Molecular Thermodynamic Modeling Research Articles

The Entropy of Mixing in Self-Assembly and the Role of Surface Tension in Modeling the Critical Micelle Concentration

A theory for the micelle formation of nonionic head-tail amphiphiles (detergents) in aqueous solutions is derived based on the traditional molecular thermodynamic modeling approach and a variant of the Flory–Huggins theory that goes beyond lattice models. The theory is used to analyze experimental values for the critical micelle concentration of n-alkyl-ß-D-maltosides within a mass action model. To correlate those parts of the micellization free energy, which depend on the transfer of hydrophobic molecule parts into the aqueous phase, with molecular surfaces, known data for the solubility of alkanes in water are reanalyzed. The correct surface tension to be used in connection with the solvent-excluded surface of the alky tail is ~30 mN/m. This value is smaller than the measured surface tension of a macroscopic alkane–water interface, because the transfer free energy contains a contribution from the incorporation of the alkane or alkyl chain into water, representing the change in free volume in the aqueous phase. The Flory–Huggins theory works well, if one takes into account the difference in liberation free energy between micelles and monomers, which can be described in terms of the aggregation number as well as the thermal de Broglie wavelength and the free volume of the detergent monomer.

Evaluation of the Second Virial Coefficient for the Mie Potential Using the Method of Brackets

The second virial coefficient for the Mie potential is evaluated using the method of brackets. This method converts a definite integral into a series in the parameters of the problem, in this case this is the temperature T. The results obtained here are consistent with some known special cases, such as the Lenard-Jones potential. The asymptotic properties of the second virial coefficient in molecular thermodynamic systems and complex fluid modeling are described in the limiting cases of T → 0 and T → ∞ .

Investigation of the multitemperature stable phase equilibria of alkali tetraborates and bromides and molecular thermodynamic modeling based on DFT

The multitemperature stable phase equilibria of alkali tetraborate and bromide were investigated by isothermal dissolution equilibrium method. Based on the experimental data, the phase diagrams and the density-composition diagrams of the ternary systems were drawn respectively. The results demonstrate that the phase diagrams of alkali tetraborate and bromide ternary systems with water as solvent at 273.2 K, 288.2 K and 308.2 K consist of one invariant point, two univariate solubility curves and two crystallization fields. The density at the invariant points is greater than that at the adjacent points. Additionally, based on density functional theory (DFT), a molecular model of phase equilibria of alkali tetraborate and bromide was creatively established to predict the phase equilibrium solubilities of the ternary systems. Based on results of Raman spectra identification of borate ions in the ternary mixed solutions, the primary forms of borate ions in solution, namely B(OH)3, B(OH)4−, B3O3(OH)4− and B4O5(OH)42− were comprehensively considered in this work. By comparing the experimental data of these ternary systems with the calculated results of the DFT model, it is found that the DFT model can describe the solid–liquid equilibria of the ternary systems well, and has high accuracy. The investigation of the multitemperature stable phase equilibria of alkali tetraborate and bromide can provide thermodynamic data for separation of alkali tetraborates and bromides in brines.

The solubility of H2 in NaCl brine at high pressures and high temperatures: Molecular simulation study and thermodynamic modeling

To address the energy demands of a growing population and mitigate carbon emissions, it is imperative to transition from fossil fuels to renewable energy sources. However, the intermittency of renewable energies poses a significant challenge. To address this issue, deep saline aquifers have emerged as a viable option for large-scale energy storage, particularly through hydrogen (H2) storage post Power-to-Gas process. Moreover, natural H2 emissions have been documented worldwide, and the potential for underground accumulations presents promising zero-carbon energy sources. However, in these different contexts, the interaction between gas, brine, and rock can lead to physico-chemical and biochemical phenomena that can directly impact the mobility and stability of H2. Therefore, understanding the thermophysical behavior of the involved fluids is essential for the development Underground Hydrogen Storage in porous media and for exploring natural H2 reserves. However, despite recent advancements, there is still a lack of experimental data on thermophysical properties of hydrogen in contact with brine. This study investigates the equilibrium of the H2/brine system using Continuous Fractional Component Monte Carlo molecular simulation through two methods: the Gibbs ensemble method and the isobaric-isothermal simulation based on Henry's law. Different force fields for H2, water and salt (NaCl) ions were evaluated. Through a comparative analysis, two model combinations, Marx-TIP4P/EP-KBF and Marx-TIP4P/2005-Madrid, were identified as providing the most accurate results, albeit requiring a constant binary interaction for enhanced H2 solubility quantification in brine. After adjustment to some limited experimental data from literature, the simulations were extended to higher temperatures (up to 453 K), pressures (up to 100 MPa), and NaCl salinities (up to 6 mol/kgw). Finally, the newly generated data facilitated the refinement of a thermodynamic model using the Krichevsky and Kasarnovsky approach, improving estimations of H2 dissolution losses, caprock sealing capacity, and insights into natural H2 production and accumulation underground.

Molecular thermodynamic modeling of surface tension: Extension to molten polymers

A combined molecular thermodynamic model with an equation of state was successfully extended for correlating the surface tension of 7 molten polymers. The model was coming from the combination of a statistical mechanical expression according to Fowler-Kirkwood-Buff approximation with the perturbed hard-sphere-chain equation of statistical association fluid theory by an attractive term of Yukawa tail. The systems under study were of homopolymers type including Poly(ethylene oxide), High-Density Poly(ethylene), Poly(dimethyl siloxane), Poly(vinyl methyl ether), Poly(ethylene glycol), Atactic-Poly(propylene glycol), and Isotactic-Poly(propylene glycol). The model also used the dipole moment of the monomer molecule of those systems as an adjustable coefficient. The model was able to correlate 65 surface tension data points of the above-mentioned polymers in 297–532.2 K range with the average absolute relative deviation (AARD) of 2.00%. In addition, a single layer neural network comprising two input parameters (temperature and soft-core diameter of Lennard-Jones fluid) and 11 neurons was applied to complete the research, achieving more than satisfactory results with the AARD of 0.88%.

Molecular Thermodynamic Modeling of Hybrid Ionic Liquids for Biogas Upgrading

Molecular Thermodynamic Modeling of Hybrid Ionic Liquids for Biogas Upgrading

Molecular Thermodynamics for Aggregation of Surfactants with Alkylbenzene or Branched Alkane Tails: An Experimental-Modeling Approach

This work presents a molecular thermodynamic approach in which microemulsion properties are obtained by minimizing the total Gibbs energy of the system. Notably, this optimization process is carried out mainly based on the surfactant molecular structure and the solution conditions. Even though molecular thermodynamic modeling has been widely applied to oil-in-water (O/W) microemulsions, just a few studies are reported on water-in-oil (W/O) microemulsions mainly focused on ionic surfactants with linear alkyl tails. Here, we investigate the self-aggregation of different non-ionic surfactants with more complex structures acting as hydrophobic tails. In this context, we model the phase behavior of alkylphenol ethoxylate surfactant systems incorporating liquid-vapor and liquid-liquid data of alkylbenzenes from the literature. As a result, we can optimize the model parameters and describe the equilibrium micelle structure. The particle swarm optimization method was applied to minimize the Gibbs free energy for both O/W and W/O microemulsions. In order to evaluate the predictive performance of the model, we compared the experimental data with the computed critical micelle concentration and micelle size.

Mesoscience in supported nano-metal catalysts based on molecular thermodynamic modeling: A mini review and perspective

Supported nano-metal catalysts are widely used in industrial processes. There is a trade-off between the activity and stability from mesoscale, which can be effectively tackled with the principle of compromise in competition (mechanisms A and B). To apply mesoscience methodology in this specific area, this work summarized research progress, where direct H2O2 synthesis was chosen as a typical case to identify and represent mechanism A (activity) and mechanism B (stability). It was found that mechanism A has been widely studied, while mechanism B still cannot reflect explosion. Subsequently, reaction heat and fusion enthalpy were proposed to represent mechanism B in this work, and the molecular thermodynamic model was identified as an effective tool for the study. A corresponding framework for mechanism B was constructed and the progress in developing the model for this particular purpose was provided. Finally, perspectives were discussed based on the linear non-equilibrium thermodynamics.

Study of nickel-coated aluminum nanoparticles using molecular dynamic simulations and thermodynamic modeling

Aluminum nanoparticles have widely been used as fuel additives to solid propellants for rocket propulsion, but the formation of the oxide layer has been a setback for their application. A viable solution to this problem is to passivate aluminum (Al) with a layer of nickel (Ni), which offers multiple advantages. The current study focuses on energetic intermetallic interaction within Ni-coated Al nanoparticles and also the interaction/coalescence between two Ni-coated Al nanoparticles of varying sizes. Molecular dynamics (MD) method is employed to study the size-dependent variation of these interactions. A thermodynamic formulation is devised to calculate the adiabatic reaction temperature of single as well as coated nanoparticles. The results obtained using this formulation are compared with the results obtained from MD simulations. The estimation of dead layer thickness formed at the interface of Ni and Al is critical to correctly capture the energetic behavior. In this work, the dead layer thickness is estimated and used to predict the adiabatic reaction temperature of the coalescence of two equal-/unequal-sized Ni-coated Al nanoparticles. It has been found that particle size can affect the adiabatic reaction temperature because of the varying surface energy. It has also been found that the dead layer thickness plays a vital role in accurately determining the adiabatic reaction temperature of the system. It has been observed that the reaction time decreases proportionately with increase in specific reaction surface area (between Al and Ni) for single as well as coated particles.

Solubility of Water in Hydrogen at High Pressures: A Molecular Simulation Study

Hydrogen is one of the most popular alternatives for energy storage. Because of its low volumetric energy density, hydrogen should be compressed for practical storage and transportation purposes. Recently, electrochemical hydrogen compressors (EHCs) have been developed that are capable of compressing hydrogen up to P = 1000 bar, and have the potential of reducing compression costs to 3 kWh/kg. As EHC compressed hydrogen is saturated with water, the maximum water content in gaseous hydrogen should meet the fuel requirements issued by the International Organization for Standardization (ISO) when refuelling fuel cell electric vehicles. The ISO 14687-2:2012 standard has limited the water concentration in hydrogen gas to 5 μmol water per mol hydrogen fuel mixture. Knowledge on the vapor liquid equilibrium of H2O-H2 mixtures is crucial for designing a method to remove H2O from compressed H2. To the best of our knowledge, the only experimental high pressure data (P > 300 bar) for the H2O-H2 phase coexistence is from 1927 [J. Am. Chem. Soc., 1927, 49, 65-78]. In this paper, we have used molecular simulation and thermodynamic modeling to study the phase coexistence of the H2O-H2 system for temperatures between T = 283 K and T = 423 K and pressures between P = 10 bar and P = 1000 bar. It is shown that the Peng-Robinson equation of state and the Soave Redlich-Kwong equation of state with van der Waals mixing rules fail to accurately predict the equilibrium coexistence compositions of the liquid and gas phase, with or without fitted binary interaction parameters. We have shown that the solubility of water in compressed hydrogen is adequately predicted using force-field-based molecular simulations. The modeling of phase coexistence of H2O-H2 mixtures will be improved by using polarizable models for water. In the Supporting Information, we present a detailed overview of available experimental vapor-liquid equilibrium and solubility data for the H2O-H2 system at high pressures.

Molecular Thermodynamic Modeling of the Specific Effect of Salt on the Aggregation of Nonionic Surfactants

The specific chemistry of added salt has a strong effect on the aggregation of surfactants. Although the molecular mechanism of this effect is still debated in the literature and there is no genera...

Molecular thermodynamic modeling of surface tensions of some fatty acid esters and biodiesels

This work addresses the molecular thermodynamic and artificial neural network (ANN) modeling of surface tensions of several fatty acid esters and biodiesels. Two biodiesels were considered as pure fluid and the other as a binary mixture. The molecular thermodynamic model is based on the statistical mechanical expression according to Fowler-Kirkwood-Buff approximation. Regarding this, contributions to surface tension from the hard-chain repulsions, Lennard-Jones dispersion forces, and dipolar interactions were considered and assumed to be additive in the model development. The molecular thermodynamic model used three molecular parameters reflecting the hard-core diameter, dispersive energy and segment number as well as the liquid densities for which the values were predicted from perturbed Yukawa-chain equation of state. Further, the model used dipole moment as an adjustable parameter for the accurate calculation of surface tensions. The model could predict 149 surface tension data points for 9 FAEs and 3 biodiesels in 268.6–393 K range with the average absolute relative deviation (AARD) of 1.82%. The degree of accuracy of proposed model has also been compared with some empirical equations. Concerning ANN modeling, a network comprising two hidden layers and 9 neurons for each layer has been trained, according to the constructive approach. The result of the training was quite good, the AARD of the pure fluid dataset of 137 points was found to be 0.44%.

Size effect on melting temperatures of alumina nanocrystals: Molecular dynamics simulations and thermodynamic modeling

Molecular dynamics (MD) simulations and thermodynamic analysis are conducted to investigate size effect on melting point of alumina nanocrystals. Different geometries including spherical and cubic particles, planar thin films, and spherical shells are considered. The atomic interactions in MD simulations are captured using Vashishta et al.’s potential function. Thermophysical properties of concern such as the bulk melting point, latent heat, density, and surface free energy are calculated using MD simulations and fed as inputs to the thermodynamic models. Predictions of MD simulations are compared with those of thermodynamic melting models. For all cases, heterogeneous melting is observed, where nucleation of the melt phase occurred at the free surface and the melting front propagated into the interior regions of the crystal. Results suggest that the melting point drops sharply below a threshold particle size, which is a function of the geometry. The threshold particle size of spherical particles is greater than that of planar films. Melting point predictions are quite sensitive to the choice of thermodynamic model and thermophysical property values. To ascertain the effects of curvature and core size on shell melting point, melting points of planar semi-infinite films and spherical shells are calculated and compared. For particle sizes of concern to practical applications (∼100 nm or greater), shell melting point is nearly independent of core size and the semi-infinite planar film approximation is reasonable to estimate the melting point of alumina shells. In this size regime, melting points of 2–4 nm thick spherical oxide shells vary roughly in the range of 1800–2350 K, which is relatively close to the bulk melting point. Results of the present study do not indicate an enormous depression in the melting point, as the previous works suggest. This implies that the melting point depression of the oxide layer cannot fully describe the scatter in the measured ignition temperature of aluminum particles.

Molecular thermodynamic modeling of a bilayer perforation in mixed catanionic surfactant systems.

Perforated bilayers play an essential role in biology and in surface science. Here, we extend the classical aggregation model of catanionic surfactant mixtures to describe perforations in a self-assembled bilayer in aqueous salt. The model predicts that changing solution salinity and anionic-to-cationic surfactant ratio may lead to the spontaneous formation of pores in the bilayer and to the assembly of a micellar network. We estimate the dimensions of an optimal pore as a function of solution salinity and aggregate composition and show that with an increase of concentration of the deficient surfactant in a catanionic mixture, both the diameter and the thickness of the optimal pore decrease. This decrease is stronger for pores enriched in surfactant having a longer tail than for the pores enriched in the oppositely charged surfactant with a shorter tail. Our model helps to quantify the driving forces for the formation of a pore in a catanionic bilayer and to understand its role. For the aqueous mixtures C16TAB/SOS/NaBr and DTAB/SDS/NaBr, our predictions are in reasonable although not quantitative agreement with available cryo-TEM and SANS data. Predicted radii of perforations are in the range of those obtained from SANS data for perforated bilayer disks.

Molecular Thermodynamic Modeling of Self-Assembly into Branches and Spatial Networks in Solution

Molecular-thermodynamic models are applied to network-forming systems of three types: (1) wormlike micelles of ionic surfactant, (2) water + oil + surfactant mixtures, and (3) mixtures of reversibly associating chainlike molecules. For ionic surfactants, we illustrate the stabilization mechanism for the bilayer perforation that has a toroidal rim and describe the sequence of shape transitions induced by adding salt, including formation of bicontinuous structures and branched versus nonbranched wormlike micelles. For both ionic and nonionic surfactants, we show the zones of stable perforated bilayers and stable branched structures in an extended state diagram of a microemulsion derived from the Helfrich–Safran curvature expansion. For mixtures of reversibly associating sticky chains, our molecular dynamic (MD) simulations demonstrate crowding: an enhancement of association caused by the presence of chains that carry nonsticky monomers. An easy-to-use mean-field correction to the apparent association consta...

Molecular thermodynamic modeling of ionic liquids using the perturbation-based linear Yukawa isotherm regularity

In this paper, we present the results of an extensive study on a novel approach to the molecular modeling of pure ionic liquids (ILs) that incorporates the perturbed thermodynamic linear Yukawa isotherm regularity (LYIR), which is derived based on an effective nearest neighboring pair attractive interaction of the Yukawa potential. The LYIR was used to model the densities of ILs up to high pressures (35 MPa) and in the temperature range 293.15 to 393.15 K. To use the LYIR for ILs, a simple molecular model was proposed to describe their molecular structure, in which they were considered as a liquid consisting of the ion pairs moving together in the fluid, and each ion pair was assumed to be a one-center spherical united atom. The ILs under consideration contained one of the IL cations [C2mim]+, [C4mim]+, [C7mim]+, [C8mim]+, [C3mpy]+, [C3mpip]+, [C3mpyr]+ or [C4mpyr]+, and one of the IL anions [BF4]−, [C(CN)3]−, [CF3SO4]− or [NTf2]−. The reliability and physical significance of the parameters as well as the proposed molecular model were tested by calculating the densities of pure imidazolium-, pyridinium-, piperidinium- and pyrrolidimium-based ILs. The results showed that the LYIR can be used to predict and reproduce the density of ILs in good agreement with the experimental data. In addition, the LYIR enabled us to determine the physical quantities, such as an effective Yukawa screening length, λeff, the product of the effective energy well depth and the effective coordination number, (εeff/k)zeff, the contribution of the non-reference thermal pressure and also the influence of the anionic and cationic structure on the λeff parameter. The standard deviation of the IL densities predicted in this work is lower than those calculated by the one other important equation of state reported in the literature.

Molecular Thermodynamic Modeling of Reverse Micelles and Water-in-Oil Microemulsions.

Surfactant aggregation plays an important role in a variety of chemical and biological nanoscale processes. On a larger scale, using small amounts of amphiphiles compared to large volumes of bulk-phase modifiers can improve the efficiency and reduce the environmental impact of many chemical and industrial processes. To model ternary mixtures of polar, nonpolar, and amphiphilic molecules, we develop a molecular thermodynamic theory for polydisperse water-in-oil (W/O) droplet-type microemulsions and reverse micelles based on global minimization of the Gibbs free energy of the system. The incorporation of size polydispersity into the theoretical formulation has a significant effect on the Gibbs free energy landscape and allows us to accurately predict micelle size distributions and micelle size variation with composition. Results are presented for two sample ionic surfactant/water/oil systems and compared with experimental data. By predicting the structural and compositional characteristics of w/o microemulsions, the molecular thermodynamic approach provides an important bridge between the modeling of ternary systems at the molecular and the macroscopic level.

Evaluation of Ion Effects on Surfactant Aggregation from Improved Molecular Thermodynamic Modeling

An improved molecular thermodynamic model has been developed and applied to various pure, binary, and ternary mixed surfactants in aqueous solution containing salt (0–3 M). The effect of counterion activity and surfactant activity on surfactant aggregation is considered. The effect of counterion and co-ion specificity on aggregation properties is successfully evaluated. The predicted aggregation properties, including critical micelle concentration (cmc), micelle shape, micelle size, and sphere-to-rod transition, agree well with experimental data. The developed model provides a potential method to evaluate ion effects on aggregation properties of various surfactants in salt solution at various concentration levels, and thus will be of great value to guide the application of surfactants in industrial products and processes, such as corrosion prevention, oil recovery, and pharmaceuticals.

The influence of poly(ethylene glycol) on the micelle formation of alkyl maltosides used in membrane protein crystallization.

With the aim of better understanding the phase behavior of alkyl maltosides (n-alkyl-β-d-maltosides, CnG2) under the conditions of membrane protein crystallization, we studied the influence of poly(ethylene glycol) (PEG) 2000, a commonly used precipitating agent, on the critical micelle concentration (CMC) of the alkyl maltosides by systematic variation of the number n of carbon atoms in the alkyl chain (n = 10, 11, and 12) and the concentration of PEG2000 (χ) in a buffer suitable for the crystallization of cyanobacterial photosystem II. CMC measurements were based on established fluorescence techniques using pyrene and 8-anilinonaphthalene-1-sulfonate (ANS). We found an increase of the CMC with increasing PEG concentration according to ln(CMC/CMC0) = kPχ, where CMC0 is the CMC in the absence of PEG and kP is a constant that we termed the "polymer constant". In parallel, we measured the influence of PEG2000 on the surface tension of detergent-free buffer solutions. At PEG concentrations χ > 1% w/v, the surface pressure πs(χ) = γ(0) - γ(χ) was found to depend linearly on the PEG concentration according to πs(χ) = κχ + πs(0), where γ(0) is the surface tension in the absence of PEG. Based on a molecular thermodynamic modeling, CMC shifts and surface pressure due to PEG are related, and it is shown that kP = κc(n) + η, where c(n) is a detergent-specific constant depending inter alia on the alkyl chain length n and η is a correction for molarity. Thus, knowledge of the surface pressure in the absence of a detergent allows for the prediction of the CMC shift. The PEG effect on the CMC is discussed concerning its molecular origin and its implications for membrane protein solubilization and crystallization.

Molecular dynamics simulations and thermodynamic modeling of NaCl–KCl–ZnCl2 ternary system

The NaCl–KCl–ZnCl2 ternary system is examined and modeled using the CALPHAD methodology in conjunction with molecular dynamics (MD) simulations. In particular, MD simulations are used for calculating liquid enthalpies of mixing as a function of composition for the ternary and its binary sub-systems. In addition, key structural features are obtained from MD that is then used for informing the employed two-sublattice ionic liquid model (Na+1, K+1: Cl−1, ZnCl2), which describes the ternary liquid phase. The structure of the simulated liquid systems show that Zn+2 cations primarily exhibit 4-fold coordination in addition to a smaller percentage of 5-fold followed by 3-fold coordination; in contrast, the coordination of both Na+ and K+ cations are distributed between 2- and 4-fold states. The optimized self-consistent thermodynamic model parameters show good agreement with MD data obtained in this work and available experimental literature data.