Molecules bulk/surface

The microscopic understanding of tire chemical reactivity of surfaces is of fundamental interest in chemical physics and important for heterogeneous catalysis. Cluster science provides a new approach for tire study of tire microscopic mechanisms of surface chemical reactivity [48]. Surfaces of small clusters possess a very rich variation of chemisoriDtion sites and are ideal models for bulk surfaces. Chemical reactivity of many transition-metal clusters has been investigated [49]. Transition-metal clusters are produced using laser vaporization, and tire chemical reactivity studies are carried out typically in a flow tube reactor in which tire clusters interact witli a reactant gas at a given temperature and pressure for a fixed period of time. Reaction products are measured at various pressures or temperatures and reaction rates are derived. It has been found tliat tire reactivity of small transition-metal clusters witli simple molecules such as H2 and NH can vary dramatically witli cluster size and stmcture [48, 49, M and 52]. 

Consider spherical molecules A and B having radii and Tb and diffusion coefficients Da and Db- First, suppose that B is fixed and that the rate of reaction is limited by the rate at which A molecules diffuse to the B molecule. We calculate the flux 7(A- B) of A molecules to one B molecule. Let a and b be the concentrations (in molecules/cm ) of A and B in the bulk, and let r be the radius of a sphere centered at the B molecule. The surface area of this sphere is Aitr, so by Pick s first law we obtain... 

This article reviews progress in the field of atomistic simulation of liquid crystal systems. The first part of the article provides an introduction to molecular force fields and the main simulation methods commonly used for liquid crystal systems molecular mechanics, Monte Carlo and molecular dynamics. The usefulness of these three techniques is highlighted and some of the problems associated with the use of these methods for modelling liquid crystals are discussed. The main section of the article reviews some of the recent science that has arisen out of the use of these modelling techniques. The importance of the nematic mean field and its influence on molecular structure is discussed. The preferred ordering of liquid crystal molecules at surfaces is examined, along with the results from simulation studies of bilayers and bulk liquid crystal phases. The article also discusses some of the limitations of current work and points to likely developments over the next few years. 

In the previous chapters, you have learned how to use DFT calculations to optimize the structures of molecules, bulk solids, and surfaces. In many ways these calculations are very satisfying since they can predict the properties of a wide variety of interesting materials. But everything you have seen so far also substantiates a common criticism that is directed toward DFT calculations namely that it is a zero temperature approach. What is meant by this is that the calculations tell us about the properties of a material in which the atoms are localized at equilibrium or minimum energy positions. In classical mechanics, this corresponds to a description of a material at 0 K. The implication of this criticism is that it may be interesting to know about how materials would appear at 0 K, but real life happens at finite temperatures. 

A drop of a methanol solution of CV was spin coated on an 30-nm-thick PMMA film previously spin coated on a quartz surface. The concentration of a CV solution in methanol was 1 mM for fluorescence lifetime measurements in bulk, and 1.0 and 0.1 nM for single-molecule measurements. The use of nanomolar or lower concentrations of solutions is common for preparing well-separated single molecules on surfaces [13,15,18,31 12]. 

There is no reason to expect that as the dimensions of a phase are reduced to the point where it contains a small number of molecules, its surface tension remains constant. This question has obvious relevance to important problems, such as condensation of droplets from supersaturated vapors. Although a number of authors have considered this problem, in these days of supercomputers, it is probably best handled by considering individual intermolecular interactions rather than a bulk property, such as surface tension. 

During adsorption the local concentration of molecules in the nei -hoihood of a surface differs from that of the bulk phase. Figure 9.9 shows this enhanced concentration at the solid-liquid interface. At this interface, there is a sur ce excess concentration of surface active molecules. This surface excess corresponds to the shaded area in Figure 9.9. Dividing this excess number of moles of i at the surface, nf, by the area of the surface, we obtain the svuface excess concentration, Ff, of component i given by... 

Figure 4. Orbital resolved rf-band of Pts for bare [Xbuik- s]-Pt3 (left) and oxygen-chemisorbed [Xbuik- s]-Pt3-02 (right) surfaces. The spectra are numbered after the extended molecule Xs-Pt3 (see Fig. 1) used in the surface description. The corresponding bulk surfaces Xbun are 3, 8, Pt (red) 11, 12, Pt (blue) and 13, 14, Co3Pt (chocolate). The orbital resolved rf-band of the standalone Pt3 trimer (green, left) is shown as reference. In all panels, the Fermi level is the energy zero. All molecules are oriented such that the Pts cluster is in the X-Y plane.

Nanoparticles have different morphologies than flat, bulk surfaces. Perez et al. have considered the activation of water and COads + OHads reactions on Pt and PtRu clusters including the effects of solvation." They found that the presence of under-coordinated Ru adatoms on the Pt cluster surfaces enhances the production of OHads from water compared to Ru alloyed into the nanoparticle surfaces. More significantly, they found that the presence of an aqueous environment simulated by up to six water molecules dramatically stabilized the transition state and products of the reactions. For example, in a gas-phase environment they calculated a water dissociation barrier of 20 kcal/mol whereas in the solvated environment the barrier was reduced to 4.5 kcal/mol on the alloy surface. The barrier for water dissociation on the Ru adatom in the aqueous environment was only 0.9 kcal/mol. Although their results are for an adatom on a near flat (111) surface, they may have significance in describing the catalytic properties of undercoordinated Ru atoms at edge and corner sites on nanoparticles. 

Atoms and molecules at surfaces and interfaces possess energies significantly different from those of the same species in the bulk phase. The term surface is usually reserved for the region between a condensed phase (liquid or solid) and a gas phase or vacuum, while the term interface is normally applied to the region between two condensed phases. 

The definitions of the symbols are free energy (G), number of molecules (TV), chemical potentials in the bulk (//), surface area (A), surface tension (o), and mole fraction composition (x). Equation (26) is developed by Mirabel et al. (2000) by assuming that particles are spherical (even when crystalline), that the solute is not volatile, that the vapor phase reservoir of water is infinite, and that all chemical potentials behave ideally with respect to x. Note that the first and fourth approximations are gross. 

Water molecules have polar ends, and readily form hydrogen bonding. As a result, several compounds interact with water molecules by surface adsorption, condensation in capillaries, bulk retention, and chemical interaction, and are called hygroscopic. At times, the interaction between the compounds and water is so strong that the interacting water vapors result in dissolving the compound. This process is called deliquescence, wherein a saturated layer of solution is formed around the... 

The interface between the droplet and the gas is not discontinuous the average molecular density decreases over a narrow region from the liquid side to the vapor. When the size of the droplet becomes sufhctently small compared with the thickness of the transition layer, the use of classical thermodynamics and the bulk surface tension become inaccurate the Kelvin relation and Laplace formula no longer apply. This effect has been studied by molecular dynamics calculations of the behavior of liquid droplets composed of 41 to 2(X)4 molecules that interact through a Lennard-Jones (LI) intermolecular potential (Thomp.son et al., 1984). The results of this analysis are shown in Fig. 9.5, in which the nondimensional pressure difference between the drop interior and the surrounding vapor (Pd — p)rr / ij is... 

Instead of dissolving, hybrid molecules self-organize. Small amounts of these amphiphilic molecules produce surface films larger amounts lead to bulk assemblies, in which clusters of molecules minimize their destructive effect on the network of hydrogen bonds by forming micelles or vesicles (liposomes) with a speciflc topology that depends on the concentration and specific shape of the amphiphilic molecules (see Figure 19.6). 

The second step in the mechanism is diffusion into the pores leading to the reacting surface sites. Resistance to this diffusion is through collisions either with other molecules (bulk diffusion) or with the walls of the pore (Knudsen diffusion). Satterfield has described methods for calculating bulk and Knudsen diflusivities, and respectively. It is important to remember that... 

Structural sensitivity of the catalytic reactions is one of the most important problems in heterogeneous catalysis [1,2]. It has been rather thoroughly studied for metals, while for oxides, especially for dispersed ones, situation is far less clear due to inherent complexity of studies of their bulk and surface atomic structure. In last years, successful development of such methods as HREM and STM along with the infrared spectroscopy of test molecules has formed a sound bases for elucidating this problem in the case of oxides. In the work presented, the results of the systematic studies of the bulk/surface defect structure of the oxides of copper, iron, cobalt, chromium, manganese as related to structural sensitivity of the reactions of carbon monoxide and hydrocarbons oxidation are considered. 

Whenever two phases come in contact with one another, an interfacial region forms within which physical and chemical characteristics of each phase are disturbed relative to interior (bulk) regions of each phase. At the air-water interface, for example, the directional orientation of water molecules is more pionounced than in bulk solution, in order to compensate for the lack of hydiogen-bonding partners on the gas-phase side of the interface. As a consequence, the dielectric constant and other solvent characteristics that influence liemical reactions are perturbed to some degree. Solute molecules added to mi water or solvent-water systems may reside predominately in one phase or the other, or may concentrate in the interfacial region. Whether or not solute molecules are surface-active depends on the relative energies of possible dilute solute, solute-solvent, and solvent-solvent interactions (Tanford, 1980). 

In-situ STM offers unique high resolution of the dynamics of atoms and molecules at surfaces in solution [15]. The technique applies, however, also to bulk phenomena at... 

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