Understanding, predicting, and tuning the fragility of vitrimeric polymers

Molecular Simulation of Covalent Adaptable Networks and Vitrimers: A Review

Covalent adaptable networks and vitrimers are novel polymers with dynamic reversible bond exchange reactions for crosslinks, enabling them to modulate their properties between those of thermoplastics and thermosets. They have been gathering interest as materials for their recycling and self-healing properties. In this review, we discuss different molecular simulation efforts that have been used over the last decade to investigate and understand the nanoscale and molecular behaviors of covalent adaptable networks and vitrimers. In particular, molecular dynamics, Monte Carlo, and a hybrid of molecular dynamics and Monte Carlo approaches have been used to model the dynamic bond exchange reaction, which is the main mechanism of interest since it controls both the mechanical and rheological behaviors. The molecular simulation techniques presented yield sufficient results to investigate the structure and dynamics as well as the mechanical and rheological responses of such dynamic networks. The benefits of each method have been highlighted. The use of other tools such as theoretical models and machine learning has been included. We noticed, amongst the most prominent results, that stress relaxes as the bond exchange reaction happens, and that at temperatures higher than the glass transition temperature, the self-healing properties are better since more bond BERs are observed. The lifetime of dynamic covalent crosslinks follows, at moderate to high temperatures, an Arrhenius-like temperature dependence. We note the modeling of certain properties like the melt viscosity with glass transition temperature and the topology freezing transition temperature according to a behavior ruled by either the Williams-Landel-Ferry equation or the Arrhenius equation. Discrepancies between the behavior in dissociative and associative covalent adaptable networks are discussed. We conclude by stating which material parameters and atomistic factors, at the nanoscale, have not yet been taken into account and are lacking in the current literature.

Manipulating the Properties of Polymer Vitrimer Nanocomposites by Designing Dual Dynamic Covalent Bonds

Polymer vitrimer is a novel material that contains dynamic covalent bonds (DCBs) allowing it to combine the desirable characteristics of both thermoplastics and thermosets. Similar to the traditional polymer nanocomposites, introducing nanoparticles into polymer vitrimer is also an effective strategy to further enhance its properties. However, a comprehensive understanding of matrix and interfacial bond exchange reactions (BERs) to tailor the properties of polymer vitrimer nanocomposites (PVNs) is still lacking. Herein, we utilized coarse-grained molecular dynamics simulations to investigate model PVNs in which there are two different kinds of DCBs in the vitrimer matrix and at the interface. Our results show that the normalized bond autocorrelation function (Csw) confirms the independence of BERs in the vitrimer matrix and in the interface. By varying the bond swap energy barrier (Δ E sw ) in the matrix Δ E sw mat or in the interface Δ E sw int , or in both Δ E sw all , a maximum mechanical property is observed at the moderate value of Δ E sw mat , Δ E sw int , orΔ E sw all . Meanwhile, the effect of Δ E sw on the stress relaxation and the bond orientation as a function of the time under a fixed strain is well probed, which both decay more slowly at greater Δ E sw . We simulated the tension-recovery curve to examine the effect of Δ E sw on the hysteresis loss and permanent deformation of PVNs, finding an optimal value to achieve its minimum energy dissipation and maximum recovery ratio. Lastly, we investigated the efficiency of self-healing by building and removing walls from the system. Interestingly, a maximum self-healing efficiency of the stress-strain behavior is observed at moderate Δ E sw . Overall, this study provides valuable insights into the relationship between the structure and properties of PVNs, offering implications for the manipulation of their mechanical properties and enhancement of their self-healing capabilities.

Effect of intermolecular hydrogen bonding strength on the dynamic fragility of amorphous polyamides

Small-molecular-induced intermolecular hydrogen bonding (inter-HB) interactions were reported to increase the glass transition temperature (Tg) while decrease the dynamic fragility (m) of polymers. Herein, enthalpy relaxation parameters heat capacity jump (ΔCp) at Tg and enthalpy hysteresis (ΔHR) were investigated to help clarify the effect of macromolecular-induced inter-HB on Tg and m using amorphous polyamides as model polymers. The inter-HB strength was weakened by random copolymerization with varied chain rigidity, but was enhanced by decreasing steric hindrance. It was found that Tg and m increased after copolymerization due to the increased chain rigidity. Nevertheless, increasing steric hindrance leads to an increased Tg while anomalously reduced m. Further results found that m can be well correlated to Tg·ΔCp/ΔHR. ΔCp increases more significantly than ΔHR in co-polyamides, and thus the entropy change dominates the activation free energy of cooperative rearrangement. By contrast, ΔHR increases more significantly than ΔCp with increasing steric hindrance, and thus it is reasonable that Tg increases while m decreases. Most importantly, ΔCp and ΔHR decrease with increasing inter-HB strength regardless of the variation of Tg. These results indicate that the inter-HB strength may be very strong and insensitive to temperature in polyamides, thus behaving like physical cross-linking.

Next-Generation Vitrimers Design through Theoretical Understanding and Computational Simulations

Vitrimers are an innovative class of polymers that boast a remarkable fusion of mechanical and dynamic features, complemented by the added benefit of end-of-life recyclability. This extraordinary blend of properties makes them highly attractive for a variety of applications, such as the automotive sector, soft robotics, and the aerospace industry. At their core, vitrimer materials consist of crosslinked covalent networks that have the ability to dynamically reorganize in response to external factors, including temperature changes, pressure variations, or shifts in pH levels. In this review, the aim is to delve into the latest advancements in the theoretical understanding and computational design of vitrimers. The review begins by offering an overview of the fundamental principles that underlie the behavior of these materials, encompassing their structures, dynamic behavior, and reaction mechanisms. Subsequently, recent progress in the computational design of vitrimers is explored, with a focus on the employment of molecular dynamics (MD)/Monte Carlo (MC) simulations and density functional theory (DFT) calculations. Last, the existing challenges and prospective directions for this field are critically analyzed, emphasizing the necessity for additional theoretical and computational advancements, coupled with experimental validation.

The distinguishable-particle lattice model of glasses in three dimensions

The nature of glassy states in realistic finite dimensions is still under fierce debate. Lattice models can offer valuable insights and facilitate deeper theoretical understanding. Recently, a disordered-interacting lattice model with distinguishable particles in two dimensions (2D) has been shown to produce a wide range of dynamical properties of structural glasses, including the slow and heterogeneous characteristics of the glassy dynamics, various fragility behaviors of glasses, and so on. These findings support the usefulness of this model for modeling structural glasses. An important question is whether such properties still hold in the more realistic three dimensions. In this study, we aim to extend the distinguishable-particle lattice model (DPLM) to three dimensions (3D) and explore the corresponding glassy dynamics. Through extensive kinetic Monte Carlo simulations, we found that the 3D DPLM exhibits many typical glassy behaviors, such as plateaus in the mean square displacement of particles and the self-intermediate scattering function, dynamic heterogeneity, variability of glass fragilities, and so on, validating the effectiveness of the DPLM in a broader realistic setting. The observed glassy behaviors of the 3D DPLM appear similar to those of its 2D counterpart, in accordance with recent findings in molecular models of glasses. We further investigate the role of void-induced motions in dynamical relaxations and discuss their relation to dynamic facilitation. As lattice models tend to keep the minimal but important modeling elements, they are typically much more amenable to analysis. Therefore, we envisage that the DPLM will benefit future theoretical developments, such as the configuration tree theory, towards a more comprehensive understanding of structural glasses.

A bibliometric survey of research trends in vitrimer

The recent trends of vitrimer studies enhance the thermoset material with superior properties, therefore, it is particularly important to address the critical scientific inquiries in this area using their research metrics. The reported vitrimer systems have been highly required for future real-time applications; however, the inquisitiveness of material exchange mechanisms extends the research studies further. Significantly, more scientific information's are required to achieve the evident prospective outcomes via these materials. This article highlights the trends and developments of the most relevant publications, authors, articles, countries, and keywords in the vitrimer research field over the past 10 years. The represented bibliometric survey would elevate the basic understanding of the current vitrimer research stats and also help follow the particular research community to learn and develop insight. To generate bibliometric networks, bibliometric data has obtained from Scopus and visualised in VOS-viewer; as an overview of that, the highest number of publications were from China, United States, France, United Kingdom, and Spain.

Circularity in polymers: addressing performance and sustainability challenges using dynamic covalent chemistries

The circularity of current and future polymeric materials is a major focus of fundamental and applied research, as undesirable end-of-life outcomes and waste accumulation are global problems that impact our society. The recycling or repurposing of thermoplastics and thermosets is an attractive solution to these issues, yet both options are encumbered by poor property retention upon reuse, along with heterogeneities in common waste streams that limit property optimization. Dynamic covalent chemistry, when applied to polymeric materials, enables the targeted design of reversible bonds that can be tailored to specific reprocessing conditions to help address conventional recycling challenges. In this review, we highlight the key features of several dynamic covalent chemistries that can promote closed-loop recyclability and we discuss recent synthetic progress towards incorporating these chemistries into new polymers and existing commodity plastics. Next, we outline how dynamic covalent bonds and polymer network structure influence thermomechanical properties related to application and recyclability, with a focus on predictive physical models that describe network rearrangement. Finally, we examine the potential economic and environmental impacts of dynamic covalent polymeric materials in closed-loop processing using elements derived from techno-economic analysis and life-cycle assessment, including minimum selling prices and greenhouse gas emissions. Throughout each section, we discuss interdisciplinary obstacles that hinder the widespread adoption of dynamic polymers and present opportunities and new directions toward the realization of circularity in polymeric materials.

Creep and Recovery Behavior of Vitrimers with Fast Bond Exchange Rate

Vitrimers encompass the desirable mechanical properties of thermosets with the recyclability of thermoplastics. This ability arises from the rearrangement of the vitrimer covalent network upon heating via a bond shuffling mechanism while its cross-link density remains preserved. This unique feature makes vitrimers interesting candidates for the design of materials that combine dimensional stability at high temperatures and solvent resistance with the ability to be reshaped and processed. Despite these advantages, vitrimer exhibits significant creep at operating conditions where thermosets show little or no creep. As the mechanical properties of vitrimers not only depend on their chemical composition but also on the dynamics of the polymer chains, molecular dynamics (MD) simulations can provide detailed molecular mechanisms of the system of interest under macroscopic stress-induced deformations. In this regard, the recently developed MD/Monte Carlo simulation methodology capable of capturing the bond exchange mechanics in vitrimers is used to study the creep and recovery response of a coarse-grained model thermoset and vitrimer with a fast bond exchange rate. The time-stress superposition principle is then successfully applied to the creep response. The resulting universal curves enable us to predict the long-time creep behavior of both systems extending the timescale from 4 to over 10 orders of magnitude.

Dynamical susceptibilities near ideal glass transitions

Building on the recently derived inhomogeneous mode-coupling theory, we extend the generalized mode-coupling theory of supercooled liquids to inhomogeneous environments. This provides a first-principles-based, systematic, and rigorous way of deriving high-point dynamical susceptibilities from variations of the many-body dynamic structure factors with respect to their conjugate field. This framework allows for a fully microscopic possibility to probe for collective relaxation mechanisms in supercooled liquids near the mode-coupling glass transition. The behavior of these dynamical susceptibilities is then studied in the context of simplified self-consistent relaxation models.

The Interplay between the Theories of Mode Coupling and of Percolation Transition in Attractive Colloidal Systems

In the recent years a considerable effort has been devoted to foster the understanding of the basic mechanisms underlying the dynamical arrest that is involved in glass forming in supercooled liquids and in the sol-gel transition. The elucidation of the nature of such processes represents one of the most challenging unsolved problems in the field of material science. In this context, two important theories have contributed significantly to the interpretation of these phenomena: the Mode-Coupling theory (MCT) and the Percolation theory (PT). These theories are rooted on the two pillars of statistical physics, universality and scale laws, and their original formulations have been subsequently modified to account for the fundamental concepts of Energy Landscape (EL) and of the universality of the fragile to strong dynamical crossover (FSC). In this review, we discuss experimental and theoretical results, including Molecular Dynamics (MD) simulations, reported in the literature for colloidal and polymer systems displaying both glass and sol-gel transitions. Special focus is dedicated to the analysis of the interferences between these transitions and on the possible interplay between MCT and PT. By reviewing recent theoretical developments, we show that such interplay between sol-gel and glass transitions may be interpreted in terms of the extended F13 MCT model that describes these processes based on the presence of a glass-glass transition line terminating in an A3 cusp-like singularity (near which the logarithmic decay of the density correlator is observed). This transition line originates from the presence of two different amorphous structures, one generated by the inter-particle attraction and the other by the pure repulsion characteristic of hard spheres. We show here, combining literature results with some new results, that such a situation can be generated, and therefore experimentally studied, by considering colloidal-like particles interacting via a hard core plus an attractive square well potential. In the final part of this review, scaling laws associated both to MCT and PT are applied to describe, by means of these two theories, the specific viscoelastic properties of some systems.

Impact of dynamic covalent chemistry and precise linker length on crystallization kinetics and morphology in ethylene vitrimers

Vitrimers, dynamic polymer networks with topology conserving exchange reactions, have emerged as a promising platform for sustainable and reprocessable materials. While prior work has documented how dynamic bonds impact stress relaxation and viscosity, their role on crystallization has not been systematically explored. Precise ethylene vitrimers with 8, 10, or 12 methylene units between boronic ester junctions were investigated to understand the impact of bond exchange on crystallization kinetics and morphology. Compared to linear polyethylene which has been heavily investigated for decades, a long induction period for crystallization is seen in the vitrimers ultimately taking weeks in the densest networks. An increase in melting temperatures (T_m) of 25-30 K is observed with isothermal crystallization over 30 days. Both C₁₀ and C₁₂ networks initially form hexagonal crystals, while the C₁₀ network transforms to orthorhombic over the 30 day window as observed with wide angle X-ray scattering (WAXS) and optical microscopy (OM). After 150 days of isothermal crystallization, the three linker lengths led to double diamond (C₈), orthorhombic (C₁₀), and hexagonal (C₁₂) crystals indicating the importance of precision on final morphology. Control experiments on a precise, permanent network implicate dynamic bonds as the cause of long-time rearrangements of the crystals, which is critical to understand for applications of semi-crystalline vitrimers. The dynamic bonds also allow the networks to dissolve in water and alcohol-based solvents to monomers, followed by repolymerization while preserving the mechanical properties and melting temperatures.

Catalyst Control of Nanoscale Characteristic Length of the Glass Transition in Organic Strong Glass-Formers

We report the nanoscale characteristic length (ξ_α) in organic strong glass-formers at glass transition. Catalyst-dependent ξ_α of the epoxy-based covalent adaptable networks (CANs) is observed, that is, the more efficient the catalyst for the cross-linking reactions, the larger the ξ_α is, and upon thermal heating, the more broad the glass transition will be. The observed structural properties at glass transition can be correlated with the topology freezing transition where the fluctuations of network topology aroused from the bond exchange reactions are frozen. This study proposes the catalyst-dependent structural properties in CANs and may fill the structural gap between the glass transition and topology freezing transition of organic strong glass-formers.

Generalized mode-coupling theory for mixtures of Brownian particles

Generalized mode-coupling theory (GMCT) has recently emerged as a promising first-principles theory to study the poorly understood dynamics of glass-forming materials. Formulated as a hierarchical extension of standard mode-coupling theory (MCT), it is able to systematically improve its predictions by including the exact dynamics of higher-order correlation functions into its hierarchy. However, in contrast to Newtonian dynamics, a fully generalized version of the theory based on Brownian dynamics is still lacking. To close this gap, we provide a detailed derivation of GMCT for colloidal mixtures obeying a many-body Smoluchowski equation. We demonstrate that a hierarchy of coupled equations can again be established and show that these, consistent with standard MCT, are identical to the ones obtained from Newtonian GMCT when taking the overdamped limit. Consequently, the nontrivial similarity between Brownian and Newtonian MCT is maintained for our multicomponent GMCT. As a proof of principle, we also solve the generalized mode-coupling equations for the binary Kob-Andersen Lennard-Jones mixture undergoing Brownian dynamics and confirm the improved predictive power of the theory upon using more levels of the GMCT hierarchy of equations.

Glassy dynamics of sticky hard spheres beyond the mode-coupling regime

Sticky hard spheres, i.e., hard particles decorated with a short-ranged attractive interaction potential, constitute a relatively simple model with highly non-trivial glassy dynamics. The mode-coupling theory of the glass transition (MCT) offers a qualitative account of the complex reentrant dynamics of sticky hard spheres, but the predicted glass transition point is notoriously underestimated. Here we apply an improved first-principles-based theory, referred to as generalized mode-coupling theory (GMCT), to sticky hard spheres. This theoretical framework seeks to go beyond MCT by hierarchically expanding the dynamics in higher-order density correlation functions. We predict the phase diagrams from the first few levels of the GMCT hierarchy and the dynamics-related critical exponents, all of which are much closer to the empirical observations than MCT. Notably, the prominent reentrant glassy dynamics, the glass-glass transition, and the higher-order bifurcation singularity classes (A3 and A4) of sticky hard spheres are found to be preserved within GMCT at arbitrary order. Moreover, we demonstrate that when the hierarchical order of GMCT increases, the effect of the short-ranged attractive interactions becomes more evident in the dynamics. This implies that GMCT is more sensitive to subtle microstructural differences than MCT, and that the framework provides a promising first-principles approach to systematically go beyond the MCT regime.

Glass-liquid and glass-gel transitions of soft-shell particles

We study the structure and dynamics of colloidal particles with a spherical hard core and a thermo-responsive soft shell over the whole phase diagram by means of small-angle x-ray scattering and x-ray photon correlation spectroscopy. By changing the effective volume fraction by temperature and particle concentration, liquid, repulsive glass. and attractive gel phases are observed. The dynamics slow down with increasing volume fraction in the liquid phase and reflect a Vogel-Fulcher-Tamann behavior known for fragile glass formers. We find a liquid-glass transition above 50 vol.% that is independent of the particles' concentration and temperature. In an overpacked state at effective volume fractions above 1, the dispersion does not show a liquid phase but undergoes a gel-glass transition at an effective volume fraction of 34 vol.%. At the same concentration, extrema of subdiffusive dynamics are found in the liquid phase at lower weight fractions. We interpret this as dynamic precursors of the glass-gel transition.

Multi-component generalized mode-coupling theory: predicting dynamics from structure in glassy mixtures

The emergence of glassy dynamics and the glass transition in dense disordered systems is still not fully understood theoretically. Mode-coupling theory (MCT) has shown to be effective in describing some of the non-trivial features of glass formation, but it cannot explain the full glassy phenomenology due to the strong approximations on which it is based. Generalized mode-coupling theory (GMCT) is a hierarchical extension of the theory, which is able to outclass MCT by carefully describing the dynamics of higher-order correlations in its generalized framework. Unfortunately, the theory has so far only been developed for single-component systems and as a result works poorly for highly polydisperse materials. In this paper, we solve this problem by developing GMCT for multi-component systems. We use it to predict the glassy dynamics of the binary Kob-Andersen Lennard-Jones mixture, as well as its purely repulsive Weeks-Chandler-Andersen analogue. Our results show that each additional level of the GMCT hierarchy gradually improves the predictive power of GMCT beyond its previous limit. This implies that our theory is able to harvest more information from the static correlations, thus being able to better understand the role of attraction in supercooled liquids from a first-principles perspective.

Glassy dynamics of a binary Voronoi fluid: a mode-coupling analysis

The binary Voronoi mixture is a fluid model whose interactions are derived from the Voronoi-Laguerre tessellation of the configurations of the system. The resulting interactions are local and many-body. Here we perform molecular-dynamics (MD) simulations of an equimolar mixture that is weakly polydisperse and additive. For the first time we study the structural relaxation of this mixture in the supercooled-liquid regime. From the simulations we determine the time- and temperature-dependent coherent and incoherent scattering functions for a large range of wave vectors, as well as the mean-square displacements of both particle species. We perform a detailed analysis of the dynamics by comparing the MD results with the first-principles-based idealized mode-coupling theory (MCT). To this end, we employ two approaches: fits to the asymptotic predictions of the theory, and fit-parameter-free binary MCT calculations based on static-structure-factor input from the simulations. We find that many-body interactions of the Voronoi mixture do not lead to strong qualitative differences relative to similar analyses carried out for simple liquids with pair-wise interactions. For instance, the fits give an exponent parameter λ ≈ 0.746 comparable to typical values found for simple liquids, the wavevector dependence of the Kohlrausch relaxation time is in good qualitative agreement with literature results for polydisperse hard spheres, and the MCT calculations based on static input overestimate the critical temperature, albeit only by a factor of about 1.2. This overestimation appears to be weak relative to other well-studied supercooled-liquid models such as the binary Kob-Andersen Lennard-Jones mixture. Overall, the agreement between MCT and simulation suggests that it is possible to predict several microscopic dynamic properties with qualitative, and in some cases near-quantitative, accuracy based solely on static two-point structural correlations, even though the system itself is inherently governed by many-body interactions.

Fragile Glasses Associated with a Dramatic Drop of Entropy under Supercooling

We perform kinetic Monte Carlo simulations of a distinguishable-particle lattice model of structural glasses with random particle interactions. By varying the interaction distribution and the average particle hopping energy barrier, we obtain an extraordinarily wide range of kinetic fragility. A stretching exponent, characterizing structural relaxation, is found to decrease with the kinetic fragility in agreement with experiments. The most fragile glasses are those exhibiting low hopping barriers and, more importantly, dramatic drops of entropies upon cooling toward the glass transition temperatures. The entropy drops reduce possible kinetic pathways and lead to dramatic slowdowns in the dynamics. In addition, the kinetic fragility is shown to correlate with a thermodynamic fragility.

Impact of Backbone Composition on Homopolymer Dynamics and Brush Block Copolymer Self-Assembly

Four series of brush block copolymers (BBCP), with near identical side chain compositions but varying backbone structures, were synthesized to investigate the effect of backbone structure on the process of thermal BBCP self-assembly to photonic crystals (PCs). Each of the self-assembled PC films were examined by reflection measurements, small angle X-ray scattering measurements, and scanning electron microscopy to compare the resulting properties of the polymeric photonic crystal and the nanostructured morphology impacted by the backbone structure. It was found that the composition of the brush backbone within a BBCP has a dramatic effect on the ability of the BBCP to self-assemble into ordered nanostructures and on the local ordering of the nanostructure morphology accessed with higher molecular weight (MW) BBCPs (> 1,500 kg/mol). BBCPs with a norbornene imide-based backbone were able to thermally self-assemble to longer wavelength reflecting PCs and had higher fidelity ordering of lamellar nanostructures with higher MW polymers. By analyzing the melt rheological responses of the backbone compositions, both as linear polymers and homobrush polymers, it was concluded that the inherent fragility of the backbone promotes enhanced local ordering in the lamellar nanostructure morphology as well as access to larger domain sizes.

Entropy-controlled cross-linking in linker-mediated vitrimers

Recently developed linker-mediated vitrimers based on metathesis of dioxaborolanes with various commercially available polymers have shown both good processability and outstanding performance, such as mechanical, thermal, and chemical resistance, suggesting new ways of processing cross-linked polymers in industry, of which the design principle remains unknown [M. Röttger et al., Science 356, 62-65 (2017)]. Here we formulate a theoretical framework to elucidate the phase behavior of the linker-mediated vitrimers, in which entropy plays a governing role. We find that, with increasing the linker concentration, vitrimers undergo a reentrant gel-sol transition, which explains a recent experiment [S. Wu, H. Yang, S. Huang, Q. Chen, Macromolecules 53, 1180-1190 (2020)]. More intriguingly, at the low temperature limit, the linker concentration still determines the cross-linking degree of the vitrimers, which originates from the competition between the conformational entropy of polymers and the translational entropy of linkers. Our theoretical predictions agree quantitatively with computer simulations, and offer guidelines in understanding and controlling the properties of this newly developed vitrimer system.

Integral equation theory of thermodynamics, pair structure, and growing static length scale in metastable hard sphere and Weeks-Chandler-Andersen fluids

We employ the Ornstein-Zernike integral equation theory with the Percus-Yevick (PY) and modified-Verlet (MV) closures to study the equilibrium structural and thermodynamic properties of metastable monodisperse hard sphere and continuous repulsion Weeks-Chandler-Andersen (WCA) fluids under density and temperature conditions where the system is strongly overcompressed or supercooled, respectively. The theoretical results are compared to crystal-avoiding simulations of these dense monodisperse model one-component fluids. The equation of state (EOS) and dimensionless compressibility are computed using both the virial and compressibility routes. For hard spheres, the MV-based virial route EOS and dimensionless compressibility are in very good agreement with simulation for all packing fractions, much better than the PY analogs. The corresponding MV-based predictions for the static structure factor are also very good. The amplitude of density fluctuations on the local cage scale and in the long wavelength limit, and three technically different measures of the density correlation length, are studied with both closures. All five properties grow in a roughly exponential manner with density in the metastable regime up to packing fractions of 58% with no sign of saturation. The MV-based results are in good agreement with our crystal-avoiding simulations. Interestingly, the density dependences of long and short wavelength quantities are closely related. The MV-based theory is also quite accurate for the thermodynamics and structure of supercooled monodisperse WCA fluids. Overall our findings are also relevant as critical input to microscopic theories that relate the equilibrium pair correlation function or static structure factor to dynamical constraints, barriers, and activated relaxation in glass-forming liquids.