Shape anisotropy and ordered phases in reversibly assembling lyotropic systems

Adventures in interdisciplinary science: a half century at the nexus between chemistry, physics and biology

A look back over five decades of research.

Second-virial theory for shape-persistent living polymers templated by disks

Living polymers composed of noncovalently bonded building blocks with weak backbone flexibility may self-assemble into thermoresponsive lyotropic liquid crystals. We demonstrate that the reversible polymer assembly and phase behavior can be controlled by the addition of (nonadsorbing) rigid colloidal disks which act as an entropic reorienting "template" onto the supramolecular polymers. Using a particle-based second-virial theory that correlates the various entropies associated with the polymers and disks, we demonstrate that small fractions of discotic additives promote the formation of a polymer nematic phase. At larger disk concentrations, however, the phase is disrupted by collective disk alignment in favor of a discotic nematic fluid in which the polymers are dispersed antinematically. We show that the antinematic arrangement of the polymers generates a nonexponential molecular-weight distribution and stimulates the formation of oligomeric species. At sufficient concentrations the disks facilitate a liquid-liquid phase separation which can be brought into simultaneously coexistence with the two fractionated nematic phases, providing evidence for a four-fluid coexistence in reversible shape-dissimilar hard-core mixtures without cohesive interparticle forces. We stipulate the conditions under which such a phenomenon could be found in experiment.

Temperature dependence of the pitch in chiral lyotropic chromonic liquid crystals

One of the most simple cases in which chirality at the microscopic level produces a chiral macroscopic structure is the chiral nematic liquid crystal phase. In such a phase, the preferred direction of molecular orientation rotates in helical fashion, with the pitch of the helix in different systems ranging from around 100 nm to as large as can be measured (∼10 mm). For almost all thermotropic and lyotropic liquid crystals, the ordered entities are formed from strong bonds, so the pitch varies in accordance with how the interactions between these largely immutable entities are affected by changing conditions. A unique exception are lyotropic chromonic liquid crystals (LCLCs) that spontaneously form weakly bound assemblies in solution, the size of which depends strongly on experimental parameters. While the temperature dependence of the pitch has been measured for chiral LCLCs formed by short strands of DNA (DNA-LCLCs), such is not the case for chiral LCLCs formed by small molecules. Polarized optical microscopy experiments on small molecule chiral LCLCs reveal the changing assembly size through a temperature dependence of the pitch not typical for many other systems, including the most recent measurements on DNA-LCLCs. In fact, the pitch measurements in small molecule chiral LCLCs strongly increase in value as the temperature is increased and the assemblies shrink in size. Theoretical considerations provide some help in understanding this phenomena, but leave much to be explained.

Using chiral tactoids as optical probes to study the aggregation behavior of chromonics

Tactoids are nuclei of an orientationally ordered nematic phase that emerge upon cooling the isotropic phase. In addition to providing a natural setting for exploring chromonics under confinement, we show that tactoids can also serve as optical probes to delineate the role of temperature and concentration in the aggregation behavior of chromonics. For high concentrations, we observe the commonly reported elongated bipolar tactoids. As the concentration is lowered, breaking of achiral symmetry in the director configuration is observed with a predominance of twisted bipolar tactoids. On further reduction of concentration, a remarkable transformation of the director configuration occurs, wherein it conforms to a unique splay-minimizing configuration. Based on a simple model, we arrive at an interesting result that lower concentrations have longer aggregates at the same reduced temperature. Hence, the splay deformation that scales linearly with the aggregate length becomes prohibitive for lower concentrations and is relieved via twist and bend deformations in this unique configuration. Raman scattering measurements of the order parameters independently verify the trend in aggregate lengths and provide a physical picture of the nematic-biphasic transition.

Exclusion of Spherical Particles from the Nematic Phase of Reversibly Assembled Rod-Like Particles

The open-ended aggregation of amphiphilic molecules in aqueous solution generates a broadly polydisperse population of elongated particles that form a variety of partially ordered phases. Herzfeld and coworkers have shown that the phase behavior of these binary systems is well described by self-consistently combining scaled-particle theory for the effects of excluded volume in fluid dimensions, a simple cell model for the effects of excluded volume in positionally ordered dimensions, a mean-field treatment of soft-interactions, and a phenomenological model of aggregate formation. We have now extended this model to ternary systems. We find that the addition of spherical particles to a solution of rod-forming particles induces a very wide isotropic-nematic coexistence region in which a relatively dilute isotropic solution with little aggregation separates from a rather concentrated nematic solution that almost completely excludes the spherical solutes. The magnitude of this effect depends on the relative diameters of the two solutes.

Copolymer-induced stabilizing effect of highly swollen hexagonal mesophases

We show that small amounts of copolymer that decorate an oil/water interface can greatly enhance the stability of swollen surfactant hexagonal phases, comprising oil tubes regularly arranged in a water matrix. Both the radius of the tubes and the thickness of the aqueous channel between the tubes can be controlled independently over large ranges. Such soft composite materials offer a potential interest for the synthesis of mesoporous materials.

Bending Energetics of Tablet-Shaped Micelles: A Novel Approach to Rationalize Micellar Systems

A novel approach to rationalize micellar systems is expounded in which the structural behavior of tablet-shaped micelles is theoretically investigated as a function of the three bending elasticity constants: spontaneous curvature (H0), bending rigidity (k(c)), and saddle-splay constant (k(c)). As a result, experimentally accessible micellar properties, such as aggregation number, length-to-width ratio, and polydispersity, may be related to the different bending elasticity constants. It is demonstrated that discrete micelles or connected cylinders form when H0 > 1/4xi, where xi is the thickness of a surfactant monolayer, whereas various bilayer structures are expected to predominate when H0 < 1/4xi. Our theory predicts, in agreement with experiments, a transition from discrete globular (tablet-shaped) micelles to a phase of ordered, or disordered, connected cylinders above a critical surfactant concentration. Moreover, a novel explanation for the mechanism of growth, from small globular to long rodlike or wormlike micelles, follows as a consequence from the theory. In accordance, polydisperse elongated micelles (large length-to-width ratio) form as the bending rigidity is lowered, approaching the critical point at k(c) = 0, whereas monodisperse globular micelles (small length-to-width ratio) are expected to be present at large k(c) values. The spontaneous curvature mainly determines the width of tablet-shaped or ribbonlike micelles, or the radius of disklike micelles, whereas the saddle-splay constant primarily influences the size but not the shape of the micelles.

Phenomenological theory of the nematic to lamellar phase transition in lyotropic liquid crystals

A phenomenological theory is presented to describe the nematic to lamellar phase transition in lyotropic liquid crystals. The problem of the first or second order transition is explored by means of the variation of the surfactant concentration. The possibility of the tricritical point at the nematic to lamellar phase transition is discussed in a phenomenological way. The influence of the electrolyte on this transition is also discussed by varying the coupling between the electrolyte concentration variables and the order parameters. The theoretical prediction is found to be in good qualitative agreement with experimental results.

On the physical nature of mesophases of guanosine gels

The unusual columnar aqueous mesophases of self-assembled guanosine stacks, such as 2'-deoxyguanosine 5'-monophosphate and 2'-deoxyguanosine 3'-monophosphate, are analyzed in terms of a general theory of azimuthal correlations between the charged helices. This theory considers forces, specific to the helical structure of each macromolecule, which depend on the azimuthal orientations of the molecules about their long axes. More specifically, in determining the magnitudes and decay lengths of these helix specific forces we utilize the Kornyshev-Leikin theory of electrostatic interaction between helical macromolecules and quantitatively fit experimental data. Together with explaining a number of the observed features of these mesophases, several new effects are predicted. Possible limitations and developments of our theoretical model are discussed, as well as new experiments to test the implications of the theory.

Aggregation behavior and chromonic liquid crystal properties of an anionic monoazo dye

X-ray scattering and various optical techniques are utilized to study the aggregation process and chromonic liquid crystal phase of the anionic monoazo dye Sunset Yellow FCF. The x-ray results demonstrate that aggregation involves pi-pi stacking of the molecules into columns, with the columns undergoing a phase transition to an orientationally ordered chromonic liquid crystal phase at high dye concentration. Optical absorption measurements on dilute solutions reveal that the aggregation takes place at all concentrations, with the average aggregation number increasing with concentration. A simple theory based on the law of mass action and an isodesmic aggregation process is in excellent agreement with the experimental data and yields a value for the "bond" energy between molecules in an aggregate. Measurements of the birefringence and order parameter are also performed as a function of temperature in the chromonic liquid crystal phase. The agreement between these results and a more complicated theory of aggregation is quite reasonable. Overall, these results both confirm that the aggregation process for some dyes is isodesmic and provide a second example of a well-characterized chromonic system.

Concentration dependent size of reversibly assembling polymers in solution: A mean-field lattice theory

The concentration dependence of the mean length of equilibrium polymers, <s>, as a function of solute volume fraction is studied in a lattice description. Using a more detailed model of constituent interactions in comparison to previous studies we are able to find conditions under which a decrease of <s> at high solute concentration may occur.

Liquid crystal phases of self-assembled amphiphilic aggregates

Long-range order in solutions of reversibly self-assembling molecules results from interactions among the asymmetric aggregates. Even for electrically neutral species, repulsions between the aggregates become significant at high concentrations. At the very least, the excluded volume of asymmetric aggregates creates formidable packing constraints which are relieved by orientational and positional alignment. Aggregate growth thus promotes long-range order, and long-range order facilitates growth. Nematic phases occur if aggregate growth is strong enough to induce orientational ordering at concentrations lower than those that induce positional ordering. The symmetry of the positionally ordered phases reflects aggregate morphology: the polydispersity of aggregates that grow in one (two) dimension(s) to form rod-like (plate-like) particles suppresses the smectic (columnar) phase in favour of the columnar (smectic) phase. Because plate-like aggregates pack more easily than rod-like aggregates, increasing concentration induces a rearrangement from rod-like to plate-like aggregates, and a transition from columnar to smectic ordering, in solutions of molecules, such as surfactants, capable of forming both types of aggregates. In mixtures of aggregating and non-aggregating species, the difficulty of packing spherically shaped particles among elongated particles results in dramatic demixing such that a very concentrated solution of very large, highly aligned aggregates coexists with a relatively dilute solution depleted of the aggregating species.

Crowding-induced organization of cytoskeletal elements. III. Spontaneous bundling and sorting of self-assembled filaments with different flexibilities

The typical cell contains ca. 25 vol.-% protein, of which ca. 10% forms cytoskeletal filaments and ca. 90% is non-aggregating globular protein. It has previously been theoretically predicted that, under such highly crowded conditions, rigid filaments will coalesce into tight bundles coexisting with an isotropic solution of globular proteins. In the present work we show that such spontaneous bundling will occur even when filament flexibility is taken into account because the persistence length of the filaments is much longer than the diameter of the globular proteins. The theoretical results are consistent with experimentally observed bundling of F-actin (the most flexible of the three most common types of cytoskeletal filaments) in the presence of globular macromolecules.The main effect of increased filament flexibility on bundling is to cause somewhat looser packing. In mixtures of filaments, differences in flexibilities can lead to segregation. This segregation is accentuated when the stiffer filament is also wider. The results suggest that actin filaments and microtubules will spontaneously form segregated bundles in the presence of cellular concentrations of globular proteins. While cross-linking proteins may serve to stabilize these bundles, their more important function in bundling may be to fine tune the structure (e.g., polarity and registration of filaments).

Crowding-induced organization of cytoskeletal elements: II. Dissolution of spontaneously formed filament bundles by capping proteins

Through calculations of molecular packing constraints in crowded solutions, we have previously shown that dispersions of filament forming proteins and soluble proteins can be unstable at physiological concentrations, such that tight bundles of filaments are formed spontaneously, in the absence of any accessory binding proteins. Here we consider the modulation of this phenomenon by capping proteins. The theory predicts that, by shortening the average filament length, capping alleviates the packing problem. As a result, the dispersed isotropic solution is stable over an expanded range of compositions.

Crowding-induced organization of cytoskeletal elements: I. Spontaneous demixing of cytosolic proteins and model filaments to form filament bundles

The theory for the effects of crowding on the behavior of reversibly self-assembling solutes is extended to mixtures containing nonassembling solutes. The theory predicts that excluded volume will cause dramatic demixing into domains of long, tightly packed, highly aligned fibers coexisting with an isotropic solution of unaggregated species. It suggests that the bundling of fibers in cells is entropically driven and that accessory binding proteins in the cytoplasm serve to modulate the process rather than create it.