Experimentally, the effects of pressure on reaction rates are described by their pressure derivatives, known as volumes of activation. Transition state theory directly links activation volumes to partial molar volumes of reactants and transition states. We discuss a molecular dynamics method for the accurate calculation of molecular volumes, within which the volumes of molecular species are obtained as a difference between the volumes of pure solvent and solvent with a single molecule inserted. The volumes thus obtained depend on the molecular geometry, the strength and type of the solute-solvent interactions, as well as temperature and pressure. The partial molar volumes calculated using this approach agree well with experimental data. Since this method can also be applied to transition state species, it allows for quantitative analysis of experimental volumes of activation in terms of structural parameters of the corresponding transition states. The efficiency of the approach is illustrated by calculation of volumes of activation for three nonpolar reactions in nonpolar solvents. The results agree well with the experimental data.
Theoretical predictions of solubility, typically accomplished by comparing the chemical potential of pure solid and solution, currently suffer from a lack of accuracy. We suggest an alternative method for predicting solubility based on molecular dynamics simulations of the behaviour of a small seed crystalline cluster probe in solutions of varying concentrations. The size dynamics of a properly chosen seed cluster that dissolves in unsaturated solutions and grows in size in supersaturated solutions is indicative of the saturation point. This approach is illustrated by its application to NaCl in water. IntroductionThe first attempt to 'observe' the Arrhenius theory of electrolytic dissociation in action apparently belongs to Ohtaki and co-workers [1], who used for this purpose molecular dynamics (MD) simulations of dissolution of a 32-ion-pair perfect crystal of sodium chloride (NaCl) in a 216 water molecule solvent. The rapid progress of computer technology over the subsequent 20 years has made MD and Monte Carlo simulations possible for substantially more complex electrolyte systems [2][3][4][5][6][7][8]. Nevertheless, solubility calculations at the level of accuracy comparable to that of the experiment remain a challenge [3][4][5][6][7][8].Theoretical solubility predictions are typically accomplished by calculating the chemical potential of the solution and of the pure solid. In accordance with thermodynamics, the saturation point is defined as the concentration at which these chemical potentials are equal. While the methodology for performing this type of calculation is well established and widely used, solubility predictions from chemical potentials suffer from a lack of accuracy [9]. Recently, an effort was made to obtain solubilities from MD simulations directly, by following the dynamics of a supersaturated solution crystallising onto a solid crystal interface [7,8]. However, these calculations required extremely long simulations, and are thus quite expensive computationally. As a cheaper alternative, we here propose a method based on observing the behaviour of a small crystal probe in solutions of various concentrations. Properly chosen, this probe crystal will quickly dissolve in unsaturated solutions and grow in size in supersaturated solutions. These transforma-
We present a modified form of the Functionalized Cahn Hilliard (FCH) functional which models highly amphiphilic systems in solvent. A molecule is highly amphiphilic if the energy of a molecule isolated within the bulk solvent molecule is prohibitively high. For such systems once the amphiphilic molecules assemble into a structure it is very rare for a molecule to exchange back into the bulk. The highly amphiphilic FCH functional has a well with limited smoothness and admits compactly supported critical points. In the limit of molecular length ε → 0 we consider sequences with bounded energy whose support resides within an ε-neighborhood of a fixed codimension one interface. We show that the FCH energy is uniformly bounded below, independent of ε > 0, and identify assumptions on tangential variation of sequences that guarantee the existence of subsequences that converge to a weak solution of a rescaled bilayer profile equation, and show that sequences with limited tangential variation enjoy a lim inf inequality. For fixed codimension one interfaces we construct bounded energy sequences which converge to the bilayer profile and others with larger tangential variation which do not converge to the bilayer profile but whose limiting energy can violate the lim inf inequality, depending upon the energy parameters.
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