Poly(N-isopropylacrylamide): experiment, theory and application

Lipid bilayer membranes--ubiquitous in biological systems and closely associated with cell function--exhibit rich shape-transition behaviour, including bud formation and vesicle fission. Membranes formed from multiple lipid components can laterally separate into coexisting liquid phases, or domains, with distinct compositions. This process, which may resemble raft formation in cell membranes, has been directly observed in giant unilamellar vesicles. Detailed theoretical frameworks link the elasticity of domains and their boundary properties to the shape adopted by membranes and the formation of particular domain patterns, but it has been difficult to experimentally probe and validate these theories. Here we show that high-resolution fluorescence imaging using two dyes preferentially labelling different fluid phases directly provides a correlation between domain composition and local membrane curvature. Using freely suspended membranes of giant unilamellar vesicles, we are able to optically resolve curvature and line tension interactions of circular, stripe and ring domains. We observe long-range domain ordering in the form of locally parallel stripes and hexagonal arrays of circular domains, curvature-dependent domain sorting, and membrane fission into separate vesicles at domain boundaries. By analysing our observations using available membrane theory, we are able to provide experimental estimates of boundary tension between fluid bilayer domains.

Imaging coexisting fluid domains in biomembrane models coupling curvature and line tension

We review the current state of knowledge of phase separation and phase equilibria in porous materials. Our emphasis is on fundamental studies of simple fluids (composed of small, neutral molecules) and well-characterized materials. While theoretical and molecular simulation studies are stressed, we also survey experimental investigations that are fundamental in nature. Following a brief survey of the most useful theoretical and simulation methods, we describe the nature of gas‐liquid (capillary condensation), layering, liquid‐liquid and freezing/melting transitions. In each case studies for simple pore geometries, and also more complex ones where available, are discussed. While a reasonably good understanding is available for phase equilibria of pure adsorbates in simple pore geometries, there is a need to extend the models to more complex pore geometries that include effects of chemical and geometrical heterogeneity and connectivity. In addition, with the exception of liquid‐liquid equilibria, little work has been done so far on phase separation for mixtures in porous media.

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Phase separation in confined systems

Cylindrical molecular brushes: Synthesis, characterization, and properties

A wide variety of two- and three-dimensional physical-chemical systems display domain patterns in equilibrium. The phenomenology 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.

https://science.sciencemag.org/content/sci/267/5197/476.full.pdf

Domain shapes and patterns: the phenomenology of modulated phases.

The present paper discusses some properties of small, elongated particles suspended in a nematic or cholesteric phase, with low concentrations (typical volume fraction occupied by the particle f ≊ 10-3). We find that in most cases the particle axis should be locked and parallel to the local nematic axis n(r). If such colloidal suspensions could be made successfully with magnetic grains, it should be possible to prepare « ferronematics » or « ferrocholesterics », where locally all particles are magnetized in one direction (colinear to n), and also « compensated » materials with no spontaneous magnetization. These three types of samples should all show remarkable distorsions and phase changes in low external fields H. Similar effects are expected under electric fields with colloidal suspensions of polar rod molecules such as helical polypeptides.

https://hal.archives-ouvertes.fr/jpa-00206970/document

Theory of magnetic suspensions in liquid crystals

Dynamical Scaling for Polymers in Theta Solvents

Insoluble Langmuir monolayers are investigated in the presence of dipolar forces which can have two origins: permanent dipoles in neutral monolayers and induced dipoles in charged monolayers. The main effect of the additional long‐range repulsive interactions is to stabilize undulating phases at thermodynamic equilibrium. Phase diagrams are obtained in two limits: close to the liquid–gas critical point via a Ginzburg–Landau expansion of the free energy (mainly within a mean‐field approximation), and at low temperatures by free energy minimization. Possible applications of this theory to experiments at the liquid–gas, liquid expanded–liquid condensed, and solid–liquid transitions are discussed.

Phase transitions in Langmuir monolayers of polar molecules

We have combined the Maier Saupe theory [1] of the nematic-isotropic transition and the Flory Huggins theory of mixtures to describe the phase diagrams of two nematogens A+B. The two components can have different order parameters S A , S B in the mixture. We can then predict the morphology of the phase diagrams in term of a relatively small number (4) of interaction parameters. The final numerical calculations are restricted to cases where the clearing points of the two components are nearly equal (cases of chemical similarity). For certain sets of parameters we find a rather remarkable phase diagram with two consolute points ― one at high temperatures in the isotropic phase and a second one at lower temperatures in the nematic phase. We also discuss the effects of chain length on the phase diagrams: when one component is a nematogenic polymer [2] with mesogenic side groups; and when the two components are polymers Combinaison de la theorie de la transformation isotrope-nematique de Maier-Saupe et la theorie des melanges de Flory-Huggins pour decrire les diagrammes de phase de deux nematogenes (A, B) qui peuvent avoir des parametres d'ordre differents. Prevision de la forme des diagrammes de phase avec 4 parametres seulement. Discussion de l'effet de la longueur de chaine quand un composant est un polymere nematogene avec des groupes lateraux mesogenes et quand les deux composants sont des polymeres

https://hal.archives-ouvertes.fr/jpa-00209848/document

Phase diagrams of mesomorphic mixtures

We correct an earlier theory of polymer diffusion for a mixture of long (L) and short (S) chains in a melt, all chains being chemically identical. The mixing can be understood by analogy with the kinetics of polymer dissolution: up to a time τL (the reptation time of the L component) the L chains behave like a gel, progressively swollen by the S chains. Marker particles cannot move with respect to the gel, and follow its boundary displacement x(t). We find x(t) ~ (DSt)1/2 in agreement with a number of recent data. But the overall density of the mixture remains constant everywhere, and the process has nothing to do with an uneven distribution of vacancies.

F. Brochard

Papers

Theory of magnetic suspensions in liquid crystals

Dynamical Scaling for Polymers in Theta Solvents

Phase transitions in Langmuir monolayers of polar molecules

Phase diagrams of mesomorphic mixtures

Polymer-Polymer Interdiffusion