We study the critical Casimir interaction between two spherical colloids immersed in a binary liquid mixture close to its critical demixing point. The surface of each colloid prefers one species of the mixture with the exception of a circular patch of arbitrary size, where the other species is preferred. For such objects we calculate, within the Derjaguin approximation, the scaling function describing the critical Casimir potential, and we use it to derive the scaling functions for all components of the forces and torques acting on both colloids. The results are compared with available experimental data. Moreover, the general relation between the scaling function for the potential and the scaling functions for the force and the torque is derived.
We calculate the network fluid regime and phase diagrams of binary mixtures of patchy colloids, using Wertheim's first order perturbation theory and a generalization of Flory-Stockmayer's theory of polymerization. The colloids are modelled as hard spheres with the same diameter and surface patches of the same type, $A$. The only difference between species is the number of their patches -or functionality-, $f_A^{(1)}$ and $f_A^{(2)}$ (with $f_A^{(2)}>f_A^{(1)}$). We have found that the difference in functionality is the key factor controlling the behaviour of the mixture in the network (percola…
We consider a fluid of hard spheres bearing one or two uniform circular adhesive patches, distributed so as not to overlap. Two spheres interact via a ``sticky'' Baxter potential if the line joining the centers of the two spheres intersects a patch on each sphere, and via a hard sphere potential otherwise. We analyze the location of the fluid-fluid transition and of the percolation line as a function of the size of the patch (the fractional coverage of the sphere's surface) and of the number of patches within a virial expansion up to third order and within the first two terms (C0 and C1) of a …
We critically discuss the application of the Wertheim's theory to classes of complex associating fluids that can be today engineered in the laboratory as patchy colloids and to the prediction of their peculiar gas-liquid phase diagrams. Our systematic study, stemming from perturbative version of the theory, allows us to show that, even at the simplest level of approximation for the inter-cluster correlations, the theory is still able to provide a consistent and stable picture of the behavior of interesting models of self-assembling colloidal suspension. We extend the analysis of a few cases of…
We numerically study a simple fluid composed of particles having a hard-core repulsion, complemented by two short-ranged attractive (sticky) spots at the particle poles, which provides a simple model for equilibrium polymerization of linear chains. The simplicity of the model allows for a close comparison, with no fitting parameters, between simulations and theoretical predictions based on the Wertheim perturbation theory, a unique framework for the analytic prediction of the properties of self-assembling particle systems in terms of molecular parameter and liquid state correlation functions. …
Using classical density functional theory (DFT) we calculate the density profile $ρ({\mathbf r})$ and local compressibility $χ({\mathbf r})$ of a simple liquid solvent in which a pair of blocks with (microscopic) rectangular cross-section are immersed. We consider blocks that are solvophobic, solvophilic and also ones that have both solvophobic and solvophilic patches. Large values of $χ({\mathbf r})$ correspond to regions in space where the liquid density is fluctuating most strongly. We seek to elucidate how enhanced density fluctuations correlate with the solvent mediated force between the …
Two theories for associating fluids recently used to study clustering in models for self-assembling patchy particles, Wertheim's and Bjerrum-Tani-Henderson theories, are carefully compared. We show that, for a fluid allowing only for dimerization, Wertheim theory is equivalent to the Bjerrum-Tani-Henderson theory neglecting intercluster correlations. Nonetheless, while the former theory is able to account for percolation and condensation, the latter is not. For the Bjerrum-Tani-Henderson theory we also rigorously prove the uniqueness of the solution for the cluster's concentrations and the red…
We study the Kern-Frenkel model for patchy colloids using Barker-Henderson second-order thermodynamic perturbation theory. The model describes a fluid where hard sphere particles are decorated with one patch, so that they interact via a square-well (SW) potential if they are sufficiently close one another, and if patches on each particle are properly aligned. Both the gas-liquid and fluid-solid phase coexistences are computed and contrasted against corresponding Monte-Carlo simulations results. We find that the perturbation theory describes rather accurately numerical simulations all the way f…
We calculate the pair diffusion coefficient D(r) as a function of the distance r between two hard-sphere particles in a dense monodisperse suspension. The distance-dependent pair diffusion coefficient describes the hydrodynamic interactions between particles in a fluid that are central to theories of polymer and colloid dynamics. We determine D(r) from the propagators (Green's functions) of particle pairs obtained from discontinuous molecular dynamics simulations. At distances exceeding 3 molecular diameters, the calculated pair diffusion coefficients are in excellent agreement with prediction…
We present a new method based on the scattering technique to investigate fluctuation-induced forces at a fluid interface. The scattering approach, well suited to the study of many body systems of arbitrary geometries, is augmented to include boundary fluctuations. Using this method, we study the deviation of the total fluctuation-induced interaction from the sum of pairwise energies for three colloidal particles. We consider both frozen and fluctuating colloids and obtain a very good agreement between analytical and numerical results. We find a marked difference in the three body fluctuation-i…
We investigate the structure of a binary mixture of particles interacting via purely repulsive (point) Yukawa pair potentials with a common inverse screening length $λ$. Using the hyper-netted chain closure to the Ornstein-Zernike equations, we find that for a system with `ideal' (Berthelot mixing rule) pair potential parameters for the interaction between unlike species, the asymptotic decay of the total correlation functions crosses over from monotonic to damped oscillatory on increasing the fluid total density at fixed composition. This gives rise to a Kirkwood line in the phase diagram. We…
We analyse the $r \to \infty$ asymptotic decay of the total correlation function, $h(r)$, for a fluid composed of particles interacting via a (point) Yukawa pair potential. Such a potential provides a simple model for dusty plasmas. The asymptotic decay is determined by the poles of the liquid structure factor in the complex plane. We use the hypernetted-chain closure to the Ornstein-Zernike equation to determine the line in the phase diagram, well-removed from the freezing transition line, where crossover occurs in the ultimate decay of $h(r)$, from monotonic to damped oscillatory. We show: i…
We re-visit the competition between attractive and repulsive interparticle forces in simple fluids and how this governs and connects the macroscopic phase behavior and structural properties as manifest in pair correlation functions. We focus on the asymptotic decay of the total correlation function $h(r)$ which is, in turn, controlled by the form of the pair direct correlation function $c(r)$. The decay of $r h(r)$ to zero can be either exponential (monotonic) if attraction dominates repulsion and exponentially damped oscillatory otherwise. The Fisher-Widom (FW) line separates the phase diagra…
This paper continues the investigation of the exponentially repulsive EXP pair-potential system of Paper I with a focus on isomorphs in the low-temperature gas and liquid phases. As expected from the EXP system's strong virial potential-energy correlations, the system's reduced-unit structure and dynamics are isomorph invariant to a good approximation. Three methods for generating isomorphs are compared: the small-step method that is exact in the limit of small density changes and two versions of the direct-isomorph-check method that allows for much larger density changes. Results from approxi…
The effective pair potential between mesoscopic charged particles in a neutralising background medium takes a Yukawa form $\exp(-λr)/r$ with screening length $λ^{-1}$. We consider a dilute suspension of such Yukawa particles dispersed in a solvent with correlation length $ξ<λ^{-1}$ and show that the Yukawa interaction is `screened' if the pair potentials between solvent particles exhibit Yukawa decay with the same screening length $λ^{-1}$. However, if the solvent pair potentials are shorter ranged than the solute Yukawa potentials, then the effective potential between pairs of solute particle…
The exponentially repulsive EXP pair potential defines a system of particles in terms of which simple liquids' quasiuniversality may be explained [A. K. Bacher et al., Nat. Commun. 5, 5424 (2014); J. C. Dyre, J. Phys. Condens. Matter 28, 323001 (2016)]. This paper and its companion present a detailed simulation study of the EXP system. Here we study how structure monitored via the radial distribution function and dynamics monitored via the mean-square displacement as a function of time evolve along the system's isotherms and isochores. The focus is on the gas and liquid phases, which are disti…
We have used the density-functional theory to locate the freezing transitions and calculate the values of freezing parameters for a system of long elongated molecules which interact via the Gay-Berne pair potential. The pair correlation functions of isotropic phase which enter in the theory as input informations are found from the Percus-Yevick integral equation theory. At low temperatures the fluid freezes directly into the smectic A phase on increasing the density. The nematic phase is found to stabilize in between the isotropic and smectic A phases only at high temperatures and high densiti…
The effective pair potentials between different kinds of dendrimers in solution can be well approximated by appropriate Gaussian functions. We find that in binary dendrimer mixtures the range and strength of the effective interactions depend strongly upon the specific dendrimer architecture. We consider two different types of dendrimer mixtures, employing the Gaussian effective pair potentials, to determine the bulk fluid structure and phase behavior. Using a simple mean field density functional theory (DFT) we find good agreement between theory and simulation results for the bulk fluid struct…
We describe a general simulation scheme for assessing the thermodynamic consequences of neglecting many-body effects in coarse-grained models of complex fluids. The method exploits the fact that the asymptote of a simple-to-measure structural function provides direct estimates of virial coefficients. Comparing the virial coefficients of an atomistically detailed system with those of a coarse-grained version described by pair potentials, permits the role of many-body effects to be quantified. The approach is applied to two models: (i) a size-asymmetrical colloid-polymer mixture, and (ii) a solu…
Molecular dynamics simulations and instantaneous normal mode (INM) analysis of a fluid with core-softened pair interactions and water-like liquid-state anomalies are performed to obtain an understanding of the relationship between thermodynamics, transport properties and the poten- tial energy landscape. Rosenfeld-scaling of diffusivities with the thermodynamic excess and pair correlation entropy is demonstrated for this model. The INM spectra are shown to carry infor- mation about the dynamical consequences of the interplay between length scales characteristic of anomalous fluids, such as bim…
It is shown that the equilibrium Generalized Mean Spherical Model of fluid structure may be extended to nonequilibrium states with equation of state information used in equilibrium replaced by an exact condition on the two-body distribution function. The model is applied to the homogeneous cooling state of granular fluids and upon comparison to molecular dynamics simulations is found to provide an accurate picture of the pair distribution function.
It is demonstrated that the coordinates of the fcc-bcc-fluid triple point of various model systems are located in a relatively narrow region, when expressed in terms of the two proper variables, characterizing the softness and strength of the interaction force at the mean interparticle separation. This can be regarded as a consequence of the "corresponding states principle" for strongly interacting particle systems we have put forward recently [S. A. Khrapak, M. Chaudhuri, and G. E. Morfill, J. Chem. Phys. {\bf 134}, 241101 (2011)]. The related possibilities to predict the existence and approx…
A model for the pair distribution function of nonequilibrium hard-core fluids is proposed based on a model for the effect of velocity correlations on the structure. Good agreement is found with molecular dynamics simulations of granular fluids and of sheared elastic hard spheres. It is argued that the incorporation of velocity correlations are crucial to correctly modeling atomic scale structure in nonequilibrium fluids.
We present an alternative derivation of the pair correlation function for simple classical fluids by using a variational approach. That approach involves the conditional probability p(3,..., N /1, 2) of an undefined system of N particles with respect to a given pair (1,2), and the definition of a conditional entropy $σ$(3,..., N /1, 2). An additivity assumption of $σ$(3,..., N /1, 2) together with a superposition assumption for p(3 / 1, 2) allows deriving the pair probability p(1,2). We then focus onto the case of simple classical fluids, which leads to an integral, non-linear equation that fo…
We use a simple and efficient computer model to investigate the physical properties of bilayer membranes. The amphiphilic molecules are modeled as short rigid trimers with finite range pair interactions between them. The pair potentials have been designed to mimic the hydrophobic interactions, and to allow the simulation of the membranes without the embedding solvent as if the membrane is in vacuum. We find that upon decreasing the area density of the molecules the membrane undergoes a solid-fluid phase transition, where in the fluid phase the molecules can diffuse within the membrane plane. T…
An iterative Monte Carlo inversion method for the calculation of particle pair potentials from given particle pair correlations is proposed in this paper. The new method, which is best referred to as Iterative Ornstein-Zernike Inversion, represents a generalization and an improvement of the established Iterative Boltzmann Inversion technique [Reith, Pütz \& Müller-Plathe, J. Comput. Chem. 24, 1624 (2003)]. Our modification of Iterative Boltzmann Inversion consists of replacing the potential of mean force as an approximant for the pair potential with another, generally more accurate approximant…
We have performed extensive Monte Carlo simulations in the canonical (NVT) ensemble of the pair correlation function for square-well fluids with well widths $λ-1$ ranging from 0.1 to 1.0, in units of the diameter $σ$ of the particles. For each one of these widths, several densities $ρ$ and temperatures $T$ in the ranges $0.1\leqρσ^3\leq 0.8$ and $T_c(λ)\lesssim T\lesssim 3T_c(λ)$, where $T_c(λ)$ is the critical temperature, have been considered. The simulation data are used to examine the performance of two analytical theories in predicting the structure of these fluids: the perturbation theor…
We report a straightforward, model-free approach for measuring pair potentials from particle-coordinate data, based on enforcing consistency between the pair distribution function measured separately by the distance-histogram and test-particle insertion routes. We demonstrate the method's accuracy and versatility in simulations of simple fluids, before applying it to an experimental system composed of superparamagnetic colloidal particles. The method will enable experimental investigations into many-body interactions and allow for effective coarse-graining of interactions from simulations.
Partial pair-correlation functions of colloidal suspensions with continuous polydispersity can be challenging to characterize from optical microscopy or computer simulation data due to inadequate sampling. As a result, it is common to adopt an effective one-component description of the structure that ignores the differences between particle types. Unfortunately, whether this kind of simplified description preserves or averages out information important for understanding the behavior of the fluid depends on the degree of polydispersity and can be difficult to assess, especially when the corresp…
In this paper, we theoretically study the electrostatic interaction between a pair of identical colloids with constant surface potentials sitting in close vicinity of each other at a fluid interface. By employing a simplified yet reasonable model system, the problem is solved within the framework of classical density functional theory and linearized as well as nonlinear Poisson-Boltzmann (PB) theory. Apart from providing a sound theoretical framework generally applicable to any such problem, our novel findings, all of which contradict common beliefs, include the following: first, quantitative …
The two-body (pair) contribution to the entropy of two-dimensional Yukawa systems is calculated and analyzed. It is demonstrated that in the vicinity of the fluid-solid (freezing) phase transition the pair entropy exhibits an abrupt jump in a narrow temperature range and this can be used to identify the freezing point. Relations to the full excess entropy and some existing freezing indicators are briefly discussed.
A statistical mechanical study of fluidized granular media is presented. Using a special energy injection mechanism, homogeneous fluidized stationary states are obtained. Molecular dynamics simulations and theoretical analysis of the inelastic hard-disk model show that there is a large asymmetry in the two-particle distribution function between pairs that approach and separate. Large velocity correlations appear in the postcollisional states, due to the dissipative character of the collision rule. These correlations can be well characterized by a state dependent pair correlation function at co…
Ensembles of biological and artificial microswimmers produce long-range velocity fields with strong nonequilibrium fluctuations, which result in dramatic increase diffusivity of embedded particles (tracers). While such enhanced diffusivity may point to enhanced mixing of the fluid, a rigorous quantification of the mixing efficiency requires analysis of pair dispersion of tracers, rather than simple one-particle diffusivity. Here, we calculate analytically the scale-dependent coefficient of relative diffusivity of passive tracers embedded in a dilute suspension of run-and-tumble microswimmers. …
The static local-field factor (LFF) of the 2-D electron fluid is calculated {\it nonperturbatively} using a mapping to a classical Coulomb fluid $\lbrack$Phys. Rev. Lett., {\bf 87}, 206$\rbrack$. The LFF for the paramagnetic fluid {\it differs markedly} from perturbation theory where a maximum near 2$k_F$ is expected. Our LFF has a quasi-linear small-k region leading to a maximum close to 3$k_F$, in agreent with currently available quantum Monte Carlo data. The structure in the LFF and its dependence on the density and temperature are interpretted as a signature of correlated scattering of ele…
We use the extension of scaled particle theory (ESPT) presented in the accompanying paper [Stillinger et al. J. Chem. Phys. xxx, xxx (2007)] to calculate numerically pair correlation function of the hard sphere fluid over the density range $0\leq ρσ^3\leq 0.96$. Comparison with computer simulation results reveals that the new theory is able to capture accurately the fluid's structure across the entire density range examined. The pressure predicted via the virial route is systematically lower than simulation results, while that obtained using the compressibility route is lower than simulation p…
A systematic field theory is presented for charged systems. The one-loop level corresponds to the classical Debye-Hückel (DH) theory, and exhibits the full hierarchy of multi-body correlations determined by pair-distribution functions given by the screened DH potential. Higher-loop corrections can lead to attractive pair interactions between colloids in asymmetric ionic environments. The free energy follows as a loop-wise expansion in half-integer powers of the density; the resulting two-phase demixing region shows pronounced deviations from DH theory for strongly charged colloids.
A vibrational model of heat conduction in liquids with soft pairwise interactions is applied to estimate the thermal conductivity coefficient of strongly coupled Yukawa fluids. A reasonable agreement with the available data from numerical simulations is observed. The results can be useful in the context of strongly coupled plasma and complex (dusty) plasma fluids, when Yukawa (or screened Coulomb) interaction potential is applicable.
We study a class of one-dimensional classical fluids with penetrable particles interacting through positive, purely repulsive, pair-potentials. Starting from some lower bounds to the total potential energy, we draw results on the thermodynamic limit of the given model.
Recently we have proposed (J. Chem. Phys. 128 (2008) 134508) a new rescaling of fluid density $ρ$ by its critical value $ρ_c^{2/3}$ to apply the corresponding states law for the attractive Yukawa fluids study. Analysis of precise simulation results allows us to generalize this concept to the case of simple fluids with different interparticle interactions, like Mie (n,m) and Sutherland pair potentials. It is shown, that there is a linear relationship between the critical pressure and critical temperature, as well as the critical density and inverse critical temperature for these frequently used…
A novel stochastic fluid model is proposed with non-ideal structure factor consistent with compressibility, and adjustable transport coefficients. This Stochastic Hard Sphere Dynamics (SHSD) algorithm is a modification of the Direct Simulation Monte Carlo (DSMC) algorithm and has several computational advantages over event-driven hard-sphere molecular dynamics. Surprisingly, SHSD results in an equation of state and pair correlation function identical to that of a deterministic Hamiltonian system of penetrable spheres interacting with linear core pair potentials. The fluctuating hydrodynamic be…
