Single-molecule analysis of solvent-responsive mechanically interlocked ring polymers and the effects of nanoconfinement from coarse-grained simulations.

In this study, we simulate mechanically interlocked semiflexible ring polymers inspired by the minicircles of kinetoplast DNA (kDNA) networks. Using coarse-grained molecular dynamics simulations, we investigate the impact of molecular topological linkage and nanoconfinement on the conformational properties of two- and three-ring polymer systems in varying solvent qualities. Under good-quality solvents, for two-ring systems, a higher number of crossing points lead to a more internally constrained structure, reducing their mean radius of gyration. In contrast, three-ring systems, which all had the same crossing number, exhibited more similar sizes. In unfavorable solvents, structures collapse, forming compact configurations with increased contacts. The morphological diversity of structures primarily arises from topological linkage rather than the number of rings. In three-ring systems with different topological conformations, structural uniformity varies based on link types. Extreme confinement induces isotropic and extended conformations for catenated polymers, aligning with experimental results for kDNA networks and influencing the crossing number and overall shape. Finally, the flat-to-collapse transition in extreme confinement occurs earlier (at relatively better solvent conditions) compared to non-confined systems. This study offers valuable insights into the conformational behavior of mechanically interlocked ring polymers, highlighting challenges in extrapolating single-molecule analyses to larger networks such as kDNA.

Impact of Molecular-level Structural Disruption on Relaxation Dynamics of Polymers with End-on and Side-on Liquid Crystal Moieties.

In side-chain liquid crystal polymers (SCLCPs), short side chains are attached on a flexible polymer backbone, and each side chain can have a liquid crystal (LC) group attached at the final bead in either an end-on or a side-on configuration. SCLCPs with random sequences of end-on and side-on LC moieties exhibit nonmonotonic thermal behavior as a function of composition, with some mixed sequences having a lower isotropic to LC phase transition than either purely end-on or side-on configurations. The origin of this nonmonotonic thermal trend lies in the disruption of molecular-level positional ordering and alignment due to the different preferred types of ordering of the different LC attachment types. We compare coarse-grained molecular dynamics (MD) simulations and experiments on SCLCP systems with only one type of LC moiety and demonstrate qualitative agreement in the observed mesophases of end-on and side-on SCLCP systems. Specifically, end-on SCLCPs display a smectic B-like mesophase, with layers of polymer between LC layers, while side-on SCLCPs exhibit a quasi-hexagonal columnar structure of polymer and a nematic surrounding the LC mesophase. Detailed analysis of SCLCP systems with various compositions of these types of LC attachments via MD reveals structural disruption in systems with intermediate compositions. Simulation snapshots and anisotropy ratio measurements show how random SCLCP systems deviate from the expected behavior of prolate or oblate systems in terms of their conformation. This molecular disruption in random SCLCP systems, particularly with a high composition of side-on LC moieties, also significantly impacts the relaxation dynamics. Modifying the composition of the LC type of attachment (molecular structure) is a possible route to tuning both the phase behavior and mechanical response of these systems.

Coarse-grained modeling of polymers with end-on and side-on liquid crystal moieties: Effect of architecture.

Mesogens, which are typically stiff rodlike or disklike molecules, are able to self-organize into liquid crystal (LC) phases in a certain temperature range. Such mesogens, or LC groups, can be attached to polymer chains in various configurations including within the backbone (main-chain LC polymers) or at the ends of side-chains attached to the backbone in an end-on or side-on configuration (side-chain LC polymers or SCLCPs), which can display synergistic properties arising from both their LC and polymeric character. At lower temperatures, chain conformations may be significantly altered due to the mesoscale LC ordering; thus, when heated from the LC ordered state through the LC to isotropic phase transition, the chains return from a more stretched to a more random coil conformation. This can cause macroscopic shape changes, which depend significantly on the type of LC attachment and other architectural properties of the polymer. Here, to study the structure-property relationships for SCLCPs with a range of different architectures, we develop a coarse-grained model that includes torsional potentials along with LC interactions of a Gay-Berne form. We create systems of different side-chain lengths, chain stiffnesses, and LC attachment types and track their structural properties as a function of temperature. Our modeled systems indeed form a variety of well-organized mesophase structures at low temperatures, and we predict higher LC-to-isotropic transition temperatures for the end-on side-chain systems than for analogous side-on side-chain systems. Understanding these phase transitions and their dependence on polymer architecture can be useful in designing materials with reversible and controllable deformations.

The influence of spacer composition on thermomechanical properties, crystallinity, and morphology in ionene segmented copolymers.

A series of segmented ammonium ionenes with varying weight fractions of 2000 g mol-1 poly(ethylene glycol) (PEG) or poly(tetramethylene oxide) (PTMO) soft segments were synthesized, and a simplified coarse-grained model of these materials was implemented using molecular dynamics simulations. In addition to varying soft segment type (PTMO vs. PEG), charge density and soft segment content were varied to create a comprehensive series of segmented ammonium ionenes; thermogravimetric analysis reveals that all segmented ionenes in the series are thermally stable up to 240 °C. Differential scanning calorimetry (DSC) and dynamic mechanical analysis (DMA) show the formation of phase separated microdomains at low soft segment content. In particular, DSC shows that the hard and soft domains have distinct glass transition temperatures. Similarly, simulations show that reduced soft segment content induces stronger microphase separation, reduces soft segment mobility, and increases ionic aggregate connectivity and size. These increased ionic associations result in elastomeric behavior, as evidenced by the higher rubbery plateau moduli observed at lower soft segment contents through DMA. Moreover, simulations show that ionic aggregation increases when switching from PEG to the less polar PTMO repeat units, which is consistent with DMA results showing higher plateau moduli for PTMO-based ionenes relative to PEG ionenes. DSC and X-ray diffraction determined that the degree of crystallinity increased with soft segment content regardless of segment type. Overall, these results suggest a semi-crystalline microphase-separated morphology strongly influenced by charge density, the degree of ionic aggregation, and the resulting level of confinement and mobility of the soft segments.

Role of Solvation on Diffusion of Ions in Diblock Copolymers: Understanding the Molecular Weight Effect through Modeling.

Salt-doped diblock copolymers with microphase-separated domains of both an ion conductive and a mechanically strong polymer have been extensively studied due to their potential in transport applications. Several unusual or counterintuitive trends regarding their transport properties have been observed experimentally, such as increasing ion conduction as a function of molecular weight. A crucial feature of these systems is the strong solvation of ions in the conducting microphase due to its higher dielectric constant. Here, we perform molecular dynamics simulations using a coarse-grained model that includes a 1/r4 potential form to generically represent ion solvation, allowing us to reproduce experimentally observed trends and explore their molecular underpinnings. We find that increasing ion concentration can increase or decrease ion diffusion, depending on solvation strength. We also show that the trend of increasing diffusion with molecular weight becomes more dramatic as ions are solvated in one polymer block more strongly or as the ion-ion interactions get stronger. In contrast to expectations, the interfacial width or the overlap of ions with the nonconductive polymer block does not adequately explain this phenomenon; instead, local ion agglomeration best explains reduced diffusion. Interfacial sharpening, controlled by the Flory χ parameter and molecular weight, tends to allow ions to spread more uniformly, and this increases their diffusion.

Uniaxial Deformation and Crazing in Glassy Polymer-Grafted Nanoparticle Ultrathin Films.

The deformation behavior of neat, glassy polymer-grafted nanoparticle (PGN) monolayer films is studied using coarse-grained molecular dynamics simulations and experiments on polystyrene-grafted silica. In both the simulations and experiments, apparent crazing behavior is observed during deformation. The PGN systems show a relatively more uniform, perforated sheet craze structure and significantly higher strain at break than reference homopolymers of the same length. Short chain, unentangled PGN monolayers are also simulated for comparison; these are brittle and break apart without crazing. The entangled PGN simulations are analyzed in detail for systems at both high and moderate graft density. Stress-strain curves show three distinct regions: yielding and strain localization, craze widening, and strain hardening preceding catastrophic failure. The PGN stress-strain behavior appears more similar to that of longer chain, highly entangled homopolymer films than to the reference homopolymer films of the same length as the graft chains, suggesting that the particles effectively add additional entanglement points. The moderate graft density particles have higher strain-to-failure and maximum stress than the high graft density particles. We suggest this increased robustness for lower graft density systems is due to their increased interpenetration of graft chains between neighboring particles, which leads to increased interparticle entanglements per chain.

Impact of ion content and electric field on mechanical properties of coarse-grained ionomers.

Using a coarse-grained ionomer model for polyethylene-co-methacrylic acid that includes associating acid groups along with pendant anions and unbound counterions, we investigate how ionomer mechanical behavior depends on the acid and ion content. We find that the modulus and yield stress increase as the ion content increases, at all strain rates considered. This is in agreement with prior experimental results. We also apply a very strong external electric field in the melt state and then cool the system to set the aggregate order induced by the field. We find that the application of electric field increases the modulus in the direction parallel to the field, and we postulate that this is related to the observed increase in aggregate ordering in the direction perpendicular to the field.

Effect of copolymer sequence on structure and relaxation times near a nanoparticle surface.

We simulate a simple nanocomposite consisting of a single spherical nanoparticle surrounded by coarse-grained polymer chains. The polymers are composed of two different monomer types that differ only in their interaction strengths with the nanoparticle. We examine the effect of adjusting copolymer sequence on the structure as well as the end-to-end vector autocorrelation, bond vector autocorrelation, and self-intermediate scattering function relaxation times as a function of distance from the nanoparticle surface. We show how the range and magnitude of the interphase of slowed dynamics surrounding the nanoparticle depend strongly on sequence blockiness. We find that, depending on block length, blocky copolymers can have faster or slower dynamics than a random copolymer. Certain blocky copolymer sequences lead to relaxation times near the nanoparticle surface that are slower than those of either homopolymer system. Thus, tuning copolymer sequence could allow for significant control over the nanocomposite behavior.

Influence of a nanoparticle on the structure and dynamics of model ionomer melts.

We simulate a single spherical nanoparticle (NP) surrounded by partially neutralized ionomers. The coarse-grained ionomers consist of a linear backbone of neutral monomer beads with charged pendant beads and counterions, along with pendant 'sticker' beads that represent unneutralized acid groups. Two different NP interactions are considered; one in which the NP interacts uniformly with all beads in the system (neutral NP) and another in which the NP has higher cohesive interactions with ions and stickers (sticky NP). Ions are depleted around the neutral NP relative to the bulk, but are denser around the surface of the sticky NP. The bond vector autocorrelation function was computed as a function of distance from the NP. For the neutral NP, due to the absence of ions, there is an increase in bond rotational dynamics near the surface relative to the bulk, while the reverse trend is observed in the case of the sticky NP. These analyses were done systematically for differing mole content of pendants, levels of neutralization, and NP sizes; lower pendant content causes a significantly larger difference in the bond dynamics near and far from the NP surface.

Ion Correlation Effects in Salt-Doped Block Copolymers.

We apply classical density functional theory to study how salt changes the microphase morphology of diblock copolymers. Polymers are freely jointed and one monomer type favorably interacts with ions, to account for the selective solvation that arises from different dielectric constants of the microphases. By including correlations from liquid state theory of an unbound reference fluid, the theory can treat chain behavior, microphase separation, ion correlations, and preferential solvation, at the same coarse-grained level. We show good agreement with molecular dynamics simulations.

Modeling individual and pairs of adsorbed polymer-grafted nanoparticles: structure and entanglements.

We analyze the canopy structure and entanglement network of isolated polymer-grafted nanoparticles (PGNs) adsorbed on a surface. As expected, increasing the monomer-surface adsorption strength causes the polymer chains to spread out to increase contact with the surface, leading to a canopy shape that is in qualitative agreement with recent experimental results. We compare height profiles and other structural features of four PGN systems to show the separate and combined effects of increasing chain length and graft density. At moderate graft density and low surface attraction strength, nearby PGN canopies interpenetrate substantially and their combined shape is similar to that of a single PGN canopy. At high graft density or surface interaction, the interparticle spacing increases significantly. We use a geometrical primitive path analysis to calculate average entanglement properties including canopy-canopy entanglements between pairs of PGNs. The longer chain systems are well entangled at both graft densities considered, and we find that as the monomer-surface interaction strength is increased (and the interparticle distance increases), entanglements between the two PGNs are reduced. We find that the number of inter-PGN entanglements per chain is slightly larger at the lower graft density, likely because steric constraints at high graft density tend to reduce interparticle entanglements.

Diffusion in Lamellae, Cylinders, and Double Gyroid Block Copolymer Nanostructures.

We study transport of penetrants through nanoscale morphologies motivated by common block copolymer morphologies, using confined random walks and coarse-grained simulations. Diffusion through randomly oriented grains is 1/3 for cylinder and 2/3 for lamellar morphologies versus an unconstrained (homopolymer) system, as previously understood. Diffusion in the double gyroid structure depends on the volume fraction and is 0.47-0.55 through the minority phase at 30-50 vol % and 0.73-0.80 through the majority at 50-70 vol %. Thus, among randomly oriented standard minority phase structures with no grain boundary effects, lamellae is preferable for transport.

Impact of ionic aggregate structure on ionomer mechanical properties from coarse-grained molecular dynamics simulations.

Using coarse-grained molecular dynamics simulations, we study ionomers in equilibrium and under uniaxial tensile deformation. The spacing of ions along the chain is varied, allowing us to consider how different ionic aggregate morphologies, from percolated to discrete aggregates, impact the mechanical properties. From the equilibrium simulations, we calculate the stress-stress auto correlation function, showing a distinct deviation from the Rouse relaxation due to ionic associations that depends on ion content. We then quantify the morphology during strain, particularly the degree to which both chains and ionic aggregates tend to align. We also track the location of the ionomer peak in the anisotropic structure factor during strain. The length scale of aggregate order increases in the axial direction and decreases in the transverse direction, in qualitative agreement with prior experimental results.

Intradomain Textures in Block Copolymers: Multizone Alignment and Biaxiality.

Block copolymer (BCP) melt assembly has been studied for decades, focusing largely on self-organized spatial patterns of periodically ordered segment density. Here, we demonstrate that underlying the well-known composition profiles (i.e., ordered lamella, cylinders, spheres, and networks) are generic and heterogeneous patterns of segment orientation that couple strongly to morphology, even in the absence of specific factors that promote intra or interchain segment alignment. We employ both self-consistent field theory and coarse-grained simulation methods to measure polar and nematic order parameters of segments in a freely jointed chain model of diblock melts. We show that BCP morphologies have a multizone texture, with segments predominantly aligned normal and parallel to interdomain interfaces in the respective brush and interfacial regions of the microdomain. Further, morphologies with anisotropically curved interfaces (i.e., cylinders and networks) exhibit biaxial order that is aligned to the principal curvature axes of the interface.

Diffusion of Selective Penetrants in Interfacially Modified Block Copolymers from Molecular Dynamics Simulations.

To show the influence of the interface on structure and dynamics of microphase separated polymer systems, we study interfacially modified AB block copolymers with small molecule penetrants. The polymers have a random midblock or tapered midblock whose composition varies from pure A to pure B (or from pure B to pure A for an inverse taper) between two pure blocks of A and B. We perform simple coarse-grained molecular dynamics simulations of symmetric polymers that form lamellae. With normal tapering, both polymer and penetrant diffusion parallel to the lamellae increases as taper length increases. Inverse tapered polymers exist in different conformational states (e.g., stretched vs folded back and forth across the interface) with different dynamic behavior, leading to nonmonotonic trends in their diffusion. However, the local mixing of monomers (rather than polymer conformation) appears to be the most important factor in determining penetrant diffusion.

Effect of sequence dispersity on morphology of tapered diblock copolymers from molecular dynamics simulations.

Tapered diblock copolymers are similar to typical AB diblock copolymers but have an added transition region between the two blocks which changes gradually in composition from pure A to pure B. This tapered region can be varied from 0% (true diblock) to 100% (gradient copolymer) of the polymer length, and this allows some control over the microphase separated domain spacing and other material properties. We perform molecular dynamics simulations of linearly tapered block copolymers with tapers of various lengths, initialized from fluids density functional theory predictions. To investigate the effect of sequence dispersity, we compare systems composed of identical polymers, whose taper has a fixed sequence that most closely approximates a linear gradient, with sequentially disperse polymers, whose sequences are created statistically to yield the appropriate ensemble average linear gradient. Especially at high segregation strength, we find clear differences in polymer conformations and microstructures between these systems. Importantly, the statistical polymers are able to find more favorable conformations given their sequence, for instance, a statistical polymer with a larger fraction of A than the median will tend towards the A lamellae. The conformations of the statistically different polymers can thus be less stretched, and these systems have higher overall density. Consequently, the lamellae formed by statistical polymers have smaller domain spacing with sharper interfaces.

Encapsulation of Nanoparticles During Polymer Micelle Formation: A Dissipative Particle Dynamics Study.

The formation of block copolymer micelles with and without hydrophobic nanoparticles is simulated using dissipative particle dynamics. We use the model developed by Spaeth et al. [ Spaeth , J. R. , Kevrekidis , I. G. , and Panagiotopoulos , A. Z. J. Chem. Phys. 2011 , 134 ( (16) ) 164902 ], and drive micelle formation by adjusting the interaction parameters linearly over time to represent a rapid change from organic solvent to water. For different concentrations of added nanoparticles, we determine characteristic times for micelle formation and coagulation, and characterize micelles with respect to size, polydispersity, and nanoparticle loading. Four block copolymers with different numbers of hydrophobic and hydrophilic polymer beads, are examined. We find that increasing the number of hydrophobic beads on the polymer decreases the micelle formation time and lowers polydispersity in the final micelle distribution. Adding more nanoparticles to the simulation has a negligible effect on micelle formation and coagulation times, and monotonically increases the polydispersity of the micelles for a given polymer system. The presence of relatively stable free polymer in one system decreases the amount of polymer encapsulating the nanoparticles, and results in an increase in polydispersity and the number of nanoparticles per micelle for that system, especially at high nanoparticle concentration. Longer polymers lead to micelles with a more uniform nanoparticle loading.

Fluids density functional theory and initializing molecular dynamics simulations of block copolymers.

Classical, fluids density functional theory (fDFT), which can predict the equilibrium density profiles of polymeric systems, and coarse-grained molecular dynamics (MD) simulations, which are often used to show both structure and dynamics of soft materials, can be implemented using very similar bead-based polymer models. We aim to use fDFT and MD in tandem to examine the same system from these two points of view and take advantage of the different features of each methodology. Additionally, the density profiles resulting from fDFT calculations can be used to initialize the MD simulations in a close to equilibrated structure, speeding up the simulations. Here, we show how this method can be applied to study microphase separated states of both typical diblock and tapered diblock copolymers in which there is a region with a gradient in composition placed between the pure blocks. Both methods, applied at constant pressure, predict a decrease in total density as segregation strength or the length of the tapered region is increased. The predictions for the density profiles from fDFT and MD are similar across materials with a wide range of interfacial widths.

Phase Behavior of Tapered Diblock Copolymers from Self-Consistent Field Theory.

Tapered diblock copolymers are similar to AB diblock copolymers, but the sharp junction between the A and B blocks is replaced with a gradient region in which composition varies from mostly A to mostly B along its length. The A side of the taper can be attached to the A block (normal) or the B block (inverse). We demonstrate how taper length and direction affect the phase diagrams and density profiles using self-consistent field theory. Adding tapers shifts the order-disorder transition to lower temperature versus the diblock, and this effect is larger for longer tapers and for inverse tapers. However, tapered systems' phase diagrams and interfacial profiles do not simply match those of diblocks at a shifted effective temperature. For instance, we find that normal tapering widens the bicontinuous gyroid region of the phase diagram, while inverse tapering narrows this region, apparently due to differences in polymer organization at the interfaces.