691 research outputs found
Virial expansion for charged colloids and electrolytes
Using a field-theoretic approach, we derive the first few coefficients of the
exact low-density (``virial'') expansion of a binary mixture of positively and
negatively charged hard spheres (two-component hard-core plasma, TCPHC). Our
calculations are nonperturbative with respect to the diameters and
and charge valences and of positive and negative ions.
Consequently, our closed-form expressions for the coefficients of the free
energy and activity can be used to treat dilute salt solutions, where typically
and , as well as colloidal suspensions, where the
difference in size and valence between macroions and counterions can be very
large. We show how to map the TCPHC on a one-component hard-core plasma (OCPHC)
in the colloidal limit of large size and valence ratio, in which case the
counterions effectively form a neutralizing background. A sizable discrepancy
with the standard OCPHC with uniform, rigid background is detected, which can
be traced back to the fact that the counterions cannot penetrate the colloids.
For the case of electrolyte solutions, we show how to obtain the cationic and
anionic radii as independent parameters from experimental data for the activity
coefficient.Comment: 15 page
Phase behavior of three-component ionic fluids
We study the phase behavior of solutions consisting of positive and negative
ions of valence z to which a third ionic species of valence Z>z is added. Using
a discretized Debye-Hueckel theory, we analyze the phase behavior of such
systems for different values of the ratio Z/z. We find, for Z/z>1.934, a
three-phase coexistence region and, for Z/z>2, a closed (reentrant) coexistence
loop at high temperatures. We characterize the behavior of these ternary ionic
mixtures as function of charge asymmetry and temperature, and show the complete
phase diagrams for the experimentally relevant cases of Z/z=2 and Z/z=3,
corresponding to addition of divalent and trivalent ions to monovalent ionic
fluids, respectively.Comment: 6 pages, 4 figures; to appear in the European Physical Journal
Electrostatic Interactions in Strongly-Coupled Soft Matter
Charged soft-matter systems--such as colloidal dispersions and charged
polymers--are dominated by attractive forces between constituent like-charged
particles when neutralizing counterions of high charge valency are introduced.
Such counter-intuitive effects indicate strong electrostatic coupling between
like-charged particles, which essentially results from electrostatic
correlations among counterions residing near particle surfaces. In this paper,
the attraction mechanism and the structure of counterionic correlations are
discussed in the limit of strong coupling based on recent numerical and
analytical investigations and for various geometries (planar, spherical and
cylindrical) of charged objects.Comment: 26 pages, 13 figure
Strong-Coupling Theory for Counter-Ion Distributions
The Poisson-Boltzmann approach gives asymptotically exact counter-ion density
profiles around charged objects in the weak-coupling limit of low valency and
high temperature. In this paper we derive, using field-theoretic methods, a
theory which becomes exact in the opposite limit of strong coupling. Formally,
it corresponds to a standard virial expansion. Long-range divergences, which
render the virial expansion intractable for homogeneous bulk systems, are shown
to be renormalizable for the case of inhomogeneous distribution functions by a
systematic expansion in inverse powers of the coupling parameter. For a planar
charged wall, our analytical results compare quantitatively with extensive
Monte-Carlo simulations.Comment: 7 pages, 3 figures; to appear in Europhys. Let
Counterions at Charged Cylinders: Criticality and universality beyond mean-field
The counterion-condensation transition at charged cylinders is studied using
Monte-Carlo simulation methods. Employing logarithmically rescaled radial
coordinates, large system sizes are tractable and the critical behavior is
determined by a combined finite-size and finite-ion-number analysis. Critical
counterion localization exponents are introduced and found to be in accord with
mean-field theory both in 2 and 3 dimensions. In 3D the heat capacity shows a
universal jump at the transition, while in 2D, it consists of discrete peaks
where single counterions successively condense.Comment: 4 pages, 3 figures; submitted to Phys. Rev. Lett. (2005
Non-Markovian data-driven modeling of single-cell motility
Trajectories of human breast cancer cells moving on one-dimensional circular tracks are modeled by thenon-Markovian version of the Langevin equation that includes an arbitrary memory function. When averagedover cells, the velocity distribution exhibits spurious non-Gaussian behavior, while single cells are characterizedby Gaussian velocity distributions. Accordingly, the data are described by a linear memory model whichincludes different random walk models that were previously used to account for various aspects of cell motilitysuch as migratory persistence, non-Markovian effects, colored noise, and anomalous diffusion. The memoryfunction is extracted from the trajectory data without restrictions or assumptions, thus making our approachtruly data driven, and is used for unbiased single-cell comparison. The cell memory displays time-delayedsingle-exponential negative friction, which clearly distinguishes cell motion from the simple persistent randomwalk model and suggests a regulatory feedback mechanism that controls cell migration. Based on the extractedmemory function we formulate a generalized exactly solvable cell migration model which indicates thatnegative friction generates cell persistence over long timescales. The nonequilibrium character of cell motionis investigated by mapping the non-Markovian Langevin equation with memory onto a Markovian model thatinvolves a hidden degree of freedom and is equivalent to the underdamped active Ornstein-Uhlenbeck process
Counterion density profiles at charged flexible membranes
Counterion distributions at charged soft membranes are studied using
perturbative analytical and simulation methods in both weak coupling
(mean-field or Poisson-Boltzmann) and strong coupling limits. The softer the
membrane, the more smeared out the counterion density profile becomes and
counterions pentrate through the mean-membrane surface location, in agreement
with anomalous scattering results. Membrane-charge repulsion leads to a
short-scale roughening of the membrane.Comment: 4 pages, 4 figure
Counterions at charge-modulated substrates
We consider counterions in the presence of a single planar surface with a
spatially inhomogeneous charge distribution using Monte-Carlo simulations and
strong-coupling theory. For high surface charges, multivalent counterions, or
pronounced substrate charge modulation the counterions are laterally correlated
with the surface charges and their density profile deviates strongly from the
limit of a smeared-out substrate charge distribution, in particular exhibiting
a much increased laterally averaged density at the surface.Comment: 7 page
New Criticality of 1D Fermions
One-dimensional massive quantum particles (or 1+1-dimensional random walks)
with short-ranged multi-particle interactions are studied by exact
renormalization group methods. With repulsive pair forces, such particles are
known to scale as free fermions. With finite -body forces (m = 3,4,...), a
critical instability is found, indicating the transition to a fermionic bound
state. These unbinding transitions represent new universality classes of
interacting fermions relevant to polymer and membrane systems. Implications for
massless fermions, e.g. in the Hubbard model, are also noted. (to appear in
Phys. Rev. Lett.)Comment: 10 pages (latex), with 2 figures (not included
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