Lennard-Jones Parameters Research Articles

Revised 4-Point Water Model for the Classical Drude Oscillator Polarizable Force Field: SWM4-HLJ.

In this work the 4-point polarizable SWM4 Drude water model is reparametrized. Multiple models were developed using different strategies toward reproduction of specific target data. Results indicate that no individual model can reproduce all the selected target data in the context of the present form of the potential energy function. The changes considered in the new models include, 1) variations in the gas phase dipole moment, 2) variations in the molecular polarizability, 3) variations of the distance between the oxygen and the M site, 4) variation of the oxygen Lennard-Jones (LJ) parameters, 5) introduction of a LJ potential to the hydrogen atoms, and 6) variations of the H-O-H angle. Detailed analysis is presented for 3 new water models from which a final model, SWM4-HLJ, is selected as the future default model for the Drude polarizable force field. The model maintains the gas phase dipole moment as the experimental value while the remaining listed terms were adjusted including a larger H-O-H angle (108.12). Compared to its predecessor, SWM4-NDP, the self-diffusion coefficient, water dimer properties, and water cluster energies are greatly improved. The temperature dependence of the density of the new model also performs better. Overall, the new SWM4-HLJ water model is a general improvement and a good balance between microscopic and bulk properties is achieved.

Force Fields for Deep Eutectic Mixtures: Application to Structure, Thermodynamics and 2D-Infrared Spectroscopy.

Parametrizing energy functions for ionic systems can be challenging. Here, the total energy function for an eutectic system consisting of water, SCN-, K+ and acetamide is improved vis-a-vis experimentally measured properties. Given the importance of electrostatic interactions, two different types of models are considered: the first (model M0) uses atom-centered multipole whereas the other two (models M1 and M2) are based on fluctuating minimal distributed charges (fMDCM) that respond to geometrical changes of SCN-. The Lennard-Jones parameters of the anion are adjusted to best reproduce experimentally known hydration free energies and densities, which are matched to within a few percent for the final models irrespective of the electrostatic model. Molecular dynamics simulations of the eutectic mixtures with varying water content (between 0 and 100%) yield radial distribution functions and frequency correlation functions for the CN-stretch vibration. Comparison with experiments indicates that models based on fMDCM are considerably more consistent than those using multipoles. Computed viscosities from models M1 and M2 are within 30% of measured values and their change with increasing water content is consistent with experiments. This is not the case for model M0.

Molecular modeling and simulation of organic electrolyte solutions for lithium ion batteries.

Multi-criteria optimization is used for developing molecular models for ethylene carbonate (EC) and propylene carbonate (PC), organic solvents commonly used in Li-ion batteries. The molecular geometry and partial charges of the solvents are obtained from quantum mechanical calculations. Using a novel optimization strategy that combines systematic variations of the Lennard-Jones parameters with a reduced units approach, the models are fitted to experimental data on the liquid density, vapor pressure, relative permittivity, and self-diffusion coefficient. Since no experimental data for the self-diffusion coefficient of pure EC were available in the literature, they are measured in this work using a gradient-based nuclear magnetic resonance technique. For all pure component properties, excellent agreement between experiment and simulation is obtained. Moreover, the predictive capabilities of the new solvent models are assessed by comparison to experimental data for the liquid density and relative permittivity of mixtures of EC and PC. In addition, molecular models for the anions PF6-, BF4-, and ClO4- in solutions of their lithium electrolytes in PC are developed using experimental data on the solution densities. Finally, the self-diffusion coefficients of LiPF6 in PC and in aqueous solution are predicted and compared, showing that diffusion is much slower in the organic solution due to the formation of larger solvent shells around the ions. Furthermore, an analysis of the radial distribution functions in these solutions suggests that the ions have much less impact on the structure of the solvent PC than on water.

Force field for halide and alkali ions in water based on single-ion and ion-pair thermodynamic properties for a wide range of concentrations.

A classical non-polarizable force field for the common halide (F-, Cl-, Br-, and I-) and alkali (Li+, Na+, K+, and Cs+) ions in SPC/E water is presented. This is an extension of the force field developed by Loche et al. for Na+, K+, Cl-, and Br- (JPCB 125, 8581-8587, 2021): in the present work, we additionally optimize Lennard-Jones parameters for Li+, I-, Cs+, and F- ions. Li+ and F- are particularly challenging ions to model due to their small size. The force field is optimized with respect to experimental solvation free energies and activity coefficients, which are the necessary and sufficient quantities to accurately reproduce the electrolyte thermodynamics. Good agreement with experimental reference data is achieved for a wide range of concentrations (up to 4 mol/l). We find that standard Lorentz-Berthelot combination rules are sufficient for all ions except F-, for which modified combination rules are necessary. With the optimized parameters, we show that, although the force field is only optimized based on thermodynamic properties, structural properties are reproduced quantitatively, while ion diffusion coefficients are in qualitative agreement with experimental values.

Targeting spectroscopic accuracy for dispersion bound systems from abinitio techniques: Translational eigenstates of Ne@C70.

We investigate the endofullerene system Ne@C70 by constructing a three-dimensional Potential Energy Surface (PES) describing the translational motion of the Ne atom. This is constructed from electronic structure calculations from a plethora of methods, including MP2, SCS-MP2, SOS-MP2, RPA@PBE, and C(HF)-RPA, which were previously used for He@C60 in Panchagnula et al. [J. Chem. Phys. 160, 104303 (2024)], alongside B86bPBE-25X-XDM and B86bPBE-50X-XDM. The reduction in symmetry moving from C60 to C70 introduces a double well potential along the anisotropic direction, which forms a test of the sensitivity and effectiveness of the electronic structure methods. The nuclear Hamiltonian is diagonalized using a symmetrized double minimum basis set outlined in Panchagnula and Thom [J. Chem. Phys. 159, 164308 (2023)], with translational energies having error bars ±1 and ±2 cm-1. We find no consistency between electronic structure methods as they find a range of barrier heights and minima positions of the double well and different translational eigenspectra, which also differ from the Lennard-Jones (LJ) PES given in Mandziuk and Bačić [J. Chem. Phys. 101, 2126-2140 (1994)]. We find that generating effective LJ parameters for each electronic structure method cannot reproduce the full PES nor recreate the eigenstates, and this suggests that the LJ form of the PES, while simple, may not be best suited to describe these systems. Even though MP2 and RPA@PBE performed best for He@C60, due to the lack of concordance between all electronic structure methods, we require more experimental data in order to properly validate the choice.

A transferable classical force field to describe glyme based lithium solvate ionic liquids.

A non-polarizable force field for lithium (Li+) and bis(trifluoromethanesulfonyl)imide (TFSI-) ions solvated in diglyme at around 0.2 mol fraction salt concentration was developed based on abinitio molecular dynamics (AIMD) simulations and a modified polymer consistent force field model. A force-torque matching based scheme, in conjunction with a genetic algorithm, was used to determine the Lennard-Jones (LJ) parameters of the ion-ion and ion-solvent interactions. This force field includes a partial charge scaling factor and a scaling factor for the 1-4 interactions. The resulting force field successfully reproduces the radial distribution function of the AIMD simulations and shows better agreement compared to the unmodified force field. The new force field was then used to simulate salt solutions with glymes of increasing chain lengths and different salt concentrations. The comparison of the MD simulations, using the new force field, with experimental data at different salt concentrations and AIMD simulations on equimolar concentrations of the triglyme system demonstrates the transferability of the force field parameters to longer glymes and higher salt concentrations. Furthermore, the force field appears to reproduce the features of the experimental x-ray structure factors, suggesting accuracy beyond the first solvation shell, for equimolar salt solutions using both triglyme and tetraglyme as the solvent. Overall, the new force field was found to accurately reproduce the molecular descriptions of LiTFSI-glyme systems not only at various salt concentrations but also with glymes of different chain lengths. Thus, the new force field provides a useful and accurate tool to perform in silico studies of this family of systems at the atomistic level.

A Simple Generic Model of Elastin-Like Polypeptides with Proline Isomerization.

A generic model of elastin-like polypeptides (ELP) is derived that includes proline isomerization (ProI). As a case study, conformational transition of a -[valine-proline-glycine-valine-glycine]- sequence is investigated in aqueous ethanol mixtures. While the non-bonded interactions are based on the Lennard-Jones (LJ) parameters, the effect of ProI is incorporated by tuning the intramolecular 3- and 4-body interactions known from the underlying all-atom simulations into the generic model. One of the key advantages of such a minimalistic model is that it readily decouples the effects of geometry and the monomer-solvent interactions due to the presence of ProI, thus gives a clearer microscopic picture that is otherwise rather nontrivial within the all-atom setups. These results are consistent with the available all-atom and experimental data. The model derived here may pave the way to investigate large scale self-assembly of ELPs or biomimetic polymers ingeneral.

Quantifying the Uncertainty of Force Field Selection on Adsorption Predictions in MOFs.

Comparisons between simulated and experimental adsorption isotherms in MOFs are fraught with challenges. On the experimental side, there is significant variation between isotherms measured on the same system, with a significant percentage (∼20%) of published data being considered outliers. On the simulation side, force fields are often chosen "off-the-shelf" with little or no validation. The effect of this choice on the reliability of simulated adsorption predictions has not yet been rigorously quantified. In this work, we fill this gap by systematically quantifying the uncertainty arising from force field selection on adsorption isotherm predictions. We choose methane adsorption, where electrostatic interactions are negligible, to independently study the effect of the framework Lennard-Jones parameters on a series of prototypical materials that represent the most widely studied MOF "families". Using this information, we compute an adsorption "consensus isotherm" from simulations, including a quantification of uncertainty, and compare it against a manually curated set of experimental data from the literature. By considering many experimental isotherms measured by different groups and eliminating outliers in the data using statistical analysis, we conduct a rigorous comparison that avoids the pitfalls of the standard approach of comparing simulation predictions to a single experimental data set. Our results show that (1) the uncertainty in simulated isotherms can be as large as 15% and (2) standard force fields can provide reliable predictions for some systems but can fail dramatically for others, highlighting systematic shortcomings in those models. Based on this, we offer recommendations for future simulation studies of adsorption, including high-throughput computational screening of MOFs.

Binding of Phosphate Species to Ca2+ and Mg2+ in Aqueous Solution.

Phosphate derivatives and their interaction with metal cations are involved in many important biological phenomena, so an accurate characterization of the phosphate-metal interaction is necessary to properly understand the role of phosphate-metal contacts in mediating biological function. Herein, we improved the standard 12-6 Lennard-Jones (LJ) potential via the usage of the 12-6-4 LJ model, which incorporates ion-induced dipole interactions. Via parameter scanning, we fine-tuned the 12-6-4 LJ polarizability values to obtain accurate absolute binding free energies for the phosphate anions H2PO4-, HPO42-, PO43- coordinating with Ca2+ and Mg2+. First, we modified the phosphate 12-6-4 LJ parameters to reproduce the solvation free energies of the series of phosphate anions using the thermodynamic integration (TI) method. Then, using the potential mean force (PMF) method, the polarizability of the metal-phosphate interaction was obtained. We show that the free energy profiles of phosphate ions coordinated to Ca2+ and Mg2+ generally show similar trends at longer metal-phosphate distances, while the absolute binding energy values increased with deprotonation. The resulting parameters demonstrate the flexibility of the 12-6-4 LJ-type nonbonded model and its usefulness in accurately describing cation-anion interactions.

Coarse-grained molecular dynamics model of AB diblock copolymers composed of blocks with different Lennard-Jones parameters forming lamellar structures

In thermoplastic elastomers, the structure formation of hard and soft domains and the mechanical response to deformation remain vital areas of interest. To realize the coarse-grained molecular dynamics (CGMD) simulations of systems incorporating the difference in glass transition temperature Tg between domains, we studied AB diblock copolymers (di-BCPs) with asymmetric Lennard-Jones (LJ) parameters (the strength coefficient εLJ and cutoff length rc). For instance, hard and soft domains were realized by assigning the cutoff lengths of each segment to rc,(A,A) = 2.5 (high Tg) and rc,(B,B) = 1.5 (low Tg), respectively. To identify how the cutoff length rc,(B,B) corresponds to the strength coefficient ε(B,B) in the phase separation behavior against the fixed LJ parameters for the A block (rc,(A,A) = 2.5 and ε(A,A) = 1.0), we focused on lamellar structures in which the A and B blocks possess equal segment numbers. For the asymmetric cases with rc,(B,B) < rc,(A,A), we estimated the effective ε(B,B)' on the basis of the DA/DB ratio of the partial domain spacings. We confirmed that the scaling relations (D ∼ Δε1/6, D/N0.7 ∼ Δε, and D/N1/2 ∼ ΔεN) hold, where ε(A,A) = 1, Δε = ((1 + ε(B,B)')/2 – ε(A,B)), and N denotes the number of segments per AB di-BCP chain. Therefore, this work will provide valuable insights for guiding applied research on BCPs.

FFParam-v2.0: A Comprehensive Tool for CHARMM Additive and Drude Polarizable Force-Field Parameter Optimization and Validation.

Developing production quality CHARMM force-field (FF) parameters is a very detailed process involving a variety of calculations, many of which are specific for the molecule of interest. The first version of FFParam was developed as a standalone Python package designed for the optimization of electrostatic and bonded parameters of the CHARMM additive and polarizable Drude FFs by using quantum mechanical (QM) target data. The new version of FFParam has multiple new capabilities for FF parameter optimization and validation, with an emphasis on the ability to use condensed-phase target data in optimization. FFParam-v2 allows optimization of Lennard-Jones (LJ) parameters using potential energy scans of interactions between selected atoms in a molecule and noble gases, viz., He and Ne, and through condensed-phase calculations, from which experimental observables such as heats of vaporization and free energies of solvation may be obtained. This functionality serves as a gold standard for both optimizing parameters and validating the performance of the final parameters. A new bonded parameter optimization algorithm has been introduced to account for simultaneously optimizing multiple molecules sharing parameters. FFParam-v2 also supports the comparison of normal modes and the potential energy distribution of internal coordinates towards each normal mode obtained from QM and molecular mechanics calculations. Such comparison capability is vital to validate the balance among various bonded parameters that contribute to the complex normal modes of molecules. User interaction has been extended beyond the original graphical user interface to include command-line interface capabilities that allow for integration of FFParam in workflows, thereby facilitating the automation of parameter optimization. With these new functionalities, FFParam is a more comprehensive parameter optimization tool for both beginners and advanced users.

Predicting Solvation Free Energies from the Minnesota Solvation Database Using Classical Density Functional Theory Based on the PC-SAFT Equation of State.

We critically assess the capabilities of classical density functional theory (DFT) based on the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state to predict the solvation free energies of small molecules in various hydrocarbon solvents. We compare DFT results with experimental data from the Minnesota solvation database and utilize statistical methods to analyze the accuracy of our approach, as well as its weaknesses. The mean absolute error of the solvation free energies is 3.7 kJ mol-1 for n-alkane solvents, ranging from pentane to hexadecane, with 473 solute-solvent systems. For solvents consisting of cyclic hydrocarbons (cyclohexane, benzene, toluene, and ethylbenzene) with 245 solute-solvent systems, we report a slightly larger mean absolute error of 4.2 kJ mol-1. We identify three possible sources of errors: (i) the neglect of solute-solvent and solvent-solvent Coulomb interactions, which limits the applicability of PC-SAFT DFT to nonpolar and weakly polar molecules; (ii) the solute's Lennard-Jones parameters supplied by the general AMBER force field, which are not parametrized toward solvation free energies; and (iii) the application of the Lorentz-Berthelot combining rules to the dispersive interactions between a segment of the PC-SAFT solvent and a Lennard-Jones interaction site of the solute. The approach is more accurate than standard implementations of phenomenological models in common chemistry software packages, which exhibit mean absolute errors larger than 9.12 kJ mol-1, even though newer phenomenological models achieve a mean absolute error of about 2 kJ mol-1. PC-SAFT DFT is more computationally efficient than state of the art explicit molecular simulations in combination with free energy perturbation methods. It is predictive with respect to solvation free energies, i.e., the input for the model is the (element-specific) molecular force field, the solute configuration from molecular dynamics simulations, and the (substance-specific) PC-SAFT parameters. The PC-SAFT parametrization uses pure-component data and does not require experimental solvation free energies. The PC-SAFT equation of state, without applying a DFT formalism, can also be used to calculate solvation free energies, provided that the PC-SAFT parameters for the solute are available. A large number of substances was recently parametrized by members of our group (Esper, T.; Bauer, G.; Rehner, P.; Gross, J. Ind. Eng. Chem. Res. 2023, 62), which enables a comparison to the DFT approach for 103 substances. Accurate results are obtained from the PC-SAFT equation of state with an MAE below 2.51 kJ mol-1. The DFT approach does not require PC-SAFT parameters for the solute and can be applied to all solutes that can be represented by the molecular force field.

Nonbonded Force Field Parameters from MBIS Partitioning of the Molecular Electron Density Improve Binding Affinity Predictions of the T4-Lysozyme Double Mutant.

The use of computer simulation for binding affinity prediction is growing in drug discovery. However, its wider use is constrained by the accuracy of the free energy calculations. The key sources of error are the force fields used to depict molecular interactions and insufficient sampling of the configurational space. To improve the quality of the force field, we developed a Python-based computational workflow. The workflow described here uses the minimal basis iterative stockholder (MBIS) method to determine atomic charges and Lennard-Jones parameters from the polarized molecular density. This is done by performing electronic structure calculations on various configurations of the ligand when it is both bound and unbound. In addition, we validated a simulation procedure that accounts for the protein and ligand degrees of freedom to precisely calculate binding free energies. This was achieved by comparing the self-adjusted mixture sampling and nonequilibrium thermodynamic integration methods using various protein and ligand conformations. The accuracy of predicting binding affinity is improved by using MBIS-derived force field parameters and a validated simulation procedure. This improvement surpasses the chemical precision for the eight aromatic ligands, reaching a root-mean-square error of 0.7 kcal/mol.

Tailoring parameters for QM/MM simulations: accurate modeling of adsorption and catalysis in zirconium-based metal-organic frameworks.

Quantum mechanics/molecular mechanics (QM/MM) simulations offer an efficient way to model reactions occurring in complex environments. This study introduces a specialized set of charge and Lennard-Jones parameters tailored for electrostatically embedded QM/MM calculations, aiming to accurately model both adsorption processes and catalytic reactions in zirconium-based metal-organic frameworks (Zr-MOFs). To validate our approach, we compare adsorption energies derived from QM/MM simulations against experimental results and Monte Carlo simulation outcomes. The developed parameters showcase the ability of QM/MM simulations to represent long-range electrostatic and van der Waals interactions faithfully. This capability is evidenced by the prediction of adsorption energies with a low root mean square error of 1.1 kcal mol-1 across a wide range of adsorbates. The practical applicability of our QM/MM model is further illustrated through the study of glucose isomerization and epimerization reactions catalyzed by two structurally distinct Zr-MOF catalysts, UiO-66 and MOF-808. Our QM/MM calculations closely align with experimental activation energies. Importantly, the parameter set introduced here is compatible with the widely used universal force field (UFF). Moreover, we thoroughly explore how the size of the cluster model and the choice of density functional theory (DFT) methodologies influence the simulation outcomes. This work provides an accurate and computationally efficient framework for modeling complex catalytic reactions within Zr-MOFs, contributing valuable insights into their mechanistic behaviors and facilitating further advancements in this dynamic area of research.

MetalDock: An Open Access Docking Tool for Easy and Reproducible Docking of Metal Complexes.

Despite the proven potential of metal complexes as therapeutics, the lack of computational tools available for the high-throughput screening of their interactions with proteins is a limiting factor toward clinical developments. To address this challenge, we introduce MetalDock, an easy-to-use, open access docking software for docking metal complexes to proteins. Our tool integrates the AutoDock docking engine with three well-known quantum software packages to automate the docking of metal-organic complexes to proteins. We used a Monte Carlo sampling scheme to obtain the missing Lennard-Jones parameters for 12 metal atom types and demonstrated that these parameters generalize exceptionally well. Our results show that the poses obtained by MetalDock are highly accurate, as they predict the binding geometries experimentally determined by crystal structures with high spatial reproducibility. Three different case studies are presented that demonstrate the versatility of MetalDock for the docking of diverse metal-organic compounds to different biomacromolecules, including nucleic acids.

Collisional broadening of molecular rovibronic lines

To meet burning needs of high-resolution pressure-induced line-shape parameters in the UV/visible regions for hot-temperature industrial and atmospheric applications as well as current and future space missions, phase-shift theory is examined in its historical context, tested and revisited using accurate numerical potentials and advanced trajectory models. First, a general analysis for arbitrary molecular systems is conducted in terms of the dimensionless parameter α determined by the differences of the Lennard-Jones parameters in the final and initial electronic absorber’s states. Temperature dependence, use of the power law and influence of Maxwell–Boltzmann averaging over relative velocities are addressed. Then, interaction-potential calculations are attempted for some representative molecular pairs (NO-Ar, NO-N2, OH-Ar and OH-N2) and the isotropic parts are fitted using the 12-6 Lennard-Jones form to get room and high-temperature line-broadening and line-shift coefficients which are compared to available measurements. It is shown that the phase-shift theory in its standard rectilinear-trajectory formulation provides linewidth and shift estimates accurate within 30%–40%. Attempted improvements using numerical potentials and curved trajectories lead to closer matches with measurements for some cases but also worsen the agreement for others. To ensure better theoretical predictions, introduction of correction terms to the usual phase-shift integral is suggested.

CGCompiler: Automated Coarse-Grained Molecule Parametrization via Noise-Resistant Mixed-Variable Optimization.

Coarse-grained force fields (CG FFs) such as the Martini model entail a predefined, fixed set of Lennard-Jones parameters (building blocks) to model virtually all possible nonbonded interactions between chemically relevant molecules. Owing to its universality and transferability, the building-block coarse-grained approach has gained tremendous popularity over the past decade. The parametrization of molecules can be highly complex and often involves the selection and fine-tuning of a large number of parameters (e.g., bead types and bond lengths) to optimally match multiple relevant targets simultaneously. The parametrization of a molecule within the building-block CG approach is a mixed-variable optimization problem: the nonbonded interactions are discrete variables, whereas the bonded interactions are continuous variables. Here, we pioneer the utility of mixed-variable particle swarm optimization in automatically parametrizing molecules within the Martini 3 coarse-grained force field by matching both structural (e.g., RDFs) as well as thermodynamic data (phase-transition temperatures). For the sake of demonstration, we parametrize the linker of the lipid sphingomyelin. The important advantage of our approach is that both bonded and nonbonded interactions are simultaneously optimized while conserving the search efficiency of vector guided particle swarm optimization (PSO) methods over other metaheuristic search methods such as genetic algorithms. In addition, we explore noise-mitigation strategies in matching the phase-transition temperatures of lipid membranes, where nucleation and concomitant hysteresis introduce a dominant noise term within the objective function. We propose that noise-resistant mixed-variable PSO methods can both improve and automate parametrization of molecules within building-block CG FFs, such as Martini.

Exploring the parameter space of an endohedral atom in a cylindrical cavity.

Endohedral fullerenes, or endofullerenes, are chemical systems of fullerene cages encapsulating single atoms or small molecules. These species provide an interesting challenge of Potential Energy Surface determination as examples of non-covalently bonded, bound systems. While the majority of studies focus on C60 as the encapsulating cage, introducing some anisotropy by using a different fullerene, e.g., C70 can unveil a double well potential along the unique axis. By approximating the potential as a pairwise Lennard-Jones (LJ) summation over the fixed C cage atoms, the parameter space of the Hamiltonian includes three tunable variables: (M, ɛ, σ) representing the mass of the trapped species, the LJ energy, and length scales respectively. Fixing the mass and allowing the others to vary can imitate the potentials of endohedral species trapped in more elongated fullerenes. We choose to explore the LJ parameter space of an endohedral atom in C70 with ɛ ∈ [20, 150 cm-1], and σ ∈ [2.85, 3.05 Å]. As the barrier height and positions of these wells vary between [1, 264 cm-1] and [0.35, 0.85 Å] respectively, using a 3D direct product basis of 1D harmonic oscillator (HO) wavefunctions centred at the origin where there is a local maximum is unphysical. Instead we propose the use of a non-orthogonal basis set, using 1D HO wavefunctions centred in each minimum and compare this to other choices. The ground state energy of the X@C70 is tracked across the LJ parameter space, along with its corresponding nuclear translational wavefunctions. A classification of the wavefunction characteristics, namely the prolateness and "peanut-likeness" based on its statistical moments is also proposed. Excited states of longer fullerenes are assigned quantum numbers, and the fundamental transitions of Ne@C70 are tracked across the parameter space.

Monte Carlo simulation of the crystallization of polyethylene nanocomposites with different shape nanofillers

Monte Carlo simulation of coarse-grained models of polyethylene (PE) nanocomposites was developed to study the effect of nanofiller shapes (nanosphere, nanoplate and nanostick) on the early stage of polymer crystallization under stepwise cooling from the melts. The “polymer forcefield” to describe intra- and intermolecular interaction is composed of the rotational isomeric state (RIS) model of PE and the Lennard-Jones (LJ) potential energetics of ethylene units, respectively. Carbon-based nanofillers were used such that polymer-nanofiller interaction was treated using the same LJ parameters as polymer–polymer interaction. The content of trans conformation and the chain/bond order parameter were determined to quantify the degree of polymer crystallization. Simulation suggests that PE nanocomposites filled with nanostick and nanoplate tend to induce earlier crystalline formation and have more ordered structures, especially nanocomposites with nanoplate filler. In contrast, PE nanocomposites filled with nanosphere exhibit slower crystallization with a lower amount of trans fraction and, as a result, form less ordered structures.

Self-Consistent Implementation of a Solvation Free Energy Framework to Predict the Salt Solubilities of Six Alkali Halides.

To assess the salt solubilities of six alkali halides in aqueous systems, we proposed a thermodynamic cycle and an efficient molecular modeling methodology. The Gibbs free energy changes for vaporization, dissociation, and dissolution were calculated using the experimental data of ionic thermodynamic properties obtained from the NBS tables. Additionally, the Marcus' and Tissandier's solvation free energy data for Li+, Na+, K+, Cl-, and Br- ions were compared with the conventional solvation free energies by substituting into our self-consistent thermodynamic cycle. Furthermore, Tissandier's absolute solvation free energy data were used as the training set to refit the Lennard-Jones parameters of OPLS-AA force field for ions. To predict salt solubilities, an assumption of a pseudo-solvent was proposed to characterize the coupling work of a solute with its environment from infinitely diluted to saturated solutions, indicating that the Gibbs energy change of solvation process is a function of ionic strength. Following the self-consistency of the cycle, the newly derived formulas were used to determine the salt solubilities by interpolating the intersection of Gibbs free energy of dissolution and the zero free energy line. The refined ion parameters can also predict the structure and thermodynamic properties of aqueous electrolyte solutions, such as densities, pair correlation functions, hydration numbers, mean activity coefficients, vapor pressures, and the radial dependences of the net charge at 298.15 K and 1 bar. Our method can be used to characterize the solid-liquid equilibria of ions or charged particles in aqueous systems. Furthermore, for highly concentrated strong electrolyte systems, it is essential to introduce accurate water models and polarizable force fields.