Liquid Coexistence Curve Research Articles

The Relationship between Protein–Protein Interactions and Liquid–Liquid Phase Separation for Monoclonal Antibodies

Being able to predict and control concentrated solution properties for solutions of monoclonal antibodies (mAbs) is critical for developing therapeutic formulations. At higher protein concentrations, undesirable solution properties include high viscosities, opalescence, particle formation, and precipitation. The overall aim of this work is to understand the relationship between commonly measured dilute solution parameters, the reduced osmotic second virial coefficient b22 and the diffusion interaction parameter kD and liquid-liquid phase separation, which occurs at higher protein concentrations. For globular proteins such as lysozyme or γB-crystallin, the location of the liquid-liquid coexistence curve is controlled by the net protein-protein interaction, which is related to b22. Because many mAbs undergo reversible self-association due to forming highly directional interactions, it is not known if b22 can be used as a reliable predictor for LLPS since increasing the anisotropy in the interaction potential causes phase separation to occur at much stonger net protein-protein attractions or lower values of b22. Here, we map the coexistence curves for three mAbs, referred to as COE-01, COE-07, and COE-19, in terms of b22 and kD values. The measurements are carried out at a low salt condition near the pI, where protein-protein interactions are expected to be anisotropic due to the presence of electrostatic attractions, and under salting-out conditions at high ammonium sulfate concentrations, which is expected to reduce the anisotropy by screening electrostatic interactions. We also show that deviations from a linear correlation between b22 and kD can be used as an indicator of reversible self-association. Each of the mAbs under salting-out conditions follows the correlation supporting the hypothesis that protein-protein interactions are nonspecific, while deviations from the correlation occur for COE-01 and COE-19 under low salt conditions indicating the mAbs undergo reversible self-association. For five out of the six conditions, the onset of phase separation, as reflected by the reduced virial coefficient at the critical point b22c occurs in a small window -1.6 > b22c > -2.3, which is similar to what has been observed for lysozyme and for bovine γB-crystallin. Under low salt conditions, b22c ≈ -5.1 for COE-19, which we previously showed to self-associate into small oligomers. Our findings suggest that under conditions where mAb interactions are weakly anisotropic, such as occur at high salt conditions, phase separation will begin to occur in a small window of b22. Deviations from the window can occur when mAbs undergo reversible self-association, although this is not always the case and likely depends upon whether or not highly directional interactions are passivated in the oligomer formation. We expect fitting LLPS measurements to simplified interaction models for mAbs will provide additional insight into the nature of the protein-protein interactions and guide their development for calculating concentrated solution properties.

On the force scheme influence on pseudopotential method coexistence curve

Pseudopotential method has been drawing attention in simulating multiphase flows by adding an interparticle force to lattice Boltzmann method (LBM). However, implementing a known force field effect into evolution of particle distribution function is still an active field of interest, specially when higher order terms play significant role in resulting macroscopic equations. A considerable number of forcing schemes has already been proposed, and although many have shown their differences up to second order analysis, there is still some debate about high order terms. In this work, a study taking into account third order forcing terms is carried out, in order to better identify the reasons for existing distinct coexistence curves when the same interparticle force is employed through distinct forcing schemes. Third order terms related to spatial interparticle force gradients are taken into account, and a theoretical analysis is carried out in order to study gas–liquid coexistence curves. It is shown that this curve can be characterized by a single parameter, Γ, dependent on employed relaxation time and forcing scheme, which allows the current analysis to be used for other schemes as well. Flat interface simulations are carried out in order to study the behavior of gas–liquid coexistence curve. A good agreement between the numerical and theoretical results validates the presented approach. Static droplet simulations were carried out, where surface tension behavior also respect the expected trend of higher values for lower Γ. Maximum spurious velocities of renowned forcing schemes from literature were also studied, without a clear correlation with Γ parameter.

Predicting Melt Curves of Energetic Materials Using Molecular Models

AbstractIn this work, the solid–liquid coexistence curves of classical fully flexible atomistic models of α‐RDX and β‐HMX were calculated using thermodynamically rigorous methodologies that identify where the free energy difference between the phases is zero. The free energy difference between each phase at a given state point was computed using the pseudosupercritical path (PSCP) method, and Gibbs–Helmholtz integration was used to evaluate the solid–liquid free energy difference as a function of temperature. This procedure was repeated for several pressures to determine points along the coexistence curve, which were then fit to the Simon–Glatzel functional form. While effective, this method is computationally expensive. An alternative approach is to compute the melting point at a single pressure via the PSCP method, and then use the Gibbs–Duhem integration technique to trace out the coexistence curve in a more computationally economical manner. Both approaches were used to determine the coexistence curve of α‐RDX. The Gibbs–Duhem integration method was shown to generate a melt curve that is in good agreement with the PSCP‐derived melt curve, while only costing ∼10 % of the computational resources used for the PSCP method. For α‐RDX, the predicted melting temperature increases significantly more for a given increase in pressure when compared to available experimental data.

Thermodynamics of carbon dioxide mixtures at cryogenic conditions

Carbon capture and sequestration / utilization using cryogenic conditions have found attention due to lower energy penalty compared to other separation methods. In cryogenic processes, carbon dioxide is likely to desublimate from a vapor phase or freezes out from a liquid phase. This study deals with phase equilibrium calculations where solid carbon dioxide forms in the presence of vapor phase (SLV), liquid phase (SLE), or both (SLVE). Two of the successful solid fugacity models are used with predictive cubic equations of state (EOSs) in calculating the phase equilibrium of carbon dioxide mixtures. The advantages and limitations of the models are discussed. In addition, a new fugacity model which describes solid carbon dioxide along solid–liquid coexistence curve is developed. This model remedies the previous models and is used from low to very high pressure. This model reduces to an analytical expression for describing carbon dioxide melting curve. When coupled with the predictive cubic EOSs, this model satisfactorily describes the SVE, SLE, and SVLE of carbon dioxide mixtures.

Liquid–Liquid Phase Equilibria of Binary Solutions of {1-Butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide + 1-Butanol or 2-Methyl-1-propanol}

The liquid–liquid coexistence curves for the room temperature ionic liquid (RTIL) solutions of 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([C4mim][NTf2]) in 1-butanol and 2-methyl-1-propanol have been precisely measured. The values of the critical exponent corresponding to the coexistence curve were found to be consistent with theoretical predictions of the 3D-Ising universality. The complete scaling theory was used to analyze the asymmetric behavior of the coexistence curve. The reduced consolute temperatures and the reduced consolute densities of the binary solutions of [C4mim][NTf2] and alcohols were also calculated to discuss the interactions in the RTIL solutions driving the liquid–liquid phase separations.

Prediction of Thermodynamic Properties of Levulinic Acid via Molecular Simulation Techniques.

Second-generation biofuels are a complex mixture of organic compounds that can be further processed to hydrocarbon fuels and other valuable chemicals. One such chemical is levulinic acid (IUPAC name: 4-oxo pentanoic acid), which is a highly versatile ketoacid obtained from cellulose present in agricultural byproducts. For oxygen-containing compounds that decompose at elevated temperatures and pressures, determining the vapor–liquid equilibria data at high temperatures via the experimental route may be challenging. The molecular simulation approach is a cost-effective tool to obtain the necessary data while also allowing us to understand the microscopic origins of macroscopic observable properties. We have employed the transferable potential for phase equilibria-united atom force field to describe the interactions in this system with the parameters for a torsional interaction that are not reported in the literature (levulinic acid is a ketoacid) being determined from density functional theory calculations. We have verified our parameterization via density computations in the isothermal–isobaric ensemble and by comparing our simulation results with the corresponding data from experiments reported in the literature. We have performed grand-canonical transition-matrix Monte Carlo simulations in the temperature range from 580 to 690 K to estimate the vapor–liquid coexistence curves in the temperature–density plane and the Clapeyron plots. From this data, the critical point (TC = 755 K, ρC = 285.4 kg/m3, and PC = 30.57 bar) has been estimated, and this may be used as input to the equations of state employed in process simulation software for design of industrial separation processes including those for “biorefining”. As levulinic acid is a “ketoacid”, hydrogen bonding occurs, and the liquid phase structure has also been studied using radial distribution functions.

Predicting vapor liquid equilibria using density functional theory: A case study of argon.

Predicting vapor liquid equilibria (VLE) of molecules governed by weak van der Waals (vdW) interactions using the first principles approach is a significant challenge. Due to the poor scaling of the post Hartree-Fock wave function theory with system size/basis functions, the Kohn-Sham density functional theory (DFT) is preferred for systems with a large number of molecules. However, traditional DFT cannot adequately account for medium to long range correlations which are necessary for modeling vdW interactions. Recent developments in DFT such as dispersion corrected models and nonlocal van der Waals functionals have attempted to address this weakness with a varying degree of success. In this work, we predict the VLE of argon and assess the performance of several density functionals and the second order Møller-Plesset perturbation theory (MP2) by determining critical and structural properties via first principles Monte Carlo simulations. PBE-D3, BLYP-D3, and rVV10 functionals were used to compute vapor liquid coexistence curves, while PBE0-D3, M06-2X-D3, and MP2 were used for computing liquid density at a single state point. The performance of the PBE-D3 functional for VLE is superior to other functionals (BLYP-D3 and rVV10). At T = 85 K and P = 1 bar, MP2 performs well for the density and structural features of the first solvation shell in the liquid phase.

Liquid–liquid equilibrium, heat capacity and turbidity of binary solution nitrobenzene + n -pentadecane

Abstract The liquid–liquid coexistence curve, the isobaric heat capacity per unit volume and the turbidity for the binary solution of nitrobenzene + n-pentadecane have been measured at various temperatures. The upper consolute mole fraction xc of nitrobenzene and the upper consolute temperature Tc of the binary solution were determined to be xc = 0.696 and Tc = 307.298 K, respectively. The values of the critical exponents related to the width of the coexistence curve, the heat capacity, the osmotic compressibility and the correlation length were deduced and found to be in good agreements with that of the 3-D Ising universality. With the heat capacity data the asymmetric behavior of the diameter of the coexistence curve was studied in terms of the complete scaling theory. The critical amplitudes related to the above four quantities were used to calculate the universal scaling ratios and to confirm their theoretical predictions.

Performance of density functionals for modeling vapor liquid equilibria of CO2 and SO2.

Vapor liquid equilibria (VLE) and condensed phase properties of carbon dioxide and sulfur dioxide are calculated using first principles Monte Carlo (FPMC) simulations to assess the performance of several density functionals, notably PBE-D3, BLYP-D3, PBE0-D3, M062X-D3, and rVV10. GGA functionals were used to compute complete vapor liquid coexistence curves (VLCCs) to estimate critical properties, while the hybrid and nonlocal van der Waals functionals were used only for computing density at a single state point due to the high computational cost. Our results show that the BLYP-D3 functional performs well in predicting VLE properties for both molecules when compared with other functionals. In the liquid phase, pair correlation functions reveal that there is not a significant difference in the location of the peak for the first solvation shell while the peak heights are different for different functionals. Overall, the BLYP-D3 functional is a good choice for modeling VLE of acidic gases with significant environmental implications such as CO2 and SO2 . © 2017 Wiley Periodicals, Inc.

Phase Equilibria and Critical Point Predictions of Mixtures of Molecular Fluids Using Grand Canonical Transition Matrix Monte Carlo

Mixtures of molecular fluids are encountered often in chemical industry, and the vapor–liquid coexistence curves are required for efficient design of separation processes. Hence, a computational scheme employing the Wang–Landau and grand canonical transition matrix Monte Carlo molecular simulation techniques is used for the first time to compute the fluid phase diagrams of molecular mixtures. Binary mixtures of n-alkanes, viz., methane–ethane, ethane–propane, propane–n-butane systems, are studied here as examples of molecular mixtures. The total molecule number probability distribution, obtained from the GC-TMMC simulations, allows us to directly calculate coexistence properties such as pressure, density, and composition. On comparison with experimental data, reported in the literature, it was observed that the predicted VLE properties, with the exception of pressure, are in close agreement with the corresponding experimental values. The deviation of calculated pressure from experiments could be attribute...

Optimized Mie Potentials for Phase Equilibria: Application to Branched Alkanes

A transferable united-atom (UA) force field based on Mie potentials is presented for branched alkanes. The performance of the optimized Mie potential parameters is assessed for 32 branched isomers of butane, pentane, hexane, heptane, and octane using grand canonical histogram-reweighting Monte Carlo simulations. For each compound, vapor–liquid-coexistence curves, vapor pressures, heats of vaporization, critical properties, and normal boiling points are predicted and compared to experiment. Experimental saturated liquid densities and critical temperatures are reproduced with a median absolute average error of 0.6%, while vapor pressures are reproduced with a median absolute average error of 2.2%. Calculations performed with the TraPPE and NERD force fields produce median absolute average errors for saturated liquid densities and vapor pressures of 1.3–1.8% and 14.3–23.5%, respectively. Binary phase diagrams predicted by the Mie potentials for argon+neopentane, methane+neopentane, and ethane+isobutane are i...

Optimised Mie potentials for phase equilibria: application to alkynes

ABSTRACTA transferable united-atom force field, based on Mie potentials, is presented for alkynes. The performance of the optimised Mie potential parameters is assessed for 1-alkynes and 2-alkynes using grand canonical histogram-reweighting Monte Carlo simulations. For each compound, vapour–liquid coexistence curves, vapour pressures, heats of vapourisation, critical properties and normal boiling points are predicted and compared to experiment. Experimental saturated liquid densities are reproduced to within 2% average absolute deviation (AAD), except for 1-hexyne, which are reproduced with 3% AAD. Experimental saturated vapour pressures are reproduced to within 3% AAD, except for 1-pentyne, 2-pentyne and 2-hexyne, where deviations from experiment of up to 20% AAD were observed. Binary phase diagrams, predicted from Gibbs ensemble Monte Carlo simulations, for propane + propyne, propene + propyne and propadiene + propyne, are in close agreement with experiment.

Hot magnetized nuclear matter: Thermodynamic and saturation properties

We have used a realistic nuclear potential, AV18, and a many body technique, the lowest order constraint variational (LOCV) approach, to calculate the properties of hot magnetized nuclear matter. By investigating the free energy, spin polarization parameter, and symmetry energy, we have studied the temperature and magnetic field dependence of the saturation properties of magnetized nuclear matter. In addition, we have calculated the equation of state of magnetized nuclear matter at different temperatures and magnetic fields. It was found that the flashing temperature of nuclear matter decreases by increasing the magnetic field. In addition, we have studied the effect of the magnetic field on liquid gas phase transition of nuclear matter. The liquid gas coexistence curves, the order parameter of the liquid gas phase transition, and the properties of critical point at different magnetic fields have been calculated.

Fluid phase equilibria of triangle-well fluids confined inside slit pores: A transition matrix Monte Carlo simulation study

The phase behaviour of triangle-well (TW) fluids confined inside three types of slit pores: slit pores with or without uniform attraction and slit pores with square-well (SW) type pore-fluid interactions is studied using molecular simulations. The TW potential is chosen to model the fluid-fluid interactions as this model provides a good compromise between realism and simplicity. The simple nature of the models enables us to obtain a qualitative understanding of the effects of confinement on the vapour liquid coexistence curves (VLCCs) of the TW fluids with variable well-width. We note the significant differences in the VLCCs of the confined fluid from the bulk phase behaviour; and also the dependence of the VLCCs on the type of slit pore. These differences have been explained on the basis of the plots of local density along the axis perpendicular to the walls of the slit pore.

Vapor Liquid Equilibria of Hydrofluorocarbons Using Dispersion-Corrected and Nonlocal Density Functionals.

Recent developments in dispersion corrected and nonlocal density functionals are aimed at accurately capturing dispersion interactions, a key shortcoming of local and semilocal approximations of density functional theory. These functionals have shown significant promise for dimers and small clusters of molecules as well as crystalline materials. However, their efficacy for predicting vapor liquid equilibria is largely unexplored. In this work, we examine the accuracy of dispersion-corrected and nonlocal van der Waals functionals by computing the vapor liquid coexistence curves (VLCCs) of hydrofluoromethanes. Our results indicate that the PBE-D3 functional performs significantly better in predicting saturated liquid densities than the rVV10 functional. With the PBE-D3 functional, we also find that as the number of fluorine atoms increase in the molecule, the accuracy of saturated liquid density prediction improves as well. All the functionals significantly underpredict the saturated vapor densities, which also result in an underprediction of saturated vapor pressure of all compounds. Despite the differences in the bulk liquid densities, the local microstructures of the liquid CFH3 and CF2H2 are relatively insensitive to the density functional employed. For CF3H, however, rVV10 predicts slightly more structured liquid than the PBE-D3 functional.

Vapor–liquid phase equilibrium diagram for uranium hexafluoride (UF6) using simplified temperature dependent intermolecular potential parameters (TDIP)

The properties of uranium hexafluoride (UF6, CAS: 7783-81-5) are of importance to the nuclear industry as a precursor for the enrichment and product spent fuel reprocessing. This work is focused on obtaining the vapor–liquid equilibrium (VLE) curve for UF6 using temperature dependent intermolecular potential parameters (TDIP) as opposed to temperature independent intermolecular potential parameters (TIIP). TDIP indeed improves the simulated vapor–liquid coexistence curve, critical constants, and vapor pressure of UF6. However, both approaches need improvement since the predictions are still far from reproducing experimental saturated liquid density data for UF6.

Asymmetric criticality of ionic solution containing 1-hexyl-3-methylimidazolium tetrafluoroborate and 2-propanol

The liquid–liquid coexistence curve for binary solution {2-propanol+1-hexyl-3-methylimidazolium tetrafluoroborate ([C6mim][BF4])} has been measured. The isobaric heat capacities per unit volume were obtained in both critical and non-critical regions. The critical exponents α and β were deduced and showed good agreement with those predicted for the 3D-Ising universality class. The asymmetric behaviour of the diameter of the coexistence curve was analysed based on the complete scaling theory, which indicated that the heat capacity related term plays an important role in describing the asymmetric behaviour of the coexistence curve. Furthermore, the RPM (restricted primitive model)-rescaled critical parameters were calculated and suggested the solvophobic criticality for this system.

Prediction of fluid phase equilibria and interfacial tension of triangle-well fluids using transition matrix Monte Carlo

The triangle-well (TW) potential is a simple model which is able to capture the essence of the intermolecular attraction in real molecules. Transition matrix Monte Carlo simulations in the grand canonical ensemble (GC-TMMC) are performed to investigate the role of the range of attraction on the features of fluid phase equilibria. As the TW potential range increases, the vapour–liquid coexistence curves shift towards a higher temperature range with the critical temperature and pressure increasing, and the critical density values decreasing. These GC-TMMC results are in excellent agreement with the predictions of Gibbs ensemble Monte Carlo and replica exchange Monte Carlo (REMC) simulations reported in literature. Using the GC-TMMC method, the vapour pressures are also computed directly from the particle number probability distributions (PNPDs). It has been noted in literature that the surface tension values are computationally more expensive and difficult to determine than other coexistence properties using molecular simulations. The PNPDs from GC-TMMC simulations along with Binder’s formalism allow for the calculation of the interfacial tension with relative ease. Also, our simulation generated results for the interfacial tension are in good agreement with the literature data obtained using REMC (via the virial route) and the plots of our interfacial tension values as a function of temperature are smooth unlike the literature data.

A Simple Generic Model for Estimating Saturated Vapor Pressure

Arguably, the most important of the basic thermodynamic properties of fluids, vapor pressure has been the focus of investigation for over a century. The two main drawbacks of the models currently used for its correlation are that they either exhibit large deviations near critical temperature and triple point or that they have a large number of compound-specific adjusted parameters and hence the inconvenient necessity of having at hand large tabulations of hundreds of model parameters. In this study, by employing the up and coming procedure of genetic programming, a new model, which to a large extent remedies these shortcomings, is proposed. Essentially, having only two compound-specific adjusted parameters and also using two readily available substance parameters of molecular weight and normal boiling point ensure a high level of convenience, yet precision and applicability over a large portion of the vapor–liquid coexistence curve. Concisely, a sizable database comprised of 58,272 data points was gathered for 243 organic and inorganic compounds and elements belonging to a diverse set of chemical families; these were then used in both developing and validating the proposed model and reporting generic and compound/element-specific adjusted parameters. Average absolute relative deviations (AARDs) of 1.47% (for a subset of 40,852 data points) and 1.82% (for a subset of 17,420 data points) for the general model and a slightly modified model applicable to hydrogen-bonded alcohols and phenols, respectively, are a testament to the reliability of the new proposed model.

(Liquid + liquid) phase equilibria of binary mixtures 1-butyl-3-methylimidazolium tetrafluoroborate and tert-butanol or 1,2-butanediol

Precise (liquid+liquid) coexistence curves of binary mixtures {1-butyl-3-methylimidazolium tetrafluoroborate ([C4mim][BF4])+tert-butanol or RS-1,2-butanediol} have been measured. Critical exponent β and critical amplitude B̂0Z were deduced from the (liquid+liquid) equilibria data in the critical regions, and it was found that the critical exponent β coincided well with the 3D-Ising value. The complete scaling theory was applied to describe the asymmetry behavior of the diameter of the coexistence curves, which suggested that the heat capacity related term showed significant importance. The reduced critical temperature and density were calculated by the restricted primitive model (RPM), which were used to discuss the driven force of phase separation. Moreover, the dependences of the critical temperature, the critical mole fraction, the reduced critical temperature and the reduced critical density on the permittivity of alcohol for a series of binary solutions of RTIL in alcohols are discussed.