Phase behavior of polydisperse sticky hard spheres: analytical solutions and perturbation theory

We discuss phase coexistence of polydisperse colloidal suspensions in the presence of adhesion forces. The combined effect of polydispersity and Baxter's sticky-hard-sphere (SHS) potential, describing hard spheres interacting via strong and very short-ranged attractive forces, give rise, within the Percus-Yevick (PY) approximation, to a system of coupled quadratic equations which, in general, cannot be solved either analytically or numerically. We review and compare two recent alternative proposals, which we have attempted to by-pass this difficulty. In the first one, truncating the density expansion of the direct correlation functions, we have considered approximations simpler than the PY one. These $C_{n}$ approximations can be systematically improved. We have been able to provide a complete analytical description of polydisperse SHS fluids by using the simplest two orders $C_{0}$ and $C_{1}$, respectively. Such a simplification comes at the price of a lower accuracy in the phase diagram, but has the advantage of providing an analytical description of various new phenomena associated with the onset of polydispersity in phase equilibria (e.g. fractionation). The second approach is based on a perturbative expansion of the polydisperse PY solution around its monodisperse counterpart. This approach provides a sound approximation to the real phase behavior, at the cost of considering only weak polydispersity. Although a final seattlement on the soundness of the latter method would require numerical simulations for the polydisperse Baxter model, we argue that this approach is expected to keep correctly into account the effects of polydispersity, at least qualitatively.Comment: 12 pages, 4 figures, to appear in Molec. Phys. special issue Liblice 200

On the compressibility equation of state for multicomponent adhesive hard sphere fluids

The compressibility equation of state for a multicomponent fluid of particles interacting via an infinitely narrow and deep potential, is considered within the mean spherical approximation (MSA). It is shown that for a class of models leading to a particular form of the Baxter functions $q_{ij}(r)$ containing density-independent stickiness coefficient, the compressibility EOS does not exist, unlike the one-component case. The reason for this is that a direct integration of the compressibility at fixed composition, cannot be carried out due to the lack of a reciprocity relation on the second order partial derivatives of the pressure with respect to two different densities. This is, in turn, related to the inadequacy of the MSA. A way out to this drawback is presented in a particular example, leading to a consistent compressibility pressure, and a possible generalization of this result is discussed.Comment: 13 pages, no figures, accepted for publication Molec. Physics (2002

Effect of Polydispersity and Anisotropy in Colloidal and Protein Solutions: an Integral Equation Approach

Application of integral equation theory to complex fluids is reviewed, with particular emphasis to the effects of polydispersity and anisotropy on their structural and thermodynamic properties. Both analytical and numerical solutions of integral equations are discussed within the context of a set of minimal potential models that have been widely used in the literature. While other popular theoretical tools, such as numerical simulations and density functional theory, are superior for quantitative and accurate predictions, we argue that integral equation theory still provides, as in simple fluids, an invaluable technique that is able to capture the main essential features of a complex system, at a much lower computational cost. In addition, it can provide a detailed description of the angular dependence in arbitrary frame, unlike numerical simulations where this information is frequently hampered by insufficient statistics. Applications to colloidal mixtures, globular proteins and patchy colloids are discussed, within a unified framework.Comment: 17 pages, 7 figures, to appear in Interdiscip. Sci. Comput. Life Sci. (2011), special issue dedicated to Prof. Lesser Blu

Probing the existence of phase transitions in one-dimensional fluids of penetrable particles

Phase transitions in one-dimensional classical fluids are usually ruled out by making appeal to van Hove's theorem. A way to circumvent the conclusions of the theorem is to consider an interparticle potential that is everywhere bounded. Such is the case of, {\it e.g.}, the generalized exponential model of index 4 (GEM-4 potential), which in three dimensions gives a reasonable description of the effective repulsion between flexible dendrimers in a solution. An extensive Monte Carlo simulation of the one-dimensional GEM-4 model [S. Prestipino, {\em Phys. Rev. E} {\bf 90}, 042306 (2014)] has recently provided evidence of an infinite sequence of low-temperature cluster phases, however also suggesting that upon pushing the simulation forward what seemed a true transition may eventually prove to be only a sharp crossover. We hereby investigate this problem theoretically, by three different and increasingly sophisticated approaches ({\it i.e.}, a mean-field theory, the transfer matrix of a lattice model of clusters, and the exact treatment of a system of point clusters in the continuum), to conclude that the alleged transitions of the one-dimensional GEM4 system are likely just crossovers.Comment: 18 pages, 9 figure

A corresponding states approach to Small-Angle-Scattering for polydisperse ionic colloidal fluids

Approximate scattering functions for polydisperse ionic colloidal fluids are obtained by a corresponding states approach. This assumes that all pair correlation functions $g_{\alpha \beta}(r)$ of a polydisperse fluid are conformal to those of an appropriate monodisperse binary fluid (reference system) and can be generated from them by scaling transformations. The correspondence law extends to ionic fluids a {\it scaling approximation} (SA) successfully proposed for nonionic colloids in a recent paper. For the primitive model of charged hard spheres in a continuum solvent, the partial structure factors of the monodisperse binary reference system are evaluated by solving the Orstein-Zernike (OZ) integral equations coupled with an approximate closure. The SA is first tested within the mean spherical approximation (MSA) closure, which allows analytical solutions. The results are found in good overall agreement with exact MSA predictions up to relevant polidispersity. The SA is shown to be an improvement over the ``decoupling approximation'' extended to the ionic case. The simplicity of the SA scheme allows its application also when the OZ equations can be solved only numerically. An example is then given by using the hypernetted chain (HNC) closure. Shortcomings of the SA approach, its possible use in the analysis of experimental scattering data and other related points are also briefly addressed.Comment: 29 pages, 7 postscript figures (included), Latex 3.0, uses aps.sty, to appear in Phys. Rev. E (1999

A numerical study of a binary Yukawa model in regimes characteristic of globular proteins in solutions

The main goal of this paper is to assess the limits of validity, in the regime of low concentration and strong Coulomb coupling (high molecular charges), for a simple perturbative approximation to the radial distribution functions (RDF), based upon a low-density expansion of the potential of mean force and proposed to describe protein-protein interactions in a recent Small-Angle-Scattering (SAS) experimental study. A highly simplified Yukawa (screened Coulomb) model of monomers and dimers of a charged globular protein ($\beta$-lactoglobulin) in solution is considered. We test the accuracy of the RDF approximation, as a necessary complementary part of the previous experimental investigation, by comparison with the fluid structure predicted by approximate integral equations and exact Monte Carlo (MC) simulations. In the MC calculations, an Ewald construction for Yukawa potentials has been used to take into account the long-range part of the interactions in the weakly screened cases. Our results confirm that the perturbative first-order approximation is valid for this system even at strong Coulomb coupling, provided that the screening is not too weak (i.e., for Debye length smaller than monomer radius). A comparison of the MC results with integral equation calculations shows that both the hypernetted-chain (HNC) and the Percus-Yevick (PY) closures have a satisfactory behavior under these regimes, with the HNC being superior throughout. The relevance of our findings for interpreting SAS results is also discussed.Comment: Physical Review E, in press (2005

Structure of ternary additive hard-sphere fluid mixtures

Monte Carlo simulations on the structural properties of ternary fluid mixtures of additive hard spheres are reported. The results are compared with those obtained from a recent analytical approximation [S. B. Yuste, A. Santos, and M. Lopez de Haro, J. Chem. Phys. 108, 3683 (1998)] to the radial distribution functions of hard-sphere mixtures and with the results derived from the solution of the Ornstein-Zernike integral equation with both the Martynov-Sarkisov and the Percus-Yevick closures. Very good agreement between the results of the first two approaches and simulation is observed, with a noticeable improvement over the Percus-Yevick predictions especially near contact.Comment: 11 pages, including 8 figures; A minor change; accepted for publication in PR

Fluids of spherical molecules with dipolar-like nonuniform adhesion. An analytically solvable anisotropic model

We consider an anisotropic version of Baxter's model of `sticky hard spheres', where a nonuniform adhesion is implemented by adding, to an isotropic surface attraction, an appropriate `dipolar sticky' correction (positive or negative, depending on the mutual orientation of the molecules). The resulting nonuniform adhesion varies continuously, in such a way that in each molecule one hemisphere is `stickier' than the other. We derive a complete analytic solution by extending a formalism [M.S. Wertheim, J. Chem. Phys. \textbf{55}, 4281 (1971) ] devised for dipolar hard spheres. Unlike Wertheim's solution which refers to the `mean spherical approximation', we employ a \textit{Percus-Yevick closure with orientational linearization}, which is expected to be more reliable. We obtain analytic expressions for the orientation-dependent pair correlation function $g(1,2)$. Only one equation for a parameter $K$ has to be solved numerically. We also provide very accurate expressions which reproduce $K$ as well as some parameters, $\Lambda_{1}$ and $\Lambda_{2}$, of the required Baxter factor correlation functions with a relative error smaller than 1%. We give a physical interpretation of the effects of the anisotropic adhesion on the $g(1,2)$. The model could be useful for understanding structural ordering in complex fluids within a unified picture.Comment: 30 pages, 6 Figures, Physical Review E in pres

Population inversion of a NAHS mixture adsorbed into a cylindrical pore

A cylindrical nanopore immersed in a non-additive hard sphere binary fluid is studied by means of integral equation theories and Monte Carlo simulations. It is found that at low and intermediate values of the bulk total number density the more concentrated bulk species is preferentially absorbed by the pore, as expected. However, further increments of the bulk number density lead to an abrupt population inversion in the confined fluid and an entropy driven prewetting transition at the outside wall of the pore. These phenomena are a function of the pore size, the non-additivity parameter, the bulk number density, and particles relative number fraction. We discuss our results in relation to the phase separation in the bulk.Comment: 7 pages, 8 Figure

Behavioural and emotional changes during covid-19 lockdown in an italian paediatric population with neurologic and psychiatric disorders

On 11 March 2020, a national lockdown was imposed by the Italian government to contain the spread of COVID19 disease. This is an observational longitudinal study conducted at Fondazione Stella Maris (FSM), Italy to investigate lockdown-related emotional and behavioural changes in paediatric neuropsychiatric population. Families having children (1.5–18 years) with neuropsychiatric disorders referred to FSM have been contacted and proposed to fulfil two online questionnaires (General questionnaire and Child Behaviour Check List (CBCL)) to (i) compare (paired two-sample t-tests) the CBCL scores during lockdown with previous ones, and (ii) investigate the influence (multiple linear regression models) of variables such as age, diagnosis grouping (neurological, neurodevelopmental, emotional, and behavioural disorders) and financial hardship. One hundred and forty-one parents fulfilled the questionnaires. Anxiety and somatic problems increased in 1.5–5 years subpopulation, while obsessive-compulsive, post-traumatic and thought problems increased in 6–18 years subpopulation. In the regression models, younger age in the 1.5–5 years subpopulation resulted as “protective” while financial hardship experienced by families during lockdown was related to psychiatric symptoms increasing in the 6–18 years subpopulation. Some considerations, based on first clinical impressions, are provided in text together with comments in relation to previous and emerging literature on the topic