Integral equation theories for complex fluids

The prediction of thermodynamic properties of fluids is of central importance to the chemical engineer. For fluid systems composed of molecules modeled using interaction site potentials, the structural and bulk thermodynamic properties can be determined "exactly" using Monte Carlo or molecular dynamics simulations. However, these techniques have several shortcomings, including limitations in the length and time scales that can be examined, and the computational expense. On the other hand, integral equation theories do not suffer from such limitations. These equations, when combined with an approximate closure relation, yield the intermolecular site-site correlation functions, which provide physical insight into the underlying structure of the fluid. From these correlation functions, the thermodynamic behavior of the system can be computed. The primary goal of this thesis is to bring integral equation theories for molecular fluids to a level where they can provide a useful computational tool for the chemical engineer. This involves assessing the applicability of existing integral equations and improving their predictive capabilities as needed. For this purpose, two integral equations for interaction site fluids, the site-site Ornstein-Zernike (SSOZ) equation and the Chandler-Silbey-Ladanyi (CSL) equations, were examined for various complex fluids. For water, the SSOZ equation was solved for several different potential models at ambient conditions. The SSOZ equation captured the short-ranged correlations in water properly, however, for the second coordination shell and beyond, the predicted pair correlation functions deviated significantly from those found using computer simulations and experimental measurements. The predictions for the thermodynamic properties of water were found to be reasonable. For hydrocarbons at infinite dilution in water, the SSOZ equation was solved under a variety of different closure relations in order to compare their quantitative predictive capabilities. When used with certain approximate closures, the SSOZ equation yielded reasonable predictions of the structural and bulk thermodynamic properties of the hydrocarbon-water systems examined. In addition, the chain conformations of hydrocarbons in vacuum and at infinite dilution in water were computed. While all the closure relations which were examined predicted that the hydrocarbon chain becomes more collapsed when placed in water, which is what is physically expected due to the hydrophobic effect, the magnitude of this effect was found to depend on the particular closure used. The SSOZ equation was then applied to a model surfactant-water system, in which micellar aggregates can form, and was found to yield several unphysical results. In particular, it yielded large negative regions in the predicted surfactant-surfactant pair correlation functions. In addition, no solutions to the SSOZ-PY equation were found over a large region in the temperature-surfactant concentration plane. When the HNC closure was employed, no solutions were found except at very high temperatures and low surfactant densities, which is unphysical. The disparate and unphysical behavior of the SSOZ equation with different simple fluid closures suggests that this equation may not be sufficiently accurate to adequately model self-assembling systems. Although the SSOZ equation has been fairly successful in predicting the behavior of interaction site fluids such as water and hydrocarbons in water, it has several limitations. The major limitation is that when the known approximate closures fail to provide physically reasonable results, such as in the case of the Lennard-Jones surfactant model system discussed above, no straightforward method exists to improve their accuracy. This led to the use of a new set of integral equations, known as the Chandler-Silbey-Ladanyi (CSL) equations, the primary advantage of which is that, in principle, their accuracy can be systematically improved using liagrammatic methods. In spite of this appealing aspect of the CSL equations, they have found limited application in the past. Accordingly, in this thesis, expressions for the free energy for the CSL equations were developed, and various computational aspects of these equations were analyzed. Comparisons have been made between the capabilities of the CSL and SSOZ equations to predict the structure of homonuclear and heteronuclear diatomic LennardJones molecules at various temperatures, densities, and bond lengths. In general, the CSL-HNC equations were found to be in better agreement with the computer simulation results as the bond length increases or as the density decreases, while temperature was found to have little effect. A method was developed for computing the low-order corrections to the correlation functions. The addition of the zeroth-order corrections was found to have little effect on the predictions of the CSL equations, while the addition of the first-order corrections resulted in a significant improvement in the predictive capabilities of the CSL equations. Finally, the CSL equations and the SSOZ equation were applied to several different potential models of water. The predictions for the pair correlation functions and the thermodynamic properties of the CSL equations were found to be in slightly better agreement with computer simulation results than those of the SSOZ equation. The phase behavior of water was also predicted using these integral equations, and found to be in fair agreement with results from computer simulations and experimental measurements. Thesis Supervisor: Daniel Blankschtein Title: Associate Professor Acknowledgments To begin, I would like to thank my advisor, Professor Daniel Blankschtein, who has been more than just an advisor to me. From the day I joined his group, he has continually provided me both scientific guidance and moral support. With his help, I feel I have grown tremendously as a scientist and, more importantly, as a person. I will always be indebted to him and hope someday to make him proud. I would also like to thank Professors Robert Armstrong, Sow-Hsin Chen, and Jonathan Harris for serving on my thesis committee. In particular, I owe a great debt to Professor Harris who, no matter how busy, always made time for me to discuss ideas. I thank Xinjin Zhao for being a true friend since the day I met him. Xinjin is a person whom I could always rely on, both extremely patient and understanding, helping me through all my troubled times. I look up to him as the older brother I never had. I wish him, his wife, Luhong Bo, and their son, Daniel, the best of luck. I consider myself lucky to call Reza Mehrabi a friend. His interests in cooking, modern dance, painting, and art in general greatly broadened me as a person. Whenever I needed anything, he was always willing to help. Reza is a person I greatly admire and deeply respect. I wish him and his wife the best. I would like to thank the Ehh! gang, Stathis Avgoustiniatos, Abdul Barakat, Brian Laffey, and Joy Mendoza, with whom I spent most of my time here at MIT, either eating dinner, watching all night movie marathons in 66-110, ortalking in the lab till 4am. To each of them, I owe a special debt which I can never repay: Stathis for sharing his quest for truth and knowledge, Abdul for showing me dedication and perseverance, Brian for opening my ears to music and my mind to social responsibility, and Joy for teaching me to accept people as they are. They are the closest friends I have ever known in my life. I thank them for keeping life interesting and fun. I will always remember the times we have spent together. I am grateful to the other members of the group. In my initial years at MIT, Sudhakar Puvvada, as Blankschtein's first student, served as a mentor for me, always there to offer guidance. I want to thank him and let him know that I missed him greatly when he graduated. I want to thank Ayal Naor (SPORE rules! ) and Pak Yuet for being around late at night to bounce ideas off of, for all their help, encouragement, as well as advice, and for their friendship. I would like to thank my UROP Denise Ciotti and wish her good luck at BU. I thank Nick Abbott, Giuseppe Briganti, Teresa Carale, Chia-li Liu, Mark Johnson, Yvonne Nikas, and Claudia Sarmoria for all their help and the times we have spend together. I also want to wish the newer students, Crist Clark, Samir Mitragotri, Anat Shiloach, Ginger Tse, and Nancy Zoeller, well and the best of luck on their research. Thanks to the Friday night Basketball Crew for the many enjoyable hours on the court: Davy Chang, Alex "Koulalex" Koulouris, Mike Kwan, Dave "College Boy" Lathrop, Nelson Lin, Marc Moran, Gokaraju Raju, Bruce Scruggs, Hiroshi Saito, and "I wanna be like" Mike Thompson. I also owe thanks to the guys down on the second floor in Brown's crystal growth group: Howard Covert, Angelos Kyrilidis, John Lee, and Dimitri Maroudas. They were always willing to discuss anything from numerical methods to music theory and from statistical physics to life in general. Thanks for all the help. Thanks to all my other friends in the department, who made each day enjoyable: Elaine Aufiero-Peters, Arline Benford, Diane Burke, Alex Diaz (Hey Alex,.BANG! ), Barbara Driscoll, Janet Fischer, Dave Oda, Sujatha Karoor, Nancy Masley, Sandeep Patel, Costas Patrikios (Ehh, man! ), Gerald Prioleau, Mike Pomianek, and Gordon Smith. I would also like to thank the National Science Foundation and the National Institute of Health for financial support through their fellowship programs. Finally, I thank my parents, to whom I owe everything.