Communication: Self-assembly of semiflexible-flexible block copolymers

Interfacial properties of the hexane + carbon dioxide + water system in the presence of hydrophilic silica

Molecular dynamics simulations were conducted to study the interfacial behavior of the CO₂ + H₂O and hexane + CO₂ + H₂O systems in the presence of hydrophilic silica at geological conditions. Simulation results for the CO₂ + H₂O and hexane + CO₂ + H₂O systems are in reasonable agreement with the theoretical predictions based on the density functional theory. In general, the interfacial tension (IFT) of the CO₂ + H₂O system exponentially (linearly) decreased with increasing pressure (temperature). The IFTs of the hexane + CO₂ + H₂O (two-phase) system decreased with the increasing mole fraction of CO₂ in the hexane/CO₂-rich phase x_CO2 . Here, the negative surface excesses of hexane lead to a general increase in the IFTs with increasing pressure. The effect of pressure on these IFTs decreased with increasing x_CO2 due to the positive surface excesses of carbon dioxide. The simulated water contact angles of the CO₂ + H₂O + silica system fall in the range from 43.8° to 76.0°, which is in reasonable agreement with the experimental results. These contact angles increased with pressure and decreased with temperature. Here, the adhesion tensions are influenced by the variations in fluid-fluid IFT and contact angle. The simulated water contact angles of the hexane + H₂O + silica system fall in the range from 58.0° to 77.0° and are not much affected by the addition of CO₂. These contact angles increased with pressure, and the pressure effect was less pronounced at lower temperatures. Here, the adhesion tensions are mostly influenced by variations in the fluid-fluid IFTs. In all studied cases, CO₂ molecules could penetrate into the interfacial region between the water droplet and the silica surface.

Tunable Thin Film Periodicities by Controlling the Orientation of Cylindrical Domains in Side Chain Liquid Crystalline Block Copolymers

A facile approach to block copolymer (BCP) domain orientation control in thin films has been demonstrated by employing a BCP with liquid crystalline semifluorinated side chains by tuning the composition of the copolymers of the bottom surface layer (BSL). 1H,1H,2H,2H-Perfluorodecanethiol was attached to a precursor polymer, polystyrene-block-poly(glycidyl methacrylate) (PS-b-PGMA), to obtain a novel BCP with a C8F17-containing liquid crystal (LC) side chain (PS-b-P8FMA). Anisotropic hexagonally packed cylinder domains in a bulk state were first characterized by transmission electron microscopy (TEM) and small angle X-ray scattering (SAXS). The observed morphology transition of BCPs with different fluorinated side chain lengths of –CF3, –C4F9, and –C6F13 suggested the decisive effects of LC side chain ordering on the anisotropic nanostructures. In the thin film study, poly(methyl methacrylate-random-2,2,2-trifluoroethyl methacrylate-random-methacrylic acid) (PMMA-ran-PTFEMA-ran-PMAA) solution was used as BSLs for tuning the desired periodicities. The surface free energy (SFE) of BSL was simply tailored by changing the composition of comonomers. In atomic force microscopy (AFM) characterization, long-range ordered perpendicularly oriented BCP domains in a hexagonally packed array or parallel oriented BCP domains as striation patterns were easily fabricated on non-preferential or preferential BSL, respectively. The study presents a novel approach to tunable thin film periodicities without changing or modifying BCPs, which is desired in next-generation BCP lithography.

An experimental and theoretical investigation into the self-assembly of a chemically modified high-χ coil-rod diblock copolymer

A precursor diblock copolymer with a silicon backbone, polystyrene-block-poly(methylvinylsiloxane), was synthesized, and 1H,1H,2H,2H-perfluorodecanethiol was quantitatively introduced into the backbone via a thiol-ene reaction to yield a novel coil-rod diblock copolymer, poly(styrene-block-poly(2-((3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,10-heptadecafluorodecyl)thio)ethyl)methylsiloxane). The ultra-hydrophobicity of the introduced perfluoroalkyl side chain enhanced the segregation between counter-blocks and significantly increased the χ value, which is essential for minimizing the size of self-assembled domains for lithographic applications. Thus, self-assembled domains with a minimal spacing of approximately 10 nm were formed. A hexagonally packed array with significant anisotropy was observed in the self-assembled morphology by small-angle X-ray scattering and transmission electron microscopy. Such an array was precisely reproduced by modified self-consistent field theory (SCFT) calculation developed for the coil-rod structure. Furthermore, the phase diagram was estimated, and the morphological dependence on the relative scale of the rod unit was investigated by SCFT prediction.

Bulk and Interfacial Properties of the Decane + Water System in the Presence of Methane, Carbon Dioxide, and Their Mixture

Molecular dynamics simulations are carried out to study the two-phase behavior of the n-decane + water system in the presence of methane, carbon dioxide, and their mixture under reservoir conditions. The simulation studies were complemented by theoretical modeling using the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) and density gradient theory. Our results show that the presence of methane and carbon dioxide decreases the interfacial tension (IFT) of the decane + water system. In general, the IFT increases with increasing pressure and decreasing temperature for the methane + decane + water and carbon dioxide + decane + water systems, similar to what has been found for the corresponding decane + water system. The most important finding of this study is that the presence of carbon dioxide decreases the IFT of the methane + decane + water system. The atomic density profiles provide evidence of the local accumulation of methane and carbon dioxide at the interface, in most of the studied systems. The results of this study show the preferential dissolution in the water-rich phase and enrichment at the interface for carbon dioxide in the methane + carbon dioxide + decane + water system. This indicates the preferential interaction of water with carbon dioxide relative to methane and decane. Notably, there is an enrichment of the interface by decane at high mole fractions of methane in the methane/decane-rich or methane/carbon dioxide/decane-rich phase. Overall, the solubility of methane and carbon dioxide in the water-rich phase increases with increasing pressure and temperature. Additionally, we find that the overall performance of the PC-SAFT EoS and the cubic-plus-association EoS is similar with respect to the calculation of bulk and interfacial properties of these systems.

Sorption and Diffusion of Methane and Carbon Dioxide in Amorphous Poly(alkyl acrylates): A Molecular Simulation Study

Molecular simulations were carried out to understand the structural features and the sorption and diffusion behavior of methane and carbon dioxide in amorphous poly(alkyl acrylates) in the temperature range of 300-600 K. The hybrid Monte Carlo/molecular dynamics approach was employed to address the effects of polymer swelling and framework flexibility on the gas sorption. Simulations show that the glass-transition temperature decreases with the side-chain length of poly(alkyl acrylate), consistent with experiments. This is due to the fact that the shielding of the polar ester groups increases with the side-chain length. The simulated sorption isotherms for methane and carbon dioxide were in agreement with the experimental data. The polymer swelling becomes more pronounced, especially in the case of sorption of carbon dioxide. A significant swelling occurs, possibly because of the greater interaction between carbon dioxide and the polar ester groups in the polymers. The uptake of methane and carbon dioxide by poly(alkyl acrylates) generally increases with the side-chain length. Our simulations confirm the experimental findings that the diffusion coefficients of methane and carbon dioxide in poly(alkyl acrylates) increase with the side-chain length. Interestingly, the activation energies of gas diffusion decrease with the side-chain length. The diffusion coefficients of the penetrants have an exponential relationship with the void fraction, which is in agreement with the free volume theory.

Bulk and interfacial properties of decane in the presence of carbon dioxide, methane, and their mixture

Molecular dynamics simulations were performed to study the bulk and interfacial properties of methane + n-decane, carbon dioxide + n-decane, and methane + carbon dioxide + n-decane systems under geological conditions. In addition, theoretical calculations using the predictive Peng-Robinson equation of state and density gradient theory are carried out to compare with the simulation data. A key finding is the preferential dissolution in the decane-rich phase and adsorption at the interface for carbon dioxide from the methane/carbon dioxide mixture. In general, both the gas solubility and the swelling factor increase with increasing pressure and decreasing temperature. Interestingly, the methane solubility and the swelling of the methane + n-decane system are not strongly influenced by temperature. Our results also show that the presence of methane increases the interfacial tension (IFT) of the carbon dioxide + n-decane system. Typically, the IFT of the studied systems decreases with increasing pressure and temperature. The relatively higher surface excess of the carbon dioxide + n-decane system results in a steeper decrease in its IFT as a function of pressure. Such systematic investigations may help to understand the behavior of the carbon dioxide-oil system in the presence of impurities such as methane for the design and operation of carbon capture and storage and enhanced oil recovery processes.

Molecular Architecture Directs Linear-Bottlebrush-Linear Triblock Copolymers to Self-Assemble to Soft Reprocessable Elastomers

Linear-bottlebrush-linear (LBBL) triblock copolymers represent an emerging system for creating multifunctional nanostructures. Their self-assembly depends on molecular architecture but remains poorly explored. We synthesize polystyrene-block-bottlebrush polydimethylsiloxane-block-polystyrene triblock copolymers with controlled molecular architecture and use them as a model system to study the self-assembly of LBBL polymers. Unlike classical stiff rod-flexible linear block copolymers that are prone to form highly ordered nanostructures such as lamellae, at small weight fractions of the linear blocks, LBBL polymers self-assemble to a disordered sphere phase, regardless of the bottlebrush stiffness. Microscopically, characteristic lengths increase with the bottlebrush stiffness by a power of 2/3, which is captured by a scaling analysis. Macroscopically, the formed nanostructures are ultrasoft, reprocessable elastomers with shear moduli of about 1 kPa, two orders of magnitude lower than that of conventional polydimethylsiloxane elastomers. Our results provide insights on exploiting the self-assembly of LBBL polymers to create soft functional nanostructures.

Polymer Semiflexibility Induces Nonuniversal Phase Transitions in Diblock Copolymers

The order-disorder phase transition and the associated phase diagrams of semiflexible diblock copolymers are investigated using the wormlike chain model, incorporating concentration fluctuations. The free energy up to quartic order in concentration fluctuations is developed with chain-rigidity-dependent coefficients, evaluated using our exact results for the wormlike chain model, and a one-loop renormalization treatment is used to account for fluctuation effects. The chain length N and the monomer aspect ratio α directly control the strength of immiscibility (defined by the Flory-Huggins parameter χ) at the order-disorder transition and the resulting microstructures at different chemical compositions f_{A}. When monomers are infinitely thin (i.e., large aspect ratio α), the finite chain length N lowers the χN at the phase transition. However, fluctuation effects become important when chains have a finite radius, and a decrease in the chain length N elevates the χN at the phase transition. Phase diagrams of diblock copolymers over a wide range of N and α are calculated based on our fluctuation theory. We find that both finite N and α enhance the stability of the lamellar phase above the order-disorder transition. Our results demonstrate that polymer semiflexibility plays a dramatic role in the phase behavior, even for large chain lengths (e.g., N≈100).

Influence of topographically patterned angled guidelines on directed self-assembly of block copolymers

Single chain in mean-field Monte Carlo simulations were employed to study the self-assembly of block copolymers (BCP) in thin films that use trapezoidal guidelines to direct the orientation and alignment of lamellar patterns. The present study explored the influence of sidewall interactions and geometry of the trapezoidal guidelines on the self-assembly of perpendicularly oriented lamellar morphologies. When both the sidewall and the top surface exhibit preferential interactions to the same block of the BCP, trapezoidal guidelines with intermediate taper angles were found to result in less defective perpendicularly orientated morphologies. Similarly, when the sidewall and top surface are preferential to distinct blocks of the BCP, intermediate tapering angles were found to be optimal in promoting defect free structures. Such results are rationalized based on the energetics arising in the formation of perpendicularly oriented lamella on patterned substrates.

Ion transport mechanisms in lamellar phases of salt-doped PS-PEO block copolymer electrolytes

We use a multiscale simulation strategy to elucidate, at an atomistic level, the mechanisms underlying ion transport in the lamellar phase of polystyrene-polyethylene oxide (PS-PEO) block copolymer (BCP) electrolytes doped with LiPF₆ salts. Explicitly, we compare the results obtained for ion transport in the microphase separated block copolymer melts to those for salt-doped PEO homopolymer melts. In addition, we also present results for dynamics of the ions individually in the PEO and PS domains of the BCP melt, and locally as a function of the distance from the lamellar interfaces. When compared to the PEO homopolymer melt, ions were found to exhibit slower dynamics in both the block copolymer (overall) and in the PEO phase of the BCP melt. Such results are shown to arise from the effects of slower polymer segmental dynamics in the BCP melt and the coordination characteristics of the ions. Polymer backbone-ion residence times analyzed as a function of distance from the interface indicate that ions have a larger residence time near the interface compared to that near the bulk of lamella, and demonstrates the influence of the glassy PS blocks and microphase segregation on the ion transport properties. Ion transport mechanisms in BCP melts reveal that there exist five distinct mechanisms for ion transport along the backbone of the chain and exhibit qualitative differences from the behavior in homopolymer melts. We also present results as a function of salt concentration which show that the mean-squared displacements of the ions decrease with increasing salt concentration, and that the ion residence times near the polymer backbone increase with increasing salt concentration.

Thermodynamics of a Compressible Maier-Saupe Model Based on the Self-Consistent Field Theory of Wormlike Polymer

This paper presents a theoretical formalism for describing systems of semiflexible polymers, which can have density variations due to finite compressibility and exhibit an isotropic-nematic transition. The molecular architecture of the semiflexible polymers is described by a continuum wormlike-chain model. The non-bonded interactions are described through a functional of two collective variables, the local density and local segmental orientation tensor. In particular, the functional depends quadratically on local density-variations and includes a Maier–Saupe-type term to deal with the orientational ordering. The specified density-dependence stems from a free energy expansion, where the free energy of an isotropic and homogeneous homopolymer melt at some fixed density serves as a reference state. Using this framework, a self-consistent field theory is developed, which produces a Helmholtz free energy that can be used for the calculation of the thermodynamics of the system. The thermodynamic properties are analysed as functions of the compressibility of the model, for values of the compressibility realizable in mesoscopic simulations with soft interactions and in actual polymeric materials.

Complex liquid-crystal nanostructures in semiflexible ABC linear triblock copolymers: A self-consistent field theory

We show that two series of ABC linear triblock copolymers possess sequences of order-to-order phase transitions between microphase-separated states, as the degree of flexibility of the semiflexible middle B-blocks varies. The spatial and orientational symmetries of these phases, some of them containing liquid-crystal ordering, are analysed in comparison with related structures previously determined experimentally and theoretically. A theoretical framework based on the self-consistent field treatment of the wormlike-chain model, which incorporates the Flory-Huggins and Maier-Saupe interactions in the free energy, is used here as a basic foundation for numerical calculations. We suggest that tuning the flexibility parameter, which reduces to the concept of degree of polymerization in the coil-like limit and characterizes the chain-persistency in the rod-like limit, provides a promising approach that can be used to design the resulting microphase-separated structures in semiflexible copolymer melts.

Perspective: parameters in a self-consistent field theory of multicomponent wormlike-copolymer melts

We review a formalism that can be used to calculate the microphase-separated crystallographic structures of multi-component wormlike polymer melts. The approach is based on a self-consistent field theory of wormlike polymers where the persistence length of each component is an important parameter. We emphasize on an analysis of the number of independent parameters required to specify a problem in general, for a system that includes Flory-Huggins and Maier-Saupe energies. Examples of recent applications are also briefly demonstrated: AB homopolymer interface, AB diblock copolymers, and rod-coil copolymers.

Microphase separation of short wormlike diblock copolymers with a finite interaction range

We investigate several structural properties of low-molecular weight AB diblock copolymer melts, focusing on a number of features that substantially deviate from those of high-molecular weight copolymer melts. The study is based on the wormlike chain formalism aided by random phase approximation and self-consistent field theory. We examine the effects that stemmed from both the finite molecular weight and the finite interaction range between unlike AB monomers. The latter yields profound effects on systems consisting of short wormlike block copolymers. The noticeable shift of the order-disorder transition point is discussed. Attention is also paid to the strong-segregation regime, where low molecular weight polymers are subject to finite stretchability.

Directed self assembly of block copolymers using chemical patterns with sidewall guiding lines, backfilled with random copolymer brushes

Recently, alignment of block copolymer domains has been achieved using a topographically patterned substrate with a sidewall preferential to one of the blocks. This strategy has been suggested as an option to overcome the patterning resolution challenges facing chemoepitaxy strategies, which utilize chemical stripes with a width of about half the period of block copolymer to orient the equilibrium morphologies. In this work, single chain in mean field simulation methodology was used to study the self assembly of symmetric block copolymers on topographically patterned substrates with sidewall interactions. Random copolymer brushes grafted to the background region (space between patterns) were modeled explicitly. The effects of changes in pattern width, film thicknesses and strength of sidewall interaction on the resulting morphologies were examined and the conditions which led to perpendicular morphologies required for lithographic applications were identified. A number of density multiplication schemes were studied in order to gauge the efficiency with which the sidewall pattern can guide the self assembly of block copolymers. The results indicate that such a patterning technique can potentially utilize pattern widths of the order of one-two times the period of block copolymer and still be able to guide ordering of the block copolymer domains up to 8X density multiplication.

Interactions and Aggregation of Charged Nanoparticles in Uncharged Polymer Solutions

We employ an extension of the single chain in mean field simulation method to study mixtures of charged particles and uncharged polymers. We examine the effect of particle charge, polymer concentration, and particle volume fraction on the resulting particle aggregates. The structures of aggregates were characterized using particle-particle radial distribution functions and cluster size distributions. We observe that the level of aggregation between particles increases with increasing particle volume fraction and polymer concentration and decreasing particle charge. At intermediate regimes of particle volume fraction and polymer concentrations, we observe the formation of equilibrium clusters with a preferred size. We also examined the influence of manybody effects on the structure of a charged particle-polymer system. Our results indicate that the effective two-body approximation overpredicts the aggregation between particles even at dilute particle concentrations. Such effects are thought to be a consequence of the interplay between the respective manybody effects on the depletion and electrostatic interactions.

Achieving Bicontinuous Microemulsion Like Morphologies in Organic Photovoltaics

It is believed that the optimal morphology of an organic solar cell may be characterized by cocontinuous, interpenetrating donor and acceptor domains with nanoscale dimensions and high interfacial areas. One well-known equilibrium morphology that fits these characteristics is the bicontinuous microemulsion achieved by the addition of block copolymer compatibilizers to flexible polymer-polymer blends. However, there does not exist design rules for using block copolymer compatibilizers to produce bicontinuous microemulsion morphologies from the conjugated polymer/fullerene mixtures typically used to form the active layer of organic solar cells. Motivated by these considerations, we use single chain in mean field simulations to study the equilibrium phase behavior of semiflexible polymer + flexible-semiflexible block copolymer + solvent mixtures. Based on our results, we identify design rules for producing large channels of morphologies with characteristics like that of the bicontinuous microemulsion.

Aggregation behavior of rod-coil-rod triblock copolymers in a coil-selective solvent

Recent experiments have reported that the self-assembly of conjugated polymers mimicking rod-coil-rod triblock copolymers (BCPs) in selective solvents exhibits unique aggregate morphologies. However, the nature of the arrangement of the polymers within the aggregates and the spatial organization of the aggregates remain an unresolved issue. We report the results of coarse-grained Langevin dynamics simulations, which investigated the self-assembly behavior of rod-coil-rod BCPs in a coil-selective solvent. We observe a rapid formation of cylindrically shaped multichain clusters. The initial stages of formation of the aggregates was seen to be independent of the strength of the solvent selectivity. However, for higher solvent selectivities, the clusters were seen to merge into larger units at later stages. A reduction in rod to coil block ratio was observed to decrease the size and number of clusters. In the limit of a highly concentrated solution, we observe the formation of a networked system of distinct clusters, which however retain the cylindrical arrangement observed at lower polymer concentrations.

Phase transitions in semiflexible-rod diblock copolymers: a self-consistent field theory

We investigate the phase behavior of semiflexible-rod diblock copolymers in a parameter range where the system displays columnar and lamella structures, using a self-consistent field theory based on the wormlike-chain model. Both Flory-Huggins and Maier-Saupe orientational interactions are incorporated in the formalism, which allows us to explore microphase separation and liquid-crystal ordering simultaneously. Order-to-order phase transitions induced by chain rigidity and orientational interaction are both reported and analyzed. Coupled orientational ordering and spatial inhomogeneity of the four microphase-separated states are discussed in this work: hexagonal column, ellipse column, smectic-A, and smectic-C.

Influence of chain rigidity on the phase behavior of wormlike diblock copolymers

We utilize the wormlike chain model in the framework of the self-consistent field theory to investigate the influence of chain rigidity on the phase diagram of AB diblock copolymers in the full three-dimensional space. We develop an efficient numerical scheme that can be used to calculate the physical properties of ordered microstructures self-assembled from semiflexible block copolymers. The calculation describes the entire physical picture of the phase diagram, crossing from the flexible over to rodlike polymer behavior.