Models on the CD-ROM

The models contained on the CD-ROM have all been generated from standard procedures using Spartan. Most models could also have been generated from MacSPARXAN Plus or PC Spartan Plus.  

With the exception of very large systems, e.g., polymer strands (Chapter 18) and polypeptides and polynucleotides (Chapter 16), all calculations have been carried out using ab initio Hartree-Fock theory with the 3-21G basis seF. The perfomance of this technique with regard to the calculation of geometries, relative energies, dipole moments and vibrational frequencies has been extensively documented.  

Geometries Calculated bond distances are typically within 0.02A of experimental values and bond angles within 2°. Geometries for transition states are not available from experiment. Here it must be assumed that the calculations provide descriptions of similar quality to those for equilibrium geometries. 

Dipole moments The 3-21G method generally yields dipole moments which are too large by 0.5 to 1.0 debyes. Trends in dipole moments are usually well reproduced. 

Vibrational frequencies Calculated vibrational frequencies are larger than measured values, typically by about 12%. Systematic scaling of calculated frequencies (by 0.88) leads to values which are generally suitable for assignment and interpretation of experimental infrared/Raman spectra. 

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Now would be a good time to study the molecular mechanics section of Molecular Modelling on the CD-ROM associated with this Book. 

First, we need to create models to describe these transistors. When you look up the MOSFET models in the Cadence PSpice reference manual on the CD-ROM that accompanies this text, you will find the following equations to describe MOSFET operation ... 

In this part we will demonstrate how to modify existing PSpice models and how to create new models. We will assume that the user is familiar with PSpice models and knows how he or she would like to modify the models. A discussion of the various models requires too much detail to be given here. The user is referred to the PSpice Reference Manual available from Oread Corporation for model details. This manual is contained on the CD-ROM that accompanies this text. You will probably need to review the many references that Oread gives to understand the model parameters. Here, we will show how to make changes to existing models or create simple new models. Section 7.E contains simplified models for some of the commonly used parts. The model parameters given are for firsttime users. For more accurate models, you will need to refer to more detailed texts covering SPICE models. If you are more familiar with the models, you can use these procedures to modify all parameters in a model. 

The procedures we have covered can be used to create a model using any of the breakout parts. Before you create any new parts, you must know the definition of the model parameters. The user is strongly urged to refer to the Oread PSpice A/D Reference Manual for the definitions of the model parameters. This manual is contained on the CD-ROM that accompanies this text and is located in file D VDocument pspcref.pdf. This file can be viewed with the Adobe Acrobat Reader. 

This section gives brief descriptions of model parameters for most of the parts mentioned in this manual. Only a few of the parameters for each model are given to allow the user to create simple models. To create more detailed models, the reader is referred to the PSpice Reference Manual, which is contained on the CD-ROM that accompanies this manual. The semiconductor models presented here include only the simple DC parameters because the models get complicated very quickly when dynamics are included. Temperature dependence parameters for some models are discussed. 

Without solving any equations, suggest a better model for describing ihe wetlands. Hint An extended version of this problem can be found on the CD-ROM.)... 

The segregation model and maximum mixedness model are further compared on the CD-ROM for reaction orders between zero and one. 

As the gas is cooled, it becomes supersaturated, leading to the nucleation of particles. This nucleation is a result of molecules colliding and agglomerating until a critical nucleus size is reached and a panicle is formed. As these particles move down, the supersaturated gas molecules conden.se on the particles causing them to grow in size and then to flocculate. In the development on the CD-ROM. w c will model the formation and growth of aluminum nanoparticles in an, AFPR. 

In nonlinear regression analysis, we search for those parameter t alues that minimize the sum of the squares of the differences beiw een the measured values and the calculated values for all the data points.- Not only can nonlinear regression find the best estimates of parameter values, it can al,so be used to discriminate between different rate law models, such as the Langmutr-Hin-shelw ood models discussed in Chapter 10. Many software programs are available to find these parameter values so that all one has to do is enter the data, The Polymath software will be used to illustrate this technique. In order to carry out the search efficiently, in some cases one has to enter initial estimates of the parameter -alues close to the actual values. These estimates can be obtained using Ihe linear-least-squares technique discussed on the CD-ROM Professional Reference Shelf. 

Model Discrimination. One can also determine which model or equation best fits the experimental data by comparing the sums of the squares for each model and then choosing the equation with a smaller sum of squares and/or carrying out an F-test. Alternatively, we can compare the residual plots for each model. The.se plots show the error associated with each data point, and one looks to see if the error is randomly distributed or if there is a trend in the error. When the error is randomly distributed, this is an additional indication that the correct rate law has been chosen. An example of model discrimination using nonlinear regression is given on the CD-ROM in Chapter 10 of the Sum-marv Notes. 

The concentrations exiting the last CSTR are Ci and C, . Equations (E7-7.I) ihiDugh (87-7.15) along with the parameter values are given on %e CD-ROM summary notes and the Polymath living example problem. The Polymath program can be loaded directly from (he CD-ROM so that the reader can vary the model parameters. You can print or view the complete Polymath program and read the complete paper [Alcohol 35 (I). p.iO, 2(X)5] in Summary Notts on the CD-ROM. 

The Kunii-Levenspiel model for fluidization is given on the CD-ROM along with a comprehensive example problem. The rale limiting transpon steps are also discussed. See Professional Reference Shelf R12.3. 

Con.sequemly. if we have the batch reactor equation for X(/) and measure the RTD experimentally, we can find the mean conversion in the exit stream. Thus, if we have the RTD, the reaction rate expression, then for a segregated flow sih nation (i.e model), we have sufficient information to calculate the conversion. An example that may help give additional physical insight to the segregation Summary Motes model is given in the Summary Notes on the CD-ROM. click the Back button just before section 4A.2. 

In the previous example we saw that the conversion predicted by the segregation model. was greater than that by the maximum mixedness model Will this always be the case No. To learn the answer we take the second derivative of the rate law as shown in the Professional Reference Shelf R13.3 on the CD-ROM. 

You are going to look in this Book at some of the methods used to model molecules and at the principles behind them. On the CD-ROM, you will study some examples. 

You have studied the ideas behind molecular modelling, but how would you actually carry out a calculation In this Section we present a brief overview of how modelling is done. This is reinforced on the CD-ROM. 

On the CD-ROM. the program Molecular modelling Illustrates the results of molecular mechanics calculations and. at an elementary level, allows you to explore the effects of quantum mechanical basis sets and methods on calculated properties. The program Electrons In solids on the CD-ROM explores the behaviour of electrons In crystal structures. Including semiconductors. The CD-ROM also contains several Interactive self-assessment questions. 

The activity coefficient model parameters in Problems 11.2-18 to 11.2-25 are easily determined using the MATHCAD worksheet ACTCOEFF on the CD-ROM accompanying this book and described in Appendix B.lll. 

Figure 13.1-2 Chemical equilibrium constants as a function of temperature. [Reprinted with permission from M. Modell and R. C. Reid. Thermodynamics and Its Applications, Prentice Hall, Englewood Cliffs, N.J. (1974), p- 396. This figure appears as an Adobe PDF file on the CD-ROM accompanying this book, and may be enlarged and printed for easier reading and for use in solving problems. Also, the values of the chemical equilibrium constants can be calculated using Visual Basic and DOS-Basic Programs on the CD-ROM accompanying this book. These programs. are discussed in Appendix B.I and B.K.)...

Giovine, P. Palumbo, A. 2003. Modeling contaminant transport in soils. Proceed, of Mediterranean Conference on Modelling and Simulation 03 , Reggio Calabria, 25-27 June 2003, Session on Modeling, Technical Note n.l78 on the CD rom, Reggio Calabria NeuroLab. 

Name corresponds to the name of the job on the CD-ROM. Nobs is the number of reflections agtdnst which the structure has been refined. Npar is the number of parameters refined in the respective model. i work and Rfree are the R-values for F > 4a(F) calculated against work and test-set, respectively. 

In HYSYS.Plant, the Shortcut Column model is used, which is described in the modules under HYSYS Separations —> Distillation —> Shortcut Distillation Column on the CD-ROM. 

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