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LIST OF FIGURES Figure 2-1: Perspective view of the PE surface for the A+BCAB+C reaction. The arrangement consisting of the separated atoms is the corner coming towards us, while that corresponding to the atoms being compressed together is at rear. Note how the cross-sections at large rAB and rBC are identical to the usual PE curves for diatomics. Modified figure from Hirst work (Hirst, 1985)...........................................................................................................................18 Figure 2-2: Energy and volume profile of a general reaction .........................................................21 Figure 2-3: Free energy sketches for reaction coordinates representing two different responses to density.(a) preferential solvation of the transition state as density increases, leading to a net decrease in ΔG# with increasing density. In (b) the reactants and products are preferentially solvated by increased density. Modified figure from Levert Sengers’ book (Levert Sengers, 1998). .....................................................................................................................................22 Figure 3-1: A diatomic molecule in phase space. The position and motion of the particle are presented by a point with coordinates (q1x, q1y, q1z, q2x, q2y, q2z, p1x, p1y, p1z, p2x, p2y, p2z) in a 2-dimensional phase space.....................................................................................................31 Figure 3-2: Trajectory in two-dimensional phase space .................................................................32 Figure 3-3: A diagram showing how the use of multiple thermocouples can be used to lower the noise in a temperature measurement ......................................................................................34 Figure 3-4: Integration sampling between a and b..........................................................................39 Figure 3-5: Unbiased and biased sampling for Monte Carlo integration. The biased roulette is not proportional in size, different sized portions..........................................................................40 Figure 4-1: Phase diagram for pure carbon dioxide. .......................................................................47 Figure 4-2: The critical points of selected solvents in table 4-1......................................................48 Figure 4-3: Reagent clustering in a supercritical fluid. ...................................................................50 Figure 4-4: Different character of clusters formed in different temperature ranges. Near the critical temperature, the solvent molecules tend to form a large cluster even without a solute molecule. At higher temperatures, the solute molecule with strong attractive interaction is necessary to trigger the clustering of solvent molecules (Reprinted from Baker’s work (Baiker, 1999). .......................................................................................................................51 Figure 4-5: Schematic illustration of regions of the phase diagram; near-critical regime (dark area); compressible-regime (light dark area); supercritical regime (slanted hatch) ...............60 Figure 4-6: The gas–liquid coexistence curve. The blue colour indicates a high density region (liquid like) and the red colour a low density region (gas like). The dashed line represents the locus of the points with the maximum local densities fluctuation (drawn on data representing vapour-liquid curve for carbon dioxide). ...............................................................................67 Figure 5-1: Schematic representation of periodic boundary conditions for two–dimensional system ...............................................................................................................................................72 Figure 5-2: Typical arrangement of a fluid of spherical particles. The density at a given radius r with respect to a reference particle is shown. ........................................................................75 Figure 5-3: Parameters for EPM2 model for carbon dioxide. The distance between carbon and oxygen at 1.149Å...................................................................................................................77 Figure 5-4: Van der Waals interactions between two carbon atoms in carbon dioxide molecule...78 Figure 5-5: Coulomb repulsion of the two Carbons in CO2............................................................78 Figure 5-6: A two dimensional diagram of an inhomogeneous system. In the Ωκ physical space there, M elements interact with elements with the other elements of different physical spaces ...............................................................................................................................................79 Figure 5-7: The molecule i interacts with the molecules in the molecules within the kth element, volume dV. The element is outside the cutoff and Rc is the cutoff. ......................................80 Figure 6-1: Schematic representation of potential energy during the Monte Carlo progress..........89 Figure 7-1: Dependence of residual potential energy with pressure along an isotherm (T=310K) for fluoroform (Tc=299.1K). Comparison between simulated literature values (Ulit) and simulated values (Usim). .......................................................................................................96 Figure 7-2: Dependence of residual potential energy with pressure along an isotherm (T=310K) for ethane (Tc=305.33K). Comparison between simulated literature (Ulit) values and our simulated values (Usim). .......................................................................................................97 vPDF Image | MOLECULAR SIMULATION STUDIES IN THE SUPERCRITICAL REGION
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