860 research outputs found
Electroneutrality and Phase Behavior of Colloidal Suspensions
Several statistical mechanical theories predict that colloidal suspensions of
highly charged macroions and monovalent microions can exhibit unusual
thermodynamic phase behavior when strongly deionized. Density-functional,
extended Debye-H\"uckel, and response theories, within mean-field and
linearization approximations, predict a spinodal phase instability of charged
colloids below a critical salt concentration. Poisson-Boltzmann cell model
studies of suspensions in Donnan equilibrium with a salt reservoir demonstrate
that effective interactions and osmotic pressures predicted by such theories
can be sensitive to the choice of reference system, e.g., whether the microion
density profiles are expanded about the average potential of the suspension or
about the reservoir potential. By unifying Poisson-Boltzmann and response
theories within a common perturbative framework, it is shown here that the
choice of reference system is dictated by the constraint of global
electroneutrality. On this basis, bulk suspensions are best modeled by
density-dependent effective interactions derived from a closed reference system
in which the counterions are confined to the same volume as the macroions.
Linearized theories then predict bulk phase separation of deionized suspensions
only when expanded about a physically consistent (closed) reference system.
Lower-dimensional systems (e.g., monolayers, small clusters), depending on the
strength of macroion-counterion correlations, may be governed instead by
density-independent effective interactions tied to an open reference system
with counterions dispersed throughout the reservoir, possibly explaining
observed structural crossover in colloidal monolayers and anomalous
metastability of colloidal crystallites.Comment: 12 pages, 5 figures. Discussion clarified, references adde
Variational collision integrator for polymer chains
The numerical simulation of many-particle systems (e.g., in molecular dynamics) often involves constraints of various forms. We present a symplectic integrator for mechanical systems with holonomic (bilateral) and unilateral contact constraints, the latter being in the form of a nonpenetration condition. The scheme is based on a discrete variant of Hamilton’s principle in which both the discrete trajectory and the unknown collision time are varied (cf. [Fetecau et al., 2003, SIAM J. Applied Dynamical Systems, 2, pp. 381–416]). As a consequence, the collision event enters the discrete equations of motion as an unknown that has to be computed on-the-fly whenever a collision is imminent. The additional bilateral constraints are e ciently dealt with employing a discrete null space reduction (including a projection and a local reparametrisation step) which considerably reduces the number of unknowns and improves the condition number during each time-step as compared to a standard treatment with Lagrange multipliers. We illustrate the numerical scheme with a simple example from polymer dynamics, a linear chain of beads, and test it against other standard numerical schemes for collision problems
Nonlinear Screening and Effective Electrostatic Interactions in Charge-Stabilized Colloidal Suspensions
A nonlinear response theory is developed and applied to electrostatic
interactions between spherical macroions, screened by surrounding microions, in
charge-stabilized colloidal suspensions. The theory describes leading-order
nonlinear response of the microions (counterions, salt ions) to the
electrostatic potential of the macroions and predicts microion-induced
effective many-body interactions between macroions. A linear response
approximation [Phys. Rev. E 62, 3855 (2000)] yields an effective pair potential
of screened-Coulomb (Yukawa) form, as well as a one-body volume energy, which
contributes to the free energy. Nonlinear response generates effective
many-body interactions and essential corrections to both the effective pair
potential and the volume energy. By adopting a random-phase approximation (RPA)
for the response functions, and thus neglecting microion correlations,
practical expressions are derived for the effective pair and triplet potentials
and for the volume energy. Nonlinear screening is found to weaken repulsive
pair interactions, induce attractive triplet interactions, and modify the
volume energy. Numerical results for monovalent microions are in good agreement
with available ab initio simulation data and demonstrate that nonlinear effects
grow with increasing macroion charge and concentration and with decreasing salt
concentration. In the dilute limit of zero macroion concentration,
leading-order nonlinear corrections vanish. Finally, it is shown that nonlinear
response theory, when combined with the RPA, is formally equivalent to the
mean-field Poisson-Boltzmann theory and that the linear response approximation
corresponds, within integral-equation theory, to a linearized hypernetted-chain
closure.Comment: 30 pages, 8 figures, Phys. Rev. E (in press
Statics and Dynamics of Strongly Charged Soft Matter
Soft matter materials, such as polymers, membranes, proteins, are often
electrically charged. This makes them water soluble, which is of great
importance in technological application and a prerequisite for biological
function. We discuss a few static and dynamic systems that are dominated by
charge effects. One class comprises complexation between oppositely charged
objects, for example the adsorption of charged ions or charged polymers (such
as DNA) on oppositely charged substrates of different geometry. The second
class comprises effective interactions between similarly charged objects. Here
the main theme is to understand the experimental finding that similarly and
highly charged bodies attract each other in the presence of multi-valent
counterions. This is demonstrated using field-theoretic arguments as well as
Monte-Carlo simulations for the case of two homogeneously charged bodies.
Realistic surfaces, on the other hand, are corrugated and also exhibit
modulated charge distributions, which is important for static properties such
as the counterion-density distribution, but has even more pronounced
consequences for dynamic properties such as the counterion mobility. More
pronounced dynamic effects are obtained with highly condensed charged systems
in strong electric fields. Likewise, an electrostatically collapsed highly
charged polymer is unfolded and oriented in strong electric fields. At the end
of this review, we give a very brief account of the behavior of water at planar
surfaces and demonstrate using ab-initio methods that specific interactions
between oppositely charged groups cause ion-specific effects that have recently
moved into the focus of interest.Comment: 61 pages, 31 figures, Physics Reports (2005)-in press (high quality
figures available from authors
Ferromagnetic zigzag chains and properties of the charge ordered perovskite manganites
The low-temperature properties of the so-called ''charge ordered'' state in
50% doped perovskite manganites are described from the viewpoint of the
magnetic spin ordering. In these systems, the zigzag antiferromagnetic
ordering, combined with the double-exchange physics, effectively divides the
whole sample into the one-dimensional ferromagnetic zigzag chains and results
in the anisotropy of electronic properties. The electronic structure of one
such chain is described by an effective 33 Hamiltonian in the basis of
Mn() orbitals. We treat this problem analytically and consider the
following properties: (i) the nearest-neighbor magnetic interactions; (ii) the
distribution of the Mn() and Mn() states near the Fermi level, and
their contribution to the optical conductivity and the resonant x-ray
scattering near the Mn -absorption edge. We argue that the anisotropy of
magnetic interactions in the double-exchange limit, combined with the isotropic
superexchange interactions, readily explains both the local and the global
stability of the zigzag antiferromagnetic state. The two-fold degeneracy of
levels plays a very important role in the problem and explains the
insulating behavior of the zigzag chain, as well as the appearance of the
orbital ordering in the double-exchange model. Importantly, however, the charge
ordering itself is expected to play only a minor role and is incompatible with
the ferromagnetic coupling within the chain. We also discuss possible effects
of the Jahn-Teller distortion and compare the tight-binding picture with
results of band structure calculations in the local-spin-density approximation.Comment: 35 pages, 8 figure
Bistable collective behavior of polymers tethered in a nanopore.
Polymer-coated pores play a crucial role in nucleo-cytoplasmic transport and in a number of biomimetic and nanotechnological applications. Here we present Monte Carlo and Density Functional Theory approaches to identify different collective phases of end-grafted polymers in a nanopore and to study their relative stability as a function of intermolecular interactions. Over a range of system parameters that is relevant for nuclear pore complexes, we observe two distinct phases: one with the bulk of the polymers condensed at the wall of the pore, and the other with the polymers condensed along its central axis. The relative stability of these two phases depends on the interpolymer interactions. The existence the two phases suggests a mechanism in which marginal changes in these interactions, possibly induced by nuclear transport receptors, cause the pore to transform between open and closed configurations, which will influence transport through the pore
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