Density dependence of structure of supercritical carbon dioxide along an isotherm

A high pressure cell for supercritical CO₂ on-line chemical reactions studied with X-ray techniques

A versatile high pressure X-ray sample cell has been developed for conducting in situ time-resolved X-ray scattering experiments in the pressure and temperature regime required (pressures up to 210 bars and temperatures up to 120 °C) for chemical reactions in supercritical fluids. The large exit opening angle of the cell allows simultaneous performance of SAXS-WAXS experiments. Diamond windows are used in order to benefit from the combination of maximum strength, minimal X-ray absorption and chemical inertia. The sample cell can also be utilised for X-ray spectroscopy experiments over a wide range of photon energies. Results of the online synthesis of a block copolymer, poly(methyl methacrylate-block-poly(benzyl methacrylate), by Reversible Addition-Fragmentation Chain Transfer (RAFT) in a supercritical CO2 dispersion polymerisation will be discussed. The contribution of the density fluctuations, as function of temperature, to the X-ray scattering signal has been quantified in order to allow appropriate background subtractions.

Structural Evolution of Supercritical CO2 across the Frenkel Line

Here, we study structural properties of the supercritical carbon dioxide and discover the existence of persistent medium-range order correlations, which make supercritical carbon dioxide nonuniform and heterogeneous on an intermediate length scale. We report on the CO2 heterogeneity shell structure where, in the first shell, both carbon and oxygen atoms experience gas-like-type interactions with short-range order correlations while within the second shell, oxygen atoms essentially exhibit a liquid-like type of interactions due to localization of transverse-like phonon packets. Importantly, we highlight a catalytic role of atoms inside of the nearest-neighbor heterogeneity shell in providing a mechanism for diffusion and proving the existence of an additional thermodynamic boundary in the supercritical carbon dioxide on an intermediate length scale. Finally, we discuss important implications for answering the intriguing question whether Venus may have had CO2 oceans and urge for an experimental detection of this persistent local-order heterogeneity.

Molecular simulations of carbon dioxide and water: cation solvation

Proposed carbon dioxide sequestration scenarios in sedimentary reservoirs require investigation into the interactions between supercritical carbon dioxide, brines, and the mineral phases found in the basin and overlying caprock. Molecular simulations can help to understand the partitioning of metal cations between aqueous solutions and supercritical carbon dioxide where limited experimental data exist. In this effort, we used classical molecular dynamics simulations to compare the solvation of alkali and alkaline-earth metal cations in water and liquid CO(2) at 300 K by combining a flexible simple point charge model for water and an accurate flexible force field for CO(2). Solvation energies for these cations are larger in water than in carbon dioxide, suggesting that they will partition preferentially into water. In both aqueous and CO(2) solutions, the solvation energies decrease with cation size and increase with cation charge. However, changes in solvation energy with ionic radii are smaller in CO(2) than in water suggesting that the partitioning of cations into CO(2) will increase with ion size. Simulations of the interface between aqueous solution and supercritical CO(2) support this suggestion in that some large cations (e.g., Cs(+) and K(+)) partition into the CO(2) phase, often with a partial solvation sphere of water molecules.

Solvation and evolution dynamics of an excess electron in supercritical CO2

We present an ab initio molecular dynamics simulation of the dynamics of an excess electron solvated in supercritical CO2. The excess electron can exist in three types of states: CO2-core localized, dual-core localized, and diffuse states. All these states undergo continuous state conversions via a combination of long lasting breathing oscillations and core switching, as also characterized by highly cooperative oscillations of the excess electron volume and vertical detachment energy. All of these oscillations exhibit a strong correlation with the electron-impacted bending vibration of the core CO2, and the core-switching is controlled by thermal fluctuations.

A COMPUTER SIMULATION STUDY ON LEWIS ACID–BASE INTERACTIONS AND COOPERATIVE C-H⋯O WEAK HYDROGEN BONDING IN VARIOUS CO2 COMPLEXES

The Lewis acid–base interaction and cooperative C-H⋯O weak hydrogen bonding have been widely suggested as two key factors in the solubility of CO2 -philic materials. In this work, both ab initio and Monte Carlo simulations were performed to investigate the properties of the two important interactions between CO2 and several common organic molecules. Binding energies, geometries and charge transfer were calculated by ab initio method, showing that the mutual enhancement between the two sorts of interactions plays an important role in the stability of the CO2 complexes. Monte Carlo simulations were employed to investigate the effect of many-body interactions in real solutions. The results show that the many-body interactions also have a significant impact on the energetic and geometric properties of the CO2 complexes. Moreover, the self-aggregation of strong polar molecules will greatly weaken the effective Lewis acid–base interaction due to the zone overlapping, which needs to be taken into account in the design of future CO2 -philes.

Broadband electric spectroscopy at high CO2 pressure: dipole moment of CO2 and relaxation phenomena of the CO2-poly(vinyl chloride) system

Broadband electric spectroscopy (BES) is a technique that shows promise in studying the interactions of dense or supercritical gases with polymers, particularly with respect to chain mobility. Polymers that are treated with dense gases show a reduction in the viscosity, glass transition, and melting temperature. A high pressure cell for BES has been constructed that can be used from ambient temperature and pressure to 353 K and 15 MPa and over a frequency range from 20 Hz to 1 MHz. In the past, the dielectric constant of CO(2) was determined by measurements at only one or two frequency values. New instrumentation and technology allow this experiment to be expanded to cover a wider frequency range. BES measurements of CO(2) do not show any relaxation peaks in the permittivity from 20 Hz to 1 MHz and 1 to 6 MPa. By these measurements, the CO(2) dielectric constant was evaluated between 0.1 and 6 MPa. Cell testing with poly(vinyl chloride) (PVC) at 323 K and CO(2) pressures from 0.1 to 13 MPa indicate an increase in the chain segmental motion at high pressures resulting from a reduction in the glass transition temperature of the PVC-CO(2) system due to plasticization by CO(2).

Molecular dynamics simulation of benzene-propene-cumene mixtures in different phases

Molecular dynamics simulations have been performed to study the microscopic configuration and dynamic behavior of mixtures of benzene, propene, and cumene for the cumene synthesis process. The comparisons have been made for the intermolecular radial distribution functions of the binary and ternary mixtures at the conditions that are near, below, and above their respective critical points. The results have shown that in both binary and ternary mixtures propene molecules have a small tendency to cluster in the liquid state, but at supercritical conditions they tend to be uniformly distributed. Contrary to propene, cumene molecules have a tendency to cluster in ternary mixtures. A moderate local density augmentation is also found in the benzene-propene binary supercritical fluid. The excess functions for benzene-propene binary mixtures have shown that there exists an enhancement of the potential energy when benzene mixes with propene. This enhancement provides a rational explanation for the experimental critical properties, which exhibit the behavior of the nonmonotonous dependence of critical pressure on compositions.

Computational studies of load-dependent guest dynamics and free energies of inclusion for CO2 in low-density p-tert-butylcalix[4]arene at loadings up to 2:1

The structure, dynamics, and free energies of absorption of CO(2) by a low-density structure (P4/n) of calixarene p-tert-butylalix[4]arene (TBC4) at loadings up to 2:1 CO(2):TBC4 have been studied by using molecular dynamics simulations with two sources of initial TBC4 structures (TBC4-T and TBC4-U). The CO(2)/TBC4 complex structure is very sensitive to the initial lattice spacing of TBC4. From the computed radial distribution functions of CO(2) molecules, a CO(2) dimer is observed for TBC4-T and a cage-interstitial CO(2) structure is suggested for TBC4-U. The dynamics of the CO(2) molecules show little initial TBC4 structural dependency. The free energy of inclusion for a single CO(2) in this TBC4 structure for various loadings is -4.0 kcal/mol at 300 K and -1.8 kcal/mol at 450 K, showing that CO(2) inclusion is favored. The fully loaded 1:1 CO(2):TBC4 system is slightly less favorable at -3.9 and -1.2 kcal/mol at 300 and 450 K, respectively. The first CO(2) added beyond 1:1 loading shows a significant drop in absorption energy to -1.9 and +1.9 kcal/mol at 300 and 450 K. These data are consistent with experimental results showing that low-density structures of TBC4 are able to absorb CO(2) at loadings greater than 1:1 but retention is lower than for 1:1 loaded systems indicating the free energy of inclusion for addition of the CO(2) above 1:1 is less favorable.

Structural difference between liquidlike and gaslike phases in supercritical fluid

Density fluctuation structures of supercritical carbon dioxide along the isothermal and isochoric lines were observed with small-angle neutron scattering (SANS). All the scattering intensities in the low-Q range were well described with the Ornstein-Zernike (OZ) equation. It was confirmed that there exists a locus where the OZ correlation length and scattering intensity at Q=0 exhibit extrema on the isothermal lines: this locus, named the ridge, was interpreted as the boundary by which the supercritical state is divided into liquidlike and gaslike phases. In order to clarify the difference of the fluctuation structure between the liquidlike and the gaslike phases, a real-space molecular distribution was obtained with a reverse Monte Carlo (RMC) method. Number density distributions of CO2 molecules at all measured states were calculated with the real-space molecular distributions obtained. In addition, the statistical parameters of the number density distributions, the standard deviations, and the skewnesses, were examined. The standard deviations of the number density distributions almost coincide with the results of the OZ analysis. On the other hand, the skewnesses, which describe the asymmetric nature of the number density distribution, clearly showed a difference between the two phases: the skewness became negative in the liquidlike phase, positive in the gaslike phase, and almost zero at the nearest state to the ridge in all isotherms. It was proved with simple equations of statistical mechanics that the skewness is described as the first differential of the magnitude of the density fluctuation with respect to the pressure. We conclude that the skewness, obtained with a RMC analysis for SANS data, is an important structural parameter distinguishing between the liquidlike and gaslike phases.

Orientational correlations in liquid, supercritical and gaseous carbon dioxide

Neutron and x-ray diffraction results obtained for liquid CO(2) have been modelled by means of the reverse Monte Carlo method. Partial pair correlation functions, centre-centre pair correlation functions and relative orientations of molecular axes as a function of distances between molecular centres have been calculated from the models. It was found that well defined orientational correlations exist in the liquid state. Close to the critical point, these correlations seem to disappear, but further away from the critical point, in the high density supercritical state, they reappear. Using large particle configurations, the density fluctuations close to the critical point could be visualized.

Molecular simulations of outersphere reorganization energies in polar and quadrupolar solvents. The case of intramolecular electron and hole transfer

Outersphere reorganization energies (lambda) for intramolecular electron and hole transfer are studied in anion- and cation-radical forms of complex organic substrates (p-phenylphenyl-spacer-naphthyl) in polar (water, 1,2-dichloroethane, tetrahydrofuran) and quadrupolar (supercritical CO2) solvents. Structure and charge distributions of solute molecules are obtained at the HF/6-31G(d,p) level. Standard Lennard-Jones parameters for solutes and the nonpolarizable simple site-based models of solvents are used in molecular dynamics (MD) simulations. Calculation of lambda is done by means of the original procedure, which treats electrostatic polarization of a solvent in terms of a usual nonpolarizable MD scheme supplemented by scaling of reorganization energies at the final stage. This approach provides a physically relevant background for separating inertial and inertialless polarization responses by means of a single parameter epsilon(infinity), optical dielectric permittivity of the solvent. Absolute lambda values for hole transfer in 1,2-dichloroethane agree with results of previous computations in terms of the different technique (MD/FRCM, Leontyev, I. V.; et al. Chem. Phys. 2005, 319, 4). Computed lambda values for electron transfer in tetrahydrofuran are larger than the experimental values by ca. 2.5 kcal/mol; for the case of hole transfer in 1,2-dichloroethane the discrepancy is of similar magnitude provided the experimental data are properly corrected. The MD approach gives nonzero lambda values for charge-transfer reaction in supercritical CO2, being able to provide a uniform treatment of nonequilibrium solvation phenomena in both quadrupolar and polar solvents.

An optimized molecular potential for carbon dioxide

An optimized molecular potential model for carbon dioxide is presented in this paper. Utilizing the established techniques of molecular-dynamics and histogram reweighting grand canonical Monte Carlo simulations, this model is demonstrated to show excellent predictability for thermodynamic, transport, and liquid structural properties in a wide temperature-pressure range with remarkable accuracies. The average deviations of this new model from experimental data for the saturated liquid densities, vapor densities, vapor pressures, and heats of vaporization are around 0.1%, 2.3%, 0.7%, and 1.9%, respectively. The calculated critical point is almost pinpointed by the new model. The experimental radial distribution functions ranging from 240.0 to 473.0 K are well reproduced as compared to neutron-diffraction measurements. The predicted self-diffusion coefficients are in good agreement with the nuclear-magnetic-resonance measurements. The previously published potential models for CO2 are also systematically evaluated, and our proposed new model is found to be superior to the previous models in general.

Evolution of Intermolecular Structure and Dynamics in Supercritical Carbon Dioxide with Pressure: An ab Initio Molecular Dynamics Study

The effect of pressure on supercritical carbon dioxide (scCO2) has been characterized by using Car-Parrinello molecular dynamics simulations. Structural and dynamical properties along an isotherm of 318.15 K and at pressures ranging from 190 to 5000 bar have been obtained. Intermolecular pair correlation functions and three-dimensional atomic probability density map calculations indicate that the local environment of a central CO2 molecule becomes more structured with increasing pressure. The closest neighbors are predominantly oriented in a distorted T-shaped geometry while neighbors separated by larger distances are likely oriented in a slipped parallel arrangement. The structure of scCO2 at high densities has been compared with that of crystalline CO2. The probability distributions of intramolecular distances narrow down with increasing pressure. A marginal but non-negligible effect of pressure on the instantaneous intramolecular OCO angle is observed, lending credence to the idea that intermolecular interactions between CO2 molecules in an inhomogeneous near neighbor environment could contribute to the observed instantaneous molecular dipole moment. The extent of deviation from a perfect linear geometry of the carbon dioxide molecule decreases with increasing pressure. Time constants derived from reorientational time correlation functions of the molecular backbone compare well with experimental data. Within the range of thermodynamic conditions explored here, no significant changes are observed in the frequencies of intramolecular vibrational modes. However, a blue shift is observed in the low-frequency cage rattling mode with increasing pressure.

Molecular Dynamics Simulation of the Cybotactic Region in Gas-Expanded Methanol−Carbon Dioxide and Acetone−Carbon Dioxide Mixtures

Local solvation and transport effects in gas-expanded liquids (GXLs) are reported based on molecular simulation. GXLs were found to exhibit local density enhancements similar to those seen in supercritical fluids, although less dramatic. This approach was used as an alternative to a multiphase atomistic model for these mixtures by utilizing experimental results to describe the necessary fixed conditions for a locally (quasi-) stable molecular dynamics model of the (single) GXL phase. The local anisotropic pair correlation function, orientational correlation functions, and diffusion rates are reported for two systems: CO2-expanded methanol and CO2-expanded acetone at 298 K and pressures up to 6 MPa.

Density dependences of long-range fluctuations and short-range correlation lengths of CHF3 and CH2F2 in supercritical states

Small-angle x-ray scattering (SAXS) measurements are carried out for supercritical polar fluorocarbons, CHF3 and CH2F2, along the isotherm of 1.04 in reduced temperatures with the density range from 0.3 to 1.5 in reduced units. A novel apparatus for determination of absorption factors of the sample fluids is used in the present measurements. The apparatus enables us to detect simultaneously the accurate factors during the observation of the SAXS signals. Long-range fluctuations such as density fluctuations and correlation lengths are evaluated from the obtained SAXS data. The reduced correlation lengths are obtained by normalization by each molecular size, in order to discuss the fluctuations independent of the difference of the individual molecular size. The density fluctuations and the reduced correlation lengths of CHF3 and CH2F2 are compared with those of CO2 and H2O. The results are as follows: H2O>CH2F2>CHF3 approximately CO2 in the order of magnitude. The fluctuations of CH2F2 are significantly distinguishable from those of CHF3 and show intermediate aspect between H2O and a group of CO2 and CHF3. In addition, the short-range correlation lengths, i.e., the Ornstein-Zernike direct correlation lengths, are firstly discussed from both viewpoints of density and substance dependences. The reduced short-range correlation lengths normalized by individual molecular size are found to trace a universal curve as a function of the reduced density.

Dielectric Constant and Density Dependence of the Structure of Supercritical Carbon Dioxide Using a New Modified Empirical Potential Model: A Monte Carlo Simulation Study

Two modified versions of the Elementary Physical Model (EPM) [J. Phys. Chem. 1995, 99, 12021] for supercritical carbon dioxide have been proposed in this work and their validities are affirmed by computing the thermodynamic properties and dielectric constant up to 910 kg/m3 with use of canonical ensemble Monte Carlo simulation. Simulations performed for 500 molecules with the EPM2-M model reproduce the experimental data accurately at all thermodynamic states. The structural analyses demonstrate that the aggregation is strong at low density while the coordination number is large at high density. In addition, a detailed study on the radial and angular correlation functions reveals that the T-shaped geometry is dominate while a variety of other structures still appear in the first coordination shell. Furthermore, the angular correlation functions show that the probability of a molecule being oriented toward the convex side of another molecule is equal to that pointing toward the concave side since the molecular nonlinearity of carbon dioxide is only marginal. As the distance between two molecules increases, the preferred orientations disappear quickly and all the results are in good agreement with the prior ab initio calculation [J. Chem. Phys. 2004, 120, 9694].

Ab initio molecular-dynamics study of supercritical carbon dioxide

Car-Parrinello molecular-dynamics simulations of supercritical carbon dioxide (scCO(2)) have been performed at the temperature of 318.15 K and at the density of 0.703 g/cc in order to understand its microscopic structure and dynamics. Atomic pair correlation functions and structure factors have been obtained and good agreement has been found with experiments. In the supercritical state the CO(2) molecule is marginally nonlinear, and thus possesses a dipole moment. Analyses of angle distributions between near neighbor molecules reveal the existence of configurations with pairs of molecules in the distorted T-shaped geometry. The reorientational dynamics of carbon dioxide molecules, investigated through first- and second-order time correlation functions, exhibit time constants of 620 and 268 fs, respectively, in good agreement with nuclear magnetic resonance experiments. The intramolecular vibrations of CO(2) have been examined through an analysis of the velocity autocorrelation function of the atoms. These reveal a red shift in the frequency spectrum relative to that of an isolated molecule, consistent with experiments on scCO(2). The results have also been compared to classical molecular-dynamics calculations employing an empirical potential.

Density dependence of vibrational energy relaxation rates in supercritical solution: a hydrodynamic model

An approximate expression describing the density dependence of vibrational energy relaxation rates in fluids in terms of thermodynamic and transport parameters of the fluid is developed on the basis of a classical statistical mechanical theory of vibrational energy relaxation of highly excited molecules in polyatomic solvents. The energy relaxation rate is expressed via the friction coefficient, which describes the interaction between solute oscillator and solvent molecules. The corresponding force-force time correlation function is expressed in terms of the dynamic structure factor of the solvent and the force of interaction between solute and solvent molecules. Approximating the dynamic structure factor appropriately leads to expressions for the density dependence of vibrational relaxation rates in terms of thermophysical solvent parameters. Using these expressions the density dependence of vibrational relaxation rates in supercritical ethane and propane both in the vicinity of the critical point and far from it are evaluated and compared with measured relaxation rates obtained under the same physical conditions.