Vojko Vlachy

Multidensity integral equation theory for highly asymmetric electrolyte solutions

Integral equation theory based on a recently developed multidensity formalism [Mol. Phys. 78, 1247 (1993)] is proposed to study highly asymmetric electrolyte (polyelectrolyte) solutions. The system studied consists of large and highly charged polyions and small counterions having one or two elementary charges. The potential energy of interaction between counterions and polyions is separated into two parts, a strongly attractive part responsible for the association and a nonassociative part. Due to the strong asymmetry in size we can treat each counterion as bondable to a limited number of polyions n, while each polyion can bond arbitrary number of counterions. In our cluster expansion appropriate to the problem the diagrams appearing in the activity expansion of the one‐point counterion density are classified in terms of the number of associating bonds incident upon the labeled white counterion circle. The corresponding diagrams for the one‐point polyion density are classified in the usual way. A generali...

A two-dimensional model of water: Theory and computer simulations

We develop an analytical theory for a simple model of liquid water. We apply Wertheim’s thermodynamic perturbation theory (TPT) and integral equation theory (IET) for associative liquids to the MB model, which is among the simplest models of water. Water molecules are modeled as 2-dimensional Lennard-Jones disks with three hydrogen bonding arms arranged symmetrically, resembling the Mercedes-Benz (MB) logo. The MB model qualitatively predicts both the anomalous properties of pure water and the anomalous solvation thermodynamics of nonpolar molecules. IET is based on the orientationally averaged version of the Ornstein-Zernike equation. This is one of the main approximations in the present work. IET correctly predicts the pair correlation function of the model water at high temperatures. Both TPT and IET are in semi-quantitative agreement with the Monte Carlo values of the molar volume, isothermal compressibility, thermal expansion coefficient, and heat capacity. A major advantage of these theories is that...

A two-dimensional model of water: Solvation of nonpolar solutes

We recently applied a Wertheim integral equation theory (IET) and a thermodynamic perturbation theory (TPT) to the Mercedes–Benz (MB) model of pure water. These analytical theories offer the advantage of being computationally less intensive than the Monte Carlo simulations by orders of magnitudes. The long-term goal of this work is to develop analytical theories of water that can handle orientation-dependent interactions and the MB model serves as a simple workbench for this development. Here we apply the IET and TPT to the hydrophobic effect, the transfer of a nonpopular solute into MB water. As before, we find that the theories reproduce the Monte Carlo results quite accurately at higher temperatures, while they predict the qualitative trends in cold water.

Clustering of macroions in solutions of highly asymmetric electrolytes.

In this paper, we present results of computer simulations for a primitive model of asymmetric electrolyte solutions containing macroions, counterions and in a few cases, also co-ions. The results show that the valency of counterions plays an important role in shaping the net interaction between the macroions. For solutions with monovalent counterions, the macroions are distributed at larger distances, and in solutions with divalent counterions, the macroions come closer to each other and share a layer of counterions, whereas, in solutions with trivalent counterions, the macroions form clusters. These clusters dissolve upon dilution or addition of a simple electrolyte. These findings suggest a mechanism whereby the nonuniform distribution of macroions observed experimentally in charged systems may occur.

Orientation-dependent integral equation theory for a two-dimensional model of water

We develop an integral equation theory that applies to strongly associating orientation-dependent liquids, such as water. In an earlier treatment, we developed a Wertheim integral equation theory (IET) that we tested against NPT Monte Carlo simulations of the two-dimensional Mercedes Benz model of water. The main approximation in the earlier calculation was an orientational averaging in the multidensity Ornstein–Zernike equation. Here we improve the theory by explicit introduction of an orientation dependence in the IET, based upon expanding the two-particle angular correlation function in orthogonal basis functions. We find that the new orientation-dependent IET (ODIET) yields a considerable improvement of the predicted structure of water, when compared to the Monte Carlo simulations. In particular, ODIET predicts more long-range order than the original IET, with hexagonal symmetry, as expected for the hydrogen bonded ice in this model. The new theoretical approximation still errs in some subtle properti...

Protein aggregation in salt solutions

Significance Protein aggregation is a problem in amyloid and other diseases, and it is a challenge when formulating solutions of biological drugs, such as monoclonal antibodies. The physical processes of aggregation, especially in salt solutions, are not well understood. We model a protein as having multiple binding sites to other proteins, leading to orientational variations, dependent on salt. With few parameters and with knowledge of the cloud-point temperatures as a function of added salt, the model gives good predictions for properties including the liquid–liquid coexistence curves, the second virial coefficients, and others for lysozyme and gamma-crystallin. Protein aggregation is broadly important in diseases and in formulations of biological drugs. Here, we develop a theoretical model for reversible protein–protein aggregation in salt solutions. We treat proteins as hard spheres having square-well-energy binding sites, using Wertheim’s thermodynamic perturbation theory. The necessary condition required for such modeling to be realistic is that proteins in solution during the experiment remain in their compact form. Within this limitation our model gives accurate liquid–liquid coexistence curves for lysozyme and γ IIIa-crystallin solutions in respective buffers. It provides good fits to the cloud-point curves of lysozyme in buffer–salt mixtures as a function of the type and concentration of salt. It than predicts full coexistence curves, osmotic compressibilities, and second virial coefficients under such conditions. This treatment may also be relevant to protein crystallization.

Solubility of lysozyme in polyethylene glycol-electrolyte mixtures: the depletion interaction and ion-specific effects.

The solubility of aqueous solutions of lysozyme in the presence of polyethylene glycol and various alkaline salts was studied experimentally. The protein-electrolyte mixture was titrated with polyethylene glycol, and when precipitation of the protein occurred, a strong increase of the absorbance at 340 nm was observed. The solubility data were obtained as a function of experimental variables such as protein and electrolyte concentrations, electrolyte type, degree of polymerization of polyethylene glycol, and pH of the solution; the last defines the net charge of the lysozyme. The results indicate that the solubility of lysozyme decreases with the addition of polyethylene glycol; the solubility is lower for a polyethylene glycol with a higher degree of polymerization. Further, the logarithm of the protein solubility is a linear function of the polyethylene glycol concentration. The process is reversible and the protein remains in its native form. An increase of the electrolyte (NaCl) concentration decreases the solubility of lysozyme in the presence and absence of polyethylene glycol. The effect can be explained by the screening of the charged amino residues of the protein. The solubility experiments were performed at two different pH values (pH = 4.0 and 6.0), where the lysozyme net charge was +11 and +8, respectively. Ion-specific effects were systematically investigated. Anions such as Br(-), Cl(-), F(-), and H(2)PO(4)(-) (all in combination with Na(+)), when acting as counterions to a protein with positive net charge, exhibit a strong effect on the lysozyme solubility. The differences in protein solubility for chloride solutions with different cations Cs(+), K(+), and Na(+) (coions) were much smaller. The results at pH = 4.0 show that anions decrease the lysozyme solubility in the order F(-) < H(2)PO(4)(-) < Cl(-) < Br(-) (the inverse Hofmeister series), whereas cations follow the direct Hofmeister series (Cs(+) < K(+) < Na(+)) in this situation.

Understanding polyelectrolyte solutions: Macroion condensation with emphasis on the presence of neutral co-solutes

The multi-faceted applications of polyelectrolyte solution systems to a kaleidoscope of technological and biological processes make the understanding of these systems important and of interest. The highly relevant issue of instabilities that may occur in a polyelectrolyte solution and the ensuing macroion condensation constitute the premise of this review. An abundance of experimental and numerical simulation results in recent years provide evidence that a net electrostatic attractive force may exist between macroions and may lead to a phase separation. Specifically, in this review, three different types of instability involving macroions of spherical geometry are discussed. (i) The instability arising out of strong Coulomb correlations between counterions in the solution; this is most likely to occur in solutions containing multivalent counterions and/or in the presence of solvents of low relative permittivity. (ii) The instability caused by the macroion surface-charge fluctuations; the resultant charge correlations may induce an effective attraction between the weakly charged macroions. (iii) The instability due to the combined effect of electrostatic and crowding interactions when an inert co-solute is added to the solution. A sufficient increase in the concentration of the neutral species leads to a gradual change in the nature of the interaction between two macroions, from being repulsive to less repulsive and ultimately attractive. The structural features and thermodynamics in these complex systems are shaped by the collective and often competing effects of the species.

Ion–ion correlations in electrolyte solutions adsorbed in disordered electroneutral charged matrices from replica Ornstein–Zernike equations

The replica Ornstein–Zernike (ROZ) equations, supplemented by the hypernetted chain and mean spherical closures, were solved for an ionic fluid adsorbed in a disordered charged matrix. To obtain the numerical solution of the ROZ equations we performed renormalization of the initial equations. Both the matrix and adsorbed fluid were modeled as charged hard spheres in a dielectric continuum, i.e., in the so-called restricted primitive model. As a result, the pair distribution functions between fluid ions and for fluid-matrix correlations were obtained. Structural properties were studied as a function of the matrix density, the concentration of adsorbed electrolyte and for different prequenching conditions. The isothermal compressibility, excess internal energy, and the chemical potential were calculated and discussed with respect to of the model parameters. Comparison with the Monte Carlo computer simulations of Bratko and Chakraborty [J. Chem. Phys. 104, 7700 (1996)] indicates that the theory yields qualit...

Correlations between macroions in mixtures of charged and uncharged macroparticles

Addition of uncharged or charged macroparticles to a solution of macroions and counterions significantly affects the macroion–macroion correlation function. This effect is studied using the hypernetted‐chain integral equation. Two simple models are examined: (i) a multicomponent primitive model treats a solution as a mixture of charged and uncharged hard spheres, (ii) a one‐component model where the electrostatic interactions are accounted for by the screened Coulomb potential and the effect of neutral macroparticles is given by an approximate ‘‘volume exclusion’’ potential. Both models ignore the molecular nature of solvent. The calculations presented here indicate that the one‐component model is a poor representation of the actual interactions between macroions in the presence of the neutral macroparticles represented as hard spheres. In the second part of the work we study the mixtures of macroions (two positively charged macroions that differ in size) with a common counterion. The radial distribution ...