198 research outputs found
Colloidal electrophoresis: Scaling analysis, Green-Kubo relation, and numerical results
We consider electrophoresis of a single charged colloidal particle in a
finite box with periodic boundary conditions, where added counterions and salt
ions ensure charge neutrality. A systematic rescaling of the electrokinetic
equations allows us to identify a minimum set of suitable dimensionless
parameters, which, within this theoretical framework, determine the reduced
electrophoretic mobility. It turns out that the salt-free case can, on the Mean
Field level, be described in terms of just three parameters. A fourth
parameter, which had previously been identified on the basis of straightforward
dimensional analysis, can only be important beyond Mean Field. More complicated
behavior is expected to arise when further ionic species are added. However,
for a certain parameter regime, we can demonstrate that the salt-free case can
be mapped onto a corresponding system containing additional salt. The
Green-Kubo formula for the electrophoretic mobility is derived, and its
usefulness demonstrated by simulation data. Finally, we report on
finite-element solutions of the electrokinetic equations, using the commercial
software package COMSOL.Comment: To appear in Journal of Physics: Condensed Matter - special issue on
occasion of the CODEF 2008 conferenc
Optimisation of a Brownian dynamics algorithm for semidilute polymer solutions
Simulating the static and dynamic properties of semidilute polymer solutions
with Brownian dynamics (BD) requires the computation of a large system of
polymer chains coupled to one another through excluded-volume and hydrodynamic
interactions. In the presence of periodic boundary conditions, long-ranged
hydrodynamic interactions are frequently summed with the Ewald summation
technique. By performing detailed simulations that shed light on the influence
of several tuning parameters involved both in the Ewald summation method, and
in the efficient treatment of Brownian forces, we develop a BD algorithm in
which the computational cost scales as O(N^{1.8}), where N is the number of
monomers in the simulation box. We show that Beenakker's original
implementation of the Ewald sum, which is only valid for systems without bead
overlap, can be modified so that \theta-solutions can be simulated by switching
off excluded-volume interactions. A comparison of the predictions of the radius
of gyration, the end-to-end vector, and the self-diffusion coefficient by BD,
at a range of concentrations, with the hybrid Lattice Boltzmann/Molecular
Dynamics (LB/MD) method shows excellent agreement between the two methods. In
contrast to the situation for dilute solutions, the LB/MD method is shown to be
significantly more computationally efficient than the current implementation of
BD for simulating semidilute solutions. We argue however that further
optimisations should be possible.Comment: 17 pages, 8 figures, revised version to appear in Physical Review E
(2012
Numerical electrokinetics
A new lattice method is presented in order to efficiently solve the
electrokinetic equations, which describe the structure and dynamics of the
charge cloud and the flow field surrounding a single charged colloidal sphere,
or a fixed array of such objects. We focus on calculating the electrophoretic
mobility in the limit of small driving field, and systematically linearise the
equations with respect to the latter. This gives rise to several subproblems,
each of which is solved by a specialised numerical algorithm. For the total
problem we combine these solvers in an iterative procedure. Applying this
method, we study the effect of the screening mechanism (salt screening vs.
counterion screening) on the electrophoretic mobility, and find a weak
non-trivial dependence, as expected from scaling theory. Furthermore, we find
that the orientation of the charge cloud (i. e. its dipole moment) depends on
the value of the colloid charge, as a result of a competition between
electrostatic and hydrodynamic effects.Comment: accepted for publication in Journal of Physics Condensed Matter
(proceedings of the 2012 CODEF conference
Universal scaling and characterisation of gelation in associative polymer solutions
A Brownian dynamics algorithm is used to describe the static behaviour of
associative polymer solutions. Predictions for the fractions of stickers bound
by intra-chain and inter-chain association, as a function of system parameters,
such as the number of stickers, the number of monomers between stickers, the
solvent quality, and concentration are obtained. A systematic comparison with
the scaling relations predicted by the mean-field theory of Dobrynin
(Macromolecules, 37, 3881, 2004) is carried out. Different regimes of scaling
behaviour are identified depending on the monomer concentration, the density of
stickers on a chain, and the solvent quality for backbone monomers. Simulation
results validate the predictions of the mean-field theory across a wide range
of parameter values in all the scaling regimes. The value of the des Cloizeaux
exponent proposed by Dobrynin for sticky polymer solutions, is shown to lead to
a collapse of simulation data for all the scaling relations considered here.
Three different signatures for the characterisation of gelation are identified,
with each leading to a different value of the concentration at the sol-gel
transition. The modified Flory-Stockmayer expression is found to be validated
by simulations for all three gelation signatures. Simulation results confirm
the prediction of scaling theory for the gelation line that separates sol and
gel phases, when the modified Flory-Stockmayer expression is used. Phase
separation is found to occur with increasing concentration for systems in which
the backbone monomers are under theta-solvent conditions, and is shown to
coincide with a breakdown in the predictions of scaling theory.Comment: 34 pages, 22 figures, includes Supplemental Material, accepted
versio
Electrophoresis of colloidal dispersions in the low-salt regime
We study the electrophoretic mobility of spherical charged colloids in a
low-salt suspension as a function of the colloidal concentration. Using an
effective particle charge and a reduced screening parameter, we map the data
for systems with different particle charges and sizes, including numerical
simulation data with full electrostatics and hydrodynamics and experimental
data for latex dispersions, on a single master curve. We observe two different
volume fraction-dependent regimes for the electrophoretic mobility that can be
explained in terms of the static properties of the ionic double layer.Comment: Substantially revised versio
Dynamics and Scaling of 2D Polymers in a Dilute Solution
The breakdown of dynamical scaling for a dilute polymer solution in 2D has
been suggested by Shannon and Choy [Phys. Rev. Lett. {\bf 79}, 1455 (1997)].
However, we show here both numerically and analytically that dynamical scaling
holds when the finite-size dependence of the relevant dynamical quantities is
properly taken into account. We carry out large-scale simulations in 2D for a
polymer chain in a good solvent with full hydrodynamic interactions to verify
dynamical scaling. This is achieved by novel mesoscopic simulation techniques
Implicit and explicit solvent models for the simulation of a single polymer chain in solution: Lattice Boltzmann vs Brownian dynamics
We present a comparative study of two computer simulation methods to obtain
static and dynamic properties of dilute polymer solutions. The first approach
is a recently established hybrid algorithm based upon dissipative coupling
between Molecular Dynamics and lattice Boltzmann (LB), while the second is
standard Brownian Dynamics (BD) with fluctuating hydrodynamic interactions.
Applying these methods to the same physical system (a single polymer chain in a
good solvent in thermal equilibrium) allows us to draw a detailed and
quantitative comparison in terms of both accuracy and efficiency. It is found
that the static conformations of the LB model are distorted when the box length
L is too small compared to the chain size. Furthermore, some dynamic properties
of the LB model are subject to an finite size effect, while the BD
model directly reproduces the asymptotic behavior. Apart from
these finite size effects, it is also found that in order to obtain the correct
dynamic properties for the LB simulations, it is crucial to properly thermalize
all the kinetic modes. Only in this case, the results are in excellent
agreement with each other, as expected. Moreover, Brownian Dynamics is found to
be much more efficient than lattice Boltzmann as long as the degree of
polymerization is not excessively large.Comment: 11 figures, submitted to J. Chem. Phy
Dynamic crossover scaling in polymer solutions
The crossover region in the phase diagram of polymer solutions, in the regime
above the overlap concentration, is explored by Brownian Dynamics simulations,
to map out the universal crossover scaling functions for the gyration radius
and the single-chain diffusion constant. Scaling considerations, our simulation
results, and recently reported data on the polymer contribution to the
viscosity obtained from rheological measurements on DNA systems, support the
assumption that there are simple relations between these functions, such that
they can be inferred from one another.Comment: 4 pages, 6 figures, 1 Table. Revised version to appear in Physical
Review Letters. Includes supplemental material
What is the Entanglement Length in a Polymer Melt ?
We present results of molecular dynamics simulations of very long model
polymer chains analyzed by various experimentally relevant techniques. The
segment motion of the chains is found to be in very good agreement with the
repatation model. We also calculated the plateau-modulus G_N. The predicitions
of the entanglement length N_e from G_N and from the mean square displacements
of the chains segments disagree by a factor of about 2.2(2), indicating an
error in the prefactor in the standard formula for G_N. We show that recent
neutron spin echo measurements were carried out for chain lengths which are too
small for a correct determination of N_e.Comment: 5 pages, 4 figures, RevTe
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