Limit Of Infinite Dilution Research Articles

3He adsorbed on molecular hydrogen surfaces.

Using a diffusion Monte Carlo technique, we calculated the phase diagram of 3He adsorbed on a first solid layer of a molecular hydrogen isotope (H2, HD, and D2) on top of graphite. The results are qualitatively similar in all cases: a two-dimensional gas spanning from the infinite dilution limit to a second-layer helium density of 0.048 ± 0.004 Å-2. That gas is in equilibrium with a 7/12 commensurate structure, more stable than any incommensurate triangular solid of similar density. These findings are in reasonably good agreement with available experimental data.

Studies of monomer–dimer equilibria of methylene blue as a probe to investigate the solute–solvent and hydrophobic interactions in aqueous solutions of polyethylene glycols at 298 K

Electronic absorption spectrums of methylene blue (MB) in the concentration range wherein monomer–dimer equilibria exist have been systematically investigated in aqueous solutions of polyethylene glycols (PEG's) having molar mass 400, 1000 and 4000 g∙mol–1, at 298 K. The data on the absorption spectrums (550–700 nm) of MB are resolved to obtain monomer and dimer spectrums as well the geometrical details of the species (such as oscillatory strength, dipole moment etc.) are calculated. The molar absorption extinction coefficients for monomer and dimer cations of MB, the dimer dissociation constant values are calculated as a function of PEG concentrations. It has been noted that, absorption maximum occurs at 664 ± 1 and 605 ± 1 nm, respectively, for monomer and dimers which do not get affected much by presence of polymeric molecules and the data show perfect obedience of Beer–Lambert's law. The changes in dimer geometry from sandwich type to end–on–end type have been studied by applying exciton theory of Kasha et al. The dimer dissociation constant values at finite as well for infinitely dilute concentration of PEG's exhibit orderly amendment with respect to molar mass of PEG's and alteration in chain length of molecules. We report the free energy changes of transfer of dimeric cations of different concentrations from water to aqueous solutions of PEG's of fixed concentration, that is, to probe the interactions of water and PEG molecules with a hope of getting information about salting–in/salting–out effects, as well of binding of dye molecules with PEG's. We have suggested complexation of end hydroxylic groups of PEG's with dimer cations. The results are further interpreted as salting–in of PEG complex with MB–dimers only in the limit of infinite dilution (solute–solvent interactions) while salting–out of these complexed species is observed as a function of MB–dimer concentration.

Effects of intramolecular chain conformation on the hydration and miscibility of polyethylene glycol in water studied by means of polymer reference interaction site model theory.

To examine the conventional idea that the gauche conformation of the OCCO dihedral angle promotes the dissolution of polyethylene glycol (PEG) in water through strong hydration, the thermodynamic properties of liquid mixtures of PEG and water were studied by means of polymer reference interaction site model (PRISM) theory. The intramolecular correlation functions required as input for PRISM theory were calculated by the generator matrix method, accompanied by changes in the distribution of dihedral angles. In the infinite dilution limit, the increased probability of gauche conformation of the OCCO dihedral angles stabilizes the hydration of PEG through enhanced hydrogen bonding between the ether oxygen of PEG and water. The mixing Gibbs energies of the liquid mixtures were also calculated in the whole concentration range based on the Gibbs-Duhem equation, as per our recent proposal. A liquid-liquid phase separation was observed when all the dihedral angles of PEG were in the trans conformation; for the liquid mixture to be miscible in the whole concentration range, the introduction of the OCCO gauche conformation was found to be indispensable. The above theoretical results support the conventional idea that the OCCO gauche conformation is important for the high miscibility of PEG and water.

Molecular dynamics study of fission product behaviour in molten [formula omitted]-[formula omitted] salt

The solvation of fission products in fuel salts and the effects due to their accumulation are important factors to understand in molten salt reactor design. In this contribution, we use ab initio Molecular Dynamics (AIMD) and polarizable ion model (PIM) based MD to study the structural and dynamic characteristics of the fission products (Cs, I and Xe) in the model fuel salt ThF4-LiF with different compositions at the infinite dilution limit. We first develop or refine existing PIM potentials to better reproduce the results of AIMD simulations. The AIMD and PIM-MD results are then compared in terms of the structures present in the salt, and the dynamics of their coordination. The results of this study indicate that, at 1200 K and 1400 K the fission products studied here have weak interactions with all composition ranges of fuel salt. This is evident, as first coordination shell associations being generally short-lived, as determined by cage correlation times. The diffusion coefficients determined through PIM-MD match the AIMD results reasonably well. The three fission products studied here are diffuse at similar rates; however, the Cs+ diffusion is slightly lower likely due to its more tightly bound associated F−. With all solutes, the diffusion coefficients decrease with a greater ThF4 fraction. Additionally, the behaviour of these solutes was studied at finite concentration ranges, up to 4 atom %. Here, it was found that the presence of Cs+ has little effect on the density, heat capacity and viscosity. However, these properties were affected by higher I+ and Xe concentrations.

Critical Review of Transport Properties of HCl, KOH, and NaOH in High Temperature Water and Correlations for Transport Properties of H3O+ and OH−

High-temperature tracer diffusion coefficients for H3O+ and OH− are important parameters in the modeling of diffusion-controlled reaction kinetics and mass transport processes under hydrothermal conditions, and these tracer diffusion coefficients are directly related to the ionic electrical conductivities in the limit of infinite dilution through the Nernst–Einstein relationship. The limiting conductivity of H3O+ and OH− in water is controlled by two separate mechanisms of ionic movement: (i) the bulk ionic diffusion and (ii) proton hopping, also known as “Grotthuss” mechanism and/or “prototropic transfer.” This work reports a critical assessment of the limiting electrical conductivity data (Λ°) for aqueous HCl, KOH, and NaOH measured above room temperature. The initial assessed dataset included temperatures from 273.15 K up to 873.15 K and water densities from 1000 kg m−3 down to 270 kg m−3 and was reduced down to a final critically evaluated dataset spanning temperatures between 273.15 and 678.15 K and densities between 346 and 1006 kg m−3. The results were used to derive values for the excess conductivity due to prototropic transfer, λE°, of H3O+ and OH− using correlations previously reported for aqueous KCl. Simple empirical correlations of water viscosity and density were derived for Λ°(HCl), Λ°(KOH), Λ°(NaOH), λE°(H3O+), and λE°(OH−). Tests using the λE°(OH−) correlation and a previously reported function for Λ°(NaCl) show that the NaOH data can be accurately reproduced to within the estimated uncertainties. The reported correlations provide a means to model more accurately the tracer diffusion coefficients for H3O+ and OH− to supercritical conditions.

Bruce-Vincent transference numbers from molecular dynamics simulations.

Transference number is a key design parameter for electrolyte materials used in electrochemical energy storage systems. However, the determination of the true transference number from experiments is rather demanding. On the other hand, the Bruce-Vincent method is widely used in the lab to approximately measure transference numbers of polymer electrolytes, which becomes exact in the limit of infinite dilution. Therefore, theoretical formulations to treat the Bruce-Vincent transference number and the true transference number on an equal footing are clearly needed. Here, we show how the Bruce-Vincent transference number for concentrated electrolyte solutions can be derived in terms of the Onsager coefficients, without involving any extrathermodynamic assumptions. By demonstrating it for the case of poly(ethylene oxide)-lithium bis(trifluoromethane)sulfonimide system, this work opens the door to calibrating molecular dynamics (MD) simulations via reproducing the Bruce-Vincent transference number and using MD simulations as a predictive tool for determining the true transference number.

Diffusivities in Binary Mixtures of Cyclohexane or Ethyl Butanoate with Dissolved CH4 or R143a Close to Infinite Dilution

This work is part of a series of studies focusing on binary mixtures consisting of a liquid with a dissolved gas close to infinite dilution. A particular focus is on the study of the influence of molecular characteristics on mutual or self-diffusivity. Heterodyne dynamic light scattering (DLS) experiments and equilibrium molecular dynamics (EMD) simulations are applied to determine the Fick diffusion coefficient D11 and the self-diffusion coefficient of the gas solute in the mixture Dself,1. Often, the latter is referred to in the literature as the intradiffusion coefficient, which is equal to D11 in the limit of infinite dilution. Both DLS and EMD simulations are applied in macroscopic thermodynamic equilibrium at or close to saturation conditions. In the present study, mixtures of methane (CH4) or the refrigerant 1,1,1-trifluoroethane (R143a) dissolved in cyclohexane or ethyl butanoate are investigated at temperatures T between 303 and 423 K. The average expanded experimental uncertainty (coverage factor k = 2) of D11 from DLS experiments is 10%, and the average expanded statistical uncertainty (k = 2) of Dself,1 from EMD simulations is 6.4%. Unexpectedly, D11 in mixtures of CH4 dissolved in cyclohexane or ethyl butanoate essentially matches within uncertainties at a given T, and mixtures of cyclohexane with R143a show smaller D11 values in comparison to ethyl butanoate with R143a.

Usefulness of higher-order system-size correction for macromolecule diffusion coefficients: A molecular dynamics study

Yeh and Hummer’s simplified estimation method has often been adopted to obtain diffusion coefficients for solute molecules using molecular dynamic simulation. However, the simplified formula is not necessarily valid when a small basic cell is used. Therefore, we conducted molecular dynamics simulations of aqueous protein solution to estimate the diffusion coefficient for the infinite dilution limit. We confirmed a deviation from the simplified formula in the simulation data and rationalized the discrepancy based on the unsimplified formula.

Note on the physical basis of spatially resolved thermodynamic functions

ABSTRACT The spatial resolution of extensive thermodynamic functions is discussed. A physical definition of the spatial resolution based on a spatial analogy of partial molar quantities is advocated, which is shown to be consistent with how hydration energies are typically spatially resolved in the molecular simulation literature. It is then shown that, provided the solvent is not at a phase transition, the spatially resolved entropy function calculated by first-order grid inhomogeneous solvation theory [Nguyen CN, Young TK, Gilson MK. Grid inhomogeneous solvation theory: hydration structure and thermodynamics of the miniature receptor cucurbit [7] uril. J Chem Phys. 2012;137(4):044101] satisfies the definition rigorously, whereas that calculated by grid cell theory [Gerogiokas G, Calabro G, Henchman RH, et al. Prediction of small molecule hydration thermodynamics with grid cell theory. J Chem Theory Comput. 2014;10(1):35–48] most likely does not. Moreover, for an ideal gas in an external field, the former theory is shown consistent whereas the latter is not. Finally, consistent with the proposed definition and with the case of an ideal gas in an external field, we derive an approximate expression for the solvent contribution to the free energy of solvation in the limit of infinite dilution from the spatial variation of the density around the solute.

Henry’s law constants (IUPAC Recommendations 2021)

Abstract Henry’s law states that the abundance of a volatile solute dissolved in a liquid is proportional to its abundance in the gas phase. It applies at equilibrium and in the limit of infinite dilution of the solute. For historical reasons, numerous different definitions, names, and symbols are used in the literature to express the proportionality coefficient, denoted the “Henry’s law constant”. Here, a consistent set of recommendations is presented. An important distinction is made between two new recommended reciprocal quantities: “Henry’s law solubility constant” (H s) and “Henry’s law volatility constant” (H v). Eight recommended variants of H s and H v are described and relations among them presented.

Solutions, in Particular Dilute Solutions of Nonelectrolytes: A Review

The liquid state is one of the three principal states of matter and arguably the most important one; and liquid mixtures represent a large research field of profound theoretical and practical interest. This topic is of importance in many areas of the applied sciences, such as in chemical engineering, geochemistry, the environmental sciences, biophysics and biomedical technology. First, I will concisely present a review of important concepts from classical thermodynamics of nonelectrolyte solutions; this will be followed by a survey of (semi-)empirical approaches to representing the composition and temperature dependence of selected thermodynamic mixture properties, and finally the focus will be on dilute binary nonelectrolyte solutions where one component, a supercritical solute, is present in much smaller quantity than the other component, called the solvent. Partial molar properties in the limit of infinite dilution (indicated by a superscript ∞) are of particular interest. For instance, activity coefficients (Lewis–Randall (LR) convention) are customarily used to characterize mixing behavior, and infinite-dilution values gamma_{i}^{{{text{LR,}}infty }}provide a convenient route for obtaining binary parameters for several popular solution models. When discussing solute (j)—solvent (i) interactions in solutions where the solute is supercritical, the Henry fugacity h_{j,i} left( {T,P} right), also known as Henry’s law (HL) constant, is a measurable thermodynamic key quantity. Its temperature dependence yields information on the partial molar enthalpy change on solution Delta H_{j}^{infty } left( {T,P} right), while its pressure dependence yields information on the partial molar volume V_{j}^{{{text{L,}}infty }} left( {T,P} right) of solute j in the liquid phase (superscript L). I will clarify issues frequently overlooked, touch upon solubility data reduction and correlation, report a few recent high-precision experimental results on dilute aqueous solutions of supercritical nonelectrolytes, and show the equivalency of results for caloric quantities (e.g. Delta H_{j}^{infty }) obtained via van ’t Hoff analysis of high-precision solubility data with directly measured calorimetric data.

Derivation of limiting ion mobility equation based on the application of solvation effect-incorporated Poisson-Boltzmann equation

Interaction potential energy between ion and solvent molecular dipole moments in solvation shell around ion was derived on basis of the application of the solution of linear SEI-PB (Solvation Effects-Incorporated Poisson-Boltzmann) equation. Based on application of the solution of linear SEI-PB equation, distribution of solvent molecules in solvation shell around ion in electrolyte solution at thermodynamic equilibrium was derived. In case approaching to limit of infinite dilution, analytical expression for evaluating limiting ion mobility is derived from the boundary condition that the average number of solvent molecules accompanying with translational motion of ion is equal to the mean solvation number of ion. The derived limiting ion mobility formula is different from the Stokes–Einstein relation and lies in relation to direct proportion with the cube of dynamic size of ion in solution, depending not only on the viscous coefficient, dielectric constant, the density and molecular weight of solvent but also on temperature.By virtue of the equation, it was possible to estimate dynamic sizes of ions in solution. It was found the estimated dynamic sizes of ions in aqueous solution to be compatible with the average ion–water distances, and to be always greater than crystallographic ionic radii in size.A new relation between the limiting ion mobility and the solvent molecular dipole moment in solvation shell was established based on the interaction potential energy between ion and solvent molecular dipole moments in solvation shell around ion. By virtue of the proposed relation, we could find out the average water molecular dipole moment in hydration shell to be different more or less in size from that in bulk solution according to ionic species in aqueous solution.

On the virial expansion of model adsorptive systems

We investigate the thermodynamic properties of various super-critical model adsorptive systems with different fluid–solid attractive strengths using the confined density virial expansion, with coefficients calculated using the Mayer-sampling Monte Carlo method up to fifth order. We find that the virial expansion converges for adsorptive systems over a density range corresponding approximately to the film-formation regime. Beyond this regime, higher-order effects become increasingly important. The virial expansion of the density profile is also investigated. It is determined that this expansion gives insight into the structure associated with adsorption. We also find that weakly attractive systems have a more negative second virial coefficient than strongly attractive systems. This runs counter to the usual interpretation of bulk fluid virial coefficients. This is due to the infinite-dilution limit being very different for adsorbed fluids compared to bulk fluids.

Calculating Soft-Sphere Ionic Radii for Solid-State Arrangements from Solution Measurements

Despite extensive conceptualization of ions as hard spheres in most textbooks, solid-state structures are more accurately modeled as overlapping soft spheres that better reflect the size of the ions. The corresponding soft-sphere ionic radii of alkali and halide ions can be empirically established from the partial molar volume of the ions in aqueous solution. Partial molar volumes for 15 alkali halide solutes are calculated from the slope of solution density (g/L) versus the solution molarity (mol/L) at the infinite dilution limit. The set of resulting ion sizes for the lithium, sodium, potassium, rubidium, cesium, chloride, bromide, and iodide is both self-consistent, being composed of quantities that are mathematically additive, and physically meaningful. Upon setting the volume of Li(I) to 5.2 mL/mol, the solid-state structures of all 15 alkali halides, whether rock salt or CsCl, can be constructed to accurately model ion overlap as well as hole volume, though the size ordering of the ions is different than the ordering found for hard spheres. This new conceptual and empirical bridge between the solution and solid phases should help advance the teaching of these commonly disparate subjects by reinforcing aspects of both while drawing new connections between them.

Studies of osmotic and activity coefficient properties of aqueous solutions of triethylammonium formate and triethylammonium glycolate protic ionic liquids at 298.15 K

The triethylammonium-based carboxylate protic ionic liquids (PILs) are called as truly bio-ionic liquids. They can be used as green solvent, additives (biphasic catalysis) and for other considerable effects involving nano-material specially related to biomolecules. In this work, osmotic coefficient (φ) measurements using vapor pressure osmometry technique for aqueous solutions of two PILs, namely, triethylammonium formate [TEAF] (0.01290–0.55988 mol·kg−1) and triethylammonium glycolate [TEAG] (0.00989–0.53176 mol·kg−1) have been reported at 298.15 K. The water activity (aw) and solvent activity coefficient (γ1), mean molal activity coefficient (γ±) of PILs and osmotic pressure (π) of solutions properties in a binary mixture, were determined using experimentally measured φ data. The analysis of osmotic pressure data revealed that the studied PILs are electrolytes in the limit of infinite dilution and yield correct molecular weights as well as show negative values for virial coefficients. The variations of osmotic coefficient and mean molal activity coefficient of studied PILs with concentration indicate positive deviations from Debye-Hückel limiting law similar to that of ammonium ions. Further, Gibbs free energy changes due to mixing (ΔGm) and excess Gibbs free energy changes (ΔGE) for the studied binary systems are estimated. The solute-solute virial coefficient (NB22∗0) for the studied PILs in aqueous solutions were estimated by an application of the McMillan−Mayer theory of solutions. The results indicate that the hydration effect is dominant in PILs through the cooperative H–bonding with water-structure making effect suggesting the significance of hydrophobic hydration as observed in tetraalkylammonium salts and aprotic ionic liquids. A need to study the water molecule splitting at nitrogen charge centre and possible attenuation of water structural effects due to hydrophobic moieties present in the molecule is emphasized.

Using Molecular Simulation to Compute Transport Coefficients of Molecular Gases.

The existing kinetic theory of gases is based on an analytical approach that becomes intractable for all but the simplest molecules. Here we propose a simple numerical scheme to compute the transport properties of molecular gases in the limit of infinite dilution. The approach that we propose is approximate, but our results for the diffusivity D, the viscosity η, and the thermal conductivity λ of hard spheres, Lennard-Jones particles, and rough hard spheres agree well with the standard (lowest order) Chapman-Enskog results. We also present results for a Lennard-Jones-dimer model for nitrogen, for which no analytical results are available. In the case of polyatomic molecules (we consider n-octane), our method remains simple and gives good predictions for the diffusivity and the viscosity. Computing the thermal conductivity of polyatomic molecules requires an approximate treatment of their quantized internal modes. We show that a well-known approximation that relates λ to D and η yields good results. We note that our approach should yield a lower limit to the exact value of D, η, and λ. Interestingly, the most sophisticated (higher-order) Chapman-Enskog results for rough hard spheres seem to violate this bound.

Conformation and Diffusivity of Ring and Linear Polyethylene Oxide in Aqueous Solution: Molecular Topology Dependent Concentration Effects and Comparison with Experimental Data

AbstractAtomistic molecular dynamics simulations are performed on aqueous solutions of ring and linear polyethylene oxide (PEO) under good solvent conditions for the investigation of their conformation and diffusion dynamics. The systems simulated span a wide range of molecular weights (from 2 to 10 k) and polymer concentrations. In the limit of infinite dilution, both conformational and dynamic properties appear to be practically molecular topology independent as far as their dependence on chain length and concentration is concerned, and a very favorable agreement is observed with respect to relevant well‐established theoretical predictions, experimental data, and earlier simulation studies. Crossing over to the semidilute regime, molecular topology starts to bear a distinct effect on the observed conformations of the two different molecular geometries. On the other hand, the diffusion dynamics of PEO in the semidilute regime appears to be practically molecular topology independent judging from the dependence of the chain center‐of‐mass diffusivity on chain length and concentration. Indeed, and despite the fact that ring molecules exhibit consistently a faster dynamics than their linear homologs over the entire concentration range simulated, the estimated concentration scalings for both types of architecture are strikingly similar. The findings of this work are compared with scaling arguments and available experimental data.

Extending the Phantom Network Theory to Account for Cooperative Effect of Defects

Recent developments in network theory have extended the classical phantom network theory to account for different types of defects. These theories are typically linear and adopt the ideal defect gas approximation, which is valid only in the infinite dilution limit of defects. In this study, the Virial expansion is used to determine the cooperative effects of multiple loops. It was found that in most cases, the Virial coefficients of all order vanish, and adjacent loops have no more negative impact than the individual isolated loops. Furthermore, a general nonlinear theory was developed to calculate the elasticity of phantom networks beyond the dilute limit. It was found that for a tree‐like complete network, the dispersity of network strands does not affect the elasticity of the network. However, for a tree‐like incomplete network, as conversion is lowered, a much slower decrease in the elasticity is predicted by the nonlinear theory. Finally, for loopy networks, the nonlinear theory gave predictions almost identical to that of the linear theory in small loop fraction regime. However, as loop fraction is increased, the nonlinear theory predicts a significant negative deviation from the linear theory. This behavior qualitatively matches with the behavior observed in experiments.

Modeling Gas and Vapor Sorption and Swelling in Triptycene-Based Polybenzoxazole: Evidence for Entropy-Driven Sorption Behavior

The nonequilibrium lattice fluid model was used to describe and sometimes predict nitrogen, methane, carbon dioxide, ethane, and water vapor sorption at multiple temperatures (5–50 °C) and pressures (up to 32 atm) in novel triptycene-based polybenzoxazole (TPBO) prepared via a thermal rearrangement (TR) process from an ortho-functional polyimide precursor. The polymer lattice fluid parameters were determined using a few sorption data in the limit of infinite dilution and used to predict the solubility of nonswelling gases at several temperatures with no adjustable parameter. To calculate the solubility of swelling gases, the polymer–penetrant interaction parameter was adjusted to experimental sorption data at low pressure at a reference temperature. The second adjustable parameter, that is, the swelling coefficient, was calculated at each temperature using only one experimental sorption datum at high pressure. TPBO exhibits better dimensional stability upon exposure to swelling penetrants relative to prev...

Statistical thermodynamics of regular solutions and solubility parameters

Solubility parameters, developed originally for regular solutions, have been applied to solutions beyond the presumed weak non-ideality, implying that the true foundation of the solubility parameters may be more general than the regular solution theory. To assess the root of regularity on rigorous statistical thermodynamics, here we re-examine the classical iodine dissolution experiments by Shinoda and Hildebrand, who concluded that the entropy of mixing is ideal regardless of solute-solvent size ratio. We show that iodine solubility is concerned with the limit of infinite dilution, while the regular solution theory is a scheme to describe the dependence on the solute concentration. This means that the solubility of iodine cannot be a foundation of the regular solution; it is further shown that the differences in the solvation free energy among organic solvents are dominated by enthalpy with negligible role of the entropic component. In addition, the validity of the regular solution concept, i.e., the enthalpic nature of the solution non-ideality, can now be examined quantitatively by expressing the Margules model in terms of the Kirkwood-Buff integrals, which incorporate the excluded volume effects and the potential of mean force nature of interactions that were beyond the reach of the classical thermodynamic models. Such insights into the physical basis of solubility parameters may be useful for improving solubility prediction.