Osmotic Coefficients Research Articles

Refined Protein-Sugar Interactions in the Martini Force Field.

Sugar molecules play important roles as mediators of biomolecular interactions in cellular functions, disease, and infections. Molecular dynamics simulations are an indispensable tool to explore these interactions at the molecular level. The large time and length scales involved frequently necessitate the use of coarse-grained representations, which heavily depend on the parametrization of sugar-protein interactions. Here, we adjust the sugar-protein interactions in the widely used Martini 2.2 force field to reproduce the experimental osmotic second virial coefficients between sugars and proteins. In simulations of two model proteins in glucose solutions with adjusted force field parameters, we observe weak protein-sugar interactions. The sugar molecules are thus acting mainly as crowding agents, in agreement with experimental measurements. The procedure to fine-tune sugar-protein interactions is generally applicable and could also prove useful for atomistic force fields.

Methodical evaluation of Boyle temperatures using Mayer sampling Monte Carlo with application to polymers in implicit solvent.

The Boyle temperature, TB, for an n-segment polymer in solution is the temperature where the second osmotic virial coefficient, A2, is zero. This characteristic is of interest for its connection to the polymer condensation critical temperature, particularly for n → ∞. TB can be measured experimentally or computed for a given model macromolecule. For the latter, we present and examine two approaches, both based on the Mayer-sampling Monte Carlo (MSMC) method, to calculate Boyle temperatures as a function of model parameters. In one approach, we use MSMC calculations to search for TB, as guided by the evaluation of temperature derivatives of A2. The second approach involves numerical integration of an ordinary differential equation describing how TB varies with a model parameter, starting from a known TB. Unlike general MSMC calculations, these adaptations are appealing because they neither invoke a reference for the calculation nor use special averages needed to avoid bias when computing A2 directly. We demonstrate these methods by computing TB lines for off-lattice linear Lennard-Jones polymers as a function of chain stiffness, considering chains of length n ranging from 2 to 512 monomers. We additionally perform calculations of single-molecule radius of gyration Rg and determine the temperatures Tθ, where linear scaling of Rg2 with n is observed, as if the polymers were long random-walk chains. We find that Tθ and TB seem to differ by 6% in the n → ∞ limit, which is beyond the statistical uncertainties of our computational methodology. However, we cannot rule out systematic error relating to our extrapolation procedure as being the source of this discrepancy.

Calculations of mean ionic activity coefficients of copper and manganese salts in aqueous solutions

Accurately predicting the activity coefficients of copper and manganese salts in aqueous solutions is crucial for treating industrial wastewater, and it is of practical interest to calculate the activity coefficients of heavy metals in aqueous solutions using the Equation of State because of its high flexibility and wide range of applicability. This work conducts a modeling study on the mean ionic activity coefficients of copper and manganese salts in aqueous solutions. The thermodynamic framework used in this work is an electrolyte version of the Cubic Plus Association Equation of State (e-CPA). The model's ion-water binary interaction parameters are obtained by regressing the osmotic coefficients and mean ionic activity coefficients in aqueous solutions. The modeling results indicate that the electrolyte Equation of State can satisfactorily correlate the water activity, osmotic coefficients, and mean ionic activity coefficients of copper and manganese salts in aqueous solutions over a wide range of salt concentrations. Among all the systems at 298.15 K, the biggest average relative deviation between calculated and experimental values is within 6.7 % and 2.3 % for the mean ionic activity coefficients and water activity, respectively. Furthermore, this work discusses the impact of ion pairs on the phase equilibrium of aqueous systems from a microscopic mechanism perspective and analyzes and discusses the model's adaptability. The model used in this work can accurately predict the activity coefficients of a variety of copper and manganese salts in aqueous solutions over wide concentration ranges and provides an improved interface for improving the calculation accuracy of the model under high concentration or other complex conditions.

Thermodynamic Properties of the Mixture of Potassium Phosphate Fertilizer with KCl: Water Activity, Osmotic and Activity Coefficients, Excess Energy, and Solubility of KH2PO4–KCl–H2O at 298.15 K

Thermodynamic Properties of the Mixture of Potassium Phosphate Fertilizer with KCl: Water Activity, Osmotic and Activity Coefficients, Excess Energy, and Solubility of KH₂PO₄–KCl–H₂O at 298.15 K

General Condition for Polymer Cononsolvency in Binary Mixed Solvents.

Starting from a generic model based on the thermodynamics of mixing and abstracted from the chemistry and microscopic details of solution components, three consistent and complementary computational approaches are deployed to investigate the general condition for polymer cononsolvency in binary mixed solvents at the zeroth order. The study reveals χPS - χPC + χSC as the underlying universal parameter that regulates cononsolvency, where χαβ is the immiscibility parameter between the α- and β-component. Two disparate cononsolvency regimes are identified for χPS - χPC + χSC < 0 and χPS - χPC + χSC > 2, respectively, based on the behavior of the second osmotic virial coefficient at varying solvent mixture composition x C. The predicted condition is verified using self-consistent field calculations by directly examining the polymer conformational transition as a function of x C. It is further shown that in the regime χPS - χPC + χSC < 0, the reentrant polymer conformation transition is driven by maximizing the solvent-cosolvent contact, but in the regime χPS - χPC + χSC > 2, it is driven by promoting polymer and cosolvent contact. In-between the two regimes when neither effect is dominant, a monotonic response of polymer conformation to x C is observed. Effects of the mean-field approximation on the predicted condition are evaluated by comparing the mean-field calculations with computer simulations. It shows that the fluctuation effects lead to a higher threshold value of χPS - χPC + χSC in the second regime, where local enrichment of cosolvent in polymer proximity plays a critical role.

Flow Activation Energy of High-Concentration Monoclonal Antibody Solutions and Protein-Protein Interactions Influenced by NaCl and Sucrose.

The solution viscosity and protein-protein interactions (PPIs) as a function of temperature (4-40 °C) were measured at a series of protein concentrations for a monoclonal antibody (mAb) with different formulation conditions, which include NaCl and sucrose. The flow activation energy (Eη) was extracted from the temperature dependence of solution viscosity using the Arrhenius equation. PPIs were quantified via the protein diffusion interaction parameter (kD) measured by dynamic light scattering, together with the osmotic second virial coefficient and the structure factor obtained through small-angle X-ray scattering. Both viscosity and PPIs were found to vary with the formulation conditions. Adding NaCl introduces an attractive interaction but leads to a significant reduction in the viscosity. However, adding sucrose enhances an overall repulsive effect and leads to a slight decrease in viscosity. Thus, the averaged (attractive or repulsive) PPI information is not a good indicator of viscosity at high protein concentrations for the mAb studied here. Instead, a correlation based on the temperature dependence of viscosity (i.e., Eη) and the temperature sensitivity in PPIs was observed for this specific mAb. When kD is more sensitive to the temperature variation, it corresponds to a larger value of Eη and thus a higher viscosity in concentrated protein solutions. When kD is less sensitive to temperature change, it corresponds to a smaller value of Eη and thus a lower viscosity at high protein concentrations. Rather than the absolute value of PPIs at a given temperature, our results show that the temperature sensitivity of PPIs may be a more useful metric for predicting issues with high viscosity of concentrated solutions. In addition, we also demonstrate that caution is required in choosing a proper protein concentration range to extract kD. In some excipient conditions studied here, the appropriate protein concentration range needs to be less than 4 mg/mL, remarkably lower than the typical concentration range used in the literature.

Theory of effective interactions between identical and different non-ionic solutes in a binary solvent

The introduction of cosolvents and other additives significantly has a profound impact on the physicochemical properties and phases of solutions. This study develops a thermodynamic theory to investigate the effective interactions between identical and different non-ionic solutes in a binary solvent. We derive the rigorous thermodynamic identity for the osmotic second virial coefficients among two solute species, which includes an adsorption contribution unique to multi-component solvents. Numerical analyses based on a model free energy show that co-nonsolvency and depletion effects between the identical solute species emerge from this adsorption contribution. On the other hand, the adsorption contribution intensifies the repulsion between different solute species that exhibit opposite preferences to the solvent components. These findings unify seemingly disparate phenomena under a common framework, providing insights into solute–solute and intra-molecular interactions in mixed solvents.

A Method for Efficiently Predicting the Radial Distribution Function and Osmotic Coefficients of Aqueous Electrolyte Solutions.

The prediction of the structural and thermodynamic properties of electrolyte solutions is critical for a huge range of practical situations where these solutions play a vital role. Theoretical models, such as the continuum solvent model, attempt to explain the behavior of solutions using a coarse-grained description of the interactions of species in the solution, whereas molecular simulations aim to directly compute the behavior of the solution, including the interactions between all ions and molecules in the system. Both methods have limitations: theoretical models are generally less accurate because they rely on assumptions, while molecular simulations require significant computational resources, particularly if higher accuracy is desired. To address these issues, we propose an affordable and effective method that combines the advantages of the modified Poisson-Boltzmann equation (MPBE) with classical molecular dynamics (MD) simulations to predict the radial distribution functions and thermodynamic properties of electrolyte solutions. We demonstrate a method of using the MPBE to compute the short-range potential of mean force (PMF) from the radial distribution functions (RDFs) and vice versa. Furthermore, we provide insights into the relationship between the RDFs and the short-range PMF based on the MPBE. Our analysis reveals that the effective short-range PMFs can be approximately calculated using low concentration simulations but the short-range PMFs are slightly concentration-dependent in simulations at higher concentrations. Additionally, we demonstrate that for concentrated solutions, osmotic coefficients can be calculated in agreement with experiment using a virial approach. This is based on the effective short-range PMFs and RDFs obtained from the MPBE method. Our proposed MPBE can therefore accelerate the calculation of the structural and thermodynamic properties of electrolyte solutions.

Binary aqueous solutions of choline salts: Determination and modelling of liquid density (298.15 or 313.15 K) and Vapour Pressure Osmometry (313.15 K)

Salts composed of the cholinium cation (such as choline hydroxide and choline chloride) have become one of the main reactants for the synthesis of greener ionic liquids, but, for a proper description of the aqueous solutions of these strong electrolytes by thermodynamic modelling, reliable data on liquid density (ρ) and vapour pressure (p) are needed, which are often unavailable. So, in this work, the liquid density (ρ) of binary aqueous solutions of choline bicarbonate ([Ch][Bic]), choline (2R,3R)-bitartrate ([Ch][Bit]), choline chloride ([Ch]Cl), choline dihydrogen citrate ([Ch][H2Cit]) and choline hydroxide ([Ch]OH) were measured at 298.15 or 313.15 K and 0.1 MPa and correlated using second-degree polynomials with salt molality (m), obtaining determination coefficients (R2) higher than 0.9974. Furthermore, the osmotic coefficients (ϕ) of these binaries were determined using vapour pressure osmometry (VPO), at 313.15 K and 0.1 MPa, being satisfactorily described by the Extended Pitzer Model of Archer, which yielded low values of standard deviation (3.58<σϕ·103<12.86). Then, the mean molal activity coefficients (γ±) and excess Gibbs free energies (GE/RT) were calculated, following the order [Ch][H2Cit] > [Ch][Bit] > [Ch][Bic] > [Ch]OH > [Ch]Cl, which corresponds to the decreasing polarity of the choline salts and agrees with the empirical law of matching water affinities (LMWA).

Equilibrium vapor pressure of aqueous sodium acetate and potassium acetate solutions used as working fluids in frost-free air–source heat pumps at 263–328 K

Aqueous solutions of sodium acetate (CH3COONa) and potassium acetate (CH3COOK) are considered effective alternative heat exchange media for frost-free air–source heat pumps (FFASHPs) owing to the low corrosiveness, low viscosity, and low cost. Equilibrium vapor pressure is the most crucial property that characterizes freezing point and latent heat transfer. However, studies on this property, especially in subzero temperature ranges are scarce. This study was conducted to experimentally investigate the equilibrium vapor pressure of CH3COONa and CH3COOK solutions. The developed apparatus and procedures were based on the static method, and validated by evaluating the vapor pressure of distilled water, n-heptane, and calcium chloride (CaCl2) aqueous solution. Their average absolute deviations were within 1.94%. As the temperature increased from 263 to 328 K and solute concentration increased from 9.27 to 33.81 wt%, 124 data points of the vapor pressure of the CH3COONa and CH3COOK solutions were obtained, ranging from 0.2759 to 13.2608 kPa. Modified Antoine equation and ion interaction (Pitzer) model were established for correlation of the experimental data. The average absolute deviations of the CH3COONa and CH3COOK solutions produced by Antoine equation were 2.08 and 2.48%, respectively. Those produced by Pitzer model further decreased to 1.36 and 1.45% due to the import of osmotic coefficient and the accuracy improvement. Furthermore, according to the experimental and calculation results, the vapor pressure of the CH3COONa solution was lower than that of the CH3COOK solution. Therefore, under the same antifreezing conditions, the CH3COONa solution facilitates latent heat absorption from ambient air, while the CH3COOK solution is conducive to achieve regeneration. The results of this study provide foundational data for the vapor pressure of the two solutions and can promote their application in FFASHPs.

Modulating Weak Protein-Protein Cross-Interactions by the Addition of Free Amino Acids at Millimolar Concentrations.

In this paper, we quantify weak protein-protein interactions in solution using cross-interaction chromatography (CIC) and surface plasmon resonance (SPR) and demonstrate that they can be modulated by the addition of millimolar concentrations of free amino acids. With CIC, we determined the second osmotic virial cross-interaction coefficient (B23) as a proxy for the interaction strength between two different proteins. We perform SPR experiments to establish the binding affinity between the same proteins. With CIC, we show that the amino acids proline, glutamine, and arginine render the protein cross-interactions more repulsive or equivalently less attractive. Specifically, we measured B23 between lysozyme (Lys) and bovine serum albumin (BSA) and between Lys and protein isolates (whey and canola). We find that B23 increases when amino acids are added to the solution even at millimolar concentrations, corresponding to protein/ligand stoichiometric ratios as low as 1:1. With SPR, we show that the binding affinity between proteins can change by 1 order of magnitude when 10 mM glutamine is added. In the case of Lys and one whey protein isolate (WPI), it changes from the mM to the M range, thus by 3 orders of magnitude. Interestingly, this efficient modulation of the protein cross-interactions does not alter the protein's secondary structure. The capacity of amino acids to modulate protein cross-interactions at mM concentrations is remarkable and may have an impact across fields in particular for specific applications in the food or pharmaceutical industries.

THERMODYNAMIC ANALYSIS OF PHASE DIAGRAMS BASED ON THE CONCEPT OF THE BJERRUM–GUGGENHEIM OSMOTIC COEFFICIENT

The aim of this study is to theoretically confirm or refute the high degree of lead and zinc volatilisation from the Shalkiya deposit (polymetallic refractory ores) by means of analysing the phase diagrams and the behaviour of the osmotic coefficient according to the Bjerrum-Guggenheim equation along the liquidus line for binary systems based on calcium. From the plots depicting the dependence of the Bjerrum-Guggenheim osmotic coefficient on activity, one can infer the structure of the melt (positive &lt;1 or negative &gt;1). That is, if the values of the Bjerrum-Guggenheim osmotic coefficient in a binary system indicate a positive character of interaction between the components, it implies interaction between like atoms in the melt, whereas negative values indicate interaction between unlike atoms, suggesting the formation of complex, high-temperature compounds, which would be undesirable in our case. The question related to the formation of complex high-temperature chemical compounds with impurity elements such as zinc and lead in the Fe-Si-Al-Ca-Mg-Zn-Pb system remains unresolved.

Experimental and theoretical studies on thermodynamic activities of binaries ferric and magnesium chlorides in aqueous solutions at various temperatures

The investigation of the thermodynamic properties of binary systems of ferric and magnesium chlorides in aqueous solutions was reported at various temperatures using both the hygrometric method and thermodynamic modeling. Water activities were measured over a molality range of 0.100 up to mmax(FeCl3)= 2.500 mol·kg−1 and to mmax(MgCl2)=(5.798, 6.090, 6.394, and 6.839) mol·kg−1at temperatures from 298.15 K to 353.15 K, respectively. From the new measurements, the osmotic coefficients of water were evaluated and compared with the existing literature data at ambient temperature. These coefficients were treated at various temperatures using established thermodynamic models of the Pitzer, Filippov–Charykov–Rumyantsev, extended ion interaction, and Clegg–Pitzer–Brimblecombe. The relevant properties of ferric and magnesium electrolyte solutions were determined in the temperature range. Indeed, the parameterizations of FeCl3(aq) and MgCl2(aq) were evaluated and employed for the computation of solute activity and osmotic coefficients. Based on literature emf data for MgCl2(aq) at a temperature of 298.15 K, the consistency of the activity coefficients was evaluated using an adequate model, and an excellent description of the prediction activity coefficients is obtained by the extended ion interaction model. Then, the recommended activity coefficients were given at various temperatures by extending this procedure. An experimental investigation was also carried out to evaluate the solubility equilibrium of MgCl2 in aqueous solutions at different temperatures. The solubility product and standard Gibbs energies of dissolution and formation were also calculated at different temperatures and compared with those existing in the literature.

Step-wise ion hydration modeling of aqueous solutions of 1:1 acid neutral electrolytes at different temperatures

In a previous work, we showed that the current stepwise ion hydration framework was promising for modeling electrolyte activities at 298.15 K. Briefly, the model assumes that (1) ions are hydrated in solution and this hydration is governed by an equilibrium between the bound and free water, (2) the mean spherical approximation (MSA) models the long range electrostatic interactions in the solution sufficiently well, and (3) this solution behaves ideally. In this work, we continue developing this model by exploring its temperature dependence. MSA has no temperature-dependent adjustable parameters. The hydration equilibrium constants are temperature dependent due to non-zero enthalpy and specific heat of the hydration equilibrium. Their values were adjusted. The calculated osmotic coefficients from the model are in good agreement with measured values.

Osmotic and Activity Coefficients of Aqueous Lithium Sulfate Solutions within the Temperature Range 293.15–498.15 K to 40 MPa

Osmotic and Activity Coefficients of Aqueous Lithium Sulfate Solutions within the Temperature Range 293.15–498.15 K to 40 MPa

Theoretical and practical investigation of ion-ion association in electrolyte solutions.

In this study, we present a new equation of state for electrolyte solutions, integrating the statistical associating fluid theory for variable range interactions utilizing the generic Mie form and binding Debye-Hückel theories. This equation of state underscores the pivotal role of ion-ion association in determining the properties of electrolyte solutions. We propose a unified framework that simultaneously examines the thermodynamic properties of electrolyte solutions and their electrical conductivity, given the profound impact of ion pairing on this transport property. Using this equation of state, we predict the liquid density, mean ionic activity coefficient, and osmotic coefficient for binary NaCl, Na2SO4, and MgSO4 aqueous solutions at 298.15K. Additionally, we evaluate the molar conductivity of these systems by considering the fraction of free ions derived from our equation of state in conjunction with two advanced electrical conductivity models. Our results reveal that, while ion-ion association has a minimal influence on the modification of the predicted properties of sodium chloride solutions, their impact on sodium and magnesium sulfate solutions is considerably more noticeable.

Balancing Group I Monatomic Ion-Polar Compound Interactions for Condensed Phase Simulation in the Polarizable Drude Force Field.

Molecular dynamics (MD) simulations are a commonly used method for investigating molecular behavior at the atomic level. Achieving reliable MD simulation results necessitates the use of an accurate force field. In the present work, we present a protocol to enhance the quality of group 1 monatomic ions (specifically Li+, Na+, K+, Rb+, and Cs+) with respect to their interactions with common polar model compounds in biomolecules in condensed phases in the context of the Drude polarizable force field. Instead of adjusting preexisting individual parameters for ions, model compounds, and water, we employ atom-pair specific Lennard-Jones (LJ) (known as NBFIX in CHARMM) and through-space Thole dipole screening (NBTHOLE) terms to fine-tune the balance of ion-model compound, ion-water, and model compound-water interactions. This involved establishing a protocol for the optimization of NBFIX and NBTHOLE parameters targeting the difference between molecular mechanical (MM) and quantum mechanical (QM) potential energy scans (PES). It is shown that targeting PES involving complexes that include multiple model compounds and/or ions as trimers and tetramers yields parameters that produce condensed phase properties in agreement with experimental data. Validation of this protocol involved the reproduction of experimental thermodynamic benchmarks, including solvation free energies of ions in methanol and N-methylacetamide, osmotic pressures, ionic conductivities, and diffusion coefficients within the condensed phase. These results show the importance of including more complex ion-model compound complexes beyond dimers in the QM target data to account for many-body effects during parameter fitting. The presented parameters represent a significant refinement of the Drude polarizable force field, which will lead to improved accuracy for modeling ion-biomolecular interactions.

Influence of solvent quality on the swelling and shear modulus of polymer gels chemically cross-linked in solution

The effect of temperature (T) is studied on the swelling of model poly(vinyl acetate) (PVAc) gels in isopropyl alcohol. The theta temperature Θ of these gels, at which the second osmotic virial coefficient A2 vanishes, is close to that of the corresponding high molecular mass polymer solution without cross-links so that solvent quality may be defined in the same way as the corresponding precursor polymer solution. We quantified the swelling and deswelling of PVAc gels relative to their size at the theta temperature, and also determined the effect of T on the shear modulus of these gels. It was found that both swelling and deswelling data could be reduced to a universal scaling equation of the same general form as derived from renormalization group (RG) theory for flexible linear polymer chains in solutions.Graphical abstractVariaton of the volumetric swelling factor as a function of the reduced temperature for PVAc gels swollen in isopropyl alcohol.

Modeling Osmotic Coefficients in Aqueous Solutions of 1-Alkyl-3-methylimidazolim Halides: A Theory That Reflects the Electrical Structure of Ions and ePC-SAFT

Modeling Osmotic Coefficients in Aqueous Solutions of 1-Alkyl-3-methylimidazolim Halides: A Theory That Reflects the Electrical Structure of Ions and ePC-SAFT

Electrodialysis of moderately concentrated solutions: Experiment and modeling based on a simplified characterization of ion-exchange membranes

Electrodialysis (ED) is a cost-effective and environmentally friendly process; it is considered a key step in Zero Liquid Discharge systems. However, the ED process producing a fairly concentrated solution is not well understood. An ED process where 10 L of 0.5 M NaCl was circulated in diluate stream (DS) and 0.1 L of initially 2.0 M NaCl circulated in concentrate stream (CS) was studied. The concentration of concentrate increased up to 3.5 M. The electrodialyzer's design eliminated current leakage. Ion-exchange membranes, MK-40, MA-41 (Shchekinoazot) and CJMA-3 (Chemjoy Polymer Materials), were characterized prior to ED. Based on the concentration dependences of membrane conductivity and diffusion permeability, the “true” (ti⁎) ion transport numbers in the membranes were found; the water transport number (tw) was found from volumetric measurements. It was shown that the current efficiency, η, found using ti⁎ is quantitatively consistent with η found in the ED experiments. To calculate the time dependences of solution concentration and volume in CS, a mathematical model was built. For the first time, ti⁎ and tw determined in independent experiments, were used as parameters. The only fitting parameter was the osmotic permeability coefficient. A good agreement with experimental results is obtained.