We report the results of atomistic simulations of the structural equilibrium properties of PS–PEO block copolymer (BCP) melt in the ordered lamellar phase doped with LiPF6 salt. A hybrid simulation strategy, consisting of steps of coarse-graining and inverse coarse-graining, was employed to equilibrate the melt at an atomistic resolution in the ordered phase. We characterize the structural distributions between different atoms/ions and compare the features arising in BCPs against the corresponding behavior in PEO homopolymers for different salt concentrations. In addition, the local structural distributions are characterized in the lamellar phase as a function of distance from the interface. The cation–anion radial distribution functions (RDF) display stronger coordination in the block copolymer melts at high salt concentrations, whereas the trends are reversed for low salt concentrations. Radial distribution functions isolated in the PEO and PS domains demonstrate that the stronger coordination seen in BCPs arises from the influence of both the higher fraction of ions segregated in the PS phase and the influence of interactions in the PS domain. Such a behavior also manifests in the cation–anion clusters, which show a larger fraction of free ions in the BCP. While the average number of free anions (cations) decreases with increasing salt concentration, higher order aggregates of LiPF6 increase with increasing salt concentration. Further, the cation–anion RDFs display spatial heterogeneity, with a stronger cation–anion binding in the interfacial region compared to bulk of the PEO domain.

We report the results of atomistic molecular dynamics simulations informed by quantum-mechanically parametrized force fields, which identify the mechanisms underlying ion motion and diffusivities in poly(1-butyl-3-vinylimidazolium-hexafluorophosphate) polymerized ionic liquid (polyIL) electrolytes. Our results demonstrate that anion transport in polyILs occurs through a mechanism involving intra- and intermolecular ion hopping through formation and breaking of ion-associations involving four polymerized cationic monomers bonded to two different polymer chains. The resulting ion mobilities are directly correlated to the average lifetimes of the ion-associations. Such a trend is demonstrated to contrast with the behavior in pure ILs, wherein structural relaxations and the associated times are dominant mechanism. Our results establish the basis for experimental findings that reported ion transport in polyILs to be decoupled from polymer segmental relaxations.

•Recently, the use of block copolymer (BCP) compatibilizers in donor-acceptor blends has emerged as a popular strategy to improve the device stability of organic photovoltaics (OPV). In recent studies, we demonstrated that BCP additives can serve a role that extends beyond compatibilization; namely, BCPs can be utilized in BHJ OPVs to actively modulate both the mesoscale morphology and the interfacial properties.•In a subsequent work, we demonstrated that, if the energy levels of the BCP are chosen appropriately for such ternary blend systems, an “energy cascade” can be formed at the interface between donor and acceptor domains. Such cascaded heterojunctions can be tuned to stabilize charges away from the interface thereby reducing charge recombination and improving the device efficiency. The resulting device performance of such ternary blends reflect the combined influence of morphology and energy cascades, and, in some instances, can be made to outperform even idealized columnar morphologies proposed for bulk heterojunction devices.•In the present study, we probe whether morphological simulations can be used in conjunction with simple morphological descriptors as a means to screen the performance characteristics of energy cascade based donor-acceptor-block copolymer ternary blend devices as predicted using device-level simulations. Towards this objective, we present results from different parameter combinations to demonstrate that the domain size, percolation ratio, tortuosity of domains, and concentration gradient at the interface between donors and acceptors correlate strongly with the device performance of such ternary blend systems.•Subsequently, we present extensive parameter studies where we simultaneously vary the blend composition, the degree of polymerization of the donor homopolymer, and the acceptor composition of the donor-acceptor block copolymer to identify blend formulations that give rise to such optimal morphological and device characteristics.•Finally, we demonstrate that, while the overall device performance depends on a combination of morphological factors, the morphological descriptors identified in our work may help identify promising blend formulations for the fabrication of ternary blend organic photovoltaic devices.In a recent work, we studied donor-acceptor blend based organic photovoltaics and, by utilizing a combination of morphology simulations and device modeling, demonstrated that block copolymer compatibilizers with appropriately selected energy levels can be used in such systems to give rise to highly efficient devices that, in some cases, can even outperform idealized morphologies. In the present study, we probe whether morphological simulations can be used in conjunction with simple morphological descriptors as a means to screen the performance characteristics of such energy cascade based ternary blend devices as predicted using device-level simulations. Towards this objective, we present results from different parameter combinations to demonstrate that the domain size, percolation ratio, tortuosity of domains, and concentration gradient at the interface between donors and acceptors correlate strongly with the device performance of such ternary blend systems. Subsequently, we present extensive parameter studies where we simultaneously vary the blend composition, the degree of polymerization of the donor homopolymer, and the acceptor composition of the donor-b-acceptor block copolymer to identify blend formulations that give rise to such optimal morphological and device characteristics. Finally, we demonstrate that, while the overall device performance depends on a combination of morphological factors, the morphological descriptors identified in our work may help identify promising blend formulations.

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.

We report the results of atomistic molecular dynamics simulations on polymerized 1-butyl-3-vinylimidazolium-hexafluorophosphate ionic liquids, studying the influence of the polymer molecular weight on the ion mobilities and the mechanisms underlying ion transport, including ion-association dynamics, ion hopping, and ion–polymer coordinations. With an increase in polymer molecular weight, the diffusivity of the hexafluorophosphate (PF6−) counterion decreases and plateaus above seven repeat units. The diffusivity is seen to correlate well with the ion-association structural relaxation time for pure ionic liquids, but becomes more correlated with ion-association lifetimes for larger molecular weight polymers. By analyzing the diffusivity of ions based on coordination structure, we unearth a transport mechanism in which the PF6− moves by “climbing the ladder” while associated with four polymeric cations from two different polymers.

•Molecular dynamics simulations are used to study the influence of the surface chemistry on the transport of ions in polymer electrolytes containing Alumina nanoparticles.•With increasing loading of the nanoparticles, we observed reduced ionic mobilities and conductivities compared to pure PEO melt.•The observed diffusivities of ionic species correlated well with the polymer segmental dynamics with however quantitative deviations apparent for higher particle loadings.•Quantitative disparities between ionic mobilities and polymer segmental dynamics were justified by invoking the changes in local environment of ions in the electrolyte.Using atomistic molecular dynamics simulations, we study the ion diffusivities and conductivities of polyethylene oxide polymer electrolytes doped with LiBF4 salt and containing dispersed Al2O3 nanoparticles. We consider nanoparticles of two different surface chemistries: (a) containing acid rich surface sites (α‐Al2O3); (b) containing roughly equal acidic and basic surface sites (γ‐Al2O3). We compare the ionic diffusivities and conductivities of such systems with our earlier results [Mogurampelly et al. Macromolecules 2015, 48, 2773–2786] for systems containing basic surface sites on the nanoparticles (β‐Al2O3). In the presence of α‐Al2O3 and γ‐Al2O3 nanoparticles, we observe a monotonic decrease of ionic conductivities and mobilities with particle loading. These results are consistent with our earlier findings in the context of β‐Al2O3 nanoparticles. Our analysis identifies that the ionic mobilities and conductivities correlate with the combined effects of the changes in polymer segmental dynamics and the modifications in the local environment of ionic species arising from the introduction of nanoparticles.

We use molecular dynamics simulations to study the normal mode dynamics and frequency dependent dielectric relaxation spectra of diblock copolymers in lamellar phases. In contrast to previous works which have relied on the applicability of Rouse modes, we effect an explicit normal-mode analysis of the chain dynamics in the ordered phases in the directions parallel and perpendicular to the lamellar plane. We considered two models to isolate the specific effects arising from the morphological ordering and mobility disparities between the blocks. For systems with no mobility disparity between the blocks, our analysis demonstrates that both the normal modes and their relaxation dynamics in the planes parallel and perpendicular to the lamella exhibit deviations from the Rouse modes. For systems in which the mobility of one of the blocks was frozen in the lamellar phase, the normal modes closely resembled the Rouse modes for tethered polymers. However, the relaxation dynamics of such modes exhibited deviations from expectations for tethered chains. The changes in the normal mode dynamics manifest as shifts and broadening of the normal dielectric spectra. Together, our results serve to clarify the dielectric spectra effects resulting from the ordering of diblock copolymers into self-assembled morphologies.

In recent works, we demonstrated that donor-b-acceptor block copolymer compatibilizers can be utilized in donor–acceptor blends of conjugated homopolymer donors and PCBM acceptors to target equilibrium morphologies containing the interconnected, cocontinuous structures that are desired for efficient bulk heterojunction devices. In this article, we utilize a combination of morphology and device-level simulations to demonstrate that by tuning the photoelectronic properties of the block copolymer additives, the device characteristics of such ternary blend systems can be made to outperform the idealized morphologies envisioned in donor–acceptor systems. Explicitly, we propose that by appropriately choosing the HOMO and LUMO energy levels of the block copolymer additives, an energy cascade can be exploited to reduce charge recombination and increase fill factors. The resulting device performance of such ternary blends reflects the combined influence of morphology and energy cascades, and in some instances, ternary blend morphologies can outperform even the idealized columnar morphologies proposed for bulk heterojunction devices. Together, our results suggest that the use of block copolymer additives in ternary blend systems may represent a unique strategy to exploit the combined influence of photoelectronic properties and morphology on the device characteristics.

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.

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.

Using molecular dynamics (MD) simulations in conjunction with topological analysis algorithms, we investigate the changes, if any, in entanglement lengths of flexible polymers in ordered lamellar phases of diblock copolymers. Our analysis reveals a reduction in the average entanglement spacing of the polymers with increasing degree of segregation between the blocks. Furthermore, the results of the topological analysis algorithms indicate an inhomogeneous distribution of entanglement junctions arising from the segregated morphology of the block copolymer. To understand such trends, we invoke the packing arguments proposed by Kavassalis and Noolandi in combination with the framework of polymer self-consistent-field theory (SCFT) and Monte Carlo simulations. Such an analysis reveals qualitatively similar characteristics as our MD results for both the average entanglement spacing and the inhomogeneities in entanglements. Together, our results provide evidence for the changes in entanglement features arising from compositional inhomogeneities and suggest that the ideas embodied in packing arguments may provide a simple means to semiquantitatively characterize such modifications.

Using all atom molecular dynamics and trajectory-extending kinetic Monte Carlo simulations, we study the influence of Al2O3 nanoparticles on the transport properties of ions in polymer electrolytes composed of poly(ethylene oxide) (PEO) melt solvated with LiBF4 salt. We observe that the mobility of Li+ cations and BF4– anions and the overall conductivity decrease upon addition of nanoparticles. Our results suggest that the nanoparticles slow the dynamics of polymer segments near their surfaces. Moreover, the preferential interactions of the ions with the nanoparticles are seen to lead to an enhancement of ion concentration near the particle surfaces and a further reduction in the polymer mobilities near the surface. Together, these effects are seen to increase the residence times of Li+ cations near the polymer backbone in the vicinity of the nanoparticles and reduce the overall mobility and conductivity of the electrolyte. Overall, our simulation results suggest that both the nanoparticle-induced changes in polymer dynamical properties and the interactions between the nanoparticles and ions influence the conductivity of the electrolyte.

We present the results of a computational study of the interactions, phase-behavior and aggregation characteristics of charged nanoparticles (CNPs) suspended in solution of oppositely charged polyelectrolytes (PEs). We used an extension of the mean-field polymer self-consistent field theory (SCFT) model presented in our earlier work ( Macromolecules, 2014, 47, 6095−6112) to explicitly characterize the multibody interactions in such systems. For dilute–moderate particle volume fractions, the magnitudes of three and higher multibody interactions were seen to be weak relative to the contributions from pair interactions. On the basis of such results, we embeded the pair-interaction potentials within a thermodynamic perturbation theory approach to identify the phase behavior of such systems. The results of such a framework suggested that the gas and FCC crystal phases were thermodynamically stable, whereas the fluidlike phase was metastable in such systems. To complement the parameters studied using SCFT, we used a recently developed multibody simulation approach to study the aggregation and cluster morphologies in CNP–PE mixtures. For low particle charges, such systems mainly exhibited clusters arising from direct contact aggregation between CNPs. However, for higher particle and PE charges and low PE concentrations, large regions of PE-bridged clusters were seen to form. We present a morphological phase diagram summarizing such results.

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.

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.

We study the influence of block copolymer (BCP) compatibilizers on the domain and interfacial characteristics of the equilibrium morphological structures of semiflexible polymer/solvent blends. Our study is motivated by the question of whether block copolymer compatibilizers can be used to influence the phase separation morphologies resulting in conjugated polymer/fullerene blends. Toward this objective, we use a single chain in mean field Monte Carlo simulations for the phase behavior of semiflexible polymer/solvent blends and study the influence of BCP compatibilizers on the morphologies. Our results reveal a range of blend compositions and molecular chemistries that result in equilibrium structures with domain sizes on the order of 5–20 nm. To elucidate the morphological characteristics of these structures, we first present a series of ternary phase diagrams and then present results demonstrating that the blend composition, semiflexible chain rigidity, BCP composition, and component miscibility each provide unique handles to control the phase separation morphologies and interfacial characteristics in such blends.

We carry out a systematic analysis of static properties of the clusters formed by complexation between charged dendrimers and linear polyelectrolyte (LPE) chains in a dilute solution under good solvent conditions. We use single chain in mean-field simulations and analyze the structure of the clusters through radial distribution functions of the dendrimer, cluster size, and charge distributions. The effects of LPE length, charge ratio between LPE and dendrimer, the influence of salt concentration, and the dendrimer generation number are examined. Systems with short LPEs showed a reduced propensity for aggregation with dendrimers, leading to formation of smaller clusters. In contrast, larger dendrimers and longer LPEs lead to larger clusters with significant bridging. Increasing salt concentration was seen to reduce aggregation between dendrimers as a result of screening of electrostatic interactions. Generally, maximum complexation was observed in systems with an equal amount of net dendrimer and LPE charges, whereas either excess LPE or dendrimer concentrations resulted in reduced clustering between dendrimers.

We use a numerical implementation of polymer self-consistent field theory to study the effective interactions between two spherical particles in polyelectrolyte solutions. We consider a model in which the particles possess fixed charge density and the polymers contain a prespecified amount of dissociated charges. We quantify the polymer-mediated interactions between the particles as a function of the particle charge, polymer concentrations and particle sizes. We study the interplay between depletion interactions, which arise as a consequence of polymer exclusion from the particle interiors, and the electrostatic forces which result from the presence of charges on the polymers and particles. Our results indicate that for weakly charged and uncharged particles, the polymer-mediated interactions predominantly consist of a short-range attraction and a long-range repulsion. When the particle charge is increased, the interactions become purely repulsive. A longer range, albeit weaker, bridging attraction was also evident for some parametric regimes. We demonstrate that the short-range attraction and the longer-range repulsion can be modeled as a sum of a depletion-like attraction and an electrostatic Debye–Huckel like repulsion. However, the amplitude and range underlying the depletion and electrostatic interactions are shown to possess a complex relationship to the parameters of our system. We present scaling arguments and analytical theory to rationalize some of the dependencies underlying the parameters governing the interaction potentials.

Recently, a number of experiments have demonstrated that addition of ceramics with nanoscale dimensions can lead to substantial improvements in the low-temperature conductivity of the polymeric materials. However, the origin of such behaviors and, more generally, the manner by which nanoscale fillers impact the ion mobilities remain unresolved. In this communication, we report the results of atomistic molecular dynamics simulations which used multibody polarizable force fields to study lithium ion diffusivities in an amorphous poly(ethylene-oxide) (PEO) melt containing well-dispersed TiO2 nanoparticles. We observed that the lithium ion diffusivities decrease with increased particle loading. Our analysis suggests that the ion mobilities are correlated to the nanoparticle-induced changes in the polymer segmental dynamics. Interestingly, the changes in polymer segmental dynamics were seen to be related to the nanoparticle’s influence on the polymer conformational features. Overall, our results indicate that addition of nanoparticle fillers modifies polymer conformations and the polymer segmental dynamics and thereby influence the ion mobilities of polymer electrolytes.

We develop and implement a new hybrid methodology combining self-consistent field theory (SCFT) and Monte Carlo simulations to study the complexation between negatively charged semiflexible linear polyelectrolyte (LPE) molecules and a positively charged dendrimer containing grafts of neutral polymers. We examine the influence of LPE stiffness, length of the dendrimer grafts, and solution pOH upon the characteristics of the resulting complexes. Our results indicate that increasing LPE stiffness reduces the dendrimer–LPE binding affinity and results in an overall higher net charge carried within the dendrimer molecule. When we varied the size of the grafts, the dendrimer–LPE binding strength was seen to decrease with increasing grafting chain length for the flexible LPE chains. In contrast, for stiff LPE chains, the binding strength was not seen to vary significantly with the grafting lengths. Overall, longer grafting lengths were seen to reduce the fraction of exposed LPE molecules, suggesting that grafted dendrimers may better shield nucleic acid material from serum nucleases. Lastly, we found that increasing the solution pOH was seen to enhance both the binding between the dendrimer and LPE molecules and the total positive charge carried by the complex.

Atomistic molecular dynamics simulations were used to study the water and methanol diffusivities in acid–base polymer blend membranes consisting of sulfonated poly(ether ether ketone) (SPEEK) and polysulfone tethered with different bases (2-amino-benzimidazole, 5-amino-benzotriazole, and 1H-perimidine). Consistent with experimental trends, methanol and water diffusivities in all the SPEEK-based systems were found to be lower than those in Nafion. When the base group attached to the polysulfone was varied, the methanol diffusivities were found to exhibit the same trends as observed in the experimentally measured crossover current densities. Such trends were however observed only when we explicitly accounted for hydrogen bonding interactions between the hydrogen attached to the nitrogen of the base and the oxygen of the sulfonate of SPEEK. Furthermore, in almost all cases, methanol diffusivities were found to be highly correlated with the pore sizes of the membranes, which, in the case of blends, were found to be influenced by the strength of parasitic hydrogen bonding interactions between the sulfone oxygen of polysulfone and H(N-base). The influence of pore sizes on the methanol diffusivity behavior was rationalized by using both the coordination behavior and the residence time distributions of methanol in various regions of pores. Together, our results unravel the physicochemical origins of methanol diffusivities in acid–base blend membranes and highlight the crucial role played by the hydrogen bonding interactions in influencing methanol transport in acid–base polymer blend membranes.

We use polymer self-consistent field theory to study the physics involved in the permeation of charged dendrimer molecules across anionic lipid bilayer membranes. We specifically examine the influence of dendrimer shape deformations, neutral grafts, and pH conditions on the interactions between dendrimers and membranes. Our results indicate that the ability of the dendrimer to undergo conformational rearrangements plays a crucial role in influencing the interactions between the dendrimer and the membrane. At neutral pH, we observe that dendrimers with grafted chains are repelled by the anionic bilayers. However, decreasing the solution pH to endosomal conditions results in attractive dendrimer–membrane interactions under some parametric conditions. We observe that dendrimer insertion into the membrane results in a decreased value in membrane tension at which rupture occurs and, furthermore, that the rupture tension decreases with the addition of grafts to the dendrimer. Our results suggest that dendrimers grafted with neutral polymers can serve as effective pH sensitive delivery vectors.

Polymeric microemulsions are formed in a narrow range of phase diagram when a blend of immiscible homopolymers is compatibilized by copolymers. In this study, we consider the ternary blend system of A and B homopolymers mixed with block copolymers containing A and B segments and probe the efficacy of different copolymer configurations in promoting the formation of microemulsion phases. Specifically, we consider (a) monodisperse diblock copolymers (D), (b) diblock copolymers with bidisperse molecular weights (MW) (BDL), (c) block copolymers having MW polydispersity in one of the blocks (PD), (d) diblock copolymers having monodisperse MW but bidispersity in average composition (BDC), and (e) gradient copolymers exhibiting a linear variation in the average composition (G). Using single chain in mean field simulations effected in two dimensions, we probe the onset of formation and the width of the bicontinuous microemulsion channel in the ternary phase diagram of homopolymer blended with compatibilizer. We observed that diblock copolymers having bidisperse composition are most efficient (i.e., microemulsion phases occupy the largest area of phase diagram) in forming microemulsions. On the other hand, monodisperse diblock copolymers and diblock copolymers having bidisperse MW distribution form microemulsions with the least amount of compatibilizers. We rationalize our results by explicitly quantifying the interfacial activity and the influence of fluctuation effects in the respective copolymer systems.

Recent experiments have reported intriguing trends for the molecular weight (MW) dependence of the conductivity of block copolymer lamellae that contrast with the behavior of homopolymer matrices. By using coarse-grained simulations of the sorption and transport of penetrant cations, we probe the possible mechanisms underlying such behavior. Our results indicate that the MW dependence of conductivity of homopolymeric and block copolymeric matrices arise from different mechanisms. On the one hand, the solvation energies of cations, and, in turn, the charge carrier concentrations, themselves, exhibit a MW dependence in block copolymer matrices. Such trends are shown to arise from variations in the thickness of the conducting phase relative to that of the interfacial zones. Moreover, distinct mechanisms are shown to be responsible for the diffusivities of ions in homopolymer and block copolymer matrices. In the former, diffusivity effects associated with the free ends of the polymers play an important role. In contrast, in block copolymer lamellae, the interfacial zone between the blocks presents a zone of hindered diffusivity for ions and manifests as a molecular weight dependence of the ionic diffusivity. Together, the preceding mechanisms are shown to provide a plausible explanation for the experimentally observed trends for the conductivity of block copolymer matrices.

We examine the role of neutral dendrimer grafts upon the conformations and the drug complexation efficacy of weakly basic polyelectrolyte dendrimers by using a self-consistent field theory approach. Our results indicate that grafted chains modify the conformations of the dendrimers and lead to a swelling of the dendrimer, the degree of which increases with increasing chain length of the grafts. In turn, such conformational changes leads to a higher charge being carried by the dendrimer molecule. We compare the encapsulation efficacy of grafted and non-grafted dendrimers and find that for strong enough enthalpic and/or electrostatic interactions, the grafted dendrimers are capable of higher amounts of encapsulation than the non-grafted counterparts. By isolating the influences of electrostatic and enthalpic interactions, we clarify the physics behind the observed enhanced encapsulation.

We use computer simulations to study the phase separation behavior of amphiphilic linear gradient copolymer solution under poor solvent conditions. Using the bond fluctuation model and parallel tempering algorithm, we explore the influence of the gradient strength (the largest difference in the instantaneous composition along the copolymer) upon the phase separation characteristics. Under poor solvent conditions, the chains collapse to form micelle-like aggregates. We find that the critical temperature for this transition exhibits a linear dependence on the gradient strength of the copolymers. A systematic quantification of the cluster characteristics formed during the phase separation also reveals a strong dependence of aggregation numbers and the bridging statistics upon the gradient strength of the copolymers. Analysis of our results reveals that the critical parameter determining the thermodynamic behavior of gradient copolymers is in fact the average length of the hydrophobic sequences in the gradient copolymers. We demonstrate that the latter provides a useful measure to quantitatively predict the critical transition temperature of the gradient copolymer solution. We also present a few results from the framework of an annealed representation of the sequences of the gradient copolymer to demonstrate the limitations arising from such a model representation.

Highly asymmetric lamellar microdomains, such as those required for many lithographic line patterns, cannot be straightforwardly achieved by conventional block copolymer self-assembly. We present a conceptually new and versatile approach to produce highly asymmetric lamellar morphologies by the use of binary blends of block copolymers whose components are capable of hydrogen bonding. We first demonstrate our strategy in bulk systems and complement the experimental results observed by transmission electron microscopy and small-angle X-ray scattering with theoretical calculations based on strong stretching theory to suggest the generality of the strategy. To illustrate the impact on potential lithographic applications, we demonstrate that our strategy can be transferred to thin film morphologies. For this purpose, we used solvent vapor annealing to prepare thin films with vertically oriented asymmetric lamellar patterns that preserve the bulk morphological characteristics. Due to the highly asymmetric lamellar microdomains, the line width is reduced to sub-10 nm scale, while its periodicity is precisely tuned.Keywords: blend of block copolymers; block copolymer lithography; highly asymmetric lamellar microdomains; hydrogen bonding; tunable nanoscopic line patterns

We consider the influence of sequence polydispersity upon the phase behavior and interfacial characteristics of gradient copolymers. By adapting the algorithmic procedure proposed for random copolymers, we design sequences of varying blockiness and compositional polydispersities for specified composition profiles of the gradient copolymers. Using the sequences so generated, we studied the dependence of the spinodals, the phase behavior, and interfacial properties of gradient copolymers as a function of gradient strengths and blockiness of the sequences. We demonstrate that the interplay between compositional polydispersity and the overall blockiness of the sequences can play a significant role in determining the morphologies, phase behavior, and interfacial activity of gradient copolymer systems. In systems wherein the inherent blockiness of the sequences is small, such as in gradient copolymers with weak gradient strengths, the introduction of such polydispersity and blockiness effects leads to substantial changes in the self-assembly behavior and interfacial properties. In contrast, in systems for which the inherent blockiness is already large, such as in gradient copolymers with strong gradient strengths, the effects of sequence correlations upon the self-assembly characteristics and interfacial properties are seen to be much more mitigated.

We model the self-assembly of a diblock copolymer thin film in contact with a random copolymer brush using self-consistent field theory employing a quenched distribution for the brush chains. We focus on the regime of parameters where the diblock copolymers exhibit lamellar morphologies, and study the alignment behavior of the lamellar morphologies on the grafted substrates. Our results reveal a templating of the self-assembly morpology by the brush chains. We find two novel features of this templating behavior: The ends of the grafted chains rearrange themselves to create a more favorable interface, an effect which is present in both the parallel and perpendicular morphologies, and is enhanced with increasing blockiness of the sequences of the random copolymer. In addition, the brush chains may splay laterally in perpendicular morphologies and enrich the interface even further in the favorable component. The latter feature leads to nontrivial free energy differences between the parallel and perpendicularly aligned lamellae on the grafted surface. We explicitly find the parametric window for the stability of perpendicular lamellae and compare against the trends suggested by surface energies of the pure homopolymeric components. Such comparisons indicate that viewing the grafted surface purely in terms of the surface energies of the components of the diblock copolymer may not necessarily capture the stabilities of the parallel and perpendicular morphologies.

Phase behavior of binary blends consisting of high molecular weight polystyrene-block-poly(2-vinylpyridine) copolymer (PS-b-P2VP) and low molecular weight polystyrene-block-poly(4-hydroxystyrene) copolymer (PS-b-PHS) was investigated by using small-angle X-ray scattering and transmission electron microscopy. Both PS-b-P2VP and PS-b-PHS exhibited lamellar microdomain over the entire experimental temperatures up to 300 °C. When the weight fraction of PS-b-PHS in the blend was less than 0.1, the lamellar microdomains were maintained. However, with increasing amount of PS-b-PHS, the microdomains in the blends were transformed to hexagonally packed (HEX) cylindrical microdomains and body-centered cubic (BCC) spherical microdomains. On the other hand, when a relatively high molecular weight of PS-b-PHS was used, the BCC spherical microdomains were not observed even at a large weight fraction of PS-b-PHS in the blend, but HEX cylindrical microdomains were formed. The phase behaviors observed experimentally were rationalized by the results of the self-consistent mean-field theory. Based on the theoretical results, some of the PS-b-PHS dissolves into P2VP microdomains and thereby increases the effective volume of P2VP/PHS phase because of hydrogen bonding between P2VP and PHS blocks. In the case of smaller molecular weight of PS-b-PHS, the dissolved amount is significant because the favorable interactions of P2VP/PHS chains becomes dominant over the relatively small enthalpic penalty between PS/P2VP in the P2VP microdomains as well as the gain of the translational entropy of the PS-b-PHS chains. The increase in the effective volume of the PHS/P2VP phase leads to a transformation of the microdomains in the blends from lamellar to HEX cylindrical microdomains and BCC spherical microdomains. On the other hand, when a relatively higher molecular weight of PS-b-PHS was used, the effective volume of the P2VP/PHS phase was not increased greatly because of a large enthalpic loss arising from the contact between PS/P2VP as well as a small gain in the translational entropy. Consequently, only lamellar and HEX cylindrical microdomains are observed.

We report the results of coarse-grained simulations of the transport of penetrants in polymer nanocomposite materials. This work was motivated by recent experimental results in the context of conductivity and barrier properties of polymer nanocomposites. We adopt a coarse-grained simulation formalism which is suitable for studying issues surrounding the transport of ions, large gas molecules and probes in polymer nanocomposite systems. The results presented focuses on two issues: (i) the role of polymer interfacial layers and (ii) the influence of polymer matrix dynamics upon the transport properties of polymer–nanoparticle mixtures. Our results indicate that in our model the penetrant transport properties are dominated by the “filler” effect, in which the particles act as obstructions for the penetrant diffusion. Interfacial effects, which are driven by the polymer–particle interactions play a role, but their impact is shown to be less important than the filler effect. A second outcome of our work is a demonstration that matrix segmental dynamics play a very important role in determining the overall transport properties of the PNC. For nanoparticle systems, such effects are shown to lead to significant deviations from continuum mechanical theories for the effective properties of particulate dispersions.

We present experimental results for the glass transition behavior of polystyrene (PS) films on grafted PS layers of the same chemical identity as a function of film thickness. Our results suggest that the Tg of PS films on brush substrates decreases with decreasing film thickness. The thickness dependence of Tg was observed to be more pronounced for the films on the shorter brushes with the high grafting density. We propose a qualitative rationalization of the observations by invoking both interfacial energy considerations as well as by adapting the percolation model for the glass transition of polymer films.

The results of extensive all-atom molecular dynamics (MD) simulations of water- and methanol-solvated SPEEK (sulfonated poly(ether ether ketone)) are reported. In this Part II of the two-part article, we present results elucidating the spatial distributions of hydronium ion (vehicular proton) and methanol and the transport properties of water, hydronium ions, and methanol. Our results suggest that hydronium ions escape attraction shells of sulfonic groups with increasing water and methanol contents but move closer to sulfur with an increase in temperature. The localization of the hydronium ion near sulfonate anion was seen to be significantly more pronounced than in Nafion, suggesting stronger basicity of sulfonate anion and therefore weaker acidity of its conjugate acid in SPEEK than in Nafion. In contrast with Nafion, methanol competes with hydronium ions and water to solvate sulfonate anion and also lies closer to aromatic backbone. Water diffusion coefficients follow experimentally observed trends where they are lower in SPEEK than in Nafion at low water weight percent but approach the Nafion values at higher water weight percent. The vehicular proton diffusivity, as quantified by hydronium ion diffusivity, was found to be an order of magnitude lower than that in Nafion. The transport results are rationalized based on the structural insights presented in Part I and the present article.

The results of extensive all-atom molecular dynamics (MD) simulations of water- and methanol-solvated SPEEK (sulfonated poly(ether ether ketone)) are reported. In this Part I of the two-part article, we present results elucidating the key structural features of hydrophilic domains with varying water, methanol content, and temperature. With increasing hydration, the membrane was observed to swell appreciably and transform from a state containing a large number of water clusters containing just few molecules at low water content to very large water clusters encompassing almost all molecules at the highest water contents. In comparison with the results reported for Nafion, SPEEK was observed to be characterized by more isolated and smaller sized water clusters and less pronounced percolation than Nafion at lower water contents, but the percolation characteristics became comparable to Nafion at higher water content. Water confined in SPEEK showed less internal structure than bulk water or water confined in Nafion. With increasing water content, solvation of sulfonic acid groups was noted. The average sulfur−sulfur separation in SPEEK was found to be higher compared with the results reported for Nafion. The backbone of SPEEK was found to be more rigid and more hydrophobic than that of Nafion. These observations suggest that the nanophase segregation in SPEEK is less pronounced than that in Nafion, which may contribute to the diminished crossover characteristics of SPEEK noted in experiments on direct methanol fuel cells (DMFC) and reported in Part II of this work.

We present results obtained using a drift-diffusion model for the structure−property correlations in photovoltaic devices based on self-assembly of rod−coil block copolymers. We use a self-consistent field theory model to generate the self-assembly morphologies of rod−coil block copolymers in confined situations. The density and orientational order parameter profiles so-obtained are then used as input to a recently proposed drift-diffusion model which predicts the photovoltaic device characteristics. The latter model allows for prescription of arbitrary morphologies of donor and acceptor phases while simultaneously incorporating the role of anisotropic charge transport of holes and excitons that arise in the ordered phases of rod−coil block copolymers. We present results elucidating the role of morphology of self-assembly, orientation of lamellar phases, domain widths, and the degree of phase separation and orientational ordering, upon the photovoltaic device characteristics.

We present experimental results quantifying the dewetting behavior of poly(methyl methacrylate) (PMMA) melt on polymer brushes of polystyrene (PS) molecules. Our studies indicate contact angles which display a brush molecular weight dependence similar to that expected for autophobic dewetting situation. We use strong segregation theory calculations to model the interfacial tension behavior in our observations and delineate the interplay between enthalpic and entropic effects in polymer wetting upon polymer brushes.

Sulfonated poly(ether ether ketone) (sPEEK) membranes were blended with various functionalized imidazoles. The effect of the pKa of the added heterocycle on the dry proton conductivities of the blended membranes was evaluated over the temperature range of 40−150 °C. These membranes showed nonmonotonous conductivities with respect to temperature, as well as a clear correlation of peak temperature conductivity to the pKa of the heterocycle. We use a theoretical model based on the reaction equilibria between sPEEK’s sulfonic acid groups and the basicity of the added heterocycles in order to better understand the mechanistic origins of the observed temperature−conductivity profiles.

Efficient strategies for dispersion of carbon nanotubes in polymeric and solvent matrices constitutes an area of active interest. In this article, we examine from a theoretical perspective the hypothesis that a combination of AC electric and shear fields oriented at an angle may be used to enhance the dispersion of aggregated rod solutions. We present a deterministic and a Smoluchowski equation based analysis of the dynamics of homogeneous rod suspensions in a configuration involving combined electric and shear fields. We use this analysis to suggest that a cross-field shear and electric field configuration may potentially disperse aggregated nanotube suspensions. We test the predictions of our analytical models through Brownian dynamics simulations to analyze the dynamics of rod suspensions in a cross-field configuration. The results of our simulations display good agreement with our analytical results and serve to delineate the parametric regimes in which the use of a combination of electric and shear fields may enhance the dispersion of aggregated nanotubes.

We present a strong stretching theory model for microphase segregation of AB + AC block copolymer blends in which the B and C segments possess strongly attractive (hydrogen bonding) interactions. In microphase separated morphologies, we demonstrate that the attraction between the B and the C segments causes a bending force toward the A layers. Such bending forces may induce transitions from lamellar and A-majority cylindrical morphologies in the pure component systems to “inverted” cylindrical and spherical morphologies in blends in which the B and C segments constitute the matrix phase. Similar driving forces may also drive transitions from A-majority spherical phases in pure component systems to highly asymmetric lamellar morphologies in blends. The predictions of our model are in excellent agreement with the trends observed in recent experimental results.

In recent studies, we demonstrated that the addition of block copolymers to binary donor–acceptor blends represents an effective approach to target equilibrium, co-continuous morphologies of interpenetrating donors and acceptors. Here, we report a study of the impact of all-conjugated poly(thieno[3,4-b]-thiophene-co-benzodithiophene)-b-polynaphthalene diimide (PTB7-b-PNDI) block copolymer additives on the electronic properties and photovoltaic performance of bulk heterojunction organic photovoltaic active layers comprised of a PTB7 donor and a phenyl-C61-butyric acid methyl ester (PCBM61) acceptor. We find that small amounts of BCP additives lead to improved performance due to a large increase in the device open-circuit voltage (VOC), and the VOC is pinned to this higher value for higher BCP additive loadings. Such results contrast prior studies of ternary blend OPVs where either a continuous change in VOC or a value of VOC pinned to the lowest value is observed. We hypothesize and provide evidence in the form of device and morphology analyses that the impact of VOC is likely due to the formation of a parallel bulk heterojunction made up of isolated PCBM and PNDI acceptor domains separated by intermediate PTB7 donor domains. Altogether, this work demonstrates that all-conjugated block copolymers can be utilized as additives to both dictate morphology and modulate the electronic properties of the active layer.