Interplay between Depletion and Electrostatic Interactions in Polyelectrolyte–Nanoparticle Systems

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

Efficacy of Different Block Copolymers in Facilitating Microemulsion Phases in Polymer Blend Systems

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

Mean-Field Modeling of the Encapsulation of Weakly Acidic Molecules in Polyelectrolyte Dendrimers

The unique architecture of dendrimers has attracted interest in a wide variety of biomedical applications such as drug delivery. In order to gain insight into the solubilization of drugs inside dendrimer architectures, we have developed and numerically implemented a self-consistent field theory model for the equilibrium characteristics of charged dendrimer molecules in the presence of weakly acidic drug molecules. Using such a model, we examine the relative influence of excluded volume, electrostatic, and local enthalpic interactions upon the solubilization of drugs in dendrimers. When only excluded volume interactions are accounted, there is no driving force for drug solubilization inside the dendrimer, and hence depletion of the drug from the dendrimer molecule (relative to the bulk drug concentration) is observed. The inclusion of electrostatic interactions within the model results in solubilization of drugs within the dendrimer. The solubilization of the drugs is shown to increase with increasing drug charge density and increasing dendrimer generation number. We probe the effect of enthalpic interactions and demonstrate that the number of drug molecules encapsulated through enthalpic interaction is dependent upon the number of dendrimer monomers, the enthalpic interaction parameters between the dendrimer and drug (χ_PD), and the drug and solvent (χ_DS). We also analyze the combined effects of the preceding interactions to identify the synergism in their influence and delineate the relative importance of different parameters such as pOH, size of the drugs, and the Bjerrum length of the solution in influencing the encapsulation of drugs by dendrimer molecules

Influence of Block Copolymer Compatibilizers on the Morphologies of Semiflexible Polymer/Solvent Blends

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

Effect of Nanoparticles on Ion Transport in Polymer Electrolytes

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

Computer Simulations of Dendrimer–Polyelectrolyte Complexes

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

Influence of Hydrogen Bonding Effects on Methanol and Water Diffusivities in Acid–Base Polymer Blend Membranes of Sulfonated Poly(ether ether ketone) and Base Tethered Polysulfone

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 1<i>H</i>-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

Entanglements in Lamellar Phases of Diblock Copolymers

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

Multiscale Simulations of Lamellar PS–PEO Block Copolymers Doped with LiPF₆ Ions

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

Mechanisms Underlying Ionic Mobilities in Nanocomposite Polymer Electrolytes

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