Exploration of Entropy Pair Functional Theory.

Evaluation of the entropy from molecular dynamics (MD) simulation remains an outstanding challenge. The standard approach requires thermodynamic integration across a series of simulations. Recent work Nicholson et al. demonstrated the ability to construct a functional that returns excess entropy, based on the pair correlation function (PCF); it was capable of providing, with acceptable accuracy, the absolute excess entropy of iron simulated with a pair potential in both fluid and crystalline states. In this work, the general applicability of the Entropy Pair Functional Theory (EPFT) approach is explored by applying it to three many-body interaction potentials. These potentials are state of the art for large scale models for the three materials in this study: Fe modelled with a modified embedded atom method (MEAM) potential, Cu modelled with an MEAM and Si modelled with a Tersoff potential. We demonstrate the robust nature of EPFT in determining excess entropy for diverse systems with many-body interactions. These are steps toward a universal Entropy Pair Functional, EPF, that can be applied with confidence to determine the entropy associated with sophisticated optimized potentials and first principles simulations of liquids, crystals, engineered structures, and defects.

Entropy Pair Functional Theory: Direct Entropy Evaluation Spanning Phase Transitions.

We prove that, within the class of pair potential Hamiltonians, the excess entropy is a universal, temperature-independent functional of the density and pair correlation function. This result extends Henderson's theorem, which states that the free energy is a temperature dependent functional of the density and pair correlation. The stationarity and concavity of the excess entropy functional are discussed and related to the Gibbs-Bugoliubov inequality and to the free energy. We apply the Kirkwood approximation, which is commonly used for fluids, to both fluids and solids. Approximate excess entropy functionals are developed and compared to results from thermodynamic integration. The pair functional approach gives the absolute entropy and free energy based on simulation output at a single temperature without thermodynamic integration. We argue that a functional of the type, which is strictly applicable to pair potentials, is also suitable for first principles calculation of free energies from Born-Oppenheimer molecular dynamics performed at a single temperature. This advancement has the potential to reduce the evaluation the free energy to a simple modification to any procedure that evaluates the energy and the pair correlation function.

Rotating phenyl rings as a guest-dependent switch in two-dimensional metal-organic frameworks.

A semirigid bis(1,2,4-triazole) ligand binds in a syn conformation between copper(I) chains to form a series of two-dimensional metal-organic frameworks that display a topology of fused one-dimensional metal-organic nanotubes. These anisotropic frameworks undergo two different transformations in the solid state as a function of solvation. The 2D sheet layers can expand or contract, or, more remarkably, the phenyl rings can rotate between two distinct positions. Rotation of the phenyl rings allows for the adjustment of the tube size, depending on the guest molecules present. This "gate" effect along the 1D tubes has been characterized through single-crystal X-ray diffraction. The transformations can also be followed by powder X-ray diffraction (PXRD) and solid-state (13)C cross-polarization magic-angle-spinning (CP-MAS) NMR. Whereas PXRD cannot differentiate between transformations, solid-state (13)C CP-MAS NMR can be employed to directly monitor phenyl rotation as a function of solvation, suggesting that this spectroscopic method is a powerful approach for monitoring breathing in this novel class of frameworks. Finally, simulations show that rotation of the phenyl ring from a parallel orientation to a perpendicular orientation occurs at the cost of framework-framework energy and that this energetic cost is offset by stronger framework-solvent interactions.

Nanoscale Stabilization Mechanism of Sodium Sulfate Decahydrate at Polyelectrolyte Interfaces.

Sodium sulfate decahydrate (SSD) is a low-cost phase-change material (PCM) for thermal energy storage applications that offers substantial melting enthalpy and a suitable temperature range for near-ambient applications. However, SSD's consistent phase separation with decreased melting enthalpy over repeated thermal cycles limits its application as a PCM. Sulfonated polyelectrolytes, such as dextran sulfate sodium (DSS), have shown great effectiveness in preventing phase separation in SSD. However, there is limited understanding of the stabilization mechanism of SSD by DSS at the atomic length and time scales. In this work, we investigate SSD stabilization via DSS using neutron scattering and molecular dynamics (MD) simulations. Neutron scattering and pair distribution function analysis revealed the structural evolution of the PCM samples below and above the phase change temperatures. MD simulations revealed that water from the hydrate structure migrates from the hydrate crystal to the SSD-DSS interfacial region upon melting. The water is stabilized at this interface by aggregation around the hydrophilic sulfonic acid groups attached to the backbone of the polyelectrolyte. This architecture retains water near the dehydrated sodium sulfate, preventing phase separation and, consequently, stabilizing SSD rehydration. This work provides atomistic insight into selecting and designing stable and high-performance PCMs for heating and cooling applications in building technologies.

Novel Kraft Softwood Lignin-Derived Carbon Quantum Dots: Synthesis, Characterization, and In Vitro Cytocompatibility.

Carbon quantum dots (CQDs) have been investigated for biomedical applications in medical imaging due to their fluorescent properties, overall long-term stability, and excellent cytocompatibility and biocompatibility. Lignin is an organic polymer in the tissues of woody plants. It is also considered a byproduct of the wood and pulp industries. Hence, it presents as a renewable source of carbon nanoparticles. In this study, we report the synthesis and material and biological characterization of two colloidal suspensions of CQDs in water derived from lignin-based carbon. One was the native form of CQDs derived from lignin carbon, and the second was doped with nitrogen to evaluate material differences. Material characterization was carried out using various commonly used techniques, including Fourier transform infrared spectroscopy (FTIR), emission and absorbance spectra, zeta potential, transmission electron microscopy (TEM), and scanning electron microscopy (SEM). Thin films of CQDs were formed on glass and silicon substrates to assess the in vitro cytocompatibility with human mesenchymal stem cells (hMSCs). Observations suggest that the two forms of CQDs promote cell attachment within 24 h and sustain it for at least 7 days. The overall structure and shape of cells suggest a lack of any adverse or toxic effects of CQDs. The data lay down the novel foundation to support the use of lignin-derived CQDs in tissue engineering applications.

Kinetics of methane hydrate decomposition studied via in situ low temperature X-ray powder diffraction.

Gas hydrate is known to have a slowed decomposition rate at ambient pressure and temperatures below the melting point of ice. As hydrate exothermically decomposes, gas is released and water of the clathrate cages transforms into ice. Based on results from the decomposition of three nominally similar methane hydrate samples, the kinetics of two regions, 180-200 and 230-260 K, within the overall decomposition range 140-260 K, were studied by in situ low temperature X-ray powder diffraction. The kinetic rate constants, k(a), and the reaction mechanisms, n, for ice formation from methane hydrate were determined by the Avrami model within each region, and activation energies, E(a), were determined by the Arrhenius plot. E(a) determined from the data for 180-200 K was 42 kJ/mol and for 230-260 K was 22 kJ/mol. The higher E(a) in the colder temperature range was attributed to a difference in the microstructure of ice between the two regions.

Stabilization of low-cost phase change materials for thermal energy storage applications.

Sodium sulfate decahydrate (Na2SO4.10H2O, SSD), a low-cost phase change material (PCM), can store thermal energy. However, phase separation and unstable energy storage capacity (ESC) limit its use. To address these concerns, eight polymer additives-sodium polyacrylate (SPA), carboxymethyl cellulose (CMC), Fumed silica (SiO2), potassium polyacrylate (PPA), cellulose nanofiber (CNF), hydroxyethyl cellulose (HEC), dextran sulfate sodium (DSS), and poly(sodium 4-styrenesulfonate) (PSS)-were used to explore several stabilization mechanisms. The ESC of PCMs deteriorated when thickeners, SPA, PPA, and CNF, were added. DSS-modified PCMs exhibited greater stability up to 150 cycles. Rheology measurements indicated that DSS did not impact SSD viscosity significantly during stabilization. Dynamic light scattering showed that DSS reduces SSD particle size and electrostatically suspends salt particles in a stable homogeneous solution, avoiding phase separation. This study proposes a promising method to improve the thermal stability of salt hydrate PCMs by utilizing polyelectrolyte-salt hydrate mixture for thermal energy storage applications.

Local Structure Analysis and Modelling of Lignin-Based Carbon Composites through the Hierarchical Decomposition of the Radial Distribution Function.

Carbonized lignin has been proposed as a sustainable and domestic source of activated, amorphous, graphitic, and nanostructured carbon for many industrial applications as the structure can be tuned through processing conditions. However, the inherent variability of lignin and its complex physicochemical structure resulting from feedstock and pulping selection make the Process-Structure-Property-Performance (PSPP) relationships hard to define. In this work, radial distribution functions (RDFs) from synchrotron X-ray and neutron scattering of lignin-based carbon composites (LBCCs) are investigated using the Hierarchical Decomposition of the Radial Distribution Function (HDRDF) modelling method to characterize the local atomic environment and develop quantitative PSPP relationships. PSPP relationships for LBCCs defined by this work include crystallite size dependence on lignin feedstock as well as increasing crystalline volume fraction, nanoscale composite density, and crystallite size with increasing reduction temperature.

A coarse-grained model for polyethylene glycol polymer.

A coarse-grained (CG) model of polyethylene glycol (PEG) was developed and implemented in CG molecular dynamics (MD) simulations of PEG chains with degree of polymerization (DP) 20 and 40. In the model, two repeat units of PEG are grouped as one CG bead. Atomistic MD simulation of PEG chains with DP = 20 was first conducted to obtain the bonded structural probability distribution functions (PDFs) and nonbonded pair correlation function (PCF) of the CG beads. The bonded CG potentials are obtained by simple inversion of the corresponding PDFs. The CG nonbonded potential is parameterized to the PCF using both an inversion procedure based on the Ornstein-Zernike equation with the Percus-Yevick approximation (OZPY(-1)) and a combination of OZPY(-1) with the iterative Boltzmann inversion (IBI) method (OZPY(-1)+IBI). As a simple one step method, the OZPY(-1) method possesses an advantage in computational efficiency. Using the potential from OZPY(-1) as an initial guess, the IBI method shows fast convergence. The coarse-grained molecular dynamics (CGMD) simulations of PEG chains with DP = 20 using potentials from both methods satisfactorily reproduce the structural properties from atomistic MD simulation of the same systems. The OZPY(-1)+IBI method yields better agreement than the OZPY(-1) method alone. The new CG model and CG potentials from OZPY(-1)+IBI method was further tested through CGMD simulation of PEG with DP = 40 system. No significant changes are observed in the comparison of PCFs from CGMD simulations of PEG with DP = 20 and 40 systems indicating that the potential is independent of chain length.

Effective potentials between nanoparticles in suspension.

Results of molecular dynamics simulations are presented for the pair distribution function between nanoparticles in an explicit solvent as a function of nanoparticle diameter and interaction strength between the nanoparticle and solvent. The effect of including the solvent explicitly is demonstrated by comparing the pair distribution function of nanoparticles to that in an implicit solvent. The nanoparticles are modeled as a uniform distribution of Lennard-Jones particles, while the solvent is represented by standard Lennard-Jones particles. The diameter of the nanoparticle is varied from 10 to 25 times that of the solvent for a range of nanoparticle volume fractions. As the strength of the interactions between nanoparticles and the solvent increases, the solvent layer surrounding the nanoparticle is formed which increases the effective radii of the nanoparticles. The pair distribution functions are inverted using the Ornstein-Zernike integral equation to determine an effective pair potential between the nanoparticles mediated by the introduction of an explicit solvent.

Lithium and Sodium Ion Binding Mechanisms and Diffusion Rates in Lignin-Based Hard Carbon Models.

Hard carbons are the primary candidate for the anode of next-generation sodium-ion batteries for large-scale energy storage, as they are sustainable and can possess high charge capacity and long cycle life. These properties along with diffusion rates and ion storage mechanisms are highly dependent on nanostructures. This work uses reactive molecular dynamics simulations to examine lithium and sodium ion storage mechanisms and diffusion in lignin-based hard carbon model systems with varying nanostructures. It was found that sodium will preferentially localize on the surface of curved graphene fragments, while lithium will preferentially bind to the hydrogen dense interfaces of crystalline and amorphous carbon domains. The ion storage mechanisms are explained through ion charge and energy distributions in coordination with snapshots of the simulated systems. It was also revealed that hard carbons with small crystalline volume fractions and moderately sized sheets of curved graphene will yield the highest sodium-ion diffusion rates at ∼10-7 cm2/s. Self-diffusion coefficients were determined by mean square displacement of ions in the models with extension through a confined random walk theory.

Hierarchical Lignin-Based Carbon Matrix and Carbon Dot Composite Electrodes for High-Performance Supercapacitors.

This work adopts an efficient chemical-wet method to build a three-dimensional (3D) carbon composite as an electrode material for high-performance supercapacitors (SCs). Carbon dots (CDs), prepared by thermal pyrolysis of citric acid and urea under microwaves at 280 °C, are homogeneously coated onto lignin-based activated carbons (ACs), thus forming the 3D composites possessing an interior surface decorated with CD binding sites. Benefiting from the hydrophilicity and ultrafine size of CDs, the affinity of the electrode surface toward aqueous electrolytes is significantly improved with the addition of CDs, leading to the enhanced effective surface area (i.e., abundant electroactive sites) and a decreased ionic diffusion path. The capacitance of the SCs is improved from 125.8 to 301.7 F g-1 with CD addition. The SC with CD addition possesses improved cycle stability with a coulombic efficiency around 100% after 3000 cycles. After cycling, the ion diffusion coefficient of the CD@AC-11 electrode is enhanced by 25.5 times as compared to that of the pristine AC one. This unique and robust carbon framework can be utilized for engineering the desired pore structure and micropore/mesopore fraction within the AC electrodes. This strategy of CD@AC electrodes demonstrates a promising route for using renewable porous carbon materials in advanced energy-storage devices.

Local structure and distortions of mixed methane-carbon dioxide hydrates.

A vast source of methane is found in gas hydrate deposits, which form naturally dispersed throughout ocean sediments and arctic permafrost. Methane may be obtained from hydrates by exchange with hydrocarbon byproduct carbon dioxide. It is imperative for the development of safe methane extraction and carbon dioxide sequestration to understand how methane and carbon dioxide co-occupy the same hydrate structure. Pair distribution functions (PDFs) provide atomic-scale structural insight into intermolecular interactions in methane and carbon dioxide hydrates. We present experimental neutron PDFs of methane, carbon dioxide and mixed methane-carbon dioxide hydrates at 10 K analyzed with complementing classical molecular dynamics simulations and Reverse Monte Carlo fitting. Mixed hydrate, which forms during the exchange process, is more locally disordered than methane or carbon dioxide hydrates. The behavior of mixed gas species cannot be interpolated from properties of pure compounds, and PDF measurements provide important understanding of how the guest composition impacts overall order in the hydrate structure.

Effect of charge distribution on RDX adsorption in IRMOF-10.

Quantum mechanical (QM) calculations, classical grand canonical Monte Carlo (GCMC) simulations, and classical molecular dynamics (MD) simulations are performed to test the effect of charge distribution on hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX) adsorption and diffusion in IRMOF-10. Several different methods for mapping QM electron distributions onto atomic point charges are explored, including the electrostatic potential (ESP) method, Mulliken population analysis, Lowdin population analysis, and natural bond orbital analysis. Classical GCMC and MD simulations of RDX in IRMOF-10 are performed using 15 combinations of charge sources of RDX and IRMOF-10. As the charge distributions vary, interaction potential energies, the adsorption loading, and the self-diffusivities are significantly different. None of the 15 combinations are able to quantitatively capture the dependence of the energy of adsorption on local configuration of RDX as observed in the QM calculations. We observe changes in the charge distributions of RDX and IRMOF-10 with the introduction of an RDX molecule into the cage. We also observe a large dispersion contribution to the interaction energy from QM calculations that is not reproduced in the classical simulations, indicating that the source of discrepancy may not lie exclusively with the assignment of charges.

Comparison of the hydration and diffusion of protons in perfluorosulfonic acid membranes with molecular dynamics simulations. scui@utk.edu.

Classical molecular dynamics (MD) simulations were performed to determine the hydrated morphology and hydronium ion diffusion coefficients in two different perfluorosulfonic acid (PFSA) membranes as functions of water content. The structural and transport properties of 1143 equivalent weight (EW) Nafion, with its relatively long perfluoroether side chains, are compared to the short-side-chain (SSC) PFSA ionomer at an EW of 977. The separation of the side chains was kept uniform in both ionomers consisting of -(CF 2) 15- units in the backbone, and the degree of hydration was varied from 5 to 20 weight % water. The MD simulations indicated that the distribution of water clusters is more dispersed in the SSC ionomer, which leads to a more connected water-channel network at the low water contents. This suggests that the SSC ionomer may be more inclined to form sample-spanning aqueous domains through which transport of water and protons may occur. The diffusion coefficients for both hydronium ions and water molecules were calculated at hydration levels of 4.4, 6.4, 9.6, and 12.8 H 2O/SO 3H for each ionomer. When compared to experimental proton diffusion coefficients, this suggests that as the water content is increased the contribution of proton hopping to the overall proton diffusion increases.

A quantum mechanical study of the decomposition of CF3OCF3 and CF3CF2OCF2CF3 in the presence of AlF3.

The effect of AlF3 on the decomposition of CF3OCF3 and CF3CF2OCF2CF3 is investigated using ab initio theory. Previous work by Pancansky et al. [Pacansky, J.; Waltman, R. J. J Fluorine Chem. 1997, 83, 41] showed that AlF3 significantly reduces the activation energy of the decomposition of CF3OCF3 due to the strong electrostatic interaction between the aluminum trifluoride and the reactant. In this work, a new transition-state structure and reaction mechanism have been identified for the decomposition of CF3OCF3 in the presence of AlF3. This new mechanism shows that AlF3 functions by accepting a fluorine atom from one carbon and simultaneously donating a fluorine atom to the other carbon. We show that the same pathway is obtained independently of the level of theory. The reaction rate, generated via statistical mechanics and transition-state theory, is 2-3 orders of magnitude higher for the new transition state when compared to that of the old one. The study was also performed for CF3CF2OCF2CF3 in order to ascertain the effect of chain length on the reaction mechanism and rate. We find that an analogous transition state, with lower activation energy, provides the lowest-energy path for decomposition of the longer chain.

Measuring coexisting densities from a two-phase molecular dynamics simulation by voronoi tessellations.

A new algorithm is presented that allows for the determination of bulk liquid and vapor densities from a two-phase Molecular Dynamics (2phiMD) simulation. This new method does not use any arbitrary cutoffs for phase definitions; rather it uses single-phase simulations as a self-consistency check. The method does not use any spatial bins for generating histograms of local properties, thereby avoiding the statistical issues associated with bins. Finally, it allows one to approach very close to the critical point. The new method utilizes Voronoi tessellations to determine the molecular volume of every point at every instance in a molecular dynamics simulation. Since the molecular volume is calculated throughout the simulation, statistical parameters such as the average molecular volume and average molecular variance are easy to obtain. To define the phases, the normalized variance of the molecular volume from 1phiMD and 2phiMD is used as a self-consistency check. The new method gives new insight into the nature of the near-subcritical fluid. The critical properties from this analysis are T(c) = 1.293 and rho(c) = 0.313. Direct simulation of the two-phase system was performed up to a temperature of 1.292. The results show excellent agreement to experimental results and Gibbs Ensemble Monte Carlo for coexisting densities. We see that well below the critical temperature, some particles are neither liquid nor vapor. These interfacial particles are primarily, but not exclusively, concentrated at the bulk interface. However, as we approach the critical point, some particles are considered both liquid and vapor. These interfacial particles are distributed through the system.

Vapor-liquid equilibrium of ethanol by molecular dynamics simulation and Voronoi tessellation.

Explicit atom simulations of ethanol were performed by molecular dynamics using the OPLS-AA potential. The phase densities were determined self-consistently by comparing the distribution of Voronoi volumes from two-phase and single-phase simulations. This is the first demonstration of the use of Voronoi tessellation in two-phase molecular dynamics simulation of polyatomic fluids. This technique removes all arbitrary determination of the phase diagram by using single-phase simulations to self-consistently validate the probability distribution of Voronoi volumes of the liquid and vapor phases extracted from the two-phase molecular dynamics simulations. Properties from the two phase simulations include critical temperature, critical density, critical pressure, phase diagram, surface tension, and molecule orientation at the interface. The simulations were performed from 375 to 472 K. Also investigated were the vapor pressure and hydrogen bonding along the two phase envelope. The phase envelope agrees extremely well with literature values from GEMC at lower temperatures. The combined use of two-phase molecular dynamics simulation and Voronoi tessellation allows us to extend the phase diagram toward the critical point.

A molecular dynamics study of a nafion polyelectrolyte membrane and the aqueous phase structure for proton transport.

A molecular dynamics simulation study of hydrated Nafion at water contents ranging from 5 to 20 wt % was performed to examine the structure and dynamics of the hydrated polyelectrolyte system. The simulations show that the system forms segregated hydrophobic regions consisting primarily of the polymer backbone and hydrophilic regions with an inhomogeneous water distribution. We find that the water clustering strongly depends on the water content. At low water content, only isolated small water clusters are formed. As the water content increases, it becomes increasingly possible that a predominant majority of water molecules form a single cluster, suggesting that the hydrophilic regions become connected. We characterize the atomic structures formed within the system by various atomic pair correlation functions. The water structure factor shows a peak at q values corresponding to an intercluster distance about 2.5 nm and greater. With increasing water content, the distance moves to larger values, consistent with findings from scattering experiments. We find that the degree of solvation of hydronium ions by water molecules is a strong function of water content. At 5 wt %, a majority of the hydronium ions are hydrated by no more than two water molecules, prohibiting structural diffusion. As water content increases, the hydronium ions continue to become increasingly hydrated, resulting in structures capable of forming eigen ions, a necessary step in structural diffusion. Addressing the experimentally observed fact that conductivity in these membranes abruptly drops near 5 wt %, we find that both the local structure of the poorly hydrated hydronium ions and the disconnected nature of the global morphology of the water nanonetwork at low water content should contribute to poor conductivity.

Li-Ion Localization and Energetics as a Function of Anode Structure.

In this work, we study the effect of carbon composite anode structure on the localization and energetics of Li-ions. A computational molecular dynamics study is combined with experimental results from neutron scattering experiments to understand the effect of composite density, crystallite size, volume fraction of crystalline carbon, and ion loading on the nature of ion storage in novel, lignin-derived composite materials. In a recent work, we demonstrated that these carbon composites display a fundamentally different mechanism for Li-ion storage than traditional graphitic anodes. The edges of the crystalline and amorphous fragments of aromatic carbon that exist in these composites are terminated by hydrogen atoms, which play a crucial role in adsorption. In this work, we demonstrate how differences in composite structure due to changes in the processing conditions alter the type and extent of the interface between the amorphous and crystalline domains, thus impacting the nature of Li-ion storage. The effects of structural properties are evaluated using a suite of pair distribution functions as well as an original technique to extract archetypal structures, in the form of three-dimensional atomic density distributions, from highly disordered systems. The energetics of Li-ion binding are understood by relating changes in the energy and charge distributions to changes in structural properties. The distribution of Li-ion energies reveals that some structures lead to greater chemisorption, while others have greater physisorption. Carbon composites with a high volume fraction of small crystallites demonstrate the highest ion storage capacity because of the high interfacial area between the crystalline and amorphous domains. At these interfaces, stable H atoms, terminating the graphitic crystallites, provide favorable sites for reversible Li adsorption.