arXiv subjects
Publications and source records attributed to David Andelman.
Gemini (dimeric) surfactants are composed of two monomeric surfactant molecules linked by a spacer chain. Their self-assembly behavior differs qualitatively from that of monomeric surfactants. We review the various theoretical attempts to account for the behavior of this new class of amphiphilic molecules.
The persistence length of a single, intrinsically rigid polyelectrolyte chain, above the Manning condensation threshold is investigated theoretically in 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 mechanical 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.
The persistence length of a single, strongly charged, stiff polyelectrolyte chain is investigated theoretically. Path integral formulation is used to obtain the effective electrostatic interaction between the monomers. We find significant deviations from the classical Odijk, Skolnick and Fixman (OSF) result. An induced attraction between monomers is due to thermal fluctuations and correlations between bound counterions. The electrostatic persistence length is found to be smaller than the OSF value and indicates a possible mechanical instability (collapse) for highly charged polyelectrolytes with multivalent counterions. In addition, we calculate the amount of condensed counterions on a slightly bent polyelectrolyte. More counterions are found to be adsorbed as compared to the Manning condensation on a cylinder.
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 chemically 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 persistence of the surface pattern into the disordered bulk is given for several types of patterns (e.g. uniform and striped surface). It further is shown that complex morphology 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 will appear tilted 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 lamellae form perpendicular to the surface. Lastly, the transition from parallel to perpendicular lamellae to the surfaces in a thin film is presented. The transition between the two states depends on the surface separation and strength of surface interactions. We further calculate the phase diagram in the presence of perpendicular electric field favoring perpendicular ordering. In the strong segregation limit we introduce a simple model to calculate the phase diagram of the fully parallel, fully perpendicular and mixed (parallel and perpendicular) states.
We consider the coupling between an external electric field and dissociated ions embedded in anisotropic polarizable media such as block copolymers. We argue that the presence of such ions can induce strong morphological changes and even lead to a structural phase transition. We investigate, in particular, diblock copolymers in the body centered cubic (bcc) phase. In pure dielectric materials (no free charges), a dielectric breakdown is expected to occur for large enough electric fields, preempting any structural phase transition. On the other hand, dissociated ions can induce a phase transition for fields of about 10 V/$μ$m or even lower. This transition is from an insulator state, where charges are preferentially localized inside bcc spherical domains, to a conducting state where charges can move along the long axis of oriented cylinders (forming a hexagonal phase). The cylinders diameter is small and is determined by the volume fraction of the minority copolymer component. The strength of this mechanism can be tuned by controlling the amount of free ions present as is observed by our experiments. These theoretical predictions support recent experimental findings on the bcc to hexagonal phase transition in copolymer systems.
We examine the alignment of thin film diblock copolymers subject to a perpendicular electric field. Two regimes are considered separately: weak segregation and strong segregation. For weakly segregated blocks, below a critical value of the field, E_c, 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 morphology 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 E_1 and E_2>E_1. As the field is increased from zero above E_1, 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 E_2 the perpendicular alignment spans the whole film.
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. [Phys. Rev. Lett. 88, 138102 (2002)]. Bellow a critical end-point temperature, we find that the unbinding transition becomes first-order for multi-component membranes.
Biomimetic membranes in contact with a planar substrate or a second membrane are studied theoretically. 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.
This chapter 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 counter-ions increases the osmotic pressure of polyelectrolyte solutions, making such polymers water soluble as is of great importance to many applications. At surfaces, the same interplay between monomer-monomer repulsion and counter-ion 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 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 amount 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.
We investigate the effect of chemically patterned surfaces on the morphology 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'' morphology is examined. Our analytic calculation agrees with previous computer simulations and self consistent field theories.
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, it is shown that 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.
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 chemically 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 point and in a thin-film geometry, our procedure enables the analytic calculation of distorted perpendicular and tilted lamellar phases in the presence of uniform or modulated surface fields.
We investigate 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.
The problem of charged polymer chains (polyelectrolytes) as they adsorb on a planar surface is addressed theoretically. We review the basic mechanisms and theory underlying polyelectrolyte adsorption on a single surface in two situations: adsorption of a single charged chain, and adsorption from a bulk solution in $θ$ solvent conditions. The behavior of flexible and semi-rigid chains is discussed separately and is expressed as function of the polymer and surface charges, ionic strength of the solution and polymer bulk concentration. We mainly review mean-field results and briefly comment about fluctuation effects. The phenomenon of polyelectrolyte adsorption on a planar surface as presented here is of relevance to the stabilization of colloidal suspensions. In this respect we also mention calculations of the inter-plate force between two planar surfaces in presence of polyelectrolyte. Finally, we comment on the problem of charge overcompensation and its implication to multi-layers formation of alternating positive and negative polyelectrolytes on planar surfaces and colloidal particles.
We present a general linear response description of membrane adhesion at rough or chemically structured surfaces. Our method accounts for non-local Van der Waals effects and contains the more approximate (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, 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 fair agreement with an exact numerical solution.
We investigate the morphology of diblock copolymers in the vicinity of flat, chemically patterned surfaces. Using a Ginzburg-Landau free energy, spatial variations of the order parameter are given 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 $q$-modes are calculated in terms of system parameters. We observe lateral order parallel to the surface as a result of order perpendicular to the surface. Surfaces which has a finite size chemical pattern (e.g., a stripe of finite width) induces lamellar ordering extending into the bulk. Close to the surface pattern the lamellae are strongly perturbed adjusting to the pattern.
We investigate symmetric grain boundaries in a lamellar diblock copolymer system. The form of the interface between two grains 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 morphology. As $θ$ increases, a gradual transition is observed to an omega morphology characterized by a protrusion of the lamellae along the interface between the two phases. We present a theoretical approach to find these tilt boundaries in two-dimensional systems, based on a Ginzburg-Landau expansion of the free energy. Calculated order parameter profiles and energies agree well with transmission electron microscope experiments, and with full numerical solution of the same problem.
Adhesion between membranes is studied using a phenomenological model, where the inter-membrane distance is coupled to the concentration of sticker molecules on the membranes. The model applies to both for adhesion of two flexible membranes and to adhesion of one flexible membrane onto a second membrane supported on a solid substrate. We 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. We also discuss the non-monotonous shape of the inter-membrane distance occurring when the lateral phase separation takes place. The inter-membrane distance relaxes to the bulk values with two symmetric overshoots. Adhesion mediated by other types of stickers is also considered.