64,048 research outputs found
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
Crystallization and phase-separation in non-additive binary hard-sphere mixtures
We calculate for the first time the full phase-diagram of an asymmetric
non-additive hard-sphere mixture. The non-additivity strongly affects the
crystallization and the fluid-fluid phase-separation. The global topology of
the phase-diagram is controlled by an effective size-ratio y_{eff}, while the
fluid-solid coexistence scales with the depth of the effective potential well.Comment: 4 pages, 4 figures, to appear in Phys. Rev.
The structure of colloid-polymer mixtures
We investigate the structure of colloid-polymer mixtures by calculating the
structure factors for the Asakura-Oosawa model in the PY approximation. We
discuss the role of potential range, polymer concentration and polymer-polymer
interactions on the colloid-colloid structure. Our results compare reasonably
well with the recent experiments of Moussa\"{i}d et. al. for small wavenumber
, but we find that the Hansen-Verlet freezing criterion is violated when the
liquid phase becomes marginal.Comment: 7 pages, 4 figures, to appear in EuroPhys. Let
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.Comment: 15 pages, 12 figures (one added in revised version), revTeX
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.Comment: uses eps.cls, v2 is close to final published versio
Hydrophobic interactions with coarse-grained model for water
Integral equation theory is applied to a coarse-grained model of water to
study potential of mean force between hydrophobic solutes. Theory is shown to
be in good agreement with the available simulation data for methane-methane and
fullerene-fullerene potential of mean force in water; the potential of mean
force is also decomposed into its entropic and enthalpic contributions. Mode
coupling theory is employed to compute self-diffusion coefficient of water, as
well as diffusion coefficient of a dilute hydrophobic solute; good agreement
with molecular dynamics simulation results is found
Eighth-order phase-field-crystal model for two-dimensional crystallization
We present a derivation of the recently proposed eighth order phase field
crystal model [Jaatinen et al., Phys. Rev. E 80, 031602 (2009)] for the
crystallization of a solid from an undercooled melt. The model is used to study
the planar growth of a two dimensional hexagonal crystal, and the results are
compared against similar results from dynamical density functional theory of
Marconi and Tarazona, as well as other phase field crystal models. We find that
among the phase field crystal models studied, the eighth order fitting scheme
gives results in good agreement with the density functional theory for both
static and dynamic properties, suggesting it is an accurate and computationally
efficient approximation to the density functional theory
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