Mixed supercrystalline structures in mixtures of ABC triblock and ab(bc) diblock copolymers, 2. Lamellar structures in tricomponent mixtures

The theory of lamellar superstructures in ternary mixtures of ab and bc diblock and linear ABC triblock copolymers under the condition of strong segregation between chemically different blocks is developed. This system is considered using Alexander‐de Gennes (box) and self‐consistent field (SCF) models. The theory predicts the possibility of phase segregation in the microphase‐segregated superstructures. It is shown that the ABC triblock copolymer has unlimited capacity with respect to ab and bc diblock copolymers which include cooperatively into mixed lamella.     

Mixed supercrystalline structures in mixtures of ABC‐triblock and AB(BC)‐diblock copolymers, 1. Lamellar structures in bicomponent mixtures

The theory of lamellar superstructures in binary mixtures of AB diblock and linear ABC triblock copolymers under the condition of strong segregation between chemically different blocks is developed. This system is considered using Alexander‐de Gennes (box‐model) and self‐consistent field (SCF) models. The formation of a mixed lamellar superstructure comprising both mixture components is proved. It is shown that a mixed lamella may be the only type of lamellae in the mixture, or it may coexist with pure diblock lamellae, depending on the mixture composition, local characteristics of blocks (thickness and Kuhn segment length), and surface tension coefficients at the A/B and B/C interfaces. Preliminary experimental results provide support of these theoretical estimations. The formation of mixed lamellae in a mixture of linear ABC and branched (AB)₂C block copolymers is also considered.     

Microphase coexistence in polymeric brushes

A collapse of polymeric brushes in a solvent can be induced by a change in external conditions, for example, solvent quality or its temperature. The systems with following specific interactions are considered in this paper, namely, polyelectrolyte brushes, amphiphilic brushes in a mixture of incompatible solvents, and brushes with possibility of liquid-crystalline ordering of polymer segments. For all the systems it is shown that the brush collapse can be observed under certain conditions, and it occurs through a microphase segregation. There are two microphases of different densities that coexist in the brush. The effect is caused by general properties of the swollen phase of polymeric brush and hence appears at all types of the interactions that can induce a phase transition of the brush into collapsed state.     

Self-assembly of lipid domains in the extracellular leaflet of the plasma membrane and models thereof

Lipid domain formation and phase coexistence in biological membranes is a subject which has received considerable attention during the last two decades, especially the topic concerning so-called lipid rafts, a theory which has become as popular to confirm as to disproof. Regardless of the existence or precise composition and function of the classical rafts, the occurrence of lateral lipid segregation in biological membranes is indisputable. This review starts by focusing on state of the art findings concerning lipid domains and lateral heterogeneity in a biological context. Then, the physicochemical properties of lipid mixtures, phase properties and domain dynamics are considered. Canonical lipid models of the exofacial leaflet of the plasma membrane are treated in detail and the proper choices of model lipids are discussed. A special attention is given to polar lateral interactions (including carbohydrate–carbohydrate head group interactions), whose importance for spatial segregation and crystallization is commencing to be appreciated by the scientific community.     

Communication: lateral phase separation of mixed polymer brushes physisorbed on planar substrates

Here, we present a new method to model lateral phase separation in mixed polymer brushes physisorbed to a planar surface with mobile grafting points. The model is based on a local mean field theory that combines a Flory-Huggins approximation for interaction enthalpies with an Alexander-de Gennes brush entropy contribution. Using Monte Carlo sampling, the application of these two interactions to a lattice model yields a range of phase behavior consistent with previous theoretical and experimental work. This model will be useful for predicting mixed polymer brush morphologies on planar surfaces and in principle can be extended to other geometries (e.g., spheres) and polymer systems.     

Liquid crystal polymers: Studies of labelled parts by Neutron scattering

The studies of the conformation of comb-like liquid crystal polymers have been made by Small Angle Neutron Scattering (SANS) with samples containing mixtures of totally protonated polymers and homologous polymers with deuterated backbones. For a polymethacrylate the conformation of a chain is determined in the isotropic nematic and smectic phases. Theoretical predictions of Renz and Warner (similar to the hairpin model of de Gennes) are verified from the temperature dependence of the radius, parallel to the director, of one chain in the smectic phase. When the terminal groups of the pendant part of the monomer are deuterated a segregation seems to occur. The problem of the generalization of results is raised.     

Opposing Phase‐Segregation and Hydrogen‐Bonding Forces in Supramolecular Polymers

Phase segregation between different macromolecules and specific weak interactions are the basis of molecular organization in many biological systems, which are held together by attractive hydrogen bonds (H‐bonds) and dissociated by phase segregation. We report significant changes in the association behavior of covalent H‐bonds by the phase of attached polymer chains. Depending on the aggregation state, we observed either intact H‐bonds despite segregation of the phases, or macrophase separation with a larger amount of H‐bonding dissociation.     

Influence of measurement frequency on the pretransitional behaviour of the no-linear dielectric effect in the isotropic phase of liquid crystalline materials

Results are presented of the non-linear dielectric effect (NDE) as a function of temperature (T) in the isotropic phase on approaching the nematic phase for the liquid crystalline materials 4-cyano-4-hexylbiphenyl (6CB), 5-heptyl-2-(4-cyanophenyl)pyrimidine smectic A phase of 4-cyano-4-decylbiphenyl (10CB). For low measurement frequencies (f) the NDE 1(T) exhibits linear behaviour from the clearing temperature (T) up to about C TC50 K. Increase of f causes an increased deviation from this dependence near T C. The influence of the measurement frequency can be associated with the link between the system time-scale, and the measurement time-scale defined by the relaxation time of pretransitional processes (tau ),(f1). A quantitative agreement with de Gennes model NDE 1(T) analysis and with the results of time- and frequency-resolved the relation derived from the Landauof Kerr effect studies is shown. A possible influence of the intensity of the weak measurement field on the pretransitional effect in the immediate vicinity of TC is discussed. Similiarities between pretransitional behaviour in the isotropic phase of the nematogens and in the homogeneous phase of a critical binary solution are considered. (HCPP) and the     

Order electricity reconsidered

We have considered the Landau-de Gennes expansion of the distortion free energy to examine a possible connection between the electric polarization in terms of a gradient of the order parameter and the electric polarization resulting from splay and bend distortions of the director. In addition we have considered the electric polarization connected with the electric quadrupole density, which is not contained in the Landau-de Gennes expansion.     

Order electricity reconsidered

We have considered the Landau-de Gennes expansion of the distortion free energy to examine a possible connection between the electric polarization in terms of a gradient of the order parameter and the electric polarization resulting from splay and bend distortions of the director. In addition we have considered the electric polarization connected with the electric quadrupole density, which is not contained in the Landau-de Gennes expansion.     

Spreading of block copolymer films and domain alignment at moving terrace steps

We investigate spreading of phase separated copolymer films, where domain walls and thickness steps influence polymer flow. We show that at early stages of spreading its rate is determined by slow activated flow at terrace steps (i.e., thickness steps). At late stages of spreading, on the other hand, the rate is determined by the flow along terraces, with diffusionlike time dependence t(-1/2). This dependence is similar to de Gennes and Cazabat's prediction for generic layered liquids [P. G. de Gennes and A. M. Cazabat, C.R. Acad. Sci. Paris II 310, 1601 (1990)], as opposed to the classical Tanner's law of drop spreading. We also argue that chain hopping at the spreading terrace steps should lead to the formation of aligned, defect-free domain patterns on the growing terraces.     

Comparison between protein-polyethylene glycol (PEG) interactions and the effect of PEG on protein-protein interactions using the liquid-liquid phase transition

Phase transitions of protein aqueous solutions are important for protein crystallization and biomaterials science in general. One source of thermodynamic complexity in protein solutions and their phase transitions is the required presence of additives such as polyethylene glycol (PEG). To investigate the effects of PEG on the thermodynamic behavior of protein solutions, we report measurements on the liquid-liquid phase separation (LLPS) of aqueous bovine serum albumin (BSA) in the presence of relatively small amounts of PEG with an average molecular weight of 1450 g/mol (PEG1450) as a model system. We experimentally characterize two thermodynamically independent properties of the phase boundary: (1) the effect of PEG1450 concentration on the LLPS temperature, (2) BSA/PEG1450 partitioning in the two liquid coexisting phases. We then use a thermodynamic perturbation theory to relate the first property to the effect of PEG concentration on protein-protein interactions and the second property to protein-PEG interactions. As criteria to determine the accuracy of a microscopic model, we examine the model's ability to describe both experimental thermodynamic properties. We believe that the parallel examination of these two properties is a valuable tool for verifying the validity of existing models and for developing more accurate ones. For our system, we have found that a depletion-interaction model satisfactorily explains both protein-PEG interactions and the effect of PEG concentration on protein-protein interactions. Finally, due to the general importance of LLPS, we will experimentally show that protein-PEG-buffer mixtures can exhibit two distinct types of liquid-liquid phase transitions.     

Competing interactions in two dimensional Coulomb systems: surface charge heterogeneities in coassembled cationic-anionic incompatible mixtures

A binary mixture of oppositely charged components confined to a plane such as cationic and anionic lipid bilayers may exhibit local segregation. The relative strengths of the net short range interactions, which favors macroscopic segregation, and the long range electrostatic interactions, which favors mixing, determine the length scale of the finite size or microphase segregation. The free energy of the system can be examined analytically in two separate regimes, when considering small density fluctuations at high temperatures and when considering the periodic ordering of the system at low temperatures [F. J. Solis, S. I. Stupp, and M. Olvera de la Cruz, J. Chem. Phys. 122, 054905 (2005)]. A simple molecular dynamics simulation of oppositely charged monomers, interacting with a short range Lennard-Jones potential and confined to a two dimensional plane, is examined at different strengths of short and long range interactions. The system exhibits well-defined domains that can be characterized by their periodic length scale as well as the orientational ordering of their interfaces. By adding salt, the ordering of the domains disappears and the mixture macroscopically phase segregates in agreement with analytical predictions.     

Microphase segregation in bridging polymeric brushes: Regular and singular phase diagrams

A mean-field theory of deformation-induced microphase segregation in bridging polymeric brushes anchored to two parallel surfaces is presented. Models with isotropic and orientation-dependent liquid-crystalline interactions between segments are considered. For the first model, the problem is similar to that of classical liquid-vapor phase separation, and the phase diagram in the P-T plane has a line of first-order transitions terminating at the critical point. We show that the critical pressure is negative implying that a free brush tethered only to one surface always exists at supercritical conditions and hence cannot undergo the collapse phase transition. In the second model, the free energy density depends on two coupled order parameters, one related to segment density and the other to the orientational order, which strongly modifies the phase behavior. Depending on the grafting density the system is described by a phase diagram of a regular or a singular type. In the regular phase diagram the first-order transition line terminates at the critical point. In a singular diagram, the first-order transition line extends to infinity; the critical point corresponds to infinite pressure so that the system undergoes the phase transition at arbitrary external pressures. Regular phase diagrams correspond to dense grafting, and singular ones to sparse grafting. The change from a regular phase behavior to another occurs at a certain marginal value of the grafting density. On approaching this value the critical point on the regular diagram moves to infinity, logarithmically with the deviation from the critical grafting density. We relate the analytical properties of the free energy density as a function of the segment concentration to the type of the phase diagram and the shape of the coexistence curve in the temperature- concentration plane.     

Luckhurst-Romano model of thermotropic biaxial nematic phase

Recent experiments show that the long looked for thermotropic biaxial nematic phase is finally stabilized in a low mass liquid crystalline system. Inspired by this experimental observation we concentrate on some theoretical issues concerned with this phase. In particular we show that the simplest Lebwohl-Lasher biaxial model, as introduced by Luckhurst and Romano, is consistent with the minimal coupling Landau-de Gennes phenomenological approach. The model shows a rich spectrum of possibilities, in particular a direct isotropic-biaxial nematic phase transition. A possible bridge between molecular and phenomenological approaches, in particular an interpretation of the alignment tensor, is discussed.     

Configurational bias Monte Carlo simulation of phase segregation in block copolymer networks

Cross-linked block copolymers are used as adhesives in fiber-reinforced composite material manufactures for automotive applications. Good adhesion between the polymer matrix and fibers in the interphase region is required for the structural integrity of these materials. Experimental evidence indicates that superior adhesion is obtained when phase segregation occurs between the two matrix phase block copolymers. It is therefore desirable to predict the conditions under which phase segregation is expected to occur. Configurational bias Monte Carlo simulations of two-component, trifunctional block copolymer networks were carried out to investigate phase segregation in these materials. The effects of four principal parameters on phase segregation were examined: the weight fractions of the two components, the cross-link length, the connectivity of the network, and the ratio of the square-well interactions. The molecular simulation results confirmed trends observed in laboratory measurements.     

Nematic-isotropic phase transition in lyotropic liquid crystals

We propose a Landau-de Gennes phenomenological model to describe the nematic-isotropic phase transition in lyotropic liquid crystals. The possibility of a first or second order transition is explored by means of the variation of the concentration of surfactant. We show that a Landau point on the nematic-isotropic phase transition line can be achieved under certain conditions. The theoretical predictions are found to be in good qualitative agreement with available experimental results.     

Nematic-isotropic phase transition in lyotropic liquid crystals

We propose a Landau-de Gennes phenomenological model to describe the nematic-isotropic phase transition in lyotropic liquid crystals. The possibility of a first or second order transition is explored by means of the variation of the concentration of surfactant. We show that a Landau point on the nematic-isotropic phase transition line can be achieved under certain conditions. The theoretical predictions are found to be in good qualitative agreement with available experimental results.