31 research outputs found
Complex Fluids with Mobile Charge-Regulated Macro-Ions
We generalize the concept of charge regulation of ionic solutions, and apply
it to complex fluids with mobile macro-ions having internal non-electrostatic
degrees of freedom. The suggested framework provides a convenient tool for
investigating systems where mobile macro-ions can self-regulate their charge
(e.g., proteins). We show that even within a simplified charge-regulation
model, the charge dissociation equilibrium results in different and notable
properties. Consequences of the charge regulation include a positional
dependence of the effective charge of the macro-ions, a non-monotonic
dependence of the effective Debye screening length on the concentration of the
monovalent salt, a modification of the electric double-layer structure, and
buffering by the macro-ions of the background electrolyte.Comment: 7 pages, 5 figure
Charged Membranes: Poisson-Boltzmann theory, DLVO paradigm and beyond
In this chapter we review the electrostatic properties of charged membranes
in aqueous solutions, with or without added salt, employing simple physical
models. The equilibrium ionic profiles close to the membrane are governed by
the well-known Poisson-Boltzmann (PB) equation. We analyze the effect of
different boundary conditions, imposed by the membrane, on the ionic profiles
and the corresponding osmotic pressure. The discussion is separated into the
single membrane case and that of two interacting membranes. For one membrane
setup, we show the different solutions of the PB equation and discuss the
interplay between constant-charge and constant-potential boundary conditions. A
modification of the PB theory is presented to treat the extremely high
counter-ion concentration in the vicinity of a charge membrane. For two
equally-charged membranes, we analyze the different pressure regimes for the
constant-charge boundary condition, and discuss the difference in the osmotic
pressure for various boundary conditions. The non-equal charged membranes is
reviewed as well, and the crossover from repulsion to attraction is calculated
analytically. We then examine the charge-regulation boundary condition and
discuss its effects on the ionic profiles and the osmotic pressure for two
equally-charged membranes. In the last section, we briefly review the van der
Waals (vdW) interactions and their effect on the free energy between two planar
membranes. We explain the simple Hamaker pair-wise summation procedure, and
introduce the more rigorous Lifshitz theory. The latter is a key ingredient in
the DLVO theory, which combines repulsive electrostatic with attractive vdW
interactions, and offers a simple explanation for colloidal or membrane
stability. Finally, the chapter ends by a short account of the limitations of
the approximations inherent in the PB theory.Comment: 57 pages, 19 figures, From the forthcoming Handbook of Lipid
Membranes: Molecular, Functional, and Materials Aspects. Edited by Cyrus
Safinya and Joachim Radler, Taylor & Francis/CRC Press, 201
Surface Tension of Electrolyte Solutions: A Self-consistent Theory
We study the surface tension of electrolyte solutions at the air/water and
oil/water interfaces. Employing field-theoretical methods and considering
short-range interactions of anions with the surface, we expand the Helmholtz
free energy to first-order in a loop expansion and calculate the excess surface
tension. Our approach is self-consistent and yields an analytical prediction
that reunites the Onsager-Samaras pioneering result (which does not agree with
experimental data), with the ionic specificity of the Hofmeister series. We
obtain analytically the surface-tension dependence on the ionic strength, ionic
size and ion-surface interaction, and show consequently that the
Onsager-Samaras result is consistent with the one-loop correction beyond the
mean-field result. Our theory fits well a wide range of concentrations for
different salts using one fit parameter, reproducing the reverse Hofmeister
series for anions at the air/water and oil/water interfaces.10.1029Comment: 5 pages, 2 figure
Charge regulation: a generalized boundary condition?
The three most commonly-used boundary conditions for charged colloidal
systems are constant charge (insulator), constant potential (conducting
electrode) and charge regulation (ionizable groups at the surface). It is
usually believed that the charge regulation is a generalized boundary condition
that reduces in some specific limits to either constant charge or constant
potential boundary conditions. By computing the disjoining pressure between two
symmetric planes for these three boundary conditions, both numerically (for all
inter-plate separations) and analytically (for small inter-plate separations),
we show that this is not, in general, the case. In fact, the limit of charge
regulation is a separate boundary condition, yielding a disjoining pressure
with a different characteristic separation-scaling. Our findings are supported
by several examples demonstrating that the disjoining pressure at small
separations for the charge regulation boundary-condition depends on the details
of the dissociation/association process.Comment: 6 pages, 3 figure
Effective Medium Theory for Mechanical Phase Transitions of Fiber Networks
Networks of stiff fibers govern the elasticity of biological structures such
as the extracellular matrix of collagen. These networks are known to stiffen
nonlinearly under shear or extensional strain. Recently, it has been shown that
such stiffening is governed by a strain-controlled athermal but critical phase
transition, from a floppy phase below the critical strain to a rigid phase
above the critical strain. While this phase transition has been extensively
studied numerically and experimentally, a complete analytical theory for this
transition remains elusive. Here, we present an effective medium theory (EMT)
for this mechanical phase transition of fiber networks. We extend a previous
EMT appropriate for linear elasticity to incorporate nonlinear effects via an
anharmonic Hamiltonian. The mean-field predictions of this theory, including
the critical exponents, scaling relations and non-affine fluctuations
qualitatively agree with previous experimental and numerical results
Field theory for mechanical criticality in disordered fiber networks
Strain-controlled criticality governs the elasticity of jamming and fiber
networks. While the upper critical dimension of jamming is believed to be
=2, non mean-field exponents are observed in numerical studies of 2D and
3D fiber networks. The origins of this remains unclear. In this study we
propose a minimal mean-field model for strain-controlled criticality of fiber
networks. We then extend this to a phenomenological field theory, in which non
mean-field behavior emerges as a result of the disorder in the network
structure. We predict that the upper critical dimension for such systems is
=4 using a Gaussian approximation. Moreover, we identify an order
parameter for the phase transition, which has been lacking for fiber networks
to date