Derived Dimensions and Common Units

A.2 DERIVED DIMENSIONS AND COMMON UNITS TABLE A.3 Multiplier Prefixes for Use with SI Units"... 

The effects of coupling of the DTO and RB units in not only one- but also three-dimensional arrays are discussed below and molecular weight trends illustrated. A fundamental connection between relaxation times and normal mode frequencies, shown to hold in all dimensions, allows the rapid derivation of the common viscoelastic and dielectric response functions from a knowledge of the appropriate lattice vibration spectra. It is found that the time and frequency dispersion behavior is much sharper when the oscillator elements are established in three-dimensional quasi-lattices as in the case of organic glasses. 

Among the simplest derived dimensions are area [L2] and volume [L3]. While the square meter (m2) is a common SI unit of area, numerous other units [e.g., square foot (ft2), acre, hectare (ha), and square mile (mi2)] are in use, as shown in Table A-4. A common SI unit of volume is the cubic meter (m3), although for environmental chemical problems the liter is often used. Note that liter is spelled out throughout this book, whereas [L] refers to the dimension length. Table A-5 presents common volume units and interconversion factors. 

Every system of units has a large number of derived units which are, as the name implies, derived from the base units. The new units are based on the physical definitions of other quantities which involve the combination of different variables. Below is a list of several common derived system properties and the corresponding dimensions (= denotes unit equivalence). If you don t know what one of these properties is, you will learn it eventually ... 

The mole and kelvin units cancel, and we are left with units of J m , a combination of an SI derived unit (the joule) and an SI base unit (the meter). The units J m must have dimensions of pressure, but are not commonly used to express pressure. 

Mass, length and time are commonly used primary units, other units being derived from them. Their dimensions are written as M, L and T respectively. Sometimes force is used as a primary unit. In the Systeme International d Unites, commonly known as the SI system of units, the primary units are the kilogramme kg, the metre m, and the second s. A number of derived units are listed in Table 1.1. 

The rate of transport of particles across a surface at a point, expressed as number per unit time per unit area, is culled the jinx at the point. Common dimensions for the flux are paTticle.s/cm. sec. Expressions for the diffusion flux and diffusion coefflcienl (hat apply to submicron particles are derived from first principles in this chapter. The presence of an external force Retd acting on the particles leads to an additional term in the flux. The transport of particles larger than about a micron is analyzed by solving a momentum balance that incorporates the external force fields. 

The rate at which reactants are converted to products is a key quantity for characterizing a chemical reaction. The rate of a stoichiometric reaction may be dehned by dividing the observed rate of consumption of moles of each individual reactant and the rate of formation of moles of each individual product by their respective stoichiometric coefficients, where the rates are time derivatives. Division by the stoichiometric coefficients reduces the individual species rates to a common value, R, having the dimensions of moles per unit time. For the stoichiometric reaction of equation (1) the rate is defined by... 

The derived unit known as the plane angle refers to the angular separation of two lines from a common point in a two-dimensional plane. The SI derived unit for plane angles is the radian. A complete rotation about a point origin is an angular displacement of 2ti radians. The extension of this into three dimensions is known as the solid angle and is measured by the SI derived unit called the steradian. 

The impressive development in molecular simulation stems from important improvement in both codes and computers. It made available accurate atomistic simulation of fluorine derivatives. Depiction of the SPF is most commonly achieved by quantum calculations. The major difficulty in describing interactions involving fluorine atoms actually lies in a correct description of the electrostatic effects [38]. Crystal unit cell dimensions [39,40] and the thermal behavior of fluoropolymers [41 3] were thus originally difficult to reproduce. Dihedral potential energy (Equation 6.3) that plays a central role in the backbone dynamics was also incorrectly depicted. In this section, illustrative examples of force fields specifically dedicated to fluoropolymers and more transferable force fields are reviewed. 

---