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Modeling of Activity Coefficients Using Computational Modelling of activity coefficents by comp. chem. 1 Modelling of activity coefficients using computational chemistry Eirik Falck da Silva Report in DIK 2099 Faselikevekter June 2002 Modelling of activity coefficents by comp. chem. 2 SUMMARY ......................................................................................................3 INTRODUCTION .............................................................................................3 background .............................................................................................................................................3 The use of computational chemistry .....................................................................................................4 REVIEW...........................................................................................................4 Introduction ............................................................................................................................................4 Free energy of solvation .........................................................................................................................5 Cosmo-RS ............................................................................................................................................7 SMx models..........................................................................................................................................7 Application of infinite dilution solvation energy..................................................................................8 Equation of state (EOS) approaches.....................................................................................................8 UNIQUAC............................................................................................................................................8 UNIFAC .............................................................................................................................................10 General issues.....................................................................................................................................10 Direct approaches ...............................................................................................................................11 Indirect methods .................................................................................................................................11 Explicit solvent modelling....................................................................................................................12 RESULTS AND PROPOSED PROCEDURES..............................................13 Activity coefficients predicted with free energy of solvation ............................................................13 UNIQUAC parameters from Sandlers method..................................................................................14 Ab Initio Fitting to UNIFAC parameters...........................................................................................15 Monte Carlo modelling of UNIFAC parameters ...............................................................................17 DISCUSSION ................................................................................................21 CONCLUSION...............................................................................................22 LITERATURE ................................................................................................24 APPENDIX 1 .................................................................................................26 APPENDIX 2 .................................................................................................29 APPENDIX 3 .................................................................................................30 APPENDIX 4 .................................................................................................32 Modelling of activity coefficents by comp. chem. 3 Summary In this work I have looked at various approaches to the estimation of activity coefficients by computational methods. I have worked on binary systems consisting of neutral molecules. I have looked at several approaches described in the literature. Some I only discuss briefly, while others I have studied and applied. I have focused mostly on using computational methods to obtain parameters for the UNIQUAC and UNIFAC equations. Use of Monte Carlo modelling to obtain energy parameters for UNIQUAC has been fairly successful, supporting an interpretation of UNIQUAC energy parameters as a residual form of the free-energy of solvation. Introduction background My group is working on the processes of CO2 removal from exhaust gases. We are looking at processes using chemical absorption of CO2 from a gas phase into a liquid phase. In order to understand, control and improve on the absorption process a detailed understanding of the chemistry is necessary. This understanding should include a model for the activities in the liquid phase. Use of models such as UNIFAC and UNIQUAC on these absorption processes has been reported in literature1,2. Published data does not seem to be very reliable and there is no consistency in reported data. The uncertainty is not surprising since almost all of the work is based on limited experimental data. Often only temperature, pressure, the partial pressure of CO2 and initial concentration of different species in the system is known. Concentration of various species are often unknown and even the understanding of the reaction chemistry can be limited. Various assumptions must be made and the activity coefficients are only one of a larger set of properties that must be fitted to the data. Group contribution models such as UNIFAC can be used, but their reliability for the systems in question is unknown and the group contribution factors available to us do not cover all molecules formed. Any form of modelling that can generate independent estimates of the activity coefficients would obviously be useful to improve the understanding and modelling of the absorption processes. The main goal of my own work is to predict the performance of new absorbers for these processes. A predictive model for the activity of these new absorbers is then desirable. Modelling of activity coefficents by comp. chem. 4 The use of computational chemistry Computational chemistry is a term used to refer to molecular Monte Carlo methods, molecular dynamics and the so called "Ab Initio" methods, based on solving some (simplified) form of the Schrødinger equation. All these methods are well established. Ab Initio methods have been very successful in modelling of molecular geometry, particularly in the gas-phase. Most molecular properties can be calculated with reasonable precision using these methods. The behaviour of a liquid mixture is a function of molecular properties and it is therefore natural to ask if computational chemistry can not be used to model activity in solvents. While I have not found much work on the modelling of activity in the literature, modelling of solvation effects is a major topic in computational chemistry. The methods in use can be used to calculate activities and use theory and concepts that would seem applicable to overall activity modelling. Review Introduction Activity coefficients are defined as the ratio between activity and some measure of the concentration, often the mole fraction. Relating this to the chemical potential we get: 0 RT ln(x ) 1 It is usual to relate activity to the excess Gibbs energy, defined as: E V G G(actual solution at T,P and x) - G (ideal solution at T,P and x) 2 Using this we get that: RG E . / RT ln( ) 3 R / i N i 0 T ,P,n j Borrowing from Tomasi et al3 we can divide the approaches to modelling activity into three categories: S Methods based on the continuum model. S Elaboration of physical functionals, here we find models such as UNIQUAC and NRTL. S Methods based on computational simulations of liquids. Modelling of activity coefficents by comp. chem. 5 While I will not go further into this approach I will finally mention the possibility of using quantum chemical descriptors and using statistical methods to find their correlation with activity4. I will discuss these various approaches and their application. Tomasi did note that the division of these methods was slightly dated since there was a convergence of these methods taking place and in this work I will also show possible combinations of these methods. Free energy of solvation One quantity often used in computational chemistry is the free energy of solvation (Gsol), giving the energy in going from (ideal) gas phase to a given solvent phase. If we can calculate Gsol for two solvent states, we in fact have data to calculate equation 1, i.e. differences in solvation free energy between two systems with the same reference state (gas-phase) is equivalent to differences in chemical potential. One main form of modelling Gsol is the Continuum models, so called because they treat the solvent as a continuum. The solvated molecule is placed in a cavity and the solvent effects are represented by the interaction with the cavity wall and the imposition of an electrostatic field. Ben Naim5 has developed the following equation to express the solvation energy based on statistical mechanics: q q . n 3 . G W (M / S) RT ln rot,g vib,g / RT ln M ,g M ,g / 4 sol / 3 / qrot,s qvib,s 0 nM ,s M ,s 0 The equation is based on separating the process in two parts. First you
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