Ab initio simulated Van Hove correlation function for time-resolved local dynamics in molten MgCl2
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We employ polymer integral equation theory to study a simplified model of semiflexible polymerized ionic liquids (PolyILs) that interact via hard core repulsions and short range screened Coulomb interactions. The multi-scale structure in real and Fourier space of PolyILs (ions chosen to mimic Li, Na, K, Br, PF 6 , and TFSI) are determined as a function of melt density, Coulomb interaction strength, and ion size. Comparisons with a homopolymer melt, a neutral polymer–solvent-like athermal mixture, and an atomic ionic liquid are carried out to elucidate the distinct manner that ions mediate changes of polymer packing, the role of excluded volume effects, and the influence of chain connectivity, respectively. The effect of Coulomb strength depends in a rich manner on ion size and density, reflecting the interplay of steric packing, ion adsorption, and charge layering. Ion-mediated bridging of monomers is found, which intensifies for larger ions. Intermediate range charge layering correlations are characterized by a many-body screening length that grows with PolyIL density, cooling, and Coulomb strength, in disagreement with Debye–Hückel theory, but in accord with experiments. Qualitative differences in the collective structure, including an ion-size-dependent bifurcation of the polymer structure factor peak and pair correlation function, are predicted. The monomer cage order parameter increases significantly, but its collective ion counterpart decreases, as ions become smaller. Such behaviors allow one to categorize PolyILs into two broad classes of small and large ions. Furthermore, dynamical implications of the predicted structural results are qualitatively discussed.
Ca 12 Ga 14 O 33 was successfully synthesized using a wet chemistry technique to promote the homogenous mixing of the Ca and Ga cations. Rietveld refinements on X-ray and neutron powder diffraction data confirm that the compound is isostructural to Ca 12 Al 14 O 33 , however, with a significantly larger lattice parameter allowing for the cages that result from the framework arrangement to expand. In naturally occurring Ca 12 Al 14 O 33 , the mineral mayenite, these cages are occupied by O 2- anions, however, experimental studies exchanging the O 2- anions with other anions has led to a host of applications, depending on the caged anion. The functional nature of the structure, where framework distortions coupled with cage occupants, are correlated to electronic band structure and modifications to the framework could lead to interesting physical properties. The phase evolution was tracked using thermogravimetric analysis and high temperature X-ray diffraction and showed a lower formation temperature for the Ca 12 Ga 14 O 33 analogue compared to Ca 12 Al 14 O 33 synthesized using the same wet chemistry technique. Analyzing both X-ray and neutron powder diffraction using the Rietveld method with two different starting models results in one structural model, with one Ca position and the caged O on a 24d special position, being preferred.
In this work, we employ the microscopic self-consistent cooperative hopping theory of penetrant activated dynamics in glass forming viscous liquids and colloidal suspensions to address new questions over a wide range of high matrix packing fractions and penetrant-to-matrix particle size ratios. The focus is on the mean activated relaxation time of smaller tracers in a hard sphere fluid of larger particle matrices. This quantity also determines the penetrant diffusion constant and connects directly with the structural relaxation time probed in an incoherent dynamic structure factor measurement. The timescale of the non-activated fast dissipative process is also studied and is predicted to follow power laws with the contact value of the penetrant–matrix pair correlation function and the penetrant–matrix size ratio. For long time penetrant relaxation, in the relatively lower packing fraction metastable regime the local cage barriers are dominant and matrix collective elasticity effects unimportant. As packing fraction and/or penetrant size grows, much higher barriers emerge and the collective elasticity associated with the correlated matrix dynamic displacement that facilitates penetrant hopping becomes important. This results in a non-monotonic variation with packing fraction of the degree of decoupling between the matrix and penetrant alpha relaxation times. The conditions required for penetrant hopping to become slaved to the matrix alpha process are determined, which depend mainly on the penetrant to matrix particle size ratio. By analyzing the absolute and relative importance of the cage and elastic barriers we establish a mechanistic understanding of the origin of the predicted exponential growth of the penetrant hopping time with size ratio predicted at very high packing fractions. A dynamics-thermodynamics power law connection between the penetrant activation barrier and the matrix dimensionless compressibility is established as a prediction of theory, with different scaling exponents depending on whether matrix collective elasticity effects are important. Quantitative comparisons with simulations of the penetrant relaxation time, diffusion constant, and transient localization length of tracers in dense colloidal suspensions and cold viscous liquids reveal good agreements. Multiple new predictions are made that are testable via future experiments and simulations. Extension of the theoretical approach to more complex systems of high experimental interest (nonspherical molecules, semiflexible polymers, crosslinked networks) interacting via variable hard or soft repulsions and/or short range attractions is possible, including under external deformation.
We propose a microscopic theory for the decoupling of self-diffusion and structural relaxation in glass-forming liquids within the Elastically Collective Nonlinear Langevin Equation (ECNLE) activated dynamics framework. Our central hypothesis is that the heterogeneity relevant to this problem is static fluctuations of local density on the scale of 3–4 particle diameters and how this changes local packing correlations. These fluctuations modify the degree of dynamical cage expansion that mechanistically couples intracage large amplitude hopping and longer range collective elasticity in ECNLE theory. Decoupling only emerges in the deeply supercooled regime where the strongly temperature dependent elastic barrier becomes non-negligible relative to its noncooperative local analog. The theory makes predictions for various aspects of the decoupling phenomenon, including apparent fractional power law Stokes-Einstein behavior, that appear to be consistent with experiments and simulations on hard sphere fluids and molecular liquids. Of central importance is a microscopic connection between the barrier fluctuation variance and most probable barrier height. Sensible results are also obtained for the nonexponential stretching of a generic relaxation time correlation function and its temperature evolution. Nonuniversality can arise from the relative importance of the local and collective barriers (related to fragility) and the precise magnitude of the length scale that defines the transition from local cage to elastic physics. Comparison is made with a traplike model based on a Gaussian distribution of barriers.
Decreasing cost of technologies for direct air capture of carbon can be achieved through the design of new materials with high CO 2 selectivity that can be incorporated into existing industrial processes. An emerging class of materials for these applications are porous liquids (PLs). PLs are mixtures of porous hosts and solvents with intrinsic porosity due to steric exclusion of solvent from inside the porous host. It is currently unknown how solvent -porous host interactions affect porous host solubility in the bulk solvent. Here, in this study, density functional theory simulations were used to investigate interactions between nine solvents and a CC13 porous organic cage (POC). Calculations identified that solvent molecules were the most stable when placed either inside the CC13 POC or in the pore window compared to interfacial binding sites. Structural changes to the CC13 POC correlated with reported experimental solubilities, including expansion of the CC13 POC with solvent molecule infiltration and expansion or contraction of the pore window. Based on these results, new PL design guidelines should include compositions with (1) high concentrations of POCs with flexible cage structures that can expand when solvated and (2) solvent molecule-POC combinations that contract the pore window during solvent molecule-host binding.
Efficient carbon capture requires the design of new materials with high CO 2 selectivity and gas adsorption capacity that can be incorporated into existing industrial processes. Porous liquids (PLs) are promising candidate materials that consist of a nanoporous host and a solvent forming a liquid with permanent porosity based on exclusion of the solvent from the interior of the nanoporous host. Stable PLs are based on solvent-nanoporous host interactions, which can be evaluated through molecular simulations. Here, time- and temperature-dependent density functional theory simulations were performed between four solvents, 2-bromophenol, 4-methylphenol, 2,4-dimethylphenol, and cyclohexanone and the CC13 porous organic cage (POC) as a prototypical PL composition. Overall, minimal reactions occurred in the PL including no changes in the POC structure. Additionally, POC-solvent coordination occurred through interactions of neighboring functional groups such as methyl/bromide and hydroxyl on the solvent molecules with the POC surface. Therefore, the location rather than the number of functional groups on the solvent molecule controls the POC-solvent interactions. Additionally, the POC pore window contracted or expanded up to 8% during solvation, which correlates with the experimental solubility and static solvent-POC binding, where solvents that caused less contraction of the POC pore window increased POC solubility. Finally, these results allow for the design of optimized POC-based PL compositions based on solvent-nanoporous host binding and variation in the pore window during solvation.
We present benchmark binding energies of naturally occurring gas molecules CH4, CO2, and H2S in the small cage, namely the pentagonal dodecahedron (512) (H2O)20, which is one of the constituent cages of the 3 major lattices (structures I, II and H) of clathrate hydrates. These weak interactions require higher levels of electron correlation and converge slowly with increasing basis set to the Complete Basis Set (CBS) limit, necessitating the use of large basis sets up to the augcc- pV5Z and subsequent correction for Basis Set Superposition Error (BSSE). For the host hollow (H2O)20 cages we have identified a most stable isomer with binding energy of -200.8 ± 2.1 kcal/mol at the CCSD(T)/CBS limit (-199.2 ± 0.5 kcal/mol at the MP2/CBS limit). Additionally, we report converged second order Moller-Plesset (MP2) CBS binding energies for the encapsulation of guests in the (H2O)20 cage of -4.3 ± 0.1 for CH4@(H2O)20, -6.6 ± 0.1 for CO2@(H2O)20 and -8.5 ± 0.1 kcal/mol for H2S@(H2O)20, respectively. For CH4@(H2O)20, exhibiting the weakest encapsulation affinity among the three, we report CCSD(T)/aug-cc-pVTZ binding energies and, based on them, a CCSD(T)/CBS estimate of -4.75 ± 0.1 kcal/mol. To the best of our knowledge, the CCSD(T)/aug-cc-pVTZ calculation for CH4@(H2O)20 is the largest one reported to date (168 valence electrons, 1978 basis functions and the correlation of 84 doubly occupied and 1873 virtual orbitals) and required a scalable implementation of the (T) module on 6144 nodes (350208 cores) of the “Cori” supercomputer at the National Energy Research Supercomputing Center (NERSC) for a total execution time of 195 minutes (for the (T) part). These efficient scalable implementations of highly correlated methods offer the capability to obtain long-lasting benchmarks of intermolecular interactions in complex systems. They also provide a path towards parametrizing classical potentials needed to study the dynamical and transport properties in these complex systems as well as assess the accuracy of lower scaling electronic structure methods such as Density Functional Theory (DFT) and MP2 including its spin-biased variants.
The relaxation dynamics of liquid and glass can be studied by inelastic x-ray or neutron scattering through the intermediate scattering function F(Q, t), where Q is the momentum transfer of scattering. Because of the time-consuming nature of these measurements, F(Q, t) is usually measured only at the first peak of the structure function S(Q), and its principal decay time is referred to as the α-relaxation time τ α . τ α is generally considered to describe the relaxation time of the bulk, which is related to viscosity and is controlled by the atomic cage around an atom. Here, through simulations on metallic liquids, we show that the α-relaxation time determined by scattering experiments does not purely reflect viscosity but is influenced by changes in spatial cooperativity. We also demonstrate that atomic caging is not exerted by the nearest neighbors but involves more cooperative atomic dynamics of the atomic medium-range order.
Here, 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.
Binary mixtures of ionic liquids with molecular solvents are gaining interest in electrochemical applications due to the improvement in their performance over neat ionic liquids. Dilution with suitable molecular solvents can reduce the viscosity and facilitate faster diffusion of ions, thereby yielding substantially higher ionic conductivity than that for a pure ionic liquid. Although viscosity and diffusion coefficients typically behave as monotonic functions of concentration, ionic conductivity often passes through a peak value at an optimum molar ratio of the molecular solvent to the ionic liquid. The ionic conductivity maximum is generally explained in terms of a balance between the ease of charge transport and the concentration of the charge carriers. In this work, fluctuation in the local environment surrounding an ion is invoked as a plausible explanation for the ionic conductivity mechanism with a binary mixture of 1-ethyl-3-methylimidazolium tetrafluoroborate and ethylene glycol as an example. The magnitude of the dynamism in the local environment is captured by measuring the spatial and temporal features of the solvation environment. Standard deviation in the number of ions in the solvation environment serves as a spatial feature, while the cage correlation lifetimes for oppositely charged ions within the first solvation shell serve as a temporal feature. Large standard deviations in the cluster ion population and short cage correlation lifetimes are indicators of highly dynamic ionic environment at the molecular level and consequently yield high ionic conductivity. Such compositions were found to be in good agreement with the optimum ionic liquid mole fractions obtained through experimental measurement. Short cage correlation lifetimes enable the identification of optimum mixture compositions using simulation trajectories significantly shorter than those required to implement the Nernst–Einstein or Einstein formalisms for calculating ionic conductivity. We validated the applicability of this approach across force fields and in six ionic liquid-molecular solvent electrolytes formed with combination of cations, anions, and solvents. We offer a computationally efficient approach of screening ionic liquid-molecular solvent binary mixture electrolytes to identify molar ratios that yield high ionic conductivity.
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Decoding the structural information contained in the interfacial vibrational spectrum of water requires understanding how the spectral signatures of individual water molecules respond to their local hydrogen bonding environments. In this study, we isolated the contributions for the five classes of sites that differ according to the number of donor (D) and acceptor (A) hydrogen bonds that characterize each site. These patterns were measured by exploiting the unique properties of the water cluster cage structures formed in the gas phase upon hydration of a series of cations M+·(H2O)n (M = Li, Na, Cs, NH4, CH3NH3, H3O, and n = 5, 20-22). This selection of ions was chosen to systematically express the A, AD, AAD, ADD, and AADD hydrogen bonding motifs. The spectral signatures of each site were measured using two-color, IR-IR isotopomer-selective photofragmentation vibrational spectroscopy of the cryogenically cooled, mass selected cluster ions in which a single intact H2O is introduced without isotopic scrambling, an important advantage afforded by the cluster regime. The resulting patterns provide an unprecedented picture of the intrinsic line shapes and spectral complexities associated with excitation of the individual OH groups, as well as the correlation between the frequencies of the two OH groups on the same water molecule, as a function of network site. The properties of the surrounding water network that govern this frequency map are evaluated by dissecting electronic structure calculations that explore how changes in the nearby network structures, both within and beyond the first hydration shell, affect the local frequency of an OH oscillator. The qualitative trends are recovered with a simple model that correlates the OH frequency with the network-modulated local electron density in the center of the OH bond.
Ab initio quantum-chemical methods that perform well for computing the electronic ground state are not straightforwardly transferable to electronically excited states, particularly in large molecular systems. Wave function theory offers high accuracy, but is often prohibitively expensive. Methods based on time-dependent density functional theory (TD-DFT) are crucially sensitive to the chosen exchange-correlation functional (XCF) parameterization, and system-specific tuning protocols were therefore proposed to address the method's robustness. Methods based on the variational relaxation of the excited-state electron density showcased promising results for the calculation of charge-transfer excitations, but the complex shape of the electronic hypersurface makes convergence to a specific excited state much more difficult than for the ground state when standard variational techniques are applied. We address the latter aspect by providing suitable initial guesses, which we obtain by two separate constrained algorithms. Combined with the squared-gradient minimization algorithm for all-electrons relaxation in a freeze-and-release scheme (FRZ-SGM), we demonstrate that orbital-optimized density functional theory (OO-DFT) calculations can reliably converge to the charge-transfer states of interest even for large molecular systems. We test the FRZ-SGM method on a phenothiazine-anthraquinone CT excitation in a supramolecular Pd(II) coordination cage complex as a function of the cage conformation. This compound has been studied experimentally prior to our work. We compare this freeze-and-release scheme to two XCF reparameterizations, which were recently proposed as low-cost TD-DFT-based alternatives to variational methods. Two dye-semiconductor complexes, which were previously investigated in the context of photovoltaic applications, serve as a second example to investigate the convergence and stability of the FRZ-SGM approach. Our results demonstrate that FRZ-SGM provides reliable convergence for charge-transfer excited states and avoids variational collapse to lower-lying electronic states, whereas time-dependent DFT calculations with an adequate tuning procedure for the range-separation parameter provide a computationally efficient initial estimate of the corresponding energies, with a computational cost comparable to that of configuration-interaction singles (CIS) calculations.
We construct a microscopic theory at the level of segment-scale correlated space–time intermolecular forces for the long-time center-of-mass (CM) diffusion constant and intermediate-time non-Fickian transport in dense solutions and melts of ring polymers. The approach combines ideas of polymer, colloid, and liquid-state statistical mechanics to quantify how the multifractal intra-ring conformational structure and inter-ring packing correlations determine dynamic caging constraints and time-dependent friction. Breakdown of Rouse theory is predicted to occur due to length scale-dependent temporal correlation of forces exerted on pairs of tagged ring segments from surrounding polymers. At large enough degrees of polymerization (N), a stronger scaling of the CM diffusion constant (D ∝ N –2 ) is predicted, with a crossover N D proportional to the product of the system-specific macromolecular volume fraction and dimensionless compressibility. In analogy with caging effects in glass-forming fluids, the theory does appear to begin to fail at sufficiently high N/N D for the center-of-mass diffusivity, likely due to another crossover to an even slower activated transport regime. However, use of N/N D with the theoretically predicted N D , in conjunction with dynamic blob scaling ideas for local Rouse friction, collapses semidilute and concentrated solution simulation data onto a master curve. Based on the same physical ideas employed to predict the diffusion constant, a generalized Langevin equation description is formulated for intermediate-time CM transport. It predicts two subdiffusive regimes that emerge due to the self-similar nature of internal ring structure. Analytic and numerical predictions for the apparent non-Fickian exponent as a function of time, N/N D and dimensionless compressibility, the evolution of the maximum degree of subdiffusive motion with N/N D , and the time scale for recovering Fickian diffusion are made, all of which are in good accordance with melt simulations. Furthermore, the present work sets the stage to address activated dynamics and glass formation on the macromolecular scale.
Here we combine polymer integral equation theory for structural correlations with a force-level theory for activated segmental relaxation to construct a microscopic theory for how ions modify the onset of segmental localization, the polymer alpha relaxation time, and glass transition temperature, T g , in dry polymerized ionic liquids (PolyILs). Our most important findings concerning the behavior of T g are (i) a weak dependence on anion–cation Coulomb attraction strength due to strong decoupling of ion and segmental dynamics, (ii) strong reduction with increasing mobile ion size due to both plasticization effects and weakening of ion-modified monomer caging, and (iii) increase with backbone rigidity and intrachain dynamic cooperativity. We quantitatively estimate T g variations as ion size and polymer static and dynamic rigidity are widely varied. The experimental data of 19 PolyILs are organized into a specific pattern consistent with the theoretical predictions with glass transition temperatures varying over a very wide range (~250 K) as observed experimentally. Based on the theoretical results, suggestions are made concerning the search for high conductivity Li- or Na-based PolyILs based on further lowering of T g via new polymer synthesis. Calculations of the alpha time as a function of packing fraction reveal the dynamic fragility increases for larger mobile ions, a more flexible backbone, and/or a smaller degree of intrachain dynamic cooperativity, as a consequence of the increasing importance of collective elasticity in determining the activation barrier. An analysis of transient segmental localization and a crossover to activated dynamics reveals similar, but not identical, trends as predicted at the laboratory vitrification timescale.
Understanding the dynamics of chemical reactions in solutions is vital, as their rates and kinetics are significantly affected by the solvent environment. Supercritical solvents offer extensive applications in chemical reactions by enabling the manipulation of the solution environment. Here, in this study, we investigate the geminate recombination of iodine in a supercritical xenon solvent by using ReaxFF-based molecular dynamics simulations. Our findings reveal that the highest iodine recombination rate occurs near supercritical conditions, while lower-pressure conditions lead to reduced collision rates and unstable recombination, and higher-pressure conditions hinder iodine diffusion, resulting in a lower recombination rate. Our analysis shows that the xenon local density at the time of recombination is at least 2.5 times higher than the global density, confirming the presence of xenon clusters surrounding the Iodine atoms. This observation is further supported by coordination number analysis, which confirms an elevated xenon local density during recombination. In addition, the correlation between the total energy of xenon atoms within a cluster and recombined iodine atoms underscores the kinetic energy transfer process, validating the occurrence of geminate recombination. The excess kinetic energy from the recombining iodine atoms is transferred to the surrounding xenon atoms. Our examination of geminate recombination demonstrates that iodine atoms confined within xenon clusters—whether through manual insertion of atoms or the fast dissociation of an iodine molecule within xenon clusters—are more likely to recombine as primary geminate recombination. However, extending the iodine molecule dissociation time allows iodine atoms to diffuse out of the cluster, and the recombination to shift toward secondary geminate recombination.