Dynamic surface tension and
kinetics
of surfactant adsorption at fluid interfaces.
Andelman, D.; Diamant,
H.
Book of Abstracts, 215th ACS National Meeting,
Abstract: Surfactant
kinetics at fluid-fluid interfaces is studied within a free energy
formalism
which provides a general method for calculating. dynamic
surface tension. For non-ionic surfactants the results coincide
with
previous models. Common non-ionic surfactants are shown to undergo
diffusion-limited adsorption, in agreement with experiments On the
other
hand, ionic surfactants such as SDS without added salt behave quite
differently. Strong electrostatic interactions lead to kinetically
limited adsorption, slower dynamics and intermediate plateau in the
kinetic
surface tension as was observed in experiments Upon
addition of salt the electrostatic interactions are screened and the
adsorption
becomes more similar to the non-ionic case.
Control of diblock copolymer
morphology in thin film.
Tsori, Y.; Andelman, D.
Abstracts of Papers, 224th ACS National
Meeting,
Abstract: Block
copolymers are polymeric systems exhibiting modulated spatial structure
on the
nanometer to micrometer scale. We present theoretical several
ordering
mechanisms in thin films of diblock copolymers. For temperatures
above
the order-disorder temperature, a linear response theory gives the
polymer
density in the vicinity of chemical patterned and flat surfaces.
The
surface pattern or template is decomposed into its Fourier modes, and
the decay
of these modes is analyzed. Below the order-disorder temperature,
the
transition of lamellar orientation from parallel to perpendicular to the
surfaces is investigated. In addition, we calc. the phase diagram
in the
presence of an externally applied perpendicular elec. field and show
that
perpendicular ordering is favored above some critical value of the
field.
The obtained phase diagram depends on elec. field strength, film
thickness and
surface interactions.
Control of diblock copolymer
morphology
in thin film.
Tsori, Y.; Andelman,
D.
Polymer Preprints (American Chemical Society,
Division
of Polymer Chemistry) (2002), 43(2), 858-859.
Abstract: A
review. Controlling the ordering of diblock copolymers is
important in
many applications. We discuss two mechanisms to control the
orientation
and ordering of diblock copolymers: above the order-disorder temperature
(ODT),
chemical patterned surfaces induce order in the thin film, although the
bulk
system is in its disordered state. For lamellar diblock copolymers
(below
the ODT), we show how elec. fields can be used to achieve a transition
from
lamellae parallel to the surfaces (electrodes) to perpendicular
lamellae.
116. Models of Gemini
surfactants.
Diamant, H.; Andelman,
D.
Los Alamos National Laboratory, Preprint
Archive,
Condensed Matter (2003), 1-16,
arXiv:cond-mat/0302184.
http://arxiv.org/abs/cond-mat/0302184
Abstract: A
review. The current state of theoretical models of Gemini
surfactants is
reviewed. After a summary of the characteristic behavior of Gemini
surfactants several theoretical models are presented. The
self-assembly
of sol. surfactants is regarded first and then the focus is on
self-assembly
theories for Gemini surfactants. These models cover surface
properties,
micellization, and phase behavior of the
surfactants
115. Parallel and
perpendicular
lamellae on corrugated surfaces.
Tsori, Y.; Andelman, D.
Submitted to Macromolecules (2003).
http://arxiv.org/abs/cond-mat/0208127
Abstract: We
consider the relative stability of parallel and perpendicular lamellar
layers
on corrugated surfaces. The model can be applied to smectic phases
of
liquid crystals, to lamellar phases of short-chain amphiphiles and to
lamellar
phases of long-chain block copolymers. The corrugated surface is
modeled
by having a single q-mode lateral corrugation of a certain height.
The
lamellae deform close to the surface as a result of chemical interaction
with
it. The competition between the energetic cost of elastic
deformations
and the gain in surface energy determines whether parallel or
perpendicular
lamellar orientation (with respect to the surface) is preferred.
Our main
results are summarized in two phase diagrams, each exhibiting a
transition line
from the parallel to perpendicular orientations. The phase
diagrams
depend on the three system parameters: the lamellar natural periodicity,
and
the periodicity and amplitude of surface corrugations. For a fixed
lamellar periodicity (or polymer chain length), the parallel orientation
is
preferred as the amplitude of surface corrugation decreases and/or its
periodicity increases. Namely, for surfaces having small
corrugations
centered at long wavelengths. For a fixed corrugation periodicity,
the
parallel orientation is preferred for small corrugation amplitude and/or
large
lamellae periodicity. Our results are in agreement with recent
experimental results carried out on thin block copolymer films of
PS-PMMA
(polystyrene-polymethylmethacrylate) in the
lamellar
phase, and in contact with several corrugated
surfaces.
114. Onset of DNA
aggregation in
presence of mono- and multivalent
counterions.
Burak, Y.; Ariel, G.; Andelman,
D.
arXiv:cond-mat/0304002.
http://arxiv.org/abs/cond-mat/0304002
Abstract:We
address theoretical aggregation of DNA segments by multivalent
polyamines such
as spermine and spermidine. In experiments, the aggregation occurs
above
a certain threshold concentration of multivalent ions. We
demonstrate
that the dependence of this threshold on the concentration of DNA has a
simple
form. When the DNA concentration c_DNA
is
smaller than the monovalent salt concentration, the threshold
multivalent ion
concentration depends linearly on c_DNA,
having the
form \alpha*c_DNA + \beta. The
coefficients
\alpha and \beta are related to the density profile of multivalent
counterions
around isolated DNA chains, at the onset of their aggregation.
This
analysis agrees extremely well with recent detailed measurements on DNA
aggregation in the presence of spermine. From the fit to the
experimental
data, the number of condensed multivalent counterions per DNA chain can
be
deduced. A few other conclusions can then be reached: i) the
number of
condensed spermine ions at the onset of aggregation decreases with the
addition
of monovalent salt; ii) the Poisson-Boltzmann theory over-estimates the
number
of condensed multivalent ions at high monovalent salt concentrations;
iii) our
analysis of the data indicates that the DNA charge is not
over-compensated by
spermine at the onset of aggregation.
113.
Adsorption and depletion of polyelectrolytes from charged surfaces.
Shafir, A.; Andelman, D.; Netz, R.
R.
To be published in J. Chemical Physical
Los Alamos National Laboratory, Preprint
Archive,
Condensed Matter (2003), 1-12,
arXiv:cond-mat/0302126.
http://arxiv.org/abs/cond-mat/0302126
Abstract: Mean-field
theory and scaling arguments are presented to model polyelectrolyte
adsorption
from semi-dilute solutions onto charged surfaces. Using numerical
solutions of the mean-field equations, we show that adsorption exists
only for
highly charged polyelectrolytes in low salt solutions. Simple
scaling
laws for the width of the adsorbed layer and the amt. of adsorbed
polyelectrolyte
are obtained. In other situations the polyelectrolyte chains will
deplete
from the surface. For fixed surface potential conditions, the salt
concentration at the adsorption-depletion crossover scales as the
product of
the charged fraction of the polyelectrolyte f and the surface
potential,
while for a fixed surface charge density, σ, it scales as
σ2/3
f2/3, in agreement with single-chain
results.
112. Structural Changes in
Block
Copolymers: Coupling of Electric Field and Mobile Ions.
Tsori,
Y.; Tournilhac, F.; Andelman, D.; Leibler,
L.
Physical Review Letters (2003),
90(14), 145504/1-145504/4.
http://arxiv.org/abs/cond-mat/0208129
Abstract: We
argue that the presence of dissociated ions in block copolymers under
elec.
fields can induce strong morphological changes and even lead to phase
transitions. We investigate, in particular, diblock copolymers in
the
bcc. (bcc) phase. In pure dielectric
materials
(no free charges), a dielectric breakdown is expected to occur for large
enough
elec. fields, preempting any structural phase transition. On the
other
hand, dissociated ions are predicted to induce a phase transition to a
hexagonal
array of cylinders, at fields of about 10 V/μm
or even lower. The strength of this mechanism can be tuned by
controlling
the amt. of free ions present.
111. Ordering Mechanisms in
Confined Diblock Copolymers.
Tsori, Y.; Andelman, D.
Interface
Science (2003), 11(2), 259-268.
http://arxiv.org/abs/cond-mat/0208127
Abstract: We
present several ordering mechanisms in diblock copolymers. For
temperatures
above the order-disorder temperature and in the weak segregation regime,
a
linear response theory is presented which gives the polymer density in
the
vicinity of confining flat surfaces. The surfaces are chemical
patterned
where different regions attract different parts of the copolymer
chain.
The surface pattern or template is decomposed into its Fourier modes,
and the
decay of these modes is analyzed. The propagation of the surface
pattern
into the disordered bulk is given for several types of patterns (e.g.
uniform
and striped surface). It is further shown that complex
morphological can
be induced in a thin film even though the bulk is disordered. We
next
consider lamellar diblock copolymers (low temperature regime) in the
presence
of a striped surface. It is shown that lamellae acquire a tilt
with
respect to the surface, if the surface periodicity is larger than the
bulk
one. The lamellae close to the surface are strongly distorted from
their
perfect shape. When the surface and lamellar periodicities are
equal, the
lamellae are perpendicular to the surface. Lastly, the transition
from
parallel to perpendicular lamellae in a thin film is presented.
The
transition between the two states depends on the surface separation and
strength
of surface interactions. We further calc. the phase diagram in the
presence of perpendicular elec. field favoring perpendicular
ordering. In
the strong segregation limit we introduce a simple model to calc. the
phase
diagram of the fully parallel, fully perpendicular and mixed (parallel
and
perpendicular) states.
110. Persistence length of a
strongly charged rod-like polyelectrolyte in the presence of salt.
Ariel, G.; Andelman, D.
Physical Review E: Statistical, Nonlinear, and
Soft
Matter Physics (2003), 67(1-1), 011805/1-011805/11.
http://arxiv.org/abs/cond-mat/0206361
Abstract: The
persistence length of a single, intrinsically rigid polyelectrolyte
chain,
above the Manning condensation threshold is investigated theoretical in
the
presence of added salt. Using a loop expansion method, the
partition
function is consistently calculated, taking into account corrections to
mean-field
theory. Within a mean-field approximation, the well-known results
of
Odijk, Skolnick, and Fixman are reproduced. Beyond mean field, it
is
found that density correlations between counterions and thermal
fluctuations
reduce the stiffness of the chain, indicating an effective attraction
between
monomers for highly charged chains and multivalent counterions.
This
attraction results in a possible mech. instability (collapse), alluding
to the
phenomenon of DNA condensation. In addition, we find that more
counterions
condense on slightly bent conformations of the chain than predicted by
the
Manning model for the case of an infinite cylinder. Finally, our
results
are compared with previous models and
experiments.
109.
The unbinding transition of mixed fluid membranes.
Komura, S.; Andelman,
D.
1-7, arXiv:cond-mat/0205144.
http://arxiv.org/abs/cond-mat/0205144
Abstract: A phenomenological
model for the unbinding transition of multi-component fluid membranes is
proposed, where the unbinding transition is described using a theory
analogous
to Flory-Huggins theory for polymers. The coupling between the
lateral
phase separation of inclusion molecules and the membrane-substrate
distance
explains the phase coexistence between two unbound phases as observed in
recent
experiments by Marx et al. Bellow a critical end-point
temperature, we find
that the unbinding transition becomes first-order for multi-component
membranes.
108. Neutral and charged
polymers at
interfaces.
Netz, R. R.; Andelman,
D.
1-117,
arXiv:cond-mat/0203364.
http://arxiv.org/abs/cond-mat
/0203364
Abstract: A
review. Chain-like macromolecules (polymers) show characteristic
adsorption properties due to their flexibility and internal degrees of
freedom. In this review we discuss concepts and features that are
relevant to the adsorption of neutral and charged polymers at
equilibrium,
including the type of polymer/surface interaction, the solvent quality,
the
characteristics of the surface, and the polymer structure. Charged
polymers (polyelectrolytes) are of practical importance due to their
water
solubility; we present a summary of recent progress in this rapidly
evolving
field. Since many experimental studies are performed with rather
stiff
biopolymers, we in detail discuss the case of semiflexible
polymers. First,
we review the behavior of neutral and charged chains in solution.
Then,
the adsorption of a single polymer chain is considered. Next, the
adsorption and depletion processes in the many-chain case are
reviewed.
Profiles, changes in the surface tension and polymer surface excess are
calculated Mean-field and corrections due to fluctuations and
lateral
correlations are discussed. The force of interaction between two
adsorbed
layers, which is important in understanding colloidal stability, is
characterized. The behavior of grafted polymers is also reviewed,
both
for neutral and charged brushes.
Ariel, G.; Andelman,
D.
Europhysics Letters (2003),
61(1),
67-73.
http://arxiv.org/abs/cond-mat/0112337
Abstract: The
persistence length of a single, strongly charged, stiff polyelectrolyte
chain
is investigated theoretical Path integral formulation is used to
obtain
the effective electrostatic interaction between the monomers. We
find
significant deviations from the classical Odijk, Skolnick and Fixman
(OSF)
result. An induced attraction between monomers is due to thermal
fluctuations and correlations between bound counterions. The
electrostatic persistence length is found to be smaller than the OSF
value and
indicates a possible mech. instability (collapse) for highly charged
polyelectrolytes with multivalent counterions. In addition, we
calc. the amt.
of condensed counterions on a slightly bent polyelectrolyte. More
counterions are found to be adsorbed as compared to the Manning
condensation on
a cylinder.
106.
Adhesion of membranes with competing specific and generic
interactions.
Weikl, T. R.; Andelman, D.; Komura, S.;
Lipowsky,
R.
1-22,
arXiv:cond-mat/0205080.
http://arxiv.org/abs/cond-mat/0205080
Abstract: Biomimetic
membranes in contact with a planar substrate or a E
second membrane are studied theoretical. The
membranes contain specific adhesion molecules (stickers) which are
attracted by
the second surface. In the absence of stickers, the
trans-interaction
between the membrane and the second surface is assumed to be repulsive
at short
separations. It is shown that the interplay of specific attractive
and
generic repulsive interactions can lead to the formation of a potential
barrier. This barrier induces a line tension between bound and
unbound
membrane segments which results in lateral phase separation during
adhesion. The mechanism for adhesion-induced phase separation is
rather
general, as is demonstrated by considering two distinct cases involving:
(i)
stickers with a linear attractive potential, and (ii) stickers with a
short-ranged square-well potential. In both cases, membrane
fluctuations
reduce the potential barrier and, therefore, decrease the tendency of
phase
separation
Diamant, H.; Andelman,
D.
1-12, arXiv:cond-mat/0109253.
http://arxiv.org/abs/cond-mat/0109253
Abstract: Chain-like
macromolecules in solution, whether biol. or synthetic, transform from a
spatially extended conformation to a compact one upon change of
temperature or
solvent qualities. This sharp transition plays a key role in
various
phenomena, including DNA condensation, protein folding, and the behavior
of
polymer solutions In biol. processes such as DNA condensation the
collapse is sensitively induced by a small amt. of added molecules
Here
we derive a general criterion for the effect of such agents on
conformational
transitions. We find two different scenarios depending on chain
stiffness. If the persistence length, the characteristic distance
along
which the chain retains its direction, is smaller than the range of
attractive
correlations induced by the agent (typically up to several nanometers),
the
chain contracts gradually. Stiffer chains undergo sharp
collapse.
We thereby suggest that the enhanced rigidity of double-stranded DNA as
compared to the single strand is a prerequisite for sharp, controllable
conformational transitions.
Tsori, Y.; Andelman,
D.
Macromolecules (2002),
35(13),
5161-5170.
http://arxiv.org/abs/cond-mat/0110282
Abstract: We
examine the alignment of thin film diblock copolymers subject to a
perpendicular elec. field. Two regimes are considered sep.: weak
segregation and strong segregation. For weakly segregated blocks
and
below a critical value of the field, Ec, surface interactions stabilize
stacking of lamellae in a direction parallel to the surfaces.
Above the
critical field, a first-order phase transition occurs when lamellae in a
direction
perpendicular to the confining surfaces (and parallel to the field)
become
stable. The film morphological is then a superposition of parallel
and
perpendicular lamellae. In contrast to Helfrich-Hurault
instability for
smectic liquid crystals, the mode that gets critical first has the
natural
lamellar periodicity. In addition, undulations of adjacent
inter-material
dividing surfaces are out-of-phase with each other. For diblock
copolymers in the strong segregation regime, we find two critical fields
E1 and
E2 > E1. As the field is increased from zero above E1, the
region in
the middle of the film develops an orientation perpendicular to the
walls,
while the surface regions still have parallel lamellae. When the
field is
increased above E2, the perpendicular alignment spans the whole
film. In
another range of parameters, the transition from parallel to
perpendicular
orientation is direct.
103.
Polyelectrolytes in
solution and at surfaces.
Netz, R. R.; Andelman, D.
Los Alamos National Laboratory, Preprint
Archive,
Condensed Matter (2001), 1-60,
arXiv:cond-mat/0101314.
http://arxiv.org/abs/cond-mat/0101314
Abstract: This
review with 111 refs. deals with charged polymers (polyelectrolytes) in
solution and at surfaces. The behavior of polyelectrolytes is
markedly
different from that of neutral polymers. In bulk solutions, i.e.
disregarding the surface effect, there are two unique features to
charged
polymers: first, due to the presence of long-ranged electrostatic
repulsion
between charged monomers, the polymer conformations are much more
extended,
giving rise to a very small overlap concentration and high solution
viscosity.
Second, the presence of a large number of counterions increases the
osmotic
pressure of polyelectrolyte solutions, making such polymers water sol.
as is of
great importance to many applications. At surfaces, the same
interplay
between monomer-monomer repulsion and counterion degrees of freedom
leads to a
number of special properties. In particular, the adsorption
behavior
depends on both the concentration of polymers and added salt in the
bulk.
We first describe the adsorption behavior of single polyelectrolyte
molecules,
and discuss the necessary conditions to obtain an adsorbed layer and
characterize its width. Depending on the stiffness of the
polyelectrolyte, the layer can be rather flat and compressed or coiled
and
extended. We then proceed and discuss the adsorption of
polyelectrolytes
from semi-dilute solutions Mean-field theory profiles of
polyelectrolyte
adsorption are calculated as function of surface charge density (or
surface
potential), the amt. of salt in the system and the charge fraction on
the
chains. The phenomenon of charge inversion is reviewed and its
relevance
to the formation of multilayers is explained. The review ends with
a
short overview of the behavior of grafted
polyelectrolytes.
Tsori, Y.; Andelman, D.
European Physical Journal E: Soft Matter
(2001), 5(5), 605-614.
http://arxiv.org/abs/cond-mat/0105213
Abstract: We
study morphologies of thin-film diblock copolymers between two flat and
parallel walls. The study is restricted to the weak segregation
regime
below the order-disorder transition temperature. The deviation
from
perfect lamellar shape is calculated for phases which are perpendicular
and
parallel to the walls. We examine the undulations of the inter
material
dividing surface and its angle with the walls, and find that the
deviation from
its unperturbed position can be much larger than in the strong
segregation
case. Evaluating the weak segregation stability of the lamellar
phases, a
surface interaction, which is quadratic in the monomer concentration,
favors
the perpendicular lamellar phase. In particular, the degeneracy
between
perpendicular and unfrustrated parallel lamellar phases for walls
without a
preferential adsorption is removed.
101. Ordered
morphologies of
confined diblock copolymers.
Tsori, Y.; Andelman,
D.
Materials Research Society Symposium
Proceedings
(2001), 651 (Dynamics in Small Confining Systems V),
T8.1.1-T8.1.11.
http://arxiv.org/abs/cond-mat/0101022
Abstract: We
study the ordered morphologies occurring in thin-films diblock
copolymer.
For temperatures above the order-disorder transition and for an
arbitrary
two-dimensional surface pattern, we use a Ginzburg-Landau expansion of
the free
energy to obtain a linear response description of the copolymer
melt. The
ordering in the directions perpendicular and parallel to the surface are
coupled. Three dimensional structures existing when a melt is
confined
between two surfaces are examined. Below the order-disorder
transition we
find tilted lamellar phases in the presence of striped surface
fields.
100. Adsorbed and grafted
polymers at equilibrium.
Netz, R.
R.;
Andelman, D.
Surfactant Science
Series (2001), 103 (Oxide Surfaces), 115-155.
http://arxiv.org/abs/cond-mat/0002266
Abstract: A
review with refs. is given on the basic
mechanisms
underlying adsorption of long-chain molecules on solid surfaces such as
oxides
with focus on the physical aspects of adsorption. The main
theories are
summarized. It is detailed how concepts taken from statistical
thermodynamics and interfacial science can explain general and universal
features of polymer adsorption. The following sections (and
topics) are
discussed: introduction (types of polymers, solvent conditions,
adsorption and
depletion, surface-polymer interactions, surface characteristics, and
polymer
physics), single-chain adsorption (mean-field and fluctuation-dominated
regime), polymer adsorption from solution (the mean-field approach,
beyond
mean-field theory, proximal region corrections, and loops and tails),
interaction between 2 adsorbed layers, adsorption of polyelectrolytes,
polymer
adsorption on heterogeneous surfaces, polymer adsorption on curved
interfaces
and fluctuating membranes, and terminally attached chains (grafted
polymer
layer and solvent, substrate, and charge effects on polymer
grafting).
99. Supported membranes on
chemically structured and rough surfaces.
Swain, P. S.; Andelman, D.
Physical Review E: Statistical, Nonlinear, and
Soft
Matter Physics (2001), 63(5-1),
051911/1-051911/12.
http://arxiv.org/abs/cond-mat/0009224
Abstract: We
present a general linear response description of membrane adhesion at
rough or chemical
structured surfaces. Our method accounts for nonlocal Van der
Waals
effects and contains the more approx. (and local) Deryagin approach in a
simple
limit. Specializing to supported membranes we consider the effects
of
substrate structure on the membrane adhesion energy and configuration.
Adhesion is usually less favorable for rough substrates and the
membrane
shape tends to follow that of the surface contours. Chemical
patterning
(described by a spatially varying Van der Waals force), however, favors
adhesion with the membrane configuration being out of phase with the
surface
structure. Finally, considering a surface indented with
"V"-shaped trenches, we show that our approach is in good
agreement
with an exact numerical solution
98.
Surface induced ordering in thin film diblock copolymers: Tilted
lamellar
phases.
Tsori, Y.; Andelman,
D.
Journal of Chemical Physics (2001),
115(4), 1970-1978.
http://arxiv.org/abs/cond-mat/0103250
Abstract: We
investigate the effect of chemical patterned surfaces on the
morphological of
diblock copolymers below the order-disorder transition. Profiles
for
lamellar phases in contact with one surface, or confined between two
surfaces
are obtained in the weak segregation limit using a Ginzburg-Landau
expansion of
the free energy, and treating it with mean-field theory. The
periodically
patterned surface induces a tilt of the lamellae in order to match the
surface
periodicity. The lamellae relax from the constrained periodicity
close to
the surface to the bulk periodicity far from it. The phases we
investigate are a generalization to the mixed (perpendicular and
parallel to
the surface) lamellar phases occurring when the two surfaces are
homogeneous. A special case when the surface pattern has a period
equal
to the bulk lamellar period showing "T-junction" morphological
is
examined. Our analytic calculation agrees with previous computer
simulations and SCF theories.
97. Diblock Copolymer
Ordering
Induced by Patterned Surfaces above the Order-Disorder Transition.
Tsori, Y.; Andelman, D.
Macromolecules (2001), 34(8),
2719-2727.
http://arxiv.org/abs/cond-mat/0007055
Abstract: We
investigate the morphological of diblock copolymers in the vicinity of
flat, chemical
patterned surfaces. We use a Ginzburg-Landau free energy to
describe the
spatial variations of the order parameter in terms of a general
two-dimensional
surface pattern above the order-disorder transition. The
propagation of
several surface patterns into the bulk is investigated. The
oscillation
period and decay length of the surface Fourier modes are calculated in
terms of
system parameters. We show that two parallel surfaces having
simple
one-dimensional patterns can induce a complex three-dimensional
copolymer
structure between them. Lateral order is observed parallel to a
patterned
surface as a result of order perpendicular to the surface.
Surfaces which
have a finite chemical pattern size (e.g., a stripe of finite width)
induce
lamellar ordering extending into the bulk. Close to the surface
pattern
the lamellae are strongly perturbed as they try to adjust to the surface
pattern.
96.
Discrete aqueous solvent effects and possible attractive
forces.
Burak, Y.; Andelman,
D.
Journal of Chemical Physics (2001),
114(7), 3271-3283.
http://arxiv.org/abs/cond-mat/0007035
Abstract: We
study discrete solvent effects on the interaction of two parallel
charged
surfaces in ionic aqueous solution. These effects are taken into
account
by adding a bilinear nonlocal term to the free energy of
Poisson-Boltzmann
theory. We study numerically the density profile of ions between
the two
plates, and the resulting interplate pressure. At large plate
separations
the two plates are decoupled and the ion distribution can be
characterized by
an effective Poisson-Boltzmann charge that is smaller than the nominal
charge. The pressure is thus reduced relative to Poisson-Boltzmann
predictions. At plate separations below approximately 20 Angstroms
the
pressure is modified considerably, due to the solvent mediated
short-range
attraction between ions in the system. For high surface charges
this
contribution can overcome the mean-field repulsion giving rise to a net
attraction between the plates.
95.
Kinetics of surfactant adsorption: the free energy approach.
Diamant,
H.;
Ariel, G.; Andelman, D.
Colloids and Surfaces, A: Physicochemical and
Engineering Aspects (2001), 183-185 259-276.
http://arxiv.org/abs/cond-mat/0007146
Abstract: A
review with 48 refs. We review the free energy approach to the
kinetics
of surfactant adsorption at fluid-fluid interfaces. The formalism
is
applied to several systems. For non-ionic surfactant solutions,
the
results coincide with earlier models while indicating their limits of
validity. We study the case of surfactant mixtures, focusing on
the
relation between the mixture kinetics and the properties of its
individual
constituents. Strong electrostatic interactions in salt-free ionic
surfactant solutions drastically modify the adsorption kinetics.
In this
case the theory accounts for experimental results, which could not be
earlier
understood. The effect of screening by added salt is studied as
well. Our theoretical predictions are compared with available
experiments
94.
Diblock copolymer ordering induced by patterned surfaces.
Tsori, Y.; Andelman, D.
Europhysics Letters (2001),
53(6),
722-728.
http://arxiv.org/abs/cond-mat/0007056
Abstract: We
use a Ginzburg-Landau free-energy functional to investigate diblock
copolymer
morphologies when the copolymer melt interacts with one surface or is
confined
between two chemical patterned surfaces. For temperatures above
the
order-disorder transition a complete linear response description of the
copolymer melt is given, in terms of an arbitrary two-dimensional
surface
pattern. The appearance of order in the direction parallel to the
surface
is found as a result of the order in the perpendicular direction.
Below
the order-disorder transition and in a thin-film geometry, our procedure
enables an analytic calculation of distorted perpendicular and tilted
lamellar
phases in the presence of uniform or striped surface
fields.
93.
Polyelectrolyte adsorption.
Andelman, D.; Joanny,
J.-F.
Comptes Rendus de
l'Academie des Sciences, Serie IV: Physique, Astrophysique
(2000),
1(9), 1153-1162.
http://arxiv.org/abs/cond-mat/0011072
Abstract: The
problem of charged polymer chains (polyelectrolytes) as they adsorb on a
planar
surface is addressed theoretical We review with 27 refs basic
mechanisms
and theory underlying polyelectrolyte adsorption on a single surface in
two
situations: adsorption of a single charged chain, and adsorption from a
bulk
solution in
solvent conditions. The behavior of flexible and semi-rigid chains
is
discussed sep. and is expressed as function of the polymer and surface
charges,
ionic strength of the solution and polymer bulk concentration. We
mainly
review mean-field results and briefly comment about fluctuation
effects. The
phenomenon of polyelectrolyte adsorption on a planar surface as
presented here
is of relevance to the stabilization of colloidal suspensions. In
this
respect we also mention Calculations of the inter-plate force between
two
planar surfaces in presence of polyelectrolyte. Finally, we
comment on
the problem of charge overcompensation and its implication to
multi-layers
formation of alternating pos. and neg. polyelectrolytes on planar
surfaces and
colloidal particles.
92. Polyelectrolyte
titration:
theory and experiment.
Borukhov, I.; Andelman, D.; Borrega, R.; Cloitre,
M.;
Leibler, L.; Orland, H.
Journal of Physical Chemistry B
(2000),
104(47), 11027-11034.
http://arxiv.org/abs/cond-mat/0005306
Abstract: Titration
of methacrylic acid/ethyl acrylate copolymers is studied experimental
and
theoretical. At low NaCl concentrations, this polyacid exhibits a
plateau
in the titration curve below the neutralization point. The plateau
has
often been attributed to a first-order phase transition associated with
polymer
conformational changes. We argue that the specific shape of
titration
curves of hydrophobic polyelectrolytes is due to electrostatics and does
not
necessarily require a conformation change of the polyelectrolyte
chains.
We calc. the free energy at the mean-field level and its first-order
(one loop)
correction using a loop expansion. The latter is dominated by
Debye-Hueckel-like charge-charge correlations as well as by correlations
between dissociation sites along the polymer chain. We show that
the
one-loop corrections to the free energy lead to titration curves that
agree
with experiments In particular, the model explains the decrease of
the pH
at the plateau when the polymer concentration is increased or when salt
is
added to the solution.
91.
Hydration interactions: Aqueous solvent effects in electric double
layers.
Burak,
Y.;
Andelman, D.
Physical Review E:
Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary
Topics (2000), 62(4-B), 5296-5312.
http://arxiv.org/abs/cond-mat/0004098
Abstract: A
model for ionic solutions with an attractive short-range pair
interaction
between the ions is presented. The short-range interaction is
accounted
for by adding a quadratic nonlocal term to the Poisson-Boltzmann free
energy. The model is used to study solvent effects in a planar
elec.
double layer. The counterion density increases near the charged
surface,
as compared with the Poisson-Boltzmann theory, and to decrease at larger
distances. The ion density profile is studied analysis in the case
where
the ion distribution near the plate is dominated only by
counterions.
Further away from the plate the density distribution can be described
using a
Poisson-Boltzmann theory, with an effective surface charge that is
smaller than
the actual one.
90.
Adhesion-induced lateral phase separation in membranes.
Komura, S.; Andelman,
D.
European Physical Journal E: Soft Matter
(2000), 3(3), 259-271.
http://arxiv.org/abs/cond-mat/0001164
Abstract: Adhesion
between membranes is studied using a phenomenological model, where the
intermembrane distance is coupled to the concentration of sticker
molecules on
the membranes. The model applies to both adhesion of two flexible
membranes and to adhesion of one flexible membrane onto a second
membrane
supported on a solid substrate. The authors mainly consider the
case
where the sticker molecules form bridges and adhere directly to both
membranes. The calculated mean-field phase diagrams show an upward
shift
of the transition temperature indicating that the lateral phase
separation in
the membrane is enhanced due to the coupling effect. Hence the
possibility of adhesion-induced lateral phase separation is
predicted.
For a particular choice of the parameters, the model exhibits a
tricritical
behavior. The authors also discuss the non-monotonous shape of the
inter-membrane distance occurring when the lateral phase separation
takes
place. The inter-membrane distance relaxes to the bulk values with
two
sym. overshoots. Adhesion mediated by other types of stickers is
also
considered..
89.
Adsorption of large ions from an electrolyte solution: a modified
Poisson-Boltzmann
equation.
Borukhov,
Electrochimica Acta (2000),
46(2-3),
221-229.
http://arxiv.org/abs/cond-mat/9911482
Abstract: The
behavior of electrolyte solutions close to a charged surface is studied
theoretical A modified Poisson-Boltzmann equation that takes into
account
the vol. excluded by the ions in addition to the electrostatic
interactions is
presented. In a formal lattice gas formalism the modified
Poisson-Boltzmann
equation can be obtained from a mean-field approximation of the
partition
function. In an alternative phenomenological approach, the same
equation
can be derived by including the entropy of the solvent molecules in the
free
energy. To visualize the effect of steric repulsion, a simple case
of a
single, highly charged, flat surface is discussed. This situation
resembles recent adsorption experiments of large ions onto a charged
monolayer. A simple criterion for the importance of the steric
effects is
expressed in terms of the surface charge density and the size of the
ions. When these effects are important a saturated layer is formed near the surface.
A
modified Grahame equation relating the ion concentration at the surface
to the
surface charge density is obtained.
88. Self-Assembly in
Mixtures of
Polymers and Small Associating Molecules.
Diamant, H.; Andelman,
D.
Macromolecules (2000),
33(21),
8050-8061.
http://arxiv.org/abs/cond-mat/9906271
Abstract: The
interaction between a flexible polymer in a good solvent and smaller
associating solute molecules such as amphiphiles (surfactants) is
considered
theoretical Attractive correlations, induced in the polymer
because of
the interaction, compete with intrachain
repulsion
and eventually drive a joint self-assembly of the two species,
accompanied by
partial collapse of the chain. Results of the analysis are found
to be in
good agreement with experiments on the onset of self-assembly in diverse
polymer-surfactant systems. The threshold concentration for
self-assembly
in the mixed system (critical aggregation concentration, cac) is always
lower
than the one in the polymer-free solution (critical micelle
concentration,
cmc). Several self-assembly regimes are distinguished, depending
on the
effective interaction between the two species. For strong
interaction,
corresponding experimental to oppositely charged species, the cac is
much lower
than the cmc. It increases with ionic strength and depends only
weakly on
polymer charge. For weak interaction, the cac is lower but
comparable to
the cmc, and the two are roughly proportional over a wide range of cmc
values. Association of small molecules with amphiphilic polymers
exhibiting intrachain aggregation (polysoaps) is gradual, having no sharp
onset.
87.
Binding of molecules to DNA and other semiflexible polymers.
Diamant, H.; Andelman,
D.
Physical Review E: Statistical Physics,
Plasmas,
Fluids, and Related Interdisciplinary Topics (2000),
61(6-B),
6740-6749.
http://arxiv.org/abs/cond-mat/9910162
Abstract: A
theory is presented for the binding of small molecules such as
surfactants to
semiflexible polymers. The persistence length is assumed to be
large
compared to the monomer size but much smaller than the total chain
length. Such polymers (e.g., DNA) represent an intermediate case
between
flexible polymers and stiff, rodlike ones, whose association with small
molecules was previously studied. The chains are not flexible
enough to
actively participate in the self-assembly, yet their fluctuations induce
long-range attractive interactions between bound molecules. In
cases
where the binding significantly affects the local chain stiffness, those
interactions lead to a very sharp, cooperative association. This
scenario is of
relevance to the association of DNA with surfactants and compact
proteins such
as RecA. External tension exerted on the chain is found to
significantly
modify the binding by suppressing the fluctuation-induced
interaction.
86.
Defects in lamellar diblock copolymers: Chevron- and Omega-shaped tilt
boundaries.
Tsori, Y.; Andelman, D.; Schick,
M
Physical Review E: Statistical Physics,
Plasmas,
Fluids, and Related Interdisciplinary Topics (2000),
61(3),
2848-2858.
http://arxiv.org/abs/cond-mat/9905378
Abstract: The
lamellar phase in diblock copolymer systems appears as a result of a
competition between mol. and entropic forces, which selects a preferred
periodicity of the lamellae. Grain boundaries are formed when 2
grains of
different orientations meet. The authors study the case where the
lamellae meet sym. with respect to the interface. The form of the
interface strongly depends on the angle, θ, between the normals of
the
grains. When this angle is small, the lamellae transform smoothly
from
one orientation to the other, creating the chevron morphological.
As θ
increases, a gradual transition is observed to an omega morphological
characterized by a protrusion of the lamellae along the interface
between the 2
phases. The authors present a theoretical approach to find these
tilt
boundaries in 2-dimensional systems, based on a Ginzburg-Landau
expansion of
the free energy, which describes the appearance of lamellae. Close
to the
tips at which lamellae from different grains meet, these lamellae are
distorted. To find this distortion for small angles, the authors
use a
phase variation ansatz which assumes that the wave vector of the bulk
lamellar
phase depends on the distance from the interface. Minimization of
the
free energy gives an expression for the order parameter φ(x,y). The results describe the chevron
morphological
very well. For larger angles, a different approach is used.
The
authors linearize φ around its bulk value φL
and expand the free energy to second order in their difference.
Minimization of the free energy results in a linear fourth-order
differential
equation for the distortion field, with proper constraints, similar to
the
Mathieu equation. The calculated monomer profile and line tension
agree
qualitative with transmission electron microscope experiments, and with
full
numerical solution of the same problem.
85. The Influence of
Substrate
Structure on Membrane Adhesion.
Swain, P. S.; Andelman,
D.
Langmuir
(1999), 15(26), 8902-8914.
http://arxiv.org/abs/cond-mat/9905205
Abstract: We
consider a membrane that adheres both weakly and strongly to a
geometrically structured
substrate. The interaction potential is assumed to be local, via
the
Deryagin approximation, and harmonic. Consequently, we can
analysis
describe a variety of different geometries; such as, smooth substrates
interrupted by an isolated cylindrical pit, a single elongated trench,
or a
periodic array of trenches. We present more general expressions
for the
adhesion energy and membrane configuration in Fourier space and find
that,
compared with planar surfaces, the adhesion energy decreases. We
also
highlight the possibility of overshoots occurring in the membrane
profile and
look at its degree of penetration into surface
indentations.
84. Kinetics of Surfactant
Adsorption at Fluid-Fluid Interfaces: Surfactant Mixtures.
Ariel,
G.;
Diamant, H.; Andelman, D.
Langmuir
(1999), 15(10), 3574-3581.
http://arxiv.org/abs/cond-mat/9903428
Abstract: The
adsorption at the interface between an aqueous solution of several
surface-active agents and another fluid (air or oil) phase is addressed
theoretical The kinetic equations from a variation of the
interfacial
free energy was derived and solved numerically, an analytic solution for
the
simple case of a linear adsorption isotherm was also provided.
Calculating asymptotic solutions analysis, the characteristic time
scales of
the adsorption process was found and the behavior of the system at
various
temporal stages was observed. In particular, the kinetic behavior
of the
mixture was related to the properties of its individual constituents and
find
good agreement with experiments In the case of kinetically limited
adsorption, the mixture kinetics is found to be considerably different
from
that of the single-surfactant solutions because of strong coupling
between the
species.
83.
Effect of Polyelectrolyte Adsorption on Intercolloidal
Forces.
Borukhov,
Journal of Physical Chemistry B
(1999),
103(24), 5042-5057.
http://arxiv.org/abs/cond-mat/9803324
Abstract: The
behavior of polyelectrolytes between charged surfaces immersed in
semidilute
solutions is investigated theoretical A continuum mean field
approach is
used for calculating. numerically concentration
profiles between two electrodes held at a const. potential. A
generalized
contact theorem relates the intersurface
forces to
the concentration profiles. The numerical results show that
overcompensation of the surface charges by adsorbing polyelectrolytes
can lead
to effective attraction between equally charged surfaces. Simple
scaling
arguments enable us to characterize qualitative the intersurface
interactions as a function of the fraction of charged monomers p and the
salt
concentration cb. In the low-salt
regime, we
find strong repulsion at short distances, where the polymers are
depleted from
the intersurface gap, followed by strong
attraction
when the two adsorbed layers overlap. The magnitude of this
attraction
scales as p1/2 and its dominant length scale is proportional to a/p1/2,
where a is the monomer size. At larger distances, the
two
adsorbing surfaces interact via a weak electrostatic repulsion.
For
strong polyelectrolytes at high salt concentration, the polymer
contribution to
attraction at short distances scales as p/cb1/2 and the length scale is
proportional to sa2/p, where s-1
is the Debye-H.ovrddot.uckel screening
length.
For weak polyelectrolytes at high salt concentration, the interaction is
repulsive for all surface separations and decays exponentially with a
decay
length equal to s-1. The effect of
irreversible adsorption is discussed as well, and it is shown that intersurface attraction can be obtained in this case
as
well.
82.
Onset of self-assembly in polymer-surfactant systems.
Diamant, H.; Andelman,
D.
Europhysics Letters (1999),
48(2), 170-176.
http://arxiv.org/abs/cond-mat/9803050
Abstract: The
onset of self-assembly in a dilute aqueous solution containing a
flexible
polymer and surfactant was theoretical studied. Focusing on the
effect of
the surfactant on polymer conformation and using a conjecture of partial
collapse of the polymer at the onset of self-assembly, results are
obtained
which agree with known experimental observations, i.e.
polymer-surfactant
self-assembly always starts at a lower concentration (cac) than the one
required for surfactant-surfactant self-assembly (cmc); in charged
systems the
cac increases with salt concentration and is almost independent of
polymer
charge; and in weakly interacting systems the cac remains roughly
proportional
to the cmc over a wide range of cmc values. The special case of
amphiphilic side-chain polymers strongly supports the basic
conjecture. A
similarity is found between the partial collapse induced by the
surfactant and
general results concerning the effect of impurities on critical
phenomena.
81.
Monolayers of diblock copolymer at the air-water interface: the
attractive
monomer-surface case.
Faure, M. C.; Bassereau,
P.; Carignano, M. A.; Szleifer,
I.; Gallot, Y.; Andelman,
D.
European Physical Journal B: Condensed Matter
Physics (1998), 3(3), 365-375.
http://arxiv.org/abs/cond-mat/9706249
Abstract: The
surface pressure isotherms of copolymers of polystyrene-polyethylene
oxide
(PS-PEO) at the air-water interface were studied both experimental and
theoretical The SCMF (single chain mean-field) theory provides a
very
good agreement with the experiments for the entire range of surface
densities
and is consistent with the experiments if an adsorption energy per PEO
monomer
at the air-water interface of about one kBT is
taken. In addition, the chain density profile was calculated for a
variety of surface densities, from the dilute to the very dense
ones. The
SCMF approach was complemented by a mean-field approach in the low
density
regime, where the PEO chains act as a 2-dimensional layer. Both
theoretical Calculations agree with the experiments in this
region.
80.
Random polyelectrolytes and polyampholytes in
solution.
Borukhov,
European Physical Journal B: Condensed Matter
Physics (1998), 5(4), 869-880; (1998),
6(2), 293
[Erratum].
http://arxiv.org/abs/cond-mat/9804304
Abstract: The
behavior of polyelectrolytes and polyampholytes in semi-dilute solutions
is
studied theoretical Various statistical charge distribution models
along
the polyelectrolyte chains were considered, i.e: (I)
smeared, where the charges are uniformly distributed along the chain;
(II)
annealed, where the charges are allowed to associate and dissociate from
the
chain; (III) permuted, where the total number of charges on the chain is
fixed,
but the charges can move along the chain; (IV) quenched, where the
charges on the chains are frozen in a random configuration;
and (V)
polyampholytes, where each monomer can be pos. or neg. charged, or
neutral. A path integral formulation was used to derive mean field
free
energies for the different models. An SCF equation is obtained for
the
polymer order parameter and a Poisson-Boltzmann like equation for the
electrostatic potential. The difference between the permuted and
the
smeared models is a const. shift in the chemical potential leading to
similar
mean field equations. Within the mean-field the quenched model is
equiv.
to the annealed one, provided that the system is coupled to a reservoir
of
polyelectrolyte chains. The RPA was used to calc. the
monomer-monomer
structure factor S(q) for the different statistical charge distribution
models. In the annealed model, fluctuations of the monomer charges
contribute to the electrostatic screening in addition to the free ions
in the
solution The strength of this screening
depends
on the variance of the monomer charge distribution and is esp. important
for
polyampholytes in bad solvent conditions where the mesophase separation
is
enhanced. The ratio between the variance and the net average
charge determines
whether polyampholytes behave more as polyelectrolytes
or as neutral chains.
79.
Interfaces and grain boundaries of lamellar phases.
Villain-Guillot,
S.; Netz, R. R.; Andelman, D.; Schick, M.
Physica A: Statistical and Theoretical Physics
(
http://arxiv.org/abs/cond-mat/9803288
Abstract: Interfaces
between lamellar and disordered phases, and grain boundaries within
lamellar
phases, are investigated employing a simple Landau free energy
functional. The former are examined using analytic, approx.
methods in
the weak segregation limit, leading to density profiles which can extend
over
many wavelengths of the lamellar phase. The latter are studied
numerically and exactly. A change from smooth chevron
configurations
typical of small tilt angles to distorted omega configurations at large
tilt
angles were found in agreement with experiment.
78. Scaling laws of
polyelectrolyte adsorption; [see also Erratum]
Borukhov,
Macromolecules
(1998),
31(5), 1665-1671; 31(5), 1704
[Erratum].
http://arxiv.org/abs/cond-mat/9706090
Abstract: Adsorption
of charged polymers (polyelectrolytes) from a semidilute solution to a
charged
surface was investigated theoretical We obtained simple scaling
laws for
(a) the amt. of polymer adsorbed to the surface
and (b)
the width D of the adsorbed layer, as a function of the fractional
charge per
monomer p and the salt concentration cb.
For
strongly charged polyelectrolytes (p .ltorsim.
1) in
a low-salt solution, both and D scale as
p-1/2. In
high-salt solutions D .apprx. cb1/2/p
whereas the scaling behavior of
depends on
the strength of the polymer charge. For weak polyelectrolytes (p
.mchlt. 1) we find that
.apprx. p/cb1/2, and for
strong
polyelectrolytes .apprx.
cb1/2/p. Our results are in good
agreement with
adsorption experiments and with numerical solutions of mean-field
equations.
77.
The lamellar-disorder interface: one-dimensional modulated
profiles.
Villain-Guillot,
S.; Andelman, D.
European Physical Journal B: Condensed Matter
Physics (1998), 4(1), 95-101.
http://arxiv.org/abs/cond-mat/9803247
Abstract: We
study interfacial behavior of a lamellar (stripe) phase coexisting with
a
disordered phase. Systematic analysis expansions are obtained for
the
interfacial profile in the vicinity of a tricritical point. They
are
characterized by a wide interfacial region involving a large number of
lamellae. Our analysis results apply to systems with
one dimensional symmetry in true thermodynamical equilibrium and
are of
relevance to metastable interfaces between lamellar and disordered
phases in
two and three dimensions. In addition, good agreement is found
with
numerical minimization schemes of the full free energy functional having
the
same one dimensional symmetry. The interfacial energy for the
lamellar to
disordered transition is obtained in accord with mean field scaling laws
of
tricritical points.
76.
Steric effects in electrolytes: a modified Poisson-Boltzmann
equation.
Borukhov,
Physical Review Letters (1997),
79(3), 435-438.
http://arxiv.org/abs/cond-mat/9803258
Abstract: The of
large ions from solution to a charged surface is investigated
theoretical
A generalized Poisson-Boltzmann equation which takes into account the
finite
size of the ions is presented. We obtain analysis expressions for
the
electrostatic potential and ion concentrations at the surface, leading
to a
modified Grahame equation. At high surface charge densities the
ionic
concentration sats. to its
max. value. Our results are in agreement
with
recent experiments
75.
Interfaces of modulated phases.
Netz, R. R.; Andelman, D.; Schick,
M.
Physical Review Letters (1997),
79(6), 1058-1061.
http://arxiv.org/abs/cond-mat/9803260
Abstract: Numerically
minimizing a continuous free-energy functional which yields several
modulated
phases, we obtain the order-parameter profiles and interfacial free
energies of
sym. and nonsym. tilt
boundaries within the lamellar phase, and of interfaces between
coexisting
lamellar, hexagonal, and disordered phases. Our findings agree
well with
chevron, omega, and T-junction tilt-boundary morphologies observed in
diblock
copolymers and magnetic garnet films.
74.
Adsorption kinetics of surfactants at fluid-fluid
interfaces.
Diamant, H.; Andelman,
D.
Progress in Colloid & Polymer Science
(1997), 103 (Amphiphiles at Interfaces), 51-59.
http://arxiv.org/abs/cond-mat/9803366
Abstract: A
review, with 32 refs. on the authors'
theoretical
approach to the kinetics of surfactant adsorption at fluid-fluid
interfaces. It yielded a more complete description of the kinetics
both
in the aqueous solution and at the interface, deriving all equations
from a
free energy functional. It also provided a general method to calc.
dynamic surface tensions. For nonionic surfactants, the results
coincided
with previous models. Nonionic surfactants usually undergo
diffusion-limited adsorption, in agreement with the experiments
Strong
electrostatic interactions in salt-free ionic surfactant solutions led
to
kinetically limited adsorption. In this case, the theory accounted
for
unusual experimental results which were not understood using previous
approaches. When salt was added, the electrostatic interactions
were
screened and the ionic surfactant adsorption became similar to the
nonionic
case. The departure from the nonionic behavior as the salt
concentration
was decreased was calculated
perturbatively.
73.
Shape of Phospholipid/Surfactant Mixed Micelles: Cylinders or Disks?
Theoretical Analysis.
Kozlov, M. M.; Lichtenberg, D.; Andelman,
D.
Journal of Physical Chemistry B
(1997),
101(33), 6600-6606
http://arxiv.org/abs/cond-mat/9803259
Abstract: We
develop a theoretical model for the solubilization of phospholipid
bilayers by
micelle-forming surfactants. Cylindrical micelles, disk-like
micelles,
and spherical micelles are considered as alternative resultant
structures. The main question addressed is, what kind of micelles
can be
expected under various thermodynamical conditions. Our analysis is
based
on a theoretical model that accounts for Helfrich energy of curvature of
amphiphile monolayers and for the entropy of mixing of lipids and
surfactants
in mixed aggregates. We conclude that for usual values of the
elastic
parameters of amphiphile monolayers cylindrical micelles are the most
probable
aggregates resulting from micellization of phospholipid by
surfactants.
This conclusion is consistent with available experimental data.
Conditions of formation of disk-like and spherical micelles are also
determined.
72. Roughness-induced
wetting.
Netz, R. R.;
Andelman,
D.
Physical Review E:
Statistical
Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
(1997), 55(1-B), 687-700.
http://arxiv.org/abs/cond-mat/9803261
Abstract: The
authors study theoretical the possibility of a wetting transition
induced by
geometric roughness of a solid substrate for the case where the flat
substrate
does not show a wetting layer. Their approach makes use of a
closed-form
expression that relates the interaction between 2 sinusoidally modulated
interfaces to the interaction between 2 flat interfaces. Within
the
harmonic approximation, the authors find that roughness-induced wetting
is
indeed possible if the substrate roughness (quantified by the substrate
surface
area) exceeds a certain threshold. In addition, the mol.
interactions
between the substrate and the wetting substance have to satisfy several
conditions. These results are expressed in terms of a lower bound
on th wetting potential for a
flat
substrate in order for roughness-induced wetting to occur. This
lower
bound has the following properties. A min. is present at zero or
very
small separation between the 2 interfaces, as characteristic for the
non-wetting
situation in the flat case. Most importantly, the wetting
potential needs
to have a pronounced max. at a separation
comparable
to the amplitude of the substrate roughness. These results are in
agreement with the experimental observation of roughness-induced surface
pre-melting
at a glass-ice interface as well as the calculation of the dispersion
interaction for the corresponding glass-water-ice
system.
71.
Theory and Phenomenology of Mixed Amphiphilic Aggregates.
M. M. Kozlov
and D.
Andelman,
Curr. Opin.
Colloid Interface Sci. 1, 362-366 (1996)
http://arxiv.org/abs/cond-mat/9803264
Abstract: We give a short overview of existing approaches
describing shapes and energetics of
amphiphilic
aggregates. In particular, we consider recent experimental data and
theory in
relation to mixed aggregates. We point out the outstanding questions
deserving
further investigations such as stability of single-component vesicles
and size
growth of mixed vesicles induced by micelle-forming
surfactants.
70.
Kinetics of Surfactant Adsorption at Fluid-Fluid
Interfaces.
Diamant, H.; Andelman,
D.
Journal of Physical Chemistry
(1996),
100(32), 13732-13742.
http://arxiv.org/abs/cond-mat/9608140
Abstract: The
authors present a theory for the kinetics of surfactant adsorption at
the
interface between an aqueous solution and another fluid (air, oil)
phase.
The model relies on a free-energy formulation and describes both the
diffusive
transport of surfactant molecules from the bulk solution to the
interface and
the kinetics taking place at the interface itself. When applied to
nonionic surfactant systems, the theory recovers results of previous
models,
justifies their assumptions, and predicts a diffusion-limited
adsorption, in
accord with experiments Electrostatic interactions are shown to
affect
drastically the kinetics for salt-free ionic surfactant solutions
The
adsorption in this case is predicted to be limited kinetically, and the
theory
accounts for unusual experimental results obtained recently for the
dynamic
surface tension of such systems. Addition of salt to an ionic
surfactant
solution leads to screening of the electrostatic interactions and to a
diffusion-limited adsorption. In addition, the free-energy
formulation
offers a general method for relating the dynamic surface tension to
surface
coverage. Unlike previous models, it does not rely on equilibrium
relations which are shown in some cases to be invalid out of
equilibrium
69. Structures with motif-forming
surfaces
may sometimes have a very simple explanation.
Andelman, D.
La Recherche
(1996), (284), 41-3. (written
in French)
Abstract: Motif-forming
structures, such as magnetic surfaces, are explained as the result of a
competition between 2 antagonistic forces.
68.
Global Phase Diagrams of Mixed Surfactant-Polymer Systems at
Interfaces.
Chatellier, X.; Andelman, D.
Journal of Physical Chemistry
(1996),
100(22), 9444-9455.
http://arxiv.org/abs/cond-mat/9803263
Abstract: Insoluble
surfactant monolayers at the air/water interface undergo a phase
transition
from a high-temperature homogeneous state to a low-temperature demixed
state,
where dilute and dense phases coexist. Alternatively, the
transition from
a dilute phase to a dense one may be induced by compressing the
monolayer at
const. temperature. The case where the insoluble surfactant monolayer
interacts
with a semidilute polymer solution solubilized in the water subphase is
considered. The phase diagrams of the mixed surfactant/polymer
system are
investigated within the framework of mean field theory. The
polymer
enhances the fluctuations of the monolayer and induces an upward shift
of the critical
temperature. The critical concentration
is
increased if the monomers are more attracted (or at least less repelled)
by the
surfactant molecules than by the bare water/air interface. In the
case
where the monomers are repelled by the bare interface but attracted by
the
surfactant molecules (or vice versa), the phase diagram may have a
triple
point. The location of the polymer special transition line appears
to
have a big effect on the phase diagram of the surfactant
monolayer.
67.
Protein adsorption on lipid monolayers at their coexistence
region.
Netz, R. R.; Andelman, D.; Orland,
H.
Journal de
Physique
II (1996), 6(7), 1023-1047.
http://arxiv.org/abs/cond-mat/9803262
Abstract: The
authors investigate theoretical the behavior of proteins as well as
other large
macromolecules which are incorporated into amphiphilic monolayers at the
air-water interface. The authors assume the monolayer to be in the
coexistence region of the "main" transition, where domains of
the
liquid condensed phase coexist with the liquid expanded
background. Using
a simple mean-field free energy accounting for the interactions between
proteins and amphiphilic molecules, the authors obtain the spatial
protein
distribution with the following characteristics. When the proteins
preferentially interact with either the liquid condensed or liquid
expanded domains,
they will be dissolved in the respective phase. When the proteins
are
energetically rather indifferent to the density of the amphiphiles, they
will
be localized at the line boundary between the (two-dimensional) liquid
expanded
and condensed phases. In between these two limiting cases, a
delocalization transition of the proteins takes place. This
transition is
accessible by changing the temperature or the amt. of incorporated
protein. These findings are in agreement with recent fluorescence
microscopy
experiments. The authors' results also apply to lipid multicomponent
membranes showing coexistence of distinct fluid
phases.
66.
Kinetics of surfactant adsorption at fluid/fluid interfaces: non-ionic
surfactants.
Diamant, H.; Andelman,
D.
Europhysics Letters (1996),
34(8),
575-580.
http://arxiv.org/abs/cond-mat/9803320
Abstract: The
authors present a model treating the kinetics of adsorption of sol.
surface-active molecules at the interface between an aqueous solution
and
another fluid phase. The model accounts for both the diffusive
transport
inside the solution and the kinetics taking place at the interface by
using a
free-energy formulation. In addition, it offers a general method
of calculating
dynamic surface tensions. Non-ionic surfactants are shown (in
general) to
undergo a diffusion-limited adsorption (in accord with experimental
results).
65.
Hydrodynamic mapping of two-dimensional electric fields in
monolayers.
Nassoy, P.; Birch, W.
R.; Andelman, D.; Rondelez, F.
Physical Review Letters (1996),
76(3), 455-8.
Abstract: We
have measured the 2D dipolar elec. fields generated by surface density
fluctuations in Langmuir monolayers using optical microscopy to monitor
the
motion of micron-size, elec. charged, particles trapped at the air-water
interface. The particle velocity is directly proportional to the
local
electric field gradient. Quantitative agreement with the theory is
demonstrated for charged polystyrene latex particles interacting with
liquid
condensed domains of pentadecanoic acid. Typical velocities are of
order
0.1-10 μm/s, corresponding to forces in
the 10-15-10-12
N range.
64. Adsorption of polymer solutions
on
surfactant monolayers: global phase diagrams.
Chatellier, X.; Andelman, D.
Europhysics Letters (1995),
32(7),
567-72.
Abstract: The
phase diagram of insoluble surfactant monolayers at the air/water
interface is
affected by the addition of polymer in the water subphase. The
case of a
condensation transition is investigated within the framework of a
mean-field
theory. The interaction of the polymer with the interface leads to
an
upward shift of the critical temperature and of the critical
concentration (if
the monomers are more attracted by the surfactant molecules than by the
bare
interface). In some situations, the phase diagram can display a
triple
point.
63. Polyelectrolyte
solutions
between charged surfaces. + (figures)
Borukhov,
Europhysics Letters (1995),
32(6),
499-504.
Abstract: The
effect of electrostatic interactions on the distribution of polymers in
a good
solvent is investigated theoretical for semi-dilute solutions containing
charged polymers (polyelectrolytes) and small ions. A mean field
approach
is used to derive two coupled differential equations: a modified
Poisson-Boltzmann equation for the electrostatic potential, and a SCF
equation
for the polymer order parameter. We compare several monomer charge
distributions;
smeared, annealed and quenched. The polymers are confined between
two
charged surfaces, and are in contact with a reservoir of polymers and
electrolyte. This makes the annealed and quenched cases
equiv.
Non-monotonous profiles are obtained for the case of competing surface
interactions: electrostatic adsorption vs. short-range
desorption.
62. Dimeric
surfactants: a
simplified model for the spacer chain. + (figures)
Diamant, H.; Andelman,
D.
Langmuir (1995), 11(9),
3605-6.
Abstract: We
present her a further simplification of our theoretical model regarding
the
interfacial behavior of dimeric surfactants. The spacer chain is
modeled
by an analogous "entropic" spring, the parameters of which are
given
by computer simulations. The spacer contribution may then be
easily
combined with other contributions to account for properties of the
dimeric
surfactant. We give an example for such a scheme by considering
the
interplay between the spacer contribution and the interaction between
two
monomers within a single dimer. The resulting dependence of the
inter-monomeric
distance on the spacer carbon number agrees with experimental
findings.
61.
Polyelectrolyte solutions between two charged
surfaces.
Borukhov,
Proceedings of the Rencontre
de Moriond (1995), 30th
(Short
and Long Chains at Interfaces), 13-20.
Abstract: We
investigate the distribution of polyelectrolytes in solution between two
charged walls. Such a situation arises, for example, in colloidal
suspensions where the polyelectrolytes affect both the aggregation and
the
stability of the colloidal particles. We consider the case of a
good
solvent, i.e. in the presence of excluded vol. interactions among the
monomers. The system is confined between two infinite flat charged
walls,
making the problem effectively one dimensional. The
polyelectrolytes are
weakly charged, and several models for the charge distribution are
considered. We use a mean field approach to derive two coupled
differential equations: a modified Poisson-Boltzmann equation for the
electrostatic
potential, and a self consistent field equation for the polymer
concentration.
The equations are solved numerically. As
an
example we present a case of competing surface interactions:
electrostatic
attraction vs. chemical repulsion resulting in a non-monotonic
concentration
profile. We discuss also the difference between a polymer with a
uniform
"smeared" charge and one in which the charges are annealed and
can
redistribute themselves at thermodynamical
equilibrium
60. The Vesicle-Micelle Transition
in Mixed
Lipid-Surfactant Systems: A Molecular Model.
Fattal, D. R.; Andelman, D.;
Ben-Shaul,
A.
Langmuir (1995), 11(4),
1154-61.
Abstract: A
mol. model is used to calc. the free energy of mixed vesicles and
cylindrical
micelles, composed of lipid molecules and short chain surfactants.
The
free energy of both aggregates (modeled as an infinite planar bilayer
and an
infinite cylindrical aggregate) is represented as a sum of internal free
energy
and mixing entropy contributions. The internal free energy is
treated as
a sum of chain (conformational), head group, and surface tension
terms. Calculating
the free energy of each aggregation geometry as
a
function of lipid/surfactant composition and using common tangent
construction
we obtain the compositions of the bilayer and the micelle at the phase
transition. By varying certain mol. parameters (such as the
"hard
core" area of the surfactant head group or the length of the
surfactant
tail) we study the role of molecular packing characteristics in
determining the
compositions at phase coexistence. We find, as expected, that upon
increasing the preference of the surfactant for the micellar geometry
(larger
spontaneous curvature) the bilayer is solubilized at lower
surfactant/lipid
concentration ratios. For some typical values of the parameters
used,
reasonable agreement with experimental results for mixtures of egg phosphatidylcholine and octylglucoside
is obtained.
59. Domain shapes and patterns: the
phenomenology of modulated phases.
Seul, M.; Andelman, D.
Science (Washington, D. C.) (1995),
267(5197), 476-83.
Abstract: A
review with 95 refs. A wide variety of two- and three-dimensional
physical-chemical
systems display domain patterns in equilibrium. The
phenomenological of these patterns, and of the shapes of their
constituent
domains, is reviewed here from a point of view that interprets these
patterns
as a manifestation of modulated phases. These phases are
stabilized by
competing interactions and are characterized by periodic spatial
variations of
the pertinent order parameter, the corresponding modulation period
generally
displaying a dependence on temperature and other external fields.
This
simple picture provides a unifying framework to account for striking and
substantial similarities revealed in the prevalent "stripe"
and
"bubble" morphologies as well as in commonly observed,
characteristic
domain-shape instabilities. Several areas of particular current
interest
are discussed.
58. Electrostatic
properties of
membranes: the Poisson-Boltzmann theory.
Andelman, D.
Handbook of Biological Physics
(1995),
1B 603-42.
Abstract: A
review with 67 refs. The review is organized in the following
manner. First some general considerations of charged surfaces in
liquids
and the deviation of the Poisson-Boltzmann equation. Then specific
solutions of several electrostatic problems starting with a single flat
and
rigid membrane and generalizing it to two flat membranes. Finally,
the
following situations are considered: a single membrane, two membranes
and a
stack of membranes.
57. Phase transitions and shapes of
two
component membranes and vesicles. II: weak segregation
limit.
Taniguchi, T.;
Journal de Physique II (1994),
4(8),
1333-62.
Abstract: We
investigate equilibrium shapes of vesicles composed of a mixture of
partially
miscible amphiphiles embedded in 2D and 3D space. The amphiphilic
molecules can diffuse within the membrane and undergo an intra-membrane
phase
separation below a critical temperature. We assume a simple
phenomenological
coupling between the local relative composition of the amphiphiles and
the
local curvature of the membrane shape. A linear stability analysis
in the
vicinity of the critical temperature indicates that a
shape
instability is induced by the coupling. Using a single mode
approximation, we obtained phase diagrams for: (i) two-dimensional
vesicles and
(ii) three-dimensional axisymmetrical
vesicles.
The equilibrium shape deformations are shown to depend on the
phenomenological
parameters of our model yielding highly non-trivial vesicle shapes which
deviate from spherical-like objects.
56. Dimeric
surfactants: spacer
chain conformation and specific area at the air/water interface.
Diamant,
H.;
Andelman, D.
Langmuir
(1994), 10(9), 2910-16.
Abstract: The
authors present a theoretical explanation for experimental results
obtained
recently regarding dimeric surfactants. The non-monotonic
dependence of
the specific area at the air/H2O interface on the spacer carbon number
is
accounted for. In addition, understanding the role of spacer
carbon
number at the air-H2O interface can help elucidate the shapes of
aggregates
formed in the aqueous solution The
attractive
and repulsive interactions of the surfactant molecules and the
conformational
entropy of the spacer chain are dominant factors in determining this
dependence. Hydrophobic repulsion of the spacer from the H2O
surface does
not seem to play an important role, if any, contrary to what was
previously
suggested.
55. Phase transitions
between
vesicles and micelles driven by competing curvatures.
Andelman, D.; Kozlov, M. M.;
Helfrich,
W.
Europhysics Letters (1994),
25(3),
231-6.
Abstract: The
authors present a model explaining the phase transition between
cylindrical
micelles and vesicles (bilayers) in a mixed dilute solution of
phospholipids
and surfactants. The model predicts a first-order transition
between
micelles and vesicles, which depends on the relative concentration of
the two
components. The phase transition boundaries are calculated as a
function
of the specific areas of the two components, their spontaneous
curvatures and
elastic moduli. The transition is driven by a very large
difference in
spontaneous curvatures between lipid and surfactant. The free
energy
takes into account the entropy of mixing as well as the curvature
energy.
The authors' predictions are in qualitative agreement with
experiments. For
mixtures of octyl glucoside
(surfactant) an phosphatidylcholine
(phospholipid), the authors obtain good agreement with experimental
data.
54. Structures and phase transitions
in
Langmuir monolayers.
Andelman, D.; Brochard,
F.; Knobler, C.; Rondelez,
F.
Micelles, Membr.,
Microemulsions, Monolayers (1994),
559-602.
Publisher: Springer,
Abstract: A
review with 103 refs. on 2-dimensional
phenomena of
adsorbed amphiphilic monolayers on liquid subphases, esp. insoluble
films such
as Langmuir monolayers.
53. Polymer adsorption at
liquid/air interfaces under lateral pressure. [see
also Erratum]
Aharonson, V.; Andelman, D.; Zilman, A.; Pincus, P. A.; Raphaeel, E.
Physica A: Statistical Mechanics and Its
Applications (
Abstract: We
present Calculations of surface tension of absorbed polymer solutions at
the
liquid/air interface. Lateral changes in the area per monomer on
the
surface are induced by changing the surface pressure (lateral
compression),
while keeping the total surface excess fixed. Lateral compression
of the
adsorbed layer immersed in a good solvent results in an increase in the
surface
monomer concentration and surface pressure up to a critical area per
monomer
value where the compressibility of the system vanishes. Our
mean-field
model is not appropriate to describe more compressed states.
Calculations
are repeated in theta and bad solvent conditions, and yield similar
behavior of
the isotherms.
52. Chiral discrimination in
solutions and
in Langmuir monolayers.
Andelman, D.; Orland, H.
Journal of the American Chemical Society
(1993), 115(26), 12322-9.
Abstract: In
this paper the authors examine theoretical the chiral discrimination of
molecules with a single chiral center. The authors propose a
definition
of the chiral discrimination parameter in
terms
of the difference between the second virial coefficient of pure
enantiomers and
their racemic mixture. This parameter
enters in
the equation of state of racemic mixtures and will determine their phase
diagrams. The authors calc. then the chiral discrimination between
D- and
L-alanine using a Monte Carlo simulation to average over 11 molecular
degrees
of freedom at fixed intermolecular distances using the CHARMM energy
function. The discrimination is found to slightly favor
homochirality and
mainly comes from steric hindrance at short distances. The authors
also
perform a direct integration for rigid chiral tetrahedron-shaped
molecules Here there are only five rotational degrees of
freedom.
For a Lennard-Jones potential, the overall chiral discrimination is
found to be
predominantly heterochiral. One of the authors' main observations
is that
the pair free energy, internal energy, and entropy differences between
the two
enantiomers may change signs as a function of the interpair
distance. The
authors find that homochirality is preferred at shorter distances
whereas
heterochirality is favored at larger distances. With the authors'
model
molecules a strong chiral discrimination of about 43% is found.
The
calculation is repeated for molecules that are restricted to lie
at the water/air interface. Those model molecules can be regarded
as
tripodal amphiphiles creating a chiral Langmuir monolayer at the
water/air
interface. Here the chiral discrimination is found to be smaller
(about
8.8%) but still significantly heterochiral.
51. Phase transitions and shapes of
two
component membranes and vesicles. I. Strong segregation
limit.
Kawakatsu, T.; Andelman, D.;
Journal de Physique II (1993),
3(7),
971-97.
Abstract: The
authors studied unilamellar membranes and vesicles composed of an A/B
mixture
of partially miscible amphiphiles. The authors show for
unilamellar
open-shape membranes that the competition between surface tension and
curvature
results in a phase with a selected periodicity (modulated phase) both in
the
shape and in the A/B composition assuming a simple bilinear coupling
between
relative composition and local curvature, and in the strong segregation
limit
of the A/B mixture The limits of large and small surface tension
are
discussed sep. These results extend previous results obtained
close to
the A/B critical point (shallow quench). The authors also studied
the
coupling between the separation of the system into A and B domains, and
the
overall shape of closed-shape vesicles for the same limit of strong
segregation.
Equilibrium shapes and phase diagrams are obtained for cylindrical
vesicles of
fixed overall area (or equivalently, vesicles embedded in a
2-dimensional
space). The authors also consider the effect of an added pressure
difference (osmotic pressure) across the vesicle. The results are
extended to axial sym. vesicles embedded in a 3-dimensional
space.
50. Electrostatic
interactions
in two-component membranes.
Guttman, G. D.; Andelman, D.
Journal de Physique II (1993),
3(9),
1411-25.
Abstract: The
effect of electrostatic interactions on membrane undulations is
examined
The authors consider a mixed membrane consisting of neutral and charged
amphiphiles in an aqueous solution In general, this system may
exhibit a
non-uniform surface charge density Two limiting cases are
distinguished:
quenched surface-charge distribution; and annealed in-plane distribution
which
is coupled to an undulation mode. For the former case the
electrostatic free
energy of an undulating membrane is calculated in the limit of strong
ionic
solution. Spatial modulations of the surface charge density induce a
local
spontaneous curvature in a single monolayer. In addition, the
electrostatic contribution to the elastic bending modulus is obtained
for a
general non-uniform surface-charge density. In the latter case of a
self-adjusting (annealed) membrane, an electrostatic coupling between
the
in-plane distribution and the membrane curvature produces an added
effective
interaction which stabilizes modulated
phases.
49. Two topics on phase separation
phenomena of amphiphilic systems.
Kawakatsu, T.;
KEK Proceedings (1993),
93-3(Proceedings
of the Workshop on Polymer Science Studied By Neutron Scattering,
1991),
3-5.
Abstract: A
review with 6 refs. discussed (1) equilibrium
shape of
2-component lamellar membranes and vesicles and (2) mol. dynamics
simulation of
phase separation processes of binary block copolymer
blends.
48. Polymer adsorption on
surfactant monolayers and heterogeneous solid surfaces.
Andelman, D.; Joanny,
J.-F.
Journal de Physique II (1993),
3(1),
121-38.
Abstract: Polymer
adsorption is studied on a flat but heterogeneous surface both when the
heterogeneity is quenched and when it is annealed. The
heterogeneity of
the adsorbing surface enhances the adsorption. Either sol.
surfactant
monolayers (at a fixed chemical potential) or insoluble monolayers (at a
fixed
concentration) are considered as examples of a surface with annealed
heterogeneity for attractive interactions between polymer and
surfactant.
Even if the monolayer is on average neutral for polymer adsorption, an
isolated
polymer chain adsorbs via a local increase of the surfactant surface
concentration. The adsorption of a polymer solution can induce phase
transitions in an insoluble monolayer that phase separates into dense
regions
where the polymer adsorbs and dilute regions from which the polymer is
depleted. Phase transitions induced by polymer adsorption can also
occur
for sol. monolayer. The authors calc. the
amt. of
adsorbed polymer as a function of the wavelength of the heterogeneity
for a
surface with periodic quenched
heterogeneities.
47. Equilibrium shape of
two-component
unilamellar membranes and vesicles.
Andelman, D.; Kawakatsu,
T.;
Europhysics Letters (1992),
19(1),
57-62.
Abstract: A
strong segregation of a 2-component surfactant system coupled to the
local
membrane curvature has a pronounced effect on the shape of unilamellar
or
closed vesicles. For an average flat lamella, the preferred
periodicity
in the local composition as well as the lamellar shape depends on the
ratio
between surface tension and bending modulus. In the case of a
closed
vesicle with a fixed total area, there is no selected periodicity in
contrast
to the unilamellar case. For vesicles subjected to pos. or neg.
inner pressure,
their shapes can be calculated numerically; in the absence of added
inner
pressure, the shape found analysis is composed of circular
sections.
46. Adsorption of polymer solutions
on
heterogeneous surfaces.
Joanny, J. F.; Andelman,
D.
Makromolekulare Chemie,
Macromolecular
Symposia (1992), 62 (Polym. Thermodyn. Radiat.
Scattering), 35-41.
Abstract: The
adsorption of polymer solutions on chemical heterogeneous surfaces is
discussed. Two types of heterogeneities are considered, annealed
and
quenched. In both cases, the disorder increases the
adsorption. For a same adsorption strength, the adsorbed amt. of
polymer is
higher on an annealed surface than on a quenched surface. The
adsorption
on an annealed surface can induce a 2-dimensional phase transition on
the
surface.
45. Thermal fluctuations
of
thin wetting films on disordered solids.
Harden, J. L.; Andelman,
D.
Langmuir (1992), 8(10),
2547-51.
Abstract: Thin
liquid layers which completely wet non-ideal (either rough or
heterogeneous in
composition) solid surfaces are considered. Two different sources
of
fluctuations of the liquid surface are identified, and the competition
between
them is examined. For thick enough films (but still in the
submicrometer
range), the liquid surface fluctuations are dominated by thermally
induced
capillary waves. For thin films, capillary waves are damped
strongly and
the liquid surface fluctuations are correlated with the disorder of the
underlying solid surface. The fluctuation spectrum is calculated
explicitly for a van der Waals liquid and for several different types of
solid
disorder. The results agree with recent x-ray specular reflection
and
diffuse scattering experiments
44. Membrane curvature
elasticity in weakly charged lamellar phases.
Harden, J. L.; Marques,
C.; Joanny, J.-F.; Andelman,
D.
Langmuir (1992), 8(4),
1170-5.
Abstract: The
effect of electrostatic interactions on the membrane bending energies
was
studied in weakly charged, swollen, lamellar phases of surfactant
solutions The surface charge density of the lamellae is treated as
a
const. and only situations where it is low enough so that the distance
2d
between lamellae is the smallest relevant length scale in the problem
are
considered. In the presence of salt (the short distance Debye-Hueckel regime), the electrostatic
contribution to
the bending energy of a membrane is in general small (in disagreement
with a
previous result), is proportional to d3, and is independent of ionic
strength. Identical results are obtained for membranes undulating
sinusoidally in phase and for concentric cylindrical membranes.
The
bending const. was also calculated for membranes held at const.
dielectric
potential and compared to the const. charge density case. In the
absence
of salt, continuity arguments predict an electrostatic contribution to
the
bending energy that scales as d3. A direct calculation for
concentric
cylindrical membranes gives exactly the same scaling behavior (including
the
numerical prefactor) as in the presence of
salt.
43. Spontaneous vesicle formation by
mixed
surfactants.
Safran, S. A.; MacKintosh,
F. C.; Pincus, P. A.; Andelman,
D.
Progress in Colloid & Polymer Science
(1991), 84 (Trends Colloid Interface Sci. 5), 3-7.
Abstract: Although
single surfactants rarely form vesicles spontaneously, mixtures of two
surfactants can lead to spontaneous vesicle formation. By
considering the
curvature elasticity of the surfactant bilayer, it was shown theoretical
how
the energetic stabilization of mixed vesicles can occur.
Interactions
between the two species (of the proper sign and magnitude) are crucial
to stabilizing
these vesicles. These interactions lead to composition asymmetries
and
effective spontaneous curvatures of the inner and outer layers that are
of
equal and opposite signs.
42. On
the adsorption of polymer solutions on random surfaces: the
annealed
case.
Andelman, D.; Joanny, J.-F.
Macromolecules (1991),
24(22),
6040-2.
Abstract: In
the adsorption of a semi-dilute polymer solution on chemical
heterogeneous
surfaces, the polymer profile equation in the presence of annealed
heterogeneities, i.e., impurities or surfactants in thermal equilibrium,
is
identical with the profile equation of polymers adsorbing on random
surfaces
proposed by T. Odijk (1990).
41. Stability and phase behavior of
mixed
surfactant vesicles.
Safran, S. A.; MacKintosh,
F. C.; Pincus, P. A.; Andelman, D.
A.
Surfactants in Solution (1991),
11
197-205.
Abstract: A
theoretical explanation is presented to show how the energetic
stabilization of
mixed vesicles can occur. Recent experiments have shown that
mixtures of
2 surfactants can exhibit spontaneous vesicle formation. The
surfactant
bilayer curvature elasticity and the interactions between the 2 types of
surfactants
(taking sign and magnitude into account) are discussed. The
interactions
lead to composition asymmetries and to effective spontaneous curvatures
of the
inner and outer layers that are equal but opposite in sign. The
stability
ranges predicted for various phases as a function of the 3
concentrations (of
the solvent (e.g., water) and of the 2 amphiphiles) agree qualitative
with
recent experimental data.
40.
Stability and phase behavior of mixed surfactant vesicles.
Safran, S. A.;
Pincus,
P. A.; Andelman, David; MacKintosh, F.
C
Physical Review A:
Atomic,
Molecular, and Optical Physics (1991), 43(2),
1071-8.
Abstract:
Although large, spherical
surfactant vesicles are generally unstable to either lamellar or
micellar
phases, mixts. of 2
surfactants can lead to spontaneous vesicle formation. It is shown
theor. how the energetic
stabilization of mixed vesicles can occur by considering the curvature
elasticity of the surfactant bilayer. Interactions between the 2
species
(of the proper sign and magnitude) are crucial to stabilizing these
vesicles. These interactions lead to compn. asymmetries and effective spontaneous curvatures of
the
inner and outer layers that are of equal and opposite signs. The
vesicles
have a Gaussian distribution about an average size determined. by the effective spontaneous curvature; the width of
the
distribution is calcd. as a
function of concn. The stability of
these
vesicles with respect to a flat lamellar phase is estd.
The predictions of the ranges of stability of the various phases as a
function
of the 3-concns. (solvent, e.g., water, and the
2
amphiphiles) are in qual. agreement with
recent expts.
39. Thin liquid films on rough or
heterogeneous
solids.
Robbins, M. O.; Andelman, D.; Joanny,
J.-F.
Physical Review A: Atomic, Molecular, and
Optical Physics (1991), 43(8), 4344-54.
Abstract: The
conformation of thin liquid films on rough or heterogeneous solid
substrates
was studied. The liquid-substrate interaction dominates for
sufficiently
thin films, and heterogeneity roughens the liquid interface. As
the film
thickens, surface tension becomes increasingly important, and the liquid
interface flattens. A general equation for the equilibrium
interface
shape is derived. Analytic results are obtained in the limit of
weak
disorder for rough or self-affine surfaces as well as chemical
heterogeneous
solids. The effect of disorder depends strongly on the wave
vector.
Fluctuations at scales smaller than the film thickness or a
"healing
length" produce little roughness. At larger
wavelengths, the
film conforms to the local fluctuations. Exact numerical solutions
of the
general equation are presented for surfaces with square grooves.
These
confirm the qualitative predictions of the analytic theory, and are in
quant.
agreement when the depth of the grooves is small. The variation of
roughness with film thickness, as well as the calculated adsorption
isotherms,
is compared to recent experimental results. Previously measured
isotherms
can be reproduced by corrugated surfaces with a single characteristic
length
scale, and do not necessarily imply that the surfaces studied were
self-similar.
Andelman,
David.
Physica A: Statistical
Mechanics
and Its Applications (
Abstract:
A review on chiral
discrimination theory for chiral mols. that form an insol.
Langmuir
monolayer on the water/air interface. For a specific type of model
mols. (tripod amphiphiles),
the
chiral discrimination is described for various types of intermol.
interactions (van der Waals, H bonding,
dipoles,
charges, etc.). In particular, van der Waals interactions prefer
chiral
segregation whereas electrostatic interactions prefer heterochiral compds. Monolayer phase diagrams are shown for
both
cases. 11 Refs.
37. Modulated
phases
in amphiphilic monolayers at the water/air interface.
Andelman,
David.
Materials Research
Society
Symposium Proceedings (1990), 177 (Macromol.
Liq.), 337-44.
Abstract:
Recently, modulated
phases of insol. monolayers of fatty acids and phospholipids
spread
on the water/air interface have been observed by fluorescence microscopy
expts. A theor.
explanation of this observation is made by including
electrostatic (dipolar) interactions in the total free energy calcn. for the
monolayer.
Dipoles can originate from 2 sources; neutral amphiphiles have a
permanent
dipole and charged amphiphiles have an induced one. Modulated
phases are
found to be stable in 2 different limits, close to the liq.-gas
transition and at low temps. Several phases with stripe and
hexagonal
symmetry are predicted and the phase transitions between them are calcd.
36. Theory of
spontaneous vesicle formation in surfactant mixtures.
Safran, S. A.;
Pincus,
P.; Andelman, David.
Science
(
Abstract:
The curvature elastic
energy of
bilayer vesicles formed by a mixt. of
two surfactants, which individually form either micelles or lamellar
bilayer
phases is described theor. In the limit
of
large bending elastic modulus being much greater than the temp. the free energy is minimized by vesicles with
different concns. of the two
surfactants in
each monolayer of the bilayer. Vesicles are more stable than
lamellar
structures only when interactions or complexing of
the two surfactants is taken into account.
35.
Electrostatic interactions, curvature elasticity, and steric repulsion
in multimembrane systems.
Pincus P.
Joanny J-F.
Andelman D.
Europhysics Letters,
vol.11,
no.8, 15 April 1990, pp.763-8.
Abstract
The effects of
electrostatic
interactions on steric repulsion and curvature elasticity are considered
for
dilute multimembrane systems as a function of
the
electrolyte strength, surface charge and inter-membrane spacing. In the
strong
electrolyte limit, the electrostatic interactions are screened and the
steric
repulsion dominates. For weak electrolytes, the electrostatic
interactions
cut-off the out-of-plane undulations and change significantly the
membrane
bending constant in qualitative agreement with recent experiments. (23
References).
34. Thermal
fluctuations and the structure of microemulsions
S. A. Safran,
D. Roux,
M. E. Cates, D. Andelman
Surfactants in Solutions,
Ed. by
K. Mittal and B. Lindman
(Plenum, New-York, 1989), Vol. 10, pp. 61-87.
Abstract:…
33. Wetting of
rough
solid surfaces by liquids.
Andelman,
David;
Joanny, Jean Francois; Robbins, Mark O.
NATO ASI Series, Series
B:
Physics (1989), 211 (Phase Transitions Soft Condens.
Matter), 161-4.
Abstract:
A theory study is made of
the
static behavior of thin liquid films that completely wet a rough solid
surface. The competition between surface tension and disjoining
pressure
determines. the extent to which liquid films
follow
the undulations of a rough solid substrate.
32.
The physics of microemulsions and amphiphilic monolayers
Andelman,
David
Statistical Mechanics of
Membranes and Surfaces, Vol. 5, Ed. by D. Nelson, T. Piran
and S. Weinberg, (World Scientific, Singapore, 1989), pp.
105-113.
Abstract:…
31. Chiral
discrimination and phase transitions in Langmuir
monolayers.
Andelman,
David.
Journal of the American
Chemical
Society (1989), 111(17), 6536-44.
Abstract:
Chiral discrimination was
studied theor. for
chiral mols. that form an insol. Langmuir monolayer at the water/air
interface.
For particular tripodal shapes mols., the
chiral
discrimination was calcd. for
various types of intermol. interactions
(van der Waals, dipole, charge, etc.). The calcn.,
based on Boltzmann-weighted averaging of mol. orientations, predicts a
preferred heterochiral behavior for van der Waals interactions and homochiral behavior for electrostatic ones.
Other
interactions are also discussed. To understand monolayer phase
diagrams,
an analogy is drawn with sublimation expts.
in bulk systems and a three-component thermodn.
model is proposed. The variable area per
mol.
and also the chiral discrimination parameter are important parameters in
the
model. Phase diagrams for conglomerates and racemic compds.
are calcd. in qual. agreement with
expts. Possible connections and interpretation
of
existing exptl. data are discussed, and some
new expts. for chiral
monolayers are
proposed.
30. Chiral discrimination in a Langmuir monolayer.
Andelman, David; De Gennes, Pierre Gilles
Comptes
Rendus de l'Academie des Sciences, Serie III: Sciences
de la
Vie (1988), 307(3), 233-7.
Abstract:
Detergents with a tripod
shape, containing
3 functional groups (i = A, B, C) bound to an asym. carbon atom, which lie at the water surface are
considered. The fourth valence of the carbon carries an aliph. chain. Two
neighboring detergent mols. are
assumed to associate via 2 intermol. bonds (ij and i'j').
To each of these bonds is assocd. an
energy Vij which is neg. (attractive) if i and
j do
tend to associate The partition functions Z++, Z+- for a pair of
mols. with the same chirality (Z++) or with opposite chiralities
(Z+-) are derived by direct counting. If D
º Z++ - Z+-
> 0,
a homochiral case (HOC) leading to segregation
in
dense phases is expected. If D < 0, the reverse, heterochiral case
(HEC)
is predicted. This model leads to certain practical rules: (1) if
the
only allowed bonds are between identical groups (Vij ® +
¥ if i
¹ j)
® HEC; (2)
if all
interactions are of the van der Waals type (with Vij
= -Maiaj, where ai is the
polarizability of group i) ® HEC; (3)
if A is apolar, B is charged (+) and C is also charged but
of
opposite sign (-) ®
HOC. A similar conclusion holds if the charges are replaced by
dipoles
normal to the water surface; (4) if A = aliph., B = arom., C = charged ® HEC; (5) if one of the bonds between
identical
groups (e.g. AA) is much stronger than the others ® HEC; (6)
is one
of the groups (A) is "passive" (VAj
independent of j) and if VBC is strongly attractive ®
HOC.
29. Complete wetting on rough surfaces: statics.
Andelman, D.; Joanny, J. F.; Robbins, M. O.
Europhysics
Letters (1988), 7(8), 731-6.
Abstract:
The profile of a thin liq. film
completely
wetting a rough solid surface was studied. The long-wavelength
undulations of the liq. interface follow those
of the
solid surface, while short-wavelength undulations are damped
strongly.
There is Lorentzian damping of wavelengths
smaller
than the healing length x determined. by
a
balance between surface tension and disjoining pressure.
Undulations with
wavelength smaller than the mean film thickness are damped
exponentially.
The case where the binary interactions between mols. may be described by an inverse power law potential
such as
the van der Waals potential was studied in detail. These results
are
relevant for recent ellipsometry and grazing
incidence
x-ray scattering expts.
28. Theory of microemulsions: comparison with
experimental
behavior.
Cates, M. E.; Andelman, D.; Safran, S. A.; Roux,
D.
Langmuir
(1988), 4(4), 802-6.
Abstract:
A previously described thermodn.
model (1987) for croemulsions was
used to predict some aspects of the phase behavior. The stability
of the
microemulsion under variation of mol. parameters (such as the bending
const.
and spontaneous curvature of the surfactant monolayer) is
discussed. An
appropriate cut through the multidimensional parameter space yields the
characteristic "fish" phase diagram, as found exptl.
This model exhibits a phase behavior close to the exptl.
one, not only in terms of the variation with surfactant concn.
but also in terms of the sensitivity of the
phase
diagram to the nature of the surfactant, particularly its spontaneous
curvature.
27. Random surface model for the L3-phase of dilute
surfactant
solutions.
Cates, M. E.; Roux, D.; Andelman,
D.;
Milner, S. T.; Safran, S. A
Europhysics Letters
(1988), 5(8), 733-9; Europhysics
Letters (1988), 7(1), 94
[erratum].
Abstract:
A simple model is given for the anomalous (flow-birefringent)
isotropic phase, known as L3, that is seen in
certain
surfactant solns. at
vol.
fractions of a few percent. The proposed structure consists of
locally sheetlike sections of semi-flexible surfactant
bilayer,
connected up at larger distances into a multiply connected random
surface,
having a preferred structural length scale of order the persistence
length of
the bilayer. A 1st-order transition between this isotropic sheetlike phase and the nearby swollen lamellar
phase is
described.
26. Correlations and structure factor of bicontinuous
microemulsions
S. T. Milner, S. A. Safran, D. Andelman, M. E. Cates, D.
Roux
J.
Physical (France), 49, 1065-1076 (1988).
Abstract: …
25. Middle-phase microemulsions and random surfaces
S. A. Safran, D. Roux, S. T. Milner, M. E. Cates, D.
Andelman
Physics
of Amphiphilic Layers, Ed. by J. Meunier, D.
Langevin
and N. Boccara,
(Springer-Verlag, Berlin, 1987), pp.
291-297.
Abstract: ….
24. Dynamics of phase transitions in Langmuir monolayers of
polar
molecules
F. Brochard, J. F. Joanny, D.
Andelman
Physics
of Amphiphilic Layers, Ed. by J. Meunier, D.
Langevin
and N. Boccara,
(Springer-Verlag, Berlin, 1987), pp.
13-19.
Abstract:
….
23. Structured monolayers of charged and polar molecules at
the
liquid/air interface.
Andelman, David; Brochard,
Francoise;
Joanny, Jean Francois
NATO
ASI Series, Series C: Mathematical and Physical Sciences
(1987), 205 (Physical Chemical Aqueous Ionic Solutions),
417-27.
Abstract:
Effective dipoles in charged monolayers and permanent dipoles
in
neutral ones have a drastic effect on the structure and phase
transitions of insol. Langmuir monolayers. These long-range
and
repulsive dipolar interactions stabilize undulating phases in thermodn. equil.
Results are presented for two cases: (i) at close to a liq.-gas
crit-point temp.; (ii) at low temps.
Possible
implications of the former on the liq.-gas
transition
and of the latter to the liq.-solid and liq. expanded-liq.
condensed
transitions are discussed. In an ionic soln.,
the undulation periodicity can be controlled by the strength of the
ionic soln.
22. Modulated structures and competing interactions in
amphiphilic
monolayers.
Andelman, David; Brochard,
Francoise; Joanny, Jean Francois.
Proceedings
of the
Abstract:
The effects of electrostatic interactions on the phase
behavior and
structure of insol. Langmuir monolayers was
investigated at the liq./air interface.
Both
for charged and neutral monolayers, the competition between such
repulsive long-range
and attractive short-range interactions of the monolayer tends
to stabilize modulated phases. Phase diagrams are obtained in two
limits:
(i) close to the liq.-gas crit.
point and (ii) at low temps.
21. Structure and phase equilibria
of
microemulsions.
Andelman, David; Cates, M. E.; Roux, D.; Safran, S.
A.
Journal
of Chemical Physics (1987), 87(12), 7229-41.
Abstract:
A simple phenomenological model is proposed to describe the
phase equil. and structural
properties
of microemulsions. Space is divided into cells of side
z; each cell
is
filled with either pure water or oil. Surfactant mols.
are presumed to form an incompressible fluid
monolayer
at the oil-water interface. The monolayer is characterized by a
size-dependent bending const. K(z), which is small for z
³zK,
the de Gennes-Taupin persistence length.
The
model predicts a middle-phase microemulsion which coexists with dil. phases of surfactant in oil and surfactant in
water. On the same ternary phase diagram, two regions of two-phase
equil. exist involving
upper- and
lower-phase microemulsions that coexist with either almost pure water or
oil. At low temps. and/or high values of
the
bare bending const., K0 º K(a), the middle-phase microemulsion
may be
entirely precluded by sepn. to
a lamellar phase, whereas at high temp. and/or
low
values of K0, there is a first-order transition between a disordered
microemulsion and a lamellar phase. In the absence of spontaneous
curvature the phase diagram is oil-water sym. It may be asymmetrized by: (1) spontaneous curvature in the
middle
phase or (2) a difference between the free energy of the two dil. phases. If the asymmetry is sufficiently
large,
the three-phase region disappears.
20. Ordered and curved meso-structures in
membranes and amphiphilic films.
Leibler, S.; Andelman, D..
Journal de Physique (Paris)
(1987),
48(11), 2013-18.
Abstract:
Curvature-induced instabilities in membranes and amphiphilic
films
are investigated by introducing a general coupling between a shape
variable
(such as curvature) and internal degrees of freedom (such as area per
mol.,
tilt angle, or local compn.). A
mean-field
treatment of the Ginzburg-Landau free energy expansion shows the
existence of
various undulated phases (on a mesoscopic scale) that can appear between
condensed (solid-like) and dil. (fluid-like)
homogeneous phases of the membrane. These undulated phases are
characterized by undulations in their local compn. as well as in their local
curvature.
19. Steady-state motion of a liquid/liquid/solid contact
line.
Joanny, Jean Francois;
Andelman, David.
Journal
of Colloid and Interface Science (1987), 119(2),
451-8.
Abstract:
The steady-state motion of a liq.
A/liq. B interface on a flat solid surface is
investigated. Hydrodynamic equations for the flow are obtained and
in
principle could yield a soln. for the profile
of a
general curved A/B interface. For small contact angles this
problem is
quite similar to the dynamics of a liq./vapor/solid
contact line. Both a "dry" solid surface and one that
has been prewetted by an invading liq.
were analyzed. Interesting Saffman-Taylor-like
instabilities could appear close to the tip of the advancing contact
line for
appropriate viscosity ratios.
18. Phase transitions in Langmuir monolayers of polar
molecules.
Andelman, David; Brochard,
Francoise; Joanny, Jean Francois.
Journal
of Chemical Physics (1987), 86(6), 3673-81.
Abstract:
Insol. Langmuir
monolayers are
investigated in the presence of dipolar forces which can have 2 origins:
permanent dipoles in neutral monolayers and induced dipoles in charged
monolayers. The main effect of the addnl.
long-range repulsive interactions is to stabilize undulating phases at
thermodn. equil.
Phase diagrams are obtained in 2 limits: close to the liq.-gas
crit. point via a Ginzburg-Landau expansion of
the
free energy (mainly within a mean-field approxn.),
and at low temps. by free energy
minimization.
Possible applications of this theory to expts.
at the liq.-gas, liq. expanded-liq.
condensed, and
solid-liq. transitions are
discussed.
17. Origin of middle-phase
microemulsions.
Safran, S. A.; Roux, D.; Cates, M. E.; Andelman,
D.
Physical
Review Letters (1986), 57(4), 491-4.
Abstract:
A simple model is described to calc. the phase behavior of
microemulsions. The surfactant film at the oil-water interface is
treated
as an incompressible layer whose bending const. is renormalized by
thermal
fluctuations. Two- and three-phase equil. involving upper-, lower-, and middle-phase
microemulsions
are found. The structure of the middle phase is characterized by
the
persistence length of the film, beyond which the bending const. is
renormalized
to smaller values.
16.
One-dimensional Ising model in a variety of
random
fields.
Andelman D.
Physical
Review B-Condensed Matter, vol.34, no.9,
Abstract
The
author studies one-dimensional Ising models in
the
presence of various random-field (RF) distributions. The distribution
which
determines the average free energy and other thermodynamic properties is
found
to be a devil's staircase for discrete RF distributions and continuous
for nondiscrete RF distributions. Thus, any experiment
that can
be done on these systems will not show this devil's-staircase behavior,
due to
the natural broadening of RF distributions in real physical systems.
Experiments will show some reminiscence of the largest steps and this is
associated with the broadening of the peaks of the RF distributions. (13
References).
15. Metastability and Landau
theory for
random fields and demixing in porous
media
D. Andelman and J. F. Joanny
Scaling
Phenomena in Disordered Systems, Ed. by R. Pynn and
A. Skjeltorp, (Plenum, New-York, 1985), pp.
163-169.
Abstract:
14. Phase separation and metastability in
binary liquid mixtures in gels and porous media.
Andelman, D.; Joanny, J. F.
Springer
Proceedings in Physics (1985), 5 (Physical Finely Divided
Matter), 361-4.
Abstract:
A random field explanation is proposed for the behavior of
binary liq. mixts. immersed
in a gel matrix. When the bare fluid correlation length
(x) exceeds
the gel
mesh size (L), the observed opalescence is the result of domain freezing
due to
the random gel structure. When x < L, the system behavior resembles
biphasic
flow in porous media.
13. Monolayer transitions with polar
molecules.
Andelman, David; Brochard,
Francoise; De Gennes, Pierre Gilles; Joanny, Jean
Francois
Comptes Rendus de l'Academie
des Sciences, Serie II: Mecanique, Physique, Chimie, Sciences de la
Terre et
de l'Univers (1985), 301(10), 675-8.
Abstract:
Weak, long-range (r-3) interactions between dipoles cause
drastic
changes in the monolayer phase diagram. Over a significant part of
the liq.-gas coexistence region for the Langmuir
monolayer, a supercryst. phase is
expected
(where liq. and gas regions form a spatially
periodic
arrangement with periods of .apprx.103
.ANG.).
12. Metastability in the
random-field Ising
model.
Andelman D. Joanny J-F.
Physical
Review B-Condensed Matter, vol.32, no.7,
Abstract:
Effects of metastability in random-field Ising systems are calculated for domains that are
both
curved and rough. Villian's and Bruinsma
and Aeppli's scaling forms (1984) for the
domain size
are obtained from the same approach and the crossover between them is
simply
explained. Generalizations to random fields with nonzero averages lead
to a
'freezing line' and are relevant to experiments on binary-fluid mixtures
in
gels and in porous media. (16 References).
11. Relevance of prewetting on the
stability of transient foams in partially miscible
liquids.
Andelman, David; Joanny, Jean
Francois.
Journal
of Physical Chemistry (1985), 89(10), 2119-20.
Abstract:
In a recent letter, Gracia, Vares, and Robledo (1984)
explained the stability of certain transient foams in binary liq. mixts. by
prewetting phenomena. Such an
explanation which
is valid for infinite thickness films (early times) cannot be valid for
finite
thickness films (later times) at thermodn.
equil. A nonequil.
mechanism to explain the foam stability is
proposed.
10.
Critical behavior with axially correlated random
bonds.
Andelman D. Aharony
A.
Physical
Review B-Condensed Matter, vol.31, no.7,
Abstract
Critical
properties are studied in systems with quenched bond disorder that is
correlated along d1 of d dimensions. A renormalization-group
scheme
(based on the Migdal-Kadanoff method) which
follows
the full distribution of the random bonds and which gives correctly the
modified Harris criterion j = a
+d1n
is used. For d1<d-1, the authors find
fixed
distributions at finite temperatures, yielding new 'random' exponents
for
various q-state Potts models.
For
d1=d-1 there is no long-range order if there is a finite
weight to
zero coupling. Otherwise, they find a novel zero-temperature fixed
distribution
for which all the moments diverge to infinity with finite ratios among
them.
This fixed distribution has a magnetic eigenvalue
equal to d, indicating a first-order transition in the magnetization and
possible related essential singularities. Thus, by analogy, the
possibility of
a magnetization jump is raised for the McCoy-Wu transition on a square
lattice.
The results for d1=1 are relevant to random quantum systems.
(13
References).
9. Critical amplitude of the Potts model:
Zeroes and
divergences.
Kaufman, Miron; Andelman,
David.
Physical
Review B: Condensed Matter and Materials Physics
(1984),
29(7), 4010-16.
Abstract:
The crit. amplitude of the q-state
Potts-model free energy was studied as a function of q in two dimensions
and on
the diamond hierarchical lattice. The amplitude diverges at an
infinite
no. of q values, qn, introducing logarithmic
terms in
the free energy. In each interval (qn,qn+1) there is a value
~qn where the amplitude vanishes, affecting the
singularity
of the free energy as a function of temp. Possible consequences
for
gelation and vulcanization of polymers are
discussed.
8.
Scale-invariant quenched disorder and its stability criterion at random
critical points.
Andelman D. Berker
AN.
Physical
Review B-Condensed Matter, vol.29, no.5,
Abstract:
The critical properties of systems with quenched bond disorder are
determined
from a fixed distribution, under renormalization group, of the random
bonds.
Full fixed distributions with all moments are obtained numerically by
histograms and, to a good approximation, in terms of Lambda
distributions. For
such systems, the specific-heat exponent alpha does not equal the
crossover
exponent phi at random criticality. The authors derive a new relation
between
alpha and phi , which invokes characteristics of the fixed
distributions. The
difference between alpha and phi is noted for n-vector models in 4-
epsilon
dimensions and for Potts models on hierarchical lattices solved exactly.
In
general, stable random critical behavior with positive alpha appears to
be
possible. They develop a general treatment of quenched disorder and
illustrate
it by calculating specific-heat curves. It is suggested that the
critical
exponents of the three- and four-state random-bond Potts models in two
dimensions are nu approximately=1.06 and 1.19.
(26
References).
7. Lower critical dimension of the random-field Ising model: a Monte Carlo
study.
Andelman D. Orland H. Wijewardhana
LCR.
Physical
Review Letters, vol.52, no.2,
Abstract
This
paper presents extensive Monte Carlo simulations of the random-field
Ising model in various dimensions for long times in
moderately large systems, and specifically addresses the question of
whether
the lower critical dimension is 2 or 3. The authors find long-range
order for
d=3 and no long-range order for d=2. The marginality of the d=2 case is
further
checked by studying a system in d=ln8/ln3 approximately=1.89 dimensions
simulated by a fractal, the authors thus conclude that the lower
critical
dimension is 2. (13 References).
6. First- and second-order phase transitions with
random
fields at low temperatures.
Andelman D.
Physical
Review B-Condensed Matter, vol.27, no.5,
Abstract
It
is shown, within mean-field theory of the random-field Ising
model, that a maximum of the distribution function at zero field
does not necessarily imply a second-order transition at low temperature,
as was
previously suggested. The order of the low-temperature transition is
discussed
in terms of the maxima of the distribution function. (2
References).
5
. Preserving the free energy in a Migdal-Kadanoff
approximation for the q-state Potts model.
Andelman D. Walker JS.
Physical
Review B-Condensed Matter, vol.27, no.1,
Abstract
The
authors study a new modification of the Migdal-Kadanoff
(MK) approximation, in which the bond-shifting step is generalized so
that the
resulting transformation preserves the free energy. This method is then
utilized to study the q-state Potts model in two and three dimensions.
While
this method is just as easy to implement as the standard MK
approximation,
significant quantitative improvement is achieved by preserving the free
energy
even to very low order in a series expansion. The authors also discuss
the
limitations inherent in employing a single-parameter
renormalization-group
transformation. (19 References).
4. First- and second-order phase transitions in Potts
models:
competing mechanisms.
Berker, A.
Nihat; Andelman, David.
Journal
of Applied Physics (1982), 53(11, Pt. 2),
7923-6.
Abstract:
Many condensed matter systems, ranging from adsorbed surfaces
to
bulk magnets, are microscopically modeled by interacting q-state Potts
spins, arrayed in d dimensions. A changeover from
2nd-order
phase transitions at q £ qc(d) to
1st-order
transitions at q > qc can be understood as a condensation of effect
vacancies, which are patches of local disorder favored by entropy.
Accordingly, the renormalization-group treatment of Potts models is
within
context of Potts-lattice-gas models, where crit. and tricrit. fixed points occur
at low
q, but merge and annihilate at qc. This picture has led to exact
tricrit. exponents in 2
dimensions. It is also consistent with recent exptl.
results on intercalated systems in 3 dimensions. Effective
vacancies in
pure Potts models are also studied by Monte Carlo simulation.
Their
effective chemical potential can be controlled by a 4-point interaction,
which
proved useful in
Swendsen, Robert
H.;
Andelman, D.; Berker, A. Nihat
Physical
Review B: Condensed Matter and Materials Physics
(1981),
24(11), 6732-5.
Abstract:
The thermal crit. exponent of the
4-state
Potts model in 2 dimensions is evaluated as n-1 = 1.49
± 0.01,
using the
Monte Carlo renormalization-group method. The presence of a
marginal
scaling direction is also indicated. These results confirm
previous
conjectures, universality, and logarithmic corrections. A purely
Potts
Hamiltonian is considered. A 4-point interaction is used to
control the chemical
potential of effective vacancies, without the introduction of explicit
vacancy
states.
2. q-state
Potts models in d dimensions: Migdal-Kadanoff
approximation.
Andelman D. Berker
AN.
Journal of Physics A-Mathematical & General, vol.14, no.4, April 1981, pp.L91-6. UK.
Abstract
The first- and second-order phase transitions of the q-state Potts models are obtained in arbitrary dimension d. Critical and tricritical behaviours merge and annihilate at q/sub c/(d), clearing the way to first-order transitions at q[right angle bracket]q/sub c/(d) by the condensation of effective vacancies. The value of q/sub c/(d) decreases with increasing d, from diverging as exp(2/(d-1)) at d to 1/sup +/, to q/sub c/(2)=3.81 (cf exact value of 4), to lower values at d[right angle bracket]2. For given d, a changeover in critical behaviour occurs at q1/(d), as the critical fixed points merge from the Potts-lattice-gas region to the undiluted Potts limit. It is suggested that the power law singularities of the percolation problem (q to 1/sup +/) have logarithmic corrections. (35 References).
1. First- and second-order phase transitions of infinite-state Potts models in one dimension.
Berker AN. Andelman D. Aharony
A.
Journal of Physics A-Mathematical & General, vol.13, no.11, Nov. 1980, pp.L413-18.
Abstract
The q-state, d-dimensional Potts models exhibit a variety of phase-transition behaviour in the limit d to 1/sup +/, q to infinity , and l identical to (d-1) in q finite. The regions l[left angle bracket]1, 1[left angle bracket]l[left angle bracket]2, and 2[left angle bracket]l are distinguished, respectively, by no transition, second-order transitions (with a new changeover phenomenon at l=ln 4), and first-order transitions. The latter are due to the condensation of effective vacancies. Critical and tricritical exponent values are given. (21 References).