Binary properties

So far, we have seen several ways of calculating the Gibbs free energy of a two-component mixture. To extend calculations to ternary and higher-order mixtures, we use empirical combinatory extensions of the binary properties. We summarize here only some of the most popular approaches. An extended comparative appraisal of the properties of ternary and higher-order mixtures can be found in Barron (1976), Grover (1977), Hillert (1980), Bertrand et al. (1983), Acree (1984), and Fei et al. (1986). 

A polar surface area approximation can be calculated by summing the V, contribution of each polar atom in a molecule. A hydrophobic surface area approximation can be calculated by V) contribution of each hydrophobic atom in a molecule. More generally, for a given binary property Bt (such as is polar or is aromatic or is acceptor ) for each atom i in a molecule, an approximate surface-area based descriptor can be calculated with... 

We turn now to non-binary properties of each atom in a molecule. Suppose that for each atom i in a molecule we are given a numeric property P,. Our fundamental idea is to create a descriptor consisting of the sum of VSA contributions of each atom with P, in a specific range [ ,v). (The expression [m,v)... 

Support vector machines In addition to more traditional classification methods like clustering or partitioning, other computational approaches have recently also become popular in chemoinformatics and support vector machines (SVMs) (Warmuth el al. 2003) are discussed here as an example. Typically, SVMs are applied as classifiers for binary property predictions, for example, to distinguish active from inactive compounds. Initially, a set of descriptors is selected and training set molecules are represented as vectors based on their calculated descriptor values. Then linear combinations of training set vectors are calculated to construct a hyperplane in descriptor space that best separates active and inactive compounds, as illustrated in Figure 1.9. 

These are but few examples which illustrate the need for a continuous scale of symmetry. Thus symmetry can be, and, in many in.stances should be, treated as a continuous property, and not necessarily as a binary property which exists or does not exist. 

Presents a variety of measured thermodynamic properties of binary mixtures these properties are often represented by empirical equations. 

Compilation of data for binary mixtures reports some vapor-liquid equilibrium data as well as other properties such as density and viscosity. 

Appendix C presents properties and parameters for 92 pure fluids and characteristic binary-mixture parameters for 150 binary pairs. 

As it has appeared in recent years that many hmdamental aspects of elementary chemical reactions in solution can be understood on the basis of the dependence of reaction rate coefficients on solvent density [2, 3, 4 and 5], increasing attention is paid to reaction kinetics in the gas-to-liquid transition range and supercritical fluids under varying pressure. In this way, the essential differences between the regime of binary collisions in the low-pressure gas phase and tliat of a dense enviromnent with typical many-body interactions become apparent. An extremely useful approach in this respect is the investigation of rate coefficients, reaction yields and concentration-time profiles of some typical model reactions over as wide a pressure range as possible, which pemiits the continuous and well controlled variation of the physical properties of the solvent. Among these the most important are density, polarity and viscosity in a contimiiim description or collision frequency. 

Atre S V, Liedberg B and Allara D L 1995 Chain length dependenoe of the struoture and wetting properties in binary oomposition monolayers of OH and CHj-terminated alkanethiolates on gold Langmuir 3882-93... 

Temary and quaternary semiconductors are theoretically described by the virtual crystal approximation (VGA) [7], Within the VGA, ternary alloys with the composition AB are considered to contain two sublattices. One of them is occupied only by atoms A, the other is occupied by atoms B or G. The second sublattice consists of virtual atoms, represented by a weighted average of atoms B and G. Many physical properties of ternary alloys are then expressed as weighted linear combinations of the corresponding properties of the two binary compounds. For example, the lattice constant d dependence on composition is written as ... 

Usually, the denominator, if present in a similarity measure, is just a normalizet it is the numerator that is indicative of whether similarity or dissimilarity is being estimated, or both. The characteristics chosen for the description of the objects being compared are interchangeably called descriptors, properties, features, attributes, qualities, observations, measurements, calculations, etc. In the formiilations above, the terms matches and mismatches" refer to qualitative characteristics, e.g., binary ones (those which take one of two values 1 (present) or 0 (absent)), while the terms overlap and difference" refer to quantitative characteristics, e.g., those whose values can be arranged in order of magnitude along a one-dimensional axis. 

The program uses two ASCII input files for the SCF and properties stages of the calculation. There is a text output file as well as a number of binary or ASCII data files that can be created. The geometry is entered in fractional coordinates for periodic dimensions and Cartesian coordinates for nonperiodic dimensions. The user must specify the symmetry of the system. The input geometry must be oriented according to the symmetry axes and only the symmetry-unique atoms are listed. Some aspects of the input are cumbersome, such as the basis set specification. However, the input format is documented in detail. 

Revised material in Section 5 includes an extensive tabulation of binary and ternary azeotropes comprising approximately 850 entries. Over 975 compounds have values listed for viscosity, dielectric constant, dipole moment, and surface tension. Whenever possible, data for viscosity and dielectric constant are provided at two temperatures to permit interpolation for intermediate temperatures and also to permit limited extrapolation of the data. The dipole moments are often listed for different physical states. Values for surface tension can be calculated over a range of temperatures from two constants that can be fitted into a linear equation. Also extensively revised and expanded are the properties of combustible mixtures in air. A table of triple points has been added. 

The properties of a copolymer can be viewed as hybrids of the properties of the separate homopolymers. Because of this, a good deal of refinement can be introduced into these properties by the use of copolymers. The situation is analogous to the use of pure liquids or binary solutions as solvents. The number of binary combinations, n(n - l)/2 as noted above, greatly exceeds the number of pure liquids, and any one of these combinations can be prepared over a range of compositions. Just as mixed solvents offer a wider range of properties than... 

Thousands of compounds of the actinide elements have been prepared, and the properties of some of the important binary compounds are summarized in Table 8 (13,17,18,22). The binary compounds with carbon, boron, nitrogen, siUcon, and sulfur are not included these are of interest, however, because of their stabiUty at high temperatures. A large number of ternary compounds, including numerous oxyhaUdes, and more compHcated compounds have been synthesized and characterized. These include many intermediate (nonstoichiometric) oxides, and besides the nitrates, sulfates, peroxides, and carbonates, compounds such as phosphates, arsenates, cyanides, cyanates, thiocyanates, selenocyanates, sulfites, selenates, selenites, teUurates, tellurites, selenides, and teUurides. 

Table 8. Properties and Crystal Structure Data for Important Actinide Binary Compounds...

Binary mixtures of pentaerythritol with many other polyol species can produce heat or electrical storage media having excellent retention properties... 

The halogen fluorides are binary compounds of bromine, chlorine, and iodine with fluorine. Of the eight known compounds, only bromine trifluoride, chlorine trifluoride, and iodine pentafluoride have been of commercial importance. Properties and appHcations have been reviewed (1 7) as have the reactions with organic compounds (8). Reviews covering the methods of preparation, properties, and analytical chemistry of the halogen fluorides are also available (9). 

Alloys. GaUium has complete miscibility in the hquid state with aluminum, indium, tin, and zinc. No compounds are formed. However, these binary systems form simple eutectics having the following properties ... 

Low Expansion Alloys. Binary Fe—Ni alloys as well as several alloys of the type Fe—Ni—X, where X = Cr or Co, are utilized for their low thermal expansion coefficients over a limited temperature range. Other elements also may be added to provide altered mechanical or physical properties. Common trade names include Invar (64%Fe—36%Ni), F.linvar (52%Fe—36%Ni—12%Cr) and super Invar (63%Fe—32%Ni—5%Co). These alloys, which have many commercial appHcations, are typically used at low (25—500°C) temperatures. Exceptions are automotive pistons and components of gas turbines. These alloys are useful to about 650°C while retaining low coefficients of thermal expansion. Alloys 903, 907, and 909, based on 42%Fe—38%Ni—13%Co and having varying amounts of niobium, titanium, and aluminum, are examples of such alloys (2). 

Properties of cyclohexane are given in Table 11, and a number of binary azeotropes that are formed with cyclohexane are Hsted in Table 12. 

Isoprene [78-79-5] (2-methyl-1,3-butadiene) is a colorless, volatile Hquid that is soluble in most hydrocarbons but is practically insoluble in water. Isoprene forms binary azeotropes with water, methanol, methylamine, acetonitrile, methyl formate, bromoethane, ethyl alcohol, methyl sulfide, acetone, propylene oxide, ethyl formate, isopropyl nitrate, methyla1 (dimethoxymethane), ethyl ether, and / -pentane. Ternary azeotropes form with water—acetone, water—acetonitrile, and methyl formate—ethyl bromide (8). Typical properties of isoprene are Hsted in Table 1. 

Lead—Calcium-Tin Alloys. Tin additions to lead—calcium and lead—calcium—aluminum alloys enhances the mechanical (8) and electrochemical properties (12). Tin additions reduce the rate of aging compared to lead—calcium binary alloys. The positive grid alloys for maintenance-free lead—calcium batteries contain 0.3—1.2 wt % tin and also aluminum. 

---