Monte Carlo Simulations of Molecular Clusters in Nucleation

A better understanding of the limiting step in a first order phase transition, the nucleation process, is of major importance to a variety of scientific fields ranging from atmospheric sciences to nanotechnology and even to cosmology. This is due to the fact that in most phase transitions the new phase is separated from the mother phase by a free energy barrier. This barrier is crossed in a process called nucleation. Nowadays it is considered that a significant fraction of all atmospheric particles is produced by vapor-to liquid nucleation. In atmospheric sciences, as well as in other scientific fields, the theoretical treatment of nucleation is mostly based on a theory known as the Classical Nucleation Theory. However, the Classical Nucleation Theory is known to have only a limited success in predicting the rate at which vapor-to-liquid nucleation takes place at given conditions. This thesis studies the unary homogeneous vapor-to-liquid nucleation from a statistical mechanics viewpoint. We apply Monte Carlo simulations of molecular clusters to calculate the free energy barrier separating the vapor and liquid phases and compare our results against the laboratory measurements and Classical Nucleation Theory predictions. According to our results, the work of adding a monomer to a cluster in equilibrium vapour is accurately described by the liquid drop model applied by the Classical Nucleation Theory, once the clusters are larger than some threshold size. The threshold cluster sizes contain only a few or some tens of molecules depending on the interaction potential and temperature. However, the error made in modeling the smallest of clusters as liquid drops results in an erroneous absolute value for the cluster work of formation throughout the size range, as predicted by the McGraw-Laaksonen scaling law. By calculating correction factors to Classical Nucleation Theory predictions for the nucleation barriers of argon and water, we show that the corrected predictions produce nucleation rates that are in good comparison with experiments. For the smallest clusters, the deviation between the simulation results and the liquid drop values are accurately modelled by the low order virial coefficients at modest temperatures and vapour densities, or in other words, in the validity range of the non-interacting cluster theory by Frenkel, Band and Bilj. Our results do not indicate a need for a size dependent replacement free energy correction. The results also indicate that Classical Nucleation Theory predicts the size of the critical cluster correctly. We also presents a new method for the calculation of the equilibrium vapour density, surface tension size dependence and planar surface tension directly from cluster simulations. We also show how the size dependence of the cluster surface tension in equimolar surface is a function of virial coefficients, a result confirmed by our cluster simulations.

The Raman spectrum of cyclohexanol

The Raman spectrum of cyclohexanol has been studied in detail in the liquid state at 30° C. and at about 68° C. and in the solid state at about 13° C. The O-H stretching frequency of cyclohexanol has been found to extend from 3106-3571 cm.-1 in the liquid state at 30° C. and from 3204-3652 cm.-1 at 68° C. The 38 lines recorded in the present investigation have been following frequency shifts: 342, 408, 458, 478, 555, 653, 789, 834, 843, 863, 887, 920, 966, 978, 1024, 1047, 1070, 1139, 1173, 1184, 1210, 1235, 1252, 1301, 1329, 1346, 1362, 1438, 1448, 1464, 2660, 2684, 2710, 2854, 2896, 2925, 2940, 3106 to 3511 (band). Those lines which are italicized are the additional lines observed for the first time. The Raman lines at 966 cm.-1 and 1070 cm.-1 have been assigned to C-OH stretching vibrations of the axial and equatorial isomers. The ratio of the integrated intensity of the 1070 cm.-1 line to the 966 cm.-1 gave the equilibrium constant K as 2·896 at 30° C. and as 2·66 at 68° C. Knowing K, the free energy different Δ F was calculated and it was found to be 0·64 Kcal./mole at 30° C. and 0·66 Kcal./mole at about 68° C. Reasonable assignment has been made for most of the observed Raman lines.

Clustering and solute-vacancy binding energies in Al-4.4% Zn alloy with 0.01% ternary additions

Isochronal and isothermal ageing experiments have been carried out to determine the influence of 0.01 at. % addition of a second solute on the clustering rate in the quenched Al-4,4 a/o Zn alloy. The influence of quenching and ageing temperatures has been interpreted to obtain the apparent vacancy formation and vacancy migration energies in the various ternary alloys. Using a vacancy-aided clustering model the following values of binding free energy have been evaluated: Ce-0.18; Dy-0.24; Fe-0.18; Li-0.25; Mn-0.27; Nb-0.18; Pt-0.23; Sb-0.21; Si-0.30; Y-0.25; and Yb-0.23 (± 0.02 eV). These binding energy values refer to that between a solute atom and a single vacancy. The values of vacancy migration energy (c. 0.4 eV) and the experimental activation energy for solute diffusion (c. 1.1 eV) are unaffected by the presence of the ternary atoms in the Al-Zn alloy.

Role of entropy in the stability of cobalt titanates

The standard molar Gibbs free energy of formation of Co2TiO4, CoTiO3,and CoTi2O5 as a function of temperature over an extended range (900 to 1675) K was measured using solid-state electrochemical cells incorporating yttria-stabilized zirconia as the electrolyte, with CoO as reference electrode and appropriate working electrodes. For the formation of the three compounds from their component oxides CoO with rock-salt and TiO2 with rutile structure, the Gibbs free energy changes are given by:Delta(f)G degrees((ox))(Co2TiO4) +/- 104/(J . mol(-1)) = -18865 - 4.108 (T/K)Delta(f)G degrees((ox))(CoTiO3) +/- 56/(J . mol(-1)) = -19627 + 2.542 (T/K) Delta(f)G degrees((ox))(CoTi2O5) +/- 52/(J . mol(-1)) = -6223 - 6.933 (T/K) Accurate values for enthalpy and entropy of formation were derived. The compounds Co2TiO4 with spinel structure and CoTi2O5 with pseudo-brookite structure were found to be entropy stabilized. The relatively high entropy of these compounds arises from the mixing of cations on specific crystallographic sites. The stoichiometry of CoTiO3 was confirmed by inert gas fusion analysis for oxygen. Because of partial oxidation of cobalt in air, the composition corresponding to the compound Co2TiO4 falls inside a two-phase field containing the spinet solid solution Co2TiO4-Co3O4 and CoTiO3. The spinel solid solution becomes progressively enriched in Co3O4 with decreasing temperature. (c) 2010 Elsevier Ltd. All rights reserved.

Monte Carlo simulations of molecular clusters in nucleation

A better understanding of the limiting step in a first order phase transition, the nucleation process, is of major importance to a variety of scientific fields ranging from atmospheric sciences to nanotechnology and even to cosmology. This is due to the fact that in most phase transitions the new phase is separated from the mother phase by a free energy barrier. This barrier is crossed in a process called nucleation. Nowadays it is considered that a significant fraction of all atmospheric particles is produced by vapor-to liquid nucleation. In atmospheric sciences, as well as in other scientific fields, the theoretical treatment of nucleation is mostly based on a theory known as the Classical Nucleation Theory. However, the Classical Nucleation Theory is known to have only a limited success in predicting the rate at which vapor-to-liquid nucleation takes place at given conditions. This thesis studies the unary homogeneous vapor-to-liquid nucleation from a statistical mechanics viewpoint. We apply Monte Carlo simulations of molecular clusters to calculate the free energy barrier separating the vapor and liquid phases and compare our results against the laboratory measurements and Classical Nucleation Theory predictions. According to our results, the work of adding a monomer to a cluster in equilibrium vapour is accurately described by the liquid drop model applied by the Classical Nucleation Theory, once the clusters are larger than some threshold size. The threshold cluster sizes contain only a few or some tens of molecules depending on the interaction potential and temperature. However, the error made in modeling the smallest of clusters as liquid drops results in an erroneous absolute value for the cluster work of formation throughout the size range, as predicted by the McGraw-Laaksonen scaling law. By calculating correction factors to Classical Nucleation Theory predictions for the nucleation barriers of argon and water, we show that the corrected predictions produce nucleation rates that are in good comparison with experiments. For the smallest clusters, the deviation between the simulation results and the liquid drop values are accurately modelled by the low order virial coefficients at modest temperatures and vapour densities, or in other words, in the validity range of the non-interacting cluster theory by Frenkel, Band and Bilj. Our results do not indicate a need for a size dependent replacement free energy correction. The results also indicate that Classical Nucleation Theory predicts the size of the critical cluster correctly. We also presents a new method for the calculation of the equilibrium vapour density, surface tension size dependence and planar surface tension directly from cluster simulations. We also show how the size dependence of the cluster surface tension in equimolar surface is a function of virial coefficients, a result confirmed by our cluster simulations.

Thermodynamics of GdMnO3 and GdMn2O5 phases determined by the EMF method

Using solid oxide galvanic cells of the type: MnO + Gd2O3 + GdMnO3/O-2/Ni + NiO and Mn3O4 + GdMnO3 + GdMn2O5/O-2/air the equilibrium oxygen pressure for the following reactions :MnO + 1/2Gd(2)O(3) + 1/4O(2) = GdMnO3 1/3Mn(3)O(4) + GdMnO3 + 1/3O(2) = GdMn2O5 was determined in the temperature range from 1073 to 1450 K. From the determined equilibrium oxygen partial pressure the corresponding G i b b s free energy change for these reactions was derived: Delta G(f,GdMnO3)(0) (+/- 425J) 132721(+/ - 2240) +51.91(+/ - 0.81)T Delta G(f,GdMn2O5)(0)(+/- 670J) 121858(+/ - 6176) + 79.52(+/ - 4.83)T From these data, standard G i b b s energies, enthalpies and entropies of formation of GdMnO3 and GdMn2O5 from component oxides and from the elements are derived. Thermodynamic data tables for the two ternary phases are compiled from 298.15 to 1400 K.

Energetics of firewood plantations

An input-output analysis of firewood plantations is attempted in this paper. The inflows from free energy forms, exerted energy forms and non-energy forms, and outflows from energy products, non-energy products and side benefits is evaluated in common energy units (kilocalories). The analysis provides an insight into the performance of these plantations, reveals their defects and suggests ways of improving their productivity.

Elucidation of the mechanism of interaction of sheep spleen galectin-1 with splenocytes and its role in cell-matrix adhesion

The binding of a 14 kDa beta-galactoside animal lectin to splenocytes has been studied in detail. The binding data show that there are two classes of binding sites on the cells for the lectin: a high-affinity site with a K-a ranging from 1.1 x 10(6) to 5.1 x 10(5) M-1 and a low affinity binding site with a K-a ranging from 7.7 x 10(4) to 3.4 x 10(4) M-1 The number of receptors per cell for the high- and low-affinity sites is 9 +/- 3 x 10(6) and 2.5 +/- 0.5 x 10(6) respectively. The temperature dependence of the K value yielded the thermodynamic parameters. The energetics of this interaction shows that, although this interaction is essentially enthalpically driven (Delta H - 21 kJ lambda mol(-1)) for the high-affinity sites, there is a very favorable entropy contribution to the free energy of this interaction (-T Delta S - 17.5 Jmol(-1)), suggesting that hydrophobic interaction may also be playing a role in this interaction. Lactose brought about a 20% inhibition of this interaction, whereas the glycoprotein asialofetuin brought about a 75 % inhibition, suggesting that complex carbohydrate structures are involved in the binding of galectin-1 to splenocytes, Galectin-1 also mediated the binding and adhesion of splenocytes to the extracellular matrix glycoprotein laminin, suggesting a role for it in cell-matrix interactions. Copyright (C) 2000 John Wiley & Sons, Ltd.

Thermodynamic and structural studies of cavity formation in proteins suggest that loss of packing interactions rather than the hydrophobic effect dominates the observed energetics

The hydrophobic effect is widely believed to be an important determinant of protein stability. However, it is difficult to obtain unambiguous experimental estimates of the contribution of the hydrophobic driving force to the overall free energy of folding. Thermodynamic and structural studies of large to small substitutions in proteins are the most direct method of measuring this contribution. We have substituted the buried residue Phe8 in RNase S with alanine, methionine, and norleucine, Binding thermodynamics and structures were characterized by titration calorimetry and crystallography, respectively. The crystal structures of the RNase S F8A, F8M, and F8Nle mutants indicate that the protein tolerates the changes without any main chain adjustments, The correlation of structural and thermodynamic parameters associated with large to small substitutions was analyzed for nine mutants of RNase S as well as 32 additional cavity-containing mutants of T4 lysozyme, human lysozyme, and barnase. Such substitutions were typically found to result in negligible changes in Delta C-p and positive values of both Delta Delta H degrees and aas of folding. Enthalpic effects were dominant, and the sign of Delta Delta S is the opposite of that expected from the hydrophobic effect. Values of Delta Delta G degrees and Delta Delta H degrees correlated better with changes in packing parameters such as residue depth or occluded surface than with the change in accessible surface area upon folding. These results suggest that the loss of packing interactions rather than the hydrophobic effect is a dominant contributor to the observed energetics for large to small substitutions. Hence, estimates of the magnitude of the hydrophobic driving force derived from earlier mutational studies are likely to be significantly in excess of the actual value.

A modified least squares algorithm to treat associations in liquid alloys

The associated model for binary systems has been modified to include volume effects and excess entropy arising from preferential interactions between the associate and the free atoms or between the free atoms. Equations for thermodynamic mixing functions have been derived. An optimization procedure using a modified conjugate gradient method has been used to evaluate the enthalpy and entropy interaction energies, the free energy of dissociation of the complex, its temperature dependance and the size of the associate. An expression for the concentration—concentration structure factor [Scc (0)] has been deduced from the modified associated solution model. The analysis has been applied to the thermodynamic mixing functions of liquid Ga-Te alloys at 1120 K, believed to contain Ga2Te3 associates. It is observed that the modified associated solution model incorporating volume effects and terms for the temperature dependance of interaction energies, describes the thermodynamic properties of Ga-Te system satisfactorily.

Phase diagram of a hard-sphere system in a quenched random potential: A numerical study

We report numerical results for the phase diagram in the density-disorder plane of a hard-sphere system in the presence of quenched, random, pinning disorder. Local minima of a discretized version of the Ramakrishnan-Yussouff free energy functional are located numerically and their relative stability is studied as a function of the density and the strength of disorder. Regions in the phase diagram corresponding to liquid, glassy, and nearly crystalline states are mapped out, and the nature of the transitions is determined. The liquid to glass transition changes from first to second order as the strength of the disorder is increased. For weak disorder, the system undergoes a first-order crystallization transition as the density is increased. Beyond a critical value of the disorder strength, this transition is replaced by a continuous glass transition. Our numerical results are compared with those of analytical work on the same system. Implications of our results for the field-temperature phase diagram of type-II superconductors are discussed.

A spectroscopic study of the interaction of isoflavones with human serum albumin

Genistein and daidzein, the major isoflavones present in soybeans, possess a wide spectrum of physiological and pharmacological functions. The binding of genistein to human serum albumin (HSA) has been investigated by equilibrium dialysis, fluorescence measurements, CD and molecular visualization. One mole of genistein is bound per mole of HSA with a binding constant of 1.5 +/- 0.2 X 10(5) m(-1). Binding of genistein to HSA precludes the attachment of daidzein. The ability of HSA to bind genistein is found to be lost when the tryptophan residue of albumin is modified with N-bromosuccinimide. At 27 degrees C (pH 7.4), van't Hoff's enthalpy, entropy and free energy changes that accompany the binding are found to be -13.16 kcal.mol(-1), -21 cal.mol(-1)K(-1) and -6.86 kcal.mol(-1), respectively. Temperature and ionic strength dependence and competitive binding measurements of genistein with HSA in the presence of fatty acids and 8-anilino-1-naphthalene sulfonic acid have suggested the involvement of both hydrophobic and ionic interactions in the genistein-HSA binding. Binding measurements of genistein with BSA and HSA, and those in the presence of warfarin and 2,3,5-tri-iodobenzoic acid and Forster energy transfer measurements have been used for deducing the binding pocket on HSA. Fluorescence anisotropy measurements of daidzein bound and then displaced with warfarin, 2,3,5-tri-iodobenzoic acid or diazepam confirm the binding of daidzein and genistein to subdomain IIA of HSA. The ability of HSA to form ternery complexes with other neutral molecules such as warfarin, which also binds within the subdomain IIA pocket, increases our understanding of the binding dynamics of exogenous drugs to HSA.

Studies on removal of metal ions and sulphate reduction using rice husk and Desulfotomaculum nigrificans with reference to remediation of acid mine drainage

The utility of rice husk as an adsorbent for metal ions such as iron, zinc and copper from acid mine water was assessed. The adsorption isotherms exhibited Langmuirian behavior and were endothermic in nature. The free energy values for adsorption of the chosen metal ions onto rice husk were found to be highly negative attesting to favorable interaction. Over 99% Fe3+, 98% of Fe2+ and Zn2+ and 95% Cu2+ uptake was achieved from acid mine water, with a concomitant increase in the pH value by two units using rice husk. The remediation studies carried out on acid mine water and simulated acid mine water pretreated with rice husk indicated successful growth of Desulfotomaculum nigrificans (D. nigrificans). The amount of sulphate bioreduction in acid mine water at an initial pH of 5.3 was enhanced by D. nigrificans from 21% to 40% in the presence of rice husk filtrate supplemented with carbon and nitrogen. In simulated acid mine water with fortified husk filtrate, the sulphate reduction was even more extensive, with an enhancement to 73%. Concurrently, almost 90% Fe2+, 89% Zn2+ and 75% Cu2+ bioremoval was attained from simulated acid mine water. Metal adsorption by rice husk was confirmed in desorption experiments in which almost complete removal of metal ions from the rice husk was achieved after two elutions using 1 M HCl. The possible mechanisms of metal ion adsorption onto rice husk and sulphate reduction using D. nigrificans are discussed.

Density-wave theory of dislocations in crystals

The density-wave theory of Ramakrishnan and Yussouff is extended to provide a scheme for describing dislocations and other topological defects in crystals. Quantitative calculations are presented for the order-parameter profiles, the atomic configuration, and the free energy of a screw dislocation with Burgers vector b=(a/2, a/2, a/2) in a bcc solid. These calculations are done using a simple parametrization of the direct correlation function and a gradient expansion. It is conventional to express the free energy of the dislocation in a crystal of size R as (λb2/4π)ln(αR/‖b‖), where λ is the shear elastic constant, and α is a measure of the core energy. Our results yield for Na the value α≃1.94a/(‖c1’’‖)1/2 (≃1.85) at the freezing temperature (371 K) and α≃2.48a/(‖c1’’‖)1/2 at 271 K, where c1’’ is the curvature of the first peak of the direct correlation function c(q). Detailed results for the density distribution in the dislocation, particularly the core region, are also presented. These show that the dislocation core has a columnar character. To our knowledge, this study represents the first calculation of dislocation structure, including the core, within the framework of an order-parameter theory and incorporating thermal effects.

Effects of capillary waves on the thickness of wetting layers

The free energy contribution of capillary waves is calculated to show its significant dependence on the thickness of the liquid layer, when the thickness is very small. It is shown that these oscillations can play an important role in determining the thermodynamic stability of a wetting layer, close to the critical point of a binary liquid mixture in the case of both short range and long range forces. In particular, the thickness of the wetting layer goes to zero as the temperature T approaches Tc.