Dielectric Characterization of H2O and CO2 Uptake by Polyethylenimine Films

The absorption of CO2 by polyethylenimine polymer (PEI) materials is of great interest in connection with proposed carbon capture technologies, and the successful development of this technology requires testing methods quantifying the amount of CO2, H2O, and reaction byproducts under operating conditions. We anticipate that dielectric measurements have the potential for quantifying both the extent of CO2 and H2O absorption within the PEI matrix material as well as insights into subsequent reaction byproducts that can be expected to occur in the presence of moisture. The complexity of the chemistry involved in this reactive binding process clearly points to the need for the use of additional spectroscopic techniques to better resolve the multiple components involved and to validate the model-dependent findings from the dielectric measurements. Here, we employed noncontact resonant microwave cavity instrumentation operating at 7.435 GHz that allows for the precise determination of the complex dielectric permittivity of CO2 films exposed to atmospheres of controlled relative humidity (RH), and N2:CO2 compositions. We find that the addition of CO2 leads to a considerable increase in dielectric loss of the PEI film relative to loss measured in nitrogen (N2) atmosphere across the same RH range. We attribute this effect to a reaction between CO2 and PEI generating a charged dielectrically active species contributing to the dielectric loss in the presence of moisture. Possible reaction mechanisms accounting for these observations are discussed, including the formation of carbamate-ammonium pairs and ammonium cations stabilized by bicarbonate anions that have sufficient local mobility to be dielectrically active in the investigated microwave frequency range. Understanding of these reaction mechanisms and the development of tools to quantify the amount of reactive byproducts are expected to be critical for the design and optimization of carbon capture materials.

A closer examination of the nature of atomic motion in the interfacial region of crystals upon approaching melting

Although crystalline materials are often conceptualized as involving a static lattice configuration of particles, it has recently become appreciated that string-like collective particle exchange motion is a ubiquitous and physically important phenomenon in both the melting and interfacial dynamics of crystals. This type of collective motion has been evidenced in melting since early simulations of hard disc melting by Alder et al. [Phys. Rev. Lett. 11(6), 241-243 (1963)], but a general understanding of its origin, along with its impact on melting and the dynamics of crystalline materials, has been rather slow to develop. We explore this phenomenon further by focusing on the interfacial dynamics of a model crystalline Cu material using molecular dynamics simulations where we emphasize the geometrical nature and spatial extent of the atomic trajectories over the timescale that they are caged, and we also quantify string-like collective motion on the timescale of the fast β-relaxation time, τf, i.e., "stringlets." Direct visualization of the atomic trajectories in their cages over the timescale over which the cage persists indicates that they become progressively more anisotropic upon approaching the melting temperature Tm. The stringlets, dominating the large amplitude atomic motion in the fast dynamics regime, are largely localized to the crystal interfacial region and correspond to "excess" modes in the density of states that give rise to a "boson peak." Moreover, interstitial point defects occur in direct association with the stringlets, demonstrating a link between classical defect models of melting and more recent studies of melting emphasizing the role of this kind of collective motion.

Self-Cross-Linking of MXene-Intercalated Graphene Oxide Membranes with Antiswelling Properties for Dye and Salt Rejection

Membrane-based water purification is poised to play an important role in tackling the potable water crisis for safe and clean water access for the general population. Several studies have focused on near two-dimensional membranes for this purpose, which is based on an ion rejection technique. However, membrane swelling in these materials has emerged as a significant challenge because it leads to the loss of function. Herein, we report a self-cross-linked MXene-intercalated graphene oxide (GO) membrane that retains ion and dye rejection properties because the physical cross-linking interaction between Ti-O-Ti and neighboring nanosheets effectively suppresses the swelling of the membrane. In addition to the associative Ti-O-Ti bonds, C-O-C, O=C-O, and C-OH bonds are also formed, which are important for inhibiting the swelling of the membrane. To ensure the longevity of these membranes in a service context, they were subjected to heat pressurization and subsequent thermal annealing. The membrane subjected to this novel processing history exhibits minimal swelling upon immersion in solutions and retains function, rejecting salt and dyes over a wide range of salt and dye concentrations. Furthermore, these membranes successfully rejected dye and salt over a period of 72 h without a degradation of function, suggesting that these membranes have the requisite durability for water filtration applications.

Phase separation in the presence of fractal aggregates

Liquid-liquid phase separation in diverse manufacturing and biological contexts often occurs in the presence of aggregated particles or complex-shaped structures that do not actively participate in the phase separation process, but these "background" structures can serve to direct the macroscale phase separation morphology by their local symmetry-breaking presence. We perform Cahn-Hilliard phase-field simulations in two dimensions to investigate the morphological evolution, wetting, and domain growth phenomena during the phase separation of a binary mixture in contact with model fractal aggregates. Our simulations reveal that phase separation initially accelerates around the fractal due to the driving force of wetting, leading to the formation of the target composition patterns about the fractals, as previously observed for circular particles. After the formation of a wetting layer on the fractal, however, we observe a dramatic slowing-down in the kinetics of phase separation, and the characteristic domain size eventually "pins" to a finite value or approaches an asymptotic scaling regime as an ordinary phase if the phase separation loses memory of the aggregates when the scale of phase separation becomes much larger than the aggregate. Furthermore, we perform simulations to examine the effects of compositional interference between fractals with a view to elucidating interesting novel morphological features in the phase-separating mixture. Our findings should be helpful in understanding the qualitative aspects of the phase separation processes in mixtures containing particle aggregates relevant for coating, catalyst, adhesive, and electronic applications as well as in diverse biological contexts, where phase separation occurs in the presence of irregular heterogeneities.

Confinement effect of inter-arm interactions on glass formation in star polymer melts

We utilized molecular dynamic simulation to investigate the glass formation of star polymer melts in which the topological complexity is varied by altering the number of star arms (f). Emphasis was placed on how the "confinement effect" of repulsive inter-arm interactions within star polymers influences the thermodynamics and dynamics of star polymer melts. All the characteristic temperatures of glass formation were found to progressively increase with increasing f, but unexpectedly the fragility parameter KVFT was found to decrease with increasing f. As previously observed, stars having more than 5 or 6 arms adopt an average particle-like structure that is more contracted relative to the linear polymer size having the same mass and exhibit a strong tendency for intermolecular and intramolecular segregation. We systematically analyzed how varying f alters collective particle motion, dynamic heterogeneity, the decoupling exponent ζ phenomenologically linking the slow β- and α-relaxation times, and the thermodynamic scaling index γt. Consistent with our hypothesis that the segmental dynamics of many-arm star melts and thin supported polymer films should exhibit similar trends arising from the common feature of high local segmental confinement, we found that ζ increases considerably with increasing f, as found in supported polymer films with decreasing thickness. Furthermore, increasing f led to greatly enhanced elastic heterogeneity, and this phenomenon correlates strongly with changes in ζ and γt. Our observations should be helpful in building a more rational theoretical framework for understanding how molecular topology and geometrical confinement influence the dynamics of glass-forming materials more broadly.

Efficient single-run implementation of generalized Einstein relation to compute transport coefficients: A binary-based time sampling

A robust and simple implementation of the generalized Einstein formulation using single equilibrium molecular dynamics simulation is introduced to compute diffusion and shear viscosity. The unique features underlying this framework are as follows: (1) The use of a simple binary-based method to sample time-dependent transport coefficients results in a uniform distribution of data on a logarithmic time scale. Although we sample "on-the-fly," the algorithm is readily applicable for post-processing analysis. Overlapping same-length segments are not sampled as they indicate strong correlations. (2) Transport coefficients are estimated using a power law fitting function, a generalization of the standard linear relation, that accurately describes the long-time plateau. (3) The use of a generalized least squares (GLS) fitting estimator to explicitly consider correlations between fitted data points results in a reliable estimate of the statistical uncertainties in a single run. (4) The covariance matrix for the GLS method is estimated analytically using the Wiener process statistics and computed variances. (5) We provide a Python script to perform the fits and automate the procedure to determine the optimal fitting domain. The framework is applied to two fluids, binary hard sphere and a Lennard-Jones near the triple point, and the validity of the single-run estimates is verified against multiple independent runs. The approach should be applicable to other transport coefficients since the diffusive limit is universal to all of them. Given its rigor and simplicity, this methodology can be readily incorporated into standard molecular dynamics packages using on-the-fly or post-processing analysis.

Competing Effects of Molecular Additives and Cross-Link Density on the Segmental Dynamics and Mechanical Properties of Cross-Linked Polymers

The introduction of molecular additives into thermosets often results in changes in their dynamics and mechanical properties that can have significant ramifications for diverse applications of this broad class of materials such as coatings, high-performance composites, etc. Currently, there is limited fundamental understanding of how such additives influence glass formation in these materials, a problem of broader significance in glass-forming materials. To address this fundamental problem, here, we employ a simplified coarse-grained (CG) model of a polymer network as a model of thermoset materials and then introduce a polymer additive having the same inherent rigidity and polymer-polymer interaction strength as the cross-linked polymer matrix. This energetically "neutral" or "self-plasticizing" additive model gives rise to non-trivial changes in the dynamics of glass formation and provides an important theoretical reference point for the technologically more important case of interacting additives. Based on this rather idealized model, we systematically explore the combined effect of varying the additive mass percentage (m) and cross-link density (c) on the segmental relaxation dynamics and mechanical properties of a model thermoset material with additives. We find that increasing the additive mass percentage m progressively decreases both the glass-transition temperature Tg and the fragility of glass formation, a trend opposite to increasing c so that these thermoset variables clearly have a competing effect on glass formation in these model materials. Moreover, basic mechanical properties (i.e., bulk, shear, and tensile moduli) likewise exhibit a competitive variation with the increase of m and c, which are strongly correlated with the Debye-Waller parameter ⟨u2⟩, a measure of material stiffness at a molecular scale. Our findings prove beneficial in the development of structure-property relationships for the cross-linked polymers, which could help guide the design of such network materials with tailored physical properties.

Ion Partition in Polyelectrolyte Gels and Nanogels

Polyelectrolyte gels provide a load-bearing structural framework for many macroscopic biological tissues, along with the organelles within the cells composing tissues and the extracellular matrices linking the cells at a larger length scale than the cells. In addition, they also provide a medium for the selective transportation and sequestration of ions and molecules necessary for life. Motivated by these diverse problems, we focus on modeling ion partitioning in polyelectrolyte gels immersed in a solution with a single type of ionic valence, i.e., monovalent or divalent salts. Specifically, we investigate the distribution of ions inside the gel structure and compare it with the bulk, i.e., away from the gel structure. In this first exploratory study, we neglect solvation effects in our gel by modeling the gels without an explicit solvent description, with the understanding that such an approach may be inadequate for describing ion partitioning in real polyelectrolyte gels. We see that this type of model is nonetheless a natural reference point for considering gels with solvation. Based on our idealized polymer network model without explicit solvent, we find that the ion partition coefficients scale with the salt concentration, and the ion partition coefficient for divalent ions is higher than for monovalent ions over a wide range of Bjerrum length (lB) values. For gels having both monovalent and divalent salts, we find that divalent ions exhibit higher ion partition coefficients than monovalent salt for low divalent salt concentrations and low lB. However, we also find evidence that the neglect of an explicit solvent, and thus solvation, provides an inadequate description when compared to experimental observations. Thus, in future work, we must consider both ion and polymer solvation to obtain a more realistic description of ion partitioning in polyelectrolyte gels.

Molecular Dynamics Simulation of the Influence of Temperature and Salt on the Dynamic Hydration Layer in a Model Polyzwitterionic Polymer PAEDAPS

We investigate the hydration of poly(3-[2-(acrylamido) ethyldimethylammonio] propanesulfonate) over a range of temperatures in pure water and with the inclusion of 0.1 mol/L NaCl using atomistic molecular dynamics simulation. Drawing on concepts drawn from the field of glass-forming liquids, we use the Debye-Waller parameter () for describing the water mobility gradient around the polybetaine backbone extending to an overall distance ≈18 Å. The water mobility in this layer is defined through the mean-square water molecule displacement at a time on the order of water's β-relaxation time. The brushlike topology of polybetaines leads to two regions in the dynamic hydration layer. The inner region of ≈10.5 Å is explored by pendant group conformational motions, and the outer region of ≈7.5 Å represents an extended layer of reduced water mobility relative to bulk water. The dynamic hydration layer extends far beyond the static hydration layer, adjacent to the polymer.

Influence of solvent quality on the swelling and deswelling and the shear modulus of semi-dilute solution cross-linked poly(vinyl acetate) gels

We systematically examine the influence of varying temperature (T) over a large range in model poly(vinyl acetate) gels swollen in isopropyl alcohol. The theta temperature Θ, at which the second virial coefficient A2 vanishes, is found to be equal to within numerical uncertainty to the corresponding high molecular mass polymer solution value without cross-links, and we quantify the swelling and deswelling of our model gels relative to their size at T = Θ, as customary for individual flexible polymer chains in solutions. We also quantify the "solvent quality" dependence of the shear modulus G relative to G(T = Θ) and compare to the hydrogel swelling factor, α. We find that all our network swelling and deswelling data can be reduced to a scaling equation of the same general form as derived from renormalization group theory for flexible linear polymer chains in solutions so that it is not necessary to invoke either the Flory-Huggins mean field theory or the Flory-Rehner hypothesis that the elastic and mixing contributions to the free energy of network swelling are separable to describe our data. We also find that changes of G relative to G(T = Θ) are directly related to α. At the same time, we find that classical rubber elasticity theory describes many aspects of these semi-dilute solution cross-linked networks, regardless of the solvent quality, although the prefactor clearly reflects the existence of network defects whose concentration depends on the initial polymer concentration of the polymer solution from which the networks were synthesized.

Approach to hyperuniformity in a metallic glass-forming material exhibiting a fragile to strong glass transition

We investigate a metallic glass-forming (GF) material (Al₉₀Sm₁₀) exhibiting a fragile-strong (FS) glass-formation by molecular dynamics simulation to better understand this highly distinctive pattern of glass-formation in which many of the usual phenomenological relations describing relaxation times and diffusion of ordinary GF liquids no longer apply, and where instead genuine thermodynamic features are observed in response functions and little thermodynamic signature is exhibited at the glass transition temperature, T_g. Given the many unexpected similarities between the thermodynamics and dynamics of this metallic GF material with water, we first focus on the anomalous static scattering in this liquid, following recent studies on water, silicon and other FS GF liquids. We quantify the "hyperuniformity index" H of our liquid, which provides a quantitative measure of molecular "jamming". To gain insight into the T-dependence and magnitude of H, we also estimate another more familiar measure of particle localization, the Debye-Waller parameter 〈u²〉 describing the mean-square particle displacement on a timescale on the order of the fast relaxation time, and we also calculate H and 〈u²〉 for heated crystalline Cu. This comparative analysis between H and 〈u²〉 for crystalline and metallic glass materials allows us to understand the critical value of H on the order of 10^-3 as being analogous to the Lindemann criterion for both the melting of crystals and the "softening" of glasses. We further interpret the emergence of FS GF and liquid-liquid phase separation in this class of liquids to arise from a cooperative self-assembly process in the GF liquid.

Polymer-Grafted Nanoparticles with Variable Grafting Densities for High Energy Density Polymeric Nanocomposite Dielectric Capacitors

Designing high energy density dielectric capacitors for advanced energy storage systems needs nanocomposite-based dielectric materials, which can utilize the properties of both inorganic and polymeric materials. Polymer-grafted nanoparticle (PGNP)-based nanocomposites alleviate the problems of poor nanocomposite properties by providing synergistic control over nanoparticle and polymer properties. Here, we synthesize "core-shell" barium titanate-poly(methyl methacrylate) (BaTiO₃-PMMA) grafted PGNPs using surface-initiated atom transfer polymerization (SI-ATRP) with variable grafting densities of (0.303 to 0.929) chains/nm² and high molecular masses (97700 g/mL to 130000 g/mol) and observe that low grafted density and high molecular mass based PGNP show high permittivity, high dielectric strength, and hence higher energy densities (≈ 5.2 J/cm³) as compared to the higher grafted density PGNPs, presumably due to their "star-polymer"-like conformations with higher chain-end densities that are known to enhance breakdown. Nonetheless, these energy densities are an order of magnitude higher than their nanocomposite blend counterparts. We expect that these PGNPs can be readily used as commercial dielectric capacitors, and these findings can serve as guiding principles for developing tunable high energy density energy storage devices using PGNP systems.

Hiking down the Free Energy Landscape Using Sequential Solvent and Thermal Processing for Versatile Ordering of Block Copolymer Films

The kinetics and morphology of the ordering of block copolymer (BCP) films are highly dependent on the processing pathway, as the enthalpic and entropic forces driving the ordering processes can be quite different depending on process history. We may gain some understanding and control of this variability of BCP morphology with processing history through a consideration of the free energy landscape of the BCP material and a consideration of how the processing procedure moves the system through this energy landscape in a way that avoids having the system becoming trapped into well-defined metastable minima having a higher free energy than the target low free energy ordered structure. It is well known that standard thermal annealing (TA) of BCPs leads to structures corresponding to a well-defined stable free energy minimum; however, the BCP must be annealed for a very long time before the target low free energy structures can be achieved. Herein, we show that the same target low-energy structure can be achieved relatively quickly by subjecting as-cast films to an initial solvent annealing [direct immersion annealing (DIA) or solvent vapor annealing (SVA)] procedure, followed by a short period of TA. This process relies on lowering the activation energy barrier by reducing the glass-transition temperature through DIA (or SVA), followed by a multi-interface chain rearrangement through sequential TA. This energy landscape approach to ordering should be applicable to the process design for ordering many other complex materials.

Applicability of the Generalized Stokes-Einstein Equation of Mode-Coupling Theory to Near-Critical Polyelectrolyte Complex Solutions

We examine whether the mode-coupling theory of Kawasaki and Ferrell (KF) [Kawasaki, K. Kinetic Equations and Time Correlation Functions of Critical Fluctuations. Ann. Phys. 1970, 61 (1), 1-56; Ferrell, R. A. Decoupled-Mode Dynamical Scaling Theory of the Binary-Liquid Phase Transition. Phys. Rev. Lett. 1970, 24 (21), 1169-1172] can describe dynamic light scattering (DLS) measurements of the dynamic structure factor of near-critical polyelectrolyte complex (PC) solutions that have been previously shown to exhibit a theoretically unanticipated lower critical solution temperature type phase behavior, i.e., phase separation upon heating, and a conventional pattern of static critical properties (low angle scattering intensity and static correlation, ξ_s) as a function of reduced temperature. Good qualitative accord is observed between our DLS measurements and the KF theory. In particular, we observe that the collective diffusion coefficient D_c of the PC solutions obeys the generalized Stokes-Einstein equation (GSE), D_c = k_BT/6πηξ_s, where ξ_s is specified from our previous measurements and where η is measured by capillary rheometry under the same thermodynamic conditions as in our previous study of these solutions, allowing for a no-free-parameter test of the GSE. We also find that even the wavevector (q)-dependent collective diffusion coefficient D_c(q), measured by varying the scattering angle in the DLS measurements over a large range, is also well-described by the mean-field version of the KF theory. We find it remarkable that the KF theory provides such a robust description of collective diffusion in these complex charged polyelectrolyte blends under near-critical conditions given that charge fluctuations and association of the polymers might be expected to lead to physical complications that would invalidate the standard model of uncharged fluid mixtures.

Probabilistic Computations of Virial Coefficients of Polymeric Structures Described by Rigid Configurations of Spherical Particles: A Fundamental Extension of the ZENO Program

We describe an extension of the ZENO program for polymer and nanoparticle characterization that allows for the precise calculation of the virial coefficients, with uncertainty estimates, of polymeric structures described by arbitrary rigid configurations of hard spheres. The probabilistic method of virial computation used for this extension employs a previously developed Mayer-sampling Monte Carlo method with overlap sampling that allows for a reduction of bias in the Monte Carlo averaging. This capability is an extension of ZENO in the sense that the existing program is also based on probabilistic sampling methods, and involves the same input file formats describing polymer and nanoparticle structures. We illustrate the capabilities, demonstrate the accuracy, and quantify the efficiency of this extension of ZENO by computing second, third and fourth virial coefficients and associated difficulty metrics for model polymeric structures having different shapes. We obtain good agreement with literature estimates available for some of the model structures considered.

Prestressed Composite Polymer Gels as a Model of the Extracellular-Matrix of Cartilage

Articular cartilage is a composite hydrogel found in animal and human joints, which exhibits unique load-bearing properties that have been challenging to reproduce in synthetic materials and model in molecular dynamics (MD) simulations. We computationally investigate a composite hydrogel that mimics key functional properties of articular cartilage as a potential biomimetic model to investigate its unique load-bearing properties. Specifically, we find that the emergence of prestress in composite gels derives primarily from the stiffness of the polymer matrix and the asymmetry in the enthalpic interactions of the embedded particles and polymer matrix. Our MD simulations of the development of prestress agree qualitatively with osmotic pressure measurements observed in our model composite hydrogel material.

Comparison of the static structure factor at long wavelengths for a dusty plasma liquid and other liquids

Especially small values of the static structure factor S(k) at long wavelengths, i.e., small k, were obtained in an analysis of experimental data, for a two-dimensional dusty plasma in its liquid state. For comparison, an analysis of S(k) data was carried out for many previously published experiments with other liquids. The latter analysis indicates that the magnitude of S(k) at small k is typically in a range 0.02-0.13. In contrast, the corresponding value for a dusty plasma liquid was found to be as small as 0.0139. Another basic finding for the dusty plasma liquid is that S(k) at small k generally increases with temperature, with its lowest value, noted above, occurring near the melting point. Simulations were carried out for the dusty plasma liquid, and their results are generally consistent with the experiment. Since a dusty plasma has a soft interparticle interaction, our findings support earlier theoretical suggestions that a useful design strategy for creating materials having exceptionally low values of S(0), so-called hyperuniform materials, is the use of a condensed material composed of particles that interact softly at their periphery.

Enhanced Dielectric Strength and Capacitive Energy Density of Cyclic Polystyrene Films

The maximum capacitive energy stored in polymeric dielectric capacitors, which are ubiquitous in high-power-density devices, is dictated by the dielectric breakdown strength of the dielectric polymer. The fundamental mechanisms of the dielectric breakdown, however, remain unclear. Based on a simple free-volume model of the polymer fluid state, we hypothesized that the free ends of linear polymer chains might act as “defect” sites, at which the dielectric breakdown can initiate. Thus, the dielectric breakdown strength of cyclic polymers should exhibit enhanced stability in comparison to that of their linear counterparts having the same composition and similar molar mass. This hypothesis is supported by the ∼50% enhancement in the dielectric breakdown strength and ∼80% enhancement in capacitive energy density of cyclic polystyrene melt films in comparison to corresponding linear polystyrene control films. Furthermore, we observed that cyclic polymers exhibit a denser packing density than the linear chain melts, an effect that is consistent with and could account for the observed property changes. Our work demonstrates that polymer topology can significantly influence the capacitive properties of polymer films, and correspondingly, we can expect polymer topology to influence the gas permeability, shear modulus, and other properties of thin films dependent on film density.

Facile Entropy-Driven Segregation of Imprinted Polymer-Grafted Nanoparticle Brush Blends by Solvent Vapor Annealing Soft Lithography

Polymer-grafted nanoparticles (PGNPs) have attracted extensive research interest due to their potential for enhancing mechanical and electrical properties of both bulk polymer composite materials, as well as thin polymer films incorporating these nanoparticles (NPs). In previous studies, we have shown that an entropic driving force serves to organize low-molecular-mass PGNPs in imprinted blend films of PGNPs with low-molecular-mass homopolymers. In this work, we developed a novel solvent vapor annealing soft lithography (SVA-SL) method to overcome the technical difficulties in processing the high-molecular-mass PGNP blends due to the intrinsically sluggish melt annealing kinetics found in the phase separation of these blend PGNP materials. In particular, we utilized SVA-SL to create nanopatterns in blends of PGNPs having relatively high-molecular-mass-grafted layers but with cores of NPs having greatly different sizes. The minimization of the entropic free energy in the present system corresponded to larger PGNPs partitioning almost exclusively into the "mesa" regions of the imprinted PGNP blend films, as quantified by the estimation of the partition coefficient, K_p. The use of the SVA-SL processing method is important because it allows facile imprint patterning of PGNP materials and large-scale organization of the PGNPs even when the grafted chain lengths are long enough for the chains to be highly entangled, allowing enhanced thermo-mechanical property enhancements of the resulting films and a corresponding extended range of potential nanotech applications.

Solution properties of spherical gold nanoparticles with grafted DNA chains from simulation and theory

There has been a rapidly growing interest in the use of functionalized Au nanoparticles (NPs) as platforms in multiple applications in medicine and manufacturing. The sensing and targeting characteristics of these NPs, and the realization of precisely organized structures in manufacturing applications using such NPs, depend on the control of their surface functionalization. NP functionalization typically takes the form of polymer grafted layers, and a detailed knowledge of the chemical and structural properties of these layers is required to molecularly engineer the particle characteristics for specific applications. However, the prediction and experimental determination of these properties to enable the rational engineering of these particles is a persistent problem in the development of this class of materials. To address this situation, molecular dynamic simulations were performed based on a previously established coarse-grained single-stranded DNA (ssDNA) model to determine basic solution properties of model ssDNA-grafted NP-layers under a wide range of conditions. In particular, we emphasize the calculation of the hydrodynamic radius for ssDNA-grafted Au NPs as a function of structural parameters such as ssDNA length, NP core size, and surface coverage. We also numerically estimate the radius of gyration and the intrinsic viscosity of these NPs, which in combination with hydrodynamic radius estimates, provide valuable information about the fluctuating structure of the grafted polymer layers. We may then understand the origin of the commonly reported variation in effective NP "size" by different measurement methods, and then exploit this information in connection to material design and characterization in connection with the ever-growing number of applications utilizing polymer-grafted NPs.

Relating Dynamic Free Volume to Cooperative Relaxation in a Glass-Forming Polymer Composite

There are a variety of complementary descriptions of the temperature dependence of the structural relaxation time τ in glass-forming materials, which we interpret positively as suggesting an underlying unified description. We examine the inter-relation between the string model, an outgrowth of the Adam and Gibbs approach that emphasizes collective particle exchange motion, and the localization model, which emphasizes the volume explored by particles in their caged states, a kind of dynamic "free volume". Each model of liquid dynamics is described by a limited set of parameters that must be interrelated if both descriptions simultaneously describe the relaxation behavior. We pursue the consequences of this idea by performing coarse-grained molecular simulations of polymer melts with additives of variable size and interaction strength with the polymer matrix, thereby significantly altering the relaxation of the composite material. Boththe string and localization models describe our relaxation time data well, and a comparison of the model parameters allows us to relate the local caging scale ⟨u2⟩ (the Debye-Waller parameter) to the entropy of activation for molecular rearrangements in the string model, thereby developing a bridge between these seemingly disparate approaches to liquid dynamics.

Molecular dynamics study of the swelling and osmotic properties of compact nanogel particles

Owing to their great importance in materials science and other fields, we investigate the solution and osmotic properties of uncharged compact nanogel particles over a wide range of solvent quality and particle concentration by molecular dynamics (MD) simulations. We characterize the osmotic pressure by estimating the second and third virial coefficients, and by extension, we identify the θ-point where the second virial coefficient vanishes. Calculations of the structure factor indicate that these particles are similar to macrogels in that the particle-like scattering profile disappears at moderate concentrations. We also find that improving the solvent quality enhances the spatial segmental uniformity, while significant heterogeneous structure arises near the θ-point. Well below the θ-point where the second osmotic virial coefficient vanishes, these heterogeneous structures become less prevalent as the particles tend to collapse. We also investigate the degree of swelling and structure of compact nanogel particles with a variable excluded volume interaction and gel particle concentration. The osmotic modulus and the scaling exponents in good and θ-point conditions of these gels are characteristic of interacting randomly branched polymers, i.e., "lattice animals".

Understanding the role of cross-link density in the segmental dynamics and elastic properties of cross-linked thermosets

Cross-linking is known to play a pivotal role in the relaxation dynamics and mechanical properties of thermoset polymers, which are commonly used in structural applications because of their light weight and inherently strong nature. Here, we employ a coarse-grained (CG) polymer model to systematically explore the effect of cross-link density on basic thermodynamic properties as well as corresponding changes in the segmental dynamics and elastic properties of these network materials upon approaching their glass transition temperatures (T_g). Increasing the cross-link density unsurprisingly leads to a significant slowing down of the segmental dynamics, and the fragility K of glass formation shifts in lockstep with T_g, as often found in linear polymer melts when the polymer mass is varied. As a consequence, the segmental relaxation time τ_α becomes almost a universal function of reduced temperature, (T - T_g)/T_g, a phenomenon that underlies the applicability of the "universal" Williams-Landel-Ferry (WLF) relation to many polymer materials. We also test a mathematical model of the temperature dependence of the linear elastic moduli based on a simple rigidity percolation theory and quantify the fluctuations in the local stiffness of the network material. The moduli and distribution of the local stiffness likewise exhibit a universal scaling behavior for materials having different cross-link densities but fixed (T - T_g)/T_g. Evidently, T_g dominates both τ_α and the mechanical properties of our model cross-linked polymer materials. Our work provides physical insights into how the cross-link density affects glass formation, aiding in the design of cross-linked thermosets and other structurally complex glass-forming materials.

Manipulation of coacervate droplets with an electric field

Many biopolymers are highly charged, and as in the case of many polymer mixtures, they tend to phase separate as a natural consequence of chain connectivity and an associated relatively low entropy of polymer mixing. Recently, it has become appreciated that the phase-separated structures formed by such polyelectrolyte blends, called "complex coacervates," underlie numerous biological structures and processes essential to living systems, and there has been intense interest in understanding the unique physical features of this type of phase-separation process. In the present work, we are particularly concerned with the field responsiveness of stabilized coacervate droplets formed after the phase separation of polyelectrolyte blend solution and then exposed to deionized water, making the droplet interfacial layer acquire a viscoelastic character that strongly stabilizes it against coalescence. We show that we can precisely control the positions of individual droplets and arrays of them with relatively low-voltage electric fields (on the order of 10 V/cm) and that the imposition of an oscillatory field gives rise to chain formation with coarsening of these chains into long fibers. Such a phase-separation-like process is generally observed in electrorheological fluids of solid colloidal particles subjected to much larger field strengths. The key to these coacervates' electrorheological properties is the altered interfacial viscoelastic properties when the droplets are introduced into deionized water and the associated high polarizability of the droplets, similar to the properties of many living cells. Since many different molecular payloads can be incorporated into these stable droplets, we anticipate many applications.

Reactive Molecular Dynamics Simulations of the Depolymerization of Polyethylene Using Graphene-Oxide-Supported Platinum Nanoparticles

While plastic materials offer many benefits to society, the slow degradation and difficulty in recycling plastics raise important environmental and sustainability concerns. Traditional recycling efforts often lead to materials with inferior properties and correspondingly lower value, making them uneconomical to recycle. Recent efforts have shown promising chemical pathways for converting plastic materials into a wide range of value-added products, feedstocks or monomers. This is commonly referred to as "chemical recycling". Here, we use reactive molecular dynamics (MD) simulations to study the catalytic process of depolymerization of polyethylene (PE) using platinum (Pt) nanoparticles (NPs) in comparison to PE pyrolysis (thermal degradation). We apply a simple kinetic model to our MD results for the catalytic reaction rate as a function of temperature, from which we obtain the activation energy of the reaction, which shows the that the Pt NPs reduce the barrier for depolymerization. We further evaluate the molecular mass distribution of the reaction products to gain insight into the influence of the Pt NPs on reaction selectivity. Our results demonstrate the potential for the reactive MD method to help the design of recycling approaches for polymer materials.

Soft-Shear-Aligned Vertically Oriented Lamellar Block Copolymers for Template-Free Sub-10 nm Patterning and Hybrid Nanostructures

The template-free unidirectional alignment of lamellar block copolymers (l-BCPs) for sub-10 nm high-resolution patterning and hybrid multicomponent nanostructures is important for technological applications. We demonstrate a modified soft-shear-directed self-assembly (SDSA) approach for aligning pristine l-BCPs and l-BCPs with incorporated polymer-grafted nanoparticles (PGNPs), as well as the l-BCP conversion to aligned gold nanowires, and hybrid of metallic gold nanowire and dielectric silica nanoparticle in the form of line-dot nanostructures. The smallest patterns have a half-pitch as small as 9.8 nm. In all cases, soft-shear is achieved using a high-molecular-mass polymer topcoat layer, with support on a neutral bottom layer. We also show that the hybrid line-dot nanostructures have a red-shifted plasmonic response in comparison to neat gold nanowires. These template-free aligned BCPs and nanowires have potential use in nanopatterning applications, and the line-dot nanostructures should be useful in the sensing of biomolecules and other molecular species based on the plasmonic response of the nanowires.

Influence of network defects on the conformational structure of nanogel particles: From "closed compact" to "open fractal" nanogel particles

We propose an approach to generate a wide range of randomly branched polymeric structures to gain general insights into how polymer topology encodes a configurational structure in solution. Nanogel particles can take forms ranging from relatively symmetric sponge-like compact structures to relatively anisotropic open fractal structures observed in some nanogel clusters and in some self-associating polymers in solutions, such as aggrecan solutions under physiologically relevant conditions. We hypothesize that this broad "spectrum" of branched polymer structures derives from the degree of regularity of bonding in the network defining these structures. Accordingly, we systematically introduce bonding defects in an initially perfect network having a lattice structure in three and two topological dimensions corresponding to "sponge" and "sheet" structures, respectively. The introduction of bonding defects causes these "closed" and relatively compact nanogel particles to transform near a well-defined bond percolation threshold into "open" fractal objects with the inherent anisotropy of randomly branched polymers. Moreover, with increasing network decimation, the network structure of these polymers acquires other configurational properties similar to those of randomly branched polymers. In particular, the mass scaling of the radius of gyration and its eigenvalues, as well as hydrodynamic radius, intrinsic viscosity, and form factor for scattering, all undergo abrupt changes that accompany these topological transitions. Our findings support the idea that randomly branched polymers can be considered to be equivalent to perforated sheets from a "universality class" standpoint. We utilize our model to gain insight into scattering measurements made on aggrecan solutions.

Explaining the Sensitivity of Polymer Segmental Relaxation to Additive Size Based on the Localization Model

We use molecular simulations to examine how the dynamics of a coarse-grained polymer melt are altered by additives of variable size and interaction strength with the polymer matrix. The effect of diluent size σ on polymer dynamics changes significantly when its size is comparable to the polymer segment size. For each σ, we show that the localization model (LM) quantitatively describes the dependence of the segmental relaxation time τ on temperature T in terms of dynamic free volume, quantified by the Debye-Waller factor ⟨u^{2}⟩. Within this model, we show that the additive size alone controls the functional form of the T dependence. The LM parameters reach asymptotic values when the diluent size exceeds the monomer size, converging to a limit applicable to macroscopic interfaces.

The initiation of shear band formation in deformed metallic glasses from soft localized domains

It has long been thought that shear band (SB) formation in amorphous solids initiates from relatively "soft" regions in the material in which large-scale non-affine deformations become localized. The test of this hypothesis requires an effective means of identifying "soft" regions and their evolution as the material is deformed to varying degrees, where the metric of "softness" must also account for the effect of temperature on local material stiffness. We show that the mean square atomic displacement on a caging timescale ⟨u²⟩, the "Debye-Waller factor," provides a useful method for estimating the shear modulus of the entire material and, by extension, the material stiffness at an atomic scale. Based on this "softness" metrology, we observe that SB formation indeed occurs through the strain-induced formation of localized soft regions in our deformed metallic glass free-standing films. Unexpectedly, the critical strain condition for SB formation occurs when the softness (⟨u²⟩) distribution within the emerging soft regions approaches that of the interfacial region in its undeformed state, initiating an instability with similarities to the transition to turbulence. Correspondingly, no SBs arise when the material is so thin that the entire material can be approximately described as being "interfacial" in nature. We also quantify relaxation in the glass and the nature and origin of highly non-Gaussian particle displacements in the dynamically heterogeneous SB regions at times longer than the caging time.

Activation free energy gradient controls interfacial mobility gradient in thin polymer films

We examine the mobility gradient in the interfacial region of substrate-supported polymer films using molecular dynamics simulations and interpret these gradients within the string model of glass-formation. No large gradients in the extent of collective motion exist in these simulated films, and an analysis of the mobility gradient on a layer-by-layer basis indicates that the string model provides a quantitative description of the relaxation time gradient. Consequently, the string model indicates that the interfacial mobility gradient derives mainly from a gradient in the high-temperature activation enthalpy ΔH₀ and entropy ΔS₀ as a function of depth z, an effect that exists even in the high-temperature Arrhenius relaxation regime far above the glass transition temperature. To gain insight into the interfacial mobility gradient, we examined various material properties suggested previously to influence ΔH₀ in condensed materials, including density, potential and cohesive energy density, and a local measure of stiffness or u²(z)^-3/2, where u²(z) is the average mean squared particle displacement at a caging time (on the order of a ps). We find that changes in local stiffness best correlate with changes in ΔH₀(z) and that ΔS₀(z) also contributes significantly to the interfacial mobility gradient, so it must not be neglected.

Structure and conformational properties of ideal nanogel particles in athermal solutions

We investigate the conformational properties of "ideal" nanogel particles having a lattice network topology by molecular dynamics simulations to quantify the influence of polymer topology on the solution properties of this type of branched molecular architecture. In particular, we calculate the mass scaling of the radius of gyration (Rg), the hydrodynamic radius, as well as the intrinsic viscosity with the variation of the degree of branching, the length of the chains between the branched points, and the average mesh size within these nanogel particles under good solvent conditions. We find competing trends between the molecular characteristics, where an increase in mesh size or degree of branching results in the emergence of particle-like characteristics, while an increase in the chain length enhances linear polymer-like characteristics. This crossover between these limiting behaviors is also apparent in our calculation of the form factor, P(q), for these structures. Specifically, a primary scattering peak emerges, characterizing the overall nanogel particle size. Moreover, a distinct power-law regime emerges in P(q) at length scales larger than the chain size but smaller than Rg of the nanogel particle, and the Rg mass scaling exponent progressively approaches zero as the mesh size increases, the same scaling as for an infinite network of Gaussian chains. The "fuzzy sphere" model does not capture this feature, and we propose an extension to this popular model. These structural features become more pronounced for values of molecular parameters that enhance the localization of the branching segments within the nanogel particle.

Enhanced resistance to decay of imprinted nanopatterns in thin films by bare nanoparticles compared to polymer-grafted nanoparticles

We extend a previous study on the influence of nanoparticles on the decay of nanoimprinted polymer film patterns to compare the effects of "bare" silica (SiO₂) nanoparticles and SiO₂ nanoparticles with grafted polymer layers having the same chemical composition as the polymer matrix. This method involves nanoimprinting substrate-supported polymer films using a pattern replicated from a digital versatile disc (DVD), and then annealing the patterned polymer nanocomposite films at elevated temperatures to follow the decay of the topographic surface pattern with time by atomic force microscopy imaging after quenching. We quantified the relaxation of the pattern height ("slumping") and determined the relaxation time τ for this pattern decay process as a function of nanoparticle filler type and concentration to determine how nanoparticle additives influence relative film stability. Attractive interactions between the bare nanoparticles and the polymer matrix significantly enhance the thermal resilience of the nanopatterns to decay, compared to those of the particle brushes, wherein the particle core interactions are screened from the matrix via the brush layer. A novel aspect of this method is that it readily lends itself to in situ film relaxation measurements in a manufacturing context. We observe that the relaxation time of the pattern relaxation exhibits entropy-enthalpy compensation in the free energy parameters governing the pattern relaxation process as a function of temperature, irrespective of the NP system used, consistent with our previous experimental and computational studies.

Comparative experimental and computational study of synthetic and natural bottlebrush polyelectrolyte solutions

We systematically investigate model synthetic and natural bottlebrush polyelectrolyte solutions through an array of experimental techniques (osmometry and neutron and dynamic light scattering) along with molecular dynamics simulations to characterize and contrast their structures over a wide range of spatial and time scales. In particular, we perform measurements on solutions of aggrecan and the synthetic bottlebrush polymer, poly(sodium acrylate), and simulations of solutions of highly coarse-grained charged bottlebrush molecules having different degrees of side-branch density and inclusion of an explicit solvent and ion hydration effects. While both systems exhibit a general tendency toward supramolecular organization in solution, bottlebrush poly(sodium acrylate) solutions exhibit a distinctive "polyelectrolyte peak" in their structure factor, but no such peak is observed in aggrecan solutions. This qualitative difference in scattering properties, and thus polyelectrolyte solution organization, is attributed to a concerted effect of the bottlebrush polymer topology and the solvation of the polymer backbone and counterions. The coupling of the polyelectrolyte topological structure with the counterion distribution about the charged polymer molecules along with direct polymer segmental hydration makes their solution organization and properties "tunable," a phenomenon that has significant ramifications for biological function and disease as well as for numerous materials applications.

Control of Phase Morphology of Binary Polymer Grafted Nanoparticle Blend Films via Direct Immersion Annealing

While the phase separation of binary mixtures of chemically different polymer-grafted nanoparticles (PGNPs) is observed to superficially resemble conventional polymer blends, the presence of a "soft" polymer-grafted layer on the inorganic core of these nanoparticles qualitatively alters the phase separation kinetics of these "nanoblends" from the typical pattern of behavior seen in polymer blends and other simple fluids. We investigate this system using a direct immersion annealing method (DIA) that allows for a facile tuning of the PGNPs phase boundary, phase separation kinetics, and the ultimate scale of phase separation after a sufficient "aging" time. In particular, by switching the DIA solvent composition from a selective one (which increases the interaction parameter according to Timmerman's rule) to an overall good solvent for both PGNP components, we can achieve rapid switchability between phase-separated and homogeneous states. Despite a relatively low and non-classical power-law coarsening exponent, the overall phase separation process is completed on a time scale on the order of a few minutes. Moreover, the roughness of the PGNP blend film saturates at a scale that is proportional to the in-plane phase separation pattern scale, as observed in previous blend and block copolymer film studies. The relatively low magnitude of the coarsening exponent n is attributed to a suppression of hydrodynamic interactions between the PGNPs. The DIA method provides a significant opportunity to control the phase separation morphology of PGNP blends by solution processing, and this method is expected to be quite useful in creating advanced materials.

Late Stage Domain Coarsening Dynamics of Lamellar Block Copolymers

Block copolymer (BCP) phase separation dynamics can be expected to differ significantly from that of the polymer blends due to the constraint of chain connectivity. BCP phase separation dynamics has been studied theoretically, but there has been little experimental evidence to confirm the BCP domain growth scaling laws put forward theoretically. Here, we investigate the dynamics of late-stage lamellar BCP domain coarsening and find that the scaling exponent for lamellar domain growth is ≈1/6 (0.17), irrespective of the annealing temperature, a value close to the scaling exponent of 0.2 predicted by theoretical studies. Furthermore, we show that the prefactors in the domain coarsening equation show Arrhenius dependence on temperature, indicating that the BCP domain growth dynamics is Arrhenius over the temperature range investigated.

Dynamic heterogeneity, cooperative motion, and Johari-Goldstein [Formula: see text]-relaxation in a metallic glass-forming material exhibiting a fragile-to-strong transition

We investigate the Johari-Goldstein (JG) [Formula: see text]-relaxation process in a model metallic glass-forming (GF) material ([Formula: see text]), previously studied extensively by both frequency-dependent mechanical measurements and simulation studies devoted to equilibrium properties, by molecular dynamics simulations based on validated and optimized interatomic potentials with the primary aim of better understanding the nature of this universal relaxation process from a dynamic heterogeneity (DH) perspective. The present relatively low temperature and long-time simulations reveal a direct correspondence between the JG [Formula: see text]-relaxation time [Formula: see text] and the lifetime of the mobile particle clusters [Formula: see text], defined as in previous DH studies, a relationship dual to the corresponding previously observed relationship between the [Formula: see text]-relaxation time [Formula: see text] and the lifetime of immobile particle clusters [Formula: see text]. Moreover, we find that the average diffusion coefficient D nearly coincides with [Formula: see text] of the smaller atomic species (Al) and that the 'hopping time' associated with D coincides with [Formula: see text] to within numerical uncertainty, both trends being in accord with experimental studies. This indicates that the JG [Formula: see text]-relaxation is dominated by the smaller atomic species and the observation of a direct relation between this relaxation process and rate of molecular diffusion in GF materials at low temperatures where the JG [Formula: see text]-relaxation becomes the prevalent mode of structural relaxation. As an unanticipated aspect of our study, we find that [Formula: see text] exhibits fragile-to-strong (FS) glass formation, as found in many other metallic GF liquids, but this fact does not greatly alter the geometrical nature of DH in this material and the relation of DH to dynamical properties. On the other hand, the temperature dependence of the DH and dynamical properties, such as the structural relaxation time, can be significantly altered from 'ordinary' GF liquids.

Localization model description of the interfacial dynamics of crystalline Cu and [Formula: see text] metallic glass nanoparticles

Many of the special properties of nanoparticles (NPs) and nanomaterials broadly derive from the significant fraction of particles (atoms, molecules or segments of polymeric molecules) in the NP interfacial region in which the interparticle interactions are characteristically highly anharmonic in comparison to the bulk material. This leads to relatively large mean square particle displacements relative to the material interior, often resulting in a strong increase interfacial mobility and reactivity in both crystalline and glass NPs. The 'Debye-Waller factor', or the mean square particle displacement [Formula: see text] on a ps 'caging' timescale relative to the square of the average interparticle distance [Formula: see text], provides an often experimentally accessible measure of the strength of this anharmonic interaction. The Localization Model (LM) of the dynamics of condensed materials relates this thermodynamic property to the structural relaxation time [Formula: see text], determined from the intermediate scattering function, without any free parameters. Moreover, the LM allows for the prediction of the diffusion coefficient D when combined with the 'decoupling' or Fractional Stokes-Einstein relation linking [Formula: see text] to D. In the current study, we employed classical molecular dynamics simulation to investigate the structural relaxation and diffusion of model [Formula: see text] metallic glass and Cu crystalline NPs with different sizes. As with previous studies validating the LM on model bulk and crystalline materials, and for the interfacial dynamics of thin crystalline and metallic glass films, we find the LM model also describes the interfacial dynamics of model crystalline metal (Cu) and metallic glass ([Formula: see text] NPs to a good approximation, further confirming the generality of the model.