A Numerical Test of a High-Penetrability Approximation for the One-Dimensional Penetrable-Square-Well Model

The one-dimensional penetrable-square-well fluid is studied using both analytical tools and specialized Monte Carlo simulations. The model consists of a penetrable core characterized by a finite repulsive energy combined with a short-range attractive well. This is a many-body one-dimensional problem, lacking an exact analytical solution, for which the usual van Hove theorem on the absence of phase transition does not apply. We determine a high-penetrability approximation complementing a similar low-penetrability approximation presented in previous work. This is shown to be equivalent to the usual Debye-H\"{u}ckel theory for simple charged fluids for which the virial and energy routes are identical. The internal thermodynamic consistency with the compressibility route and the validity of the approximation in describing the radial distribution function is assessed by a comparison against numerical simulations. The Fisher-Widom line separating the oscillatory and monotonic large-distance behavior of the radial distribution function is computed within the high-penetrability approximation and compared with the opposite regime, thus providing a strong indication of the location of the line in all possible regimes. The high-penetrability approximation predicts the existence of a critical point and a spinodal line, but this occurs outside the applicability domain of the theory. We investigate the possibility of a fluid-fluid transition by Gibbs ensemble Monte Carlo techniques, not finding any evidence of such a transition. Additional analytical arguments are given to support this claim. Finally, we find a clustering transition when Ruelle's stability criterion is not fulfilled. The consequences of these findings on the three-dimensional phase diagrams are also discussed.Comment: 17 pages, 12 figures; to be published in JC

Radial distribution function of penetrable sphere fluids to second order in density

The simplest bounded potential is that of penetrable spheres, which takes a positive finite value $\epsilon$ if the two spheres are overlapped, being 0 otherwise. In this paper we derive the cavity function to second order in density and the fourth virial coefficient as functions of $T^*\equiv k_BT/\epsilon$ (where $k_B$ is the Boltzmann constant and $T$ is the temperature) for penetrable sphere fluids. The expressions are exact, except for the function represented by an elementary diagram inside the core, which is approximated by a polynomial form in excellent agreement with accurate results obtained by Monte Carlo integration. Comparison with the hypernetted-chain (HNC) and Percus-Yevick (PY) theories shows that the latter is better than the former for $T^*\lesssim 1$ only. However, even at zero temperature (hard sphere limit), the PY solution is not accurate inside the overlapping region, where no practical cancelation of the neglected diagrams takes place. The exact fourth virial coefficient is positive for $T^*\lesssim 0.73$, reaches a minimum negative value at $T^*\approx 1.1$, and then goes to zero from below as $1/{T^*}^4$ for high temperatures. These features are captured qualitatively, but not quantitatively, by the HNC and PY predictions. In addition, in both theories the compressibility route is the best one for $T^*\lesssim 0.7$, while the virial route is preferable if $T^*\gtrsim 0.7$.Comment: 10 pages, 2 figures; v2: minor changes; to be published in PR

On extrapolation of virial coefficients of hard spheres

Several methods of extrapolating the virial coefficients, including those proposed in this work, are discussed. The methods are demonstrated on predicting higher virial coefficients of one-component hard spheres. Estimated values of the eleventh to fifteenth virial coefficients are suggested. It has been speculated that the virial coefficients, B_n, beyond B_{14} may decrease with increasing n, and may reach negative values at large n. The extrapolation techniques may be utilized in other fields of science where the art of extrapolation plays a role.Comment: 8 pages, 1 figur

Phase diagram of the penetrable square well-model

We study a system formed by soft colloidal spheres attracting each other via a square-well potential, using extensive Monte Carlo simulations of various nature. The softness is implemented through a reduction of the infinite part of the repulsive potential to a finite one. For sufficiently low values of the penetrability parameter we find the system to be Ruelle stable with square-well like behavior. For high values of the penetrability the system is thermodynamically unstable and collapses into an isolated blob formed by a few clusters each containing many overlapping particles. For intermediate values of the penetrability the system has a rich phase diagram with a partial lack of thermodynamic consistency.Comment: 6 pages and 5 figure

Structure of penetrable-rod fluids: Exact properties and comparison between Monte Carlo simulations and two analytic theories

Bounded potentials are good models to represent the effective two-body interaction in some colloidal systems, such as dilute solutions of polymer chains in good solvents. The simplest bounded potential is that of penetrable spheres, which takes a positive finite value if the two spheres are overlapped, being 0 otherwise. Even in the one-dimensional case, the penetrable-rod model is far from trivial, since interactions are not restricted to nearest neighbors and so its exact solution is not known. In this paper we first derive the exact correlation functions of penetrable-rod fluids to second order in density at any temperature, as well as in the high-temperature and zero-temperature limits at any density. Next, two simple analytic theories are constructed: a high-temperature approximation based on the exact asymptotic behavior in the limit $T\to\infty$ and a low-temperature approximation inspired by the exact result in the opposite limit $T\to 0$. Finally, we perform Monte Carlo simulations for a wide range of temperatures and densities to assess the validity of both theories. It is found that they complement each other quite well, exhibiting a good agreement with the simulation data within their respective domains of applicability and becoming practically equivalent on the borderline of those domains. A perspective on the extension of both approaches to the more realistic three-dimensional case is provided.Comment: 19 pages, 11 figures, 4 tables: v2: minor changes; published final versio

Density functional approach for inhomogeneous star polymers

We propose microscopic density functional theory for inhomogeneous star polymers. Our approach is based on fundamental measure theory for hard spheres, and on Wertheim's first- and second-order perturbation theory for the interparticle connectivity. For simplicity we consider a model in which all the arms are of the same length, but our approach can be easily extended to the case of stars with arms of arbitrary lengths.Comment: 4 pages, 3 figures, submitte

Modelling the evaporation of nanoparticle suspensions from heterogeneous surfaces

We present a Monte Carlo (MC) grid-based model for the drying of drops of a nanoparticle suspension upon a heterogeneous surface. The model consists of a generalised lattice-gas in which the interaction parameters in the Hamiltonian can be varied to model different properties of the materials involved. We show how to choose correctly the interactions, to minimise the effects of the underlying grid so that hemispherical droplets form. We also include the effects of surface roughness to examine the effects of contact-line pinning on the dynamics. When there is a `lid' above the system, which prevents evaporation, equilibrium drops form on the surface, which we use to determine the contact angle and how it varies as the parameters of the model are changed. This enables us to relate the interaction parameters to the materials used in applications. The model has also been applied to drying on heterogeneous surfaces, in particular to the case where the suspension is deposited on a surface consisting of a pair of hydrophilic conducting metal surfaces that are either side of a band of hydrophobic insulating polymer. This situation occurs when using inkjet printing to manufacture electrical connections between the metallic parts of the surface. The process is not always without problems, since the liquid can dewet from the hydrophobic part of the surface, breaking the bridge before the drying process is complete. The MC model reproduces the observed dewetting, allowing the parameters to be varied so that the conditions for the best connection can be established. We show that if the hydrophobic portion of the surface is located at a step below the height of the neighbouring metal, the chance of dewetting of the liquid during the drying process is significantly reduced.Comment: 14 pages, 14 figure

Breaking Cassie's Law for condensation in a nanopatterned slit

We study the phase transitions of a fluid confined in a capillary slit made from two adjacent walls, each of which are a periodic composite of stripes of two different materials. For wide slits the capillary condensation occurs at a pressure which is described accurately by a combination of the Kelvin equation and the Cassie law for an averaged contact angle. However, for narrow slits the condensation occurs in two steps involving an intermediate bridging phase, with the corresponding pressures described by two new Kelvin equations. These are characterised by different contact angles due to interfacial pinning, with one larger and one smaller than the Cassie angle. We determine the triple point and predict two types of dispersion force induced Derjaguin-like corrections due to mesoscopic volume reduction and the singular free-energy contribution from nanodroplets and bubbles. We test these predictions using a fully microscopic density functional model which confirms their validity even for molecularly narrow slits. Analogous mesoscopic corrections are also predicted for two-dimensional systems arising from thermally induced interfacial wandering

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