arXiv subjects

A. A. Louis

Publications and source records attributed to A. A. Louis.

At least 37 records · Page 2Linked to original sources

arXiv2004

Influence of solvent quality on polymer solutions: a Monte Carlo study of bulk and interfacial properties

The effect of solvent quality on dilute and semi-dilute regimes of polymers in solution is studied by means of Monte Carlo simulations. The equation of state, adsorptions near a hard wall, wall-polymer surface tension and effective depletion potentials are all calculated as a function of concentration and solvent quality. We find important differences between polymers in good and theta solvents. In the dilute regime, the physical properties for polymers in a theta solvent closely resemble those of ideal polymers. In the semi-dilute regime, however, significant differences are found.

cond-mat.soft↗

arXiv2003

The Asakura-Oosawa model in the protein limit: the role of many-body interactions

We study the Asakura-Oosawa model in the "protein limit", where the penetrable sphere radius $R_{AO}$ is much greater than the hard sphere radius $R_c$. The phase behaviour and structure calculated with a full many-body treatment show important qualitative differences when compared to a description based on pair potentials alone. The overall effect of the many-body interactions is repulsive.

cond-mat↗

arXiv2003

Effect of polymer-polymer interactions on the surface tension of colloid-polymer mixtures

The density profile and surface tension for the interface of phase-separated colloid-polymer mixtures have been studied in the framework of the square gradient approximation for both ideal and interacting polymers in good solvent. The calculations show that in the presence of polymer-polymer excluded volume interactions the interfaces have lower widths and surface tensions compared to the case of ideal polymers. These results are a direct consequence of the shorter range and smaller depth of the depletion potential between colloidal particles induced by interacting polymers.

cond-mat.soft↗

arXiv2003

Thermodynamic perturbation theory of the phase behaviour of colloid / interacting polymer mixtures

We use thermodynamic perturbation theory to calculate the free energies and resulting phase diagrams of binary systems of spherical colloidal particles and interacting polymer coils in good solvent within an effective one-component representation of such mixtures, whereby the colloidal particles interact via a polymer-induced depletion potential. MC simulations are used to test the convergence of the high temperature expansion of the free energy. The phase diagrams calculated for several polymer to colloid size ratios differ considerably from the results of similar calculations for mixtures of colloids and ideal (non-interacting) polymers, and are in good overall agreement with the results of an explicit two-component representation of the same system, which includes more than two-body depletion forces.

cond-mat.soft↗

arXiv2003

Influence of solvent quality on effective pair potentials between polymers in solution

Solutions of interacting linear polymers are mapped onto a system of ``soft'' spherical particles interacting via an effective pair potential. This coarse-graining reduces the individual monomer-level description to a problem involving only the centers of mass (CM) of the polymer coils. The effective pair potentials are derived by inverting the CM pair distribution function, generated in Monte Carlo simulations, using the hypernetted chain (HNC) closure. The method, previously devised for the self-avoiding walk model of polymers in good solvent, is extended to the case of polymers in solvents of variable quality by adding a finite nearest-neighbor monomer-monomer attraction to the previous model and varying the temperature. The resulting effective pair potential is found to depend strongly on temperature and polymer concentration. At low concentration the effective interaction becomes increasingly attractive as the temperature decreases, eventually violating thermodynamic stability criteria. However, as polymer concentration is increased at fixed temperature, the effective interaction reverts to mostly repulsive behavior. These issues help illustrate some fundamental difficulties encountered when coarse-graining complex systems via effective pair potentials.

cond-mat.soft↗

arXiv2002

Using isosbestic points to extract interactions from structure factors

Inverting scattering experiments to obtain effective interparticle interactions for particles in solution is generally a poorly conditioned problem. More accurate potentials can be obtained through the use of isosbestic points, values of k where the scattering intensity I(k) or the structure factor S(k) is invariant to changes in potential well-depth. These points also suggest a new extended corresponding states principle for particles in solution based on the particle density or packing fraction, the second osmotic virial coefficient, and a new measure of potential range.

cond-mat.soft↗

arXiv2002

Influence of polymer excluded volume on the phase behavior of colloid-polymer mixtures

We determine the depletion-induced phase-behavior of hard sphere colloids and interacting polymers by large-scale Monte Carlo simulations using very accurate coarse-graining techniques. A comparison with standard Asakura-Oosawa model theories and simulations shows that including excluded volume interactions between polymers leads to qualitative differences in the phase diagrams. These effects become increasingly important for larger relative polymer size. Our simulations results agree quantitatively with recent experiments.

cond-mat.soft↗

arXiv2002

Non-monotonic variation with salt concentration of the second virial coefficient in protein solutions

The osmotic virial coefficient $B_2$ of globular protein solutions is calculated as a function of added salt concentration at fixed pH by computer simulations of the ``primitive model''. The salt and counter-ions as well as a discrete charge pattern on the protein surface are explicitly incorporated. For parameters roughly corresponding to lysozyme, we find that $B_2$ first decreases with added salt concentration up to a threshold concentration, then increases to a maximum, and then decreases again upon further raising the ionic strength. Our studies demonstrate that the existence of a discrete charge pattern on the protein surface profoundly influences the effective interactions and that non-linear Poisson Boltzmann and Derjaguin-Landau-Verwey-Overbeek (DLVO) theory fail for large ionic strength. The observed non-monotonicity of $B_2$ is compared to experiments. Implications for protein crystallization are discussed.

cond-mat.soft↗

arXiv2002

How to derive and parameterize effective potentials in colloid-polymer mixtures

Polymer chains in colloid-polymer mixtures can be coarse-grained by replacing them with single soft particles interacting via effective polymer-polymer and polymer-colloid pair potentials. Here we describe in detail how Ornstein-Zernike inversion techniques, originally developed for atomic and molecular fluids, can be generalized to complex fluids and used to derive effective potentials from computer simulations on a microscopic level. In particular, we consider polymer solutions for which we derive effective potentials between the centers of mass, and also between mid-points or end-points from simulations of self-avoiding walk polymers. In addition, we derive effective potentials for polymers near a hard wall or a hard sphere. We emphasize the importance of including both structural and thermodynamic information (through sum-rules) from the underlying simulations. In addition we develop a simple numerical scheme to optimize the parameterization of the density dependent polymer-polymer, polymer-wall and polymer-sphere potentials for dilute and semi-dilute polymer densities, thus opening up the possibility of performing large-scale simulations of colloid-polymer mixtures. The methods developed here should be applicable to a much wider range effective potentials in complex fluids.

cond-mat.soft↗

arXiv2002

Relating monomer to centre-of-mass distribution functions in polymer solutions

A relationship between the measurable monomer-monomer structure factor, and the centre-of-mass (CM) structure factor of dilute or semi-dilute polymer solutions is derived from Ornstein-Zernike relations within the ``polymer reference interaction site model'' (PRISM) formalism, by considering the CM of each polymer as an auxiliary site and neglecting direct correlations between the latter and the CM and monomers of neighbouring polymers. The predictions agree well with Monte Carlo data for self-avoiding walk polymers, and are considerably more accurate than the predictions of simple factorization approximations.

cond-mat.soft↗

arXiv2002

Beware of density dependent pair potentials

Density (or state) dependent pair potentials arise naturally from coarse-graining procedures in many areas of condensed matter science. However, correctly using them to calculate physical properties of interest is subtle and cannot be uncoupled from the route by which they were derived. Furthermore, there is usually no unique way to coarse-grain to an effective pair potential. Even for simple systems like liquid Argon, the pair potential that correctly reproduces the pair structure will not generate the right virial pressure. Ignoring these issues in naive applications of density dependent pair potentials can lead to an apparent dependence of thermodynamic properties on the ensemble within which they are calculated, as well as other inconsistencies. These concepts are illustrated by several pedagogical examples, including: effective pair potentials for systems with many-body interactions, and the mapping of charged (Debye-Hückel) and uncharged (Asakura-Oosawa) two-component systems onto effective one-component ones.

cond-mat.soft↗

arXiv2002

Polymer induced depletion potentials in polymer-colloid mixtures

The depletion interactions between two colloidal plates or between two colloidal spheres, induced by interacting polymers in a good solvent, are calculated theoretically and by computer simulations. A simple analytical theory is shown to be quantitatively accurate for case of two plates. A related depletion potential is derived for two spheres; it also agrees very well with direct computer simulations. Theories based on ideal polymers show important deviations with increasing polymer concentration: They overestimate the range of the depletion potential between two plates or two spheres at all densities, with the largest relative change occurring in the dilute regime. They underestimate the well depth at contact for the case of two plates, but overestimate it for two spheres. Depletion potentials are also calculated using a coarse graining approach which represents the polymers as ``soft colloids'': good agreement is found in the dilute regime. Finally, the effect of the polymers on colloid-colloid osmotic virial coefficients is related to phase behavior of polymer-colloid mixtures.

cond-mat.soft↗

arXiv2002

Effective forces in colloidal mixtures: from depletion attraction to accumulation repulsion

Computer simulations and theory are used to systematically investigate how the effective force between two big colloidal spheres in a sea of small spheres depends on the basic (big-small and small-small) interactions. The latter are modeled as hard-core pair potentials with a Yukawa tail which can be both repulsive or attractive. For a repulsive small-small interaction, the effective force follows the trends as predicted by a mapping onto an effective non-additive hard-core mixture: both a depletion attraction and an accumulation repulsion caused by small spheres adsorbing onto the big ones can be obtained depending on the sign of the big-small interaction. For repulsive big-small interactions, the effect of adding a small-small attraction also follows the trends predicted by the mapping. But a more subtle ``repulsion through attraction'' effect arises when both big-small and small-small attractions occur: upon increasing the strength of the small-small interaction, the effective potential becomes more repulsive. We have further tested several theoretical methods against our computer simulations: The superposition approximation works best for an added big-small repulsion, and breaks down for a strong big-small attraction, while density functional theory is very accurate for any big-small interaction when the small particles are pure hard-spheres. The theoretical methods perform most poorly for small-small attractions.

cond-mat.soft↗

arXiv2001

Coarse-graining polymers as soft colloids

We show how to coarse grain polymers in a good solvent as single particles, interacting with density-independent or density-dependent interactions. These interactions can be between the centres of mass, the mid-points or end-points of the polymers. We also show how to extend these methods to polymers in poor solvents and mixtures of polymers. Treating polymers as soft colloids can greatly speed up the simulation of complex many-polymer systems, including polymer-colloid mixtures.

cond-mat.soft↗

arXiv2001

Density profiles and surface tensions of polymers near colloidal surfaces

The surface tension of interacting polymers in a good solvent is calculated theoretically and by computer simulations for a planar wall geometry and for the insertion of a single colloidal hard-sphere. This is achieved for the planar wall and for the larger spheres by an adsorption method, and for smaller spheres by a direct insertion technique. Results for the dilute and semi-dilute regimes are compared to results for ideal polymers, the Asakura-Oosawa penetrable-sphere model, and to integral equations, scaling and renormalization group theories. The largest relative changes with density are found in the dilute regime, so that theories based on non-interacting polymers rapidly break down. A recently developed ``soft colloid'' approach to polymer-colloid mixtures is shown to correctly describe the one-body insertion free-energy and the related surface tension.

cond-mat.soft↗

arXiv2001

Phase separation of penetrable core mixtures

A two-component system of penetrable particles interacting via a gaussian core potential is considered, which may serve as a crude model for binary polymer solutions. The pair structure and thermodynamic properties are calculated within the random phase approximation (RPA) and the hypernetted chain (HNC) integral equation. The analytical RPA predictions are in semi-quantitative agreement with the numerical solutions of the HNC approximation, which itself is very accurate for gaussian core systems. A fluid-fluid phase separation is predicted to occur for a broad range of potential parameters. The pair structure exhibits a nontrivial clustering behaviour of the minority component. Similiar conclusions hold for the related model of parabolic core mixtures, which is frequently used in dissipative particle dynamics (DPD) simulations.

cond-mat.soft↗

arXiv2001

Combining quantum and classical density functional theory for ion-electron mixtures

We combine techniques from quantum and from classical density functional theory (DFT) to describe electron-ion mixtures. For homogeneous systems, we show how to calculate ion-ion and ion-electron correlation functions within Chihara's quantum hypernetted chain approximation, which we derive within a DFT formulation. We also sketch out how to apply the DFT formulation to inhomogeneous electron-ion mixtures, and use this to study the electron distribution at the liquid-solid interface of Al.

cond-mat.mtrl-sci↗

arXiv2001

Discrete charge patterns, Coulomb correlations and interactions in protein solutions

The effective Coulomb interaction between globular proteins is calculated as a function of monovalent salt concentration $c_s$, by explicit Molecular Dynamics simulations of pairs of model proteins in the presence of microscopic co and counterions. For discrete charge patterns of monovalent sites on the surface, the resulting osmotic virial coefficient $B_2$ is found to be a strikingly non-monotonic function of $c_s$. The non-monotonicity follows from a subtle Coulomb correlation effect which is completely missed by conventional non-linear Poisson-Boltzmann theory and explains various experimental findings.

cond-mat.soft↗