From ionic clusters dynamics to network constraints in ionic polymer solutions.

Physical networks formed by ionizable polymers with ionic clusters as crosslinks are controlled by coupled dynamics that transcend from ionic clusters through chain motion to macroscopic response. Here, the coupled dynamics, across length scales, from the ionic clusters to the networks in toluene swollen polystyrene sulfonate networks, were directly correlated, as the electrostatic environment of the physical crosslinks was altered. The multiscale insight is attained by coupling neutron spin echo measurements with molecular dynamics simulations, carried out to times typical of relaxation of polymers in solutions. The experimental dynamic structure factor is in outstanding agreement with the one calculated from computer simulations, as the networks are perturbed by elevating the temperature and changing the electrostatic environment. In toluene, the long-lived clusters remain stable over hundreds of ns across a broad temperature range, while the polymer network remains dynamic. Though the size of the clusters changes as the dielectric constant of the solvent is modified through the addition of ethanol, they remain stable but morph, enhancing the polymer chain dynamics.

From Molecular Constraints to Macroscopic Dynamics in Associative Networks Formed by Ionizable Polymers: A Neutron Spin Echo and Molecular Dynamics Simulations Study.

The association of ionizable polymers strongly affects their motion in solutions, where the constraints arising from clustering of the ionizable groups alter the macroscopic dynamics. The interrelation between the motion on multiple length and time scales is fundamental to a broad range of complex fluids including physical networks, gels, and polymer-nanoparticle complexes where long-lived associations control their structure and dynamics. Using neutron spin echo and fully atomistic, multimillion atom molecular dynamics (MD) simulations carried out to times comparable to that of chain segmental motion, the current study resolves the dynamics of networks formed by suflonated polystryene solutions for sulfonation fractions 0 ≤ f ≤ 0.09 across time and length scales. The experimental dynamic structure factors were measured and compared with computational ones, calculated from MD simulations, and analyzed in terms of a sum of two exponential functions, providing two distinctive time scales. These time constants capture confined motion of the network and fast dynamics of the highly solvated segments. A unique relationship between the polymer dynamics and the size and distribution of the ionic clusters was established and correlated with the number of polymer chains that participate in each cluster. The correlation of dynamics in associative complex fluids across time and length scales, enabled by combining the understanding attained from reciprocal space through neutron spin echo and real space, through large scale MD studies, addresses a fundamental long-standing challenge that underline the behavior of soft materials and affect their potential uses.

Response of ionizable block copolymer assemblies to solvent dielectrics: A molecular dynamics study.

Ionizable copolymers assembly in solutions is driven by the formation of ionic clusters. Fast clustering of the ionizable blocks often leads to the formation of far-from equilibrium assemblies that ultimately impact the structure of polymer membranes and affect their many applications. Using large-scale atomistic molecular dynamics simulations, we probe the effects of electrostatics on the formation of ionizable copolymer micelles that dominate their solution structure, with the overarching goal of defining the factors that control the assembly of structured ionizable copolymers. A symmetric pentablock ionizable copolymer, with a randomly sulfonated polystyrene center tethered to polyethylene-r-propylene block, terminated by poly(t-butyl styrene), in solvents of varying dielectric constants from 2 to 20, serves as the model system. We find that independent of the solvents, this polymer forms a core-shell micelle with the ionizable segment segregating to the center of the assembly. The specific block conformation, however, strongly depends on the sulfonation levels and the dielectric constant and the polarity of the solvents.

Molecular Insight into the Effects of Clustering on the Dynamics of Ionomers in Solutions.

Ionizable groups tethered to polymers enable their many current and potential applications. However, these functionalities drive the formation of physical networks through clustering of the ionic groups, resulting in constrained dynamics of the macromolecules. Understanding the molecular origin of this hindrance remains a critical fundamental question, whose solution will directly impact the processing of ionizable polymers from molecules to viable materials. Here, using quasielastic neutron scattering accompanied by molecular dynamics simulations, segmental dynamics of slightly sulfonated polystyrene is studied in solutions as the cohesion of the ionic assemblies is tuned. We find that in cyclohexane the ionic assemblies act as centers of confinement, affecting dynamics both on macroscopic lengths and in the vicinity of the ionic assemblies. Addition of a small amount of ethanol affects the packing of the ionizable groups within the assemblies, which in turn enhances the chain dynamics.

Polydots, soft nanoparticles, at membrane interfaces.

Soft nanoparticles (NPs) are emerging candidates for nano medicine, particularly for intercellular imaging and targeted drug delivery. Their soft nature, manifested in their dynamics, allows translocation into organisms without damaging their membranes. A crucial step towards incorporating soft dynamic NPs in nano medicine, is to resolve their interrelation with membranes. Here using atomistic molecular dynamics (MD) simulations we probe the interaction of soft NPs formed by conjugated polymers with a model membrane. These NPs, often termed polydots, are confined to their nano dimensions without any chemical tethers, forming dynamic long lived nano structures. Specifically, polydots formed by dialkyl para poly phenylene ethylene (PPE), with a varying number of carboxylate groups tethered to the alkyl chains to tune the interfacial charge of the surface of the NP are investigated at the interface with a model membrane that consists of di-palmitoyl phosphatidylcholine (DPPC). We find that even though polydots are controlled only by physical forces, they retain their NP configuration as they transcend the membrane. Regardless of their size, neutral polydots spontaneously penetrate the membrane whereas carboxylated polydots must be driven in, with a force that depends on the charge at their interface, all without significant disruption to the membrane. These fundamental results provide a means to control the position of the nanoparticles with respect to the membrane interfaces, which is key to their therapeutic use.

Effects of interaction strength of associating groups on linear and star polymer dynamics.

A small number of associating groups incorporated onto a polymer backbone have dramatic effects on the mobility and viscoelastic response of the macromolecules in melts. These associating groups assemble, driving the formation of clusters, whose lifetime affects the properties of the polymers. Here, we probe the effects of the interaction strength on the structure and dynamics of two topologies, linear and star polymer melts, and further investigate blends of associative and non-associating polymers using molecular dynamics simulations. Polymer chains of approximately one entanglement length are described by a bead-spring model, and the associating groups are incorporated in the form of interacting beads with an interaction strength between them that is varied from 1 to 20 kBT. We find that, for all melts and blends, interaction of a few kBT between the associating groups drives cluster formation, where the size of the clusters increases with increasing interaction strength. These clusters act as physical crosslinkers, which slow the chain mobility. Blends of chains with and without associating groups macroscopically phase separate for interaction strength between the associating groups of a few kBT and above. For weakly interacting associating groups, the static structure function S(q) is well fit by functional form predicted by the random phase approximation where a clear deviation occurs as phase segregation takes place, providing a quantitative assessment of phase segregation.

Temperature response of soft ionizable polymer nanoparticles.

The temperature response of luminescent ionizable polymers confined into far from equilibrium nanoparticles without chemical links was studied using molecular dynamics simulations. These nanoparticles, often referred to as polydots, are emerging as a promising tool for nanomedicine. Incorporating ionizable groups into these polymers enables biofunctionality; however, they also affect the delicate balance of interactions that hold these nanoparticles together. Here polydots formed by a model polymer dialkyl p-phenylene ethynylene with varying number of carboxylate groups along the polymer backbone were probed. We find that increasing temperature affects neutral and charged polydots differently, where neutral polydots exhibit a transition above which their structure becomes dynamic and they unravel. The dependence of the transition temperature on the surface to volume ratio of these polydots is much stronger than what has previously been observed in polymeric thin films. Charged polydots become dynamic enabling migration of the ionizable groups toward the particle interface, while retaining the overall particle shape.

Effect of Chain Length Dispersity on the Mobility of Entangled Polymers.

While nearly all theoretical and computational studies of entangled polymer melts have focused on uniform samples, polymer synthesis routes always result in some dispersity, albeit narrow, of distribution of molecular weights (D_{M}=M_{w}/M_{n}∼1.02-1.04). Here, the effects of dispersity on chain mobility are studied for entangled, disperse melts using a coarse-grained model for polyethylene. Polymer melts with chain lengths set to follow a Schulz-Zimm distribution for the same average M_{w}=36 kg/mol with D_{M}=1.0 to 1.16, were studied for times of 600-800 µs using molecular dynamics simulations. This time frame is longer than the time required to reach the diffusive regime. We find that dispersity in this range does not affect the entanglement time or tube diameter. However, while there is negligible difference in the average mobility of chains for the uniform distribution D_{M}=1.0 and D_{M}=1.02, the shortest chains move significantly faster than the longest ones offering a constraint release pathway for the melts for larger D_{M}.

Structured Ionomer Thin Films at Water Interface: Molecular Dynamics Simulation Insight.

Controlling the structure and dynamics of thin films of ionizable polymers at water interfaces is critical to their many applications. As the chemical diversity within one polymer is increased, controlling the structure and dynamics of the polymer, which is a key to their use, becomes a challenge. Here molecular dynamics simulations (MD) are used to obtain molecular insight into the structure and dynamics of thin films of one such macromolecule at the interface with water. The polymer consists of an ABCBA topology with randomly sulfonated polystyrene (C), tethered symmetrically to flexible poly(ethylene-r-propylene) blocks (B), and end-capped by a poly(t-butylstyrene) block (A). The compositions of the interfacial and bulk regions of thin films of the ABCBA polymers are followed as a function of exposure time to water. We find that interfacial rearrangements take place where buried ionic segments migrate toward the water interface. The hydrophobic blocks collapse and rearrange to minimize their exposure to water. The water that initially drives interfacial reengagements breaks the ionic clusters within the film, forming a dynamic hydrophilic internal network within the hydrophobic segments.

Luminescent tunable polydots: Charge effects in confined geometry.

Long-lived soft nanoparticles, formed by conjugated polymers, constitute a new class of far-from-equilibrium responsive structures for nano-medicine. Tethering ionizable groups to the polymers enables functionality. However concurrently, the ionic groups perturb the delicate balance of interactions that governs these particles. Using fully atomistic molecular dynamics simulations, this study probed the effects of charged groups tethered to poly para phenylene ethynylene substituted by alkyl groups on the polymer conformation and dynamics in confined geometry. We find that the ionizable groups affect the entire shape of the polydots and impact the conformation and dynamics of the polymer.

Coarse-Grained Modeling of Polyethylene Melts: Effect on Dynamics.

The distinctive viscoelastic behavior of polymers results from a coupled interplay of motion on multiple length and time scales. Capturing the broad time and length scales of polymer motion remains a challenge. Using polyethylene (PE) as a model macromolecule, we construct coarse-grained (CG) models of PE with three to six methyl groups per CG bead and probe two critical aspects of the technique: pressure corrections required after iterative Boltzmann inversion (IBI) to generate CG potentials that match the pressure of reference fully atomistic melt simulations and the transferability of CG potentials across temperatures. While IBI produces nonbonded pair potentials that give excellent agreement between the atomistic and CG pair correlation functions, the resulting pressure for the CG models is large compared with the pressure of the atomistic system. We find that correcting the potential to match the reference pressure leads to nonbonded interactions with much deeper minima and slightly smaller effective bead diameter. However, simulations with potentials generated by IBI and pressure-corrected IBI result in similar mean-square displacements (MSDs) and stress autocorrelation functions G(t) for PE melts. While the time rescaling factor required to match CG and atomistic models is the same for pressure- and non-pressure-corrected CG models, it strongly depends on temperature. Transferability was investigated by comparing the MSDs and stress autocorrelation functions for potentials developed at different temperatures.

Soft nanoparticles: nano ionic networks of associated ionic polymers.

Directing the formation of nanostructures that serve as building blocks of membranes presents an immense step towards engineering controlled polymeric ion transport systems. Using the exquisite atomic detail captured by molecular dynamics simulations, we follow the assembly of a co-polymer that consists of polystyrene sulfonate tethered symmetrically to hydrophobic blocks, realizing a new type of long lived solvent-responsive soft nanoparticle.

Association of a multifunctional ionic block copolymer in a selective solvent.

The self-assembly of multiblock copolymers in solutions is controlled by a delicate balance between inherent phase segregation due to incompatibility of the blocks and the interaction of the individual blocks with the solvent. The current study elucidates the association of pentablock copolymers in a mixture of selective solvents which are good for the hydrophobic segments and poor for the hydrophilic blocks using small angle neutron scattering (SANS). The pentablock consists of a center block of randomly sulfonated polystyrene, designed for transport, tethered to poly-ethylene-r-propylene and end-capped by poly-t-butyl styrene, for mechanical stability. We find that the pentablock forms ellipsoidal core-shell micelles with the sulfonated polystyrene in the core and Gaussian decaying chains of swollen poly-ethylene-r-propylene and poly-t-butyl styrene tertiary in the corona. With increasing solution concentration, the size of the micelle, the thickness of the corona, and the aggregation number increase, while the solvent fraction in the core decreases. In dilute solution the micelle increases in size as the temperature is increased, however, temperature effects dissipate with increasing solution concentration.

Cluster Morphology-Polymer Dynamics Correlations in Sulfonated Polystyrene Melts: Computational Study.

Reaching exceptionally long times up to 500 ns in equilibrium and nonequilibrium molecular dynamics simulations studies, we have attained a fundamental molecular understanding of the correlation of ionomer clusters structure and multiscale dynamics, providing new insight into one critical, long-standing challenge in ionic polymer physics. The cluster structure in melts of sulfonated polystyrene with Na^{+} and Mg^{2+} counterions are resolved and correlated with the dynamics on multiple length and time scales extracted from measurements of the dynamic structure factor and shear rheology. We find that as the morphology of the ionic clusters changes from ladderlike for Na^{+} to disordered structures for Mg^{2+}, the dynamic structure factor is affected on the length scale corresponding to the ionic clusters. Rheology studies show that the viscosity for Mg^{2+} melts is higher than for Na^{+} ones for all shear rates, which is well correlated with the larger ionic clusters' size for the Mg^{2+} melts.

Resolving Dynamic Properties of Polymers through Coarse-Grained Computational Studies.

Coupled length and time scales determine the dynamic behavior of polymers and underlie their unique viscoelastic properties. To resolve the long-time dynamics it is imperative to determine which time and length scales must be correctly modeled. Here we probe the degree of coarse graining required to simultaneously retain significant atomistic details and access large length and time scales. The degree of coarse graining in turn sets the minimum length scale instrumental in defining polymer properties and dynamics. Using linear polyethylene as a model system, we probe how the coarse-graining scale affects the measured dynamics. Iterative Boltzmann inversion is used to derive coarse-grained potentials with 2-6 methylene groups per coarse-grained bead from a fully atomistic melt simulation. We show that atomistic detail is critical to capturing large-scale dynamics. Using these models we simulate polyethylene melts for times over 500 µs to study the viscoelastic properties of well-entangled polymer melts.

Structure of Rigid Polymers Confined to Nanoparticles: Molecular Dynamics Simulations Insight.

Nanoparticles (NPs) grafted with organic layers form hybrids able to retain their unique properties through integration into the mesoscopic scale. The organic layer structure and response often determine the functionality of the hybrids on the mesoscopic length scale. Using molecular dynamics (MD) simulations, we probe the conformation of luminescent rigid polymers, dialkyl poly(p-phenylene ethynylene)s (PPE), end-grafted onto a silica nanoparticle in different solvents as the molecular weights and polymer coverages are varied. We find that, in contrast to NP-grafted flexible polymers, the chains are fully extended independent of the solvent. In toluene and decane, which are good solvents, the grafted PPEs chains assume a similar conformation to that observed in dilute solutions. In water, which is a poor solvent for the PPEs, the polymer chains form one large cluster but remain extended. The radial distribution of the chains around the core of the nanoparticle is homogeneous in good solvents, whereas in poor solvents clusters are formed independent of molecular weights and coverages. The clustering is distinctively different from the response of grafted flexible and semiflexible polymers.

Solvent controlled ion association in structured copolymers: Molecular dynamics simulations in dilute solutions.

Tailoring the nature of individual segments within ion containing block co-polymers is one critical design tool to achieve desired properties. The local structure including the size and distribution of the ionic blocks, as well as the long range correlations, are crucial for their transport ability. Here, we present molecular dynamics simulations on the effects of varying the concentrations of the ionizable groups on the conformations of pentablock ionomer that consist of a center block of ionic sulfonated styrene tethered to polyethylene and terminated by a bulky substituted styrene in dilute solutions. Sulfonation fractions f (0 ≤ f ≤ 0.55), spanning the range from ionomer to polyelectrolytes, were studied. Results for the equilibrium conformation of the chains in water and a 1:1 mixture of cyclohexane and heptane are compared to that in implicit poor solvents with dielectric constants ε = 1.0 and 77.73. In water, the pentablock collapses with the sulfonated groups on the outer surface. As f increases, the ionic, center block increasingly segregates from the hydrophobic regions. In the 1:1 mixture of cyclohexane and heptane, the flexible blocks swell, while the center ionic block collapses for f > 0. For f = 0, all blocks swell. In both implicit poor solvents, the pentablock collapses into a nearly spherical shape for all f. The sodium counterions disperse widely throughout the simulation cell for both water and ε = 77.73, whereas for ε = 1.0 and mixture of cyclohexane and heptane, the counterions largely condense onto the collapsed pentablock.

Clustering effects in ionic polymers: Molecular dynamics simulations.

Ionic clusters control the structure, dynamics, and transport in soft matter. Incorporating a small fraction of ionizable groups in polymers substantially reduces the mobility of the macromolecules in melts. These ionic groups often associate into random clusters in melts, where the distribution and morphology of the clusters impact the transport in these materials. Here, using molecular dynamic simulations we demonstrate a clear correlation between cluster size and morphology with the polymer mobility in melts of sulfonated polystyrene. We show that in low dielectric media ladderlike clusters that are lower in energy compared with spherical assemblies are formed. Reducing the electrostatic interactions by enhancing the dielectric constant leads to morphological transformation from ladderlike clusters to globular assemblies. Decrease in electrostatic interaction significantly enhances the mobility of the polymer.

In Situ Self Assembly of Nanocomposites: Competition of Chaotic Advection and Interfacial Effects as Observed by X-Ray Diffreaction.

The effects of chaotic advection on the in situ assembly of a hierarchal nanocomposite of Poly Amide 6, (nylon 6 or PA6) and platelet shape nanoparticles (NPs) were studied. The assemblies were formed by chaotic advection, where melts of pristine PA6 and a mixture of PA6 with NPs were segregated into discrete layers and extruded into film in a continuous process. The process assembles the nanocomposite into alternating pristine-polymer and oriented NP/polymer layers. The structure of these hierarchal assemblies was probed by X-rays as a processing parameter, N, was varied. This parameter provides a measure of the extent of in situ structuring by chaotic advection. We found that all assemblies are semi-crystalline at room temperature. Increasing N impacts the ratio of α to γ crystalline forms. The effects of the chaotic advection vary with the concentration of the NPs. For nanocomposites with lower NP concentrations the amount of the γ crystalline form increased with N. However, at higher NP concentrations, interfacial effects of the NP play a significant role in determining the structure, where the NPs oriented along the melt flow direction and the polymer chains oriented perpendicular to the NP surfaces.

Healing of polymer interfaces: Interfacial dynamics, entanglements, and strength.

Self-healing of polymer films often takes place as the molecules diffuse across a damaged region, above their melting temperature. Using molecular dynamics simulations we probe the healing of polymer films and compare the results with those obtained for thermal welding of homopolymer slabs. These two processes differ from each other in their interfacial structure since damage leads to increased polydispersity and more short chains. A polymer sample was cut into two separate films that were then held together in the melt state. The recovery of the damaged film was followed as time elapsed and polymer molecules diffused across the interface. The mass uptake and formation of entanglements, as obtained from primitive path analysis, are extracted and correlated with the interfacial strength obtained from shear simulations. We find that the diffusion across the interface is significantly faster in the damaged film compared to welding because of the presence of short chains. Though interfacial entanglements increase more rapidly for the damaged films, a large fraction of these entanglements are near chain ends. As a result, the interfacial strength of the healing film increases more slowly than for welding. For both healing and welding, the interfacial strength saturates as the bulk entanglement density is recovered across the interface. However, the saturation strength of the damaged film is below the bulk strength for the polymer sample. At saturation, cut chains remain near the healing interface. They are less entangled and as a result they mechanically weaken the interface. Chain stiffness increases the density of entanglements, which increases the strength of the interface. Our results show that a few entanglements across the interface are sufficient to resist interfacial chain pullout and enhance the mechanical strength.