SINCLAIR

The origins of the Finnis-Sinclair potential [Finnis and Sinclair 1984] lie in the density of states and the moments theorem. Recall that the density of states D(E) (see Section 3.8.5) describes the distribution of electronic states in the system. D(E) gives the number of states between E and E - - 8E. Such a distribution can be described in terms of its moments. The moments are usually defined relative to the energy of the atomic orbital from which the molecular orbitals are formed. The mth moment, fi", is given by ... 

Finnis-Sinclair potential a pairwise contribution is added to the many-body term to he following form ... 

Sutton and Chen extended the potential to longer range to enable the study of certain problems such as the interactions between clusters of afoms [Sutton and Chen 1990]. Their objective was to combine the superior Fiimis-Sinclair description of short-range interactions with a van der Waals tail to model the long-range interactions. The form of the Sutton-Chen potential is ... 

The Tersoff potential [Tersoff 1988] is based on a model known as the empirical bond-order potential. This potential can be written in a form very similar to the Finnis-Sinclair potential ... 

The key term is which is the bond order between the atoms i and j. This parameter depends upon the number of bonds to the atom i the strength of the bond between i and j decreases as the number of bonds fo fhe atom i increases. The original bond-order potential [Abell 1985] is mathematically equivalent to the Finnis-Sinclair model if the bond order by is given by ... 

Finnis M W and J E Sinclair 1984. A Simple Empirical N-body Potential for Transition Metals. Philosophical Magazine A50-.45-55. 

Sutton A P and J Chen 1990. Long-range Finnis-Sinclair Potentials. Philosophical Magazine Letters 61 139-146. 

Figure 9.47 Part of the observed 0[j band (top), an expansion of a small portion (middle) and a computer simulation (bottom) of (a) aniline and (b) aniline Ar. (Reproduced, with permission, from Sinclair, W. E. and Pratt, D. W., J. Chem. Phys., 105, 7942, 1996)...

AH corrosion inhibitors in use as of this writing are oil-soluble surfactants (qv) which consist of a hydrophobic hydrocarbon backbone and a hydrophilic functional group. Oil-soluble surfactant-type additives were first used in 1946 by the Sinclair Oil Co. (38). Most corrosion inhibitors are carboxyhc acids (qv), amines, or amine salts (39), depending on the types of water bottoms encountered in the whole distribution system. The wrong choice of inhibitors can lead to unwanted reactions. Eor instance, use of an acidic corrosion inhibitor when the water bottoms are caustic can result in the formation of insoluble salts that can plug filters in the distribution system or in customers vehicles. Because these additives form a strongly adsorbed impervious film at the metal Hquid interface, low Hquid concentrations are usually adequate. Concentrations typically range up to 5 ppm. In many situations, pipeline companies add their own corrosion inhibitors on top of that added by refiners. 

R. C. Denney and R. Sinclair, Visible and JJItravioletSpectroscopy ]ohxs Wiley Sons, Inc., New York, 1988. 

C. G. Sinclair [Chem. Process. E/ig., 47, 147 (1966)] has considered similar parameters to the (EMIP) and (IRP) based on a cumulative-discounted-cash-flow curve. 

Bismethylaminoanthraquinone (Disperse Blue 14) [2475-44-7] M 266.3, A,max 640 (594)nm. Purified by thin-layer chromatography on silica gel plates, using toluene/acetone (3.1) as eluent. The main band was scraped off and extracted with MeOH. The solvent was evapd and the dye was dried in a drying pistol [Land, McAlpine, Sinclair and Truscott J Chem Soc, Faraday Trans I 72 2091 7976]. 

This chapter solely reviews tlie kinetics of enzyme reactions, modeling, and simulation of biochemical reactions and scale-up of bioreactors. More comprehensive treatments of biochemical reactions, modeling, and simulation are provided by Bailey and Ollis [2], Bungay [3], Sinclair and Kristiansen [4], Volesky and Votruba [5], and Ingham et al. [6]. 

A. D. McKnight, P. K. Marstrand and T. C. Sinclair (eds.). Environmental Pollution Control, Chap. 5 Pollution of inland waters Chap. 6 The Law relating to pollution of inland waters George, Allen and Unwin, London, 1974. 

---