Revealing the Origin of Cooperative Adsorption of Chains on Nanoparticle Surfaces through Coarse-Grained Simulations.

This work aims to deepen our understanding of the molecular origin of the recently observed phenomenon of polymer cooperative adsorption onto faceted nanoparticle (NP) surfaces. By exploring a large parameter space for polymer/NP interactions through coarse-grained (CG) molecular dynamics (MD) simulations, it is found that consistent with experiments the presence or absence of cooperativity is related to solvent quality and relative interaction strengths between the polymer and the adsorbent. Specifically, positive cooperativity is associated with stronger polymer-polymer interaction than polymer-surface interactions and vice versa for negative cooperativity. This contrast in interaction energies manifests in positive cooperativity (i.e., increased affinity) and negative cooperativity (i.e., decreased affinity) as concentration increases. It is also found that increasing chain length strengthens cooperativity effects and that the nanoscale confinement of polymer chains to the adsorbing facet (due to weaker affinity to corners and edges) enhances positive cooperativity but weakens negative cooperativity. Moreover, adsorption onto a spherical NP shows stronger positive cooperativity but weaker negative cooperativity compared with adsorption onto a cubic NP of equal surface area. It was further found that as polymer bulk concentration increases, the free energy of adsorption decreases in positive cooperativity, increases in negative cooperativity, and is independent of concentration in noncooperative systems consistent with the phenomenological explanation of cooperativity. We further found that positive cooperativity is associated with growing fluctuations in the adsorption density at critical bulk polymer concentrations. This behavior can be attributed to the competition between enthalpic gains and entropic losses upon adsorption. Overall, our results shed light on the microscopic origin of cooperative adsorption and the role of solvent quality, which can be leveraged in, for example, controlling NP growth into target shapes and designing NP catalysts with improved performance.

Coarse-Grained Molecular Simulation of Bolapolyphiles with a Multident Lateral Chain: Formation and Structural Analysis of Cubic Network Phases.

Bolapolyphiles constitute a versatile class of materials with a demonstrated potential to form a wide variety of complex ordered mesophases. In particular, cubic network phases (like the gyroid, primitive, and diamond phases) have been a target of many studies for their ability to create percolating 3D nanosized channels. In this study, molecular simulations are used to explore the phase behavior of bolapolyphiles containing a rigid rodlike core, associating hydrophilic core ends and a hydrophobic side chain with a multident architecture, i.e., where the branching pattern can vary from bident (two branches) to hexadent (six branches). Upon network phase formation, its skeleton is made up of "nodes" populated by the core ends and "struts" populated by the cores. It is shown that, by varying the side chain length, branching pattern, and attachment point to the core, one can alter the crowding around the cores and hence tune the nodal size and nodal valence (i.e., number of connecting struts) which lead to different types of network morphologies. For example, for a fixed total side chain length, having more branches generates a stronger crowding around the molecular core, driving them to form bundlelike domains with curvier interfaces that result in thinner struts. Also, attaching the lateral chain closer to one core end breaks the symmetry between the environments around the two core ends, leading to networks with bimodal nodal sizes. Importantly, since the characterization of (ordered or partially ordered) network phases is challenging given the potential incompatibilities between the simulation box size with the structure's space group periodic symmetry and the effect of morphological defects, a detailed framework is presented to analyze and fully characterize the unit cell parameters and structure factor of such systems.

Self-Assembling of Nonadditive Mixtures Containing Patchy Particles with Tunable Interactions.

Mixtures of nanoparticles (NPs) with hybridizing grafted DNA or DNA-like strands have been of particular interest because of the tunable selectivity provided for the interactions between the NP components. A richer self-assembly behavior would be accessible if these NP-NP interactions could be designed to give nonadditive mixing (in analogy to the case of molecular components). Nonadditive mixing occurs when the mixed-state volume is smaller (negative) or larger (positive) than the sum of the individual components' volumes. However, instances of nonadditivity in colloidal/NP mixtures are rare, and systematic studies of such mixtures are nonexistent. This work focuses on patchy NPs whose patches (coarsely representing grafted hybridizing DNA strands) not only encode selectivity across components but also impart a tunable nonadditivity by varying their extent of protrusion. To guide the exploration of the relationship between phase behavior and nonadditivity for different patches' designs, the NP-NP potential of mean force (PMF) and a nonadditive parameter were first calculated. For one-patch NPs, different lamellar morphologies were predominantly observed. In contrast, for mixtures of two-patch NPs and (fully grafted) spherical particles, a rich phase behavior was found depending on patch-patch angle and degree of nonadditivity, resulting in phases such as the gyroid, cylinder, honeycomb, and two-layered crystal. Our results also show that both minimum positive nonadditivity and multivalent interactions are necessary for the formation of ordered network mesophases in the class of models studied.

Influence of Nonadditive Mixing on Colloidal Diamond Phase Formation from Patchy Particles.

Mixtures of nanoparticles (NPs) with hybridizing grafted DNA or DNA-like strands have been shown to create highly tunable NP-NP interactions, which, if designed to give nonadditive mixing, could lead to a richer self-assembly behavior. While nonadditive mixing is known to result in nontrivial phase behavior in molecular fluids, its effects on colloidal/NP materials have been much less studied. Such effects are explored here via molecular simulations for a binary system of tetrahedral patchy NPs, known to self-assemble into the diamond phase. The NPs are modeled with raised patches that interact through a coarse-grained interparticle potential representing DNA hybridization between grafted strands. It was found that these patchy NPs spontaneously nucleate into the diamond phase, and that hard-interacting NP cores eliminated the competition between the diamond and BCC phases at the conditions studied. Our results also showed that while higher nonadditivity had a small effect on phase behavior, it kinetically enhanced the formation of the diamond phase. Such a kinetic enhancement is argued to arise from changes in phase packing densities and how these modulate the interfacial free energy of the crystalline nucleus by favoring high-density motifs in the isotropic phase and larger NP vibrations in the diamond phase.

Effect of particle anisotropy on the thermodynamics and kinetics of ordering transitions in hard faceted particles.

Monte Carlo simulations were used to study the influence of particle aspect ratio on the kinetics and phase behavior of hard gyrobifastigia (GBF). First, the formation of a highly anisotropic nucleus shape in the isotropic-to-crystal transition in regular GBF is explained by the differences in interfacial free energies of various crystal planes and the nucleus geometry predicted by the Wulff construction. GBF-related shapes with various aspect ratios were then studied, mapping their equations of state, determining phase coexistence conditions via interfacial pinning, and computing nucleation free-energy barriers via umbrella sampling using suitable order parameters. Our simulations reveal a reduction of the kinetic barrier for isotropic-crystal transition upon an increase in aspect ratio, and that for highly oblate and prolate aspect ratios, an intermediate nematic phase is stabilized. Our results and observations also support two conjectures for the formation of the crystalline state from the isotropic phase: that low phase free energies at the ordering phase transition correlate with low transition barriers and that the emergence of a mesophase provides a steppingstone that expedites crystallization.

Ion Transport in 2D Nanostructured π-Conjugated Thieno[3,2-b]thiophene-Based Liquid Crystal.

Leveraging the self-assembling behavior of liquid crystals designed for controlling ion transport is of both fundamental and technological significance. Here, we have designed and prepared a liquid crystal that contains 2,5-bis(thien-2-yl)thieno[3,2-b]thiophene (BTTT) as mesogenic core and conjugated segment and symmetric tetra(ethylene oxide) (EO4) as polar side chains for ion-conducting regions. Driven by the crystallization of the BTTT cores, BTTT/dEO4 exhibits well-ordered smectic phases below 71.5 °C as confirmed by differential scanning calorimetry, polarized optical microscopy, temperature-dependent wide-angle X-ray scattering, and grazing incidence wide-angle X-ray scattering (GIWAXS). We adopted a combination of experimental GIWAXS and molecular dynamics (MD) simulations to better understand the molecular packing of BTTT/dEO4 films, particularly when loaded with the ion-conducting salt lithium bis(trifluoromethanesulfonyl)imide (LiTFSI). Ionic conduction of BTTT/dEO4 is realized by the addition of LiTFSI, with the material able to maintain smectic phases up to r = [Li+]/[EO] = 0.1. The highest ionic conductivity of 8 × 10-3 S/cm was attained at an intermedium salt concentration of r = 0.05. It was also found that ion conduction in BTTT/dEO4 is enhanced by forming a smectic layered structure with irregular interfaces between the BTTT and EO4 layers and by the lateral film expansion upon salt addition. This can be explained by the enhancement of the misalignment and configurational entropy of the side chains, which increase their local mobility and that of the solvated ions. Our molecular design thus illustrates how, beyond the favorable energetic interactions that drive the assembly of ion solvating domains, modulation of entropic effects can also be favorably harnessed to improve ion conduction.

Computing free energy barriers for the nucleation of complex network mesophases.

A previously introduced framework to identify local order parameters (OPs) distinctive of incipient complex mesophases, such as bicontinuous network phases, is used in this work to evaluate nucleation free-energy barriers. The sampling techniques considered are the mean-first-passage-time (MFPT) method and novel variants of umbrella sampling, including Hybrid Monte Carlo (HMC) and a dual-OP-method that uses a blunter global OP for the umbrella bias while keeping record of configurations for analysis with a local OP. These methods were chosen for their ability to minimize or avoid frequent calculation of the expensive local OP, which makes their continuous on-the-fly tracking computationally very inefficient. These techniques were first validated by studying phase-transition barriers of model systems, i.e., the vapor-liquid nucleation of Lennard-Jones argon and a binary nanoparticle model. The disorder-to-order free energy barrier was then traced for the double gyroid and single diamond formed by mesoscopic bead-spring macromolecular models. The dual OP method was found to be the most robust and computationally efficient, since, unlike HMC, it does not require the expensive local OP to be computed on-the-fly, and unlike the MFPT method, it can negotiate large barriers aided by the biased sampling. The dual OP method requires, however, that a cheap global OP be identified and correlated (in a post-processing step) with the local OP that describes the structure of the critical nucleus, a process that can be aided by machine learning.

Re-entrant transition as a bridge of broken ergodicity in confined monolayers of hexagonal prisms and cylinders.

The entropy-driven monolayer assembly of hexagonal prisms and cylinders was studied under hard slit confinement. At the conditions investigated, the particles have two distinct and dynamically disconnected rotational states: unflipped and flipped, depending on whether their circular/hexagonal face is parallel or perpendicular to the wall plane. Importantly, these two rotational states cast distinct projection areas over the wall plane that favor either hexagonal or tetragonal packing. Monte Carlo simulations revealed a re-entrant melting transition where an intervening disordered Flipped-Unflipped (FUN) phase is sandwiched between a fourfold tetratic phase at high concentrations and a sixfold triangular solid at intermediate concentrations. The FUN phase contains a mixture of flipped and unflipped particles and is translationally and orientationally disordered. Complementary experiments were conducted with photolithographically fabricated cylindrical microparticles confined in a wedge cell. Both simulations and experiments show the formation of phases with comparable fraction of flipped particles and structure, i.e., the FUN phase, triangular solid, and tetratic phase, indicating that both approaches sample analogous basins of particle-orientation phase-space. The phase behavior of hexagonal prisms in a soft-repulsive wall model was also investigated to exemplify how tunable particle-wall interactions can provide an experimentally viable strategy to dynamically bridge the flipped and unflipped states.

On the calculation of free energies over Hamiltonian and order parameters via perturbation and thermodynamic integration.

In this work, complementary formulas are presented to compute free-energy differences via perturbation (FEP) methods and thermodynamic integration (TI). These formulas are derived by selecting only the most statistically significant data from the information extractable from the simulated points involved. On the one hand, commonly used FEP techniques based on overlap sampling leverage the full information contained in the overlapping macrostate probability distributions. On the other hand, conventional TI methods only use information on the first moments of those distributions, as embodied by the first derivatives of the free energy. Since the accuracy of simulation data degrades considerably for high-order moments (for FEP) or free-energy derivatives (for TI), it is proposed to consider, consistently for both methods, data up to second-order moments/derivatives. This provides a compromise between the limiting strategies embodied by common FEP and TI and leads to simple, optimized expressions to evaluate free-energy differences. The proposed formulas are validated with an analytically solvable harmonic Hamiltonian (for assessing systematic errors), an atomistic system (for computing the potential of mean force with coordinate-dependent order parameters), and a binary-component coarse-grained model (for tracing a solid-liquid phase diagram in an ensemble sampled through alchemical transformations). It is shown that the proposed FEP and TI formulas are straightforward to implement, perform similarly well, and allow robust estimation of free-energy differences even when the spacing of successive points does not guarantee them to have proper overlapping in phase space.

Low Interfacial Free Energy Describes the Bulk Ordering Transition in Colloidal Cubes.

Many hard faceted nanoparticles are known to undergo disorder-to-order phase transitions following a classical nucleation and growth mechanism. In a previous study [J. Phys. Chem. B 2018, 122, 9264-9273], it was shown that hard cubes undergo a nonclassical phase transition with a bulk character instead of originating from consolidated nuclei. Significantly, an unusually high fraction of ordered particles was observed in the metastable basin of the disordered phase, even for very low degrees of supersaturation. This work aims to substantiate the conjecture that these unique properties originate from a comparatively low interfacial free energy between the disordered and ordered phases for hard cubes relative to other hard particle systems. Using the cleaving wall method to directly measure the interfacial free energy for cubes, it is found that its values are indeed small; e.g., at phase coexistence conditions, it is only one-fifth that for hard spheres. A theoretical nucleation model is used to explore the broader implications of low interfacial tension values and how this could result in a bulk ordering mechanism.

Molecular Simulations of Laser Spike Annealing of Block Copolymer Lamellar Thin-Films.

We use molecular dynamics simulations to study the phase behavior of a coarse-grained lamella-forming A-b-B diblock copolymer under thin-film soft confinement for different heating cycle lengths, film thicknesses, and substrate-polymer affinities. This model describes the effect on thin-film morphology with a free surface (air-polymer interface) and a solid substrate. Our simulation results were first validated by showing that they capture changes for the order-disorder transition temperature with annealing conditions consistent with those found in laser spike annealing experiments, when the vertical lamella phase formed on neutral substrates. In addition, simulations with a substrate selective for a particular block revealed the formation of other phases, including a mixed vertical-horizontal lamella and a metastable island phase having horizontal but incomplete lamella layers. The nanoscale roughness features of this island phase, and hence its surface wettability, can be tuned with suitable choices of chemistry and annealing conditions.

Thermal Stability of π-Conjugated n-Ethylene-Glycol-Terminated Quaterthiophene Oligomers: A Computational and Experimental Study.

This work represents a joint computational and experimental study on a series of n-ethylene glycol (PEOn)-terminated quaterthiophene (4T) oligomers for 1 < n < 10 to elucidate their self-assembly behavior into a smectic-like lamellar phase. This study builds on an earlier study for n = 4 that showed that our model predictions were consistent with experimental data on the melting behavior and structure of the lamellar phase, with the latter consisting of crystal-like 4T domains and liquid-like PEO4 domains. The present study aims to understand how the length of the terminal PEOn chains modulates the disordering temperature of the lamellar phase and hence the relative stability of the ordered structure. A simplified bilayer model, where the 4T domains are not explicitly described, is put forward to efficiently estimate the disordering effect of the PEO domains with increasing n; this method is first validated by correctly predicting that layers of alkyl (PE)-capped 4T oligomers (for 1 < n < 10) stay ordered at room temperature. Both 4T-domain implicit and explicit model simulations reveal that the order-disorder temperature decreases with the length of the PEO capping chains, as the associated increase in conformational entropy drives a tendency toward disorder that overtakes the cohesive energy, keeping the ordered packing of the 4T domains.

Framework for Inverse Mapping Chemistry-Agnostic Coarse-Grained Simulation Models into Chemistry-Specific Models.

Coarse-grained (CG) models have allowed molecular simulations to access large enough time and length scales to elucidate relationships between macroscale properties and microscale molecular interactions. However, an unaddressed inverse-design problem concerns the identification of an optimal chemistry-specific (CS) molecule that the generic CG model represents. This has been addressed here by introducing new tools for automatically generating and refining the mapping of CS-molecule candidates to the constraints of a CG model, based on representative optimization criteria. With these tools, for each CS-molecule from a candidate group, the best mapping of that molecule onto the CG model is found and their fit is assessed by an objective function designed to emphasize matching key properties of the CG model. We employ this methodology to a range of CG models from small solvent molecules up to block copolymer systems to show its ability to find optimal candidates and to uncover the underlying length scale of some of the CG models. For instances where the identity of the CG model is known a priori, the methodology identifies the correct AA chemistry. For instances where the identity is unknown and a pool of candidates is provided, the method selects a chemistry that aligns well with physical intuition. The best candidate chemistry is also found to be sensitive to changes to the CG model.

Structure Control of a π-Conjugated Oligothiophene-Based Liquid Crystal for Enhanced Mixed Ion/Electron Transport Characteristics.

Developing soft materials with both ion and electron transport functionalities is of broad interest for energy-storage and bioelectronics applications. Rational design of these materials requires a fundamental understanding of interactions between ion and electron conducting blocks along with the correlation between the microstructure and the conduction characteristics. Here, we investigate the structure and mixed ionic/electronic conduction in thin films of a liquid crystal (LC) 4T/PEO4, which consists of an electronically conducting quarterthiophene (4T) block terminated at both ends by ionically conducting oligoethylenoxide (PEO4) blocks. Using a combined experimental and simulation approach, 4T/PEO4 is shown to self-assemble into smectic, ordered, or disordered phases upon blending the materials with the ionic dopant bis(trifluoromethane)sulfonimide lithium (LiTFSI) under different LiTFSI concentrations. Interestingly, at intermediate LiTFSI concentration, ordered 4T/PEO4 exhibits an electronic conductivity as high as 3.1 × 10-3 S/cm upon being infiltrated with vapor of the 2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane (F4TCNQ) molecular dopant while still maintaining its ionic conducting functionality. This electronic conductivity is superior by an order of magnitude to the previously reported electronic conductivity of vapor co-deposited 4T/F4TCNQ blends. Our findings demonstrate that structure and electronic transport in mixed conduction materials could be modulated by the presence of the ion transporting component and will have important implications for other more complex mixed ionic/electronic conductors.

Revealing the atomic ordering of binary intermetallics using in situ heating techniques at multilength scales.

Ordered intermetallic nanoparticles are promising electrocatalysts with enhanced activity and durability for the oxygen-reduction reaction (ORR) in proton-exchange membrane fuel cells (PEMFCs). The ordered phase is generally identified based on the existence of superlattice ordering peaks in powder X-ray diffraction (PXRD). However, after employing a widely used postsynthesis annealing treatment, we have found that claims of "ordered" catalysts were possibly/likely mixed phases of ordered intermetallics and disordered solid solutions. Here, we employed in situ heating, synchrotron-based, X-ray diffraction to quantitatively investigate the impact of a variety of annealing conditions on the degree of ordering of large ensembles of Pt3Co nanoparticles. Monte Carlo simulations suggest that Pt3Co nanoparticles have a lower order-disorder phase transition (ODPT) temperature relative to the bulk counterpart. Furthermore, we employed microscopic-level in situ heating electron microscopy to directly visualize the morphological changes and the formation of both fully and partially ordered nanoparticles at the atomic scale. In general, a higher degree of ordering leads to more active and durable electrocatalysts. The annealed Pt3Co/C with an optimal degree of ordering exhibited significantly enhanced durability, relative to the disordered counterpart, in practical membrane electrode assembly (MEA) measurements. The results highlight the importance of understanding the annealing process to maximize the degree of ordering in intermetallics to optimize electrocatalytic activity.

Correlation between morphology and anisotropic transport properties of diblock copolymers melts.

Molecular simulations of coarse-grained diblock copolymers (DBP) were conducted to study the effect of segregation strength and morphology on transport properties. It was found that in the strong segregation limit (i.e., high χN, where χ is the Flory-Huggins parameter and N is the degree of polymerization), the presence of the DBP interfaces imposes topological constraints similar to those of entanglements as manifested in the rheological signature of the polymer (i.e., a plateau modulus). Furthermore, compared to the behavior of isotropic melts, the crossover from Rouse to reptation scaling of the self-diffusion coefficient (D) parallel to the DBP interface takes place at a smaller N, an effect that depends on temperature and is more pronounced in the Lamellae morphology than in the hexagonal cylinder morphology. Additionally, it is shown that for an entangled melt (i.e., N ≫ Ne where Ne is the entanglement length) block retraction is instrumental for chains to diffuse parallel to the interface of lamellar layers. Lastly, it is found that the anisotropic viscosity of different morphologies is mostly affected by the orientation of the chains relative to the shear flow direction, exhibiting reduced values when chains align in the neutral or flow directions.

Computational affinity maturation of camelid single-domain intrabodies against the nonamyloid component of alpha-synuclein.

Improving the affinity of protein-protein interactions is a challenging problem that is particularly important in the development of antibodies for diagnostic and clinical use. Here, we used structure-based computational methods to optimize the binding affinity of VHNAC1, a single-domain intracellular antibody (intrabody) from the camelid family that was selected for its specific binding to the nonamyloid component (NAC) of human α-synuclein (α-syn), a natively disordered protein, implicated in the pathogenesis of Parkinson's disease (PD) and related neurological disorders. Specifically, we performed ab initio modeling that revealed several possible modes of VHNAC1 binding to the NAC region of α-syn as well as mutations that potentially enhance the affinity between these interacting proteins. While our initial design strategy did not lead to improved affinity, it ultimately guided us towards a model that aligned more closely with experimental observations, revealing a key residue on the paratope and the participation of H4 loop residues in binding, as well as confirming the importance of electrostatic interactions. The binding activity of the best intrabody mutant, which involved just a single amino acid mutation compared to parental VHNAC1, was significantly enhanced primarily through a large increase in association rate. Our results indicate that structure-based computational design can be used to successfully improve the affinity of antibodies against natively disordered and weakly immunogenic antigens such as α-syn, even in cases such as ours where crystal structures are unavailable.

Stability of the Gyroid Phase in Rod-Coil Systems via Thermodynamic Integration with Molecular Dynamics.

The stability of the gyroid phase in a coarse-grained model of rod-coil block copolymers is ascertained by using a field-based thermodynamic integration method to calculate free-energy differences between competing phases. The scope of the original methodology is expanded in terms of both its implementation by designing guiding fields suitable for molecular dynamics simulations (besides Monte Carlo simulations) and its applications by describing the formation of bicontinuous phases with linear rod-coil amphiphilic chains and with bolaamphiphilic molecules. For both types of systems, results are presented that complement those from previous studies, providing a quantitative metric to pinpoint the conditions and molecular parameters that render the gyroid phase more stable than other competing morphologies.

Disorder Foreshadows Order in Colloidal Cubes.

Monte Carlo simulations are used to investigate the mechanism of the disorder-to-order phase transition for a bulk system of colloidal hard cubes. It is observed that the structure of the ordered state is foreshadowed in the disordered state through multiple spontaneously occurring ordered domains. Such domains arise due to the entropic preference for local facet alignment between particles and occur transiently and sparsely throughout the system even in the stable isotropic phase. At pressures (and degrees of supersaturation) where the isotropic phase becomes marginally metastable, a classical nucleation process is never observed; instead, the ordered domains increase in number and size, eventually reaching a critical point where they percolate the entire system and spontaneously consolidate to form the ordered phase. The critical number of particles and the per particle free-energy barrier both decrease with pressure. Using the total number of locally ordered particles as a global order parameter, it is predicted that for large systems the ordering transition would only be spontaneous above a critical pressure. Finally, a test designed to probe the ability of the system to favor a single monodomain solid from initially misaligned-ordered domains, reveals that an active interdomain zone mediates the concerted reorientation of particles.