG) using three molar ratios of 1:4, 1:10 and 1:16 salt to HBDs. The temperature range for experimental viscosity was from 293.15 to 343.15K and that of the experimental surface tension was between 298.15 and 343.15K. The results disclosed that hydrogen bonding in DESs has a great effect on the properties. Among all DESs with the same components, the DESs with the strong hydrogen bonding in their structures had the higher viscosity and surface tension. Besides, by increasing the temperature and quantity of HBDs in DESs, both of these properties experienced a decreasing trend in the amount. It was found that the molecular weight of DESs with the same component has an effect on the properties. The higher molecular weight caused the higher viscosity and surface tension. Further, ATPPB-TEG DESs had the higher viscosity and lower surface tension than ATPPB-DEG DESs because of the higher alkyl chain in their structures. Several models and a new empirical equation were used to correlate the experimental viscosity data. It was found that there is a well agreement between theoretical and experimental values especially when the new empirical equation is used. In addition, the activation parameters for all DESs were calculated using the experimental viscosity data and application of Eyring's absolute rate theory. The experimental surface tension was employed to predict the critical temperature, surface entropy and internal surface energy of DESs. Finally, two empirical equations were used for relating the experimental surface tension to the experimental viscosity of DESs.

Correlation for viscosities of pure liquids at high pressures

Abstract An accurate model for the viscosities of nonpolar and polar liquids at high pressure based on the Eyring's absolute rate theory and the equation of state has been proposed by Martins et al. in 2003. One characteristic of this model is requiring two adjustable parameters at each temperature, which limits its application. In this work, we modified their model by establishing correlations between the adjustable parameters and temperature to improve its predictive potential. The present model coupled with Soave-Redlich-Kwong equation of state was applied to correlate the viscosities of 30 compounds including alkanes, alkenes, aromatics, alcohols, oxygen, argon and nitrogen at temperatures from 65 K to 460 K and pressures from 0.1 MPa to 253.1 MPa. The calculated values from the present model agree well with the experimental data in all cases, with the average absolute relative deviations lower than 3.7%.

VOLUMETRIC PROPERTIES AND VISCOSITIES OF ACETIC ACID WITH ETHYLENE GLYCOL AND DIETHYLENE GLYCOL AT TEMPERATURES FROM 303.15 TO 323.15 K

Densities and viscosities of the binary mixtures of acetic acid with ethylene glycol and diethylene glycol were measured over the entire range of composition at five temperatures T = 303.15, 308.15, 313.15, 318.15, and 323.15 K. The excess molar volumes and viscosity deviations were calculated and fitted to the Redlich-Kister type polynomial equation. The viscosity data reported herein were used to examine the modeling capabilities of viscosity equations based on Eyring's absolute reaction rate theory and excess Gibbs free energy functions, namely, the Eyring-Van Laar, the Eyring-Scatchard and Hamer, and the Eyring-UNIQUAC equations. Some one-parameter models such as the Fang and He equation and the Grunberg and Nissan equation were also tested.

Correlation of Viscosity of Aqueous Solutions of Alkanolamine Mixtures Based on the Eyring's Theory and Wong-Sandler Mixing Rule

A viscosity model, based on Eyring's absolute rate theory combined with a cubic PR equation of state and Wong-Sandler mixing rule, has been proposed in order to correlate viscosities of aqueous solutions of alkanolamine mixtures at atmospheric pressure and different temperatures. In the proposed method, the energy and size parameters in studied Equation of State (EoS) have been obtained using the Wong - Sandler (WS) mixing rule combined with the NRTL and Wilson Gibbs equations. The NRTL and Wilson parameters for aqueous solutions of alkanolamine mixtures have been correlated using measured viscosity data at atmospheric pressure and different temperatures. The overall average deviation between the experimental and calculated viscosities of studied aqueous solutions of alkanolamine mixtures using Wilson model is 0.92%.

Electrochemical determination of ferrocene diffusion coefficient in [C6MIM][PF6]–CO2 biphasic system

Diffusion coefficient is an important property in chemical industry and precise measurements can be achieved by electrochemical techniques. Study of ferrocene diffusion was carried out in 1-hexyl-3-methyl imidazolium hexafluorophosphate-dense CO2 ([C6MIM][PF6–CO2]) biphasic system using microelectrode technique. Diffusion coefficients were determined by cyclic voltammetry and Randles–Ševčík relationship in the temperature and pressure ranging from 303.15 to 333.15K and 1–10MPa, respectively. Computed phase simulations were also used. Two-phase system was determined whatever experimental conditions and composition tested. Volumes of heavy and light phase were estimated as well. Both electroanalytical and computed studies showed that [C6MIM][PF6]–CO2 biphasic system containing initial molar fraction of CO2 up to 0.9 can be used without decrease in diffusion coefficient values. The order of magnitude of these diffusion coefficients of ferrocene in greener aprotic media is about 10−6m2s−1. Theoretical analysis of ferrocene mass transport was also carried out using Sutherland formula and viscosity model based on Eyring's absolute rate theory. Dramatic decrease in [C6MIM][PF6]-CO2 mixture viscosity with x(CO2) was estimated by calculations.

New local composition model for modeling of thermodynamic and transport properties of binary aqueous electrolyte solutions

A new local composition model, which is an NRF–modified-NRTL (NRF–mNRTL) model, is developed for the representation of the excess Gibbs energy of electrolyte solutions. In this model for excess Gibbs energy the sum of a long-range and a short-range term is used. The contribution of the long-range excess Gibbs energy is represented by the Pitzer–Debye–Hückel model. A new expression based on the local composition concept has been developed to account for the contribution of the short range excess Gibbs energy. The model is applied to correlate the mean ionic activity coefficients and osmotic coefficients of more than respectively 150 and 290 binary aqueous electrolyte solutions at 25 °C. The fitting quality of the new model has been favorably compared with the electrolyte NRTL, Wilson, modified NRTL, NRTL–NRF, NRF–Wilson, UNIQUAC–NRF, Pitzer and TCPC models. Viscosity values of the binary aqueous solution of electrolytes have also successfully been correlated with the proposed local composition model by considering the Eyring absolute rate theory. The validity of the proposed model is specially demonstrated for multivalent electrolyte binary solutions encompassing the entire range of composition.

A new one parameter viscosity model for binary mixtures

AbstractThe Grunberg &amp; Nissian equation with one parameter is widely recommended in the viscosity calculation. However, it is demonstrated that this equation fails to generate satisfactory results for size‐asymmetric mixtures containing large and small molecules. In this work, a new one parameter viscosity model for binary mixtures has been developed on the basis of Eyring's absolute reaction rate theory and the Flory‐Huggins equation. The concept of molecular surface fraction is introduced for modeling liquid mixture viscosities. The viscosity calculations of the new equation are compared with the Grunberg &amp; Nissian equation for a broad range of chemical mixtures including 527 binary systems (containing 63 binary ionic liquid cosolvent systems) and total 17,268 viscosity points. The new equation was found to have an improved performance over the frequently employed Grunberg &amp; Nissian equation, especially for size‐asymmetric mixtures containing large and small molecules. © 2010 American Institute of Chemical Engineers AIChE J, 57: 517–524, 2011

Mixing properties of Tris(2-ethylhexyl) phosphate with alkanes at different temperatures and data treatment using several correlation equations based on Eyring's absolute reaction theory

Densities and viscosities of binary mixtures of Tris(2-ethylhexyl) phosphate with n-heptane, or n-octane have been determined over the entire range of composition at T = (298.15, 303.15, and 308.15) K and atmospheric pressure. The excess molar volumes are calculated and fitted to a Redlich–Kister type equation. The excess molar volumes are negative over the whole composition range. Several semi-theoretical equations based on Eyring's absolute rate theory and the excess Gibbs free energy function have been applied to correlate the experimental viscosity data and compared. The evaluated models include the Eyring–Van Laar, Eyring–Margules, Eyring–NRTL, Eyring–UNIQUAC and the Grunberg–Nissan equations.

Justification of biexponential rate law of spreading over heterogeneous and rough surfaces

Both surface roughness and chemical heterogeneity can be viewed as surface energy fluctuations acting as energy barriers for the three phase contact (TPC) line motion. This viewpoint provides a way to obtain the TPC line propagation rate as a function of the TPC contact angle in the frame of either nucleation rate theory or Eyring's absolute rate theory. In this study, a general biexponential rate law is deduced, and the wetting kinetic characteristics are related to statistical characteristics of the surface chemical heterogeneity and roughness, experimentally available from surface image analysis. A step mechanism for TPC line propagation is proposed; the barrier for a step is due to solid surface roughness and liquid surface corrugation, and the absolute frequency of steps is estimated through the dispersion relation of the capillary waves at the liquid surface. The free energy vs. TPC contact angle diagram of a randomly rough surface is deduced and found to be very similar to Dettre–Johnson's diagrams of periodically rough surfaces. The TPC propagation rate law is generally asymmetric, in accordance with the available experimental data. A comparison with experimental dynamic contact angle hysteretic curves gives reasonable values of the model's parameters.

Semi-ideal Solution Theory. 2. Extension to Conductivity of Mixed Electrolyte Solutions

Conductivities were measured for the ternary systems NaCl-LaCl(3)-H(2)O and KCl-CdCl(2)-H(2)O and their binary subsystems NaCl-H(2)O, KCl-H(2)O, CdCl(2)-H(2)O, and LaCl(3)-H(2)O at 298.15 K. The semi-ideal solution theory for thermodynamic properties of aqueous solutions of electrolyte mixtures was used together with the Eyring absolute rate theory to study conductivity of mixed electrolyte solutions. A novel simple equation for prediction of the conductivity of mixed electrolyte solutions in terms of the data of their binary solutions was established. The measured conductivities and those reported in literature were used to test the newly established equation and the generalized Young's rule for conductivity of mixed electrolyte solutions. The comparison results show that the deviation of a ternary solution from the new conductivity equation is closely related to its isopiestic behavior and that the deviations are often within experimental uncertainty if the examined system obeys the linear isopiestic relation. While larger deviations are found in the system with large ion pairing effect, the predictions can be considerably improved by using the parameters calculated from its isopiestic results. These results imply that the previous formulation of the thermodynamic properties of aqueous solutions of electrolyte mixtures has a counterpart for transport properties.

Extension of the electrolyte NRTL and Wilson models for correlation of viscosity of strong electrolyte solutions at different temperatures

The electrolyte NRTL model [C.C. Chen, L.B. Evans, AIChE J. 32 (1986) 444–454] and electrolyte Wilson model [E. Zhao, M. Yu, R.E. Sauvé, M. Khoshkbarchi, Fluid Phase Equilibr. 173 (2000) 161–175] have been extended for the representation of the dynamic viscosity of strong electrolyte solutions. The models are based on Eyring's absolute rate theory and the electrolyte NRTL and Wilson models for calculating the excess Gibbs energy of activation of the viscous flow. The utility of the models is demonstrated with a successful representation of the viscosity of several electrolyte solutions at different temperatures. The results show that, the model is valid for the whole range of salt concentration and it is reliable for correlation of the viscosity of electrolyte solutions at different temperatures by only four adjustable parameters per binary system.