Segregation Strength Research Articles

An ab-initio study of hydrogen trapping energetics at BCC tungsten metal-noble gas interfaces

Density functional theory (DFT) calculations have been performed to assess the trapping and segregation strength of hydrogen (H) to noble gas interfaces in tungsten (W). These calculations consist of a supercell containing a slab of BCC W and an initial lattice of FCC noble gas atoms. The interfaces included noble gases of helium, neon, and argon, with densities in the range of 1-4 atoms-per-vacancy (V), and W surface orientations of (100), (110), and (111). We report on the binding energy of H to these interfaces as well as the modification to the migration barriers in the W slab, which together provide information on the segregation strength and de-trapping energy for H at noble gas bubbles. These calculations indicate that the binding energy of H to W-noble gas interfaces varies with surface orientation and decreases with increasing gas density; whereas the H migration energy is sensitive to the noble gas density, surface orientation, and diffusion pathway, and typically increases with gas density. Together, the de-trapping energy of H to these interfaces is shown to depend less significantly on noble gas density. These DFT calculations provide valuable first-principles energetics necessary for mesoscale models, and provide insight into the temperatures required to de-trap tritium from He bubbles in fusion plasma facing components.

Simplicity in mean-field phase behavior of two-component miktoarm star copolymers.

Using self-consistent field theory, we systematically explore the microphase separation in the class of two-component miktoarm star copolymers containing a single conjunction point between different blocks by considering an extended list of candidate microphases. We plot mean-field phase diagrams in the plane of segregation strength and composition for an array of representative star copolymers. Three principal phase diagram topologies, dictated by different phase stabilities, are exposed, displaying a hierarchy in complexity by increasing the molecular asymmetry. Our investigation indicates that the phase diagram topology depends on the ratios of arm numbers and Kuhn segment lengths, which highlights the role of the coordination number ratio between different polymers at the domain interface. These findings reveal the simplicity of the general phase behavior and suggest a complete list of stable microphases for the entire class, which provide useful insight into studying copolymers with more complicated architectures and conformational properties.

Order and Disorder in ABCA' Tetrablock Terpolymers.

Self-assembly of poly(styrene)-block-poly(isoprene)-block-poly(lactide)-block-poly(styrene) (PS-PI-PLA-PS' or SILS') tetrablock terpolymers, where the volume fractions of the first three blocks are nearly equivalent, was studied both experimentally and using the self-consistent field theory (SCFT). SCFT indicates that addition of the terminal PS' chain to a low-molecular-mass, hexagonally packed cylinders forming, SIL precursor can produce a disordered state due to preferential mixing of the polystyrene end-blocks with the PI and PLA midblocks in the SILS' tetrablock, alleviating the unfavorable contact between the highly incompatible PI and PLA segments. In contrast, SCFT predicts that higher-molar-mass triblock precursors will maintain an ordered morphology upon addition of the terminal PS' block due to stronger overall segregation strengths. These predictions were tested using three sets of SILS' polymers that were synthesized based on three precursor SIL triblock polymers differing in total molar mass (14, 30, and 47 kg mol-1) and varying the length of the terminal PS' chain. In the lowest-molar-mass set of tetrablock polymers, the shift from order to disorder was observed in the materials at ambient temperature as the molar mass of the terminal PS' block was increased, consistent with SCFT calculations. Disorder with longer S' chain lengths was not found in the two higher-molar-mass polymer sets; the medium-molar-mass set showed both microphase separation and long-range order based on transmission electron microscopy (TEM) and small-angle X-ray scattering (SAXS), while the largest of these block polymers microphase separated but showed limited long-range order. The combination of the experimental and theoretical results presented in this work provides insights into the self-assembly of ABCA'-type polymers and highlights potential complications that arise from frustration in accessing well-ordered materials.

Complete Photonic Band Gaps with Nonfrustrated ABC Bottlebrush Block Polymers.

Bottlebrush block polymers are a promising platform for self-assembled photonic materials, yet most work has been limited to one-dimensional photonic crystals based on the lamellar phase. Here we demonstrate with simulation that nonfrustrated ABC bottlebrush block polymers can be used to self-assemble three-dimensional photonic crystals with complete photonic band gaps. To show this, we have developed a computational approach that couples self-consistent field theory (SCFT) simulations to Maxwell's equations, thereby permitting a direct link between molecular design, self-assembly, and photonic band structures. Using this approach, we calculate the phase diagram of nonfrustrated ABC bottlebrush block polymers and identify regions where the alternating gyroid and alternating diamond phases are stable. By computing the photonic band structures of these phases, we demonstrate that complete band gaps can be found in regions of thermodynamic stability, thereby suggesting a route to realize these photonic materials experimentally. Furthermore, we demonstrate that gap size depends on volume fraction, segregation strength, and polymer architecture, and we identify a design strategy based on symmetry breaking that can achieve band gaps for lower values of refractive index contrast. Taken together, the approach presented here provides a powerful and flexible tool for predicting both the self-assembly and photonic band structures of polymeric materials.

Molecular theory of the tilting transition and computer simulations of the tilted lamellar phase of rod-coil diblock copolymers.

Symmetric rod-coil diblock copolymers have been simulated using the method of dissipative particle dynamics in the broad range of the Flory-Huggins parameter. It has been found that the tilted lamellar phase appears to be the most stable one at strong segregation. The rod-coil copolymer tilt angle and orientational order parameters have been determined as functions of the segregation strength. The density functional theory of rod-coil diblock copolymers has been generalized to the case of the tilted lamellar phase and used to study the stability of the orthogonal lamellar phase with respect to tilt. The orthogonal phase indeed appears to be unstable in the broad region of the parameter space in the case of relatively strong segregation. It has also been shown that the transition into the tilted lamellar phase is determined by a strong coupling between two independent tilt order parameters.

Molecular Engineering of Nanostructures in Disordered Block Polymers.

A series of symmetric poly(methyl methacrylate-stat-styrene)-block-polylactide (P(MMA-s-S)-b-PLA) diblock terpolymers with nearly constant molar masses yet varying block interaction parameters were synthesized as a model system to probe the extent and utility of composition fluctuations in the disordered state. A combination of differential scanning calorimetry, dynamic mechanical analysis, and small-angle X-ray scattering revealed that a broad range of segregation strengths ranging from what we ascribe to essentially a mean-field disordered to a fluctuating disordered to an ordered system could be readily obtained by tuning the molar fraction of styrene in these diblocks. The P(MMA-s-S)-b-PLA diblocks were annealed above their order-disorder transition temperatures (TODT) and rapidly quenched to low temperatures to trap the disordered state via vitrification, as confirmed by scanning electron microscopy. Small-angle X-ray scattering and N2 sorption analysis post-removal of PLA demonstrated that a transition from a very weakly structured, mean-field-like melt to a bicontinuous fluctuating disordered state occurred with increasing segregation strength. This work demonstrates that the extent of microphase segregation as well as the domain continuity of the disordered block polymer melt can be tuned using both synthetic design and thermal stimuli, guiding the design of disordered block polymers with targeted nanostructures that have potential technological utility.

Self-Assembly of Large Magnetic Nanoparticles in Ultrahigh Molecular Weight Linear Diblock Copolymer Films.

The development of diblock copolymer (DBC) nanocomposite films containing magnetic nanoparticles (NPs) with diameters (D) over 20 nm is a challenging task. To host large iron oxide NPs (Fe3O4, D = 27 ± 0.6 nm), an ultrahigh molecular weight (UHMW) linear DBC polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) is used as a template in the present work. Due to hydrogen bonding between the carboxylic acid ligands of the NPs and the ester groups in PMMA, the NPs show an affinity to the PMMA block. The localization of the NPs inside the DBC is investigated as a function of the NP concentration. At low NP concentrations, NPs are located preferentially at the interface between PS and PMMA domains to minimize the interfacial tension caused by the strong segregation strength of the UHMW DBC. At high NP concentrations (≥10 wt %), chain-like NP aggregates (a head-to-tail orientation) are observed in the PMMA domains, resulting in a change of the morphology from sphere to ellipsoid for part of the PMMA domains. Magnetic properties of the hybrid films are probed via superconducting quantum interference device magnetometry. All hybrid films show ferrimagnetism and are promising for potential applications in magnetic data storage.

Secondary structure drives self-assembly in weakly segregated globular protein–rod block copolymers

Imparting secondary structure to the polymer block can drive self-assembly in globular protein–helix block copolymers, increasing the effective segregation strength between blocks with weak or no repulsion.

Effect of Ion Concentration on the Formation of Bicontinuous Microemulsions in Partially Charged Ternary Polymer Blends

We describe the formation of bicontinuous microemulsions (BμE) from a series of three model charged ternary polymer blends comprising an AB diblock copolymer and the constituent A and B homopolymers, where A is a partially charged poly[(oligo(ethylene glycol) methyl ether methacrylate-co-oligo(ethylene glycol) propyl sodium sulfonate methacrylate)] (POEGMA) block with systematically tuned ion concentration and B is a neutral polystyrene (PS) block. The mole fraction of charged groups in the POEGMA block and the corresponding POEGMA homopolymer was 7, 23, or 36%. The phase diagrams of ternary blends with variable ion concentrations have been mapped out along the volumetrically symmetric isopleth by using a combination of rheology, small-angle neutron and X-ray scattering, and cloud point measurements. A well-defined BμE channel is found over an unusually wide range of homopolymer compositions (2–7%), in the proximity of the Lifshitz multicritical point anticipated by mean-field theory. While the ion concentration significantly impacts both the morphological length scale and the extent of the BμE phase over a wide range of compositions and temperatures, it is remarkable that the BμE persists over a significant range of segregation strength. This study provides new insight into the rational design of charged ternary polymer blends to tune the structural characteristics of the BμE by modulating ion concentration.

Order-to-Disorder Transitions in Lamellar Melt Self-Assembled Core-Shell Bottlebrush Polymers.

We report the synthesis and melt self-assembly behaviors of densely grafted, core-shell bottlebrush (csBB) polymers derived from covalently linking narrow dispersity, symmetric composition ABA-type triblock polymers through their chain midpoints. Derived from sequential ring-opening polymerizations of ε-decalactone and rac-lactide initiated from 5-norbornene-2-exo,3-exo-dimethanol, poly(lactide-block-ε-decalactone-block-lactide) macromonomers (Mn = 9.2-17.8 kg/mol; Đ = 1.19-1.25) were enchained by living ring-opening metathesis polymerization (ROMP) into csBBs with backbone degrees of polymerization Nbb = 8-43. Temperature-dependent small-angle X-ray scattering (SAXS) studies indicate that the critical triblock arm degree of polymerization (Narm) required for melt segregation decreases with increasing Nbb, leading to reductions in the accessible ordered lamellar microdomain (d) spacings. We derive a phenomenological relationship between the critical triblock arm segregation strength at the order-disorder transition (χNarm)ODT and Nbb to enable the future design of microphase separated core-shell bottlebrushes, which self-assemble at sub-10 nm length scales for nanolithography and nanotemplating applications.

Directional Self‐Assembly of Fluorinated Star Block Polymer Thin Films Using Mixed Solvent Vapor Annealing

ABSTRACTWe demonstrate the directional alignment of perpendicular‐lamellae domains in fluorinated three‐armed star block polymer (BP) thin films using solvent vapor annealing with shear stress. The control of orientation and alignment was accomplished without any substrate surface modification. Additionally, three‐armed star poly(methyl methacrylate‐block‐styrene) [PMMA‐PS] and poly(octafluoropentyl methacrylate‐block‐styrene) were compared to their linear analogues to examine the impact of fluorine content and star architecture on self‐assembled BP feature sizes and interdomain density profiles. X‐ray reflectometry results indicated that the star BP molecular architecture increased the effective polymer segregation strength and could possibly facilitate reduced polymer domain spacings, which are useful in next‐generation nanolithographic applications. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019, 57, 1663–1672

Regression models to predict workability and strength of flowable concrete containing recycled aggregates

Regression models are rigorous computational techniques for developing and optimizing performance of cementitious-based concrete materials used for civil and infrastructure engineering works. This paper is part of a comprehensive research program undertaken to develop regression models that predict the behavior of self-consolidating concrete (SCC) containing recycled aggregates, for given proportioning constraints while minimizing the number of trials. Two series of SCC mixtures prepared with 375 and 450 kg/m3 cement are tested. The water-to-cement ratios varied from 0.5 to 0.38, while the natural coarse aggregates were partially substituted by recycled ones at different rates varying from 0% to 100%. Tested properties include the rheology, passing ability, segregation, bleeding, surface settlement, and 28-days compressive strength. Reported regression models can be of particular interest to concrete researchers and engineering seeking for higher recycling technologies and improved sustainability in construction through conservation of virgin aggregate resources, energy savings, landfill reduction, and reduced CO2 emissions.

Structure of Nonsolvent‐Quenched Block Copolymer Solutions after Exposure to Electric Fields during Solvent Evaporation

AbstractIn this work, an electric field is incorporated during the solvent evaporation step of the block copolymer self‐assembly and nonsolvent induced phase separation (SNIPS) process. This study investigates the structure of nonsolvent‐quenched polystyrene‐block‐poly(2‐vinylpyridine) (PS‐b‐P2VP) and polystyrene‐block‐poly(4‐vinylpyridine) (PS‐b‐P4VP) diblock copolymer solutions after exposure to electric fields during solvent evaporation. The results indicate an emphasizing effect of the electric field, enhancing self‐assembly and compensating mediocre experimental parameters to a certain degree. However, the impact is found to be different for the two diblock copolymer membranes depending on the selection of experimental parameters as well as the segregation strength of the systems. In addition, an increasing length of the vertically aligned cylindrical pores by the electric field is observed for both membranes, scaling with the applied voltage. This effect is primarily attributed to the suppression of defects and ill‐alignment of polymer domains in the course of structure formation during SNIPS by the electric field. Scanning electron microscopy is used to image the surface and cross‐sectional morphology of the integral asymmetric membranes.

Identification of Some New Triply Periodic Mesophases from Molten Block Copolymers.

Using field-theoretic simulations based on a self-consistent field theory (SCFT) with or without finite compressibility, nanoscale mesophase formation in molten linear AB and ABC block copolymers is investigated in search of candidates for new and useful nanomaterials. At selected compositions and segregation strengths, the copolymers are shown to evolve into some new nanostructures with either unusual crystal symmetry or a peculiar morphology. There exists a holey layered morphology with Im3 symmetry, which lacks one mirror reflection compared with Im3m symmetry. Also, a peculiar cubic bicontinuous morphology, whose channels are connected with tetrapod units, is found to have Pn3m symmetry. It is shown that there is another network morphology with tripod connections, which reveals P432 symmetry. The optimized free energies of these new mesophases and their relative stability are discussed in comparison with those of double gyroids and double diamonds.

Confined, Templated, and Break-Through Crystallization Modes in Poly(3-dodecylthiophene)-block-poly(ethyl methacrylate) Block Copolymers

The crystallization modes of conjugated–amorphous block copolymers (BCPs) are determined by an interplay between segregation strength (χN), softness of the amorphous block (i.e., rubbery or glassy)...

Phase Behavior of Melts of Diblock-Copolymers with One Charged Block.

In this work, we investigated the phase behavior of melts of block-copolymers with one charged block by means of dissipative particle dynamics with explicit electrostatic interactions. We assumed that all the Flory–Huggins χ parameters were equal to 0. We showed that the charge- correlation attraction solely can cause microphase separation with a long-range order; a phase diagram was constructed by varying the volume fraction of the uncharged block and the electrostatic interaction parameter λ (dimensionless Bjerrum length). The obtained phase diagram was compared to the phase diagram of “equivalent” neutral diblock-copolymers with the non-zero χ-parameter between the beads of different blocks. The neutral copolymers were constructed by grafting the counterions to the corresponding co-ions of the charged block with further switching off the electrostatic interactions. Surprisingly, the differences between these phase diagrams are rather subtle; the same phases in the same order are observed, and the positions of the order-disorder transition ODT points are similar if the λ-parameter is considered as an “effective” χ-parameter. Next, we studied the position of the ODT for lamellar structure depending on the chain length N. It turned out that while for the uncharged diblock copolymer the product χcrN was almost independent of N, for the diblock copolymers with one charged block we observed a significant increase in λcrN upon increasing N. This can be attributed to the fact that the counterion entropy prevents the formation of ordered structures, and its influence is more pronounced for longer chains since they undergo the transition to ordered structures at smaller values of λ, when the electrostatic energy becomes comparable to kbT. This was supported by studying the ODT in diblock-copolymers with charged blocks and counterions cross-linked to the charged monomer units. The ODT for such systems was observed at significantly lower values of λ, with the difference being more pronounced at longer chain lengths N. The fact that the microphase separation is observed even at zero Flory–Huggins parameter can be used for the creation of “high-χ” copolymers: The incorporation of charged groups (for example, ionic liquids) can significantly increase the segregation strength. The diffusion of counterions in the obtained ordered structures was studied and compared to the case of a system with the same number of charged groups but a homogeneous structure; the diffusion coefficient along the lamellar plane was found to be higher than in any direction in the homogeneous structure.

Estimating the Segregation Strength of Microphase-Separated Diblock Copolymers from the Interfacial Width.

The ever-growing catalog of monomers being incorporated into block polymers affords exceptional control over phase behavior and nanoscale structure. The segregation strength, , is the fundamental link between the molecular-level detail and the thermodynamics. However, predicting phase behavior mandates at least one experimental measurement of for each pair of blocks. This typically requires access to the disordered state. We describe a method for estimating from small-angle X-ray scattering measurements of the interfacial width between lamellar microdomains, , in the microphase-separated melt. The segregation strength is determined by comparing to self-consistent field theory calculations of the intrinsic interfacial width, , as a function of the mean-field . The method is validated using a series of independent experimental measurements of and , measured via the order-disorder transition temperature, . The average absolute relative difference between calculated from and the value calculated from is a modest 11%. Corrections for nonplanarity of the interfaces are investigated but do not improve the agreement between the experiments and theory. Published 2019. This article is a U.S. Government work and is in the public domain in the USA.

Structure and Thermodynamics of Hybrid Organic–Inorganic Diblock Copolymers with Salt

We examine the phase behavior of a hybrid organic–inorganic diblock copolymer/salt mixtures. The experimental system comprises poly(ethylene oxide)-block-polyhedral oligomeric silsesquioxane (PEO–POSS) mixed with a lithium bis(trifluoromethane sulfonyl) imide (LiTFSI) salt. Although the diblock copolymers without salt exhibit a classical order-to-disorder transition behavior with increasing temperature, the PEO–POSS/salt mixtures exhibit disorder-to-order transitions with increasing temperature. The analysis of a small-angle X-ray scattering data from the disordered state using Leibler’s random phase approximation enables the determination of an effective Flory–Huggins interaction parameter, χeff, for the electrolytes. Unlike conventional systems, χeff increases with increasing temperature. A simple expression is proposed to describe the dependence of χeff on temperature and salt concentration. This enables the calculation of the segregation strength, χeffN, for both ordered and disordered electrolytes. T...

Reaction: Size Distribution in Olefin Block Copolymers: Not Bad at All

Hongyu Chen completed his PhD in macromolecular science at Case Western Reserve University in 2010. He is a fellow of the Dow Chemical Company, where he focuses on developing new products. He is also a fellow of the American Physical Society and American Chemical Society. Valeriy Ginzburg completed his PhD in polymer physics at the Moscow Institute of Physics and Technology in 1992. He is a senior scientist at the Dow Chemical Company and a fellow of the American Physical Society.

Organizing thermodynamic data obtained from multicomponent polymer electrolytes: Salt‐containing polymer blends and block copolymers

ABSTRACTThe objective of this review is to organize literature data on the thermodynamic properties of salt‐containing polystyrene/poly(ethylene oxide) (PS/PEO) blends and polystyrene‐b‐poly(ethylene oxide) (SEO) diblock copolymers. These systems are of interest due to their potential to serve as electrolytes in all‐solid rechargeable lithium batteries. Mean‐field theories, developed for pure polymer blends and block copolymers, are used to describe phenomenon seen in salt‐containing systems. An effective Flory–Huggins interaction parameter, χeff, that increases linearly with salt concentration is used to describe the effect of salt addition for both blends and block copolymers. Segregation strength, χeffN, where N is the chain length of the homopolymers or block copolymers, is used to map phase behavior of salty systems as a function of composition. Domain spacing of salt‐containing block copolymers is normalized to account for the effect of copolymer composition using an expression obtained in the weak segregation limit. The phase behavior of salty blends, salty block copolymers, and domain spacings of the latter systems, are presented as a function of chain length, composition and salt concentration on universal plots. While the proposed framework has limitations, the universal plots should serve as a starting point for organizing data from other salt‐containing polymer mixtures. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019, 57, 1177–1187