Bulk macroscopic properties

We carry out computer simulations in the hope of understanding bulk, macroscopic properties in temis of the microscopic details of molecular structure and interactions. This serves as a complement to conventional experiments, enabling us to leam something new something that cannot be found out in other ways. 

The student conceptions that were displayed could be categorised into three main types, namely (1) confusion between macroscopic and submicroscopic representations, (2) extrapolation of bulk macroscopic properties of matter to the submicroscopic level and (3) corrfusion over the multi-faceted significance of chemical symbols, chemical formulas as well as chemical and ionic equations. Student conceptions held by at least 10% of the students who were involved in the alternative instractional programme were identified. Several examples of student conceptions involving the use of the triplet relationship are discussed in the next section. 

Thermodynamics deals with relations among bulk (macroscopic) properties of matter. Bulk matter, however, is comprised of atoms and molecules and, therefore, its properties must result from the nature and behavior of these microscopic particles. An explanation of a bulk property based on molecular behavior is a theory for the behavior. Today, we know that the behavior of atoms and molecules is described by quantum mechanics. However, theories for gas properties predate the development of quantum mechanics. An early model of gases found to be very successftd in explaining their equation of state at low pressures was the kinetic model of noninteracting particles, attributed to Bernoulli. In this model, the pressure exerted by n moles of gas confined to a container of volume V at temperature T is explained as due to the incessant collisions of the gas molecules with the walls of the container. Only the translational motion of gas particles contributes to the pressure, and for translational motion Newtonian mechanics is an excellent approximation to quantum mechanics. We will see that ideal gas behavior results when interactions between gas molecules are completely neglected. 

Rather few papers have dealt with the computation of thermodynamic functions from the results of ab initio calculations, but for H2, where the latter are of spectroscopic accuracy, Kosloff, Levine, and Bernstein have computed the thermodynamic properties of Ha, Da, and HD, using the best theoretical results.75 This work represents the first example of an accurate determination of a bulk, macroscopic property from first principles. 

Analytical characterization includes measurement of absolute sizes and concentrations of species present in the catalyst. For the purpose of clarity, these techniques have been organized, starting with the bulk macroscopic properties, down to the component, microscopic features. The underlying goal of analytical characterization is to provide information about the sample which will allow research personnel to relate the properties measured to some aspect of a catalyst s performance, either in the field or in the evaluation laboratory. Macroscopic characterization includes both chemical compositions and physical properties such as particle size, density and total surface area. Chemical analysis techniques are well... 

For most smdents, the most challenging mental connections that are forged in general chemistry are those between bulk macroscopic properties and molecular level origins of those bulk properties. The Arrhenius equation provides us with a good opportunity to focus on this type of mental connection. 

One of the most obvious difficulties arises in both simulation methods from the relatively small system size, always much smaller than the Avogadro number, N, characteristic for a macroscopic system. Therefore, so-called periodic boundary conditions are usually applied to the simulated system in order to minimize surface effects and to simulate more closely its bulk macroscopic properties. This means that the basic simulation box is assumed to be surrounded by identical boxes in all three dimensions infinitely. Thus, if a particle leaves the box through one side, its image enters simultaneously through the opposite side, because of the identity of the boxes. In this way, the problem of surfaces is circumvented at the expense of the introduction of periodicity. 

Many models are used to include the microscopic effects of water molecules on biological systems, and most of them are based on parameterized force field schemes that are tuned to reproduce some bulk macroscopic properties of the solvent. For a given system, the choice of a specific water model is based on the usual tradeoff between accuracy and computational complexity. Furthermore, even if a particular model fits a type of data better than another— for example, dielectric constant better than density versus temperature—the choice of which model to use is not obvious. 

This section describes both dynamics studies at the molecular level and also cooperative bulk macroscopic properties as sensed by diffusion studies. The measurements of the proton spin-lattice relaxation time of liquid crystal 4- -octyl-4 -cyanobiphenyl (8CB) confined in randomly oriented untreated porous glass have been presented. The studies are in agreement with the model of mutually independent pores with nematic director parallel to the pore axis in each segment. The local translational diffusion of molecules within the cavities is found to be nearly as fast as in bulk. Orientational relaxation of a model discotic liquid crystal, consisting of dislike molecules... 

For simple liquids it is straightforward to relate a bulk macroscopic property to its microscopic origins. Consider, for example, how the molecular electronic polarizability a manifests itself in the refractive index n of a simple liquid. The relative permittivity (the dielectric constant) is a simple function of a and the number density Nof molecules (the number per unit volume) in the liquid ... 

To define the thennodynamic state of a system one must specify fhe values of a minimum number of variables, enough to reproduce the system with all its macroscopic properties. If special forces (surface effecls, external fields—electric, magnetic, gravitational, etc) are absent, or if the bulk properties are insensitive to these forces, e.g. the weak terrestrial magnetic field, it ordinarily suffices—for a one-component system—to specify fliree variables, e.g. fhe femperature T, the pressure p and the number of moles n, or an equivalent set. For example, if the volume of a surface layer is negligible in comparison with the total volume, surface effects usually contribute negligibly to bulk thennodynamic properties. 

The correct treatment of boundaries and boundary effects is crucial to simulation methods because it enables macroscopic properties to be calculated from simulations using relatively small numbers of particles. The importance of boundary effects can be illustrated by considering the following simple example. Suppose we have a cube of volume 1 litre which is filled with water at room temperature. The cube contains approximately 3.3 X 10 molecules. Interactions with the walls can extend up to 10 molecular diameters into the fluid. The diameter of the water molecule is approximately 2.8 A and so the number of water molecules that are interacting with the boundary is about 2 x 10. So only about one in 1.5 million water molecules is influenced by interactions with the walls of the container. The number of particles in a Monte Carlo or molecular dynamics simulation is far fewer than 10 -10 and is frequently less than 1000. In a system of 1000 water molecules most, if not all of them, would be within the influence of the walls of the boundary. Clecirly, a simulation of 1000 water molecules in a vessel would not be an appropriate way to derive bulk properties. The alternative is to dispense with the container altogether. Now, approximately three-quarters of the molecules would be at the surface of the sample rather than being in the bulk. Such a situation would be relevcUit to studies of liquid drops, but not to studies of bulk phenomena. 

A microscopic description characterizes the structure of the pores. The objective of a pore-structure analysis is to provide a description that relates to the macroscopic or bulk flow properties. The major bulk properties that need to be correlated with pore description or characterization are the four basic parameters porosity, permeability, tortuosity and connectivity. In studying different samples of the same medium, it becomes apparent that the number of pore sizes, shapes, orientations and interconnections are enormous. Due to this complexity, pore-structure description is most often a statistical distribution of apparent pore sizes. This distribution is apparent because to convert measurements to pore sizes one must resort to models that provide average or model pore sizes. A common approach to defining a characteristic pore size distribution is to model the porous medium as a bundle of straight cylindrical or rectangular capillaries (refer to Figure 2). The diameters of the model capillaries are defined on the basis of a convenient distribution function. 

Finally the example of the ring spectra demonstrated that the MAS NMR spectroscopy can give a clear and detailed molecular picture for the explanation of macroscopic changes and bulk material properties. 

Network properties and microscopic structures of various epoxy resins cross-linked by phenolic novolacs were investigated by Suzuki et al.97 Positron annihilation spectroscopy (PAS) was utilized to characterize intermolecular spacing of networks and the results were compared to bulk polymer properties. The lifetimes (t3) and intensities (/3) of the active species (positronium ions) correspond to volume and number of holes which constitute the free volume in the network. Networks cured with flexible epoxies had more holes throughout the temperature range, and the space increased with temperature increases. Glass transition temperatures and thermal expansion coefficients (a) were calculated from plots of t3 versus temperature. The Tgs and thermal expansion coefficients obtained from PAS were lower titan those obtained from thermomechanical analysis. These differences were attributed to micro-Brownian motions determined by PAS versus macroscopic polymer properties determined by thermomechanical analysis. 

The three representations that are referred to in this study are (1) macroscopic representations that describe the bulk observable properties of matter, for example, heat energy, pH and colour changes, and the formation of gases and precipitates, (2) submicroscopic (or molecular) representations that provide explanations at the particulate level in which matter is described as being composed of atoms, molecules and ions, and (3) symbolic (or iconic) representations that involve the use of chemical symbols, formulas and equations, as well as molecular structure drawings, models and computer simulations that symbolise matter (Andersson, 1986 Boo, 1998 Johnstone, 1991, 1993 Nakhleh Krajcik, 1994 Treagust Chittleborough, 2001). 

Note that we make a distinction between a solution and a mixture. When we talk of a solution, we imply that the organic solute is not a major component of the bulk liquid. Therefore, that presence of a dissolved organic compound does not have a significant impact on the properties of the bulk liquid. In contrast, in a mixture we recognize that the major components contribute substantially to the overall nature of the medium. This is reflected in macroscopic properties like air-liquid surface tensions and in molecule-scale phenomena like solubilities of trace constitutents. 

In this article we have reviewed our recent work with NMR analysis on various kinds of linear polyethylene samples. It has become evident that the refined NMR analysis gives us much important information on the phase structure of samples in terms of molecular mobility, and establishes that there is no unified phase structure for polymer samples. The phase structure of samples varies over a very wide range, depending strongly on the sort of samples involved as well as on the mode of crystallization or the history of those samples. We should emphasize that there are significant differences in phase structure among the bulk-crystals, the solution-crystals, and the fiber samples, particularly in the conformation of molecular chains in the noncrystalline content. We should not confuse these phase structures with each other. The phase structures are evidently different, sample by sample, as their macroscopic properties also differ one from another. 

In addition to the microscopic redox processes of bismuth ions and molybdenum ions, the combination of these conductivity measurements leads to the conclusion that the macroscopic, bulk conductivity properties of the bismuth molybdate catalyst affect the catalytic reaction. 

Chen (1980, p. 7) suggested that the use of bulk phase properties, such as those in Equations 3.1 through 3.3, may be satisfactory only in qualitative analyses. Microscopic critical clusters contain several tens to thousands of molecules, and as such have a spectrum of sizes and properties, which may be difficult to quantify with a single number on a macroscopic scale. 

In spite of the potential advantages, useful organic NLO materials have not yet been developed because the necessary molecular and macroscopic characteristics have only recently begun to be understood. However, because bulk NLO properties in organic materials arise directly from the constituent molecular nonlinearities, it is possible to decouple molecular and supramolecular contributions to the NLO properties. One can then semiquantitatively predict relative macroscopic nonlinearities based on theoretical analyses of the individual molecules (7). Reliable predictions of this kind are vital for the efficiency of a program aimed towards developing new organic materials with tailored NLO properties. 

However, even if a consideration of the macroscopic properties of the SSE many times is useful as a first approximation for predicting the outcome of an unknown electro-organic reaction, it must be borne in mind that the composition of the electrolyte at the electrode surface and its immediate vicinity might be completely different from that of the bulk of the solution. Current theory 19>79 assumes that the electrode surface is covered by an adsorbed layer of ions and neutral molecules during electrolysis. The thickness of this layer, the electrical... 

On a macroscopic level, the bulk solvent properties such as the dielectric constant are changed. According to the Coulomb law this weakens all electrostatic interactions and hence also hydrogen bonds. 

It has its origins in the study of macroscopic (i.e. bulk, observable) properties of materials (e.g. temperature, T pressure, P volume, V etc.) made en masse. 

Examples include the work function, specific resistance (resistivity), elasticity, and thermodynamic properties (e.g. specific heat capacity, melting point). Intrinsic properties are determined by crystallographic structure and are not susceptible to significant change by modification of the microstmcture. Some commonly used synonyms for intrinsic macroscopic properties include global, bulk, and continuum-level. As we might... 

Equation [1] relates a (macroscopic) bulk, empirical property, Y, with some set, X, of (microscopic) molecular structural parameters (descriptors). The equation as shown is linear in that each term involves a first power for its descriptor. Fligher order descriptors may also be used. The coefficients, Uj, are obtained with the aid of statistical methods, particularly, regression... 

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