147. Direct Measurement of sub-Debye-length Attraction between Oppositely Charged Surfaces [pdf]
Kampf, N. ; Ben-Yaakov, D. ; Andelman, D. ; Safran, S. ; Klein, J.
Physical Review Letters, (2009), 103, 118304.1-4.
Abstract.
Using a surface force balance with fast video analysis, we have measured
directly the attractive forces between oppositely charged solid surfaces across water over the entire range of interaction, in particular at surface separations
D below the Debye screening length. At very low salt concentration we find a long ranged
attraction between the surfaces (onset ca. 100 nm), whose variation at D less than Debye screening length
agrees well with recent predictions based on solving the non-linear Poisson-Boltzmann
theory, when due account is taken of the independently-determined surface charge
asymmetry.
146. Beyond standard Poisson-Boltzmann Theory: Ion-specific Interactions in Aqueous Solutions [pdf]
Ben-Yaakov, D. ; Andelman, D. ; Harries, D. ; Podgornik, R.
Journal of Physics: Condensed Matter, (2009), 21, 424106.1-11.
Abstract.
The Poisson–Boltzmann mean-field description of ionic solutions has been successfully used in
predicting charge distributions and interactions between charged macromolecules. While the
electrostatic model of charged fluids, on which the Poisson–Boltzmann description rests, and its
statistical mechanical consequences have been scrutinized in great detail, much less is
understood about its probable shortcomings when dealing with various aspects of real physical,
chemical and biological systems. These shortcomings are not only a consequence of the
limitations of the mean-field approximation per se, but perhaps are primarily due to the fact that
the purely Coulombic model Hamiltonian does not take into account various additional
interactions that are not electrostatic in their origin. We explore several possible
non-electrostatic contributions to the free energy of ions in confined aqueous solutions and
investigate their ramifications and consequences on ionic profiles and interactions between
charged surfaces and macromolecules.
http://arxiv.org/abs/0901.2254
144. Ions in Mixed Dielectric Solvents: Density Profiles and Osmotic Pressure
between Charged Interfaces [pdf]
Ben-Yaakov, D. ; Andelman, D. ; Harries, D. ; Podgornik, R.
J. Phys. Chem. B (2009), 113, 6001-6011.
Abstract.
The forces between charged macromolecules, usually given in terms of osmotic pressure, are highly
affected by the intervening ionic solution. While in most theoretical studies the solution is treated
as a homogeneous structureless dielectric medium, recent experimental studies concluded that for a
bathing solution composed of two solvents (binary mixture), the osmotic pressure between charged
macromolecules is affected by the binary solvent composition. By adding local solvent composition
terms to the free energy, we obtain a general expression for the osmotic pressure, in planar geometry
and within the mean-field framework. The added effect is due to the permeability inhomogeneity
and non-electrostatic short-range interactions between the ions and solvents (preferential solvation).
This effect is mostly pronounced at small distances and leads to a reduction in the osmotic pressure
for macromolecular separations of the order 1-2 nm. Furthermore, it leads to a depletion of one of
the two solvents from the charged macromolecules (modeled by us as planar interfaces). Lastly,
by comparing the theoretical results with experimental ones, an explanation based on preferential
solvation is offered to recent experiments on the osmotic pressure of solutions of DNA molecules.
http://arxiv.org/abs/0901.2254
143. Modulated Phases: Review and Recent Results [pdf]
Andelman, D. ; Rosensweig, R. E.
De Gennes Memorial Volume, J. Phys. Chem. B, (2009), 113, 3785-3798.
Abstract.
We consider aspects of patternings that occur in a wide array of physical
systems due to interacting combinations
of dipolar, interfacial, charge exchange, entropic, and geometric influences.
We review well-established
phenomena as a basis for discussion of more recent developments.
The materials of interest range from bulk
inorganic solids and polymer organic melts to fluid colloids.
Often, there are unifying principles behind the various modulated structures, such as the competition
between surface or line tension and dipolar interaction
in thermally reversible systems. Generally, their properties
can be understood by free-energy minimization.
142. An Analytical Model for ArF Photoresist Shrinkage under SEM Inspection [pdf]
Ayal, G. ; Andelman, D. ; Cohen, Y.
J. Vacuum Sci. Tech. B, (2009) 27, 1976-1983.
Abstract.
Linewidth slimming is a phenomenon occurring specifically in photolithography of 193 nm
wavelength (ArF) radiation. Photoresists for this wavelength appear to lose volume when exposed
to electron-beam radiation, as when scanned in scanning electron microscopy for critical dimension
linewidth measurement. This work is an attempt to understand this “shrinkage” from a polymer
physics point of view. More specifically, the authors try to check the applicability of free volume
theory in polymer systems by calculating some relevant physical properties, assuming that the
exposure to e-beam creates an external hardened shell for the material bulk, and continued exposure
will deliver heat into the polymer enclosed in a confined space. The authors’ main conclusion is that
the free volume loss (annealing) shows qualitative resemblance to experiment, but this effect
exclusively is not a sufficient quantitative explanation for the observed shrinkage. A possible
explanation for this discrepancy is that their model is limited due to unknown material parameters,
or that the annealing is coupled with other effects such as “wringing” solvent out.
141. The Phenomenology of Modulated Phases:
From Magnetic Solids and Fluids to Organic Films and Polymers [pdf]
Andelman, D. ; Rosensweig, R. E.
Chapter 1 in: "Polymers, Liquids and Colloids in Electric Fields: Interfacial Instabilities, Orientation, and Phase-Transitions", Eds. Y. Tsori and U. Steiner, Vol. 2 in "Series in Soft Condensed Matter", World Scientific (2009).
Abstract.
This chapter surveys aspects of patterning that occur in a wide array of
physical systems due to interacting combinations of magnetic, electric,
and interfacial energies. We review well-established phenomena as a
basis for discussion of more recent developments. While the materials
of interest range from bulk inorganic solids and polymer organic melts
to fluid colloids and granular suspensions, we note that often there are
unifying principles behind the various modulated structures, such as
the competition between surface or line tension and dipolar interaction
in thermally reversible systems; their properties can be understood by
free–energy minimization. In other cases, the patterns are determined by
dissipative forces. In all these systems the patterning is modulated by the
application of force fields. Another common feature of these disparate
systems is that a phase diagram often emerges as a convenient descriptor.
We also mention a number of interesting technological applications for
certain of the systems under review.
140. Dreaming in Plastic [pdf]
Korzhov, M. ; Shikler, R. ; Andelman, D.
Physics World, (2008) July, 29-33.
Abstract.
Plastic is one of the most versatile materials available.
It is cheap, flexible and easy to process, and as a result
it is all around us – from our computer keyboards to the
soles of our shoes. One of its most common applications
is as an insulating coating for electric wires;
indeed, plastic is well known for its insulating characteristics.
It came as something of a surprise, therefore,
when in the late 1970s a new generation of plastics was
discovered that displayed exactly the opposite behaviour
– the ability to conduct electricity. In fact, plastics
can be made with a whole range of conductivities –
there are polymer materials that behave like semiconductors
and there are those that can conduct as well
as metals. This discovery sparked a revolution in the
electronics community, and three decades of research
effort is now yielding a range of stunning new applications
for this ubiquitous material.
140. The Phenomenology of Modulated Phases: From Magnetic Solids and Fluids to Organic Films and Polymers[pdf]
Andelman, D. ; Rosensweig, R. E.
to be published in: "Polymers, Liquids and Colloids in Electric Fields: Interfacial Instabilities, Orientation, and Phase-Transitions", Eds. Y. Tsori and U. Steiner, World Scientific (2008).
Abstract.
This chapter surveys aspects of patterning that occur in a wide array of
physical systems due to interacting combinations of magnetic, electric,
and interfacial energies. We review well-established phenomena as a
basis for discussion of more recent developments. While the materials
of interest range from bulk inorganic solids and polymer organic melts
to fluid colloids and granular suspensions, we note that often there are
unifying principles behind the various modulated structures, such as
the competition between surface or line tension and dipolar interaction
in thermally reversible systems; their properties can be understood by
free.energy minimization. In other cases, the patterns are determined by
dissipative forces. In all these systems the patterning is modulated by the
application of force fields. Another common feature of these disparate
systems is that a phase diagram often emerges as a convenient descriptor.
We also mention a number of interesting technological applications for
certain of the systems under review.
139. Interfacial Instability of Charged End-Group Polymer Brushes[pdf]
Tsori, Y. ; Andelman, D. ; Joanny, J.-F.
Europhysical Letters (2008), 82, 46001.1-6
Abstract.
We consider a polymer brush grafted to a surface (acting as an electrode) and
bearing a charged group at its free end. Using a second distant electrode, the brush is subject to
a constant electric field. Based on a coarse-grained continuum model, we calculate the average
brush height and find that the brush can stretch or compress depending on the applied field and
charge end-group. We further look at an undulation mode of the flat polymer brush and find that
the electrostatic energy scales linearly with the undulation wavenumber, q. Competition with
surface tension, scaling as q^2, tends to stabilize a lateral q-mode of the polymer brush with a
well-defined wavelength. This wavelength depends on the brush height, surface separation, and
several system parameters.
137. Water, Electricity, and Between…
On Electrowetting and its Applications[pdf]
Shamai, R. ; Andelman, D. ; Berge, B. ; Hayes, R.
Soft Matter, (2008), 4, 38-45.
Abstract.
Imagine a drop of water lying on a surface, pulled into a ball by surface tension. With electricity it
is possible to change the shape of the drop and cause it to flatten out. This is electrowetting, a
physical phenomenon which has aroused great interest in recent years as it has found new
applications. Here we will describe the phenomenon and two of its applications: variable-focus
liquid lenses and paper-thin, video-rate, reflective color displays.
136. The Phase Behavior of Mixed Lipid Membranes in Presence of
the Rippled Phase [pdf]
Shimokawa, N. ; Komura, S. ; Andelman, D.
European Physical Journal E -- Soft Matter (2008), 26, 197-204
Abstract.
We propose a model describing liquid-solid phase coexistence in mixed
lipid membranes by including explicitly the occurrence of a
rippled phase.
For a single component membrane, we employ a previous model in
which the membrane thickness is used as an order parameter.
As function of temperature, this model properly accounts for the
phase behavior of the three possible membrane phases: solid, liquid
and the rippled phase.
Our primary aim is to explore extensions of this model to binary
lipid mixtures by considering the composition dependence of important
model parameters.
The obtained phase diagrams show various liquid, solid and rippled
phase coexistence regions, and are in quantitative agreement with
the experimental ones for some specific lipid mixtures.
http://arxiv.org/abs/0709.2956
135.
Dipolar Poisson-Boltzmann Equation: Ions and Dipoles Close to Charge Interfaces [pdf]
Abrashkin, A. ; Andelman, D. ; Orland, H.
Physical Review Letters, (2007), 99, 077801.
Abstract.
We present an extension to the Poisson-Boltzmann model here the dipolar features of solvent molecules are taken explicitly into account. The formulation is derived at mean-field level and can be
extended to any order in a systematic expansion. It is applied to a two-plate system with oppositely charged surfaces. The ion distribution and profiles in the dipolar order parameter are calculated and can
result in a large correction to the interplate pressure.
http://arxiv.org/abs/0705.1269
134.
Electrostatic Interactions of Asymmetrically Charged Membranes [pdf]
Ben-Yaakov, D. ; Burak, Y. ; Andelman, D. ; Safran, S. A.
Europhysics Letters, (2007), 79, 48002.
Abstract.
We predict the nature (attractive or repulsive) and range (exponentially screened or long-range power law) of the electrostatic interactions of oppositely charged, planar plates as a
function of the salt concentration and surface charge densities (whose absolute magnitudes are not necessarily equal). An analytical expression for the crossover between attractive and repulsive
pressure is obtained as a function of the salt concentration. This condition reduces to the high-salt limit of Parsegian and Gingell where the interaction is exponentially screened and to the zero salt
limit of Lau and Pincus in which the important length scales are the inter-plate separation and the Gouy-Chapman length. In the regime of low salt and high surface charges we predict --- for any
ratio of the charges on the surfaces --- that the attractive pressure is long-ranged as a function of
the spacing. The attractive pressure is related to the decrease in counter-ion concentration as the
inter-plate distance is decreased. Our theory predicts several scaling regimes with different scaling expressions for the pressure as a function of salinity and surface charge densities. The pressure
predictions can be related to surface force experiments of oppositely charged surfaces that are prepared by coating one of the mica surfaces with an oppositely charged polyelectrolyte.
http://arxiv.org/abs/0705.0893
132.
Bending Stability of Charged Membranes Immersed in
Polyelectrolyte Solutions [pdf]
Shafir, A. ; Andelman, D.
Soft Matter, (2007), 3(5), 644-650.
Abstract.
We study the contribution of polyelectrolytes in solution to the bending moduli of charged
membranes. Using the Helfrich free energy, and within the mean-field theory, we calculate the
dependence of the bending moduli on the electrostatics and short-range interactions between the
membrane and the polyelectrolyte chains. The most significant effect is seen for strong
short-range interactions and low amounts of added salt where a substantial increase in the
bending moduli of order 1 kT is obtained. For short-range repulsive membranes, the
polyelectrolyte contribution to the bending moduli is small, of the order the 0.1 kT up to at most
1 kT. For weak short-range attractions, the increase in membrane rigidity is smaller and of less
significance. It may even become negative for a large enough amount of added salt. Our numerical
results are obtained by solving the adsorption problem in spherical and cylindrical geometries. In
some cases, the bending moduli are shown to follow simple scaling laws.
http://arxiv.org/abs/cond-mat/0609166
130.
Phase Behavior of Polyelectrolyte-Surfactant Complexes at Planar
Surfaces [pdf]
Shafir, A ; Andelman, D.
Phys. Rev. E, (2006), 74(2), 021803.1-021803.11.
Abstract. We investigate theoretically the phase diagram of an insoluble charged surfactant monolayer
in contact with a semi-dilute polyelectrolyte solution (of opposite charge). The polyelectrolytes
are assumed to have long-range and attractive (electrostatic) interaction with the surfactant
molecules. In addition, we introduce a short-range (chemical) interaction which is either at-
tractive or repulsive. The surfactant monolayer can have a lateral phase separation between
dilute and condensed phases. Three different regimes of the coupled system are investigated
depending on system parameters. A regime where the polyelectrolyte is depleted due to short
range repulsion from the surface, and two adsorption regimes, one being dominated by electrostatics,
whereas the other by short range chemical attraction (similar to neutral polymers).
When the polyelectrolyte is more attracted (or at least less repelled) by the surfactant
molecules as compared with the bare water/air interface, it will shift upwards the surfactant critical
temperature. For repulsive short-range interactions the effect is opposite. Finally, the addition
of salt to the solution is found to increase the critical temperature for attractive surfaces, but
does not show any significant effect for repulsive surfaces.
http://arxiv.org/abs/cond-mat/0605501
129.
Coarse Graining in Block Copolymer Films [pdf]
Tsori, Y ; Andelman, D.
J. Polym. Science - Polymer Physics, (2006), 44, 2725-2739.
Abstract. We present few ordering mechanisms in block copolymer melts in
the coarse-graining approach. For
chemically homogeneous or modulated confining surfaces, the surface ordering is investigated above and
below the order-disorder temperature. In some cases the copolymer deformation near the surface is similar
to the copolymer morphology in bulk grain boundaries. Block copolymers in contact with rough surfaces are
considered as well, and the transition from lamellae parallel to perpendicular to the surface is investigated
as a function of surface roughness. Finally, we describe how external electric fields can be used to align
block copolymer meso-phases in a desired direction, or to induce an order-order phase transition, and dwell
on the role of mobile dissociated ions on the transition.
http://arxiv.org/abs/cond-mat/0603096
128.
Tension-Induced Morphological Transition in Mixed Lipid Bilayers [pdf]
Komura, S ; Shimokawa, N ; Andelman, D.
Langmuir, (2006), 22, 6771-6774.
Abstract. Recently, Rozovsky et al. reported
on the morphology and dynamics of superstructures in three-component lipid
bilayers containing saturated and unsaturated lipids as well as cholesterol
[J. Am. Chem. Soc. 127, 36 (2005)]. We suggest that the observed sequence
of the stripe to hexagonal morphological transition in mixed bilayers
can be attributed to an enhanced membrane surface tension that is induced
by the vesicle adhesion on the solid surface.
http://arxiv.org/abs/cond-mat/0511492
126.
Polyelectrolyte Multilayer Formation: Electrostatics and Short-Range Interactions [pdf]
Shafir, A. ; Andelman, D.
European Physical Journal E -- Soft Matter, (2006), 19, 155-162.
Abstract. We investigate the phenomenon of
multilayer formation via layer-by-layer deposition of alternating charge
polyelectrolytes. Using mean-field theory, we find that a strong
short-range attraction between the two types of polymer chains is
essential for the formation of multilayers. The dependence of the
required short-range attraction on the polymer charge fraction and
salt concentration is calculated. For weak short-range attraction
between any two adjacent layers, the adsorbed amount (per added layer)
decays as the distance from the surface increases, until the chains
stop adsorbing altogether. For strong short-range attraction, the
adsorbed amount per layer increases after an initial decrease, and
finally it stabilizes in the form of a polyelectrolyte multilayer
that can be repeated many times.
http://arxiv.org/abs/cond-mat/0509157
125.
Block Copolymers in Electric Fields: A Comparison of Single-Mode
and Self-Consistent Field Approximations [pdf]
Tsori, Y. ; Andelman, D.; Lin, C.-Y. ; Schick, M.
Macromolecules, (2005), 39(1), 289-293.
Abstract. We compare two theoretical approaches to dielectric diblock
copolymer melts in an external electric field. The first is a
relatively simple analytic expansion in the relative copolymer
concentration, and includes the full electrostatic contribution
consistent with that expansion. It is valid close to the
order-disorder transition point, the weak segregation limit. The
second employs self-consistent field (SCF) theory and includes the
full electrostatic contribution to the free energy at any copolymer
segregation. It is more accurate but computationally more intensive.
Motivated by recent experiments, we explore a section of the phase
diagram in the three-dimensional parameter space of the block
architecture, the interaction parameter and the external electric
field. The relative stability of the lamellar, hexagonal and
distorted body-centered-cubic (bcc) phases is compared within the
two models. As function of an increasing electric field, the
distorted bcc region in the phase diagram shrinks and disappears
above a triple point, at which the lamellar, hexagonal and distorted
bcc phases coexist. We examine the deformation of the bcc phase
under the influence of the external field. While the elongation of
the spheres is larger in the one-mode expansion than that predicted
by the full SCF theory, the general features of the schemes are in
satisfactory agreement. This indicates the general utility of the
simple theory for exploratory calculations.
http://arxiv.org/abs/cond-mat/0508179
124.
Ion Induced Lamellar-Lamellar Phase Transition in
Charged Surfactant Systems [pdf]
Harries, D. ; Podgornik, R. ; Parsegian, V.A.; Mar-Or, E. ; Andelman, D.
Journal of Physical Chemistry, (2006), 124(22), 224702.1-224702.14.
Abstract. We propose a model for the liquid-liquid L_alpha - L_alpha'
phase transition observed in osmotic
pressure measurements of certain charged lamellae-forming
amphiphiles. The model free energy combines mean-field electrostatic
and phenomenological non-electrostatic interactions, while the
number of dissociated counterions is treated as a variable degree of
freedom that is determined self-consistently. The model,
therefore, joins two well-known theories: the Poisson-Boltzmann
theory for ionic solutions between charged lamellae, and
Langmuir-Frumkin-Davies adsorption modified to account for charged
adsorbing species. Minimizing the appropriate free energy for each
interlamellar spacing, we find the ionic density profiles and the
resulting osmotic pressure. While in the simple Poisson-Boltzmann
theory the osmotic pressure isotherms are always smooth, we observe
a discontinuous liquid\---liquid phase transition when
Poisson-Boltzmann theory is self-consistently augmented by
Langmuir-Frumkin-Davies adsorption. This phase transition depends on
the area per amphiphilic headgroup, as well as non-electrostatic
interactions of the counterions with the lamellae, and between
interacting adsorbed ions. Coupling lateral phase transition in the
bilayer plane with electrostatic interactions in the bulk, our
results offer a qualitative explanation for the existence of the
L_alpha - L_alpha' phase-transition of
DDABr (didodecyldimethylammonium bromide), and its apparent absence
for the chloride and the iodide homologue. More quantitative
comparison with experiment requires better understanding of the
microscopic basis of the phenomenological model parameters.
http://arxiv.org/abs/cond-mat/0507244
123.
Orientational Transitions in Symmetric Diblock
Copolymers on Rough Surfaces [pdf]
Tsori, Y. ; Sivaniah, E. ;
Andelman, D. ; Hashimoto, T.
Macromolecules, (2005) 38(16), 7193-7196.
Abstract. We present a model addressing the
orientation transition of
symmetric block copolymers such as PS/PMMA on smooth and rough
surfaces. The distortion free energy of parallel and perpendicular
lamellar phases in contact with a rough solid surface is calculated
as function of the surface roughness amplitude and wavelength, as
well as the polymer lamellar periodicity (molecular weight). We find
an analytical expression for the orientation transition. This
expression is compared and agrees well with recent experiments done
with six different polymer molecular weights and surface
preparations.
http://arxiv.org/abs/cond-mat/0504410
122. Structural
changes of diblock copolymer melts due to an external electric field:
a self-consistent field theory study [pdf]
Lin, C.-Y. ; M. Schick, M. ; Andelman, D.
Macromolecules, (2005) 38(13), 5766-5773.
Abstract. We study the phase
behavior of diblock copolymers in presence of
an external electric field. We employ self-consistent field theory
and treat the relevant Maxwell equation as an additional
self-consistent equation. Because we do not treat the electric
field perturbatively, we can examine its effects even when its
magnitude is large. The electric field couples to the system's
morphology only through the difference between the dielectric
constants of the two blocks. We find that an external field aligns
a body-centered cubic phase along the (111) direction, reducing
its symmetry group to R\bar(3)m. Transitions between this phase
and the disordered or hexagonal phases can occur for external
electric fields ranging from a minimum to a maximum value beyond
which the R\bar(3)m phase disappears completely. This
electric-field range depends on diblock architecture and
temperature. We present several cuts through the phase diagram in
the space of temperature, architecture and applied field,
including one applicable to a system recently studied.
http://arxiv.org/abs/cond-mat
/0502624
120. Stripes of partially
fluorinated alkyl chains: dipolar Langmuir monolayers. [pdf]
Schneider, M.F. ; Andelman, D. ; Tanaka, M.
Journal of Chemical Physics, (2005) 122(9), 094717.1-094717.5.
Abstract. Stripe-like domains of Langmuir
monolayers formed by surfactants with partially fluorinated lipid anchors
(F-alkyl lipids, FL-8-8) are observed at the gas/liquid phase
coexistence. The average periodicity of the stripes measured by
fluorescence microscopy is in the micrometer range, varying
between 2 - 8μm. The observed stripe-like patterns are stabilized due to
dipole-dipole interactions between terminal -CF3 groups.
These interactions are particularly strong as compared with
non-fluorinated lipids because of the low dielectric constant of the
surrounding air. These long-range dipolar interactions tend to elongate
the domains in contrast to the line tension that tends to minimize the
length of the domain boundary. The monolayer of the lipids with alkyl
chains (AL-16), on the other hand, Formed spherical micro-domains
(bubbles) at comparable surface pressures.The measured stripe
periodicity agrees quantitatively with a theoretical approach. Moreover,
the reduction in line tension by adding trace (0.1 mol%) of cholesterol
results as expected in a decrease in the domain periodicity.
http://arxiv.org/abs/cond-mat
/0501364
119. Competition
between condensation of monovalent and multivalent
ions in DNA aggregation. [pdf]
Burak, Y. ; Ariel, G. ; Andelman, D.
Current Opinion in Colloid and Interface Science, (2004), 9, 53-58.
Abstract. - We discuss the distribution of ions around
highly charged PEs when there is competition between monovalent and
multivalent ions, pointing out that in this case the number of
condensed ions is sensitive to short-range interactions, salt,
and model-dependent approximations. This sensitivity is discussed
in the context of recent experiments on DNA aggregation,
induced by multivalent counterions such as spermine and spermidine.
http://arxiv.org/abs/cond-mat/0407344
118. Lateral phase separation
in mixtures of lipids and cholesterol. [pdf]
Komura, S. ; Shirotori, H. ; Olmsted, P.D. ; Andelman,
D.
Europhysics Letters, (2004), 67(2), 321-327.
Abstract. - In an effort to understand
"rafts" in biological membranes, we propose phenomenological models for
saturated and unsaturated lipid mixtures, and lipid-cholesterol mixtures.
We consider simple couplings between the local composition and
internal membrane structure, and their influence on transitions between
liquid and "gel" membrane phases. Assuming that the gel transition
temperature of the saturated lipid is shifted by the presence of the
unsaturated lipid, and that cholesterol acts as an external field on the
chain melting transition a variety of phase diagrams are obtained. The
phase diagrams for binary mixtures of saturated/unsaturated lipids and
lipids/cholesterol are in semi-quantitative agreement with the
experiments. Our results also apply to regions in the ternary phase
diagram of lipid/lipid/cholesterol systems.
http://arxiv.org/abs/cond-mat
/0402252
117. Test-charge
theory for the planar electric double layer. [pdf]
Burak, Y. ; Andelman, D. ; Orland H.
Physical Review E, (2004), 70(1), 016102.1-016102.18 .
Abstract. We present a model for the ion
distribution near a charged surface, based on the response of the ions to
the presence of a single test particle. Near an infinite planar surface
this model produces the exact density profile in the limits of weak and
strong coupling, which correspond to zero and infinite values of the
dimensionless coupling parameter. At intermediate values of the coupling
parameter our approach leads to approximate density profiles that agree
qualitatively with Monte-Carlo simulation. For large values of the
coupling parameter our model predicts a crossover from exponential to
algebraic decay at large distance from the charged plate. Based on the
test charge approach we argue that the exact density profile is described,
in this regime, by a modified mean field equation, which takes into
account the interaction of an ion with the ions close to the charged
plate.
http://arxiv.org/abs/cond-mat
/0311602
116. Polyelectrolyte
overcompensation of charged planar surfaces. [pdf]
Shafir, A. ; Andelman, D.
Physical Review E, (2004), 70(6), 061804.1-061804.12.
Abstract. Mean-field theory
is used to model polyelectrolyte adsorption and the
possibility of overcompensation of charged surfaces.
For charged surfaces that are also chemically attractive,
the overcharging is large in high salt conditions, amounting
to 20-40% of the bare surface charge. However, full charge inversion
is not obtained in thermodynamical equilibrium for physical values
of the parameters. The overcharging increases with addition of salt,
but does not have a simple scaling form with the bare surface charge.
Our results indicate that more evolved explanation is needed in order
to understand polyelectrolyte multilayer built-up. For strong
polymer-repulsive surfaces, we derive simple scaling laws for the
polyelectrolyte adsorption and overcharging. We show that the overcharging
scales linearly with the bare surface charge, but its magnitude is very
small in comparison to the surface charge. In contrast with the attractive
surface, here the overcharging is found to decrease substantially with
addition of salt. In the intermediate range of weak repulsive surfaces,
the behavior with addition of salt crosses over from increasing overcharging
(at low ionic strength) to decreasing one (at high ionic strength).
Our results for all types of surfaces are supported by full numerical
solutions of the mean-field equations.
http://arxiv.org/abs/cond-mat/0312098
115. Models of Gemini surfactants. [pdf]
Diamant, H. ; Andelman, D.
Surfactant Science Series, (2004), 117(Gemini Surfactants), 37-64.
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.
http://arxiv.org/abs/cond-mat/0302184
114. Parallel and
perpendicular lamellae on corrugated surfaces.[pdf]
Tsori, Y. ; Andelman, D.
Macromolecules, (2003), 36(22), 8560-8566.
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.
http://arxiv.org/abs/cond-mat/0208127
113. Onset of DNA
aggregation in presence of mono- and multivalent counterions.[pdf]
Burak, Y. ; Ariel, G. ; Andelman, D.
Biophysical Journal, (2003), 85(4), 2100-2110.
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 CDNA is
smaller than the monovalent salt concentration, the threshold multivalent
ion concentration depends linearly on CDNA,
having the form α CDNA + β . The
coefficients α and β 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.
http://arxiv.org/abs/cond-mat/0304002
112. Adsorption and
depletion of polyelectrolytes from charged surfaces.[pdf]
Shafir, A. ; Andelman, D. ; Netz, R. R.
Journal of Chemical Physics, (2003), 119(4), 2355-2362.
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.
http://arxiv.org/abs/cond-mat/0302126
111. Structural changes in
block copolymers: Coupling of electric field and mobile ions.[pdf]
Tsori, Y. ; Tournilhac, F. ; Andelman, D. ; Leibler,
L.
Physical Review Letters, (2003), 90(14), 145504/1-145504/4.
Abstract.We argue that the presence of
dissociated ions in block copolymers under electric 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.
http://arxiv.org/abs/cond-mat
/0208129
110. Ordering
mechanisms in diblock copolymers.[pdf]
Tsori, Y. ; Andelman, D.
Interface Science, (2003), 11(2), 259-268.
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 electric 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.
http://arxiv.org/abs/cond-mat
/0208127
109. Persistence length
of a strongly charged rod-like polyelectrolyte in the presence of
salt.[pdf]
Ariel, G. ; Andelman, D.
Physical Review E, and Soft Matter Physics, (2003), 67(1-1),
011805/1-011805/11.
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.
http://arxiv.org/abs/cond-mat
/0206361
108. The unbinding transition
of mixed fluid membranes.[pdf]
Komura, S. ; Andelman, D.
Europhysics Letters, (2003), 64(6), 844-850.
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.
http://arxiv.org/abs/cond-mat/0205144
107. Neutral and charged
polymers at interfaces. [pdf]
[2-column version]
[pdf]
Netz, R. R. ; Andelman, D.
Physics Reports, (2003), 380, 1-95 .
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.
http://arxiv.org/abs/cond-mat/0203364
106. Polyelectrolyte
persistence length: Attractive effect of counterion correlations and
fluctuations. [pdf]
Ariel, G. ; Andelman, D.
Europhysics Letters, (2003), 61(1), 67-73.
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
mechanical 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.
http://arxiv.org/abs/cond-mat
/0112337
105. Adhesion of membranes with
competing specific and generic interactions. [pdf]
Weikl, T. R. ; Andelman, D. ; Komura, S. ; Lipowsky,
R.
European Physical Journal E -- Soft Matter, (2002), 8, 59-66.
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.
http://arxiv.org/abs/cond-mat/0205080
104. Thin film diblock
copolymers in electric field: Transition from perpendicular to parallel
lamellae. [pdf]
Tsori, Y. ; Andelman, D.
Macromolecules, (2002), 35(13), 5161-5170.
Abstract. We examine the alignment of thin
film diblock copolymers subject to a perpendicular electric field. Two
regimes are considered separately: 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.
http://arxiv.org/abs/cond-mat
/0110282
103.
Polyelectrolytes in solution and at surfaces. [pdf]
Netz, R.R. ; Andelman, D.
Encyclopedia of Electrochemistry, Eds. M. Urbakh and E. Giladi, Vol. I,
Wiley-VCH, Weinheim, 2002, Chapter 2.7, pp. 282--322;
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.
http://arxiv.org/abs/cond-mat/0101314
102. Diblock copolymer thin
films: parallel and perpendicular lamellar phases in the weak
segregation limit. [pdf]
Tsori, Y. ; Andelman, D.
European Physical Journal E -- Soft Matter,(2001), 5(5), 605-614.
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.
http://arxiv.org/abs/cond-mat
/0105213
101. Ordered
morphologies of confined diblock copolymers. [pdf]
Tsori, Y. ; Andelman, D.
Materials Research Society Symposium Proceedings, (2001), 651
(Dynamics in Small Confining Systems V), T8.1.1-T8.1.11.
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.
http://arxiv.org/abs/cond-mat
/0101022
100. Adsorbed and
grafted polymers at equilibrium. [pdf]
Netz, R.R. ; Andelman, D.
Surfactant Science Series, (2001), 103 (Oxide
Surfaces), 115-155.
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).
http://arxiv.org/abs/cond-mat
/0002266
99. Supported membranes on
chemically structured and rough surfaces. [pdf]
Swain, P.S. ; Andelman, D.
Physical Review E,(2001), 63(5-1), 051911/1-051911/12.
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.
http://arxiv.org/abs/cond-mat
/0009224
98. Surface induced ordering
in thin film diblock copolymers: Tilted lamellar phases. [pdf]
Tsori, Y. ; Andelman, D.
Journal of Chemical Physics, (2001), 115(4),
1970-1978.
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.
http://arxiv.org/abs/cond-mat
/0103250
97. Diblock copolymer
ordering induced by patterned surfaces above the order-disorder
transition. [pdf]
Tsori, Y. ; Andelman, D.
Macromolecules, (2001), 34(8), 2719-2727.
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.
http://arxiv.org/abs/cond-mat/0007055
96. Discrete aqueous solvent
effects and possible attractive forces. [pdf]
Burak, Y. ; Andelman, D.
Journal of Chemical Physics, (2001), 114(7),
3271-3283.
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.
http://arxiv.org/abs/cond-mat
/0007035
95. Kinetics of surfactant
adsorption: the free energy approach. [pdf]
Diamant, H. ; Ariel, G. ; Andelman, D.
Colloids and Surfaces, A,(2001), 183-185 259-276.
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.
http://arxiv.org/abs/cond-mat/0007146
94. Diblock copolymer ordering
induced by patterned surfaces. [pdf]
Tsori, Y. ; Andelman, D.
Europhysics Letters, (2001), 53(6), 722-728.
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.
http://arxiv.org/abs/cond-mat/0007056
93. Polyelectrolyte
adsorption. [pdf]
Andelman, D. ; Joanny, J.-F.
Comptes Rendus de l'Academie des Sciences, Serie IV: Physique,
Astrophysique, (2000), 1(9), 1153-1162.
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 θ solvent conditions. The behavior of flexible and
semi-rigid chains is discussed separately 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 positive and negative polyelectrolytes on planar surfaces and
colloidal particles.
http://arxiv.org/abs/cond-mat/0011072
92. Polyelectrolyte
titration: theory and experiment. [pdf]
Borukhov, I. ; Andelman, D. ; Borrega, R. ; Cloitre,
M. ; Leibler, L. ; Orland, H.
Journal of Physical Chemistry
B, (2000), 104(47), 11027-11034.
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.
http://arxiv.org/abs/cond-mat/0005306
91. Hydration interactions:
Aqueous solvent effects in electric double layers. [pdf]
Burak, Y. ; Andelman, D.
Physical Review E,(2000), 62(4-B), 5296-5312.
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 electric 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.
http://arxiv.org/abs/cond-mat/0004098
90. Adhesion-induced lateral
phase separation in membranes. [pdf]
Komura, S. ; Andelman, D.
European Physical Journal E -- Soft Matter,(2000), 3(3), 259-271.
Abstract. Adhesion between membranes is
studied using a phenomenological model, where the inter-membrane 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
symmetric overshoots. Adhesion mediated by other types of stickers is also
considered.
http://arxiv.org/abs/cond-mat/0001164
89. Adsorption of
large ions
from an electrolyte solution: a modified Poisson-Boltzmann equation.
[pdf]
Borukhov, I. ; Andelman, D. ; Orland, H.
Electrochimica Acta, (2000), 46(2-3), 221-229.
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.
http://arxiv.org/abs/cond-mat/9911482
88. Self-assembly in
mixtures of polymers and small associating molecules. [pdf]
Diamant, H. ; Andelman, D.
Macromolecules, (2000), 33(21), 8050-8061.
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 intra-chain 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 intra-chain aggregation (polysoaps) is gradual, having
no sharp onset.
http://arxiv.org/abs/cond-mat/9906271
87. Binding of molecules to
DNA and other semiflexible polymers. [pdf]
Diamant, H. ; Andelman, D.
Physical Review E,(2000), 61(6-B), 6740-6749.
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.
http://arxiv.org/abs/cond-mat/9910162
86. Defects in lamellar
diblock copolymers: Chevron- and Omega-shaped tilt boundaries.
[pdf]
Tsori, Y. ; Andelman, D. ; Schick, M
Physical Review E,(2000), 61(3), 2848-2858.
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 symmetric 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(
http://arxiv.org/abs/cond-mat/9905378
85. The Influence of
Substrate Structure on Membrane Adhesion. [pdf]
Swain, P.S. ; Andelman, D.
Langmuir (1999), 15(26), 8902-8914.
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.
http://arxiv.org/abs/cond-mat/9905205
84. Kinetics of Surfactant
Adsorption at Fluid-Fluid Interfaces: Surfactant Mixtures. [pdf]
Ariel, G. ; Diamant, H. ; Andelman, D.
Langmuir (1999), 15(10), 3574-3581.
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.
http://arxiv.org/abs/cond-mat/9903428
83. Effect of polyelectrolyte
adsorption on intercolloidal forces. [pdf]
Borukhov, I. ; Andelman, D. ; Orland, H.
Journal of Physical Chemistry B, (1999), 103(24), 5042-5057.
Abstract. The behavior of polyelectrolytes
between charged surfaces immersed in semi-dilute 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 inter-surface 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 ksa2/p, where
ks-1 is the Debye-Hückel 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
ks-1. The effect of irreversible
adsorption is discussed as well, and it is shown that inter-surface
attraction can be obtained in this case as well.
http://arxiv.org/abs/cond-mat/9803324
82. Onset of self-assembly in
polymer-surfactant systems. [pdf]
Diamant, H. ; Andelman, D.
Europhysics Letters, (1999), 48(2), 170-176.
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.
http://arxiv.org/abs/cond-mat/9903050
81. Monolayers of diblock
copolymer at the air-water interface: the attractive monomer-surface
case. [pdf]
Faure, M.C. ; Bassereau, P. ; Carignao, M.A. ; Szleifer,
I. ; Gallot, Y. ; Andelman, D.
European Physical Journal B,(1998), 3(3), 365-375.
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 two-dimensional layer.
Both theoretical Calculations agree with the experiments in this
region.
http://arxiv.org/abs/cond-mat/9706249
80. Random polyelectrolytes
and polyampholytes in solution. [pdf]
Borukhov, I. ; Andelman, D. ; Orland, H.
European Physical Journal
B,(1998), 5(4), 869-880; (1998), 6(2), 293
[Erratum].
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 postive or negative 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.
http://arxiv.org/abs/cond-mat/9804304
79. Interfaces and
grain boundaries of lamellar phases. [pdf]
Villain-Guillot, S. ; Netz, R.R. ; Andelman,
D. ; Schick, M.
Physica A,(1998), 249(1-4), 285-292.
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.
http://arxiv.org/abs/cond-mat/9803288
78. Scaling laws of
polyelectrolyte adsorption. [pdf]
[erratum]
[pdf]
Borukhov, I. ; Andelman, D. ; Orland, H.
Macromolecules, (1998), 31(5), 1665-1671; 31(5), 1704 [Erratum].
Abstract. Adsorption of charged
polymers
(polyelectrolytes) from a semi-dilute solution to a charged surface was
investigated theoretically. We obtained simple scaling laws for (i) the
amount of polymer Γ adsorbed to the surface and (ii) 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
1)
in a low-salt solution, both Γ and D scale as
p-1/2. In
high-salt solutions
D
~ cb1/2/p whereas the scaling
behavior of
Γ depends on the strength of the polymer charge. For weak
polyelectrolytes
(p<< 1) we find that
Γ ~ p/cb1/2,
and for strong polyelectrolytes
Γ ~ cb1/2/p. Our results
are in good agreement with adsorption experiments and with numerical
solutions of mean-field equations.
http://arxiv.org/abs/cond-mat/9706090
77. The lamellar-disorder
interface: one-dimensional modulated profiles. [pdf]
Villain-Guillot, S. ; Andelman, D.
European Physical Journal B,(1998), 4(1), 95-101.
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.
http://arxiv.org/abs/cond-mat/9803247
76. Steric effects
in electrolytes: a modified Poisson-Boltzmann equation. [pdf]
Borukhov, I. ; Andelman, D. ; Orland, H.
Physical Review Letters, (1997), 79(3), 435-438.
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.
http://arxiv.org/abs/cond-mat/9803258
75. Interfaces of modulated
phases. [pdf]
Netz, R. R. ; Andelman, D. ; Schick, M.
Physical Review Letters, (1997), 79(6), 1058-1061.
Abstract. Numerically minimizing a
continuous free-energy functional which yields
several modulated phases, we obtain the order-parameter profiles and
interfacial free energies of symmetric and nonsymmetric 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.
http://arxiv.org/abs/cond-mat/9803260
74. Adsorption kinetics
of surfactants at fluid-fluid interfaces. [pdf]
Diamant, H. ; Andelman, D.
Progress in Colloid & Polymer Science, (1997), 103 (Amphiphiles at
Interfaces), 51-59.
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.
http://arxiv.org/abs/cond-mat/9803366
73. Shape of
phospholipid/surfactant mixed micelles: Cylinders or disks? Theoretical
analysis. [pdf]
Kozlov, M. M. ; Lichtenberg, D. ; Andelman,
D.
Journal of Physical Chemistry B, (1997), 101(33), 6600-6606
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.
http://arxiv.org/abs/cond-mat/9803259
72. Roughness-induced wetting.
[pdf]
Netz, R. R. ; Andelman, D.
Physical Review E,(1997), 55(1-B), 687-700.
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
minimum 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.
http://arxiv.org/abs/cond-mat/9803261
71. Theory and
phenomenology of mixed amphiphilic aggregates. [pdf]
Kozlov, M.M ; Andelman, D.
Curr. Opin. Colloid Interface Sci., (1996), 1, 362-366.
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.
http://arxiv.org/abs/cond-mat/9803264
70. Kinetics of surfactant
adsorption at fluid-fluid interfaces. [pdf]
Diamant, H. ; Andelman, D.
Journal of Physical Chemistry, (1996), 100(32), 13732-13742.
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.
http://arxiv.org/abs/cond-mat/9608140
69. Des zebrures
aux motifs a pois (From Zebra-like patterns to pea-like ones). [pdf]
Andelman, D.
La Recherche, (1996), (284), 41-43. (written in French).
Abstract. Motif-forming structures, such as magnetic surfaces, are explained as the result of a competition between two antagonistic forces.
68. Global phase diagrams of
mixed surfactant-polymer systems at interfaces. [pdf]
Chatellier, X. ; Andelman, D.
Journal of Physical Chemistry, (1996), 100(22), 9444-9455.
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 semi-dilute 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.
http://arxiv.org/abs/cond-mat/9803263
67. Protein adsorption
on lipid monolayers at their coexistence region. [pdf]
Netz, R. R.; Andelman, D. ; Orland, H.
Journal de Physique II (France), (1996), 6(7), 1023-1047.
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 multi-component membranes showing coexistence of distinct fluid
phases.
http://arxiv.org/abs/cond-mat/9803262
66. Kinetics of surfactant
adsorption at fluid/fluid interfaces: non-ionic surfactants. [pdf]
Diamant, H. ; Andelman, D.
Europhysics Letters, (1996), 34(8), 575-580.
Abstract. We present a model treating the
kinetics of adsorption of soluble 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 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 findings.
http://arxiv.org/abs/cond-mat/9803320
65. Hydrodynamic mapping of
two-dimensional electric fields in monolayers. [pdf]
Nassoy, P. ; Birch, W. R. ; Andelman, D. ; Rondelez, F.
Physical Review Letters, (1996), 76(3), 455-8.
Abstract. We have measured the 2D dipolar
electric fields generated by surface density fluctuations in Langmuir
monolayers using optical microscopy to monitor the motion of micron-size,
electrically 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. [pdf]
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. [pdf]
Borukhov, I. ; Andelman, D. ; Orland, H.
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 Self Consistent
Field 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. [pdf]
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. [pdf]
Borukhov, I. ; Andelman, D. ; Orland, H.
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. [pdf]
Fattal, D. R. ; Andelman, D. ; Ben-Shaul, A.
Langmuir, (1995), 11(4), 1154-61.
Abstract. A molecular model is used to
calculate 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. [pdf]
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. [pdf]
Andelman, D.
Handbook of Biological Physics (1995), 1B 603-42. Edited by
R. Lipowsky and E. Sackmann,(Elsevier Science B.V., Amsterdam).
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. [pdf]
Taniguchi, T. ; Kawasaki, K. ; Andelman, D. ; Kawakatsu, T.
Journal de Physique II (France), (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. [pdf]
Diamant, H. ; Andelman, D.
Langmuir, (1994), 10(9), 2910-16.
Abstract. We present a theoretical
explanation for experimental results obtained recently regarding dimeric
surfactants. The non-monotonic dependence of the specific area at the
air/water interface on the spacer carbon number is accounted for. In
addition, understanding the role of spacer carbon number at the air/water
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. On the
other hand, 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. [pdf]
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.
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. [pdf]
Aharonson, V. ; Andelman, D. ; Zilman, A. ; Pincus,
P. A. ; Raphael, E.
Physica A,(1994), 204(1-4), 1-16. [Erratum: 227, 158-160 (1996)].
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. [pdf]
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 inter-pair 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. [pdf]
Kawakatsu, T. ; Andelman, D. ; Kawasaki,
K. ; Taniguchi, T.
Journal de Physique II (France), (1993), 3(7), 971-97.
Abstract.We investigate
unilamellar membranes and vesicles composed of an A/B mixture of partially
miscible amphiphiles. Assuming a simple bilinear coupling between relative
composition and local curvature, and in the strong seregation limit of the
A/B mixture, we 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. The limits of large and small surface tension are
discussed separately. These findings extend previous results obtained
close to the A/B critical point (shallow quench).For the same limit of
strong segregation, we also investigate the coupling between the
separation of the system into A and B domains, and the overall shape of
closed-shape vesicles. For cylindrical vesicles of fixed overall area (or
equivalently vesicles embedded in a two-dimensional space), equilibrium
shapes and phase diagrams are obtained. We also consider the effect
of an added pressure difference (osmotic pressure) across the
vesicle. The results are extended to axial symmetric vesicles embedded in
a three-dimensional space.
50. Electrostatic
interactions in two-component membranes. [pdf]
Guttman, G. D. ; Andelman, D.
Journal de Physique II (France), (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.
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. [pdf]
Andelman, D. ; Joanny, J.-F.
Journal de Physique II (France), (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. [pdf]
Andelman, D. ; Kawakatsu, T. ; Kawasaki, K.
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 positive or negative inner pressure,
their shapes
can be calculated numerically; in the absence of added inner pressure, the
shape found analysis is composed of circular sections.
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. [pdf]
Harden, J. L. ; Andelman, D.
Langmuir, (1992), 8(10), 2547-51.
Abstract. We consider thin layers which
completely wet nonideal (either rough or heterogeneuos in
composition) solid surfaces. Two different sources of fluctuations
of the liquid surface are identified, and the competition between them is
investigated. For thick enough films (but still in submicrometer range),
the liquid surface fluctuations are dominated by thermally induced
capillary waves. For thin films, capillary waves are strongly damped and
the liquid surface fluctuations are correlated with the disorder of the
underlying solid surface. The fluctuation spectrum is explicitly
calculated for a van der Waals liquid and for several different types of
solid disorder. Our findings are in agreement with recent X-ray specular
reflection and diffuse scatting experiments.
44. Membrane curvature
elasticity in weakly charged lamellar phases. [pdf]
Harden, J. L. ; Marques, C. ; Joanny, J.-F.; Andelman,
D.
Langmuir, (1992), 8(4), 1170-5.
Abstract. We study the effect of
electrostatic interactions on the membrane bending energies of weakly
charged, swollen, lamellar phases of surfactant solutions. We treat the
surface charge density of the lamellae as a constant and consider only
situations where it is low enough so that the distance 2d between
lamellae is the smallest relevant length scale in the problem. In the
presence of salt (the short-distance Debye-Hückel regime) we show
that 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 constant is
also calculated for membranes held at constant electric potential and is
compared to the constant charge density case. In the absence of salt,
continuity arguments predict an electrostatic contribution to the bending
energy that scales as d3. Furthermore, a direct calculation for
concentric cylindrical membranes gives exactly the same scaling behavior
(including the numerical prefactor) as in the presence of salt.
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. [pdf]
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).
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. [pdf]
Safran, S.A. ; Pincus, P.A. ; Andelman,
D. ; MacKintosh, F.C.
Physical Review A, (1991), 43(2), 1071-8.
Abstract. Although large, spherical
surfactant vesicles are generally unstable to either lamellar or micellar
phases, mixtures of two surfactants can lead to spontaneous vesicle
formation. We show theoretically how the energetic stabilization of mixed
vesicles can occur by considering the curvature elasticity of the
surfactant bilayer. 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. The vesicles have a Gaussian distribution about an average size
determined by the effective spontaneous curvature; the width of the
distribution is calculated as a function of concnentration. The stability
of these vesicles with respect to a flat lamellar phase is estimated. The
predictions of the ranges of stability of the various phases as a function
of the three concentrations (solvent, e.g., water-and the two
amphiphiles) are in qualitative agreement with recent experiments.
39. Thin liquid films on rough or
heterogeneous solids. [pdf]
Robbins, M.O. ; Andelman, D. ; Joanny, J.-F.
Physical Review A,(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.
38.On the theory
of tripod amphiphiles, chiral discrimination and phase transitions in
Langmuir monolayers. [pdf]
Andelman, D.
Physica A,(1990), 168(1), 172-8.
Abstract. Chiral discrimination is
investigated theoretically for chiral molecules that form an insoluble
Langmuir monolayer on the water/air interface. For a specific type of
model molecules - tripod amphiphile - the chiral discrimination is
calculated
for various types of intermolecular interactions: van der Waals, hydrogen
bonding, dipoles, charges, etc. In particular, we find that van der Waals
interactions prefer chiral segregation whereas electrostatic interactions
prefer heterochiral compounds. Monolayer phase diagrams are calculated for
both cases.
37. Modulated
phases in amphiphilic monolayers at the water/air interface. [pdf]
Andelman, D.
Materials Research Society Symposium Proceedings, (1990), 177
(Macromol. Liq.), 337-44.
Abstract. Recently, modulated phases of
insoluble monolayers of fatty acids and phospholipids
spread on the water/air interface have been observed by fluorescence
microscopy experiments. We propose a theoretical explanation of this
observation by including electrostatic (dipolar) interactions in the total
free energy calculation for the monolayer. Dipoles can originate from two
sources: neutral amphiphiles have a permanent dipole and charged
amphiphiles have an induced one. Modulated phases are found to be stable in
two different limits: close to the liquid-gas transition and at low
temperatures. Several phases with stripe and hexagonal symmetry are
predicted and the phase transitions between them are calculated.
36. Theory of spontaneous
vesicle formation in surfactant mixtures. [pdf]
Safran, S.A. ; Pincus, P. ; Andelman, D.
Science (Washington, DC, United States), (1990), 248(4953), 354-6.
Abstract. The curvature elastic energy of
bilayer vesicles formed by a mixture 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
concentrations 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
multi-membrane systems. [pdf]
Pincus, P. ; Joanny, J.-F. ; Andelman, D.
Europhysics Letters, (1990), 11(8), 763-8.
Abstract. The effects of electrostatic
interactions on steric repulsion and curvature elasticity are considered
for dilute multimembrane systems as 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
cutoff the out-of-plane undulations and change significantly the membrane
bending constant in qualitative agreement with recent experiments.
Abstract.
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. [pdf]
Andelman, D.
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. Surfactants are amphiphiles that
combine hydrophobicity with hydrophilicity behavior; namely, they prefer
to reside to reside or to create spontaneously liquid/liquid or liquid/gas
interfaces. We give here three examples of amphiphilic
systems: (i) isoluble monolayers of lipids or fatty acids at the water/air
interface -called Langmuir monolayers (ii)Micellar solutions where the
solvent can be either an aqueous solution or a non-polar organic solvent
like oil. (iii)Microemulsions which are thermodynamically stable,
fluid, oil-water-surfactant mixtures; most microemulsions contain also
cosurfactant (alcohol) and /or salt. In this extended abstract we will
briefly review some of the main results obtained for Langmuir monolayers
and microemulsions.
31. Chiral discrimination
and phase transitions in Langmuir monolayers. [pdf]
Andelman, D.
Journal of the American Chemical Society, (1989), 111(17),
6536-44.
Abstract. Chiral discrimination is
investigated theoretically for chiral molecules that form an insoluble
Langmuir monolayer at the water/air interface.
For particular tripodal shaped molecules, we
calculate the chiral discrimination for various types
of intermolecular interactions: van der Waals, dipoles, charges, etc. The
calculation, based on Boltzmann-weighted averaging of molecular
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, we draw the analogy with sublimation experiments in bulk systems
and propose a three-component thermodynamic model. The variable area per
molecule and also the chiral discrimination parameter enter as important
parameters in the model. Phase diagrams for conglomerates and racemic
compounds are calculated in qualitative agreement with
experiments. Possible connections and interpretation of existing
experimental data are discussed, and some new experiments for chiral
monolayers are proposed.
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 negnegative (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. [pdf]
Andelman, D. ; Joanny, J.-F. ; Robbins, M.O.
Europhysics Letters, (1988), 7(8), 731-6.
Abstract. The profile of a thin liquid 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 molecules 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. [pdf]
Cates, M.E. ; Andelman, D. ; Safran, S.A. ; Roux,
D.
Langmuir, (1988), 4(4), 802-6.
Abstract. A thermodynamic model for
microemulsions (previously described) is used to predict some further
aspecta of the phase behavior. The stability of the microemulsion under
variation of molecular parameters (such as the bending constant 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 experimentally.
Our model exhibits a phase behavior close to the
experimental one, not only in terms of the variation with surfactant
concentration 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. [pdf]
Cates, M.E. ; Roux, D. ; Andelman, D. ; Milner,
S.T. ; Safran, S.A.
Europhysics Letters,(1988), 5(8), 733-9; [erratum], (1988),7(1), 94.
Abstract. A simple model is given for the
anomalous (flow-birefringent) isotropic phase, known as L3, that is seen
in certain surfactant solutions at volume 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. [pdf]
Milner, S.T. ; Safran, S.A. ; Andelman, D. ; Cates,
M.E. ; Roux, D.
J. de Physique (France), (1988), 49, 1065-1076.
Abstract.
The correlation functions and structure factor of microemulsions are calculated from a statistical
thermodynamic approach which has been previously used to obtain the equilibrium phase diagrams. The
structure factor, S(q), has a peak at a wavevector q_{max} ~ pi/xi where xi is the domain size of the oil and water regions. The physical origin of this peak are the correlations induced by the presence of the curvature energy of
the surfactant film; the renormalization of the bending modulus by thermal fluctuations plays an important
role in stabilizing these fluctuations. Real space representations of these correlations show that there is
significant strength in S(q) from several different wavevectors.
25. Middle-phase microemulsions and
random surfaces
Safran, S.A. ; Roux, D. ; Milner S.T. ; Cates
M.E. ; Andelman, D.
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.
Brochard, F. ; Joanny, J.-F. ; Andelman, D.
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, D. ; Brochard, F. ; Joanny, J.-F.
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 insoluble Langmuir
monolayers. These
long-range and repulsive dipolar interactions stabilize undulating phases
in thermodynamic equilibrium. 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 liquid-gas transition and of the latter to the
liq.-solid
and liquid expanded-liquid condensed transitions are discussed. In an
ionic
solution, the undulation periodicity can be controlled by the strength of
the
ionic solution.
22. Modulated structures and competing
interactions in amphiphilic monolayers.
Andelman, D. ; Brochard, F. ; Joanny, J.-F.
Proceedings of the National Academy of Sciences (USA),(1987), 84(14),
4717-18.
Abstract. The effects of electrostatic
interactions on the phase behavior and structure of insoluble Langmuir
monolayers was investigated at the liquid/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 liquid-gas crit. point and (ii) at low
temps.
21. Structure and phase
equilibria of microemulsions. [pdf]
Andelman, D. ; 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 equilibrium and structural properties of
microemulsions. Space is divided into cells of side ξ ; 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 constant
Κ(ξ), which
is small for ξ ≥ ξκ, the de Gennes-Taupin
persistence length. The model
predicts a middle-phase microemulsion of structual length scale
ξ ≈ ξκ which coexists with dilute phases of
surfactant in oil and surfactant in water.(These phases have
ξ ≈ α ,α being a molecular length.) On the same
ternary phase
diagram, we find also two regions of two-phase equilibrium involving
upper- and
lower-phase microemulsions that coexist with either almost pure water or
oil. At low temperatures and/or high values of the bare bending
constant,
Κ0 ≡ Κ(α),
the middle-phase microemulsion may be entirely precluded by
separation to a lamellar phase, whereas at high temperature and/or low
values
of Κ 0 ,
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 symmetric. It may be asymmetrized by: (i) spontaneous
curvature in the middle phase or (ii) a difference between the free energy
of the two dilute phases. If the asymmetry is sufficiently large, the
three-phase region disappears.
20. Ordered and curved
meso-structures in membranes and amphiphilic films. [pdf]
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
dilute (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, J.-F. ; Andelman, D.
Journal of Colloid and Interface Science, (1987), 119(2), 451-8.
Abstract. The steady-state motion of a
liquid A/liquid 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 liquid/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. [pdf]
Andelman, D. ; Brochard, F. ; Joanny, J.-F.
Journal of Chemical Physics, (1987), 86(6), 3673-81.
Abstract. Insoluble Langmuir monolayers are
investigated in the presence of dipolar forces which can have two
origins: permanent dipoles in neutral monolayers and induced dipoles in
charged monolayers. The main effect of the additional long-range repulsive
interactions is to stabilize undulating phases at thermodynamic
equilibrium. Phase diagrams are obtained in two limits: close to the
liquid-gas critical point via a Ginzburg-Landau expansion of the free
energy (mainly within a mean-field approximation), and at low temperatures
by free energy minimization.
Possible applications of this theory to experiments at the
liquid-gas, liquid expanded-liquid condensed, and solid-liquid transitions
are discussed.
17. Origin of middle-phase
microemulsions. [pdf]
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
calculate the phase behavior of microemulsions. The surfactant film at
the oil-water interface is treated as an incompressible layer whose
bending constant is renormalized by thermal fluctuations. Two- and
three-phase equilibria 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 constant is
renormalized to smaller values.
16. One-dimensional Ising
model in a variety of random fields. [pdf]
Andelman, D.
Physical Review B (1986) 34(9), 6214-18.
Abstract. We study 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.
15. Metastability and Landau theory for
random fields and demixing in porous media.
Andelman, D. ; Joanny, J.-F.
a
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 liquid mixtures 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, D. ; Brochard, F. ; De Gennes,
P.-G. ; Joanny, J.-F.
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 liquid-gas coexistence
region for the Langmuir monolayer, a supercryst. phase is expected (where
liquid and gas regions form a spatially periodic arrangement with periods
of .apprx.103 .ANG.).
12. Metastability in the
random-field Ising model. [pdf]
Andelman, D. ; Joanny, J.-F.
Physical Review B,(1985), 32(7), 4818-21.
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. [pdf]
Andelman, D. ; Joanny, J.-F.
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 liquid mixtures 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 thermodynamic equilibrium. A
nonequil. mechanism to explain the foam stability is proposed.
10. Critical behavior with
axially correlated random bonds. [pdf]
Andelman, D. ; Aharony, A.
Physical Review B,(1985), 31(7), 4305-12.
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
φ=α +
d1ν is used.
For d1 <
d-1, we 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.
9. Critical amplitude of the
Zeroes and divergences. [pdf]
Kaufman, M. ; Andelman, D.
Physical Review B,(1984), 29(7),4010-16.
Abstract. The critical 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 number of q values,
qn, introducing logarithmic terms in the free
energy. We expect that in each interval
(qn , qn+1) there is a value
n where the amplitude vanishes,
affecting the singularity of the free energy as a function of
temperature. Possible consequences for gelation and vulcanization of
polymers are discussed.
8. Scale-invariant quenched
disorder and its stability criterion at random critical points.
[pdf]
Andelman, D. ; Berker, A.N.
Physical Review B,(1984), 29(5), 2630-5. USA.
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 Γ distributions. For such
systems, the specific-heat exponent α does not equal the crossover
exponent φ at random criticality. We derive a new relation
between α and φ , which invokes characteristics of the fixed
distributions. The difference between α and φ is noted for
n-vector models in 4 - ε dimensions and for Potts models on
hierarchical lattices solved exactly. In general, stable random critical
behavior with positive α appears to be possible. We 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 ν
approximately=1.06 and 1.19. (26 References).
7. Lower critical dimension of
the random-field Ising model: A Monte Carlo study. [pdf]
Andelman, D. ; Orland, H. ; Wijewardhana,
L.C.R.
Physical Review Letters, (1984), 52(2), 145-8.
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. [pdf]
Andelman, D.
Physical Review B,(1983), 27(5), 3079-80.
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. [pdf]
Andelman, D. ; Walker, J.S.
Physical Review B, (1983), 27(1), 241-7. USA.
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.
[pdf]
Berker, A.N. ; Andelman, D.
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 second-order phase transitions at
q ≤ qc(d) to
first-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
critical and tricritical fixed points occur at low q, but merge and
annihilate at qc.
This picture has led to exact tricritical exponents in two
dimensions. It is also consistent with recent experimental results on
intercalated systems in three dimensions. Effective vacancies in pure
Potts models are also studied by Monte Carlo simulation. Their effective
chemical potential can be controlled by a four-point interaction, which
proved useful in Monte Carlo renormalization-group studies.
3. Critical exponents and
marginality of the four-state Potts model: Monte Carlo
renormalization group. [pdf]
Swendsen, R.H. ; Andelman, D. ; Berker,
A.N.
Physical Review B (1981), 24(11), 6732-5.
Abstract. The thermal critical exponent of
the four-state Potts model in two dimensions is evaluated as
ν-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
four-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.[pdf]
Andelman, D. ; Berker, A.N.
Journal of Physics A,(1981), 14(4), 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 qc(d), clearing the way to
first-order
transitions at q: qc(d) by the
condensation of
effective vacancies. The value of
qc(d) decreases with
increasing d, from diverging as exp[2 / (d - l)] at d
→ 1+, to qc(2) = 3.81 (cf exact value of
4), to
lower values at d : 2. For given d, a changeover in critical
behaviour occurs at ql(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 → 1+ ) have logarithmic corrections.
1. First- and
second-order phase transitions of infinite-state Potts models in one
dimension.[pdf]
Berker, A.N. ; Andelman, D. ; Aharony, A.
Journal of Physics A,(1980), 13(11), L413-18.
Abstract. The q-state,
d-dimensional Potts models exhibit a variety of phase-transition
behaviour in the limit d → l+ ,
q
→ ∞ ,and Ι≡ (d -1) In q finite.
The regions Ι < 1, 1 < Ι < 2, and 2 < Ι are
distinguished,
respectively, by no transition, second-order transitions (with a
new changeover phenomenon at Ι = ln 4), and first-order
transitions. The latter are due to the condensation of effective
vacancies. Critical and tricritical exponent values are given.
Dynamic surface tension and kinetics of surfactant adsorption at fluid
interfaces.
Andelman, D. ; Diamant, H.
Book of Abstracts, 215th ACS National Meeting, Dallas, March 29-April
2(1998), COLL-011. Publisher: American Chemical Society, Washington D.C
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, Boston, MA, United
States, August 18-22, 2002 (2002), POLY-762. Publisher: American Chemical
Society, Washington, D.C
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 electric field and
show
that perpendicular ordering is favored above some critical value of the
field. The obtained phase diagram depends on electric 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 electric fields can be used to
achieve a transition from lamellae parallel to the surfaces
(electrodes) to perpendicular lamellae.