Do Specific Ion Effects on Collective Relaxation Arise from Perturbation of Hydrogen-Bonding Network Structure?

The change in the transport properties (i.e., water diffusivity, shear viscosity, etc.) when adding salts to water has been used to classify ions as either being chaotropic or kosmotropic, a terminology based on the presumption that this phenomenon arises from respective breakdown or enhancement of the hydrogen-bonding network structure. Recent quasi-elastic neutron scattering measurements of the collective structural relaxation time, τC, in aqueous salt solutions were interpreted as confirming this proposed origin of ion effects on the dynamics of water. However, we find similar changes in τC in the same salt solutions based on molecular dynamics (MD) simulations using a coarse-grained water model in which no hydrogen bonding exists, challenging this conventional interpretation of mobility change resulting from the addition of salts to water. A thorough understanding of specific ion effects should be useful in diverse material manufacturing and biomedical applications, where these effects are prevalent, but poorly understood.

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.

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.

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.

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.

Transient Interfacial Pattern Formation in Block Copolymer Thin Films via Sequential Thermal and Solvent Immersion Annealing.

A variety of structures encountered in nature only arise in materials under highly nonequilibrium conditions, suggesting to us that the scope for creating new functional block copolymer (BCP) structures might be significantly enlarged by embracing complex processing histories that allow for the fabrication of structures quite unlike those created under "near-equilibrium" conditions. The present work examines the creation of polymer film structures in which highly nonequilibrium processing conditions allow for the creation of entirely new types of transient BCP morphologies achieved by transitioning between different ordered states. Most previous studies of BCP materials have emphasized ordering them from their disordered state obtained from a solution film casting process, followed by a slow thermal annealing (TA) process at elevated temperatures normally well above room temperature. We have previously shown that achieving the equilibrium TA state can be accelerated by a direct solvent immersion annealing (DIA) preordering step that creates nascent ordered microstructures, followed by TA. In the present work, we examine the reverse nonequilibrium sequential processing in which we first thermally anneal the BCP film to different levels of partial (lamellar) order and then subject it to DIA to swell the lamellae. This sequential processing rapidly leads to a swelling-induced wrinkle pattern that initially grows with immersion time and can be quenched by solvent evaporation into its corresponding glassy state morphology. The article demonstrates the formation of wrinkling "defect" patterns in entangled BCP films by this sequential annealing that does not form under ordinary TA conditions. At long DIA times, these highly "defective" film structures evolve in favor of the equilibrium morphology of parallel lamellae observed with DIA alone. In conjunction with our previous study of sequential DIA + TA, the present TA + DIA study demonstrates that switching the order of these processing methods for block copolymer films gives the same final state morphology in the limit of long time as any one method alone, but with drastically different intermediate transient state morphologies. These transient morphologies could have many 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.

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.

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.

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 ß-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.

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.

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, ξs) 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 Dc of the PC solutions obeys the generalized Stokes-Einstein equation (GSE), Dc = kBT/6πηξs, where ξs 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 Dc(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.

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.

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.