Dissipative Particle Dynamics Study of Order−Order Phase Transition of BCC, HPC, OBDD, and LAM Structures of the Poly(styrene)−Poly(isoprene) Diblock Copolymer

Coarse-grained molecular simulation of the effect of liquid crystal molecular pitch on structure in cylindrical confinement

Blue phases (BPs) consist of three-dimensional self-assembled structures formed by a double-twisted columnar arrangement of liquid crystal molecules. Although their unique optical and structural properties render BPs particularly useful for applications such as liquid crystal displays, BPs typically appear in a narrow temperature range between the isotropic and nematic phases. This thermodynamic instability impedes their practical applicability. However, the simulations we present here showed that, in a quasi-one-dimensional system confined to nanospace, a phase equivalent to the BP appears and persists between the nematic and smectic phases. Confinement to a nanotube (NT) with a relatively small radius enables the BP to be maintained over a wide temperature range, whereas for an NT with a relatively larger radius, the BP appears only in a very narrow temperature range between the aforementioned phases. We additionally showed that the pitch of the BP is dependent on and can be controlled by adjusting the radius of the NTs. This finding has significant implications for the potential application of these materials in fields such as photonics and chiral separation technologies.

Coarse-Grained Modeling of Ion-Containing Polymers

Ion-containing polymers have continued to be an important research focus for several decades due to their use as an electrolyte in energy storage and conversion devices. Elucidation of connections between the mesoscopic structure and multiscale dynamics of the ions and solvent remains incompletely understood. Coarse-grained modeling provides an efficient approach for exploring the structural and dynamical properties of these soft materials. The unique physicochemical properties of such polymers are of broad interest. In this review, we summarize the current development and understanding of the structure-property relationship of ion-containing polymers and provide insights into the design of such materials determined from coarse-grained modeling and simulations accompanying significant advances in experimental strategies. We specifically concentrate on three types of ion-containing polymers: proton exchange membranes (PEMs), anion exchange membranes (AEMs), and polymerized ionic liquids (polyILs). We posit that insight into the similarities and differences in these materials will lead to guidance in the rational design of high-performance novel materials with improved properties for various power source technologies.

Cylindrical defect structures formed by chiral nematic liquid crystals in quasi-one-dimensional systems

Blue phases are three-dimensional self-assembly structures of liquid crystals with a lattice of line defects. They have attracted considerable interest as photonic materials. It is well known that blue phases occur in cholesteric liquid crystals (CLCs) under certain thermodynamic conditions; however, recent studies have indicated that confining surfaces may induce distinctive structural changes. For example, in a previous study, a quasi-two-dimensional (Q2D) confinement system was investigated with the aid of numerical calculations, and a stable Q2D Skyrmion structure was attained. Here, we performed molecular simulations to investigate the CLC phase behavior at the molecular scale for a quasi-one-dimensional (Q1D) nanotube system. Various morphological behaviors of CLCs were observed by changing the temperature and the radius of the nanotubes. In particular, we discovered a self-assembled structure with cylindrical (or ring-like) defects rather than lines by introducing a novel local orientation analysis. Our simulation results show that the self-assembly of CLCs offers a guide to control the intensity in Q1D systems and fundamental knowledge for their application to optical devices.

Coarse-Grained Modelling and Temperature Effect on the Morphology of PS-b-PI Copolymer

Spontaneous spatial organization behavior and the aggregate morphology of polystyrene-block-polyisoprene (PS-b-PI) copolymer were investigated. Molecular dynamic (MD) and mesoscopic simulations using the dynamic of mean field density functional theory (DDF) were adopted to investigate the morphology changes exhibited by this block copolymer (BCP). In the mesoscopic simulations, several atoms in repeating units were grouped together into a bead representing styrene or isoprene segments as a coarse-grained model. Inter-bead interactions and essential parameters for mesoscopic models were optimized from MD simulations. Study indicated that morphology alternations can be induced in this system at annealing temperature of 393, 493, and 533 K. From our simulations, lamellar, bicontinuous, and hexagonally packed cylindrical equilibrium morphologies were achieved. Our simulated morphologies agree well with the reported experimental evidence at the selected temperature. The process of aggregate formation and morphology evolution were concretely clarified.

Thinning Approximation for Calculating Two-Dimensional Scattering Patterns in Dissipative Particle Dynamics Simulations under Shear Flow

Modifications to improve thinning approximation (TA) were considered in order to calculate two-dimensional scattering patterns (2DSPs) for dissipative particle dynamics (DPD) simulations of polymer melts under a shear flow. We proposed multipoint TA and adaptive TA because the bond lengths in DPD chains vary widely when compared to those in Kremer⁻Grest (KG) chains, and the effectiveness of these two types of TA for the two major DPD parameter sets were investigated. In this paper, we report our findings on the original DPD model with soft bonds and that with rigid bonds. Based on the behavior of the 2DSPs and the distribution of orientations of the bond vectors, two spot patterns originating from the oriented chain correlations were observed when distinct distributions of the highly oriented bond vectors in the shear direction were obtained. For multipoint TA, we concluded that at least two additional midpoints ( n mid ≥ 2 ) are required to clearly observe the two spot patterns. For adaptive TA, a dividing distance of l ATA ≤ 0.4 is sufficient for clear observation, which is consistent with the requirement of n mid ≥ 2 for multipoint TA.

Multipoint segmental repulsive potential for entangled polymer simulations with dissipative particle dynamics

A model is developed for simulating entangled polymers by dissipative particle dynamics (DPD) using the segmental repulsive potential (SRP). In contrast to previous SRP models that define a single-point interaction on each bond, the proposed SRP model applies a dynamically adjustable multipoint on the bond. Previous SRP models could not reproduce the equilibrium properties of Groot and Warren's original DPD model [R. D. Groot and P. B. Warren, J. Chem. Phys. 107, 4423 (1997)] because the introduction of a single SRP induces a large excluded volume, whereas, the proposed multipoint SRP (MP-SRP) introduces a cylindrical effective excluded bond volume. We demonstrate that our MP-SRP model exhibits equilibrium properties similar to those of the original DPD polymers. The MP-SRP model parameters are determined by monitoring the number of topology violations, thermodynamic properties, and the polymer internal structure. We examine two typical DPD polymers with different bond-length distributions; one of them was used in the modified SRP model by Sirk et al. [J. Chem. Phys. 136, 134903 (2012)], whereas the other was used in the original DPD model. We demonstrate that for both polymers, the proposed MP-SRP model captures the entangled behaviors of a polymer melt naturally, by calculating the slowest relaxation time of a chain in the melt and the shear relaxation modulus. The results indicate that the proposed MP-SRP model can be applied to a variety of DPD polymers.

Nucleation of the BCC phase from disorder in a diblock copolymer melt: Testing approximate theories through simulation

We examine nucleation of the stable body-centred-cubic (BCC) phase from the metastable uniform disordered phase in an asymmetric diblock copolymer melt. Our comprehensive, large-scale simulations of the time-dependent, mean-field Landau-Brazovskii model find that spherical droplets of the BCC phase nucleate directly from disorder. Near the order-disorder transition, the critical nucleus is large and has a classical profile, attaining the bulk BCC phase in an interior that is separated from disorder by a sharp interface. At greater undercooling, the amplitude of BCC order in the interior decreases and the nucleus interface broadens, leading to a diffuse critical nucleus. This diffuse nucleus becomes large as the simulation approaches the disordered phase spinodal. We show that our simulation follows the same nucleation pathway that Cahn and Hilliard found for an incompressible two-component fluid, across the entire metastable region. In contrast, a classical nucleation theory calculation based on the free energy of a planar interface between coexisting BCC and disordered phases agrees with simulation only in the limit of very small undercooling; we can expand this region of validity somewhat by accounting for the curvature of the droplet interface. A nucleation pathway involving a classical droplet persists, however, to deep undercooling in our simulation, but this pathway is energetically unfavourable. As a droplet grows in the simulation, its interface moves with a constant speed, and this speed is approximately proportional to the undercooling.

Chain stiffness regulates entropy-templated perfect mixing at single-nanoparticle level

The mixing on a single-particle level of chemically incompatible nanoparticles is an outstanding challenge for many applications. Burgeoning research activity suggests that entropic templating is a potential strategy to address this issue. Herein, using systematic computer simulations of model nanoparticle systems, we show that the entropy-templated interfacial organization of nanoparticles significantly depends on the stiffness of tethered chains. Unexpectedly, the optimal chain stiffness can be identified wherein a system exhibits the most perfect mixing for a certain compression ratio. Our simulations demonstrate that entropic templating regulated by chain stiffness precisely reflects various entropic repulsion states that arise from typical conformation regimes of semiflexible chains. The physical mechanism of the chain stiffness effect is revealed by analyzing the entropic repulsion states of tethered chains and quantitatively estimating the resulting entropy penalties, which provides direct evidence that supports the key role of entropic transition in the entropic templating strategy, as suggested in experiments. Moreover, the model nanoparticle systems are found to evolve into binary nanoparticle superlattices by remixing at extremely high stiffness. The findings facilitate the wide application of the entropic templating strategy in creating interfacially reactive nanomaterials with ordered structures on the single-nanoparticle level as well as mechanomutable responses.

Phase diagrams of block copolymer melts by dissipative particle dynamics simulations

Phase diagrams for monodisperse and polydisperse diblock copolymer melts and a random multiblock copolymer melt are constructed using dissipative particle dynamics simulations. A thorough visual analysis and calculation of the static structure factor in several hundreds of points at each of the diagrams prove the ability of mesoscopic molecular dynamics to predict the phase behavior of polymer systems as effectively as the self-consistent field-theory and Monte Carlo simulations do. It is demonstrated that the order-disorder transition (ODT) curve for monodisperse diblocks can be precisely located by a spike in the dependence of the mean square pressure fluctuation on χN, where χ is the Flory-Huggins parameter and N is the chain length. For two other copolymer types, the continuous ODTs are observed. Large polydispersity of both blocks obeying the Flory distribution in length does not shift the ODT curve but considerably narrows the domains of the cylindrical and lamellar phases partially replacing them with the wormlike micelle and perforated lamellar phases, respectively. Instead of the pure 3d-bicontinuous phase in monodisperse diblocks, which could be identified as the gyroid, a coexistence of the 3d phase and cylindrical micelles is detected in polydisperse diblocks. The lamellar domain spacing D in monodisperse diblocks follows the strong-segregation theory prediction, D∕N(1∕2) ~ (χN)(1∕6), whereas in polydisperse diblocks it is almost independent of χN at χN < 100. Completely random multiblock copolymers cannot form ordered microstructures other than lamellas at any composition.

ORDERED MICROPHASES OF SYMMETRIC DIBLOCK COPOLYMER IN SELECTIVE SOLVENT: DISSIPATIVE PARTICLE DYNAMICS SIMULATION AND RADIAL DISTRIBUTION FUNCTION ANALYSIS

The self-assembly process of a symmetric diblock copolymer A5B5 in a selective solvent is studied using the dissipative particle dynamics method. Four types of morphologies can form, including lamellae, perforated lamellae, cylinders and spheres. Three phase diagrams are presented to demonstrate the effect of the concentration and interaction parameters on the ordered microstructures. Radial distribution function (RDF) characterizing the spatial correlations of the blocks is calculated. RDF not only confirms the morphological observations, but also provides more quantitative details. The evolution process of hexagonally packed cylinder and lamellae is also illustrated.

Microphase separation of diblock copolymer poly(styrene-b-isoprene): A dissipative particle dynamics simulation study

Dissipative particle dynamics (DPD) simulations have been employed to study the microphase separation of the poly(styrene-b-isoprene) (PS-b-PI) diblock copolymer. The DPD model is constructed to match the physical description and structural properties of the PS-b-PI diblock copolymer. A coarse-grained force field has been developed for the diblock copolymer system in DPD simulations. The new force field contains bonded and nonbonded interaction terms, which are derived from atomistic molecular dynamics simulations and determined by fitting experimental data of the compressibility of water at room temperature and interfacial tension values, respectively. The morphologies of the PS-b-PI diblock copolymer system obtained from DPD simulations are in agreement with experimental observations as well as previous simulated results.

Multiscale modeling of emergent materials: biological and soft matter

In this review, we focus on four current related issues in multiscale modeling of soft and biological matter. First, we discuss how to use structural information from detailed models (or experiments) to construct coarse-grained ones in a hierarchical and systematic way. This is discussed in the context of the so-called Henderson theorem and the inverse Monte Carlo method of Lyubartsev and Laaksonen. In the second part, we take a different look at coarse graining by analyzing conformations of molecules. This is done by the application of self-organizing maps, i.e., a neural network type approach. Such an approach can be used to guide the selection of the relevant degrees of freedom. Then, we discuss technical issues related to the popular dissipative particle dynamics (DPD) method. Importantly, the potentials derived using the inverse Monte Carlo method can be used together with the DPD thermostat. In the final part we focus on solvent-free modeling which offers a different route to coarse graining by integrating out the degrees of freedom associated with solvent.