Towards the Quantitative Prediction of the Phase Behavior of Polymer Solutions by Computer Simulation
The phase diagram of polymer solutions (cf. e.g. alkanes dissolved in supercritical carbon dioxide) is complicated, since there are four control parameters (temperature, pressure, monomer volume fraction, chain length of the polymer) and due to the interplay of liquid-vapor transitions and fluid-fluid unmixing. As a result I very intricate phase diagram topologies can result. An attempt to develop coarse-1 grained models that can deal with this task will be described. As usual, the polymers I will be modelled as off-lattice bead-spring chains, where several chemical monomers I are integrated into one effective bond, torsional degrees of freedom being dis-I regarded. But also a coarse-graine…
Electrostatic interactions in critical solvents
The subtle interplay between critical phenomena and electrostatics is investigated by considering the effective force acting on two parallel walls confining a near-critical binary liquid mixture with added salt. The ion-solvent coupling can turn a non-critical repulsive electrostatic force into an attractive one upon approaching the critical point. However, the effective force is eventually dominated by the critical Casimir effect, the universal properties of which are not altered by the presence of salt. This observation allows a consistent interpretation of recent experimental data.
Entrapment of charged, nonwetting colloids near oil-water interfaces.
Charged, nonwetting colloids with a contact angle $\ensuremath{\theta}=180\ifmmode^\circ\else\textdegree\fi{}$ are attracted to an oil-water interface due to image charge forces. Near the interface, the attractive image charge forces are balanced by repulsive van der Waals forces, and thus the colloids are trapped at a finite distance from the interface. Electrostatic and van der Waals pressure lead to a deformation of the interface in the equilibrium state. For parameters relevant to experiment, however, the effects of the deformed interface are negligible and thus the mutual interactions of such interfacially trapped colloids should be well characterized by electrostatic dipole repulsions.
Stability and interactions of nanocolloids at fluid interfaces: effects of capillary waves and line tensions
We analyze the effective potential for nanoparticles trapped at a fluid interface within a simple model which incorporates surface and line tensions as well as a thermal average over interface fluctuations (capillary waves). For a single colloid, a reduced steepness of the potential well hindering movements out of the interface plane compared to rigid interface models is observed, and an instability of the capillary wave partition sum in case of negative line tensions is pointed out. For two colloids, averaging over the capillary waves leads to an effective Casimir--type interaction which is long--ranged, power-like in the inverse distance but whose power sensitively depends on possible res…
Free energies, vacancy concentrations, and density distribution anisotropies in hard-sphere crystals: A combined density functional and simulation study
We perform a comparative study of the free energies and the density distributions in hard sphere crystals using Monte Carlo simulations and density functional theory (employing Fundamental Measure functionals). Using a recently introduced technique (Schilling and Schmid, J. Chem. Phys 131, 231102 (2009)) we obtain crystal free energies to a high precision. The free energies from Fundamental Measure theory are in good agreement with the simulation results and demonstrate the applicability of these functionals to the treatment of other problems involving crystallization. The agreement between FMT and simulations on the level of the free energies is also reflected in the density distributions …
Charged particles at fluid interfaces as a probe into structural details of a double layer
Electrostatic interactions between charged, distant colloids in a bulk electrolyte solution do not depend on the inherent structure of ions and a solvent forming a double layer. For charged colloids trapped at an interface between an electrolyte and air this no longer holds; as the electrostatic interactions are mediated via air and the field lines determining the interactions originate at the charged surface, these details come into prominence. Using the Langevin-Poisson-Boltzmann equation we investigate how steric effects and the polarization saturation of a solvent effect the contact potential at the colloid surface and, in consequence, the long range interactions between colloids trappe…
Curvature dependence of surface free energy of liquid drops and bubbles: A simulation study.
We study the excess free energy due to phase coexistence of fluids by Monte Carlo simulations using successive umbrella sampling in finite LxLxL boxes with periodic boundary conditions. Both the vapor-liquid phase coexistence of a simple Lennard-Jones fluid and the coexistence between A-rich and B-rich phases of a symmetric binary (AB) Lennard-Jones mixture are studied, varying the density rho in the simple fluid or the relative concentration x_A of A in the binary mixture, respectively. The character of phase coexistence changes from a spherical droplet (or bubble) of the minority phase (near the coexistence curve) to a cylindrical droplet (or bubble) and finally (in the center of the misc…
Nanoparticles at fluid interfaces.
Nanoparticles at fluid interfaces are becoming a central topic in colloid science studies. Unlike in the case of colloids in suspensions, the description of the forces determining the physical behavior of colloids at interfaces still represents an outstanding problem in the modern theory of colloidal interactions. These forces regulate the formation of complex two-dimensional structures, which can be exploited in a number of applications of technological interest; optical devices, catalysis, molecular electronics or emulsions stabilization. From a fundamental viewpoint and typical for colloidal systems, nanoparticles and microparticles at interfaces are ideal experimental and theoretical mo…
Description of hard-sphere crystals and crystal-fluid interfaces: a comparison between density functional approaches and a phase-field crystal model.
In materials science the phase field crystal approach has become popular to model crystallization processes. Phase field crystal models are in essence Landau-Ginzburg-type models, which should be derivable from the underlying microscopic description of the system in question. We present a study on classical density functional theory in three stages of approximation leading to a specific phase field crystal model, and we discuss the limits of applicability of the models that result from these approximations. As a test system we have chosen the three--dimensional suspension of monodisperse hard spheres. The levels of density functional theory that we discuss are fundamental measure theory, a …
Hard sphere fluids at a soft repulsive wall: A comparative study using Monte Carlo and density functional methods
Hard-sphere fluids confined between parallel plates at a distance D apart are studied for a wide range of packing fractions including also the onset of crystallization, applying Monte Carlo simulation techniques and density functional theory. The walls repel the hard spheres (of diameter σ) with a Weeks-Chandler-Andersen (WCA) potential V(WCA)(z) = 4ε[(σ(w)/z)(12) - (σ(w)/z)(6) + 1/4], with range σ(w) = σ/2. We vary the strength ε over a wide range and the case of simple hard walls is also treated for comparison. By the variation of ε one can change both the surface excess packing fraction and the wall-fluid (γ(wf)) and wall-crystal (γ(wc)) surface free energies. Several different methods t…
Stable and metastable hard-sphere crystals in fundamental measure theory
Using fully minimized fundamental measure functionals, we investigate free energies, vacancy concentrations and density distributions for bcc, fcc and hcp hard-sphere crystals. Results are complemented by an approach due to Stillinger which is based on expanding the crystal partition function in terms of the number n of free particles while the remaining particles are frozen at their ideal lattice positions. The free energies of fcc/hcp and one branch of bcc agree well with Stillinger's approach truncated at n=2. A second branch of bcc solutions features rather spread-out density distributions around lattice sites and large equilibrium vacancy concentrations and is presumably linked to the …
Direct measurements of the effects of salt and surfactant on interaction forces between colloidal particles at water-oil interfaces
The forces between colloidal particles at a decane-water interface, in the presence of low concentrations of a monovalent salt (NaCl) and of the surfactant sodium dodecylsulfate (SDS) in the aqueous subphase, have been studied using laser tweezers. In the absence of electrolyte and surfactant, particle interactions exhibit a long-range repulsion, yet the variation of the interaction for different particle pairs is found to be considerable. Averaging over several particle pairs was hence found to be necessary to obtain reliable assessment of the effects of salt and surfactant. It has previously been suggested that the repulsion is consistent with electrostatic interactions between a small nu…
Spherically averaged versus angle-dependent interactions in quadrupolar fluids
Employing simplified models in computer simulation is on the one hand often enforced by computer time limitations but on the other hand it offers insights into the molecular properties determining a given physical phenomenon. We employ this strategy to the determination of the phase behaviour of quadrupolar fluids, where we study the influence of omitting angular degrees of freedom of molecules via an effective spherically symmetric potential obtained from a perturbative expansion. Comparing the liquid-vapor coexistence curve, vapor pressure at coexistence, interfacial tension between the coexisting phases, etc., as obtained from both the models with the full quadrupolar interactions and th…
Multipolar expansion of the electrostatic interaction between charged colloids at interfaces
The general form of the electrostatic potential around an arbitrarily charged colloid at an interface between a dielectric and a screening phase (such as air and water, respectively) is analyzed in terms of a multipole expansion. The leading term is isotropic in the interfacial plane and varies with $d^{-3}$ where $d$ is the in--plane distance from the colloid. The electrostatic interaction potential between two arbitrarily charged colloids is likewise isotropic and $\propto d^{-3}$, corresponding to the dipole--dipole interaction first found for point charges at water interfaces. Anisotropic interaction terms arise only for higher powers $d^{-n}$ with $n \ge 4$.
Hard-sphere fluids in annular wedges: density distributions and depletion potentials.
We analyze the density distribution and the adsorption of solvent hard spheres in an annular slit formed by two large solute spheres or a large solute and a wall at close distances by means of fundamental measure density functional theory, anisotropic integral equations and simulations. We find that the main features of the density distribution in the slit are described by an effective, two--dimensional system of disks in the vicinity of a central obstacle. For large solute--solvent size ratios, the resulting depletion force has a straightforward geometrical interpretation which gives a precise "colloidal" limit for the depletion interaction. For intermediate size ratios 5...10 and high sol…
Effective interactions of colloids on nematic films.
The elastic and capillary interactions between a pair of colloidal particles trapped on top of a nematic film are studied theoretically for large separations $d$. The elastic interaction is repulsive and of quadrupolar type, varying as $d^{-5}$. For macroscopically thick films, the capillary interaction is likewise repulsive and proportional to $d^{-5}$ as a consequence of mechanical isolation of the system comprised of the colloids and the interface. A finite film thickness introduces a nonvanishing force on the system (exerted by the substrate supporting the film) leading to logarithmically varying capillary attractions. However, their strength turns out to be too small to be of importanc…
Mode expansion for the density profiles of crystal–fluid interfaces: hard spheres as a test case
We present a technique for analyzing the full three-dimensional density profiles of a planar crystal-fluid interface in terms of density modes. These density modes can also be related to crystallinity order parameter profiles which are used in coarse-grained, phase field type models of the statics and dynamics of crystal-fluid interfaces and are an alternative to crystallinity order parameters extracted from simulations using local crystallinity criteria. We illustrate our results for the hard sphere system using finely-resolved, three-dimensional density profiles from density functional theory of fundamental measure type.
Optimum free energy in the reference functional approach for the integral equations theory.
We investigate the question of determining the bulk properties of liquids, required as input for practical applications of the density functional theory of inhomogeneous systems, using density functional theory itself. By considering the reference functional approach in the test particle limit, we derive an expression of the bulk free energy that is consistent with the closure of the Ornstein–Zernike equations in which the bridge functions are obtained from the reference system bridge functional. By examining the connection between the free energy functional and the formally exact bulk free energy, we obtain an improved expression of the corresponding non-local term in the standard referenc…
Anisotropies in thermal Casimir interactions: Ellipsoidal colloids trapped at a fluid interface
We study the effective interaction between two ellipsoidal particles at the interface of two fluid phases which are mediated by thermal fluctuations of the interface. In this system the restriction of the long--ranged interface fluctuations by particles gives rise to fluctuation--induced forces which are equivalent to interactions of Casimir type and which are anisotropic in the interface plane. Since the position and the orientation of the colloids with respect to the interface normal may also fluctuate, this system is an example for the Casimir effect with fluctuating boundary conditions. In the approach taken here, the Casimir interaction is rewritten as the interaction between fluctuati…
Structure and pair correlations of a simple coarse grained model for supercritical carbon dioxide
A recently introduced coarse-grained pair potential for carbon dioxide molecules is used to compute structural properties in the supercritical region near the critical point, applying Monte Carlo simulations. In this model, molecules are described as point particles, interacting with Lennard-Jones (LJ) forces and a (isotropically averaged) quadrupole–quadrupole potential, the LJ parameters being chosen such that gratifying agreement with the experimental phase diagram near the critical point is obtained. It is shown that the model gives also a reasonable account of the pair correlation function, although in the nearest neighbour shell some systematic discrepancies between the model predicti…
Glass transition of binary mixtures of dipolar particles in two dimensions
We study the glass transition of binary mixtures of dipolar particles in two dimensions within the framework of mode-coupling theory, focusing in particular on the influence of composition changes. In a first step, we demonstrate that the experimental system of K\"onig et al. [Eur. Phys. J. E 18, 287 (2005)] is well described by point dipoles through a comparison between the experimental partial structure factors and those from our Monte Carlo simulation. For such a mixture of point particles we show that there is always a plasticization effect, i.e. a stabilization of the liquid state due to mixing, in contrast to binary hard disks. We demonstrate that the predicted plasticization effect i…
Precursor-mediated crystallization process in suspensions of hard spheres.
We report on a large scale computer simulation study of crystal nucleation in hard spheres. Through a combined analysis of real and reciprocal space data, a picture of a two-step crystallization process is supported: First dense, amorphous clusters form which then act as precursors for the nucleation of well-ordered crystallites. This kind of crystallization process has been previously observed in systems that interact via potentials that have an attractive as well as a repulsive part, most prominently in protein solutions. In this context the effect has been attributed to the presence of metastable fluid-fluid demixing. Our simulations, however, show that a purely repulsive system (that ha…
Connectivity percolation in suspensions of hard platelets
We present a study on connectivity percolation in suspensions of hard platelets by means of Monte Carlo simulation. We interpret our results using a contact-volume argument based on an effective single--particle cell model. It is commonly assumed that the percolation threshold of anisotropic objects scales as their inverse aspect ratio. While this rule has been shown to hold for rod-like particles, we find that for hard plate-like particles the percolation threshold is non-monotonic in the aspect ratio. It exhibits a shallow minimum at intermediate aspect ratios and then saturates to a constant value. This effect is caused by the isotropic-nematic transition pre-empting the percolation tran…
Glass transition in confined geometry.
Extending mode-coupling theory, we elaborate a microscopic theory for the glass transition of liquids confined between two parallel flat hard walls. The theory contains the standard MCT equations in bulk and in two dimensions as limiting cases and requires as input solely the equilibrium density profile and the structure factors of the fluid in confinement. We evaluate the phase diagram as a function of the distance of the plates for the case of a hard sphere fluid and obtain an oscillatory behavior of the glass transtion line as a result of the structural changes related to layering.