Part V. Pathways to Prevention Suppose further that r short range bonds and t long range bonds are formed. The equilibrium constant for such a “reaction” will then be mis = [x] g-h [x’] h [y] r [z] t [y’] s and it remains to find the values of x, x’, y, and z. This can be done by setting up the various sets of equations among the various geometrical figures involved. Such equations are called consistency equa- tions and normalizing equations. 5.2 A Small Part of the Mechanisms from the Department of Chemistry of Leeds University **********************************************************************; * INORGANIC CHEMISTRY ; **********************************************************************; * Ox/NOx CHEMISTRY ; % J<1>: O3 = O1D ; % J<2>: O3 = O ; % 6.00D-34*O2*O2*((TEMP/300)@-2.8): O = O3; % 5.60D-34*O2*N2*((TEMP/300)@-2.8): O = O3; % 8.00D-12*EXP(-2060/TEMP): O + O3 =; % KMT01 : O + NO = NO2; % 6.50D-12*EXP(120/TEMP) : O + NO2 = NO; % KMT02 : O + NO2 = NO3; % 3.20D-11*O2*EXP(70/TEMP) : O1D = O; % 1.80D-11*N2*EXP(110/TEMP) : O1D = O; % 1.80D-12*EXP(-1370/TEMP) : NO + O3 = NO2 ; % 1.20D-13*EXP(-2450/TEMP) : NO2 + O3 = NO3; % 3.30D-39*EXP(530/TEMP)*O2: NO + NO = NO2 + NO2; % 1.67D-06*(H0/H): NO2 = HONO ; % 1.80D-11*EXP(110/TEMP): NO + NO3 = NO2 + NO2 ; % 4.50D-14*EXP(-1260/TEMP) : NO2 + NO3 = NO + NO2 ; % KMT03 % KMT04 : NO2 + NO3 = N2O5 ; % 4.00D-04 : N2O5 = NA + NA ; % J<4>: NO2 = NO + O ; 5.1 The Grand Partition Function Upon studying such topics as mass integration of El-Hawagi et alia, certain matters seem to occur in the mind of a theoretical physicist. First of all, the difference between energy integration and energy plus mass integration seem similar to that between the canonical ensembles and the grand canonical ensembles of statistical mechanics in the minds of the theoretical chemist and physicist. Very briefly, the Grand Canonical Ensemble (G.P.F.) is defined as (G.P.F.) = (P.F.) N e Nu/kT λ N , where λ N = exp(u/kT), and (P.F.)= ∑ i Ω i e -E i / kT and (P.F.) is used in the canonical ensemble. Now u is the chemical potential that controls the movement of particles (hence mass) into or out of the system, whereas E denotes the movement of energy or heat out of the system. On researching order-disorder or cooperative phe- nomena, it was found that probabilities of occur- rence of particulate matter was denoted by a direct product of the factor x times the factor y, each raised to appropriate powers. Now if x denotes matter (or material) and y denotes energy or energy of interac- tion and if the x and y are very large numbers, we would have expressions quite similar to the G.P.F. The successive filling of sites and the creation of bonds, starting with a completely empty figure of sites can be symbolized by mis. Then for each site filled, introduce a factor, x; for each short range bond formed, introduce a factor, y; for each long range interaction formed, introduce the factor, z. Each of these factors is to be raised to an appropri- ate power. The power of x is the number of sites of one type filled; the power of y is the number of short- range bonds of on type filled, and the power of z is the number of long-range bonds formed. For example, if g sites become occupied and h of these sites are of the type a, then g-h are of type b. © 2000 by CRC Press LLC © 2000 by CRC Press LLC % J<5>: NO3 = NO ; % J<6>: NO3 = NO2 + O ; * HOx FORMATION, INTERCONVERSION AND RE- MOVAL ; % 2.20D-10*H2O : O1D = OH + OH ; % 1.90D-12*EXP(-1000/TEMP) : OH + O3 = HO2 ; % 7.70D-12*EXP(-2100/TEMP) : OH + H2 = HO2; % 1.50D-13*KMT05 : OH + CO = HO2 ; % 2.90D-12*EXP(-160/TEMP) : OH + H2O2 = HO2; % 1.40D-14*EXP(-600/TEMP) : HO2 + O3 = OH ; % 4.80D-11*EXP(250/TEMP) : OH + HO2 = ; % 2.20D-13*KMT06*EXP(600/TEMP): HO2 + HO2 = H2O2 ; % 1.90D-33*M*KMT06*EXP(980/TEMP) : HO2 + HO2 = H2O2 ; % KMT07 : OH + NO = HONO ; % KMT08 : OH + NO2 = HNO3 ; % 2.30D-11 : OH + NO3 = HO2 + NO2 ; % 3.70D-12*EXP(240/TEMP): HO2 + NO = OH + NO2 ; % KMT09 % KMT10 : HO2 + NO2 = HO2NO2 ; % 3.50D-12 : HO2 + NO3 = OH + NO2 ; % 1.80D-11*EXP(-390/TEMP) :OH + HONO = NO2; % KMT11 : OH + HNO3 = NO3 ; % 1.50D-12*EXP(360/TEMP):OH + HO2NO2 = NO2; % 6.00D-06 : HNO3 = NA ; % J<3>: H2O2 = OH + OH ; % J<7>: HONO = OH + NO ; % J<8>: HNO3 = OH + NO2 ; * SOx CHEMISTRY ; % 4.00D-32*EXP(-1000/TEMP)*M:O + SO2 = SO3; % KMT12 : OH + SO2 = HSO3 ; % 1.30D-12*EXP(-330/TEMP)*O2 : HSO3 = HO2 + SO3 ; % 1.20D-15*H2O : SO3 = SA ; **********************************************************************; * ALKANES ; **********************************************************************; * METHANE ; % 7.44D-18*TEMP@2*EXP(-1361/TEMP) : OH + CH4 = CH3O2 ; % KRO2NO*0.999 : CH3O2 + NO = CH3O + NO2; % KRO2NO*0.001 : CH3O2 + NO = CH3NO3 ; % 7.20D-14*EXP(-1080/TEMP)*O2 : CH3O = HCHO + HO2 ; % KMT13 % KMT14:CH3O2 + NO2 = CH3O2NO2 ; % KRO2NO3 : CH3O2 + NO3 = CH3O + NO2; % 4.10D-13*EXP(790/TEMP) : CH3O2 + HO2 = CH3OOH ; % 1.82D-13*EXP(416/TEMP)*0.33*RO2 : CH3O2 = CH3O ; % 1.82D-13*EXP(416/TEMP)*0.335*RO2 : CH3O2 = HCHO ; % 1.82D-13*EXP(416/TEMP)*0.335*RO2 : CH3O2 = CH3OH ; % 1.00D-14*EXP(1060/TEMP) : OH + CH3NO3 = HCHO + NO2 ; % J<51> : CH3NO3 = CH3O + NO2 ; % 1.90D-12*EXP(190/TEMP) : OH + CH3OOH = CH3O2 ; % 1.00D-12*EXP(190/TEMP) : OH + CH3OOH = HCHO + OH ; % J<41> : CH3OOH = CH3O + OH ; * ETHANE ; % 1.51D-17*TEMP@2*EXP(-492/TEMP) : OH + C2H6 = C2H5O2 ; % KRO2NO*0.991:C2H5O2 + NO = C2H5O + NO2; % KRO2NO*0.009 : C2H5O2 + NO = C2H5NO3 ; % 6.00D-14*EXP(-550/TEMP)*O2 : C2H5O = CH3CHO + HO2 ; % KRO2NO3 : C2H5O2 + NO3 = C2H5O + NO2 ; % 7.50D-13*EXP(700/TEMP) : C2H5O2 + HO2 = C2H5OOH ; % 3.10D-13*0.6*RO2 : C2H5O2 = C2H5O ; % 3.10D-13*0.2*RO2 : C2H5O2 = CH3CHO ; % 3.10D-13*0.2*RO2 : C2H5O2 = C2H5OH ; % 4.40D-14*EXP(720/TEMP) : OH + C2H5NO3 = CH3CHO + NO2 ; % J<52> : C2H5NO3 = C2H5O + NO2 ; % 1.90D-12*EXP(190/TEMP) : OH + C2H5OOH = C2H5O2 ; % 1.00D-11 : OH + C2H5OOH = CH3CHO + OH; % J<41> : C2H5OOH = C2H5O + OH; * PROPANE ; % 1.50D-17*TEMP@2*EXP(-44/TEMP)*0.307 : OH + C3H8 = NC3H7O2 ; % 1.50D-17*TEMP@2*EXP(-44/TEMP)*0.693 : OH + C3H8 = IC3H7O2 ; % KRO2NO*0.71*0.98 : NC3H7O2 + NO = NC3H7O + NO2 ; % KRO2NO*0.71*0.02:NC3H7O2 + NO = NC3H7NO3 ; % 3.70D-14*EXP(-460/TEMP)*O2 : NC3H7O = C2H5CHO + HO2 ; % KRO2NO3 : NC3H7O2 + NO3 = NC3H7O + NO2 ; % KRO2HO2*0.64 : NC3H7O2 + HO2 = NC3H7OOH ; % 6.00D-13*0.6*RO2 : NC3H7O2 = NC3H7O ; % 6.00D-13*0.2*RO2 : NC3H7O2 = C2H5CHO; % 6.00D-13*0.2*RO2 : NC3H7O2 = NPROPOL ; % 7.30D-13 : OH + NC3H7NO3 = C2H5CHO + NO2 ; % J<53> : NC3H7NO3 = NC3H7O + NO2 ; % 1.90D-12*EXP(190/TEMP) : OH + NC3H7OOH = NC3H7O2 ; % 1.53D-11 : OH + NC3H7OOH = C2H5CHO + OH; © 2000 by CRC Press LLC % J<41> : NC3H7OOH = NC3H7O + OH ; % KRO2NO*0.71*0.958 : IC3H7O2 + NO = IC3H7O + NO2 ; % KRO2NO*0.71*0.042 : IC3H7O2 + NO = IC3H7NO3 ; % 1.50D-14*EXP(-200/TEMP)*O2 : IC3H7O = CH3COCH3 + HO2 ; % KRO2NO3 : IC3H7O2 + NO3 = IC3H7O + NO2 ; % KRO2HO2*0.64 : IC3H7O2 + HO2 = IC3H7OOH ; % 4.00D-14*0.6*RO2 : IC3H7O2 = IC3H7O ; % 4.00D-14*0.2*RO2 : IC3H7O2 = CH3COCH3 ; % 4.00D-14*0.2*RO2 : IC3H7O2 = IPROPOL ; % 4.90D-13 : OH + IC3H7NO3 = CH3COCH3 + NO2 ; % J<54> : IC3H7NO3 = IC3H7O + NO2 ; % 1.90D-12*EXP(190/TEMP) : OH + IC3H7OOH = IC3H7O2 ; % 2.42D-11 : OH + IC3H7OOH = CH3COCH3 + OH ; % J<41> : IC3H7OOH = IC3H7O + OH ; * BUTANE (N-BUTANE) ; % 1.51D-17*TEMP@2*EXP(190/TEMP)*0.147 : OH + NC4H10 = NC4H9O2 ; % 1.51D-17*TEMP@2*EXP(190/TEMP)*0.853 : OH + NC4H10 = SC4H9O2 ; % KRO2NO*0.60*0.967 : NC4H9O2 + NO = NC4H9O + NO2 ; % KRO2NO*0.60*0.033 : NC4H9O2 + NO = NC4H9NO3 ; % 3.70D-14*EXP(-460/TEMP)*O2 : NC4H9O = C3H7CHO + HO2 ; % 1.30D+11*EXP(-4127/TEMP) : NC4H9O = HO1C4O2 ; % KRO2NO*0.60*0.987 : HO1C4O2 + NO = HO1C4O + NO2 ; % KRO2NO*0.60*0.013 : HO1C4O2 + NO = HO1C4NO3 ; % 8.4D+10*EXP(-3523/TEMP) : HO1C4O = HOC3H6CHO + HO2 ; % KRO2NO3 : NC4H9O2 + NO3 = NC4H9O + NO2 ; % KRO2HO2*0.74 : NC4H9O2 + HO2 = NC4H9OOH; % 1.30D-12*0.6*RO2 : NC4H9O2 = NC4H9O ; % 1.30D-12*0.2*RO2 : NC4H9O2 = C3H7CHO ; % 1.30D-12*0.2*RO2 : NC4H9O2 = NBUTOL ; % KRO2NO3 : HO1C4O2 + NO3 = HO1C4O + NO2 ; % KRO2HO2*0.74 : HO1C4O2 + HO2 = HO1C4OOH ; % 1.30D-12*0.6*RO2 : HO1C4O2 = HO1C4O ; % 1.30D-12*0.2*RO2 : HO1C4O2 = HOC3H6CHO ; % 1.30D-12*0.2*RO2 : HO1C4O2 = HOC4H8OH ; % 1.78D-12 : OH + NC4H9NO3 = C3H7CHO + NO2; % J<53> : NC4H9NO3 = NC4H9O + NO2 ; % 5.62D-12 : OH + HO1C4NO3 = HOC3H6CHO + NO2 ; % J<53> : HO1C4NO3 = HO1C4O + NO2 ; % 1.90D-12*EXP(190/TEMP) : OH + NC4H9OOH = NC4H9O2 ; % 1.67D-11 : OH + NC4H9OOH = C3H7CHO + OH; % J<41> : NC4H9OOH = NC4H9O + OH ; % 1.90D-12*EXP(190/TEMP) : OH + HO1C4OOH = HO1C4O2 ; % 2.06D-11 : OH + HO1C4OOH = HOC3H6CHO + OH ; % J<41> : HO1C4OOH = HO1C4O + OH ; % 1.02D-11 : OH + HOC4H8OH = HOC3H6CHO + HO2 ; % J<15> : HOC3H6CHO = HO1C3O2 + HO2 + CO ; % 3.04D-11 : OH + HOC3H6CHO = HOC3H6CO3 ; % KNO3AL : NO3+HOC3H6CHO = HOC3H6CO3+HNO3 ; % KRO2NO*2.7 : HOC3H6CO3 + NO = HO1C3O2 + NO2 ; % KRO2NO*0.71*0.981 : HO1C3O2 + NO = HO1C3O + NO2 ; % KRO2NO*0.71*0.019 : HO1C3O2 + NO = HO1C3NO3 ; % 3.70D-14*EXP(-460/TEMP)*O2 : HO1C3O = HOC2H4CHO + HO2 ; % KFPAN % KBPAN : HOC3H6CO3 + NO2 = C4PAN1; % KRO2NO3 : HOC3H6CO3 + NO3 = HO1C3O2 + NO2 ; % KAPHO2*0.71 : HOC3H6CO3+HO2 = HOC3H6CO3H ; % KAPHO2*0.29 : HOC3H6CO3+HO2 = HOC3H6CO2H + O3 ; % 5.00D-12*0.7*RO2 : HOC3H6CO3 = HO1C3O2 ; % 5.00D-12*0.3*RO2 : HOC3H6CO3 = HOC3H6CO2H ; % KRO2NO3 : HO1C3O2 + NO3 = HO1C3O + NO2 ; % KRO2HO2*0.64 : HO1C3O2 + HO2 = HO1C3OOH; % 6.00D-13*0.6*RO2 : HO1C3O2 = HO1C3O ; % 6.00D-13*0.2*RO2 : HO1C3O2 = HOC2H4CHO ; % 6.00D-13*0.2*RO2 : HO1C3O2 = HOC3H6OH ; % 9.60D-12 : OH + C4PAN1 = HOC3H6CO3 + NO2; % 4.23D-12 : OH + HO1C3NO3 = HOC2H4CHO + NO2 ; % J<53> : HO1C3NO3 = HO1C3O + NO2 ; % 1.32D-11 : OH + HOC3H6CO3H = HOC3H6CO3 ; % J<41> : HOC3H6CO3H = HO1C3O2 + OH ; % 1.04D-11 : OH + HOC3H6CO2H = HO1C3O2 ; % 1.90D-12*EXP(190/TEMP) : OH + HO1C3OOH = HO1C3O2 ; % 1.92D-11 : OH + HO1C3OOH = HOC2H4CHO + OH ; % J<41> : HO1C3OOH = HO1C3O + OH ; % 9.10D-12 : OH + HOC3H6OH = HOC2H4CHO + HO2 ; % J<15> : HOC2H4CHO = HOCH2CH2O2+HO2+CO; % 3.50D-11 : OH + HOC2H4CHO = HOC2H4CO3 ; % KNO3AL : NO3+HOC2H4CHO = HOC2H4CO3+HNO3 ; © 2000 by CRC Press LLC % KRO2NO*2.7 : HOC2H4CO3+NO = HOCH2CH2O2 + NO2 ; % KFPAN % KBPAN : HOC2H4CO3 + NO2 = C3PAN1; % KRO2NO3 : HOC2H4CO3+NO3 = HOCH2CH2O2+NO2 ; % KAPHO2*0.71 : HOC2H4CO3+HO2 = HOC2H4CO3H ; % KAPHO2*0.29 : HOC2H4CO3+HO2 = HOC2H4CO2H + O3 ; % 5.00D-12*0.7*RO2 : HOC2H4CO3 = HOCH2CH2O2 ; % 5.00D-12*0.3*RO2 : HOC2H4CO3 = HOC2H4CO2H ; % 1.42D-11 : OH + C3PAN1 = HOC2H4CO3 + NO2; % 1.78D-11 : OH + HOC2H4CO3H = HOC2H4CO3 ; % J<41> : HOC2H4CO3H = HOCH2CH2O2 + OH ; % 1.50D-11 : OH + HOC2H4CO2H = HOCH2CH2O2; % KRO2NO*0.60*0.91 : SC4H9O2 + NO = SC4H9O + NO2 ; % KRO2NO*0.60*0.09 : SC4H9O2 + NO = SC4H9NO3 ; % 1.80D-14*EXP(-260/TEMP)*O2 : SC4H9O = MEK + HO2 ; % 2.70D+14*EXP(-7398/TEMP) : SC4H9O = CH3CHO + C2H5O2 ; % KRO2NO3 : SC4H9O2 + NO3 = SC4H9O + NO2 ; % KRO2HO2*0.74 : SC4H9O2 + HO2 = SC4H9OOH; % 2.50D-13*0.6*RO2 : SC4H9O2 = SC4H9O ; % 2.50D-13*0.2*RO2 : SC4H9O2 = MEK ; % 2.50D-13*0.2*RO2 : SC4H9O2 = BUT2OL ; % 9.20D-13 : OH + SC4H9NO3 = MEK + NO2 ; % J<54> : SC3H9NO3 = SC4H9O + NO2 ; % 1.90D-12*EXP(190/TEMP) : OH + SC4H9OOH = SC4H9O2 ; % 3.21D-11 : OH + SC4H9OOH = MEK + OH ; % J<41> : SC4H9OOH = SC4H9O + OH ; * 2-METHYL PROPANE (I-BUTANE) ; % 1.11D-17*TEMP@2*EXP(256/TEMP)*0.233 : OH + IC4H10 = IC4H9O2 ; % 1.11D-17*TEMP@2*EXP(256/TEMP)*0.767 : OH + IC4H10 = TC4H9O2 ; % KRO2NO*0.60*0.967 : IC4H9O2 + NO = IC4H9O + NO2 ; % KRO2NO*0.60*0.033 : IC4H9O2 + NO = IC4H9NO3; % 3.70D-14*EXP(-460/TEMP)*O2 : IC4H9O = IPRCHO + HO2 ; % KRO2NO3 : IC4H9O2 + NO3 = IC4H9O + NO2 ; % KRO2HO2*0.74 : IC4H9O2 + HO2 = IC4H9OOH ; % 1.30D-12*0.6*RO2 : IC4H9O2 = IC4H9O ; % 1.30D-12*0.2*RO2 : IC4H9O2 = IPRCHO ; % 1.30D-12*0.2*RO2 : IC4H9O2 = IBUTOL ; % 1.50D-12 : OH + IC4H9NO3 = IPRCHO + NO2 ; % J<53> : IC3H7NO3 = IC4H9O + NO2 ; % 1.90D-12*EXP(190/TEMP) : OH + IC4H9OOH = IC4H9O2 ; % 1.68D-11 : OH + IC4H9OOH = IPRCHO + OH ; % J<41> : IC4H9OOH = IC4H9O + OH ; % KRO2NO*0.60*0.975 : TC4H9O2 + NO = TC4H9O + NO2 ; % KRO2NO*0.60*0.025 : TC4H9O2 + NO = TC4H9NO3 ; % 2.70D+14*EXP(-8052/TEMP) : TC4H9O = CH3COCH3 + CH3O2 ; % KRO2NO3 : TC4H9O2 + NO3 = TC4H9O + NO2 ; % KRO2HO2*0.74 : TC4H9O2 + HO2 = TC4H9OOH; % 6.70D-15*0.7*RO2 : TC4H9O2 = TC4H9O ; % 6.70D-15*0.3*RO2 : TC4H9O2 = TBUTOL ; % 1.67D-13 : OH + TC4H9NO3 = CH3COCH3+HCHO+NO2 ; % J<55> : TC4H9NO3 = TC4H9O + NO2 ; % 2.20D-12*EXP(190/TEMP) : OH + TC4H9OOH = TC4H9O2 ; % J<41> : TC4H9OOH = TC4H9O + OH ; 5.3 REACTION: Modeling Complex Reaction Mechanisms Dr. Edward S. Blurock, who was at the RISC-Linz at Johannes Kepler University in Austria, has done some valuable work with computers. His program REACTION is an expert system for the generation, manipulation, and analysis of molecular and reac- tion information. The goal of the system is to assist in the modeling of complex chemical processes such as combustion. REACTION enables both “numeric” and “symbolic” analysis of mechanisms. The major portion of the numeric analysis results from an interface to the CHEMKIN system where the reac- tion and molecule data is either generated automati- cally or taken from a database. The symbolic meth- ods involve graph theoretical and network analysis techniques. The main use of this tool is to analyze and compare the chemistry within mechanisms of molecules of different structure. Current studies involve comparing hydrocarbons with up to ten car- bons and the influence of the structure on autoignition (‘knocking phenomenon and octane number’). In 1995 Dr. Blurock taught a course at Johannes Kepler University at the Research Institute for Sym- bolic Computation. It was called Methods of Com- puter Aided Synthesis. It included Symbolic Meth- ods in Chemistry CAOS REACCS LHASA SYNGEN EROS/WODCA EROS Daylight Daylight is a program providing computer algorithms for chemical information processing. Their manual © 2000 by CRC Press LLC (Daylight Theory Manual, Daylight 4.51) consists of the following sections: Smiles, Smarts, Chuckles, Chortles and Charts, Thor, Merlin, and Reactions. Smiles is a language that specifies molecular struc- ture and is a chemical nomenclature system. Smarts is a substructure searching and similarity tool. It reveals the principles of substructure searching, NP-complete problems and screening, structural keys, fingerprinting and similarity metrics. Chuck- les, Chortles and Charts are for mixtures. They are languages representing combinatorial libraries which are regular mixtures of large numbers of compounds. Thor is a chemical information database system consisting of fundamental chemical nomenclature, chemical identifiers, etc. Merlin is a chemical infor- mation database exploration system and a pool of memory-resident information and Reactions has all of the features for reaction processing. 5.4 Environmentally Friendly Catalytic Reaction Technology The establishment of a clean energy acquisition/ utilization system and environmentally friendly in- dustrial system is necessary to lower global pollu- tion and reach a higher level of human life. Here we aim to conduct systematic and basic R & D concern- ing catalytic reaction technology controlling the effi- ciency of energy and material conversion processes under friendly and environmental measures. Basic technology development for the molecular design of a catalyst using computer aided chemical design will be combined with the development of new catalysts on the strength of wide-choice/normal-temperature and pressure reaction technologies. The basic steps are: 1. Preparing model catalytic substances ideal in making controllable various catalytic proper- ties, including absorption, reaction, diffusion and desorption will be studied using thin film preparation technology, a process to synthesize materials on a nanometer scale. 2. This will be done through studies on computer- aided high functioning catalyst design, surface analyzed instruments-based catalyst properties evaluations, etc. 3. The acquisition and utilization of clean energy leads to development that is aimed at a new photo-catalyst that can quite efficiently decom- pose water not only with ultraviolet but also with rays of sunlight, thus generating hydro- gen. 4. Search for and develop methods for facilitated operation of elementary catalytic reaction pro- cesses, including light excitation, electric charge separation, oxidation, and reduction reactions that will be integrated and optimized for the creation of a hybrid-type photo-catalyst. In order to efficiently manufacture useful chemi- cal materials such as liquid fuels that emit less CO2 using natural gas and other gaseous hydrocarbons as raw materials, a new high performance catalyst acting under mild reaction conditions is to be devel- oped. 5.5 Enabling Science Building the Shortest Synthesis Route The goal is to make the target compound in the fewest steps possible, thus avoiding wasteful yield losses and minimizing synthesis time. R&D laboratories synthesize many new compounds every year, yet there seems to be no clear protocol for designing acceptable and efficient routes to target molecules. Indeed, there must be millions of ways to do it. Some years ago, in an effort to use the power of the computer to generate all the best and shortest routes to any compound, a group at Brandeis began to develop the SYNGEN program. The task is huge, even for the computer. Imagine a graph that traces the process of building up a target molecule; we call it a synthesis tree. The starting materials for the possible synthesis routes are molecules we can easily obtain. As the routes progress, new starting materials are added from time to time until the target is obtained. Each line represents a reaction step, or level, from one inter- mediate to another, and each step decreases the yield. Two of many possible routes are traced in Figure 50. To find these routes, we presume to start with the target structure and a catalog of all possible starting materials. Then, the computer generates all the points (intermediates) and lines (reactions) of the graph. If the computer has been programmed with an exten- sive knowledge of chemical reactions, it could do this by generating all possible reactions backward one step from the target structure to the intermedi- ate structures, then repeating this on each interme- diate as many times as necessary to return to the available starting materials. At this stage, the problem gets too big. Suppose there are 20 possible last reactions to the target (level 1) and that each of these reactions also has 20 possible reactions back to level 2. Going back only five levels will generate 20 5 (3.2 million) routes. How do we select only one to try in the laboratory? This generation of reactions and intermediates is a brute-force approach; clearly, it must be focused and simplified with some stringent logic. The central criterion should be economy — that is, to make the © 2000 by CRC Press LLC target in the fewest steps possible, thus avoiding wasteful yield losses and minimizing synthesis time. A Protocol for Synthesis Generation The key to finding the shortest path seems to be to join the fewest possible starting materials and those that are closest to the target on the graph. The starting material skeletons are usually smaller than the target skeleton, so joining them to assemble the target will always require reactions that construct skeletal bonds. This underlying skeleton is revealed by deleting all the functional group bonds on a structure and leaving only the framework, usually just C-C σ-bonds. The central feature of any synthesis is the assem- bly of the target skeleton from the skeletons of the starting material. Looking for all the possible ways of cutting the target skeleton into the skeletons of available starting materials represents a major focus for examining the synthesis tree. We illustrate this task by looking at the steroid skeleton of estrone and cutting it in two at different points in the structure (Figure 52). Each cut creates two intermediate skeletons, and each skeleton is then cut in two again to obtain four skeletons. This procedure creates a convergent synthesis, and con- vergent routes are the most efficient (4). With four starting skeletons, we will need to construct only 6 (or fewer) of the 21 target skeleton bonds. We could keep dividing each skeleton until we ultimately ar- rive at a set of one-carbon skeletons, but it is not necessary to go that far, that is, to a “total synthe- sis”. With our four starting skeletons, each skeleton represents a family of many compounds with differ- ent functional groups placed on the same skeleton. Suppose that we find a set in which all four skel- etons are represented by real compounds in an available library of starting materials; this set could form the basis of a synthesis route with no more than six construction steps to the steroid if the functional groups are right. The skeletal bonds we cut, which must be constructed in the synthesis route, are called a bondset, and these bondsets are a basis for generating the shortest syntheses. Each skeletal bondset represents a whole family of poten- tial syntheses. The Ideal Synthesis There are two kinds of reactions: construction reac- tions, which build the target skeletal bonds (usually C-C bonds), and refunctionalization (∆FG) reactions, which alter the functional groups without changing the skeleton. Any synthesis must do construction reactions, because the starting materials are smaller than the target, but must a synthesis route have any ∆FG reactions? Imagine a synthesis route with its set of starting materials chosen so that their functional groups are correct to initiate the first construction, leave a prod- uct correctly functionalized for the second construc- tion, and so on, continuing to construct skeletal bonds until the target skeleton is built. This is the ideal synthesis in that it must have the fewest steps possible. It requires no FG reactions to get from one construction product to the next. In a survey of many syntheses, we found that • the average nonaromatic starting material has a skeleton of only three carbons • one skeletal bond in three of the targets is constructed • there are twice as many FG reactions as con- structions Therefore, for an average synthesis, the number of steps equals the number of target skeleton bonds. We think we can do better. Building the shortest, most economical syntheses requires first finding those skeletal dissection bondsets with the fewest bonds, to minimize construction reactions. It also requires no more than four correctly functionalized starting materials, to minimize FG reactions. Com- mon targets have 20 or fewer carbons, which implies an average starting material of 5 carbons. In our experience with catalogs of starting materials, func- tional diversity on the skeletons is ample up through five carbons but decreases sharply with larger mol- ecules. Generating the Chemistry Once we find the four commercially available start- ing materials, we need to make a second pass, down from the target through the ordered designated bonds of the bondset. This process generates the actual construction reactions we require, in reverse. So, we need a method of generalizing structures and reac- tions to quickly find the reactions appropriate to the functional groups present. Any carbon in a structure can have four general kinds of bonds, as summarized in Figure 53: skel- etal bonds to other carbons (R); Π-bonds to adjacent carbons (Π); bonds to heteroatoms that are elec- tronegative (Z); and bonds to heteroatoms that are electropositive (H). The numbers of bonds are re- ferred to as σ, z, and h, respectively. If we know the values of and obtain h by subtraction from 4, only two digits (z and Π) are needed to describe each carbon. This description is summarized in Figure 53, where each carbon is marked in the example structure with its z value. This digitalized general description of the structure is easy for the computer. In Figure 53, a reaction change at each carbon is just a simple exchange of one bond type for another. © 2000 by CRC Press LLC This change may be designated by the two letters for the bond made and the bond lost. Thus, reaction HZ indicates making a bond to hydrogen by loss of a bond to heteroatom — that is, a reduction. The 16 possible combinations are shown and described with general reaction families in Figure 53. Using this system, we can generate all possible generalized reactions, forward or backward, from any structure. No routes are missed, and we can find all the best routes back from the target to real starting materials. Relatively few generalized reac- tions are created, and we refine the abstract into real chemistry only at the end. When starting mate- rials are generated through successive applications of these reaction families, we can look them up in the catalog, where they are indexed by skeleton and by generalized z lists of the functionality on each skeletal carbon. The SYNGEN Program We have applied this approach in our SYNGEN pro- gram, an earlier version of which found its way into laboratories at Glaxo-Wellcome, Wyeth-Ayerst, and SmithKline Beecham, but is currently being im- proved significantly. The two phases of the genera- tion are summarized in Figures 50 through 55 for one particular result, the Wyeth estrone synthesis. In the first phase (Figure 54, left side), we see the skeletal dissection down to four starting skeletons, all found in the catalog; in fact, the intermediate skeleton B also was found, so further dissection to E and F may not be needed. In the second phase (Figure 54, right side), this ordered bondset is followed, one bond at a time, generating the construction reactions for an ideal synthesis until all of the functional groups have been generated. These actual starting materials are found in the catalog, so a full synthesis route can be written from them that goes up the right side in a quick, constructions-only ideal synthesis of the tar- get. This three-step synthesis of a target structure can be converted to estrone in two more steps. The prediction for an average synthesis would have been much longer. The catalog for the current version of SYNGEN has about 6000 starting materials, but it is being ex- panded from available chemicals directories. After the target is drawn on the screen, the program generates the best routes in <1 min. It displays the bondsets, the starting materials used, and the ac- tual routes, which are ordered by their calculated overall cost. The output screen from SYNGEN for the example analyzed in Figures 50 through 55 is shown in Figure 55. Two other sample outputs, from a differ- ent bondset of the same target, are shown in Figures 56 and 57. The notations on the arrows use abbre- viations to describe the nature of the reaction; ex- planations are available on a help screen. The routes shown are still in a generalized form and require further elaboration of chemical detail by the user. Literature precedents, however, are being added to the program, as described later. The Future of SYNGEN Three developments are currently under way on the SYNGEN program. The first and perhaps most im- portant improvement is creating a graphical output presentation that is easy for a chemist to read and navigate; this work is nearing completion. The sec- ond deals with the problem of validating the gener- ated reactions with real chemistry. The third development, currently supported by the U.S. Envi- ronmental Protection Agency (EPA), is to assign start- ing material indexes of environmental hazard — such as toxicity and carcinogenicity — so that the routes generated may be flagged for environmental concern when these starting materials are involved. The second development deals with a major prob- lem in previous versions of SYNGEN: The program generated too many reactions that chemists saw as clearly nonviable. Such results tended to destroy their confidence in the program as a whole. We now have a way to validate the generated reactions from the literature, eliminating many of these nonviable reactions. The generalizing procedure for describing struc- tures and reactions in SYNGEN also was applied to create an index-and-retrieval system to find matches for any input query reaction from a large database of published reactions. This program, RECOGNOS, has been applied to an archive of 400,000 reactions originally published between 1975 and 1992 and packaged as a single CD-ROM that allows instant access to matching precedents in that archive. The RECOGNOS program is available on CD-ROM from InfoChem GmbH, Munich, Germany, combined with their ChemReact database of 370,000 reactions and renamed “ChemReact for Macintosh”. This archive of literature reactions, now almost double the original size, has been distilled to more than 100,000 construction reactions. These reac- tions, in turn, have been converted into a look-up table for use by the SYNGEN program. With this tool, SYNGEN can validate any reaction it generates by searching for matches in the archive and deter- mining the average yield. Unprecedented reactions are therefore set aside, and a realistic yield can be estimated for each reaction to be used in the overall cost accounting. We believe that SYNGEN has considerable poten- tial for discovering new alternatives for creating or- ganic chemicals in the most economical way pos- sible. Even when the program does not yield a directly © 2000 by CRC Press LLC usable synthesis, it often starts the chemist think- ing about different approaches previously not con- sidered. No chemist can think of all the possible routes to the target, but SYNGEN does this quickly. It also provides a powerful and focused output of the possibilities. 5.6 Greenhouse Emissions Two years ago, the nations of the world gathered in Kyoto to hammer out a plan to curb those man- made gases that are believed to be raising the tem- perature of the planet. When the Kyoto Protocol reached Washington, however, it was pronounced too expensive, too un- workable. It was dead on arrival. But on the Texas–Louisiana border a DuPont chemical plant is doing what Washington politicians and bureaucrats have been unable and unwilling to do — cutting greenhouse gases. DuPont’s Orange plant sits on 400 acres amid wetlands and waterfowl on the Texas-Louisiana bor- der. It makes the chemicals used to make nylon. It also has been emitting tons of nitrous oxide — a greenhouse gas. “Our aim was to control those emis- sions. The problem was there was no known tech- nology to do it,” said the plant manager. So DuPont invented its own. Today, the fumes from the plant run through a building packed with a catalytic filtering unit that breaks the nitrous oxide into harmless nitrogen and oxygen. Another closely watched corporate experiment was launched last year by oil giant BP Amoco. It set a goal of reducing 1990 greenhouse gas emission lev- els by 10% by 2010-regardless of sales growth. BP Amoco’s strategy involves an emissions trading program under which each BP refinery and plant is given a reduction target. Those plants that can do better than their target can “sell” their excess reduc- tion to other facilities. There have been five “trades” among BP facilities for 50,000 tons of carbon dioxide, with a ton of carbon dioxide “valued” at $17 to $22. It is widely agreed that some sort of country-to- country emissions trading will have to be part of any accord on climate change. So, BP Amoco’s experi- ment is viewed by many as a valuable test case. 5.7 Software Simulations Lead to Better Assembly Lines Many years ago this author inspected the Budd auto parts (frames) plant in Kitchener, Ontario. The frames (for all American cars) moved in and out of a station while hanging from a conveyor belt. An instrument measured a point on this frame and compared it to the blueprint in a computer. If there was no match that frame and a number of succeeding ones on the belt were scrapped. It was regarded as a technologi- cal marvel. Engineers now boot up programs that let them tinker, in three dimensions, with every permutation and combination of a product’s design. Now engi- neers aim their computers at designing and refining the assembly lines on which those products are made. As an example, Dow Chemical Co., now uses com- puters to simulate its methods for making plastics, running what-if scenarios to fine-tune the tempera- tures, pressures and rates at which it feeds in raw materials. Dow can now switch pressures and rates at which it feeds in raw materials. Dow can switch production among 15 different grades of plastics in minutes, with almost no wasted material. Before computer modeling, the process took two hours and yielded lots of useless by-products. Production engineers in industries as diverse as chemicals, automobiles, and aluminum smelting are manipulating virtual pictures of their plants and processes to see whether moving a clamp or adding a new ingredient will make existing equipment more productive, or will enable the same assembly line to skip freely from product to product. Some are even testing out a new virtual reality program that en- ables engineers wearing special goggles to detect problems by “walking through and around” a three- dimensional model of their factory designs. The entire relationship between product design and production engineering is being turned on its ear. No longer is it enough for designers to create products that can be made and maintained effi- ciently. Increasingly, management is asking them whether the products can be manufactured with a minimum of retooling or work stoppages — and if not, whether it is worth giving up a particular prod- uct feature in order to wring time and money from the manufacturing routine. The software is letting manufacturing influence design, not just the other way around. Real-life examples of modeling’s efficiency are mounting. Ford says that one of its plants now uses the same assembly line to make compact and mid- sized models. Computer simulations of the tread-etching pro- cess has enabled tire makers like Goodyear Tire and Rubber to switch production from one type of tire to another in about an hour — a process which previ- ously took an entire work shift. Simulations have shown cookie companies like Nabisco how to use the same packaging machines to make 5-pound bags for price clubs, 1-pound bags for groceries and 6-cookie packs for vending machines. Various forces are driving the trend towards com- puter modeling. For one thing, computer technology © 2000 by CRC Press LLC has finally caught up with manufacturing pipe dreams. Recently computers have been powerful enough to quickly simulate what happens if you change something in a chemical reactor. Consumers have grown increasingly picky and expect to be able to choose among myriad colors, sizes, and shapes for almost any product. This means that the manufacturers must mix and match parts as the orders come in. And that, in turn, means having tools that can respond to electronic com- mands to switch paint wells, move clamps, or change packaging and labels. Already, the modeling procedure has led to devel- opment of a conveyor belt that can sense what model is in production and instruct robotic arms to pluck the right hood or other part from a storage bin and have it ready to meet the truck chassis as it moves down the line. When a conveyor system was too slow, a computer helped us figure out why. “Freightliner” now uses work-flow simulation to figure out how to keep trucks moving evenly from worker to worker, when some models need more handling than others — putting 12 bolts into a wheel well, for example, instead of four. When a worker lost time on a difficult truck, he should make it up on an easy one. Do not wait until the line is set up to find out you could have pre- vented bottlenecks. 5.8 Cumulants There is a relationship between the equation of state and a set of irreducible integrals. These irreducible integrals have a graphical representation in which each point (or molecule) is connected by a bond (f ij ) to at least two other points. By the introduction of irreducible integrals a great economy is achieved in accounting for all possible interactions. An impor- tant property of cumulants which makes them use- ful in the treatment of interacting systems is the following: a cumulant can be explicitly represented only by the lower (not higher) moments, and vice versa. 5.9 Generating Functions Consider a function F(x,t) which has a formal (it need not converge) power series expansion in t: F(x,t) = ∑ ∞ n=0 f n (x)t n The coefficient of t is, in general, a function of x. We say that the expansion of F(x,t) has generated the set f n (x) and that F(x,t) is a generating function for the f n (x). Examples of generating functions are: Bessel func- tions, Gegenbauer polynomials, Hemite polynomi- als, Laguerre polynomials, Legendre functions of the second kind, Legendre polynomials, semidiagonal kernels, trigonometric functions, etc. 5.10 ORDKIN a Model of Order and Kinetics for the Chemical Potential of Cancer Cells A method for deriving the chemical potential of par- ticles adsorbed on a two dimensional surface has previously been derived for lateral and next nearest neighbor interactions of the particles. In order to do so a parameter called K was used and K = ((exp((µ- ε)/kT))(θ/1-θ)) 1/Z . It was found from a series of nor- malizing, consistency, and equilibrium relations shown in papers by Hijmans and DeBoer (1) and used by Bumble and Honig (2) in a paper on the adsorption of a gas on a solid. In the above, u is the chemical potential and ε is the adsorption energy. The numerical values of K were derived from com- puters for various lattices with different values of the interaction parameters for nearest neighbors (c) and next nearest neighbors (c’), where c = exp(-w/ kT) and w is the interaction energy, and the “order” of such lattices were plotted as the values of exp((µ- ε)/kT) or p/p 0 =exp((µ-ε)/kT) versus θ or the degree of occupancy of the lattice. A method for approximat- ing the lattice was accomplished mathematically by selecting basic figures such as the point ⅙, the bond ⅙—⅙, the triangle ᭝, or the rhombus □ . Other graphs were made which plotted the value of the pressure ratio vs. time. A model for the time was also selected from a previous publication (3) as L = (p/k)(1-exp(kt/ p)) where p denotes the organism, k the rate concen- tration or exposure to chemical i, and L the toxico- logical measure. Results show that the lower the value of c (or the greater the antagonism or repul- sion of cells or particles) the greater the chance of cancer. Also, the higher the chemical potential, the more the chance of cancer. Remedies are also indi- cated by changing the pressure or the diffusion of cells. The results were matched with experimental evidence from humans living near several chemical plants near the city of Pittsburgh (4). The value of K given above has the chemical poten- tial in it, and solving for this quantity we obtain K Z (θ/1-θ) where Z is the coordination number of cells in a tissue approximated as a lattice. The lattice has been approximated as triangular and was broken up into basic figures mentioned above. The larger the basic figure the more compli- cated the algebra. The bond yields K = (β-1 + 2θ)/ 2θc, where β = [1+4cθ(1-θ)(c-1)] and the triangle as basic figure yields a quartic equation K 4 -a 1 K 3 +a 2 K 2 -a 3 K + a 4 = 0 where a 1 = ((2-5θ)c + 2 - 3θ) /c(1-2 ), © 2000 by CRC Press LLC a 2 = (c+5)/c, a 3 = ((3 - 5θ)c + 1-3θ) /c(1-2θ), and a 4 =1/c 2 . Every point then derived for the triangle basic figure subfigure is then found for the solution of the above quartic equation for given values of c and θ. The solution to the rhombus approximation is yet more formidable and requires a special com- puter program to approximate the answers. One defines an order variable as order = K z θ/(1-θ) and using the model for time above, we obtain can- cer = K Z (θ/1-θ)p/k(1-exp(-kt/p)). p has a different value for each organism and for Man it is unity. k has a value for each different environmental chemi- cal. t is the time of exposure of a person to that chemical in years. The procedure used then is to select a basic figure, select a value for Z, select the proper value for k, and then use a sequence of values for θ and t. Such work was done on Quattro Pro on a PC. The value chosen for k was .05, the range of values for θ was from .0125 to .975, and the range of values for t was from 1 to 75 years. The model was called ORDKIN (abreviated from order and kinetics). The data was taken by the graduate students at the University of Pittsburgh’s Department of Public Health of some 50,000 resi- dents in three zip number areas within dispersion distance of Neville Island which contains about a dozen industrial plants. In the graphs below b stands for bond, t stands for triangle and r stands for rhombus as the basic figure. Occupancy or theta (θ) or lattice occupation stands for the fraction of sites covered. Cancer and order are the expressions given above, u is the chemical potential, k in u/kT is the Boltzmann constant, and T is the temperature (Kelvin). In Figure 90, the top two curves are for c = 0.36 (tp most) and 0.9, whereas the bottom curves are all for c = 2 or 3 and they all denote curves for cancer as in the equations and parameters listed above. Now it was of interest that for the values of c below unity, which denotes repulsion between particles, the chemical potential was higher than for those cases where c was above unity which indicates attraction between particles. It is also of interest that when the chemical potential is higher the system tends to be more unstable than when the chemical potential is lower. Indeed, when the chemical potential is at a minimum the system tends to be at equilibrium. These plots are versus occupation of the sites on a lattice which means θ = 0 when the occupation is zero and unity when it is full. In order to test what is responsible for the separa- tion of the chemical potential curves as shown in the graphs above, the order parameter was examined and two plots were made, one where the c values were >1 and one where the c values were <1, corre- sponding to regions of attraction and repulsion, re- spectively, and shown as Figures 91 and 92, respec- tively. Both graphs for c < 1 are shown as ln(order) plotted vs. age. We have neglected some terms because actually (u G +e)/kT=P/P* and P*=(2pmkT) 3/2 kTj G [exp(-e/kT)/ h 3 where j G is the internal partition function for the gas and ε is the adsorption energy with the other symbols having their usual meaning. These factors will be thought of as scaling factors in this work where individuals are construed to have approxi- mately the same values and introduce some error. Figures 93 and 94, respectively, compare the data for all observed cancer cases and breast cancer cases from the study conducted at and near Pitts- burgh. The graphs show that the worst fit for the data for all cases of cancer is the triangle basic figure with c = 0.1. The computer failed to obtain solutions for young victims in this case. The regression of all cancers and breast cancers show the linear nature of the regression in these cases. The zig–zag nature of the data from the field is clearly shown in these cases and it is possible that the linear curves are best in these cases. The following table collates the value of c and their exponents. c w/kT > 1 3 1.10 > 1 2.77 1.02 >1 2 0.70 <1 .9 -0.105 <1 .36 -1.02 <1 .1 -2.30 from which we see that the best results are obtained with a small repulsive force between cells (c = 0.9). Another very important way to lower the chemical potential of cancer cells is to impose critical condi- tions on the system containing the cancer cells. Graphically this means that the curve for the order of the cancer cells be flat or parallel to the abcissa which can be the age of the people or the values of θ. This means the order would be constant in value for varying values of the age or θ. This curve or plateau must be both low and broad to be effective. It can be achieved by varying the temperature, the pressure, the concentration, or the constitution of the medium containing the cancer cells. This is similar to techniques in chemistry or chemical engi- neering where a foreign substance can bring about critical solution temperatures or cause the volatility to increase. Results of the Study 1. If the malignant cells of the cancer can be re- lated to the chemical potential, this would lead to many therapeutic methods to “cure” the can- [...]... binomial theorem the coefficients can be seen to be (2L)!/(L-D)!(L+D) where D = pL Then g(L,x) = (2L)!/((1-p)L)!((1-p)L)! And utilizing N! = (N/e)N (2pN)1/2, we find Expanding ln(1+p) and ln(1-p) and neglecting higher terms we obtain g(L, N) = 4L/( pL)1/2(1-p2 ) 1/2(1-p)1-p(1+p)1+p g(L,x) = 4Lexp(-x2/L)/(pL)1/2 lng(L, x) = L[ln 4-( 1-p)ln(1-p )-( 1+p)ln(1+p)] © 2000 by CRC Press LLC References Section 1.1... System, J Nuclear Sci Technol., 32(4), 35 7-3 68, 19 95 Section 1.22 Design & Development of Computer- Based Clean Manufacturing : A Decision Tool for Industrial and Academic Use, Technology Reinvestment Project # 1 051 , NSF Grant #CIJ9413104, 4/ 15/ 9 4-9 /30/97, NJIT, MIT Section 1.23 Yi, J., Chah, S., Computer Aided Chemical Process Design for Pollution Prevention, Environmental Chemical Engineering Lab,... Economics Program, http://process-economics.com © 2000 by CRC Press LLC Section 5. 4 http://www.c-f-c.com/supportdocs/cl2recycle.htm Section 5. 5 Hendrikson, J B., Chem Tech., Sept.98, (2819), 3 5- 4 0, ACS, Teaching Alternative Synthesis The Syngen Program, in Green Chem: Designing Chem For the Enviromental FDAT Section 5. 6 Section 5. 13 Anastas, P T., Williamson, T C., Am Chem Soc., 21 4-2 31, Wash D.C Feynman,... Symposium, Cincinnati, OH, 19 95 Friedler, F., Tarjan, K Huang,Y W., Combinatorial Algorithms for Process Synthesis, Computers Chem Eng., 16, S1-S548, 1992 Friedler, F., Varga, J B., Fan, L T., Decision-Mapping for Design and Synthesis of Chemical Processes: Application to Reactor-Network Synthesis, AIChE Symposium Series No 304 Volume 91, 19 95 Friedler, F., K Tarjan, Y W Huang, L T Fan, ComputerAided Waste Minimizing... Research, Boulder, CO, June 1-2 , 1992 Kovacs, Z., F Friedler, L T Fan, Algorithmic Generation of the Mathematical Model for Separation Synthesis, European Symposium on Computer Aided Process Engineering-3, Escape-3, 5- 7 July 1993 Graz, Austria Friedler, F., Z Kovacs, L T Fan, Unique Separation Networks for Improved Waste Elimination, Emerging Technologies for Hazardous Waste Management, A.C.S., Atlanta,... Optimal Structures, Computers Chem Eng., 19, S107-S112, 19 95 Friedler, F., J B.Varga, L T Fan, Decision_mapping: A Tool for Consistent and Complete Decisions in Process Synthesis, Chem Eng Sci., 50 (11), 177 5- 1 768, 19 95 Personal transmission from Dr L T Fan An early Flowchart for APSCOT (Automatic Process Synthesis with Combinatorial Technique) Friedler, F., K Tarjan, Y W Huang, L T Fan, Graph-Theoretic Approach... 7, Spreadsheet for Windows 95 Section 1. 25 Section 1.33 Federal Register, Vol 62, No 120, Monday, June 23, 1997, Notices, pages 3386 8-3 3870, EPA, Notice of Availability of Waste Minimization Software and Documents Section 1.34 CLARIT web Image :53 0F 950 10 Env Fact Sheet http:// www.epa.gov/cgi.bin/clariy.gov Section 1. 35 ASTDR Information Center/ATSDRIV@cdc.gov/ 188842ATSDR or 188 8-4 2 2-8 737, 1999 Section... Explore Waste Minimization via Process Simulation, CEP, No (11), 4 0-4 2, 1994 Section 3 .5 EPA/NSF Partnership for Environmental Research, Technology for Sustainable Environment, Interagency Announcement of Opportunity, National Center for Environmental Research and Quality Assurance, ORD, US EPA, Opening Date, No 18, 1997 Section 3.6 Hypotech, Calgary, Canada Section 3.7 Varga, J B., Fan, L T., Risk Reduction... Organizational Change Mgt., 11(1), 2 6-3 7, 1998, MCB University Press, 0 95 3-4 814 Section 1.20 Satoh, Y., Soejima, T., Koga, J., Matsumoto, S., Homma, S., Sakamoto, M., Takansshi, Nammo, A., Computer Aided Process Flowsheet Design and Analysis System of Nuclear- Fuel Reprocessing, J Nuclear Sci Technol., 32(4), 357 368, 19 95 Section 1.21 Development of COMPAS, Computer- Aided Process Flowsheet Design and... two-level atoms changes in time (e and g stand for the excited and the ground states, respectively) At the right is a configuration of an assembly of one-dimensional Ising model x and o are a plus and minus spin, respectively t- t t+ t k-1 k k+1 atom 1→e→g→g→e→g→e→ atom 2→g→g→e→e→e→g→ system 1 -x–o–o–x–o–x system 2 -o–o–x–x–x–o atom N→g→g→e→g→e→e→ system N -o–x–o–o–x–x- The . C2H5O2 + NO3 = C2H5O + NO2 ; % 7 .50 D-13*EXP(700/TEMP) : C2H5O2 + HO2 = C2H5OOH ; % 3.10D-13*0.6*RO2 : C2H5O2 = C2H5O ; % 3.10D-13*0.2*RO2 : C2H5O2 = CH3CHO ; % 3.10D-13*0.2*RO2 : C2H5O2 = C2H5OH. ETHANE ; % 1 .51 D-17*TEMP@2*EXP (-4 92/TEMP) : OH + C2H6 = C2H5O2 ; % KRO2NO*0.991:C2H5O2 + NO = C2H5O + NO2; % KRO2NO*0.009 : C2H5O2 + NO = C2H5NO3 ; % 6.00D-14*EXP ( -5 50/TEMP)*O2 : C2H5O = CH3CHO. ; * HOx FORMATION, INTERCONVERSION AND RE- MOVAL ; % 2.20D-10*H2O : O1D = OH + OH ; % 1.90D-12*EXP (-1 000/TEMP) : OH + O3 = HO2 ; % 7.70D-12*EXP (-2 100/TEMP) : OH + H2 = HO2; % 1 .50 D-13*KMT 05 : OH