Modified Hypernetted-chain Research Articles

Study of the thermodynamic inconsistency of the potential of mean force calculated using the integral equation theory of molecular liquids

In this study, we investigated thermodynamic inconsistency in the potential of mean force (PMF) calculated using the Ornstein-Zernike (OZ), one-dimensional reference interaction site model (1D-RISM), and three-dimensional OZ (3D-OZ) theories. Two methods were used to obtain the PMF: converting the radial distribution function (RDF) into the PMF, and utilizing the solvation free energy (SFE) of the diatomic solute molecule with an added direct interaction between the two solute atoms. Both for the Lennard-Jones (LJ) and Coulomb systems, the hypernetted chain (HNC) closure showed the best performance among the closure relationships tested in this study. However, the performance of the HNC was not perfect and exhibited significant inconsistency in the PMF. The Kovalenko–Hirata and Kobryn–Gusarov–Kovalenko closures were also tested, with fair results when combined with the 1D-RISM equation but poor results when combined with the 3D-OZ equation. The Verlet-modified (VM) closure was found to be inapplicable to Coulomb systems. In contrast, the modified HNC (MHNC) closure showed relatively good results at high temperatures. Furthermore, we modified the Martynov–Sarkisov (MS) closure for Coulomb systems, resulting in a modified MS closure that yields relatively accurate PMF results. We also discuss the behavior of the SFE for Coulomb systems obtained from the 1D-RISM theory, a thorough analysis of both the RDF and the integrand in the Kirkwood charging formula.

Spatial distribution of reduced density of hard spheres near a hard-sphere dimer: Results from three-dimensional Ornstein–Zernike equations coupled with several different closures and from grand canonical Monte Carlo simulation

We calculated the spatial distribution function, which is the one-body reduced density distribution of solvent particles around a nonspherical solute, using the three-dimensional Ornstein–Zernike equations coupled with closures. The solvent was a hard-sphere fluid, and the contact dimer of the solvent particles was the nonspherical solute. Two traditional closures, the Percus–Yevick and hypernetted-chain approximations, and three closures with bridge functions (BFs) were examined. These spatial distribution functions were compared with the results obtained by grand canonical Monte Carlo (GCMC) simulations. Three closures with BFs, such as the modified hypernetted-chain (MHNC) closure using a bridge function proposed by Kinoshita, gave precise spatial distribution functions. These results were much more accurate than those obtained by the traditional closures. The deviations from the spatial distribution function obtained by the GCMC simulation appeared only near the concave surface of the solute dimer. However, the deviations were minor compared with those between the simulation and the predictions of the two traditional closures. By contrast, the three-body correlation functions for the closures with BFs were not more accurate than those obtained by the traditional closures.

Simulations and integral-equationtheories for dipolar density interacting disks.

Integral equationtheories (IETs) based on the Ornstein-Zernike (OZ) relation can be used as an analytical tool to predict structural and thermodynamic properties and phase behavior of fluids with low numerical cost. However, there are no studies of the IETs for the dipolar density interaction potential in two-dimensional systems, a relevant interdomain interaction in lipid monolayers with phase coexistence. This repulsive interaction arises due to the excess dipole density of the domains, which are aligned perpendicular to the interface. This work studies the performance of three closures of the OZ equationfor this novel system: Rogers-Young (RY), modified hypernetted chain (MHNC), and variational modified hypernetted chain (VMHNC). For the last two closures the bridge function of a reference system is required, with the hard disk being the most convenient reference system. Given that in two dimensions there is no analytical expressions for the hard disk correlation functions, two different approximations are proposed: one based on the Percus-Yevick (PY) approximation, and the other based on an extension of the hard spheres Verlet-Weis-Henderson-Grundke (LB) parametrization. The accuracy of the five approaches is evaluated by comparison of the pair correlation function and the structure factor with Monte Carlo simulation data. The results show that RY closure is satisfactory only for low-structured regimes. MHNC and VMHNC closures perform globally well, and there are no significant differences between them. However, the reference system in some cases affects their performance; when the pair correlation function serves as the measure, the LB-based closures quantitatively outperform the PY ones. From the point of view of its applicability, LB-based closures do not have a solution for all studied interaction strength parameters, and, in general, PY-based closures are numerically preferable.

On the structure, property, and phase behaviour of the symmetric Yukawa mixtures: testing of the consistent integral equation theories

ABSTRACTYukawa mixtures are important microscopic models of liquids. In order to obtain their properties, we must have accurate and consistent theories, without the issues arising from the multi-valued pressures and chemical potentials due to inconsistencies in the theory. This work tests two self-consistent integral equation theories (IETs): the modified hypernetted-chain (MHNC) theory and the zero-separation (ZSEP) based theory. These equations, by construction, automatically satisfy the pressure consistency the Gibbs-Duhem relation, as well as the zero-separation theorem. To verify, new Monte-Carlo (MC) simulations are carried out for temperatures 0.7 < T* < 1.1 and densities 0.4 < ρ* < 0.5. The Yukawa interactions uij are symmetric (u11 = u22). The unlike u12 is made weaker than the like-type by a factor α < 1. The structures, exemplified by the radial distribution functions, are accurately reproduced by both MHNC and ZSEP. The internal energies are predicted to within 1% of the MC data, the pressures to within 4%; and the chemical potentials to less than 3%. The vapour-liquid phase envelope is determined for a typical mixture. In this case the performance of both IETs is also shown to be satisfactory.

Theory and computer simulation of hard-core Yukawa mixtures: thermodynamical, structural and phase coexistence properties

We report extensive calculations, based on the modified hypernetted chain (MHNC) theory, on the hierarchical reference theory (HRT), and on Monte Carlo simulations, of thermodynamical, structural and phase coexistence properties of symmetric binary hard-core Yukawa mixtures (HCYM) with attractive interactions at equal species concentration. The obtained results are throughout compared with those available in the literature for the same systems. It turns out that the MHNC predictions for thermodynamic and structural quantities are quite accurate in comparison with the MC data. The HRT is equally accurate for thermodynamics, and slightly less accurate for structure. Liquid-vapor (LV) and liquid–liquid (LL) consolute coexistence conditions as emerging from simulations, are also highly satisfactorily reproduced by both the MHNC and HRT for relatively long ranged potentials. When the potential range reduces, the MHNC faces problems in determining the LV binodal line; however, the LL consolute line and the critical end point (CEP) temperature and density turn out to be still satisfactorily predicted within this theory. The HRT also predicts with good accuracy the CEP position.The possibility of employing liquid state theories HCYM for the purpose of reliably determining phase equilibria in multicomponent colloidal fluids of current technological interest, is discussed.

A thermodynamic self-consistent theory of asymmetric hard-core Yukawa mixtures

We perform structural and thermodynamic calculations in the framework of the modified hypernetted chain (MHNC) integral equation closure to the Ornstein–Zernike equation for binary mixtures of size-different particles interacting with hard-core Yukawa pair potentials. We use the Percus–Yevick (PY) bridge functions of a binary mixture of hard-sphere (HSM) particles. The hard-sphere diameters of the PY bridge functions of the HSM system are adjusted so to achieve thermodynamic consistency between the virial and compressibility equations of state. We show the benefit of thermodynamic consistency by comparing the MHNC results with the available computer simulation data reported in the literature, and we demonstrate that the self-consistent thermodynamic theory provides a better reproduction of the simulation data over other microscopic theories.

Reference interaction site model investigation of homonuclear hard dumbbells under simple fluid theory closures: Comparison with Monte Carlo simulations

We revisit the thermodynamic and structural properties of fluids of homonuclear hard dumbbells in the framework provided by the reference interaction site model (RISM) theory of molecular fluids. Besides the previously investigated Percus-Yevick (PY) approximation, we test the accuracy of other closures to the RISM equations, imported from the theory of simple fluids; specifically, we study the hypernetted chain (HNC), the modified HNC (MHNC) and, less extensively, the Verlet approximations. We implement our approach for models characterized by several different elongations, up to the case of tangent diatomics, and investigate the whole fluid density range. The theoretical predictions are assessed against Monte Carlo simulations, either available from literature or newly generated by us. The HNC and PY equations of state, calculated via different routes, share on the whole the same level of accuracy. The MHNC is applied by enforcing an internal thermodynamic consistency constraint, leading to good predictions for the equation of state as the elongation of the dumbbell increases. As for the radial distribution function, the MHNC appears superior to other theories, especially for tangent diatomics in the high density limit; the PY approximation is better than the HNC and Verlet closures in the high density or elongation regime. Our structural analysis is supplemented by an accurate inversion procedure to reconstruct from Monte Carlo data and RISM the "exact" direct correlation function. In agreement with such calculations and consistent with the forecast of rigorous diagrammatic analysis, all theories predict the occurrence in the direct correlation function of a first cusp inside the dumbbell core and (with the obvious exception of the PY) of a second cusp outside; the cusps' heights are also qualitatively well reproduced by the theories, except at high densities.

Local Structure and Thermodynamics of a Core‐Softened Potential Fluid: Theory and Simulation

Phase behavior and structural properties of homogeneous and inhomogeneous core-softened (CS) fluid consisting of particles interacting via the potential, which combines the hard-core repulsion and double attractive well interaction, are investigated. The vapour-liquid coexistence curves and critical points for various interaction ranges of the potential are determined by discrete molecular dynamics simulations to provide guidance for the choice of the bulk density and potential parameters for the study of homogeneous and inhomogeneous structures. Spatial correlations in the homogeneous CS system are studied by the Ornstein-Zernike integral equation in combination with the modified hypernetted chain (MHNC) approximation. The local structure of CS fluid subjected to diverse external fields maintaining the equilibrium with the bulk CS fluid are studied on the basis of a recently proposed third order+second order perturbation density functional approximation (DFA). The accuracy of DFA predictions is tested against the results of a grand canonical ensemble Monte Carlo simulation. Reasonable agreement between the results of both methods proves that the DFA theory applied in this work is a convenient theoretical tool for the investigation of the CS fluid, which is practically applicable for modeling numerous real systems.

Fluid–fluid and fluid–solid phase separation in nonadditive asymmetric binary hard-spheremixtures

Very asymmetric mixtures of hard spheres naturally arise in the modellization of colloidaldispersions. Effective potentials have emerged as a powerful tool for describing thesesystems and have often been employed to extract the phase diagram in both theadditive and nonadditive cases. However, most theoretical investigations havebeen carried out by means of mean-field-like approaches, so their quantitativeaccuracy remains to be assessed. Here we employ previously determined effectivepotentials for nonadditive hard-sphere mixtures to study the fluid–fluid phasetransition by the hierarchical reference theory (HRT), which is designed to takerealistically into account the effects of long-range fluctuations on phase separation.Fluid–solid equilibrium is addressed by supplementing HRT with thermodynamicperturbation theory for the solid phase. We apply this approach both to a potential withadjustable nonadditivity parameter (Louis et al 2000 Phys. Rev. E 61 R1028) and to theAsakura–Oosawa (AO) potential, which represents an extreme case of nonadditivity. Ourresults for the phase diagram, including modified hypernetted chain (MHNC)calculations, are compared to those of other liquid-state theories and are found toagree nicely with available simulation data. Unlike commonly adopted liquid-statetheories, HRT is capable both of getting arbitrarily close to the fluid–fluid criticalpoint, and of giving nontrivial critical exponents. In particular, the fluid–fluidcoexistence curve is much flatter than that obtained via perturbation theory, inagreement with a recent finite-size scaling Monte Carlo analysis of the AO model.

Prediction of the Small-k Behavior of the Structure Factor (S(k)) for Rubidium and Cesium via a New Model for the Direct Correlation Function and Evaluation of Some Reported Effective Pair Potentials

In this article, we have used a newly presented direct correlation function (DCF) and predicted the small-k behavior of the structure factor, S(k), for liquid rubidium and cesium, and this behavior is in very good agreement with the experimental data. For these calculations, the effective pair potentials have obtained using the modified hyper-netted-chain (MHNC) theory. These effective pair potentials are also accurate for the range in which no pseudopotential, or Lennard-Jones (LJ) potential, is adequate to present the thermodynamic behavior of alkali metals. We have also compared our model with the Percus−Yevick theory and random phase approximation in regard to predicting S(k) at low k, and a better agreement has been obtained. Because the applied model for the DCF generates S(k) accurately at low k, we have used it to evaluate some reported effective pair potentials for alkali metals, including LJ (n−m) and also exp-6 types. The results show that these potentials are not very accurate, at least for the moderate densities, in regard to predicting S(k), although these potentials are able to generate the pressure−volume−temperature (p−v−T) behavior of alkali metals precisely.

Theoretical description of phase coexistence in model C60.

We have investigated the phase diagram of a pair interaction model of C60 fullerene [L. A. Girifalco, J. Phys. Chem. 96, 858 (1992)], in the framework provided by two integral equation theories of the liquid state, namely, the modified hypernetted chain (MHNC) implemented under a global thermodynamic consistency constraint, and the self-consistent Ornstein-Zernike approximation (SCOZA), and by a perturbation theory (PT) with various degrees of refinement, for the free energy of the solid phase. We present an extended assessment of such theories as set against a recent Monte Carlo study of the same model [D. Costa, G. Pellicane, C. Caccamo, and M. C. Abramo, J. Chem. Phys. 118, 304 (2003)]. We have compared the theoretical predictions with the corresponding simulation results for several thermodynamic properties such as the free energy, the pressure, and the internal energy. Then we have determined the phase diagram of the model, by using either the SCOZA, the MHNC, or the PT predictions for one of the coexisting phases, and the simulation data for the other phase, in order to separately ascertain the accuracy of each theory. It turns out that the overall appearance of the phase portrait is reproduced fairly well by all theories, with remarkable accuracy as for the melting line and the solid-vapor equilibrium. All theories show a more or less pronounced discrepancy with the simulated fluid-solid coexistence pressure, above the triple point. The MHNC and SCOZA results for the liquid-vapor coexistence, as well as for the corresponding critical points, are quite accurate; the SCOZA tends to underestimate the density corresponding to the freezing line. All results are discussed in terms of the basic assumptions underlying each theory. We have then selected the MHNC for the fluid and the first-order PT for the solid phase, as the most accurate tools to investigate the phase behavior of the model in terms of purely theoretical approaches. It emerges that the use of different procedures to characterize the fluid and the solid phases provides a semiquantitative reproduction of the thermodynamic properties of the C60 model at issue. The overall results appear as a robust benchmark for further theoretical investigations on higher order C(n>60) fullerenes, as well as on other fullerene-related materials, whose description can be based on a modelization similar to that adopted in this work.

Star polymers: study of fluid–fluid transitions in a system with a repulsiveultrasoft-core

We study a model for star polymers in solution which, in addition to the ultrasoftrepulsive interaction of entropic origin, has an attractive interpolymerinteraction at longer range. This attraction can arise from a suitable tuningof the solvent and solute properties. For this model we study the phasediagram using mean-field theory and two fluid-state theories, the modifiedhypernetted chain (MHNC) integral equation and the hierarchical referencetheory, and we explore star polymers with a different number of armsf(f = 12, 24, 32, 40).All three theories give the same topology for the phase diagram in thepresence of attraction. When the strength of the interaction is strong enougha fluid–fluid phase transition appears but the coexistence curve in thedensity–temperature (strength of attraction) bifurcates at a triple point into twolines of coexistence terminating at two critical points. This peculiar phasebehaviour is related to the unusual form of the repulsive contributionVrep (r):at low density and in a semidilute regime the soft-core Yukawa-like part ofVrep (r)is relevant, at higher densities the logarithmic, ultrasoft part ofVrep (r)is the relevant one. During our study we verify that the MHNC equation alsogives a very accurate description of correlations for systems with an ultrasoft-corepotential.

Phase Diagrams and Sublimation Enthalpies of Model Cn⩾60 Fullerenes: A Comparative Study by Computer Simulation

A comparative study, strictly by computer simulation, of the phase diagrams and sublimation enthalpies of model Cn⩾60 fullerenes is presented. Gibbs ensemble and Gibbs−Duhem integration Monte Carlo simulations were carried out with the effective potentials of Girifalco. The triple-point properties were determined by a direct method recently proposed by us. It is based on the behavior of the Gibbs ensemble simulations at the lowest temperature limit, and it does not involve free-energy calculations or any other theoretical approach. According to the present results, the liquid phases of the studied fullerenes (C60, C70, C76, and C84) extend over ∼450 K. No sign of liquid supercooling was observed. The triple-point temperatures increase from C60 to C84. This and the simultaneous effect of molecular size cause a relative dislocation of the phase diagrams to higher critical temperatures and lower densities. The simulated enthalpies of sublimation increase from C60 to C84, and they are in very good agreement with the available experimental data. It is suggested that at least the predicted triple-point properties should approach those of real fullerenes. There is a strong correlation between the phase properties and the details of the interaction potentials, clearly reflected in the relative location of the phase diagram and enthalpy curves. On the whole, the simulated results are in good accordance with those recently reported by Abramo et al. (Abramo, M. C.; Caccamo, C.; Costa, D.; Pellicane, G. Europhys. Lett. 2001, 54, 468) from a combination of simulation, modified hypernetted chain (MHNC) theory, and a kind of “corresponding states” rule and confirm the consistency of the MHNC theoretical approach. The reduced properties, which also include the critical- and triple-point pressures as well as the sublimation enthalpies, confirm that some kind of corresponding states rule may be established for fullerenes. On the basis of that, the enthalpy of sublimation of C96 is predicted.

Dynamical Structure of the Liquid Ge by the Viscoelastic Theory

The dynamical structure factors of the liquid Ge are calculated theoretically and compared with the recent experimental results obtained by the inelastic X-ray scattering. The calculation is carried out by the simple purely theoretical method, i.e. by the viscoelastic theory, which is based on the effective pair potential obtained by the pseudopotential perturbation theory and the static structure factor calculated by the integral-equation theory in the modified hypernetted-chain (MHNC) approximation. It is shown that the calculated dynamical structure factors are in qualitative agreement with the experimental results and that the calculated dispersion relation agrees well with the experimental one.

Microscopic theories of model macromolecular fluids and fullerenes: The role of thermodynamic consistency

We investigate the accuracy of two well-known integral equation theories (IETs) of the fluid state, namely, the modified hypernetted chain (MHNC) approximation and the hybridized mean spherical approximation (HMSA), as applied to systems characterized by short-range interactions. The theoretical approaches are implemented by enforcing their thermodynamic consistency according to two different strategies: in one case the equality of the isothermal compressibility, as calculated via the virial and fluctuation routes from structure to thermodynamics, is imposed [“local” consistency (LC)]; in the other case the equality of the pressure as calculated either via the two previous routes, or via the virial and the energy routes, is imposed [“global” consistency (GC)]. We show that for the class of potentials at issue the GC is in general considerably more accurate than the LC. We document this result by investigating the performances of the MHNC and the HMSA, as applied to the calculation of the thermodynamic and structural properties of the hard-core Yukawa (HCY) potential, the Derjaguin–Landau–Vervey–Overbeek (DLVO) potential and the Girifalco potential for fullerenes. The obtained results are then compared with Monte Carlo simulation data, that we also produce for the same model systems. As far as the HCY potential is concerned, the investigation covers a range of the Yukawa inverse decay length, z, spanning from z=1.8 when the interaction mimics the Lennard-Jones 12-6 potential, to z=7 when the potential mimics the “effective” short range interaction between globular proteins in a highly charge-screened aqueous solution. IETs are then applied to the DLVO potential with charge and Hamaker constant values which fit the dynamical interaction factor of lysozyme in a solution of high ionic strength, and to the Girifalco potential with parameters appropriate to model C60 and C70. It emerges from the present study that the GC is able to provide Helmholtz free energies and chemical potentials which compare quite favorably with the simulation data. As a consequence, we are able to show that the GC estimates of the phase coexistence densities for the HCY and Girifalco potential agree almost quantitatively with the Monte Carlo ones, by thus definitely improving upon previous results obtained within the LC. We also comment on the relevance of confident phase diagram determinations from IETs, in connection with the prediction of protein crystallization. Possible extensions of the present thermodynamic consistency strategies to more sophisticated theories and realistic models of protein solutions and fullerenes are finally suggested.

Effective pair potentials of Molten AgBr, CuBr, CuI and RbBr estimated from the experimental partial structure factors

The effective pair potentials of molten AgBr, CuBr, CuI and RbBr have been obtained from measured structural information by solving the modified hypernetted-chain (MHNC) equation coupled with a predictor–corrector method, recently proposed for a binary system. The usefulness of the pair potentials obtained in this work was suggested by reproducing the particular pre-peak in the partial structure factor of Cu–Cu pair in molten CuBr and CuI, because such pre-peak couldnot be given while using the model potentials previously proposed for these two molten salts. Some characteristic features in these four molten salts were also detected in the bridge function, which was introduced to the MHNC equation as a many-body interaction contribution.

Three-body effects in simple insulating liquids: a small-angle neutron scattering study in Kr

A neutron diffraction experiment has been performed to measure the low- q structure of Kr at liquid densities. Deviations from a pure two-body behaviour are unambiguously determined in the explored q-range (1< q/nm −1<4) and are examined through the comparison between experimental results and Modified Hyper-Netted Chain (MHNC) calculations.

Thermodynamically self-consistent theories of fluids interacting through short-range forces.

The self-consistent Ornstein-Zernike approximation (SCOZA), the generalized mean spherical approximation (GMSA), the modified hypernetted chain (MHNC) approximation, and the hierarchical reference theory (HRT) are applied to the determination of thermodynamic and structural properties, and the phase diagram of the hard-core Yukawa fluid (HCYF). We investigate different Yukawa-tail screening lengths lambda, ranging from lambda=1.8 (a value appropriate to approximate the shape of the Lennard-Jones potential) to lambda=9 (suitable for a simple one-body modelization of complex fluids like colloidal suspensions and globular protein solutions). The comparison of the results obtained with computer simulation data shows that at relatively low lambda's all the theories are fairly accurate in the prediction of thermodynamic and structural properties; as far as the phase diagram is concerned, the SCOZA and HRT are able to predict the binodal line and the critical parameters in a quantitative manner. At lambda=4 some discrepancies begin to emerge in the performances of the different theoretical approaches: the MHNC remains, on the whole, reasonably accurate in predicting the energy and the contact value of the radial distribution function; the SCOZA predicts well the equation of state up to the highest lambda values investigated. The GMSA and the MHNC underestimate and overestimate, respectively, the liquid coexisting density, while the SCOZA and HRT yield liquid branches that fall between the two former theoretical predictions, although both appear to overestimate the critical temperature somewhat. At higher lambda's the GMSA and MHNC binodals further worsen, while the SCOZA appears to remain usefully predictive. In general, the predictions of all the theories tend to slightly worsen at low temperatures and high density. The determination of the freezing line, performed by means of a one-phase "freezing criterion" (due to other authors) is not particularly satisfactory within either the SCOZA or the MHNC; the GMSA prediction for the freezing line at lambda=7 and 9 is instead able to follow in a qualitative manner the pattern of the solid-vapor coexistence line as determined through computer simulation studies. The necessity of further assessments of the freezing predictions is also discussed. Finally, versions of the GMSA, SCOZA, and HRT that can be expected to be more accurate for interactions with extremely short-ranged attractions are identified.

A comprehensive study of the phase diagram of symmetrical hard-core Yukawa mixtures

The phase diagrams of hard-core Yukawa mixtures (HCYM), constituted of equal sized hard spheres interacting through an attractive Yukawa tail, are determined by means of Gibbs Ensemble Monte Carlo (GEMC) simulations, Semi-grand Canonical Monte Carlo (SGCMC) simulations, and through the modified hypernetted-chain (MHNC) theory. Freezing lines are obtained according to an approach recently proposed by Giaquinta and co-workers [Physica A 187, 145 (1992); Phys Rev. A 45, 6966 (1992)] in which an analysis of multiparticle contributions to the excess entropy, Δs, is performed, with the determination of the Δs=0 locus. Liquid–vapor coexistence, determined through GEMC simulations, turns out to be favored when the strength ratio ν of unlike to like particle interaction, is close to 1. For lower ν’s, liquid–vapor coexistence is favored at low densities, and liquid–liquid coexistence, determined through SGCMC simulations, at high densities. The liquid–vapor binodal shifts downward in temperature and flattens when ν decreases, with a decrease of the critical temperature. At ν=0.9 a triple point can be identified from the intersection of the freezing line with the binodal line; at ν=0.7, instead, the binodal ends on the line of liquid–liquid (consolute) critical points, the intersection of the two lines thus identifying the “crossover” density and temperature between the two equilibrium regimes which correspond to the critical end point of the mixture. We find that, for not too high densities, consolute equilibrium can be also explored through GEMC simulations; the results for liquid–liquid coexistence obtained through this method and SGCMC simulations compare quite satisfactorily with each other. The trend of the liquid–vapor binodal to disappear for relatively weak unlike interactions is discussed in connection with the disappearance of liquid–vapor equilibrium which occurs in one component hard-core Yukawa fluids characterized by very short ranged attractive forces. The latter behavior has been conjectured to be relevant for the onset of crystallization in protein solutions; the implications of the present results, which are obtained in the context of a two component, albeit rough, modelization of a realistic solution, are discussed. In agreement with similar results obtained by Giaquinta et al., we finally find that the Δs=0 locus not only brings the signature of the freezing transition, but also of structural rearrangements preluding to other phase equilibria; in fact, the Δs=0 line turns out to be coincident to a high accuracy with the line of consolute critical points and with the gas branches of the liquid–vapor binodals.

Percus-Yevick bridge functions in a thermodynamic self-consistent theory of hard sphere mixtures

Two component hard sphere mixtures are studied by means of a modified hypernetted-chain (MHNC) approach in which Percus-Yevick (PY) bridge functions are employed. The thermodynamic self-consistency of the theory is obtained by using as adjustable parameters the hard sphere diameters entering the expressions of the bridge functions. Thermodynamically consistent calculations are also performed in the Rogers-Young (RY) approximation in terms of two consistency parameters. A wide range of diameter ratios and of relative concentrations of the particle species is explored, with particular attention to strongly asymmetric mixtures in the highly diluted regime of the bigger-sized component. Comparison with Monte Carlo results, and with well known parametrizations of computer simulation data, shows that the MHNC predictions for thermodynamic and structural quantities are generally very accurate and slightly superior to the RY ones. It also turns out that the PY bridge functions, which yield the thermodynamic consistency, reproduce fairly well those of the actual mixture as obtained from the parametrizations of simulation results. Such an agreement remains valid up to diameter ratios as great as 3, and down to 2% concentration of the bigger-sized component.