1,436 research outputs found
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.Comment: uses revtex4.cls; submitted for archival purpose
Many-body interactions and correlations in coarse-grained descriptions of polymer solutions
We calculate the two, three, four, and five-body (state independent)
effective potentials between the centers of mass (CM) of self avoiding walk
polymers by Monte-Carlo simulations. For full overlap, these coarse-grained
n-body interactions oscillate in sign as (-1)^n, and decrease in absolute
magnitude with increasing n. We find semi-quantitative agreement with a scaling
theory, and use this to discuss how the coarse-grained free energy converges
when expanded to arbitrary order in the many-body potentials. We also derive
effective {\em density dependent} 2-body potentials which exactly reproduce the
pair-correlations between the CM of the self avoiding walk polymers. The
density dependence of these pair potentials can be largely understood from the
effects of the {\em density independent} 3-body potential. Triplet correlations
between the CM of the polymers are surprisingly well, but not exactly,
described by our coarse-grained effective pair potential picture. In fact, we
demonstrate that a pair-potential cannot simultaneously reproduce the two and
three body correlations in a system with many-body interactions. However, the
deviations that do occur in our system are very small, and can be explained by
the direct influence of 3-body potentials.Comment: 11 pages, 1 table, 9 figures, RevTeX (revtex.cls
Density functional theory for colloidal mixtures of hard platelets, rods, and spheres
A geometry-based density functional theory is presented for mixtures of hard
spheres, hard needles and hard platelets; both the needles and the platelets
are taken to be of vanishing thickness. Geometrical weight functions that are
characteristic for each species are given and it is shown how convolutions of
pairs of weight functions recover each Mayer bond of the ternary mixture and
hence ensure the correct second virial expansion of the excess free energy
functional. The case of sphere-platelet overlap relies on the same
approximation as does Rosenfeld's functional for strictly two-dimensional hard
disks. We explicitly control contributions to the excess free energy that are
of third order in density. Analytic expressions relevant for the application of
the theory to states with planar translational and cylindrical rotational
symmetry, e.g. to describe behavior at planar smooth walls, are given. For
binary sphere-platelet mixtures, in the appropriate limit of small platelet
densities, the theory differs from that used in a recent treatment [L. Harnau
and S. Dietrich, Phys. Rev. E 71, 011504 (2004)]. As a test case of our
approach we consider the isotropic-nematic bulk transition of pure hard
platelets, which we find to be weakly first order, with values for the
coexistence densities and the nematic order parameter that compare well with
simulation results.Comment: 39 pages, 8 figure
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
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.Comment: to appear in Physica A, special STATPHYS 2001 edition. Content of
invited talk by AA
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 is much greater than the hard sphere radius
. 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.Comment: 9 pages and 11 figures, submitted to J. Phys.: Condensed Matter,
special issue "Effective many-body interactions and correlations in soft
matter
Accurate effective pair potentials for polymer solutions
Dilute or semi-dilute solutions of non-intersecting self-avoiding walk (SAW)
polymer chains are mapped onto a fluid of ``soft'' particles interacting via an
effective pair potential between their centers of mass. This mapping is
achieved by inverting the pair distribution function of the centers of mass of
the original polymer chains, using integral equation techniques from the theory
of simple fluids. The resulting effective pair potential is finite at all
distances, has a range of the order of the radius of gyration, and turns out to
be only moderately concentration-dependent. The dependence of the effective
potential on polymer length is analyzed in an effort to extract the scaling
limit. The effective potential is used to derive the osmotic equation of state,
which is compared to simulation data for the full SAW segment model, and to the
predictions of renormalization group calculations. A similar inversion
procedure is used to derive an effective wall-polymer potential from the center
of mass density profiles near the wall, obtained from simulations of the full
polymer segment model. The resulting wall-polymer potential turns out to depend
strongly on bulk polymer concentration when polymer-polymer correlations are
taken into account, leading to a considerable enhancement of the effective
repulsion with increasing concentration. The effective polymer-polymer and
wall-polymer potentials are combined to calculate the depletion interaction
induced by SAW polymers between two walls. The calculated depletion interaction
agrees well with the ``exact'' results from much more computer-intensive direct
simulation of the full polymer-segment model, and clearly illustrates the
inadequacy -- in the semi-dilute regime -- of the standard Asakura-Oosawa
approximation based on the assumption of non-interacting polymer coils.Comment: 18 pages, 24 figures, ReVTeX, submitted to J. Chem. Phy
Refinement of the crystal structure of caesium dichloride
CslC12, trigonal, space group R'3m with a= 5.469 (2) A, ~ = 70.67 (3) °, Z= 1. The atomic positions have been determined by least-squares refinement of counter intensities, the final R being 0.031 for 256 reflexions. The I-CI bond length is 2.548 A
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