Dimensional Reduction Near the Deconfinement Transition

When ordinary nuclear matter is heated to a high temperature of ~ 10^12 K, it undergoes a deconfinement transition to a new phase, strongly interacting quark-gluon plasma. While the color charged fundamental constituents of the nuclei, the quarks and gluons, are at low temperatures permanently confined inside color neutral hadrons, in the plasma the color degrees of freedom become dominant over nuclear, rather than merely nucleonic, volumes. Quantum Chromodynamics (QCD) is the accepted theory of the strong interactions, and confines quarks and gluons inside hadrons. The theory was formulated in early seventies, but deriving first principles predictions from it still remains a challenge, and novel methods of studying it are needed. One such method is dimensional reduction, in which the high temperature dynamics of static observables of the full four-dimensional theory are described using a simpler three-dimensional effective theory, having only the static modes of the various fields as its degrees of freedom. A perturbatively constructed effective theory is known to provide a good description of the plasma at high temperatures, where asymptotic freedom makes the gauge coupling small. In addition to this, numerical lattice simulations have, however, shown that the perturbatively constructed theory gives a surprisingly good description of the plasma all the way down to temperatures a few times the transition temperature. Near the critical temperature, the effective theory, however, ceases to give a valid description of the physics, since it fails to respect the approximate center symmetry of the full theory. The symmetry plays a key role in the dynamics near the phase transition, and thus one expects that the regime of validity of the dimensionally reduced theories can be significantly extended towards the deconfinement transition by incorporating the center symmetry in them. In the introductory part of the thesis, the status of dimensionally reduced effective theories of high temperature QCD is reviewed, placing emphasis on the phase structure of the theories. In the first research paper included in the thesis, the non-perturbative input required in computing the g^6 term in the weak coupling expansion of the pressure of QCD is computed in the effective theory framework at an arbitrary number of colors. The two last papers on the other hand focus on the construction of the center-symmetric effective theories, and subsequently the first non-perturbative studies of these theories are presented. Non-perturbative lattice simulations of a center-symmetric effective theory for SU(2) Yang-Mills theory show --- in sharp contrast to the perturbative setup --- that the effective theory accommodates a phase transition in the correct universality class of the full theory. This transition is seen to take place at a value of the effective theory coupling constant that is consistent with the full theory coupling at the critical temperature.

Understanding solid-state transformations during dehydration: new insights using vibrational spectroscopy and multivariate modelling

Many active pharmaceutical ingredients (APIs) have both anhydrate and hydrate forms. Due to the different physicochemical properties of solid forms, the changes in solid-state may result in therapeutic, pharmaceutical, legal and commercial problems. In order to obtain good solid dosage form quality and performance, there is a constant need to understand and control these phase transitions during manufacturing and storage. Thus it is important to detect and also quantify the possible transitions between the different forms. In recent years, vibrational spectroscopy has become an increasingly popular tool to characterise the solid-state forms and their phase transitions. It offers several advantages over other characterisation techniques including an ability to obtain molecular level information, minimal sample preparation, and the possibility of monitoring changes non-destructively in-line. Dehydration is the phase transition of hydrates which is frequently encountered during the dosage form production and storage. The aim of the present thesis was to investigate the dehydration behaviour of diverse pharmaceutical hydrates by near infrared (NIR), Raman and terahertz pulsed spectroscopic (TPS) monitoring together with multivariate data analysis. The goal was to reveal new perspectives for investigation of the dehydration at the molecular level. Solid-state transformations were monitored during dehydration of diverse hydrates on hot-stage. The results obtained from qualitative experiments were used to develop a method and perform the quantification of the solid-state forms during process induced dehydration in a fluidised bed dryer. Both in situ and in-line process monitoring and quantification was performed. This thesis demonstrated the utility of vibrational spectroscopy techniques and multivariate modelling to monitor and investigate dehydration behaviour in situ and during fluidised bed drying. All three spectroscopic methods proved complementary in the study of dehydration. NIR spectroscopy models could quantify the solid-state forms in the binary system, but were unable to quantify all the forms in the quaternary system. Raman spectroscopy models on the other hand could quantify all four solid-state forms that appeared upon isothermal dehydration. The speed of spectroscopic methods makes them applicable for monitoring dehydration and the quantification of multiple forms was performed during phase transition. Thus the solid-state structure information at the molecular level was directly obtained. TPS detected the intermolecular phonon modes and Raman spectroscopy detected mostly the changes in intramolecular vibrations. Both techniques revealed information about the crystal structure changes. NIR spectroscopy, on the other hand was more sensitive to water content and hydrogen bonding environment of water molecules. This study provides a basis for real time process monitoring using vibrational spectroscopy during pharmaceutical manufacturing.

On the functional ordering of biomembranes : Implications for drug binding

Cells are packed with membrane structures, defining the inside and outside, and the different subcellular compartments. These membranes consisting mainly of phospholipids have a variety of functions in addition to providing a permeability barrier for various compounds. These functions involve cellular signaling, where lipids can act as second messengers, or direct regulation of membrane associating proteins. The first part of this study focuses on relating some of the physicochemical properties of membrane lipids to the association of drug compounds to membranes. A fluorescence based method is described allowing for determination of the membrane association of drugs. This method was subsequently applied to a novel drug, siramesine, previously shown to have anti-cancer activity. Siramesine was found to associate with anionic lipids. Especially interesting is its strong affinity for a second messenger lipid phosphatidic acid. This is the first example of a small molecule drug compound specifically interacting with a cellular lipid. Phosphatidic acid in cells is required for the activation of many signaling pathways mediating growth and proliferation. This provides an intriguing possibility for a simple molecular mechanism of the observed anti-cancer activity of siramesine. In the second part the thermal behavior and self assembly of charged and uncharged membrane assemblies was studied. Strong inter-lamellar co-operativity was observed for multilamellar DPPC vesicles using fluorescence techniques together with calorimetry. The commonly used membrane models, large unilamellar vesicles (LUV) and multilamellar vesicles (MLV) were found to possess different biophysical properties as interlamellar interactions of MLVs drive segregation of a pyrene labeled lipid analogue into clusters. The effect of a counter-ion lattice on the self assembly of a cationic gemini surfactant was studied. The presence of NaCl strongly influenced the thermal phase behavior of M-1 vesicles, causing formation of giant vesicles upon exceeding a phase transition temperature, followed by a subsequent transition into a more homogenous dispersion. Understanding the underlying biophysical aspects of cellular membranes is of fundamental importance as the complex picture of the structure and function of cells is evolving. Many of the cellular reactions take place on membranes and membranes are known to regulate the activity of many peripheral and intergral membrane associating proteins. From the point of view of drug design and gene technology, membranes can provide an interesting target for future development of drugs, but also a vehicle sensitive for environmental changes allowing for encapsulating drugs and targeting them to the desired site of action.

Asymmetrical flow field-flow fractionation in the study of water-soluble macromolecules

Asymmetrical flow field-flow fractionation (AsFlFFF) was constructed, and its applicability to industrial, biochemical, and pharmaceutical applications was studied. The effect of several parameters, such as pH, ionic strength, temperature and the reactants mixing ratios on the particle sizes, molar masses, and the formation of aggregates of macromolecules was determined by AsFlFFF. In the case of industrial application AsFlFFF proved to be a valuable tool in the characterization of the hydrodynamic particle sizes, molar masses and phase transition behavior of various poly(N-isopropylacrylamide) (PNIPAM) polymers as a function of viscosity and phase transition temperatures. The effect of sodium chloride salt and the molar ratio of cationic and anionic polyelectrolytes on the hydrodynamic particle sizes of poly (methacryloxyethyl trimethylammonium chloride) and poly (ethylene oxide)-block-poly (sodium methacrylate) and their complexes were studied. The particle sizes of PNIPAM polymers, and polyelectrolyte complexes measured by AsFlFFF were in agreement with those obtained by dynamic light scattering. The molar masses of PNIPAM polymers obtained by AsFlFFF and size exclusion chromatography agreed also well. In addition, AsFlFFF proved to be a practical technique in thermo responsive behavior studies of polymers at temperatures up to about 50 oC. The suitability of AsFlFFF for biological, biomedical, and pharmaceutical applications was proved, upon studying the lipid-protein/peptide interactions, and the stability of liposomes at different temperatures. AsFlFFF was applied to the studies on the hydrophobic and electrostatic interactions between cytochrome c (a basic peripheral protein) and anionic lipid, and oleic acid, and sodium dodecyl sulphate surfactant. A miniaturized AsFlFFF constructed in this study was exploited in the elucidation of the effect of copper (II), pH, ionic strength, and vortexing on the particle sizes of low-density lipoproteins.

Stabilization of Phospholipid Coatings in Capillary Electrophoresis

The development of a simple method of coating a semi-permanent phospholipid layer onto a capillary for electrochromatography use was the focus of this study. The work involved finding good coating conditions, stabilizing the phospholipid coating, and examining the effect of adding divalent cations, cetyltrimethylammonium bromide, and polyethylene glycol (PEG)-lipids on the stability of the coating. Since a further purpose was to move toward more biological membrane coatings, the capillaries were also coated with cholesterol-containing liposomes and liposomes of red blood cell ghost lipids. Liposomes were prepared by extrusion, and large unilamellar vesicles with a diameter of about 100 nm were obtained. Zwitterionic phosphatidylcholine (PC) was used as a basic component, mainly 1-palmitoyl-2-oleyl-sn-glycero-3-phosphocholine (POPC) but also eggPC and 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC). Different amounts of sphingomyelin, bovine brain phosphatidylserine, and cholesterol were added to the PC. The stability of the coating in 40 mM N-(2-hydroxyethyl)piperazine-N’-(2-ethanesulfonic acid) (HEPES) solution at pH 7.4 was studied by measuring the electroosmotic flow and by separating neutral steroids, basic proteins, and low-molar-mass drugs. The presence of PC in the coating solution was found to be essential to achieving a coating. The stability of the coating was improved by the addition of negative phosphatidylserine, cholesterol, divalent cations, or PEGylated lipids, and by working in the gel-state region of the phospholipid. Study of the effect on the PC coating of divalent metal ions calcium, magnesium, and zinc showed a molar ratio of 1:3 PC/Ca2+ or PC/Mg2+ to give increased rigidity to the membrane and the best coating stability. The PEGylated lipids used in the study were sterically stabilized commercial lipids with covalently attached PEG chains. The vesicle size generally decreased when PEGylated lipids of higher molar mass were present in the vesicle. The predominance of discoidal micelles over liposomes increased PEG chain length and the average size of the vesicles thus decreased. In the capillary electrophoresis (CE) measurements a highly stable electroosmotic flow was achieved with 20% PEGylated lipid in the POPC coating dispersion, the best results being obtained for disteroyl PEG (3000) conjugates. The results suggest that smaller particles (discoidal micelles) result in tighter packing and better shielding of silanol groups on the silica wall. The effect of temperature on the coating stability was investigated by using DPPC liposomes at temperatures above (45 C) and below (25 C) the main phase transition temperature. Better results were obtained with DPPC in the more rigid gel state than in the fluid state: the electroosmotic flow was heavily suppressed and the PC coating was stabilized. Also dispersions of DPPC with 0−30 mol% of cholesterol and sphingomyelin in different ratios, which more closely resemble natural membranes, resulted in stable coatings. Finally, the CE measurements revealed that a stable coating is formed when capillaries are coated with liposomes of red blood cell ghost lipids.

Polymer Protected Gold Nanoparticles

Polymer protected gold nanoparticles have successfully been synthesized by both "grafting-from" and "grafting-to" techniques. The synthesis methods of the gold particles were systematically studied. Two chemically different homopolymers were used to protect gold particles: thermo-responsive poly(N-isopropylacrylamide), PNIPAM, and polystyrene, PS. Both polymers were synthesized by using a controlled/living radical polymerization process, reversible addition-fragmentation chain transfer (RAFT) polymerization, to obtain monodisperse polymers of various molar masses and carrying dithiobenzoate end groups. Hence, particles protected either with PNIPAM, PNIPAM-AuNPs, or with a mixture of two polymers, PNIPAM/PS-AuNPs (i.e., amphiphilic gold nanoparticles), were prepared. The particles contain monodisperse polymer shells, though the cores are somewhat polydisperse. Aqueous PNIPAM-AuNPs prepared using a "grafting-from" technique, show thermo-responsive properties derived from the tethered PNIPAM chains. For PNIPAM-AuNPs prepared using a "grafting-to" technique, two-phase transitions of PNIPAM were observed in the microcalorimetric studies of the aqueous solutions. The first transition with a sharp and narrow endothermic peak occurs at lower temperature, and the second one with a broader peak at higher temperature. In the first transition PNIPAM segments show much higher cooperativity than in the second one. The observations are tentatively rationalized by assuming that the PNIPAM brush can be subdivided into two zones, an inner and an outer one. In the inner zone, the PNIPAM segments are close to the gold surface, densely packed, less hydrated, and undergo the first transition. In the outer zone, on the other hand, the PNIPAM segments are looser and more hydrated, adopt a restricted random coil conformation, and show a phase transition, which is dependent on both particle concentration and the chemical nature of the end groups of the PNIPAM chains. Monolayers of the amphiphilic gold nanoparticles at the air-water interface show several characteristic regions upon compression in a Langmuir trough at room temperature. These can be attributed to the polymer conformational transitions from a pancake to a brush. Also, the compression isotherms show temperature dependence due to the thermo-responsive properties of the tethered PNIPAM chains. The films were successfully deposited on substrates by Langmuir-Blodgett technique. The sessile drop contact angle measurements conducted on both sides of the monolayer deposited at room temperature reveal two slightly different contact angles, that may indicate phase separation between the tethered PNIPAM and PS chains on the gold core. The optical properties of amphiphilic gold nanoparticles were studied both in situ at the air-water interface and on the deposited films. The in situ SPR band of the monolayer shows a blue shift with compression, while a red shift with the deposition cycle occurs in the deposited films. The blue shift is compression-induced and closely related to the conformational change of the tethered PNIPAM chains, which may cause a decrease in the polarity of the local environment of the gold cores. The red shift in the deposited films is due to a weak interparticle coupling between adjacent particles. Temperature effects on the SPR band in both cases were also investigated. In the in situ case, at a constant surface pressure, an increase in temperature leads to a red shift in the SPR, likely due to the shrinking of the tethered PNIPAM chains, as well as to a slight decrease of the distance between the adjacent particles resulting in an increase in the interparticle coupling. However, in the case of the deposited films, the SPR band red-shifts with the deposition cycles more at a high temperature than at a low temperature. This is because the compressibility of the polymer coated gold nanoparticles at a high temperature leads to a smaller interparticle distance, resulting in an increase of the interparticle coupling in the deposited multilayers.

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.

Investigations of planetary boundary layer processes and particle formation in the atmosphere of planet Mars

The planet Mars is the Earth's neighbour in the Solar System. Planetary research stems from a fundamental need to explore our surroundings, typical for mankind. Manned missions to Mars are already being planned, and understanding the environment to which the astronauts would be exposed is of utmost importance for a successful mission. Information of the Martian environment given by models is already now used in designing the landers and orbiters sent to the red planet. In particular, studies of the Martian atmosphere are crucial for instrument design, entry, descent and landing system design, landing site selection, and aerobraking calculations. Research of planetary atmospheres can also contribute to atmospheric studies of the Earth via model testing and development of parameterizations: even after decades of modeling the Earth's atmosphere, we are still far from perfect weather predictions. On a global level, Mars has also been experiencing climate change. The aerosol effect is one of the largest unknowns in the present terrestrial climate change studies, and the role of aerosol particles in any climate is fundamental: studies of climate variations on another planet can help us better understand our own global change. In this thesis I have used an atmospheric column model for Mars to study the behaviour of the lowest layer of the atmosphere, the planetary boundary layer (PBL), and I have developed nucleation (particle formation) models for Martian conditions. The models were also coupled to study, for example, fog formation in the PBL. The PBL is perhaps the most significant part of the atmosphere for landers and humans, since we live in it and experience its state, for example, as gusty winds, nightfrost, and fogs. However, PBL modelling in weather prediction models is still a difficult task. Mars hosts a variety of cloud types, mainly composed of water ice particles, but also CO2 ice clouds form in the very cold polar night and at high altitudes elsewhere. Nucleation is the first step in particle formation, and always includes a phase transition. Cloud crystals on Mars form from vapour to ice on ubiquitous, suspended dust particles. Clouds on Mars have a small radiative effect in the present climate, but it may have been more important in the past. This thesis represents an attempt to model the Martian atmosphere at the smallest scales with high resolution. The models used and developed during the course of the research are useful tools for developing and testing parameterizations for larger-scale models all the way up to global climate models, since the small-scale models can describe processes that in the large-scale models are reduced to subgrid (not explicitly resolved) scale.

Theoretical and computational approaches on heterogeneous nucleation

Nucleation is the first step of a first order phase transition. A new phase is always sprung up in nucleation phenomena. The two main categories of nucleation are homogeneous nucleation, where the new phase is formed in a uniform substance, and heterogeneous nucleation, when nucleation occurs on a pre-existing surface. In this thesis the main attention is paid on heterogeneous nucleation. This thesis wields the nucleation phenomena from two theoretical perspectives: the classical nucleation theory and the statistical mechanical approach. The formulation of the classical nucleation theory relies on equilibrium thermodynamics and use of macroscopically determined quantities to describe the properties of small nuclei, sometimes consisting of just a few molecules. The statistical mechanical approach is based on interactions between single molecules, and does not bear the same assumptions as the classical theory. This work gathers up the present theoretical knowledge of heterogeneous nucleation and utilizes it in computational model studies. A new exact molecular approach on heterogeneous nucleation was introduced and tested by Monte Carlo simulations. The results obtained from the molecular simulations were interpreted by means of the concepts of the classical nucleation theory. Numerical calculations were carried out for a variety of substances nucleating on different substances. The classical theory of heterogeneous nucleation was employed in calculations of one-component nucleation of water on newsprint paper, Teflon and cellulose film, and binary nucleation of water-n-propanol and water-sulphuric acid mixtures on silver nanoparticles. The results were compared with experimental results. The molecular simulation studies involved homogeneous nucleation of argon and heterogeneous nucleation of argon on a planar platinum surface. It was found out that the use of a microscopical contact angle as a fitting parameter in calculations based on the classical theory of heterogeneous nucleation leads to a fair agreement between the theoretical predictions and experimental results. In the presented cases the microscopical angle was found to be always smaller than the contact angle obtained from macroscopical measurements. Furthermore, molecular Monte Carlo simulations revealed that the concept of the geometrical contact parameter in heterogeneous nucleation calculations can work surprisingly well even for very small clusters.

Local structure of water studied by Compton scattering

This thesis presents a novel application of x-ray Compton scattering to structural studies of molecular liquids. Systematic Compton-scattering experiments on water have been carried out with unprecedented accuracy at third-generation synchrotron-radiation laboratories. The experiments focused on temperature effects in water, the water-to-ice phase transition, quantum isotope effects, and ion hydration. The experimental data is interpreted by comparison with both model computations and ab initio molecular-dynamics simulations. Accordingly, Compton scattering is found to provide unique intra- and intermolecular structural information. This thesis thus demonstrates the complementarity of the technique to traditional real-space probes for studies on the local structure of water and, more generally, molecular liquids.

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.

Molecular Dynamics Simulations of Homogeneous Nucleation

Nucleation is the first step in a phase transition where small nuclei of the new phase start appearing in the metastable old phase, such as the appearance of small liquid clusters in a supersaturated vapor. Nucleation is important in various industrial and natural processes, including atmospheric new particle formation: between 20 % to 80 % of atmospheric particle concentration is due to nucleation. These atmospheric aerosol particles have a significant effect both on climate and human health. Different simulation methods are often applied when studying things that are difficult or even impossible to measure, or when trying to distinguish between the merits of various theoretical approaches. Such simulation methods include, among others, molecular dynamics and Monte Carlo simulations. In this work molecular dynamics simulations of the homogeneous nucleation of Lennard-Jones argon have been performed. Homogeneous means that the nucleation does not occur on a pre-existing surface. The simulations include runs where the starting configuration is a supersaturated vapor and the nucleation event is observed during the simulation (direct simulations), as well as simulations of a cluster in equilibrium with a surrounding vapor (indirect simulations). The latter type are a necessity when the conditions prevent the occurrence of a nucleation event in a reasonable timeframe in the direct simulations. The effect of various temperature control schemes on the nucleation rate (the rate of appearance of clusters that are equally able to grow to macroscopic sizes and to evaporate) was studied and found to be relatively small. The method to extract the nucleation rate was also found to be of minor importance. The cluster sizes from direct and indirect simulations were used in conjunction with the nucleation theorem to calculate formation free energies for the clusters in the indirect simulations. The results agreed with density functional theory, but were higher than values from Monte Carlo simulations. The formation energies were also used to calculate surface tension for the clusters. The sizes of the clusters in the direct and indirect simulations were compared, showing that the direct simulation clusters have more atoms between the liquid-like core of the cluster and the surrounding vapor. Finally, the performance of various nucleation theories in predicting simulated nucleation rates was investigated, and the results among other things highlighted once again the inadequacy of the classical nucleation theory that is commonly employed in nucleation studies.