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.
Abstract: Block copolymers are polymeric systems exhibiting modulated spatial structure on the nanometer to micrometer scale. We present theoreticalseveral ordering mechanisms in thin films of diblock copolymers. For temperatures above the order-disorder temperature, a linear response theory gives the polymer density in the vicinity of chemical patterned and flat surfaces. The surface pattern or template is decomposed into its Fourier modes, and the decay of these modes is analyzed. Below the order-disorder temperature, the transition of lamellar orientation from parallel to perpendicular to the surfaces is investigated. In addition, We calc. the phase diagram in the presence of an externally applied perpendicular elec. field and show that perpendicular ordering is favored above some critical value of the field. The obtained phase diagram depends on elec. field strength, film thickness and surface interactions.
Abstract: A review. Controlling the ordering of diblock copolymers is important in many applications. We discuss two mechanisms to control the orientation and ordering of diblock copolymers: above the order-disorder temperature (ODT), chemical patterned surfaces induce order in the thin film, although the bulk system is in its disordered state. For lamellar diblock copolymers (below the ODT), we show how elec. fields can be used to achieve a transition from lamellae parallel to the surfaces (electrodes) to perpendicular lamellae.
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.
Abstract: We address theoretical aggregation of DNA segments by multivalent polyamines such as spermine and spermidine. In experiments, the aggregation occurs above a certain threshold concentration of multivalent ions. We demonstrate that the dependence of this threshold on the concentration of DNA has a simple form. When the DNA concentration c_DNA is smaller than the monovalent salt concentration, the threshold multivalent ion concentration depends linearly on c_DNA, having the form \alpha*c_DNA + \beta. The coefficients \alpha and \beta are related to the density profile of multivalent counterions around isolated DNA chains, at the onset of their aggregation. This analysis agrees extremely well with recent detailed measurements on DNA aggregation in the presence of spermine. From the fit to the experimental data, the number of condensed multivalent counterions per DNA chain can be deduced. A few other conclusions can then be reached: i) the number of condensed spermine ions at the onset of aggregation decreases with the addition of monovalent salt; ii) the Poisson-Boltzmann theory over-estimates the number of condensed multivalent ions at high monovalent salt concentrations; iii) our analysis of the data indicates that the DNA charge is not over-compensated by spermine at the onset of aggregation.
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.
Abstract: We argue that the presence of dissociated ions in block copolymers under elec. fields can induce strong morphological changes and even lead to phase transitions. We investigate, in particular, diblock copolymers in the bcc. (bcc) phase. In pure dielectric materials (no free charges), a dielectric breakdown is expected to occur for large enough elec. fields, preempting any structural phase transition. On the other hand, dissociated ions are predicted to induce a phase transition to a hexagonal array of cylinders, at fields of about 10 V/μm or even lower. The strength of this mechanism can be tuned by controlling the amt. of free ions present.
Abstract: We present several ordering mechanisms in diblock copolymers. For temperatures above the order-disorder temperature and in the weak segregation regime, a linear response theory is presented which gives the polymer density in the vicinity of confining flat surfaces. The surfaces are chemical patterned where different regions attract different parts of the copolymer chain. The surface pattern or template is decomposed into its Fourier modes, and the decay of these modes is analyzed. The propagation of the surface pattern into the disordered bulk is given for several types of patterns (e.g. uniform and striped surface). It is further shown that complex morphological can be induced in a thin film even though the bulk is disordered. We next consider lamellar diblock copolymers (low temperature regime) in the presence of a striped surface. It is shown that lamellae acquire a tilt with respect to the surface, if the surface periodicity is larger than the bulk one. The lamellae close to the surface are strongly distorted from their perfect shape. When the surface and lamellar periodicities are equal, the lamellae are perpendicular to the surface. Lastly, the transition from parallel to perpendicular lamellae in a thin film is presented. The transition between the two states depends on the surface separation and strength of surface interactions. We further calc. the phase diagram in the presence of perpendicular elec. field favoring perpendicular ordering. In the strong segregation limit we introduce a simple model to calc. the phase diagram of the fully parallel, fully perpendicular and mixed (parallel and perpendicular) states.
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.
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.
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.
Abstract:The persistence length of a single, strongly charged, stiff polyelectrolyte chain is investigated theoretical Path integral formulation is used to obtain the effective electrostatic interaction between the monomers. We find significant deviations from the classical Odijk, Skolnick and Fixman (OSF) result. An induced attraction between monomers is due to thermal fluctuations and correlations between bound counterions. The electrostatic persistence length is found to be smaller than the OSF value and indicates a possible mech. instability (collapse) for highly charged polyelectrolytes with multivalent counterions. In addition, we calc. the amt. of condensed counterions on a slightly bent polyelectrolyte. More counterions are found to be adsorbed as compared to the Manning condensation on a cylinder.
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.
Abstract: Chain-like macromolecules in solution, whether biol. or synthetic, transform from a spatially extended conformation to a compact one upon change of temperature or solvent qualities. This sharp transition plays a key role in various phenomena, including DNA condensation, protein folding, and the behavior of polymer solutions In biol. processes such as DNA condensation the collapse is sensitively induced by a small amt. of added molecules Here we derive a general criterion for the effect of such agents on conformational transitions. We find two different scenarios depending on chain stiffness. If the persistence length, the characteristic distance along which the chain retains its direction, is smaller than the range of attractive correlations induced by the agent (typically up to several nanometers), the chain contracts gradually. Stiffer chains undergo sharp collapse. We thereby suggest that the enhanced rigidity of double-stranded DNA as compared to the single strand is a prerequisite for sharp, controllable conformational transitions.
Abstract: We examine the alignment of thin film diblock copolymers subject to a perpendicular elec. field. Two regimes are considered sep.: weak segregation and strong segregation. For weakly segregated blocks and below a critical value of the field, Ec, surface interactions stabilize stacking of lamellae in a direction parallel to the surfaces. Above the critical field, a first-order phase transition occurs when lamellae in a direction perpendicular to the confining surfaces (and parallel to the field) become stable. The film morphological is then a superposition of parallel and perpendicular lamellae. In contrast to Helfrich-Hurault instability for smectic liquid crystals, the mode that gets critical first has the natural lamellar periodicity. In addition, undulations of adjacent inter-material dividing surfaces are out-of-phase with each other. For diblock copolymers in the strong segregation regime, we find two critical fields E1 and E2 > E1. As the field is increased from zero above E1, the region in the middle of the film develops an orientation perpendicular to the walls, while the surface regions still have parallel lamellae. When the field is increased above E2, the perpendicular alignment spans the whole film. In another range of parameters, the transition from parallel to perpendicular orientation is direct.
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.
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.
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.
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).
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.
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.
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.
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.
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.
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.
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 sep. and is expressed as function of the polymer and surface charges, ionic strength of the solution and polymer bulk concentration. We mainly review mean-field results and briefly comment about fluctuation effects. The phenomenon of polyelectrolyte adsorption on a planar surface as presented here is of relevance to the stabilization of colloidal suspensions. In this respect we also mention Calculations of the inter-plate force between two planar surfaces in presence of polyelectrolyte. Finally, we comment on the problem of charge overcompensation and its implication to multi-layers formation of alternating pos. and neg. polyelectrolytes on planar surfaces and colloidal particles.
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.
Abstract:A model for ionic solutions with an attractive short-range pair interaction between the ions is presented. The short-range interaction is accounted for by adding a quadratic nonlocal term to the Poisson-Boltzmann free energy. The model is used to study solvent effects in a planar elec. double layer. The counterion density increases near the charged surface, as compared with the Poisson-Boltzmann theory, and to decrease at larger distances. The ion density profile is studied analysis in the case where the ion distribution near the plate is dominated only by counterions. Further away from the plate the density distribution can be described using a Poisson-Boltzmann theory, with an effective surface charge that is smaller than the actual one.
Abstract:Adhesion between membranes is studied using a phenomenological model, where the intermembrane distance is coupled to the concentration of sticker molecules on the membranes. The model applies to both adhesion of two flexible membranes and to adhesion of one flexible membrane onto a second membrane supported on a solid substrate. The authors mainly consider the case where the sticker molecules form bridges and adhere directly to both membranes. The calculated mean-field phase diagrams show an upward shift of the transition temperature indicating that the lateral phase separation in the membrane is enhanced due to the coupling effect. Hence the possibility of adhesion-induced lateral phase separation is predicted. For a particular choice of the parameters, the model exhibits a tricritical behavior. The authors also discuss the non-monotonous shape of the inter-membrane distance occurring when the lateral phase separation takes place. The inter-membrane distance relaxes to the bulk values with two sym. overshoots. Adhesion mediated by other types of stickers is also considered.
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.
Abstract:The interaction between a flexible polymer in a good solvent and smaller associating solute molecules such as amphiphiles (surfactants) is considered theoretical Attractive correlations, induced in the polymer because of the interaction, compete with intrachain repulsion and eventually drive a joint self-assembly of the two species, accompanied by partial collapse of the chain. Results of the analysis are found to be in good agreement with experiments on the onset of self-assembly in diverse polymer-surfactant systems. The threshold concentration for self-assembly in the mixed system (critical aggregation concentration, cac) is always lower than the one in the polymer-free solution (critical micelle concentration, cmc). Several self-assembly regimes are distinguished, depending on the effective interaction between the two species. For strong interaction, corresponding experimental to oppositely charged species, the cac is much lower than the cmc. It increases with ionic strength and depends only weakly on polymer charge. For weak interaction, the cac is lower but comparable to the cmc, and the two are roughly proportional over a wide range of cmc values. Association of small molecules with amphiphilic polymers exhibiting intrachain aggregation (polysoaps) is gradual, having no sharp onset.
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.
Abstract:The lamellar phase in diblock copolymer
systems appears as a result of a competition between mol. and entropic
forces, which selects a preferred periodicity of the lamellae. Grain
boundaries are formed when 2 grains of different orientations meet. The
authors study the case where the lamellae meet sym. with respect to the
interface. The form of the interface strongly depends on the angle,
θ,
between the normals of the grains. When this angle is small, the lamellae
transform smoothly from one orientation to the other, creating the chevron
morphological. As θ increases, a gradual transition is observed to an
omega morphological characterized by a protrusion of the lamellae along
the interface between the 2 phases. The authors present a theoretical
approach to find these tilt boundaries in 2-dimensional systems, based on
a Ginzburg-Landau expansion of the free energy, which describes the
appearance of lamellae. Close to the tips at which lamellae from
different grains meet, these lamellae are distorted. To find this
distortion for small angles, the authors use a phase variation ansatz
which assumes that the wave vector of the bulk lamellar phase depends on
the distance from the interface. Minimization of the free energy gives an
expression for the order parameter
φ(
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.
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.
Abstract:The behavior of polyelectrolytes between charged surfaces immersed in semidilute solutions is investigated theoretical A continuum mean field approach is used for calculating. numerically concentration profiles between two electrodes held at a const. potential. A generalized contact theorem relates the intersurface forces to the concentration profiles. The numerical results show that overcompensation of the surface charges by adsorbing polyelectrolytes can lead to effective attraction between equally charged surfaces. Simple scaling arguments enable us to characterize qualitative the intersurface interactions as a function of the fraction of charged monomers p and the salt concentration cb. In the low-salt regime, we find strong repulsion at short distances, where the polymers are depleted from the intersurface gap, followed by strong attraction when the two adsorbed layers overlap. The magnitude of this attraction scales as p1/2 and its dominant length scale is proportional to a/p1/2, where a is the monomer size. At larger distances, the two adsorbing surfaces interact via a weak electrostatic repulsion. For strong polyelectrolytes at high salt concentration, the polymer contribution to attraction at short distances scales as p/cb1/2 and the length scale is proportional to .sa2/p, where .s-1 is the Debye-H.ovrddot.uckel screening length. For weak polyelectrolytes at high salt concentration, the interaction is repulsive for all surface separations and decays exponentially with a decay length equal to .s-1. The effect of irreversible adsorption is discussed as well, and it is shown that intersurface attraction can be obtained in this case as well.
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.
Abstract:The surface pressure isotherms of copolymers of polystyrene-polyethylene oxide (PS-PEO) at the air-water interface were studied both experimental and theoretical, The SCMF (single chain mean-field) theory provides a very good agreement with the experiments for the entire range of surface densities and is consistent with the experiments if an adsorption energy per PEO monomer at the air-water interface of about one kBT is taken. In addition, the chain density profile was calculated for a variety of surface densities, from the dilute to the very dense ones. The SCMF approach was complemented by a mean-field approach in the low density regime, where the PEO chains act as a 2-dimensional layer. Both theoretical Calculations agree with the experiments in this region.
Abstract:The behavior of polyelectrolytes and polyampholytes in semi-dilute solutions is studied theoretical Various statistical charge distribution models along the polyelectrolyte chains were considered, i.e: (I) smeared, where the charges are uniformly distributed along the chain; (II) annealed, where the charges are allowed to associate and dissociate from the chain; (III) permuted, where the total number of charges on the chain is fixed, but the charges can move along the chain; (IV) quenched, where the charges on the chains are frozen in a random configuration; and (V) polyampholytes, where each monomer can be pos. or neg. charged, or neutral. A path integral formulation was used to derive mean field free energies for the different models. An SCF equation is obtained for the polymer order parameter and a Poisson-Boltzmann like equation for the electrostatic potential. The difference between the permuted and the smeared models is a const. shift in the chemical potential leading to similar mean field equations. Within the mean-field the quenched model is equiv. to the annealed one, provided that the system is coupled to a reservoir of polyelectrolyte chains. The RPA was used to calc. the monomer-monomer structure factor S(q) for the different statistical charge distribution models. In the annealed model, fluctuations of the monomer charges contribute to the electrostatic screening in addition to the free ions in the solution The strength of this screening depends on the variance of the monomer charge distribution and is esp. important for polyampholytes in bad solvent conditions where the mesophase separation is enhanced. The ratio between the variance and the net average charge determines whether polyampholytes behave more as polyelectrolytes or as neutral chains.
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.
Abstract:Adsorption of charged polymers (polyelectrolytes) from a semidilute solution to a charged surface was investigated theoretical We obtained simple scaling laws for (a) the amt. of polymer . adsorbed to the surface and (b) the width D of the adsorbed layer, as a function of the fractional charge per monomer p and the salt concentration cb. For strongly charged polyelectrolytes (p .ltorsim. 1) in a low-salt solution, both . and D scale as p-1/2. In high-salt solutions D .apprx. cb1/2/p whereas the scaling behavior of . depends on the strength of the polymer charge. For weak polyelectrolytes (p .mchlt. 1) we find that . .apprx. p/cb1/2, and for strong polyelectrolytes . .apprx. cb1/2/p. Our results are in good agreement with adsorption experiments and with numerical solutions of mean-field equations.
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.
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.
Abstract: Numerically minimizing a continuous free-energy functional which yields several modulated phases, we obtain the order-parameter profiles and interfacial free energies of sym. and nonsym. tilt boundaries within the lamellar phase, and of interfaces between coexisting lamellar, hexagonal, and disordered phases. Our findings agree well with chevron, omega, and T-junction tilt-boundary morphologies observed in diblock copolymers and magnetic garnet films.
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.
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.
Abstract:The authors study theoretical the possibility of a wetting transition induced by geometric roughness of a solid substrate for the case where the flat substrate does not show a wetting layer. Their approach makes use of a closed-form expression that relates the interaction between 2 sinusoidally modulated interfaces to the interaction between 2 flat interfaces. Within the harmonic approximation, the authors find that roughness-induced wetting is indeed possible if the substrate roughness (quantified by the substrate surface area) exceeds a certain threshold. In addition, the mol. interactions between the substrate and the wetting substance have to satisfy several conditions. These results are expressed in terms of a lower bound on th wetting potential for a flat substrate in order for roughness-induced wetting to occur. This lower bound has the following properties. A min. is present at zero or very small separation between the 2 interfaces, as characteristic for the non-wetting situation in the flat case. Most importantly, the wetting potential needs to have a pronounced max. at a separation comparable to the amplitude of the substrate roughness. These results are in agreement with the experimental observation of roughness-induced surface pre-melting at a glass-ice interface as well as the calculation of the dispersion interaction for the corresponding glass-water-ice system.
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.
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.
Abstract:Motif-forming structures, such as magnetic surfaces, are explained as the result of a competition between 2 antagonistic forces.
Abstract:Insoluble surfactant monolayers at the air/water interface undergo a phase transition from a high-temperature homogeneous state to a low-temperature demixed state, where dilute and dense phases coexist. Alternatively, the transition from a dilute phase to a dense one may be induced by compressing the monolayer at const. temperature. The case where the insoluble surfactant monolayer interacts with a semidilute polymer solution solubilized in the water subphase is considered. The phase diagrams of the mixed surfactant/polymer system are investigated within the framework of mean field theory. The polymer enhances the fluctuations of the monolayer and induces an upward shift of the critical temperature. The critical concentration is increased if the monomers are more attracted (or at least less repelled) by the surfactant molecules than by the bare water/air interface. In the case where the monomers are repelled by the bare interface but attracted by the surfactant molecules (or vice versa), the phase diagram may have a triple point. The location of the polymer special transition line appears to have a big effect on the phase diagram of the surfactant monolayer.
Abstract:The authors investigate theoretical the behavior of proteins as well as other large macromolecules which are incorporated into amphiphilic monolayers at the air-water interface. The authors assume the monolayer to be in the coexistence region of the "main" transition, where domains of the liquid condensed phase coexist with the liquid expanded background. Using a simple mean-field free energy accounting for the interactions between proteins and amphiphilic molecules, the authors obtain the spatial protein distribution with the following characteristics. When the proteins preferentially interact with either the liquid condensed or liquid expanded domains, they will be dissolved in the respective phase. When the proteins are energetically rather indifferent to the density of the amphiphiles, they will be localized at the line boundary between the (two-dimensional) liquid expanded and condensed phases. In between these two limiting cases, a delocalization transition of the proteins takes place. This transition is accessible by changing the temperature or the amt. of incorporated protein. These findings are in agreement with recent fluorescence microscopy experiments. The authors' results also apply to lipid multicomponent membranes showing coexistence of distinct fluid phases.
Abstract: The authors investigate theoretical the behavior of proteins as well as other large macromolecules which are incorporated into amphiphilic monolayers at the air-water interface. The authors assume the monolayer to be in the coexistence region of the "main" transition, where domains of the liquid condensed phase coexist with the liquid expanded background. Using a simple mean-field free energy accounting for the interactions between proteins and amphiphilic molecules, the authors obtain the spatial protein distribution with the following characteristics. When the proteins preferentially interact with either the liquid condensed or liquid expanded domains, they will be dissolved in the respective phase. When the proteins are energetically rather indifferent to the density of the amphiphiles, they will be localized at the line boundary between the (two-dimensional) liquid expanded and condensed phases. In between these two limiting cases, a delocalization transition of the proteins takes place. This transition is accessible by changing the temperature or the amt. of incorporated protein. These findings are in agreement with recent fluorescence microscopy experiments. The authors' results also apply to lipid multicomponent membranes showing coexistence of distinct fluid phases.
Abstract: We have measured the 2D dipolar elec. fields generated by surface density fluctuations in Langmuir monolayers using optical microscopy to monitor the motion of micron-size, elec. charged, particles trapped at the air-water interface. The particle velocity is directly proportional to the local electric field gradient. Quantitative agreement with the theory is demonstrated for charged polystyrene latex particles interacting with liquid condensed domains of pentadecanoic acid. Typical velocities are of order 0.1-10 μm/s, corresponding to forces in the 10-15-10-12 N range.
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.
Abstract: The effect of electrostatic interactions on the distribution of polymers in a good solvent is investigated theoretical for semi-dilute solutions containing charged polymers (polyelectrolytes) and small ions. A mean field approach is used to derive two coupled differential equations: a modified Poisson-Boltzmann equation for the electrostatic potential, and a SCF equation for the polymer order parameter. We compare several monomer charge distributions; smeared, annealed and quenched. The polymers are confined between two charged surfaces, and are in contact with a reservoir of polymers and electrolyte. This makes the annealed and quenched cases equiv. Non-monotonous profiles are obtained for the case of competing surface interactions: electrostatic adsorption vs. short-range desorption.
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.
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.
Abstract: A mol. model is used to calc. the free energy of mixed vesicles and cylindrical micelles, composed of lipid molecules and short chain surfactants. The free energy of both aggregates (modeled as an infinite planar bilayer and an infinite cylindrical aggregate) is represented as a sum of internal free energy and mixing entropy contributions. The internal free energy is treated as a sum of chain (conformational), head group, and surface tension terms. Calculating the free energy of each aggregation geometry as a function of lipid/surfactant composition and using common tangent construction we obtain the compositions of the bilayer and the micelle at the phase transition. By varying certain mol. parameters (such as the "hard core" area of the surfactant head group or the length of the surfactant tail) we study the role of molecular packing characteristics in determining the compositions at phase coexistence. We find, as expected, that upon increasing the preference of the surfactant for the micellar geometry (larger spontaneous curvature) the bilayer is solubilized at lower surfactant/lipid concentration ratios. For some typical values of the parameters used, reasonable agreement with experimental results for mixtures of egg phosphatidylcholine and octylglucoside is obtained.
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.
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.
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.
Abstract: The authors present a theoretical explanation for experimental results obtained recently regarding dimeric surfactants. The non-monotonic dependence of the specific area at the air/H2O interface on the spacer carbon number is accounted for. In addition, understanding the role of spacer carbon number at the air-H2O interface can help elucidate the shapes of aggregates formed in the aqueous solution The attractive and repulsive interactions of the surfactant molecules and the conformational entropy of the spacer chain are dominant factors in determining this dependence. Hydrophobic repulsion of the spacer from the H2O surface does not seem to play an important role, if any, contrary to what was previously suggested.
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.
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.
Abstract:In this paper the authors examine theoretical the chiral discrimination of molecules with a single chiral center. The authors propose a definition of the chiral discrimination parameter in terms of the difference between the second virial coefficient of pure enantiomers and their racemic mixture. This parameter enters in the equation of state of racemic mixtures and will determine their phase diagrams. The authors calc. then the chiral discrimination between D- and L-alanine using a Monte Carlo simulation to average over 11 molecular degrees of freedom at fixed intermolecular distances using the CHARMM energy function. The discrimination is found to slightly favor homochirality and mainly comes from steric hindrance at short distances. The authors also perform a direct integration for rigid chiral tetrahedron-shaped molecules Here there are only five rotational degrees of freedom. For a Lennard-Jones potential, the overall chiral discrimination is found to be predominantly heterochiral. One of the authors' main observations is that the pair free energy, internal energy, and entropy differences between the two enantiomers may change signs as a function of the interpair distance. The authors find that homochirality is preferred at shorter distances whereas heterochirality is favored at larger distances. With the authors' model molecules a strong chiral discrimination of about 43% is found. The calculation is repeated for molecules that are restricted to lie at the water/air interface. Those model molecules can be regarded as tripodal amphiphiles creating a chiral Langmuir monolayer at the water/air interface. Here the chiral discrimination is found to be smaller (about 8.8%) but still significantly heterochiral.
Abstract: The authors studied unilamellar membranes and vesicles composed of an A/B mixture of partially miscible amphiphiles. The authors show for unilamellar open-shape membranes that the competition between surface tension and curvature results in a phase with a selected periodicity (modulated phase) both in the shape and in the A/B composition assuming a simple bilinear coupling between relative composition and local curvature, and in the strong segregation limit of the A/B mixture The limits of large and small surface tension are discussed sep. These results extend previous results obtained close to the A/B critical point (shallow quench). The authors also studied the coupling between the separation of the system into A and B domains, and the overall shape of closed-shape vesicles for the same limit of strong segregation. Equilibrium shapes and phase diagrams are obtained for cylindrical vesicles of fixed overall area (or equivalently, vesicles embedded in a 2-dimensional space). The authors also consider the effect of an added pressure difference (osmotic pressure) across the vesicle. The results are extended to axial sym. vesicles embedded in a 3-dimensional space.
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.
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.
Abstract:A strong segregation of a 2-component surfactant system coupled to the local membrane curvature has a pronounced effect on the shape of unilamellar or closed vesicles. For an average flat lamella, the preferred periodicity in the local composition as well as the lamellar shape depends on the ratio between surface tension and bending modulus. In the case of a closed vesicle with a fixed total area, there is no selected periodicity in contrast to the unilamellar case. For vesicles subjected to pos. or neg. inner pressure, their shapes can be calculated numerically; in the absence of added inner pressure, the shape found analysis is composed of circular sections.
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.
Abstract: Thin liquid layers which completely wet non-ideal (either rough or heterogeneous in composition) solid surfaces are considered. Two different sources of fluctuations of the liquid surface are identified, and the competition between them is examined. For thick enough films (but still in the submicrometer range), the liquid surface fluctuations are dominated by thermally induced capillary waves. For thin films, capillary waves are damped strongly and the liquid surface fluctuations are correlated with the disorder of the underlying solid surface. The fluctuation spectrum is calculated explicitly for a van der Waals liquid and for several different types of solid disorder. The results agree with recent x-ray specular reflection and diffuse scattering experiments.
Abstract: The effect of electrostatic interactions on the membrane bending energies was studied in weakly charged, swollen, lamellar phases of surfactant solutions The surface charge density of the lamellae is treated as a const. and only situations where it is low enough so that the distance 2d between lamellae is the smallest relevant length scale in the problem are considered. In the presence of salt (the short distance Debye-Hueckel regime), the electrostatic contribution to the bending energy of a membrane is in general small (in disagreement with a previous result), is proportional to d3, and is independent of ionic strength. Identical results are obtained for membranes undulating sinusoidally in phase and for concentric cylindrical membranes. The bending const. was also calculated for membranes held at const. dielectric potential and compared to the const. charge density case. In the absence of salt, continuity arguments predict an electrostatic contribution to the bending energy that scales as d3. A direct calculation for concentric cylindrical membranes gives exactly the same scaling behavior (including the numerical prefactor) as in the presence of salt.
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.
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.
Abstract: Although large, spherical surfactant vesicles are generally unstable to either lamellar or micellar phases, mixts. of 2 surfactants can lead to spontaneous vesicle formation. It is shown theor. how the energetic stabilization of mixed vesicles can occur by considering the curvature elasticity of the surfactant bilayer. Interactions between the 2 species (of the proper sign and magnitude) are crucial to stabilizing these vesicles. These interactions lead to compn. asymmetries and effective spontaneous curvatures of the inner and outer layers that are of equal and opposite signs. The vesicles have a Gaussian distribution about an average size determined. by the effective spontaneous curvature; the width of the distribution is calcd. as a function of concn. The stability of these vesicles with respect to a flat lamellar phase is estd. The predictions of the ranges of stability of the various phases as a function of the 3-concns. (solvent, e.g., water, and the 2 amphiphiles) are in qual. agreement with recent expts.
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.
Abstract: A review on chiral discrimination theory for chiral mols. that form an insol. Langmuir monolayer on the water/air interface. For a specific type of model mols. (tripod amphiphiles), the chiral discrimination is described for various types of intermol. interactions (van der Waals, H bonding, dipoles, charges, etc.). In particular, van der Waals interactions prefer chiral segregation whereas electrostatic interactions prefer heterochiral compds. Monolayer phase diagrams are shown for both cases. 11 Refs.
Abstract:Recently, modulated phases of insol. monolayers of fatty acids and phospholipids spread on the water/air interface have been observed by fluorescence microscopy expts. A theor. explanation of this observation is made by including electrostatic (dipolar) interactions in the total free energy calcn. for the monolayer. Dipoles can originate from 2 sources; neutral amphiphiles have a permanent dipole and charged amphiphiles have an induced one. Modulated phases are found to be stable in 2 different limits, close to the liq.-gas transition and at low temps. Several phases with stripe and hexagonal symmetry are predicted and the phase transitions between them are calcd.
Abstract: The curvature elastic energy of bilayer vesicles formed by a mixt. of two surfactants, which individually form either micelles or lamellar bilayer phases is described theor. In the limit of large bending elastic modulus being much greater than the temp. the free energy is minimized by vesicles with different concns. of the two surfactants in each monolayer of the bilayer. Vesicles are more stable than lamellar structures only when interactions or complexing of the two surfactants is taken into account.
Abstract: The effects of electrostatic interactions on steric repulsion and curvature elasticity are considered for dilute multimembrane systems as a function of the electrolyte strength, surface charge and inter-membrane spacing. In the strong electrolyte limit, the electrostatic interactions are screened and the steric repulsion dominates. For weak electrolytes, the electrostatic interactions cut-off the out-of-plane undulations and change significantly the membrane bending constant in qualitative agreement with recent experiments. (23 References).
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.
Abstract: Chiral discrimination was studied theor. for chiral mols. that form an insol. Langmuir monolayer at the water/air interface. For particular tripodal shapes mols., the chiral discrimination was calcd. for various types of intermol. interactions (van der Waals, dipole, charge, etc.). The calcn., based on Boltzmann-weighted averaging of mol. orientations, predicts a preferred heterochiral behavior for van der Waals interactions and homochiral behavior for electrostatic ones. Other interactions are also discussed. To understand monolayer phase diagrams, an analogy is drawn with sublimation expts. in bulk systems and a three-component thermodn. model is proposed. The variable area per mol. and also the chiral discrimination parameter are important parameters in the model. Phase diagrams for conglomerates and racemic compds. are calcd. in qual. agreement with expts. Possible connections and interpretation of existing exptl. data are discussed, and some new expts. for chiral monolayers are proposed.
Abstract:
Detergents with a tripod
shape, containing
3 functional groups (i = A, B, C) bound to an asym. carbon atom, which lie at the water surface are
considered. The fourth valence of the carbon carries an aliph. chain. Two
neighboring detergent mols. are
assumed to associate via 2 intermol. bonds (ij and i'j').
To each of these bonds is assocd. an
energy Vij which is neg. (attractive) if i and
j do
tend to associate The partition functions Z++, Z+- for a pair of
mols. with the same chirality (Z++) or with opposite chiralities
(Z+-) are derived by direct counting. If D
º Z++ - Z+-
> 0,
a homochiral case (HOC) leading to segregation
in
dense phases is expected. If D < 0, the reverse, heterochiral case
(HEC)
is predicted. This model leads to certain practical rules: (1) if
the
only allowed bonds are between identical groups (Vij ® +
¥ if i
¹ j)
® HEC; (2)
if all
interactions are of the van der Waals type (with Vij
= -Maiaj, where ai is the
polarizability of group i) ® HEC; (3)
if A is apolar, B is charged (+) and C is also charged but
of
opposite sign (-) ®
HOC. A similar conclusion holds if the charges are replaced by
dipoles
normal to the water surface; (4) if A = aliph., B = arom., C = charged ® HEC; (5) if one of the bonds between
identical
groups (e.g. AA) is much stronger than the others ® HEC; (6)
is one
of the groups (A) is "passive" (VAj
independent of j) and if VBC is strongly attractive ®
HOC.
Abstract: The profile of a thin liq. film completely wetting a rough solid surface was studied. The long-wavelength undulations of the liq. interface follow those of the solid surface, while short-wavelength undulations are damped strongly. There is Lorentzian damping of wavelengths smaller than the healing length x determined. by a balance between surface tension and disjoining pressure. Undulations with wavelength smaller than the mean film thickness are damped exponentially. The case where the binary interactions between mols. may be described by an inverse power law potential such as the van der Waals potential was studied in detail. These results are relevant for recent ellipsometry and grazing incidence x-ray scattering expts.
Abstract:A previously described thermodn. model (1987) for croemulsions was used to predict some aspects of the phase behavior. The stability of the microemulsion under variation of mol. parameters (such as the bending const. and spontaneous curvature of the surfactant monolayer) is discussed. An appropriate cut through the multidimensional parameter space yields the characteristic "fish" phase diagram, as found exptl. This model exhibits a phase behavior close to the exptl. one, not only in terms of the variation with surfactant concn. but also in terms of the sensitivity of the phase diagram to the nature of the surfactant, particularly its spontaneous curvature.
Abstract: A simple model is given for the anomalous (flow-birefringent) isotropic phase, known as L3, that is seen in certain surfactant solns. at vol. fractions of a few percent. The proposed structure consists of locally sheetlike sections of semi-flexible surfactant bilayer, connected up at larger distances into a multiply connected random surface, having a preferred structural length scale of order the persistence length of the bilayer. A 1st-order transition between this isotropic sheetlike phase and the nearby swollen lamellar phase is described.
Abstract: Effective dipoles in charged monolayers and permanent dipoles in neutral ones have a drastic effect on the structure and phase transitions of insol. Langmuir monolayers. These long-range and repulsive dipolar interactions stabilize undulating phases in thermodn. equil. Results are presented for two cases: (i) at close to a liq.-gas crit-point temp.; (ii) at low temps. Possible implications of the former on the liq.-gas transition and of the latter to the liq.-solid and liq. expanded-liq. condensed transitions are discussed. In an ionic soln., the undulation periodicity can be controlled by the strength of the ionic soln.
Abstract: The effects of electrostatic interactions on the phase behavior and structure of insol. Langmuir monolayers was investigated at the liq./air interface. Both for charged and neutral monolayers, the competition between such repulsive long-range and attractive short-range interactions of the monolayer tends to stabilize modulated phases. Phase diagrams are obtained in two limits: (i) close to the liq.-gas crit. point and (ii) at low temps.
Abstract: A simple phenomenological model is proposed to describe the phase equil. and structural properties of microemulsions. Space is divided into cells of side z; each cell is filled with either pure water or oil. Surfactant mols. are presumed to form an incompressible fluid monolayer at the oil-water interface. The monolayer is characterized by a size-dependent bending const. K(z), which is small for z ³zK, the de Gennes-Taupin persistence length. The model predicts a middle-phase microemulsion which coexists with dil. phases of surfactant in oil and surfactant in water. On the same ternary phase diagram, two regions of two-phase equil. exist involving upper- and lower-phase microemulsions that coexist with either almost pure water or oil. At low temps. and/or high values of the bare bending const., K0 . K(a), the middle-phase microemulsion may be entirely precluded by sepn. to a lamellar phase, whereas at high temp. and/or low values of K0, there is a first-order transition between a disordered microemulsion and a lamellar phase. In the absence of spontaneous curvature the phase diagram is oil-water sym. It may be asymmetrized by: (1) spontaneous curvature in the middle phase or (2) a difference between the free energy of the two dil. phases. If the asymmetry is sufficiently large, the three-phase region disappears.
Abstract: Curvature-induced instabilities in membranes and amphiphilic films are investigated by introducing a general coupling between a shape variable (such as curvature) and internal degrees of freedom (such as area per mol., tilt angle, or local compn.). A mean-field treatment of the Ginzburg-Landau free energy expansion shows the existence of various undulated phases (on a mesoscopic scale) that can appear between condensed (solid-like) and dil. (fluid-like) homogeneous phases of the membrane. These undulated phases are characterized by undulations in their local compn. as well as in their local curvature.
Abstract: The steady-state motion of a liq. A/liq. B interface on a flat solid surface is investigated. Hydrodynamic equations for the flow are obtained and in principle could yield a soln. for the profile of a general curved A/B interface. For small contact angles this problem is quite similar to the dynamics of a liq./vapor/solid contact line. Both a "dry" solid surface and one that has been prewetted by an invading liq. were analyzed. Interesting Saffman-Taylor-like instabilities could appear close to the tip of the advancing contact line for appropriate viscosity ratios.
Abstract:Insol. Langmuir monolayers are investigated in the presence of dipolar forces which can have 2 origins: permanent dipoles in neutral monolayers and induced dipoles in charged monolayers. The main effect of the addnl. long-range repulsive interactions is to stabilize undulating phases at thermodn. equil. Phase diagrams are obtained in 2 limits: close to the liq.-gas crit. point via a Ginzburg-Landau expansion of the free energy (mainly within a mean-field approxn.), and at low temps. by free energy minimization. Possible applications of this theory to expts. at the liq.-gas, liq. expanded-liq. condensed, and solid-liq. transitions are discussed.
Abstract: A simple model is described to calc. the phase behavior of microemulsions. The surfactant film at the oil-water interface is treated as an incompressible layer whose bending const. is renormalized by thermal fluctuations. Two- and three-phase equil. involving upper-, lower-, and middle-phase microemulsions are found. The structure of the middle phase is characterized by the persistence length of the film, beyond which the bending const. is renormalized to smaller values.
Abstract: The author studies one-dimensional Ising models in the presence of various random-field (RF) distributions. The distribution which determines the average free energy and other thermodynamic properties is found to be a devil's staircase for discrete RF distributions and continuous for nondiscrete RF distributions. Thus, any experiment that can be done on these systems will not show this devil's-staircase behavior, due to the natural broadening of RF distributions in real physical systems. Experiments will show some reminiscence of the largest steps and this is associated with the broadening of the peaks of the RF distributions. (13 References).
Abstract: A random field explanation is proposed for the behavior of binary liq. mixts. immersed in a gel matrix. When the bare fluid correlation length ( x ) exceeds the gel mesh size (L), the observed opalescence is the result of domain freezing due to the random gel structure. When x < L , the system behavior resembles biphasic flow in porous media.
Abstract: Weak, long-range (r-3) interactions between dipoles cause drastic changes in the monolayer phase diagram. Over a significant part of the liq.-gas coexistence region for the Langmuir monolayer, a supercryst. phase is expected (where liq. and gas regions form a spatially periodic arrangement with periods of .apprx.103 .ANG.).
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).
Abstract: In a recent letter, Gracia, Vares, and Robledo (1984) explained the stability of certain transient foams in binary liq. mixts. by prewetting phenomena. Such an explanation which is valid for infinite thickness films (early times) cannot be valid for finite thickness films (later times) at thermodn. equil. A nonequil. mechanism to explain the foam stability is proposed.
Abstract: Critical properties are studied in systems with quenched bond disorder that is correlated along d1 of d dimensions. A renormalization-group scheme (based on the Migdal-Kadanoff method) which follows the full distribution of the random bonds and which gives correctly the modified Harris criterion j = a +d1n is used. For d1<d-1 , the authors find fixed distributions at finite temperatures, yielding new 'random' exponents for various q-state Potts models. For d1=d-1 there is no long-range order if there is a finite weight to zero coupling. Otherwise, they find a novel zero-temperature fixed distribution for which all the moments diverge to infinity with finite ratios among them. This fixed distribution has a magnetic eigenvalue equal to d, indicating a first-order transition in the magnetization and possible related essential singularities. Thus, by analogy, the possibility of a magnetization jump is raised for the McCoy-Wu transition on a square lattice. The results for d1=1 are relevant to random quantum systems. (13 References).
Abstract:The crit. amplitude of the q-state Potts-model free energy was studied as a function of q in two dimensions and on the diamond hierarchical lattice. The amplitude diverges at an infinite no. of q values, qn, introducing logarithmic terms in the free energy. In each interval (qn,qn+1) there is a value ~qn where the amplitude vanishes, affecting the singularity of the free energy as a function of temp. Possible consequences for gelation and vulcanization of polymers are discussed.
Abstract:The critical properties of systems with quenched bond disorder are determined from a fixed distribution, under renormalization group, of the random bonds. Full fixed distributions with all moments are obtained numerically by histograms and, to a good approximation, in terms of Lambda distributions. For such systems, the specific-heat exponent alpha does not equal the crossover exponent phi at random criticality. The authors derive a new relation between alpha and phi , which invokes characteristics of the fixed distributions. The difference between alpha and phi is noted for n-vector models in 4 - epsilon dimensions and for Potts models on hierarchical lattices solved exactly. In general, stable random critical behavior with positive alpha appears to be possible. They develop a general treatment of quenched disorder and illustrate it by calculating specific-heat curves. It is suggested that the critical exponents of the three- and four-state random-bond Potts models in two dimensions are nu approximately=1.06 and 1.19. (26 References).
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).
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).
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).
Abstract:Many condensed matter systems, ranging from adsorbed surfaces to bulk magnets, are microscopically modeled by interacting q-state Potts spins, arrayed in d dimensions. A changeover from 2nd-order phase transitions at q £ qc(d) to 1sst-order transitions at q > qc can be understood as a condensation of effect vacancies, which are patches of local disorder favored by entropy. Accordingly, the renormalization-group treatment of Potts models is within context of Potts-lattice-gas models, where crit. and tricrit. fixed points occur at low q, but merge and annihilate at qc. This picture has led to exact tricrit. exponents in 2 dimensions. It is also consistent with recent exptl. results on intercalated systems in 3 dimensions. Effective vacancies in pure Potts models are also studied by Monte Carlo simulation. Their effective chemical potential can be controlled by a -point interaction, which proved useful in Monte Carlo renormalization-group studies.
Abstract: The thermal crit. exponent of the four-state Potts model in two dimensions is evaluated as n-1 = 1.49 ± 0.01 using the Monte Carlo renormalization-group method method. The presencem These results confirm previous conjectures, universality, and logarithmic corrections . A to control the chemical pot ntial of effective vacancies, without the introduction of explicit vacancy states.
Acstract:The first- and second-order phase transitions of the q-state Potts models are obtained in arbitrary dimension d. Critical and tricritical behaviours merge and annihilate at q/sub c/(d), clearing the way to first-order transitions at q[right angle bracket]q/sub c/(d) by the condensation of effective vacancies. The value of q/sub c/(d) decreases with increasing d, from diverging as exp(2/(d-1)) at d to 1/sup +/, to q/sub c/(2)=3.81 (cf exact value of 4), to lower values at d[right angle bracket]2. For given d, a changeover in critical behaviour occurs at q1/(d), as the critical fixed points merge from the Potts-lattice-gas region to the undiluted Potts limit. It is suggested that the power law singularities of the percolation problem (q to 1/sup +/) have logarithmic corrections. (35 References).
Abstract: The q-state, d-dimensional Potts models exhibit a variety of phase-transition behaviour in the limit d to 1/sup +/, q to infinity , and l identical to (d-1) in q finite. The regions l[left angle bracket]1, 1[left angle bracket]l[left angle bracket]2, and 2[left angle bracket]l are distinguished, respectively, by no transition, second-order transitions (with a new changeover phenomenon at l=ln 4), and first-order transitions. The latter are due to the condensation of effective vacancies. Critical and tricritical exponent values are given. (21 References).