Kinetic pathway to double-gyroid structure

A computational method for rapid analysis polymer structure and inverse design strategy (RAPSIDY)

Tailoring polymers for target applications often involves selecting candidates from a large design parameter space including polymer chemistry, molar mass, sequence, and architecture, and linking each candidate to their assembled structures and in turn their properties. To accelerate this process, there is a critical need for inverse design of polymers and fast exploration of the structures they can form. This need has been particularly challenging to fulfill due to the multiple length scales and time scales of structural arrangements found in polymers that together give rise to the materials' properties. In this work, we tackle this challenge by introducing a computational framework called RAPSIDY - Rapid Analysis of Polymer Structure and Inverse Design strategY. RAPSIDY enables inverse design of polymers by accelerating the evaluation of stability of multiscale structure for any given polymer design (sequence, composition, length). We use molecular dynamics simulations as the base method and apply a guiding potential to initialize polymers chains of a selected design within target morphologies. After initialization, the guiding potential is turned off, and we allow the chains and structure to relax. By evaluating similarity between the target morphology and the relaxed morphology for that polymer design, we can screen many polymer designs in a highly parallelized manner to rank designs that are likely to remain in that target morphology. We demonstrate how this method works using an example of a symmetric, linear pentablock, AxByAzByAx, copolymer system for which we determine polymer sequences that exhibit stable double gyroid morphology. Rather than trying to identify the global free-energy minimum morphology for a specific polymer design, we aim to identify candidates of polymer design parameter space that are more stable in the desired morphology than others. Our approach reduces computational costs for design parameter exploration by up to two orders-of-magnitude compared to traditional MD methods, thus accelerating design and engineering of novel polymer materials for target applications.

pH- and temperature-responsive supramolecular assemblies with highly adjustable viscoelasticity: a multi-stimuli binary system

Stimuli-responsive materials are increasingly needed for the development of smart electronic, mechanical, and biological devices and systems relying on switchable, tunable, and adaptable properties. Herein, we report a novel pH- and temperature-responsive binary supramolecular assembly involving a long-chain hydroxyamino amide (HAA) and an inorganic hydrotrope, boric acid, with highly tunable viscous and viscoelastic properties. The system under investigation demonstrates a high degree of control over its viscosity, with the capacity to achieve over four orders of magnitude of control through the concomitant manipulation of pH and temperature. In addition, the transformation from non-Maxwellian to Maxwellian fluid behavior could also be induced by changing the pH and temperature. Switchable rheological properties were ascribed to the morphological transformation between spherical vesicles, aggregated/fused spherical vesicles, and bicontinuous gyroid structures revealed by cryo-TEM studies. The observed transitions are attributed to the modulation of the head group spacing between HAA molecules under different pH conditions. Specifically, acidic conditions induce electrostatic repulsion between the protonated amino head groups, leading to an increased spacing. Conversely, under basic conditions, the HAA head group spacing is reduced due to the intercalation of tetrahydroxyborate, facilitated by hydrogen bonding.

Multiple Routes to Bicontinuous Cubic Liquid Crystal Phases Discovered by High-Throughput Self-Assembly Screening of Multi-Tail Lipidoids

Bicontinuous cubic phases offer advantageous routes to a broad range of applied materials ranging from drug delivery devices to membranes. However, a priori design of molecules that assemble into these phases remains a technological challenge. In this article, a high-throughput synthesis of lipidoids that undergo protonation-driven self-assembly (PrSA) into liquid crystalline (LC) phases is conducted. With this screening approach, 12 different multi-tail lipidoid structures capable of assembling into the bicontinuous double gyroid phase are discovered. The large volume of small-angle X-ray scattering (SAXS) data uncovers unexpected design criteria that enable phase selection as a function of lipidoid headgroup size and architecture, tail length and architecture, and counterion identity. Surprisingly, combining branched headgroups with bulky tails forces lipidoids to adopt unconventional pseudo-disc conformations that pack into double gyroid networks, entirely distinct from other synthetic or biological amphiphiles within bicontinuous cubic phases. From a multitude of possible applications, two examples of functional materials from lipidoid liquid crystals are demonstrated. First, the fabrication of gyroid nanostructured films by interfacial PrSA, which are rapidly responsive to the external medium. Second, it is shown that colloidally-dispersed lipidoid cubosomes, for example, for drug delivery, are easily assembled using top-down solvent evaporation methods.

Phase Behavior of Alkyl Ethoxylate Surfactants in a Dissipative Particle Dynamics Model

We present a dissipative particle dynamics (DPD) model capable of capturing the liquid state phase behavior of nonionic surfactants from the alkyl ethoxylate (C_nE_m) family. The model is based upon our recent work [Anderson et al. J. Chem. Phys. 2017, 147, 094503] but adopts tighter control of the molecular structure by setting the bond angles with guidance from molecular dynamics simulations. Changes to the geometry of the surfactants were shown to have little effect on the predicted micelle properties of sampled surfactants, or the water-octanol partition coefficients of small molecules, when compared to the original work. With these modifications the model is capable of reproducing the binary water-surfactant phase behavior of nine surfactants (C₈E₄, C₈E₅, C₈E₆, C₁₀E₄, C₁₀E₆, C₁₀E₈, C₁₂E₆, C₁₂E₈, and C₁₂E₁₂) with a good degree of accuracy.

Diffuse scattering from lamellar structures

Lamellar structures are formed in a variety of soft materials including lipids, surfactants, block polymers, clays, colloids, semicrystalline polymers and others. Lamellar phases are characterized by scattering patterns containing pseudo-Bragg peaks from the layer ordering. However, fluctuations of the lamellae give rise to diffuse scattering in addition. This diffuse scattering can provide valuable information on the elastic properties of lamellae which control their fluctuations. A number of models to account for this are described in this Tutorial Review, along with examples from the literature. In addition, diffuse scattering from in-plane fluctuations or structures such as perforations or patterned nanoparticles is considered. This type of diffuse scattering can give unique information on the nature of, and positional (and bond orientational) ordering within, correlated structures within the lamellar plane. Anisotropic diffuse scattering features from thermotropic smectic phases is also briefly discussed.

Following the nucleation pathway from disordered liquid to gyroid mesophase

Mesophases have order intermediate between liquids and crystals and arise in systems with frustration, such as surfactants, block copolymers, and Janus nanoparticles. The gyroid mesophase contains two interpenetrated, nonintersecting chiral networks that give it properties useful for photonics. It is challenging to nucleate a gyroid from the liquid. Elucidating the reaction coordinate for gyroid nucleation could assist in designing additives that facilitate the formation of the mesophase. However, the complexity of the gyroid structure and the extreme weakness of the first-order liquid to gyroid transition make this a challenging quest. Here, we investigate the pathway and transition states for the nucleation of a gyroid from the liquid in molecular simulations with a mesogenic binary mixture. We find that the gyroid nuclei at the transition states have a large degree of positional disorder and are not compact, consistent with the low surface free energy of the liquid-gyroid interface. A combination of bond-order parameters for the minor component is best to describe the passage from liquid to gyroid, among those we consider. The committor analyses, however, show that this best coordinate is not perfect and suggests that accounting for the relative ordering of the two interpenetrated networks in infant nuclei, as well as for signatures of ordering in the major component of the mesophase, would improve the accuracy of the reaction coordinate for gyroid formation and its use to evaluate nucleation barriers. To our knowledge, this study is the first to investigate the reaction coordinate and critical nuclei for the formation of any mesophase from an amorphous phase.

Emergence of ordered network mesophases in kinetic pathways of order-order transition for linear ABC triblock terpolymers

Applying the string method to the self-consistent field theory (SCFT) of ABC linear triblock copolymers, we developed a new strategy to design kinetic pathways for the formation of stable or metastable network mesophases in order-order transition (OOT) processes. The design principle regarding the kinetic pathways between distinct mesophases is based on the matching relationships of both domain spacing and dominant Fourier components of the density distributions. The results suggest that complex ordered network mesophases, such as alternating diamond (D^A) and alternating plumber's nightmare (P^A) could be obtained in kinetic pathways between simple phases covering lamellae, cylinders and spheres. By virtue of the minimal free energy pathway (MEP) obtained, we could acquire the epitaxial relationship and phase transition mechanism. Furthermore, we managed to regulate the MEP by changing the block composition to adjust packing frustration. Two new metastable networks, core-shell five-pronged and six-pronged morphologies, were found in the kinetic pathways, further demonstrating the regulating mechanism. The results will contribute to a better understanding of the kinetic relationship between simple phases and complex networks, thus providing a platform for soft materials design via the OOT route and guiding experimental procedures to fabricate ordered network mesophases.

Engineering Gyroid-Structured Functional Materials via Templates Discovered in Nature and in the Lab

In search of optimal structures for functional materials fabrication, the gyroid (G) structure has emerged as a promising subject of widespread research due to its distinct symmetry, 3D interconnected networks, and inherent chiral helices. In the past two decades, researchers have made great progress fabricating G-structured functional materials (GSFMs) based on G templates discovered both in nature and in the lab. The GSFMs demonstrate extraordinary resonance when interacting with light and matter. The superior properties of GSFMs can be divided into two categories based on the dominant structural properties, namely, dramatic optical performances dominated by short-range symmetry and well-defined texture, and effective matter transport due to long-range 3D interconnections and high integrity. In this review, G templates suitable for fabrication of GSFMs are summarized and classified. State-of-the-art optical applications of GSFMs, including photonic bandgap materials, chiral devices, plasmonic materials, and matamaterials, are systematically discussed. Applications of GSFMs involved in effective electron transport and mass transport, including electronic devices, ultrafiltration, and catalysis, are highlighted. Existing challenges that may hinder the final application of GSFMS together with possible solutions are also presented.

Phase behavior and complex crystal structures of self-assembled tethered nanoparticle telechelics

Motivated by growing interest in the self-assembly of nanoparticles for applications such as photonics, organic photovoltaics, and DNA-assisted designer crystals, we explore the phase behavior of tethered spherical nanoparticles. Here, a polymer tether is used to geometrically constrain a pair of nanoparticles creating a tethered nanoparticle "telechelic". Using simulation, we examine how varying architectural features, such as the size ratio of the two end-group nanospheres and the length of the flexible tether, affects the self-assembled morphologies. We demonstrate not only that this hybrid building block maintains the same phase diversity as linear triblock copolymers, allowing for a variety of nanoparticle materials to replace polymer blocks, but also that new structures not previously reported are accessible. Our findings imply a robust underlying ordering mechanism is common among these systems, thus allowing flexibility in synthesis approaches to achieve a target morphology.

Controlling the thermodynamic stability of intermediate phases in a cationic-amphiphile-water system with strongly binding counterions

We have studied the influence of two structurally isomeric organic salts, namely, 2-sodium-3-hydroxy naphthoate (SHN) and 1-sodium-2-hydroxy naphthoate (SHN1), on the phase behavior of concentrated aqueous solutions of the cationic surfactant cetylpyridinium chloride (CPC). Partial phase diagrams of the two systems have been constructed using polarizing optical microscopy and x-ray diffraction techniques. A variety of intermediate phases is seen in both systems for a range of salt concentrations. The CPC-SHN-water system exhibits the rhombohedral and tetragonal mesh phases in addition to the random mesh phase, whereas the CPC-SHN1-water system shows only the tetragonal and random mesh phases. The CPC-SHN-water system also exhibits two nematic phases consisting of cylindrical and disk-like micelles at relatively low and high salt concentrations, respectively. These results show that the concentration of the strongly bound counterion provided by the organic salt can be used as a control parameter to tune the stability of different intermediate phases in amphiphile-water systems.

Structure of mesh phases in cationic surfactant systems with strongly bound counterions: influence of the surfactant headgroup and the counterion

We have studied the phase behavior of concentrated aqueous solutions of cetylpyridinium bromide (CPB) and sodium 3-hydroxy-2-naphthoate (SHN) using X-ray diffraction and polarizing optical microscopy. The phase behavior of this system is found to be very similar to that of the cetyltrimethylammonium bromide (CTAB)-SHN-water system, reported by us recently (Ghosh, S. K., et al. Langmuir, 2007, 23, 3606), but with the important difference that the mesh-like aggregates in the present system have square symmetry, instead of the hexagonal symmetry seen in the earlier case. A random mesh phase without long-range correlations of the in-plane structure, as well as an ordered mesh phase, where the mesh-like aggregates lock into a three-dimensional lattice, are observed, as in the CTAB-SHN-water system. The mesh-like aggregates do not form when the hydroxynaphthoate counterion is replaced by either salicylate or tosylate, which are also known to bind strongly to the surfactant micelle. Instead, the phase behavior of these ternary mixtures is akin to that of the CPB-water binary system; the only liquid crystalline phase observed being the hexagonal phase made up of cylindrical micelles. These results show the extreme sensitivity of the structure and stability of mesh phases to subtle changes in the interheadgroup interactions.

Topological validation of morphology modeling by extended reverse Monte Carlo analysis

A combination of reverse Monte Carlo (RMC) and computational homology is examined as a useful approach in connecting scattering experiments to mathematics for 3D morphology modeling. We develop a different method of morphology modeling from multiple two-dimensional (2D) scattering patterns of structure functions by RMC technique using coarse-grained particles. We perform RMC analysis for multiple 2D scattering patterns of the configuration generated from the surface equation of double gyroid morphology. Homology analysis enables us to classify complex three-dimensional morphologies by incorporating topologically invariant quantities, the so-called Betti numbers. It is demonstrated that RMC analysis reconstructs the DG morphology from multiple 2D scattering patterns.

Viscoelasticity of a nonionic lamellar phase

The linear viscoelastic properties of a nonionic lamellar phase in C-orientation were studied as a function of temperature by small-amplitude oscillatory measurements in the frequency range 0.5-5 Hz. An almost solid-like elastic response was observed at all studied temperatures, from 42 to 20 degrees C. In this range, the elastic modulus was found to increase strongly with decreasing temperature. The elasticity is attributed to screw dislocations connecting layers in the stack, and the data thus suggest that the density of screw dislocations decreases with increasing temperature. The lamellar phase forms an "onion" texture when continuously sheared at lower temperatures. It is argued that a possible origin for the shear-induced "onion" texture is the instability of the screw dislocations in shear flow. By 2H NMR experimentation, we also find the formation of a random mesh phase at lower temperatures. The presence of equilibrium bilayer perforations, however, does not correlate with the "onion" stability.

2H NMR Evidence for the Formation of Random Mesh Phases in Nonionic Surfactant−Water Systems

Random mesh phases share many common features with the classical lamellar phase in that they are layered phases; but crucially, they possess nonuniform interfacial curvature, since the lamellae are pierced by water-filled pores. The introduction of curvature into the lamellae has been posited as a transitional precursor for other lyotropic phases. In this paper, we show that simple 2H nuclear magnetic resonance (NMR) experiments provide strong indication for the formation of the random mesh phase and the NMR data correlate well with literature results from small-angle X-ray scattering. The thermal evolution of the recorded quadrupolar splitting (DeltanuQ) is monitored within the lamellar phase of two nonionic surfactants, C16E6 and C12E5, as the samples are cooled or heated, and a marked and reversible change in the evolution of DeltanuQ is observed. Data from heavy water and deuterium labeled surfactant show the same temperature dependence and consequently report on the same structural changes with temperature. The formation of the random mesh phase is quantified in terms of an effective order parameter that is unity in the classical lamellar phase and takes values of <1 in the random mesh phase, reaching 0.6 at lower temperatures.