Dual feed progressive cavity pump extrusion system for functionally graded direct ink write 3D printing.

Material extrusion Additive Manufacturing (AM), is one of the most widely practiced methods of AM. Fused Filament Fabrication (FFF) is what most associate with AM, as it is relatively inexpensive, and highly accessible, involving feeding plastic filament into a hot-end that melts and extrudes from a nozzle as the toolhead moves along the toolpath. Direct Ink Write (DIW) 3D printing falls into this same category of AM, however is primarily practiced in laboratory settings to construct novel parts from flowable feedstock materials. DIW printers are relatively expensive and often depend on custom software to print a part, limiting user-specificity. There have been recent advancements in multi-material and functionally graded DIW, but the systems are highly custom and the methods used to achieve multi-material prints are openly available to the public. The following article outlines the construction and operation method of a DIW system that is capable of printing that can produce compositionally-graded components using a dual feed progressive cavity pump extruder equipped with a dynamic mixer. The extruder and its capabilities to vary material composition while printing are demonstrated using a Prusa i3 MK3S+ desktop fused filament fabrication printer as the gantry system. This provides users ease of operation, and the capability of further tailoring to specific needs.

Scaling Law for the Onset of Solidification at Extreme Undercooling.

Quasi-isentropic compression enables one to study the solidification of metastable liquid states that are inaccessible through other experimental means. The onset of this nonequilibrium solidification is known to depend on the compression rate and material-specific factors, but this complex interdependence has not been well characterized. In this study, we use a combination of experiments, theory, and computational simulations to derive a general scaling law that quantifies this dependence. One of its applications is a novel means to elucidate melt temperatures at high pressures.

Model for the Solid-Liquid Interfacial Free Energy at High Pressures.

The free energy involved in the formation of an interface between two phases (e.g., a solid-liquid interface) is referred to as the interfacial free energy. For the case of solidification, the interfacial free energy dictates the height of the energy barrier required to nucleate stable clusters of the newly forming solid phase and is essential for producing an accurate solidification kinetics model using classical nucleation theory (CNT)-based methods. While various methods have been proposed for modeling the interfacial free energy for solid-liquid interfaces in prior literature, many of these formulations involve making restrictive assumptions or approximations, such as the system being at or near equilibrium (i.e., the system temperature is approximately equal to the melt temperature) or that the system is at pressures close to atmospheric. However, these approximations and assumptions may break down in highly non-equilibrium situations, such as in dynamic-compression experiments where metastable liquids that are undercooled by hundreds of kelvin or overpressurized by several gigapascals or more are formed before eventually solidifying. We derive a solid-liquid interfacial free-energy model for such high-pressure conditions by considering the enthalpies of interactions between pairs of atoms or molecules. We also consider the contribution of interface roughness (disordering) by incorporating a multilayer interface model known as the Temkin n-layer model. Our formulation is applicable to a diverse variety of materials, and we demonstrate it by developing models specifically for two different materials: water and gallium. We apply our interfacial free-energy formulation to CNT-based kinetics simulations of several suites of dynamic-compression experiments that cause liquid water to solidify to the high-pressure solid polymorph ice VII and have found good agreement to the observed kinetics with only minor empirical fitting.

Measuring the melting curve of iron at super-Earth core conditions.

The discovery of more than 4500 extrasolar planets has created a need for modeling their interior structure and dynamics. Given the prominence of iron in planetary interiors, we require accurate and precise physical properties at extreme pressure and temperature. A first-order property of iron is its melting point, which is still debated for the conditions of Earth's interior. We used high-energy lasers at the National Ignition Facility and in situ x-ray diffraction to determine the melting point of iron up to 1000 gigapascals, three times the pressure of Earth's inner core. We used this melting curve to determine the length of dynamo action during core solidification to the hexagonal close-packed (hcp) structure. We find that terrestrial exoplanets with four to six times Earth's mass have the longest dynamos, which provide important shielding against cosmic radiation.

Minimization of Gibbs Energy in High-Pressure Multiphase, Multicomponent Mixtures through Particle Swarm Optimization.

We present a global optimization method to construct phase boundaries in multicomponent mixtures by minimizing the Gibbs energy. The minimization method is, in essence, an extension of the Maxwell construction procedure that is used in single-component systems. For a given temperature, pressure, and overall mixture composition, it reveals the mole fractions of the thermodynamically stable phases and the composition of these phases. Our approach is based on particle swarm optimization (PSO), which is a gradient-free, stochastic method. It is not reliant on good initial guesses for the phase fractions and compositions, which is an important requirement for the high-pressure applications considered in this study because data on phase boundaries at high pressures tend to be extremely limited. One practical use of this method is to create equation-of-state tables needed by continuum-scale, multiphysics codes that are ubiquitous in high-pressure science. Currently, there does not exist a method to generate such tables that rigorously account for changes in phase boundaries due to mixing. We have done extensive testing to demonstrate that PSO can reliably determine the Gibbs energy minimum and can capture nontrivial features like eutectic and peritectic temperatures to produce coherent phase diagrams. As part of our testing, we have developed a PSO-based Helmholtz-energy minimization procedure that we have used to cross-check the results of the Gibbs energy minimization. We conclude with a critique of our approach and provide suggestions for future work, including a PSO-based entropy-maximization method that would enable the aforementioned continuum codes to perform on-the-fly, phase-equilibria calculations of multicomponent mixtures.

Metastable-solid phase diagrams derived from polymorphic solidification kinetics.

Nonequilibrium processes during solidification can lead to kinetic stabilization of metastable crystal phases. A general framework for predicting the solidification conditions that lead to metastable-phase growth is developed and applied to a model face-centered cubic (fcc) metal that undergoes phase transitions to the body-centered cubic (bcc) as well as the hexagonal close-packed phases at high temperatures and pressures. Large-scale molecular dynamics simulations of ultrarapid freezing show that bcc nucleates and grows well outside of the region of its thermodynamic stability. An extensive study of crystal-liquid equilibria confirms that at any given pressure, there is a multitude of metastable solid phases that can coexist with the liquid phase. We define for every crystal phase, a solid cluster in liquid (SCL) basin, which contains all solid clusters of that phase coexisting with the liquid. A rigorous methodology is developed that allows for practical calculations of nucleation rates into arbitrary SCL basins from the undercooled melt. It is demonstrated that at large undercoolings, phase selections made during the nucleation stage can be undone by kinetic instabilities amid the growth stage. On these bases, a solidification-kinetic phase diagram is drawn for the model fcc system that delimits the conditions for macroscopic grains of metastable bcc phase to grow from the melt. We conclude with a study of unconventional interfacial kinetics at special interfaces, which can bring about heterogeneous multiphase crystal growth. A first-order interfacial phase transformation accompanied by a growth-mode transition is examined.

Numerical modeling of solid-cluster evolution applied to the nanosecond solidification of water near the metastable limit.

Classical nucleation theory (CNT) is a promising way to predictively model the submicrosecond kinetics of phase transitions that occur under dynamic compression, such as the suite of experiments performed over the past two decades on the solidification of liquid water to the high-pressure ice VII phase. Myint et al. [Phys. Rev. Lett. 121, 155701 (2018)] presented the first CNT-based model for these types of rapid phase transitions, but relied on an empirical scaling parameter in their transient induction model to simulate the lag time that occurs prior to the onset of significant formation of ice VII clusters in the system. To build on that study, we model the liquid water-ice VII phase transformation using a numerical discretization scheme to solve the Zel'dovich-Frenkel partial differential equation, which is a fundamental CNT-based kinetic equation that describes the statistical time-dependent behavior of solid cluster formation. The Zel'dovich-Frenkel equation inherently accounts for transience in the nucleation kinetics and eliminates the need for the empirical scaling factor used by Myint et al. One major result of this research is that transience is found to play a relatively small role in the nucleation process for the dynamic-compression time scales of the liquid water-ice VII experiments being simulated. Instead, we show that it is possible to properly model the lag time using steady-state CNT by making small refinements to the interfacial free energy value. We have also developed a new dimensionless parameter that may be applied a priori to predict whether or not transient nucleation will be important in a given dynamic-compression experiment.

The thermodynamics of a liquid-solid interface at extreme conditions: A model close-packed system up to 100 GPa.

The first experimental insight into the nature of the liquid-solid interface occurred with the pioneering experiments of Turnbull, which simultaneously demonstrated both that metals could be deeply undercooled (and therefore had relatively large barriers to nucleation) and that the inferred interfacial free energy γ was linearly proportional to the enthalpy of fusion [D. Turnbull, J. Appl. Phys. 21, 1022 (1950)]. By an atomistic simulation of a model face-centered cubic system via adiabatic free energy dynamics, we extend Turnbull's result to the realm of high pressure and demonstrate that the interfacial free energy, evaluated along the melting curve, remains linear with the bulk enthalpy of fusion, even up to 100 GPa. This linear dependence of γ on pressure is shown to be a consequence of the entropy dominating the free energy of the interface in conjunction with the fact that the entropy of fusion does not vary greatly along the melting curve for simple monoatomic metals. Based on this observation, it appears that large undercoolings in liquid metals can be achieved even at very high pressure. Therefore, nucleation rates at high pressure are expected to be non-negligible, resulting in observable solidification kinetics.

Nanosecond Freezing of Water at High Pressures: Nucleation and Growth near the Metastability Limit.

The fundamental study of phase transition kinetics has motivated experimental methods toward achieving the largest degree of undercooling possible, more recently culminating in the technique of rapid, quasi-isentropic compression. This approach has been demonstrated to freeze water into the high-pressure ice VII phase on nanosecond timescales, with some experiments undergoing heterogeneous nucleation while others, in apparent contradiction, suggest a homogeneous nucleation mode. In this study, we show through a combination of theory, simulation, and analysis of experiments that these seemingly contradictory results are in agreement when viewed from the perspective of classical nucleation theory. We find that, perhaps surprisingly, classical nucleation theory is capable of accurately predicting the solidification kinetics of ice VII formation under an extremely high driving force (|Δµ/k_{B}T|≈1) but only if amended by two important considerations: (i) transient nucleation and (ii) separate liquid and solid temperatures. This is the first demonstration of a model that is able to reproduce the experimentally observed rapid freezing kinetics.

Rapid freezing of water under dynamic compression.

Understanding the behavior of materials at extreme pressures is a central issue in fields like aerodynamics, astronomy, and geology, as well as for advancing technological grand challenges such as inertial confinement fusion. Dynamic compression experiments to probe high-pressure states often encounter rapid phase transitions that may cause the materials to behave in unexpected ways, and understanding the kinetics of these phase transitions remains an area of great interest. In this review, we examine experimental and theoretical/computational efforts to study the freezing kinetics of water to a high-pressure solid phase known as ice VII. We first present a detailed analysis of dynamic compression experiments in which water has been observed to freeze on sub-microsecond time scales to ice VII. This is followed by a discussion of the limitations of currently available molecular and continuum simulation methods in modeling these experiments. We then describe how our phase transition kinetics models, which are based on classical nucleation theory, provide a more physics-based framework that overcomes some of these limitations. Finally, we give suggestions on future experimental and modeling work on the liquid-ice VII transition, including an outline of the development of a predictive multiscale model in which molecular and continuum simulations are intimately coupled.

Corrigendum: Rapid freezing of water under dynamic compression (2018 J. Phys.: Condens. Matter 30 233002).

Corrigendum.

Free energy models for ice VII and liquid water derived from pressure, entropy, and heat capacity relations.

We present equations of state relevant to conditions encountered in ramp and multiple-shock compression experiments of water. These experiments compress water from ambient conditions to pressures as high as about 14 GPa and temperatures of up to several hundreds of Kelvin. Water may freeze into ice VII during this process. Although there are several studies on the thermodynamic properties of ice VII, an accurate and analytic free energy model from which all other properties may be derived in a thermodynamically consistent manner has not been previously determined. We have developed such a free energy model for ice VII that is calibrated with pressure-volume-temperature measurements and melt curve data. Furthermore, we show that liquid water in the pressure and temperature range of interest is well-represented by a simple Mie-Grüneisen equation of state. Our liquid water and ice VII equations of state are validated by comparing to sound speed and Hugoniot data. Although they are targeted towards ramp and multiple-shock compression experiments, we demonstrate that our equations of state also behave reasonably well at pressures and temperatures that lie somewhat beyond those found in the experiments.

Efficient calculation of many-body induced electrostatics in molecular systems.

Potential energy functions including many-body polarization are in widespread use in simulations of aqueous and biological systems, metal-organics, molecular clusters, and other systems where electronically induced redistribution of charge among local atomic sites is of importance. The polarization interactions, treated here via the methods of Thole and Applequist, while long-ranged, can be computed for moderate-sized periodic systems with extremely high accuracy by extending Ewald summation to the induced fields as demonstrated by Nymand, Sala, and others. These full Ewald polarization calculations, however, are expensive and often limited to very small systems, particularly in Monte Carlo simulations, which may require energy evaluation over several hundred-thousand configurations. For such situations, it shall be shown that sufficiently accurate computation of the polarization energy can be produced in a fraction of the central processing unit (CPU) time by neglecting the long-range extension to the induced fields while applying the long-range treatments of Ewald or Wolf to the static fields; these methods, denoted Ewald E-Static and Wolf E-Static (WES), respectively, provide an effective means to obtain polarization energies for intermediate and large systems including those with several thousand polarizable sites in a fraction of the CPU time. Furthermore, we shall demonstrate a means to optimize the damping for WES calculations via extrapolation from smaller trial systems.

Fabrication and application of high impedance graded density impactors in light gas gun experiments.

Recent advances in Graded Density Impactor fabrication technique have increased the maximum achievable pressure in gas gun quasi-isentropic experiments to 5 Mbars. In this report, we outline the latest methodologies and applications of Graded Density Impactors in experiments at extreme conditions. These new Graded Density Impactors are essentially metallic discs made of nearly one hundred layers of precisely mixed Mg, Cu, and W. The density gradients in these impactors are specifically designed to generate the desired thermodynamic path required for each experiment. We carried out a number of experiments at various pressures using these Graded Density Impactors. These experimental results and their simulations will be presented here.

A Polarizable and Transferable PHAST N2 Potential for Use in Materials Simulation.

A polarizable and transferable intermolecular potential energy function, potentials with high accuracy, speed, and transferability (PHAST), has been developed from first principles for molecular nitrogen to be used in the modeling of heterogeneous processes such as materials sorption and separations. A five-site (van der Waals and point charge) anisotropic model, that includes many-body polarization, is proposed. It is parametrized to reproduce high-level electronic structure calculations (CCSD(T) using Dunning-type basis sets extrapolated to the CBS limit) for a representative set of dimer potential energy curves. Thus it provides a relatively simple yet robust and broadly applicable representation of nitrogen. Two versions are developed, differing by the type of mixing rules applied to unlike Lennard-Jones potential sites. It is shown that the Waldman-Hagler mixing rules are more accurate than Lorentz-Berthelot. The resulting potentials are demonstrated to be effective in modeling neat nitrogen but are designed to also be useful in modeling N2 interactions in a large array of environments such as metal-organic frameworks and zeolites and at interfaces. In such settings, capturing anisotropic forces and interactions with (open and coordinated) metals and charged/polar environments is essential. In developing the potential, it was found that adding a seemingly redundant dimer orientation, slip-parallel (S), improved the transferability of the potential energy surface (PES). Notably, one of the solid phases of nitrogen was not as accurately represented energetically without including S in the representative set. Liquid simulations, however, were unaffected and worked equally well for both potentials. This suggests that accounting for a wide variety of configurations is critical in designing a potential that is intended for use in heterogeneous environments where many orientations, including those not commonly explored in the bulk, are possible. Testing and validation of the potential are achieved via simulations of a thermal distribution of trimer geometries compared to analogous high level electronic structure calculations and molecular simulations of bulk pressure-density isotherms across the vapor, supercritical, and liquid phases. Crystal lattice parameters and energetics of the α-N2 and γ-N2 solid phases are also evaluated and determined to be in good agreement with experiment. Thus the proposed potential is shown to be efficacious for gas, liquid, and solid use, representing both disordered and ordered configurations.

Hydrogen adsorbed in a metal organic framework-5: coupled translation-rotation eigenstates from quantum five-dimensional calculations.

We report rigorous quantum five-dimensional (5D) calculations of the coupled translation-rotation (T-R) eigenstates of a H(2) molecule adsorbed in metal organic framework-5 (MOF-5), a prototypical nanoporous material, which was treated as rigid. The anisotropic interactions between H(2) and MOF-5 were represented by the analytical 5D intermolecular potential energy surface (PES) used previously in the simulations of the thermodynamics of hydrogen sorption in this system [Belof et al., J. Phys. Chem. C 113, 9316 (2009)]. The global and local minima on this 5D PES correspond to all of the known binding sites of H(2) in MOF-5, three of which, α-, ß-, and γ-sites are located on the inorganic cluster node of the framework, while two of them, the δ- and ε-sites, are on the phenylene link. In addition, 2D rotational PESs were calculated ab initio for each of these binding sites, keeping the center of mass of H(2) fixed at the respective equilibrium geometries; purely rotational energy levels of H(2) on these 2D PESs were computed by means of quantum 2D calculations. On the 5D PES, the three adjacent γ-sites lie just 1.1 meV above the minimum-energy α-site, and are separated from it by a very low barrier. These features allow extensive wave function delocalization of even the lowest translationally excited T-R eigenstates over the α- and γ-sites, presenting significant challenges for both the quantum bound-state calculations and the analysis of the results. Detailed comparison is made with the available experimental data.

A molecular H2 potential for heterogeneous simulations including polarization and many-body van der Waals interactions.

A highly accurate aniostropic intermolecular potential for diatomic hydrogen has been developed that is transferable for molecular modeling in heterogeneous systems. The potential surface is designed to be efficacious in modeling mixed sorbates in metal-organic materials that include sorption interactions with charged interfaces and open metal sites. The potential parameters are compatible for mixed simulations but still maintain high accuracy while deriving dispersion parameters from a proven polarizability model. The potential includes essential physical interactions including: short-range repulsions, dispersion, and permanent and induced electrostatics. Many-body polarization is introduced via a point-atomic polarizability model that is also extended to account for many-body van der Waals interactions in a consistent fashion. Permanent electrostatics are incorporated using point partial charges on atomic sites. However, contrary to expectation, the best potentials are obtained by permitting the charges to take on values that do not reproduce the first non-vanishing moment of the electrostatic potential surface, i.e., the quadrupole moment. Potential parameters are fit to match ab initio energies for a representative range of dimer geometries. The resulting potential is shown to be highly effective by comparing to electronic structure calculations for a thermal distribution of trimer geometries, and by reproducing experimental bulk pressure-density isotherms. The surface is shown to be superior to other similarly portable potential choices even in tests on homogeneous systems without strong polarizing fields. The present streamlined approach to developing such potentials allows for a simple adaptation to other molecules amenable to investigation by high-level electronic structure methods.

Understanding hydrogen sorption in a polar metal-organic framework with constricted channels.

A high fidelity molecular model is developed for a metal-organic framework (MOF) with narrow (approximately 7.3 Å) nearly square channels. MOF potential models, both with and neglecting explicit polarization, are constructed. Atomic partial point charges for simulation are derived from both fragment-based and fully periodic electronic structure calculations. The molecular models are designed to accurately predict and retrodict material gas sorption properties while assessing the role of induction for molecular packing in highly restricted spaces. Thus, the MOF is assayed via grand canonical Monte Carlo (GCMC) for its potential in hydrogen storage. The confining channels are found to typically accommodate between two to three hydrogen molecules in close proximity to the MOF framework at or near saturation pressures. Further, the net attractive potential energy interactions are dominated by van der Waals interactions in the highly polar MOF - induction changes the structure of the sorbed hydrogen but not the MOF storage capacity. Thus, narrow channels, while providing reasonably promising isosteric heat values, are not the best choice of topology for gas sorption applications from both a molecular and gravimetric perspective.

Characterization of Tunable Radical Metal-Carbenes: Key Intermediates in Catalytic Cyclopropanation.

A new class of radical metal-carbene complex has been characterized as having Fischer-like orbital interactions and adjacent π acceptor stabilization. Density Functional Theory (DFT) along with Natural Bond Orbital (NBO) analysis and Charge Decomposition Analysis (CDA) has given insight into the electronics of this catalytic intermediate in an open-shell cobalt-porphyrin, [Co(Por)], system. The complex has a single bond from the metal to the carbene and has radical character with localized spin density on the carbene carbon. In addition, the carbene carbon is found to be nucleophilic and "tunable" through the introduction of different α-carbon substituents. Finally, based on these findings, rational design strategies are proposed which should lead to the enhancement of catalytic activity.

Evidence for substrate preorganization in the peptidylglycine α-amidating monooxygenase reaction describing the contribution of ground state structure to hydrogen tunneling.

Peptidylglycine α-amidating monooxygenase (PAM) is a bifunctional enzyme which catalyzes the post-translational modification of inactive C-terminal glycine-extended peptide precursors to the corresponding bioactive α-amidated peptide hormone. This conversion involves two sequential reactions both of which are catalyzed by the separate catalytic domains of PAM. The first step, the copper-, ascorbate-, and O(2)-dependent stereospecific hydroxylation at the α-carbon of the C-terminal glycine, is catalyzed by peptidylglycine α-hydroxylating monooxygenase (PHM). The second step, the zinc-dependent dealkylation of the carbinolamide intermediate, is catalyzed by peptidylglycine amidoglycolate lyase. Quantum mechanical tunneling dominates PHM-dependent C(α)-H bond activation. This study probes the substrate structure dependence of this chemistry using a set of N-acylglycine substrates of varying hydrophobicity. Primary deuterium kinetic isotope effects (KIEs), molecular mechanical docking, alchemical free energy perturbation, and equilibrium molecular dynamics were used to study the role played by ground-state substrate structure on PHM catalysis. Our data show that all Ν-acylglycines bind sequentially to PHM in an equilibrium-ordered fashion. The primary deuterium KIE displays a linear decrease with respect to acyl chain length for straight-chain N-acylglycine substrates. Docking orientation of these substrates displayed increased dissociation energy proportional to hydrophobic pocket interaction. The decrease in KIE with hydrophobicity was attributed to a preorganization event which decreased reorganization energy by decreasing the conformational sampling associated with ground state substrate binding. This is the first example of preorganization in the family of noncoupled copper monooxygenases.