Second virial coefficient of bmimBF4/triton X-100/ cyclohexane ionic liquid microemulsion as investigated by microcalorimetry

The second virial coefficient of the ionic liquid (IL) microemulsion was obtained for the first time using microcalorimetry. The heat of dilution of the microemulsion solutions was measured by isothermal titration microcalorimetry (ITC), and the second virial coefficient was derived from the heat of dilution and the number density of the IL microemulsion solutions on the basis of a hard-sphere interaction potential assumption and as a function of the second-order polynomial. The validity of the second virial coefficient was confirmed by the percolation behavior of different ionic liquid microemulsion solutions of Triton X-100 in cyclohexane with or without added salts. The information obtained from the second virial coefficient shows that the interactions between ionic liquid microemulsion droplets are much stronger than those for traditional microemulsions, which may be attributed to the relatively larger size of the microemulsion droplets.     

The osmotic second virial coefficient and the Gibbs–McMillan–Mayer framework

The osmotic second virial coefficient is a key parameter in light scattering, protein crystallisation, self-interaction chromatography, and osmometry. The interpretation of the osmotic second virial coefficient depends on the set of independent variables. This commonly includes the independent variables associated with the Kirkwood–Buff, the McMillan–Mayer, and the Lewis–Randall solution theories. In this paper we analyse the osmotic second virial coefficient using a Gibbs–McMillan–Mayer framework which is similar to the McMillan–Mayer framework with the exception that pressure rather than volume is an independent variable. A Taylor expansion is applied to the osmotic pressure of a solution where one of the solutes is a small molecule, a salt for instance, that equilibrates between the two phases. Other solutes are retained. Solvents are small molecules that equilibrate between the two phases. The independent variables of the solvents are temperature, pressure, and chemical potentials. The derivatives in the Gibbs–McMillan–Mayer framework are transformed into derivatives in the Gibbs framework. This offers the possibility for an interpretation and correlation of the osmotic second virial coefficient using activity coefficient models.     

A multisolute osmotic virial equation for solutions of interest in biology

The osmotic virial equation was used to predict osmolalities of solutions of interest in biology. The second osmotic virial coefficients, Bi, account for the interactions between identical solute molecules. For multisolute solutions, the second osmotic virial cross coefficient, Bij, describes the interaction between two different solutes. We propose to use as a mixing rule for the cross coefficient the arithmetic average of the second osmotic virial coefficients of the pure species, so that only binary solution measurements are required for multisolute solution predictions. Single-solute data were fit to obtain the osmotic virial coefficients of the pure species. Using those coefficients with the proposed mixing rule, predictions were made of ternary solution osmolality, without any fitting parameters. This method is shown to make reasonably accurate predictions for three very different ternary aqueous solutions: (i) glycerol + dimethyl sulfoxide + water, (ii) hemoglobin + an ideal, dilute solute + water, and (iii) bovine serum albumin + ovalbumin + water.     

Second virial coefficients of polystyrene mixtures in 2-butanone

Variation of the second virial coefficient as a function of polymer composition for three pairs of polystyrene mixtures in 2-butanone has been studied using static light scattering. The results are better represented by the simple method of taking the geometric mean of the second virial coefficients of the separate polymer species rather than by the two-parameter theory. In one of the three combinations studied, the presence of a minimum in the second virial coefficient-composition plot supports similar observations by previous workers.     

Second virial coefficient of amylose acetate

The second virial coefficients of amylose acetate fractions have been determined at different temperatures and have been analyzed according to recent theories of second virial coefficient.     

On the thermodynamics of the McMillan–Mayer state function

The osmotic second virial coefficient is a key parameter in light scattering, protein crystallisation, self-interaction chromatography, and osmometry. The interpretation of the osmotic second virial coefficient depends on the solution theory. On the macroscopic level an expansion of the osmotic pressure is employed. A common statistical interpretation of the osmotic second virial coefficient of the expansion employs the McMillan–Mayer framework and the potential of mean force to characterise the solute–solute interaction. Supplementary to the statistical interpretation, it may be advantageous to develop the McMillan–Mayer framework in a classical thermodynamic context for which we develop the relationship between the state function of the McMillan–Mayer framework and the Helmholtz state function.     

A Model for Hydration Interactions between Apoferritin Molecules in Solution

We have studied how non-DLVO forces between molecules of the globular protein apoferritin in solution affect its osmotic second virial coefficient. A model explaining the effects of the solution ionic strength and pH on the interprotein interaction is developed, to give a physical interpretation of recently published experimental findings showing that the second virial coefficient of the protein apoferritin, supported by acetate buffer, goes through a minimum as a function of ionic strength. At low ionic strengths, the apoferritin second virial coefficient initially decreases with increasing sodium ion concentration, as DLVO theory predicts. However, non-DLVO hydration forces due to overlapping of the Stern layers of the protein molecules increase the second virial coefficient with further increase of sodium ion concentration, again as found experimentally at higher ionic strengths. The non-DLVO effect arises from ionic exchange between hydrogen and sodium ions at the protein surface. An adsorption shell of hydrated sodium ions forms around the protein molecules with increasing buffer concentration.     

极性气体的第二维里系数及缔合平衡常数和缔合焓方程

本文根据对一些极性气体分子聚集现象的分析,推导出计算极性气体的缔合平衡常数和缔合焓方程.还改进了描述低压下的极性气体PVT行为的简单舍项式维里方程.上述诸方程经计算检验,结果满意.     

Isotopic difference in the second virial coefficient of water: Another test of the MCY-B description of water dimer thermodynamics

Evaluation has been carried out of the component of the second virial coefficient of steam related to the formation of dimers. The necessary equilibrium constants of dimerization have been evaluated within the MCY-B water pair interaction potential. The calculated isotopic difference in the second virial coefficient reflects the qualitative features found by observation but, nevertheless, the calculation quite distinctly overestimates the value of this isotopic difference as compared with the observation. The nature of these differences and the relation to the state behaviour of water are discussed.     

Theoretical study of the contribution of physisorption to the low-pressure adsorption of hydrogen on carbon nanotubes

To investigate the contribution of geometry on the adsorption process, we present a theoretical study of the low-pressure physisorption of hydrogen on isolated nanotubes and nanotube bundles through the second virial coefficient, B(AS), computed classically with an uncorrugated adsorption potential. The optimal nanotube bundle geometry at low pressure for a Lennard-Jones adsorption potential is obtained by studying the second virial coefficient, B(AS), for variable radius or bundle lattice constant. The most favorable bundle adsorption sites at low pressures and temperatures are identified for typical bundle structures and the relative contribution of interstitial sites relative to other sites is discussed as a function of temperature and pressure. The Boyle temperature behavior for the B(AS) virial coefficient is also discussed as a function of radius for isolated nanotubes. For a given nanostructure, the maximum pressure of applicability of the B(AS) approach, below which the adsorption isotherm is linear, is estimated as a criterion which depends on temperature.     

Counterion adsorption theory of dilute polyelectrolyte solutions: apparent molecular weight, second virial coefficient, and intermolecular structure factor

Polyelectrolyte chains are well known to be strongly correlated even in extremely dilute solutions in the absence of additional strong electrolytes. Such correlations result in severe difficulties in interpreting light scattering measurements in the determination of the molecular weight, radius of gyration, and the second virial coefficient of charged macromolecules at lower ionic strengths from added strong electrolytes. By accounting for charge-regularization of the polyelectrolyte by the counterions, we present a theory of the apparent molecular weight, second virial coefficient, and the intermolecular structure factor in dilute polyelectrolyte solutions in terms of concentrations of the polymer and the added strong electrolyte. The counterion adsorption of the polyelectrolyte chains to differing levels at different concentrations of the strong electrolyte can lead to even an order of magnitude discrepancy in the molecular weight inferred from light scattering measurements. Based on counterion-mediated charge regularization, the second virial coefficient of the polyelectrolyte and the interchain structure factor are derived self-consistently. The effect of the interchain correlations, dominating at lower salt concentrations, on the inference of the radius of gyration and on molecular weight is derived. Conditions for the onset of nonmonotonic scattering wave vector dependence of scattered intensity upon lowering the electrolyte concentration and interpretation of the apparent radius of gyration are derived in terms of the counterion adsorption mechanism.     

Second virial coefficients of diblock copolymers

A perturbation theory for the second virial coefficient of A-B type diblock copolymers in solution, which can account for any branching present in the blocks, is presented. Results have been obtained for the special case of infinitely long linear blocks and it is found that the second virial coefficient is a function of five parameters, three characterizing the various interactions and two characterizing the unperturbed sizes of the two blocks, in addition to the molecular weight of the polymer chain.     

Equations of state for fluids: empirical temperature dependence of the second virial coefficients

In this paper, an empirical dependence of the second virial coefficients is derived from equations of state. The second virial coefficient B2 is found to be a linear function of 1/T1+beta, where T is the temperature and beta is a constant and has different value for different substances. Excellent experimental supports to this relationship are reported for nonpolar fluids, polar fluids, heavy globular molecule fluids, and quantum fluid He-4.     

Ab initio intermolecular potential energy surface and thermophysical properties of hydrogen sulfide

A six-dimensional potential energy hypersurface (PES) for two interacting rigid hydrogen sulfide molecules was determined from high-level quantum-mechanical ab initio computations. A total of 4016 points for 405 different angular orientations of two molecules were calculated utilizing the counterpoise-corrected supermolecular approach at the CCSD(T) level of theory and extrapolating the calculated interaction energies to the complete basis set limit. An analytical site-site potential function with eleven sites per hydrogen sulfide molecule was fitted to the interaction energies. The PES has been validated by computing the second pressure virial coefficient, shear viscosity, thermal conductivity and comparing with the available experimental data. The calculated values of volume viscosity were not used to validate the potential as the low accuracy of the available data precluded such an approach. The second pressure virial coefficient was evaluated by means of the Takahashi and Imada approach, while the transport properties, in the dilute limit, were evaluated by utilizing the classical trajectory method. In general, the agreement with the primary experimental data is within the experimental error for temperatures higher than 300 K. For lower temperatures the lack of reliable data indicates that the values of the second pressure virial coefficient and of the transport properties calculated in this work are currently the most accurate estimates for the thermophysical properties of hydrogen sulfide.     

Self-interaction nanoparticle spectroscopy: a nanoparticle-based protein interaction assay

Solution conditions conducive to protein crystallization are identified mainly in an empirical manner using screening methods. Measurements of a dilute solution thermodynamic parameter, the osmotic second virial coefficient, have been shown to be useful in guiding this search, yet the measurement of this parameter remains difficult. In this work, a nanoparticle-based assay, self-interaction nanoparticle spectroscopy, is presented as an efficient alternative. The method involves adsorbing proteins on the surface of gold nanoparticles and adding the protein/gold conjugates to solutions of interest for crystallization. The optical properties of gold colloid, including macroscopic ones such as color, are sensitive to the interparticle separation distance, and they are demonstrated to correlate with the value of the second virial coefficient for BSA and ovalbumin. Serendipitously, the conditions that correspond to second virial coefficient values within the thermodynamic region ideal for protein crystallization lead to the maximum change in color of the gold suspensions. Given the remarkable efficiency of this method, it holds significant potential to aid in the crystallization of proteins that have not been crystallized previously. Moreover, this method may find utility in the analysis of weak homo- and heterotypic interactions involved in other biological applications, including preventing protein aggregation and formulating therapeutic proteins.     

Second virial coefficient for the dipolar hard sphere fluid

The dipolar hard sphere fluid is a useful model for a polar fluid. Some years ago, the second virial coefficient, B(2), of this fluid was obtained as a series expansion in the inverse temperature or (dipole strength) by Keesom. Little work on this problem seems to have been done since that time. Using a result of Chan and Henderson for the spherical average of the Boltzmann factor of this fluid, more complete results are obtained for B(2). The more complete results are more negative than the Keesom series, as one would expect, but his expansion is remarkably accurate. This method can be used to obtain the second virial coefficient of the dipolar Lennard-Jones (Stockmayer) or dipolar Yukawa fluids.     

Thermodynamic studies of molecular interactions in aqueous alpha-cyclodextrin solutions: application of McMillan-Mayer and Kirkwood-Buff theories

Osmotic vapor pressure and density measurements were made for aqueous alpha-cyclodextrin (alpha-CD) solutions in the temperature range between 293.15 and 313.15 K. The experimental osmotic coefficient data were used to determine the corresponding activity coefficients and the excess Gibbs free energy of solutions. Further, the activity data obtained at different temperatures along with the enthalpies of dissolution (reported in the literature) were processed to obtain the excess enthalpy and excess entropy values for the solution process. The partial molar entropies of water and of alpha-cyclodextrin were calculated at different temperatures and also at different concentrations of alpha-CD. Using the partial molar volume data at infinite dilution, the solute-solvent cluster integrals were evaluated which yielded information about solute-solvent interactions. The application of McMillan-Mayer theory of solutions was made to obtain osmotic second and third virial coefficients which were decomposed into attractive and repulsive contributions to solute-solute interactions. The second and third osmotic virial coefficients are positive and show minimum at 303.15 K. The Kirkwood-Buff (KB) integrals G(ij), defined by the equation G(ij) = f(infinity)0 (g(ij)- 1)4pir(2) dr, have been evaluated using the experimental osmotic coefficient (and hence activity coefficient) and partial molar volume data. The limiting values of KB integrals, G(ij)(0) are compared with molecular interaction parameters (solute-solute i.e., osmotic second virial coefficient) obtained using McMillan-Mayer theory of solutions. We found an excellent agreement between the two approaches.     

Hard and Soft - Core Equations of State for Simple Fluids: VI. General Theory of Termination Temperatures,and a Validity Criterion for the Second Virial Coefficient

Abstract

A general proof is given that the classical second virial coefficient satisfies the requirement for the non-existence of a termination point of any locus of C_v extrema. This validity criterion is applied to some proposed forms for the second virial coefficient. The order of the termination temperatures is verified for a fairly general intermolecular potential. In particular a proof is given that T_F lies between T_C and T_A. Also the hard-core limit of the ratio T_D/T_A(～2) is examined briefly.     

Diffusion and virial coefficient in a mercury-argon gas mixture

Theoretical and experimental data on molecular beams and the mutual diffusion coefficient (MDC) and second virial coefficient (SVC) for an Hg-Ar gas mixture as a representative of the mercuryinert gas family are matched on basis of the Morse potential and the relations of the molecular kinetic theory of rarefied gases. Tables of the MDC and SVC values in the temperature range of 200–2000 K are calculated, and estimates of their accuracy are presented.     

On-line direct determination of the second virial coefficient of a natural polysaccharide using size-exclusion chromatography and multi-angle laser light scattering

By combining a size-exclusion chromatographic (SEC) separation and an on-line multi-angle light scattering (MALLS) analysis, we have elaborated an original methodology permitting on-line direct determination of the second virial coefficient of molar mass fractions of polydisperse polysaccharides. By assimilating the SEC-MALLS data to a batch mode acquisition, we have obtained on-line the complete Zimm plot of the eluted fractions, leading to knowledge of their weight-average molar mass Mw, radius of gyration r(g) and second virial coefficient A2. Our methodology was successfully applied to a iota carrageenan sample in LiCl 100 mM, EDTA 1 g/l.