Entropic patchiness drives multi-phase coexistence in discotic colloid-depletant mixtures

Insertion of anionic synthetic clay in lamellar surfactant phases

We describe the different mixed colloidal solutions that can be obtained when mixing equivalent quantities of a synthetic anionic clay to surfactants forming lamellar phases in the absence of added salt. The important quantity driving toward insertion or depletion is the osmotic pressure, of the lamellar phase and of the clay alone. Competition for water is the main driving force toward dispersion, inclusion or exclusion (phase separation). In the case of a nonionic surfactant (C 12 E 5 ) mixed with Laponite, undulations quenched by the surfactant-decorated clay lead to swelling; inclusion is not observed due to differences in rigidity. Long-range order is weakened leading eventually to the exclusion of surfactant in excess. In the case of a double anionic system (AOT-Laponite), electrostatic is dominant and the three regimes are encountered. In the catanionic case, admixing the double chain cationic lipid DDAB to the clay (in large charge excess), the platelets are coated by a positively charged bilayer. Long-range order is very efficiently dampened. From a low threshold (2% by weight), there is exclusion of a clay-poor collapsed lamellar phase, detected by the swelling of the main phase. The cationized clay does not interfere with the molecular force balance: the location of the critical point is unchanged. At high Laponite concentration, a very puzzling microstructure is observed. Some phase diagrams as well as representative SANS and SAXS data are extracted from the complete results concerning the lyotropic lamellar phase mixing problem available with all measures and evaluations of osmotic pressures in the PhD of the late Isabelle Grillo.

Depletion Strategies for Crystallized Layers of Two-Dimensional Nanosheets to Enhance Lithium-Ion Conductivity in Polymer Nanocomposites

The assembly of long-range aligned structures of two-dimensional nanosheets (2DNSs) in polymer nanocomposites (PNCs) is in urgent need for the design of nanoelectronics and lightweight energy-storage materials of high conductivity for electricity or heat. These 2DNS are thin and exhibit thermal fluctuations, leading to an intricate interplay with polymers in which entropic effects can be exploited to facilitate a range of different assemblies. In molecular dynamics simulations of experimentally studied 2DNSs, we show that the layer-forming crystallization of 2DNSs is programmable by regulating the strengths and ranges of polymer-induced entropic depletion attractions between pairs of 2DNSs, as well as between single 2DNSs and a substrate surface, by exclusively tuning the temperature and size of the 2DNS. Enhancing the temperature supports the 2DNS-substrate depletion rather than crystallization of 2DNSs in the bulk, leading to crystallized layers of 2DNSs on the substrate surfaces. On the other hand, the interaction range of the 2DNS-2DNS depletion attraction extends further than the 2DNS-substrate attraction whenever the 2DNS size is well above the correlation length of the polymers, which results in a nonmonotonic dependence of the crystallization layer on the 2DNS size. It is demonstrated that the depletion-tuned crystallization layers of 2DNSs contribute to a conductive channel in which individual lithium ions (Li ions) migrate efficiently through the PNCs. This work provides statistical and dynamical insights into the balance between the 2DNS-2DNS and 2DNS-substrate depletion interactions in polymer-2DNS composites and highlights the possibilities to exploit depletion strategies in order to engineer crystallization processes of 2DNSs and thus to control electrical conductivity.

Effects of polymer nonideality on depletion-induced phase behaviour of colloidal disks and rods

Colloidal dispersions composed of either platelets or rods exhibit liquid crystalline phase behaviour that is strongly influenced by the addition of nonadsorbing polymers. In this work we examined how polymer segment-segment interactions affect this phase behaviour as compared to using either penetrable hard spheres (PHS) or ideal ('ghost') chains as depletants. We find that the simplified polymer description predicts the same phase diagram topologies as the more involved polymer descriptions. Therefore the PHS description is still adequate for qualitative predictions. For sufficiently large polymer sizes we find however that the precise polymer description significantly alters the locations of the phase coexistence regions. Especially the stability region of isotropic-isotropic coexistence is affected by the polymer interactions. To illustrate the quantitative effects some examples are presented.

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.

Directional-dependent pockets drive columnar-columnar coexistence

The rational design of materials requires a fundamental understanding of the mechanisms driving their self-assembly. This may be particularly challenging in highly dense and shape-asymmetric systems. Here we show how the addition of tiny non-adsorbing spheres (depletants) to a dense system of hard disc-like particles (discotics) leads to coexistence between two distinct, highly dense (liquid)-crystalline columnar phases. This coexistence emerges due to the directional-dependent free-volume pockets for depletants. Theoretical results are confirmed by simulations explicitly accounting for the binary mixture of interest. We define the stability limits of this columnar-columnar coexistence and quantify the directional-dependent depletant partitioning.

Hierarchically Ordered α-Zirconium Phosphate Platelets in Aqueous Phase with Empty Liquid

Platelets of α-zirconium phosphate (α-ZrP) obtained from the reflux method in H₃PO₄ are successfully exfoliated into water via the intercalation of alkanol amines. With volume fractions greater than 0.02 they are stacked into tactoids of few layers with a repeat distance in the order of 10 nm. The tactoids align into nematic liquid crystalline phases with irregularly wide interstices of empty liquid. Colloidal processing involves the freeze-drying of such anisotropic fluids and the dispersion of the restacked tacoids into aqueous dispersions of colloidal polymer particles of largely varying size which occupy the otherwise empty liquid between the α-ZrP tactoids and induce piling of the tactoids into columns. Real-time SAXS on drying films and TEM of the obtained coatings demonstrate that the stacked α-ZrP platelets and the polymer particles comprising liquid dry separately without polymer intercalation, while the morphology of the obtained composites can be tuned primarily by the size of the polymer colloids. Concomitant α-ZrP hydrolysis in the exfoliation step is scrutinized as a function of amine basicity and temperature. The role of zirconium based hydrolysis products in the hierarchical α-ZrP assembly is indirectly though consistently confirmed by opposing impacts of ultra-filtration and added oxoanions on the platelets’ spacing, smoothness and aggregation. HAADF-TEM imaging of scattered, singular platelets and XRD peak analysis of the pristine solid shed light on the α-ZrP synthesis. Coexisting flakes and lacunae, both similar in size to the intra-layer crystal domains, suggest the stitching of proto-α-ZrP flakes into extended layers in accordance with our observations on the aging behaviour of α-ZrP dispersions as well as with literature data on related systems.

Phase behaviour of colloidal superballs mixed with non-adsorbing polymers

Inspired by experimental work on colloidal cuboid-polymer dispersions (Rossi et al., Soft Matter, 7, 4139 (2011)) we have theoretically studied the phase behaviour of such mixtures. To that end, free volume theory (FVT) was applied to predict the phase behaviour of mixtures of superballs and non-adsorbing polymer chains in a common solvent. Closed expressions for the thermodynamic properties of a suspension of hard colloidal superballs have been derived, accounting for fluid (F), face-centred cubic (FCC) and simple cubic (SC) phase states. Even though the considered solid phases are approximate, the hard superballs phase diagram semi-quantitatively matches with more evolved methods. The theory developed for the cuboid-polymer mixture reveals a rich phase behaviour, which includes not only isostructural F₁-F₂ coexistence, but also SC₁-SC₂ coexistence, several triple coexistences, and even a quadruple-phase coexistence region (F₁-F₂-SC-FCC). The model proposed offers a tool to asses the stability of cuboid-polymer mixtures in terms of the colloid-to-polymer size ratio.