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.

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.

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.

Influence of swelling on the elasticity of polymer networks cross-linked in the melt state: Test of the localization model of rubber elasticity.

The elasticity of polymer networks, formed by cross-linking high molecular mass polymers in the melt state and then swollen by a solvent, involves contributions from both the presence of cross-link network junctions and the interchain interactions associated with the combined effect of excluded volume interactions and topological constraints that become modified when the network is swollen. We test the capacity of the previously developed localization model of rubber elasticity, a mean field "tube model," to describe changes in elasticity observed in classical experimental studies of the mechanical properties of this type of network. In order to obtain a satisfactory comparison to the experiments, it was found to be necessary to account for the independently observed tendency of the network junctions to become localized in the network with appreciable swelling, as well as the interchain interactions emphasized in previous discussions of the localization model.

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.

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 ß-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.

Stringlet excitation model of the boson peak.

The boson peak (BP), a low-energy excess in the vibrational density of states over the Debye contribution, is often identified as a characteristic of amorphous solid materials. Despite decades of efforts, its microscopic origin still remains a mystery. Recently, it has been proposed, and corroborated with simulations, that the BP might stem from intrinsic localized modes involving one-dimensional (1D) string-like excitations ("stringlets"). We build on a theory originally proposed by Lund that describes the localized modes as 1D vibrating strings, but we specify the stringlet size distribution to be exponential, as observed in simulations. We provide an analytical prediction for the BP frequency ωBP in the temperature regime well below the observed glass transition temperature Tg. The prediction involves no free parameters and accords quantitatively with prior simulation observations in 2D and 3D model glasses based on inverse power law potentials. The comparison of the string model to observations is more uncertain when compared to simulations of an Al-Sm metallic glass material at temperatures well above Tg. Nonetheless, our stringlet model of the BP naturally reproduces the softening of the BP frequency upon heating and offers an analytical explanation for the experimentally observed scaling with the shear modulus in the glass state and changes in this scaling in simulations of glass-forming liquids. Finally, the theoretical analysis highlights the existence of a strong damping for the stringlet modes above Tg, which leads to a large low-frequency contribution to the 3D vibrational density of states, observed in both experiments and simulations.

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 ß- 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.

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, Tg. 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.

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.

Bottlebrush polymers in the melt and polyelectrolytes in solution share common structural features.

Uncharged bottlebrush polymer melts and highly charged polyelectrolytes in solution exhibit correlation peaks in scattering measurements and simulations. Given the striking superficial similarities of these scattering features, there may be a deeper structural interrelationship in these chemically different classes of materials. Correspondingly, we constructed a library of isotopically labeled bottlebrush molecules and measured the bottlebrush correlation peak position [Formula: see text] by neutron scattering and in simulations. We find that the correlation length scales with the backbone concentration, [Formula: see text], in striking accord with the scaling of ξ with polymer concentration cP in semidilute polyelectrolyte solutions [Formula: see text] The bottlebrush correlation peak broadens with decreasing grafting density, similar to increasing salt concentration in polyelectrolyte solutions. ξ also scales with sidechain length to a power in the range of 0.35-0.44, suggesting that the sidechains are relatively collapsed in comparison to the bristlelike configurations often imagined for bottlebrush polymers.

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".

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.

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.

The dynamics of metal nanoparticles on a supporting interacting substrate.

The interaction strength of the nanoparticles (NPs) with the supporting substrate can greatly influence both the rate and selectivity of catalytic reactions, but the origins of these changes in reactivity arising from the combined effects of NP structure and composition, and NP-substrate interaction is currently not well-understood. Since the dynamics of the NPs is implicated in many NP-based catalytic processes, we investigate how the supporting substrate alters the dynamics of representative Cu NPs on a model graphene substrate, and a formal extension of this model in which the interaction strength between the NPs and the substrate is varied. We particularly emphasize how the substrate interaction strength alters the local mobility and potential energy fluctuations in the NP interfacial region, given the potential relevance of such fluctuations to NP reactivity. We find the NP melting temperature Tm progressively shifts downward with an increasing NP-substrate interaction strength, and that this change in NP thermodynamic stability is mirrored by changes in local mobility and potential energy fluctuations in the interfacial region that can be described as "colored noise." Atomic diffusivity, D, in the "free" and substrate NP interfacial regions is quantified, and observed variations are rationalized by the localization model linking D to the mean square atomic displacement on a "caging" timescale on the order of a picosecond. In summary, we find that the supporting substrate strongly modulates the stability and dynamics of supported NPs-effects that have evident practical relevance for understanding changes in NP catalytic behavior derived from the supporting substrate.

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. Both the 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.

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 (Tg). 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 Tg, as often found in linear polymer melts when the polymer mass is varied. As a consequence, the segmental relaxation time τα becomes almost a universal function of reduced temperature, (T - Tg)/Tg, 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 - Tg)/Tg. Evidently, Tg dominates both τα 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.

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 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 extension's capabilities, demonstrate its accuracy, and quantify the efficiency of this extension of ZENO by computing the second, third, and fourth virial coefficients and metrics quantifying the difficulty of their calculation, for model polymeric structures having several different shapes. We obtain good agreement with literature estimates available for some of the model structures considered.

The effect of nanoparticle softness on the interfacial dynamics of a model polymer nanocomposite.

The introduction of soft organic nanoparticles (NPs) into polymer melts has recently expanded the material design space for polymer nanocomposites, compared to traditional nanocomposites that utilize rigid NPs, such as silica, metallic NPs, and other inorganic NPs. Despite advances in the fabrication and characterization of this new class of materials, the effect of NP stiffness on the polymer structure and dynamics has not been systematically investigated. Here, we use molecular dynamics to investigate the segmental dynamics of the polymer interfacial region of isolated NPs of variable stiffness in a polymer matrix. When the NP-polymer interactions are stronger than the polymer-polymer interactions, we find that the slowing of segmental dynamics in the interfacial region is more pronounced for stiff NPs. In contrast, when the NP-polymer interaction strength is smaller than the matrix interaction, the NP stiffness has relatively little impact on the changes in the polymer interfacial dynamics. We also find that the segmental relaxation time τα of segments in the NP interfacial region changes from values lower than to higher than the bulk material when the NP-polymer interaction strength is increased beyond a "critical" strength, reminiscent of a binding-unbinding transition. Both the NP stiffness and the polymer-surface interaction strength can thus greatly influence the relative segmental relaxation and interfacial mobility in comparison to the bulk material.

Observation of General Entropy-Enthalpy Compensation Effect in the Relaxation of Wrinkled Polymer Nanocomposite Films.

Surface-textured polymer nanocomposite (PNC) films are utilized in many device applications, and therefore understanding the relaxation behavior of such films is important. By extending an in situ wrinkle relaxation method, we observed that the thermal stability of wrinkled PNC films, both above and below the glass transition temperature (Tg), is proportional to a film's nanoparticle (polymer grafted and bare) concentration, with a slope that changes sign at a compensation temperature (Tcomp) that is determined to be in the vicinity of the film's Tg. This provides unambiguous confirmation of entropy-enthalpy compensation (EEC) as a general feature of PNC films, implying that the stability of PNC films changes from being enhanced to becoming diminished by simply passing through this characteristic temperature, a phenomenon having evident practical ramifications. We suggest EEC will also arise in films where residual stresses are associated with the film fabrication process, which is relevant to nanotech device applications.