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LISA G. BULLARD North Carolina State University Copyright ChE Division of ASEE 2010 ChE APPROACHES TO ACADEMIC INTEGRITY:Confessions of a Reluctant Expert Communication: Clearly communicate your expectations regarding academic integrity to your students, both in the Collaboration: Collaboration is desirable, as long as it curve encourages students to help classmates legally, ceptable behavior regarding collaboration on individual Homework: collaboratively as long as the contributing members names this not only educates students about your expectations Troublesome Websites: textbook problems or asked to upload such content in or
Vol. 44, No. 3, Summer 2010 173 DEPARTMENT 174 Chemical Engineering at the University of North Dakota CLASSROOM 183 Gas Pressure-Drop Experiment William L. Luyben, Kemal Tuzla 208 A Graphical Representation for the Fugacity of a Pure Substance Neil L. Book and Oliver C. Sitton 215 YouTube Fridays: Engaging the Net Generation in 5 Minutes a Week Matthew W. Liberatore 222 Polymerization Simulator for Introductory Polymer and Material Science Courses William M. Chirdon RANDOM THOUGHTS 213 The Link Between Research and Teaching 2. How to Strengthen Each Without Weakening the Other Richard Felder AIChE SPECIAL SECTION 189 Creative Learning in a Microdevice Research-Inspired Elective Course for Undergraduate and Graduate Students Adrienne R. Minerick CURRICULUM 229 Ehrenfests Lottery Time and Entropy Maximization Henry S. Ashbaugh 198 Using Aspen to Teach Chromatographic Bioprocessing: A Case Study in Weak Partitioning Chromatography for Biotechnology Applications Steven T. Evans, Xinqun Huang, and Steven M. Cramer 236 Vapor-Liquid Equilibria Using the Gibbs Energy and the Common Tan gent Plane Criterion Mara del Mar Olaya, Juan A. Reyes-Labarta, Mara Dolores Serrano, Antonio Marcilla TEACHING TIP inside front cover Approaches to Academic Integrity: Confessions of a Reluctant Expert Lisa G. Bullard BOOK REVIEW inside back cover Heat Transfer by Gregory Nellis and Sanford Klein Reviewed by Kemal Tuzla Chemical Engineering Education Volume 44 Number 3 Summer 2010 CHEMICAL ENGINEERING EDUCATION (ISSN 0009-2479) is published quarterly by the Chemical Engineering Division, American S ociety for Engineering Education, and is edited at the U niversity of Florida. C o r respondence regarding editorial matter, circulation, and changes of address should be sent to CEE, Chemical Engineering Department, University of Florida, Gainesville, FL 32611-6005. Copyright 2010 by the Chemical Engineering Division, American Society for Engineering Education. The statements and opinions expressed in this periodical are those of the writers and not necessarily 120 days of pu b lication. W rite for information on subscription costs and for back copy costs and availability. P OS TMA S TER: Send address changes to Chemical Engineering Education, Chemical Engineering Department., University of Florida, PUBLICATIONS BOARD EDITORIAL AND BUSINESS ADDRESS:Chemical Engineering Education Department of Chemical Engineering University of Florida Gainesville, FL 32611PHONE and FAX : 352-392-0861 EDITOR Tim Anderson ASSOCIATE EDITOR Phillip C. W ankat MANAGING EDITOR L ynn Heasley PROBLEM EDITOR Daina Briedis, Michigan State LEARNING IN INDUSTRY EDITOR W illiam J. Koros, Georgia Institute of Technology CHAIRMAN John P. OConnell University of Virginia VICE CHAIRMAN C. Stewart Slater Rowan University MEMBERS Lisa Bullard North Carolina State Jennifer Curtis University of Florida Rob Davis University of Colorado Pablo Debenedetti Princeton University Dianne Dorland Rowan Stephanie Farrell Rowan University Jim Henry University of Tennessee, Chattanooga Jason Keith Michigan Technological University Suzanne Kresta University of Alberta Steve LeBlanc University of Toledo Ron Miller Colorado School of Mines Lorenzo Saliceti University of Puerto Rico Stan Sandler University of Delaware Margot V igeant Bucknell University
Chemical Engineering Education 174 ChE department Founded by the Dakota Territorial Assembly in 1883six years before statehoodthe University of North Dakota (UND) has remained a university with a strong liberal arts foundation surrounded by a variety of professional and specialized programs. UND is one of only 47 public universities in the nation with accredited graduate schools of both law and medicine, and is regarded as a national leader in rural and family health issues, aerospace, energy and envi ronmental research, and edu cational programs for Ameri can Indians. Recognized for its extensive programming for native peoples, UND has more than 30 academic pro grams for American Indians. For example, 20% of American Indian doctors in the country were trained at UND through the Indians Into Medicine program (INMED). The universitys 292 tenured and 207 tenure-track faculty mentor more than 13,000 on-campus students and 21,000 distance-education and continuing-enrollment students in 193 sional degrees. Fifty-one percent come from North Dakota; the rest represent all other states, seven Canadian provinces, and more than 50 other countries. UND is located in Grand Forks, a college town of 50,000 on the Red River of the North separating North Dakota and Minnesota. The campus includes 223 build ings (5.33 million square feet under roof) on 549 acres. THE COLLEGEEngineering programs began at UND in 1889 and the School of Engineering and Mines (SEM) was formed in 1916. SEM faculty instruct more than 1,000 students through programs administered by the departments of Chemical Engi neering, Civil Engineering, Electrical Engineering, Geology Chemical Engineering at The University of North Dakota Harrington Hall is home to the ChE departments ofces and laboratories.and Geological Engineering, and Mechanical Engineering. Bachelors and masters degrees are offered in chemical, civil, electrical, geological, and mechanical engineering, as well as in geology. Additional graduate degrees include masters degrees in environmental engineering and sustain able energy engineering plus doctorates in engineering (with specialty tracks), chemical engineering, and geology. SEM further provides its ABET-accredited engineering programs via distance education to industry and individuals through a Distance Engineering Degree Program (DEDP).THE DEPARTMENTS HIST ORYThe Department of Chemical Engineering was established enrollment of 92 resident and 21 distance undergraduates per year with a Fall 2009 enrollment count of 122 and 35 resident and distance undergraduates, respectively. The gradu ate-student population grew substantially in the mid-2000s Copyright ChE Division of ASEE 2010
Vol. 44, No. 3, Summer 2010 175 to a current stable size of around 35 per year. See Table 1 for historical highlights. Transfer students are a significant portion of our stu dentsaround 10%. We encourage this source of students by providing customized programs of study for transfer stu dents that are shared with guidance counselors and chemistry professors at the community and four-year colleges in our region. We have also assisted regional two-year colleges in establishing pre-ChE programs. The key is our willingness to provide access to our introductory freshman course (ChE 102) and our sophomore fundamentals course (ChE 201) using distance techniques. This allows two-year transfers to enter into our junior-year curriculum. Formal agreements have been or are being put into place to establish formal Pre-Chemical Engineering programs at Minot State University (ND), Itasca Community College (MN), Hibbing Community College (MN), Minnesota State Moorhead, North Dakota State Col lege of Science, Turtle Mountain Community College (a North Dakota tribal college), and Benedictine College (KS).OUR MISSION ST A TEMENTIt is our vision to offer an unsurpassed, personal, under graduate chemical engineering education, coupled with a top-tier-quality, research-centered graduate program. The departments primary objective is the education of under graduate students so that, upon graduation, they are prepared to take responsible, entry-level positions in a wide range of industries. Research and professional activities by members of the faculty, conducted in collaboration with graduate and undergraduate students, provide training for our students on how to succeed as researchers.EDUCA TIONAL OBJECTIVESThe Chemical Engineering program prepares graduates who, in their professional careers:1. Have the knowledge and skills required to analyze and ing and communicate these results in verbal and written form to a diverse audience. T ABLE 1 The University of North Dakota Chemical Engineering Department Historical Highlights1889 College of Mines and College of Electrical and Mechanical Engineering founded 1916 School of Engineering and Mines formed from merger of the colleges of Mines and Electrical/Mechanical Engineering 1926 Initiation of Chemical Engineering Program at UND 1928 First Degree: Masters of Science in Chemical Engineering 1939 Program with four faculty accredited by the Engineers Council for Professional Development 1942 Program loses accreditation due to faculty loss brought on by demands of WWII 1946 Program reaccredited with new faculty 1948 ChE moves into brand new buildingHarrington Hall 1949 First doctoral degree: Fuel Technology; Charles R. Robertson Lignite Research Laboratory established 1972 Tom Owens receives the 1972 Dow Outstanding Young Faculty Award 1973 1982 Robertson laboratory ownership transferred from federal government to UND and renamed the Energy and Mineral Research Center 1989 Energy and Mineral Research Center merged with Mining and Mineral Resources Institute within the School of Engineering and Mines, and renamed the Energy and Environmental Research Center 1991 1992 UND Departmental Award for Excellence in Teaching 1993 UND Outstanding Faculty Development Award 1997 buildings 2000 Tom Owens named North Dakota Teacher of the Year 2005 UND Departmental Award for Excellence in Research; John Erjavec receives UNDs Award for Individual Faculty Excellence in Teach ing; DOE EPSCoR IIP Award allows addition of sixth tenure/tenure-track faculty member 2006 Darrin Muggli receives UNDs Award for Individual Faculty Excellence in Teaching; Michael Mann receives UNDs Award for Indi vidual Excellence in Research 2007 UND Departmental Award for Excellence in Teaching; Wayne Seames receives UNDs Award for Individual Excellence in Research; research funding level allows the addition of non-tenured faculty member 2008 NSF EPSCoR RII award allows addition of seventh tenure/tenure-track faculty member 2009 Research funding level allows the addition of second non-tenured faculty member
Chemical Engineering Education 176 2. Can succeed in entry-level positions in the chemical process and broadly related industries, and demonstrate integrity, responsibility, ownership, and accountability for their work. 3. Have a thorough grounding in fundamentals, allowing them to obtain advanced degrees in chemical engineering or to pursue other professional interests such as medicine or law. 4. Have the teamwork, leadership, and lifelong-learning skills that prepare them for future professional growth in a broad spectrum of careers. 5. Understand the role of chemical engineering as a profes sion and their role in addressing societal issues, including sustainability, environmental responsibility, and safety.The program educational objectives and the departmental mission have remained largely unchanged over the past de that time by involving the departmental students, staff, alumni, key employers, and faculty in a variety of waysmany of them informal. Alumni are invited to share their perspectives regarding the educational program offered by the department. As a part of our assessment process, we directly contact graduates from the program that have been out of the program for one and three years. Our annual newsletter (
Vol. 44, No. 3, Summer 2010 177 least two faculty members read each intermediate deliverable and participate in the technical review meetings. of the entire faculty, each of whom represents a different job function on a capital project review team (management, design projects include multiple-variable constraints and are often performed with industrial partners/mentors. Others are theme-sponsored projects from foundations or governmental agencies. Recent examples include vegetable oil extraction e.g. corn, canola, soybean, cotton), coal, methanol from syngas, renewable diesel from algae for a mission to Mars, and magnesium from seawater. Faculty participation in the capstone design course provides each faculty member with valuable feedback concerning the assimilation and retention of the key concepts from each of the core recitation courses in the curriculum. We use this feedback to improve our teaching effectiveness in these foundation courses. For example, we found that students were ances, even though these were covered extensively during the sophomore year. In response we began adding mass-balance problems to various homework sets throughout the curriculum to reinforce the techniques learned earlier. As a result, student performance generating mass balances during the capstone participation also stresses to our students the importance we place on the design component of the curriculum and on the capstone design experience in particular. The L aboratory S equence. A core value in our undergradu ate program is the importance of laboratories to produce a graduate with hands-on experience. In addition to the re quired labs in chemistry and physics, students must take a four-semester sequence in the department. The early labs are focused on the development of good laboratory techniques, to reinforce fundamental principles, and to introduce software tools. The nature of the experimental problems gradually grows in complexity and rigor as students progress through the sequence. Upper-level labs introduce students to the use of the lab to answer research-based questions and how to use published journal articles as the basis of setting up experi confront open-ended, vague problem statements where the experiments in the laboratory serve as data-gathering tools used in problem solving. Students determine how to use the laboratory apparatus to generate the data and determine the number of replicate sample sets they need to validate their results statistically. The use of computer tools is incorporated to demonstrate the importance of combining experimental results with simulation. All laboratory classes are supervised by faculty. We also utilize these labs as a tool to integrate a variety of skills into one experience. It is our philosophy that outside of cooperative education and internships, the laboratory classes, if structured properly, provide the best opportunity to expose students to the set of skills that are best obtained through experiential learning. Therefore, rather than having our laboratory classes focused only on reinforcing chemical engineering principles, we embed a variety of other learning goals. To accomplish T ABLE 2 The University of North Dakota Chemical Engineering Curriculum First Year Math 165 Calculus I 4 ChE 102 Intro to ChE 2 Chem 221 Chemistry I 3 Math 166 Calculus II 4 Chem 221L Chemistry Lab I 1 Chem 222 Chemistry II 3 Engl 110 College Comp I 3 Chem 222L Chemistry Lab II 1 Arts & Humanities Elective 3 Phys 251 University Physics I 4 Social Sciences Elective 3 Arts & Humanities Elective 3 17 17 Sophomore Year ChE 201 ChE Fundamentals 3 ChE 206 Unit Operations 3 Math 265 Calculus III 4 ChE 232 ChE Lab I 2 Phys 252 Physics II 4 ChE 315 Statistics & Numerical Methods 3 Engr 201 Statics 3 Math 266 Differential Equations 3 Engl 125 Technical & Business Writing 3 Chem 240 Survey of Organic Chemistry 4 17 Chem 240L Survey Organic Lab 1 16 Junior Year ChE 301 Transport Phenomena 4 ChE 332 Che Lab III 2 ChE 331 ChE Lab II 2 ChE 305 Separations 3 ChE 303 ChE Thermodynamics 4 ChE 321 ChE Reactor Design 3 EE 206 Circuit Analysis 3 ChE 340 Professional Integrity 3 Technical Elective II 3 Business/Entrepreneurship Elective 3 16 Technical Elective I 3 17 Senior Year ChE 408 Process Dynamics & Control 3 ChE 412 Plant Design II 5 ChE 431 ChE Lab IV 3 Arts & Humanities Elective 3 ChE 411 Plant Design I 4 Social Sciences Elective 3 Chem 465 Physical Chemistry II 3 EngSci Elective 3 Advanced Chemical Science Elective 3 Advanced Chemical Science Elective 3 16 17
Chemical Engineering Education 178 these goals we have formally mapped course content with each of the labs was consistent with the educational objectives of the department and independent of the faculty teaching the course. The current listing is shown in Table 3. DIST ANCE EDUCA TIONSince 1989, UND has offered its ABET-accredited bachelors degree program in chemical engineering using a distance delivery program concurrent with our local courses. Designed for working adults who are unable to complete a full-time, on-campus program, the distance program uses the same curriculum as the on-campus program. Courses are offered asynchronously, which provides great courses are taught for on-campus learning, they are captured digitally and made available through the Blackboard learning environment, usually within two hours of class completion. This allows students to watch recorded classroom lectures, access course materials, submit assignments, and take tests at the time of day and place of their choice within a time window for each assignment. The four-lab sequence is consolidated into three two-week, on-campus intensive lab experiences taken over the course of three summers. This provides important face-to-face contact between faculty and students and between students within the same peer group (facilitating group work throughout the cur riculum). We also allow local students to participate in these summer labs, which provides useful and exciting synergies between on-campus and distance students. UND provides extensive student support services, such as online tutoring, library access, tech support, and advising ser vices to ensure that the students can easily and readily access the resources they need for success. In 2004, UND received the WOW Award given by the Western Cooperative for Educational Telecommunications for being on the cutting edge of using technology for distance engineering degree programs. Distance students are held to the same high standards of excellence as on-campus students. Participants have come from all over North America. We even had one student com offshore oil platform! Most work in process-related jobs that motivated their interest in a chemical engineering degree but at least one student was a stay-at-home mother of two. T ABLE 3 Mapping of Learning Goals to Laboratory Sequence Content Area Lab I Lab II Lab III Lab IV ChE Principles mass balances energy balances intro thermodynamics ChE principles heat transfer mass & energy balances intro transport phenomena separations transport phenomena thermodynamics kinetics process dynamics process control reactor design separations design Statistics mean range standard deviation hypothesis test linear regression propagation of error simple DOE simple ANOVA linearization residual analysis nonlinear analysis sources of error response surface method DOE Data Analysis data information identify trends in data explain trends error analysis (qual/quant) sources of error empirical modeling error budgets causes of data reasonableness factors affecting data error testing Writing basic writing skills tables technical report content style technical clarity writing instruments editing & revisions drawings levels of detail audience additional instruments capstone synthesis standards of excellence Oral Communication basic presentation skills content of presentation style, delivery, clarity methodology of formal talks informal presentations cohesiveness engagement impact conclusions recommendations meetings Teamwork basic principles of groups team roles manage, coordinate time group analysis methods priority setting collaboration, compromise accountability negotiations Integrity plagiarism referencing manipulation of data presentation of data doing your share accountability Professionalism levels of attire working with support personnel communication etiquette independence standards of excellence Safety formal lab safety training basic lab safety formal lab safety training safety concerns in reports MSDS formal lab safety training MSDS PHAs formal lab safety training operational safety
Vol. 44, No. 3, Summer 2010 179 that are necessary for these nontraditional students to complete this program (including their summer vacations for three and assignment due dates while still moving students toward course and program completion. Faculty and staff try to pro vide at least the same level of personal attention and accessi bility to distance students as to on-campus students. This may involve online dedicated problem solving or review sessions to ensure that distance students can participate in engagement learning methods similar to on-campus students.ACCOMPLISHMENTS AND A WARDSThe current faculty members are proud to have maintained the departments long tradition of providing the highest qual ity education available to undergraduate students in chemical engineering. Annual analysis of data from our assessment instruments (undergraduate, alumni, and employer surveys; performance on standardized tests; etc.) shows that we are meeting and usually exceeding all of our educational objec tives. Our department is accredited by ABET, with our most recent accreditation visit in Fall 2009. The faculty is dedicated to excellence in teaching, and the atmosphere in the depart ment is especially conducive to learning. The department was recognized with UNDs 1992 and 2007 Departmental Awards for Excellence in Teaching. Dr. Tom Owens, then professor and chair (now profes sor emeritus) received the 1972 Dow Outstanding Young Faculty Award and the 1993 UND Outstanding Faculty Development Award, and was named the state of North Dakotas Educator of the Year in 2000. Dr. John Erjavec, then associate professor (now profes sor emeritus) received UNDs 2005 Award for Individual Faculty Excellence in Teaching. Michael Mann (distinguished professor, chair). Research interests: Performance coal and biomass, emission control; re newable and sustainable energy systems; development of energy strategies coupling thermodynamics with political, social, and economic factors. Frank Bowman (assistant professor). Research interests: Atmospheric aerosols; organic aerosol partitioning; mathematical modeling of multicomponent aerosols; air quality modeling; educational technology; assessment of student learning; educational air pollution models. Edward Kolodka (associate professor). Research interests: Polymer reaction engineering; synthesis, rheological, and mechanical properties of polymers; de velopment of polymers from agricultural products; synthesis and characterization of conducting polymers. Gautham Krishnamoorthy (assistant professor). Research interests: Compu technologies; radiative heat transfer. Wayne Seames (professor). Research interests: Novel process technologies; renewable fuels and chemicals; advanced combustion technologies; mitigation of the environmental impact of heavy metals; trace element partitioning from combustion and incineration. Brian Tande (assistant professor). Research interests: Polymer science and engineering with applications in sustainable energy; rheol phology; neutron scattering; effect of polymer branching on membrane transport; polymers and composites from renewable sources. Steve Benson (professor). Research interests: deposition; carbon products; carbon dioxide separation and capture. Yun Ji (assistant professor). Research in terests: Renewable and sustainable energy; chemicals and fuels from renewable sourc es; biomass pretreatment; biochemical and thermo-chemical of biomass for fuel pro duction, enzymatic hydrolysis; integrated energy and environmental projects; process paper technology; lignin utilization. Bob Wills (associate professor). Research interests: Non-thermal drying of solids by chemical dehydration; vegetative oil extrac tion and product enhancement; increasing process efficiencies in the fermentation industry.
Chemical Engineering Education 180 Dr. Darrin Muggli, then associate professor (now adjunct), received UNDs 2006 Award for Individual Faculty Excellence in Teaching. Drs. Wayne Seames, Darrin Muggli, Frank Bowman, and Brian Tande were voted by the students as SEM Professor of the Year in 2006, 2007, 2009, and 2010, respectively. UND ChE student Mitch Braegelmann, BSChE08/ MSChE09, was named a Tau Beta Pi Engineering Honor Society Laureate. This prestigious national award has been given to only 60 undergraduate engineering stu dents since it was started in 1982.Strong, active research programs have also become a trade mark of the department. Five faculty members have been hon for submitting patents and/or patent disclosures. The number of graduate students currently enrolled has stabilized at around 35 (34 enrolled in Fall 2009 including seven in the Engineer students are all fully supported on GRAs and GTAs. The department was awarded the Fellows of the Univer sity Award of Excellence in Research in 1973 and 2005. Dr. Michael Mann, then professor (now distinguished professor, chair, and associate dean for research), received UNDs 2006 Award for Individual Excellence in Research. Dr. Wayne Seames, then associate professor (now professor and director of ND SUNRISE) received UNDs 2007 Award for Individual Excellence in Research. Yongxin Zhao, Ph.D., Energy Engineering (advised by ChE professor Michael Mann), received UNDs 2006 Outstanding Doctoral Dissertation Award. April Hoffart (advised by ChE professor Wayne Seames) and Chris Flakker (advised by ChE professor Darrin Muggli) were awarded UNDs 2005 and 2008 Outstand ing Masters Thesis Awards, respectively.PRINCIPLES AND V ALUES as one of UNDs signature departments? UND ChEs academic excellence is due primarily to a set of principles that govern faculty selection and interaction. Preeminent among these is that the faculty must function as a team. Industry stakeholders are consistent in highlighting the ability to work in teams/groups as one of the most important tools they want chemical engi neering departments to teach their students. At UND we do not believe this is feasible unless the faculty members model this behavior. Every new faculty member comes into the depart ment with the understanding that they must function within a team environment. The keys to effective faculty teaming are collaboration, consensus, and communication. Administrators that do not know our department closely are often surprised at the consistency of voice expressed from ChE department fac ulty. This isnt because faculty do not have different opinions. It is that those differences are expressed within the group in discussions that lead to group consensus. Operating as a faculty team also has allowed us to more research laboratories and equipment are shared. Faculty do not have designated laboratories but share space as required. with purposeful mixing of students with different nationalities and different project topics. Co-advising of graduate students and collaborative proposals are the norm, not the exception. Most graduate students have two or three equally responsible faculty co-advisors overseeing their research projects. A second key principle is that outstanding teachers must have superior communications skills. So in addition to looking for faculty members that will work well in a team environ ment, faculty recruitment also focuses on oral and written communications skills and the ability of candidates to listen effectively. This emphasis on communications is passed on to our students. UND ChE is known within the university for the quality of communication preparation included in the curriculum. Students are taught that the best ideas are unlikely to be adopted if no one can understand them or if the credibility of the engineer proposing the ideas is questioned. Good oral and written communication skills cannot be taught by those that do not have this ability within themselves. It is skills if the way these concepts are communicated inhibits understanding. Some other key principles that are adopted by the entire faculty team are: The primacy of education as the departments mission. Education should not be compromised for research or service. An important element of faculty selection is the candidates passion for teaching and demonstrated competency in education. Engagement teaching methods should be maxi mized. UND ChE student Mitch Braegelmann, BSChE08/ MSChE09, was named a Tau Beta Pi Engineering Honor Society Laureate.
Vol. 44, No. 3, Summer 2010 181 Every member of the department attends the University of Buffalos Case Studies in Science workshop to learn how to incorporate case studies and problem-based learning methods into scienceoriented courses. Experiential learning is essential. Lab courses are not secondary courses in the curriculum and teach ing quality is as important in these courses as in recitation courses. All ChE lab courses are taught by faculty. All lab reports are graded by faculty. Teaching in recitation courses is weighted heavily towards engagement methods rather than lecture. Teaching objectives can be achieved across the curriculum not just within individual courses. This is made possible by teamwork and allows more objectives to be achieved in less class time. Current across-the-curriculum topics are shown in Table 4. Research projects should be student-centered. Research for research sake is not a priority in our department. Rather, we conduct research as a tool to teach students at all levels how to formulate and solve complex problems and to learn deeply in Faculty members limit travel during the academic year in order to avoid lessening the quality of education. This means that UND ChE faculty are purposely less involved in national conferences and other service activities that take them away from Grand Forks. As a consequence, the department is not as well known outside the local region as would be expected based on the level of research accomplishment achieved. Faculty mentoring is the responsibility of experienced members of the faculty. In a faculty team, peers are not seen as competi tors, they are seen as resources. Informal interactions between faculty lead to improved performance as faculty members share ideas and experiences. This is made effective by the departments teaming philosophy. Senior faculty write collaborative research of months to help them learn the process and to integrate the new member into the departments research team. Faculty share their course resources when new faculty take over a class so that new faculty have a model for how to teach effectively. Students deserve personal attention. We employ mandatory faculty advising every semes ter for every student with the same faculty advi sor for their entire program. (Students are free to request a different advisor if they are uncomfortable with their mentor.) This results in high student reten tion and minimizes graduation requirement issues. All faculty have an open door policy rather than reason, all faculty are accessible during normal business hours. We have no interest in retaining students that do not want to stay in the program for valid reasons. On the other hand, we do not want to lose students because of a poor experience in a science or math foundation course giving them the wrong impres sion about whether or not they will enjoy chemical engineering as a career. We conduct exit inter views with students who took our Fundamentals (ChE 201) class and passed with a C or better but elected not to enroll in the next technical chemical engineering class, Unit Operations (ChE 206). In the 2007-08 academic year, two students trans ferred to other programs. Our department conducts a senior exit interview. our graduating seniors rated the quality of ad visement as 4.4. Comments from these interviews are taken seriously and reviewed by all faculty at the annual retreat. Graduate programs are custom-designed for each student. For example, there are no required gradu ate classes in our ChE masters degree programs. Faculty advisors work with students to develop a program mutually acceptable to both that will best prepare students based on their objectives for obtaining an advanced degree. Core values for graduating students. every student graduating from our program should possess: The ability to work in teams, Respect for ethics and integrity chemical engineering The ability to communicate effectively Fluency in the use of statistical methods Competency in chemistry Independence and self-discipline An understanding of professional standards of quality in both technical content and personal conduct These values are built into our curriculum and reinforced through multiple learning experiences. For example, they were used to identify our acrossthe-curriculum themes that are incorporated into individual courses within the program. Experience in Applied Engineering. tion of faculty members with applied engineering experience.
Chemical Engineering Education 182 Most of our undergraduate students will go directly into industry (60-80%). Applications-oriented courses in the curriculum are best taught by those who teach what they know rather than those who teach what they learned. In general, applied engineering jobs teach certain skills more effectively than most research jobs, such as teamwork, multitasking, planning, super vising other engineers, commercialization, and communications. Many of these are skills that our stakeholders want to see us teach to our students. Applied engineering experience is equally valued to research experience within the faculty team. Students are encouraged to participate in coopera tive education assignments, internships, and/or undergraduate research. These experiential learn ing opportunities help students develop insight into what they are studying and motivation to apply themselves in their studies. Although these opportunities are voluntary, almost all UND ChE students participate in at least one of them. Teaching and research excellence are not mutually exclusive. Faculty hires must have doctoral degrees and demonstrated competency in research. Faculty are mentored in grant writing and project management to increase their effectiveness. Reasonable, but nontrivial, published tenure re quirements allow faculty the freedom to take risks and reach for excellence. Patents and nontradi tional venues for documenting research productiv ity are valued equally with peer-reviewed publica tions. For example, initiating a startup company based on faculty research is a valid productivity measure. In fact, in the current environment where universities are expected to be engines for eco nomic development, entrepreneurial activities are highly valued. Four of the current faculty are as sociated with start-up/spin-off company ventures. Faculty are considered full members of the team regardless of their contract status (tenured, tenuretrack, nontenure-track). This improves team build ing and allows faculty resources to be used most effectively.SUNRISE: THE CHEMICAL ENGINEERINGCHEMISTRY P ARTNERSHIPFaculty in ChE began collaborating on research projects with faculty in UNDs chemistry department in the 1990s. and in 2004 a decision was made to transform these smallscale collaborations into a more extensive partnership. The two departments established the Sustainable Energy Research Initiative and Supporting Education (SUNRISE) program. Seeded with around $1 million in research projects funding from existing collaborations, SUNRISE has since grown to include 33 faculty in 13 departments at both UND and North Dakotas other research university, North Dakota State University. Also participating are two faculty from North Dakota nondoctoral institutions. Working in three principle focus areasrenewable fuels and chemicals, the long-term sustainable use of coal, and harvesting energy from diverse sourcesSUNRISE has received over $32 million in research funding over the past six years. All of the UND ChE faculty are expected to maintain active to continuously support at least two graduate students. At pres ent, all ChE faculty participate in SUNRISE along with 75% of the UND Chemistry faculty. Due to the ChE departments accomplishments in research, UND agreed to add two tenuretrack faculty positions. These positions are funded during their initial three-year period with funding from the North Dakota EPSCoR program, with state-appropriated funding picking up the cost after that time. In addition, due to the level of research funding the department has received we have been able to add three nontenure-track faculty positions, one full-time and one technician, two research chemists, three research engineers, and one marketing/outreach administrative assistant. In ad dition to assisting in the research mission of the department, these extra positions allow us to increase our course offerings and improve our service to the students.A WINNING RECIPECollaboration, consensus, and communication are the cor nerstones of UNDs Department of Chemical Engineering. By continually demonstrating their commitment to teamwork, our faculty members consistently prioritize the needs of our students and the industries and universities that eventually employ them. T ABLE 4 Across-the-Curriculum Themes in UND Chemical Engineering Teamwork Sustainability Communication: writing, speaking, listening Professionalism and Integrity Environment, Health, and Safety Instrumentation and Control Independent Learning Statistical Analyses of Data Computational Tools
Vol. 44, No. 3, Summer 2010 183 For many years, one of the most important experiments in the Lehigh Undergraduate Chemical Processing Labo pressure drop through pipes of various diameters is measured which is pumped from a holding tank by a centrifugal pump. three pipes with different diameters, through another manual valve, and back to the tank. Experimental data is used to calculate friction factor vs. Reynolds number, and results are compared to literature Moody diagram  predictions. Pump characteristic curves are also generated for different motor the manual valve immediately after the pump. This means that the pipes are at a low pressure since they discharge back into the tank, which is at atmospheric pressure. In fact, under some conditions the pipes can be under vacuum because they are located at an elevation above the tank. This can lead to air being sucked into the impulse lines of the pressure gauges and can give faulty reading. To prevent this, the valve downstream of the pipes before in the pipes is only slightly lower than the pump discharge pressure of about 45 psig. Several years ago, a group of students took their data us ing the valve upstream of the pipes (low-pressure operation) and obtained some unreasonable data for pressure drops. The laboratory instructor suggested that they should have used the valve downstream of the pipes to have positive pressure in the test pipes. The response of the students was that they had to repeat all of their experiments. Of course, this is not true since liquid water is incompressible and pressure drop does not vary with pressure in the pipe. This misconception by some bright students prompted us to design and build a new experiment in which the density of very important to any engineer working with gas streams. In -GAS PRESSURE-DROP EXPERIMENTWILLIAM L. LUYBEN AND KEMAL TUZLA Lehigh University Bethlehem, PA 18015 ChE Copyright ChE Division of ASEE 2010
Chemical Engineering Education 184 tion and the hydrogen economy, the chemical engineer must be competent in dealing with gas There have been a number of papers discussing space departments use many experiments to il diverging nozzles, usually at high Mach numbers. Lam and Liu  provide a useful example of a simple laboratory set up. Forrester, et al., [3,4] dis cuss experiments in which gas discharges from a pressure vessel or is fed into a vessel. cal engineering industrial processes, we are not aware of any student laboratory experiments through pipes. DESCRIPTION OF EQUIPMENT regulator. This device holds a constant pressure at the down-stream rotameter, and this pressure can be adjusted to different levels. After passing through the rotameter, the piping consists of two a manual valve at the inlet of each line that is in service. At the discharge end of each pipe is a back-pressure regulator that is adjusted to hold different pressures in the test pipe. For example, suppose the supply pressure is 85 psig. The pressure at the rotameter could be 50 psig. The pressure at the beginning of the test pipe could be 26 psig, and pressure at the end of the pipe in service could be 25 psig due to the 1 psi pressure drop. Pressure gauges measure the total pressures at each end of test pipes, and a dif ferential pressure measurement is made between the inlet and exit of each pipe. GAS PRESSURE DROP is the effect of density on pipe pressure drop. factors and compare the experimental values to Moodys data. Since the pipe is horizontal, the measured pressure drop across the pipe is assumed to be due to frictional pressure losses only. Any effects due to small pressure changes along the pipe associated with compressibility of the gas are assumed negligible. Figure 1. Schematic of experimental test loop. Figure 2. Comparison of experimental data with Moody data for two pipe sizes.A sample comparison is presented in Figure 2. Experimental data for the roughness. There are few points that show friction factors less than a smooth tube, which is obviously due to experimental uncertainty. The apparatus permits pressure-drop data to be gathered with dif changes as pressure in the pipe changes. Pressure drop depends on kinetic energy, which is proportional to density ( ) times the square of the velocity (V 2). Higher pressure means higher gas density, but higher density decreases gas velocity. So density increases directly with line pressure, but veloc ity decreases directly with line pressure. The net effect is a linear inverse relationship between pressure drop and pressure in the pipe.
Vol. 44, No. 3, Summer 2010 185 T ABLE 1 Experimental Data and Calculated Parameters ID (inches) 0.622 Pressure at Rotameter (psig) 50 50 50 50 Gas Density at Rotameter (lb/ft 3) 0.330 0.330 0.330 0.330 Rotameter Reading (SCFM) 20.6 20.6 20.6 20.6 Pressure at Inlet of Pipe (psig) 14.5 17.0 26.0 42.8 Pressure at Outlet of Pipe (psig) 13.0 15.5 25.0 42.3 Differential Pressure (inches H 2O) 35.6 32.3 24.5 16.5 Mean Gas Density in Pipe (lb/ft 3) 0.145 0.158 0.205 0.292 Mass Flowrate (lb/min) 3.24 3.24 3.24 3.24 Velocity in Pipe (ft/sec) 176 162 125 87.7 Darcy Friction Factor 0.0170 0.0167 0.0165 0.0158 Reynolds Number 109,000 109,000 109,000 109,000 ID (inches) 0.364 Pressure at Rotameter (psig) 45 45 45 Gas Density at Rotameter (lb/ft 3) 0.306 0.306 0.306 Rotameter Reading (SCFM) 5.5 5.5 5.5 Pressure at Inlet of Pipe (psig) 40.5 32.0 21.0 Pressure at Outlet of Pipe (psig) 39.5 31.0 19.5 Differential Pressure (inches H 2O) 24.5 29.0 39.0 Mean Gas Density in Pipe (lb/ft 3) 0.279 0.235 0.178 Mass Flowrate (lb/min) 0.83 0.83 0.83 Velocity in Pipe (ft/sec) 68.7 81.4 108.0 Darcy Friction Factor 0.0235 0.0234 0.0239 Reynolds Number 47,600 47,600 47,600Students are asked to verify this relationship by carrying out several tests at similar rotameter conditions, ( i.e. different pipe pressures as tabulated in Table 1. Note that there are three gas densities involved in the calculations: density at standard condi tions, density in the pipe at pipe pressure, and density in the rotameter at rotameter pressure. From the data of Table 1, the variation of pressure drop across the pipe is plotted as a function of pressure in the test pipe and is pre the pressure drop is 24.5 inches of water when the average pressure in the pipe is 25.5 psig (arithmetic average of the inlet and outlet pres the pressure drop decreases to 16.5 inches of water when the pipe pressure is increased to Figure 3. Effect of line pressure on pressure drop at constant mass owrate.
Chemical Engineering Education 186 increases to 35.6 inches of water when the pipe pressure is decreased to 13.8 psig. Note that there is a slight curvature in the data shown in Figure 3. In theory, the relationship between pressure drop and pressure should be linear. Pressure drop in a pipe can be calculated from the friction factor f. Pf L D V 2 2 1 () where L and D are the length and diameter of the pipe, is constant in a constant-diameter pipe, the Reynolds number is constant. This means the friction factor is constant. Consider two pipes of the same diameter and length that operate with gases having different densities ( 1 and 2 ) but with the same 1 and 2) at these two conditions are Pf L D V Pf L D 1 1 1 2 2 2 2 2 2 2 2 V () Taking the ratio of the pressure drops and expressing veloc mass divided by density and pipe cross-sectional area A CS give the effect of density on pressure drop. P P f L D V f L D 1 2 1 1 2 2 2 2 2 11 2 22 2 1 1 2 V V V F A mass CS 2 2 2 2 2 1 3 F A mass CS () If the two densities are different only because of differences in pressure (same molecular weight and temperature), the ratio of the pressure drops varies inversely with pressure P. P P P P 1 2 2 1 4 () These experiments expose the students to the important ob servation that the density of the gas affects the pressure drop in the pipe. This knowledge is vital to any engineer involved can change with pressure and temperature. Very importantly, it also can change with composition. Fuel gas in a plant is a common example. The fuel gas can come from various sources (purchased natural gas or gas produced in a process, for example hydrogen or propane). Therefore the composition change. The laboratory experience provides the students with this important insight. GAS FLOW MEASUREMENT The second important concept illustrated in this experiment different than used for their calibration. This is achieved by If a turbine meter is used, which is a volumetric device, it is If the device is based on drag force (the case for a rotame ter) or on Bernoullis Principle (the case for the differential the use of the square root of the ratio of the density at actual correction factor relationship is given in Eq. (5). FF actua l mass cal mass actua l cal () 5 The F actua l mass the meter. The term F cal mass F cal vol ) times the gas density at calibration conditions. FF cal mass cal vol cal () 6 The gas densities actua l and cal are at the actual and calibra In the experiment, only gas pressure changes since the gas is air at ambient temperature. In this case, the correction factor is given in Eq. (7) in terms of pressures. FF P P actua l mass cal mass actua l cal () 7 The students in the laboratory operate the rotameter at observe that the rotameter reading is different at different pres sures because of the change in gas density with pressure. For pressure in the rotameter decreases because the lower density increases the gas velocity. The derivation of these equations for the rotameter used in the experiment is appended. Consider a numerical example. A rotameter is calibrated air at room temperature but with a pressure of 50 psig in the the rotameter.
Vol. 44, No. 3, Summer 2010 187 Assuming ideal gas behavior, the density of air (28.84 lb/lb-mole) at 70 cal f lb lb mo ll bi ni nf t 28 84 14 7 144 2 2 ./ ./ / 2 2 1545 460 70 ft lb lb mo lR R f 0 0746 8 3 ( ) lb ft FF scfm lb ft cal mass cal vol cal 20 60 0746 3 .. / 15 4 9 ./ mi n( ) lb and temperature gives Fl b l b actua l mass 15 4 14 75 0 14 7 29 7 ./ mi n ./ m mi n( ) 10 CONCLUSION This paper has described an experiment that illustrates several important numbers, which is found in many chemical engineering processes. The experi ment gives the students hands-on experience and understanding that: density. Flow measurements using a variable area rotameter or differential pressures that differ from those used for calibration. Although students are exposed to these con cepts during their classroom studies, our experi ence shows that this experiment provides very helpful reinforcement for student understanding and retention of concepts.ACKNOWLEDGMENT Initial design work of this experiment was car ried out by Lehigh ChE seniors Eric Pukszyn and Alisa Vasilenko. The authors acknowledge their meticulous work and effort.REFERENCES Trans. ASME, 66 67 (1944) 2. Lam, C.Y., and C.Y. Liu, An Experimental Facility Int. J. Eng. Ed. 15 (1), 58 (1999) 3. Forrester, S.E., and G.M. Evans, The Importance of Chem. Eng. Ed. 32 (4), 399 (1998) 4. Forrester, S.E., A.V. Nguyen, and G.M. Evans, Com Chem. Eng. Ed. 38 (3) 29 (2004) 5. Fox, R.W., A.T. McDonald, and P.J. Pritchard, Introduc tion to Fluid Mechanics 7th Ed., John Wiley& Sons (2009)APPENDIX Derivation of rotameter equa tions is summarized below. A schematic of a rotameter is shown in Figure A1. Suppose we carry out two experiments with different operating con ditions in this rotameter, and level. Furthermore assume that one of the experiments is under standard calibration conditions at which the rotameter has been calibrated, and the other condi tion is at a different pressure and temperature (actual) and perhaps a different gas with a different molecular weight. would include the drag force, FV ol g g Vo l g g A DF luid Fl oa t c Fl oa tF loat c () 1 FC A V g A DD Fl oa t Fl ui dF luid c 2 2 2 () D, consists of both pressure drag aspect ratio, however, frictional drag is negligible for a wide range of Reynolds Numbers (between 1,000 and 250,000), and therefore pressure drag dominates the C D. As a result, C D becomes a constant, independent of Reynolds Number. Combining Eqs. (A1) and (A2) gives the velocity and V gV ol CA Fl ui d Fl oa t DF loat Fl oa t Fl ui d 2 1 12 3 / () A FA VA gV ol CA Fl ui d Vo l Fl ui d Fl oa t DF loat Fl oa t 2 Fl ui d A 14 12 / () d z D FLOW Figure A1. Rotameter schematic.
Chemical Engineering Education 188where A is the annular area between the body of the rotameter tube and the float. When gases are used, the ratio of Fl oa t to Fl ui d on the right-hand side of Eq. (A4) can be neglected; FA gV ol CA Fl ui d Vo l Fl oa t DF loat Fl oa t Fl ui d 2 12 5 / () A conditions, one with density at which the rotameter has been calibrated and the other at some other actual density, the ratio F F A gV ol CA actua l Vo l cal Vo l Fl oa t DF loat Fl oa t 2 actua l Fl o A gV ol 12 2 / a at DF loat Fl oa t cal CA 12 12 6 / / () cal actua l A The term F cal vol rotameter based on its meter constant. The cal and actua l are the gas densities at standard calibration conditions and actual conditions in the rotameter, respectively. To calculate the mass F F F F actua l mass cal mass actua l Vo l cal Vo l actua l cal cal actua l 12 1 / / actua l cal actua l cal 2 2 7 () A not change, the relationship can be expressed in terms of pressures. FF P P A actua l mass cal mass actua l cal () 8 NOMENCLA TURE A CS C D F D F mass F vol density
Vol. 44, No. 3, Summer 2010 189 It is widely touted that the use of research ideas can create excitement for learning in the classroom. [5-9] This paper de scribes the development of a research-inspired Analytical Microdevice Technology (AMT) course for undergraduates and graduate students at Mississippi State University. Mi croscale research is a challenging area within which to do this because microscopes are required to observe most phenomena in microdevices. The approaches used in this course were designed to overcome the challenges with directly observ demonstrating the powerful nature of this area of engineering. The primary course goal was to get the students familiar with small-scale technology with a focus on biomedical diagnostic applications. The course covered both theoretical and experi mental advances in the realm of chemical, mechanical, opti cal, and biological analysis. This was accomplished through four activities throughout the semester (15 weeks, MWF class): a lecture, a Survivor game,  discussions of technical articles,[2, 3] and a concept development project.  Mondays were dedicated lecture days (15 total contact sessions) where the professor came with a structured set of material, in-class activities, videos, etc., to provide a foundation of knowledge for the students. Wednesdays were dedicated to a Survivor game modeled after J. Newells 2005 article.  This interac tive game had student teams solving knowledge, calculation, concept, and design problems during class. Teams with incor rect answers lost members via a voting mechanism. Fridays were comprised of student presentations and discussions of technical articles and current news articles on Analytical Microdevice Technology. The fourth activity was a semesterlong, open-ended concept development project completed in teams outside of class. These concept development projects included progress reports every two weeks; the intermittent reports built to a fully developed journal-style article outlin ing a microtechnology concept well-grounded in the research literature and featuring a novel approach or device for a bio logical analysis. This paper describes the course content and with results of student assessment of the four learning tools which have been cross-correlated with the students preferred Felder-Silverman Learning Style. [10,11]CREA TIVE LEARNING IN A MICRODEVICE RESEARCH-INSPIRED ELECTIVE COURSE ADRIENNE R. MINERICK Michigan Technical University Houghton, MI 49931 Work conducted at: 323 Presidents Circle, Dave C. Swalm School of Chemical Engineering, Mississippi State University, Mississippi State, MS, 39762. Author can be contacted at: 1400 Townsend Drive, Department of Chemical Engineering, Michigan Technological University, Houghton, MI, 49931; Phone: 906-487-2796, Email: firstname.lastname@example.org Copyright ChE Division of ASEE 2010 ChE AIChE special section
Chemical Engineering Education 190 Electrokinetics and Quantitative Analysis in Microdevices is an active area of research for the author and the development of this course was supported by an NSF CAREER Award. The course counts as a chemical engineering elective in MSUs curriculum, but was widely advertised as open to all majors and even enrolled a biochemistry graduate student. A studentscompleted the course. Course content covered both theoretical and experimental advances from the perspective of understanding the fundamental forces dominating at the microdevice applications that harnessed those forces for a biomedical diagnostic application. Course content is given in Table 1 with the reference texts listed by author. [12-21]Course objectives were structured to provide undergradu ate and graduate students with preliminary research skills as well as a solid background and an enthusiasm for analytical microdevice technology. Surveys of news and corresponding technical articles were intended to empower students with familiarity, skills, and knowledge to envision microdevice applications and apply this in research or in future job pursuits. Upon completion of the course, the students were to demon Review of micro / nano technology news and critique of corresponding technical publications Fundamental understanding of micro/nano forces Materials and methods for microdevice fabrication Contextualization of existing and future detection tools Concept plan of a fully integrated device The four main learning activities during the semesterlec tures, Survivor game, article presentations, and a large concept development projectwere drawn from various sources. The lecture content was largely governed by the content given in Table 1. Questions for the game were pulled from each of the other three activities. For article presentations, students were encouraged to actively read the literature as a learning tool and as a supplement to information provided in microfabrication facilities (photolithography, electroplating, and epitaxy) at SemiSouth, Inc., a start-up company from Mississippi State University. The second tour was of MSUs Life Sciences Biotech Institute, a multi-user genomics and ing devices. Lastly, the students were arranged into four teams each having a graduate student leader, and each team worked together to develop a concept project, which culminated in a viable draft of a journal article. Each of these activities is discussed in the following sections of this paper. In addition, the course topic of linear electrokinetics is described under each activity to demonstrate how course content was related between the activities. ACTIVITY 1: LECTURES Lectures were held each Monday in order to provide the students a well-organized foundation in the physics of ma terials at the microand nanoscales as well as fundamental knowledge of the optical and electronic tools utilized in microdevices. The topics covered are outlined in Table 1. Lectures were of traditional format with content written on a whiteboard in a sequential fashion. Calculation exercises, videos, and short class activities were interwoven into the lecture. Due to the open atmosphere of the classroom (likely facilitated by the other class activities), students regularly asked questions and began discussions to understand why ometries. When topics related to biochemistry or biology were included in the lecture, a biochemistry graduate student would frequently add insight and instruction beyond what the professor presented. It was an excellent learning opportunity for the students and professor alike. For example, linear electrokinetics included coverage of previously learned charge interactions and particle behaviors in Section 1 of the course. The introduction included applica (uniform, non-uniform) as well as energy considerations (Direct Current, Alternating Current). The linear electroki T ABLE 1 AMT Course Topics 1. Intermolecular and Surface Forces, Israelachvili, Probstein [12,13] Intermolecular interactions Interparticle forces Polar (izable) molecules Electrostatic forces 2. Microdevice Designs & Considerations, Literature, Rathore  Shape & materials Fabrication techniques & lab tour Sample injection / mixing 3. Pressure Driven Flow (micron length scales), Bird, Fournier, Truskey, Literature [15-17] COMSOL Mulitphysics DEMo 4. Linear Electrokinetics, Rathore, Li [14,18] Electrophoresis Lab tour: Life Science Biotechnology Institute 5. Nonlinear Electrokinetics, Morgan, Delgado Literature [19,20] Dielectrophoresis Magnetophoresis Traveling wave DEP Webster 
Vol. 44, No. 3, Summer 2010 191 netics discussion was limited to uniform geometry and DC and electroendoosmosis were covered as shown in cartoon in Figure 1. The apparent electrokinetic velocity observed in a microchannel is a combination of the electrophoretic (EP) velocity and the electroosmotic (EO) velocity as follows: VV V EK EP EO () 1 where the particles electrophoretic velocity is given by: v qE r EP () 2 v E EO () 3 One concept that is important to keep straight is the difference between mobility and velocity. They are related as v E () 4 The variables used in these equations are v as the velocity, Lectures were interactive in the form that in-class activities were also interspersed throughout the instructor-dominated discussions. Activities and discussions were frequent sources of questions for Survivor the following class period. ACT IVI T Y 2: M I C RO-T EC HNOLOGY S URVIVORA game of Survivor: Classroom was conducted each week and based upon J. Newells adaptation of this popular TV show in his Mass and Energy Balances class.  This game served as means for the students to apply the information learned in the lecture and as such replaced a homework component of the class. Three types of questions were asked during the game that roughly corresponded to the levels of Blooms Taxonomy.  Level 1 questions primarily queried knowledge and understanding of concepts; these were tions ranged from plug-and-chug calculations (equations not provided, students could use notes) to more involved quantita of Blooms Taxonomy. Level 3 questions typically were a team effort and involved the novel design of microdevices that capitalized upon the phenomena of interest to achieve mixing, reaction, separation, or other micro-unit operations. of cognitive development. Two surveys were conducted during the semester to gauge primarily for students to provide feedback on questions and logistics of conducting the game in class. The second was conducted halfway through the semester. In both surveys, the students were asked to respond to an open essay question and two questions on a 5-point Lickert scale from Strongly Agree down to Strongly Disagree. The responses are compiled in Table 2 and demonstrate positive student feedback to the game. Interestingly, the students recognized that the fun factor was a little greater than the learning factor. There was a slight increase by mid-semester in the number of students who felt they were learning from the Survivor game. tions were made to the rules of the game. Original rules are available in J. Newells article ; AMT class rules differed in the following ways: The tribe with fewer members was immune from losing a Students who were eliminated in any round joined the Peanut Gallery. They were given the task of designing and solving one problem per gaming session with the intention that it might be used in later rounds. Peanut Gallery students could also continue to compete independently. If they won a round, they could choose to join any team (and earn points). The team they joined then earned immunity from loss of a member for that round. T ABLE 2 Student Assessment of Survivor Game Merits Q1: I learn a great deal from the Survivor Problems. Q2: I had fun playing Survivor in class. Begin Middle Begin Middle Strongly Agree 4 6 10 9 Agree 8 6 3 4 Neutral 2 2 1 1 Disagree Strongly Disagree Figure 1. In uniform, linear DC electric elds, particles will move due to a combination of the electrophoretic forces acting on the particle as well as the electroendoosmotic forces inducing ow of the liquid. This diagram demonstrates the relative mobilities of highly charged small particles down to lowly charged large particles.
Chemical Engineering Education 192 The ability of members of the Peanut Gallery to answer questions independently helped immensely by keeping those students engaged in the game and learning. Linear electrokinetics concepts were reinforced during the Survivor game. For this particular topic, level 1 knowledge ques tions were: 1. Rank order the mobility of the following particles from slowest to fastest. A. Large, highly charged analyte, B. Small, highly charged analyte, C. Large, barely charged analyte, ANSWER: C,D,A,B Level 2 questions included the following: 1. What is the electrophoretic mobility of an analyte with a net positive charge of 2 and an effective radius of 50 nm in an aqueous solution? ANSWER: Note that 1 Crulomb is equal to the charge of 6.24 10 18 protons. EP q r C nm cp kg m 2 62 41 0 50 1 32 11 0 18 19 .* .* 2 2 2 9 3 9 2 50 1 10 11 0 64 10 Vs nm m nm kg ms m s .* V V () 5 ANSWER: No, the mobility is a property solely of the analyte and characterizes the analytes ability to move in an faster. One level 3 question was asked of the teams. While the level 3 problems were the most time intensive and hardest for which to judge team winners, the students who excelled on these questions were not usually the students who answered the level 1 questions that tended to be speed dependent. Also, it was interesting that all questions obtained from Peanut Gallery members for subsequent Survivor games were predominantly level 1 questions with a few level 2 questions and no level 3 questions. ACT IVI T Y 3: CURR E N T NE WS AN D A R C HIVAL JOURNAL ARTICLE DISCUSSIONS This section of the class was modeled after the authors research groups weekly literature discussion class termed Journal  Article discussions were intended to be a practice forum where one student would lead the class in a discussion of an article of his/her choosing. Undergraduate students were allowed to pull from popular news. Graduate students, however, could scan the science/technology news, but had to secure the archival journal article and present from that. When the student provided the article in advance, it was posted on MyCourses, an online proprietary virtual Blackboard Learning System.  No incentive or monitoring occurred to see if the other students read the articles in advance, however. The professor did keep track of questions asked and who participated in the discussion in order to give participation points, but strove to not control the progression of the discussion. Given the number of students in class, each student presented approximately once every three weeks. The students were told standing. As a result, emphasis was placed on the clarity, organization, and understandability of the students presentation. It was strongly encouraged to present at the level of the audience such that an involved discussion could develop from the article.
Vol. 44, No. 3, Summer 2010 193 Students were allowed to use any method of delivery they preferred. Most students utilized the document camera to Some students prepared handouts to overcome the awkward maneuvering of the document camera and one student put presentations into PowerPoint. An example of a linear electrokinetic article discussed was that by Amy Herr, Electroosmotic Capillary Flow with NonAnalytical Chemistry in 2001.  The student presenting enjoyed discussing the chargeACTIVITY 4: SEMESTER CONCEPT DEVELOPMENT PROJECT The skills that best serve graduates of engineering programs are not all learned from textbooks. Tangible skills that are harder to teach, but are essential to prepare students to be productive, technical, members of society, include problemtraditional classroom does not focus on these skills nor does it usually provide individual practice linking unique concepts together. This semester-long concept development project was a concerted effort to strategically develop these skills in the students enrolled in this course. This activity strove to push students to the highest level of learning in Blooms Taxonomy.  This activity, above all others, demonstrated student mastery of material. The assignment for the project teams was a large, open-ended, concept development project. The students were integrally in volved in deciding the small-scale technology that they wanted to pursue that would help address an important biomedical ap plication using either microor nanotechnologies. The concept was to build from both theoretical and experimental reported technologies in the realm of chemical, mechanical, optical, and biological analysis. Their resulting virtual microtechnology was to be a novel extension of published work. Upon completion of the project, each team member was expected to be able to conduct an extended discussion of the following topics and skills related to their project: Review of pertinent technology from peer-reviewed publi cations Microand nanoscale forces acting within their micro / nano device Materials and methods utilized in their conceptual device (and why chosen) Why and how their project was novel from existing detec tion tools The output of the effort was to be a concept plan of a fully integrated biomedical technology. The concept was to be articulated in an archival journal paper and presented via a team oral presentation. Progress reports were due throughout the semester and were designed to sequentially formulate the a) description of proposed novel analytical microtechnology, the proposed analytical microtechnology (> 10 references, fully discussed), c) prototype drawing and accompanying archival journal article. The professor provided feedback us ing a structured assessment template after each report. The The projects included: 1. Ricin Dosimetry via Lab-on-a-Chip Antibody-Mediated Detection by Daniel Barnes (Grad), Jennifer McCo ntrell (UG), Parisa Toghiani (UG), and David Quick (UG). Castor oil from the castor plant is an economi cally important, international commodity. The castor seed contains around 50% oil by weight but grinding the seed releases an extremely toxic protein, ricin. Ricin described in this paper is designed to detect airborne ricin particles and alert the wearer to the accumulation of dangerous levels in the atmosphere over the course of a 4-hour shift. 2. Carbon Nanotubes as a Drug Delivery System by Kae la Leonard (Grad), Miranda Smith (UG), Jason Strunk (UG), and Roberto Velasquez (UG). Osteosarcoma, bone cancer, is a rare form of cancer that attacks the bone tis delivery occurred directly to the affected area, and if the delivery system could be functionalized to attack only cancerous cells. By utilizing carbon nanotube technol ogy, this paper outlines a plausible system, based upon existing advances reported in the literature, which would effectively deliver the chemotherapeutic drug while simultaneously providing structural reinforcement to the bone tissue remaining after surgery. Carbon nanotubes will be preloaded with micelles containing the anticancer drug cisplatin, which will then be released upon implan tation in the bone, (and directed to any remaining cancer cells via folate functional groups on the micelles outer surface). 3. An Electric Field Gradient Focusing Method for Fluorescent Detection of Immunological Reactions by Aytug Gencoglu (Grad), Eric Rutan (UG), and Zach Wynne (UG). A conceptual design is proposed for a novel microdevice that would be used for the investiga tion of immunological reactions between proteins found presented. The operation of the proposed microdevice would be the separation of different proteins from a
Chemical Engineering Education 194 would be formed within a square channel by the use of electrodes with varying potentials along the length of the channel. Control dyes would be used to determine the be the contacting of the focused protein bands with the time required for the design of new drugs or vaccines, and could also be adapted to be used as a novel allergy testing technique. 4. Detection of Metastatic Breast Cancer: Prototype of a Rupturing Microdevice by Sheena Reeves (Grad), Sou mya S. Keshavamurthy (Grad), and Lekeith Terrell (UG). Earlier detection is recommended for preventing the spread of the disease especially for individuals who have had cancer previously. There have been many detection methods developed and explored by researchers over the past years; however, these methods are painful, intrusive, and time consuming for the patient. In this work, blood testing will be explored as a possible method for early detection of metastatic breast cancer. Cancerous cells are softer than the normal healthy cells as demonstrated by researchers. CTCs are found in the bloodstream and are obtainable for testing. Here, rupture rate of normal and cancerous cells will be used as a measure of detection. A device capable of rupturing the cells has been designed in order to quantify the rupture rate. A lab-on-a-chip system will be developed for faster and rapid diagnosis crodevice makes use of a channel, electrodes, an electric at a slower rate compared to cancerous cells since they are much harder than cancerous cells. The topic ideas were brainstormed and developed by the students with guidance from the in structor. In the following section, the assessment of each of these activities is discussed. ASSESSMENTStudents preferences for each class activity were assessed via a short sur 11-question, instructor-derived survey and the 44-item Soloman-Felder questionnaire  were ap proved by MSUs Institutional Review Board (IRB) for the protection of human subjects; the 13 students present in class all signed the consent forms giving permission for their data to be included. The survey was designed to test the hypothesis that the class activity that each student most preferred was The premise was that everyone has learning-style pref erences[10, 25] that can be measured on a sliding scale be tween two extremes in four stages of learning: processing, perception, input modality, and understanding.  During processing, students favor either active (ACT) or (REF) learning by introspectively thinking about material. In perception, sensing (SEN) learners focus on external input while intuitive (INT) learners focus on internal contemplation. Input modality preferences scale between visual (VIS) and verbal (VRB) Lastly, learners can achieve understanding in sequential (SEQ) linear logical steps or globally (GLO) where information is pieced together into a big picture. To test this hypothesis, students were directed to the Soloman-Felder online learning styles inventory and asked to complete the 44 questions.  They then self-reported their scores on the written instructor-derived survey and proceeded to answer the remaining 11 survey questions. In Figures 2 through 4, which incorporate the students learning style, T ABLE 3 Student Self-Rated Learning in Each of Four Class Activities Lecture Survivor Articles Project Average 7.7 6.5 8.2 8.5 Standard Deviation 1.5 1.3 1.5 1.3 Figure 2. Learning style prefer ences for each student who com pleted the survey. Negative values indicate a preference towards the rst of the two modalities. Nonweighted averages are provided in the legend labels.
Vol. 44, No. 3, Summer 2010 195 Figure 4. Student ratings of learning value of the four class activities (Lecture, Survi vor, Article Discussions, Concept Design Project) cross-correlated with their ActiveReective (ACT/REF) learning style preference. This trend is presented in line 1 of Table 4 using the normalized covariance. Figure 3. Composite (additive) learning style correlated with preference towards class activities.the four stages of learning are reported as ACT/REF with a negative number indicating preference towards active learning tive learning. The same nomenclature is used for SEN/INT, VIS/VRB, and SEQ/GLO. Overall student-learning preferences are included in Figure of 2.4, slightly sensory (SEN) with an average of -0.7, more visual (VIS) than verbal (VRB) with an average preference of -1.8, and equally balanced between sequential (SEQ) and global (GLO). The SEQ/GLO aver age is slightly misleading as eight of the 13 students were sequential learners, but did not show as great a preference in this direction. Given that global learners historically have not been known to gravitate into engineering, this is an interest ing distribution of students in this course. The first question asked stu dents to rank their most favorite to least favorite learning activity in this class. The activities were: lecture, Survivor game, article discussions, and concept design project. The most popular activity was the article discussions, which is interesting because this was the activity that students demonstrated the most apprehension over when the concept was introduced. While some students voiced dread over their turn to present, the remaining students became more engaged in the discussions as the semester pro gressed. Figure 3 cross-correlates the students preferred class activity with their composite learning style (style preference is summative). The stronger active learners were skewed toward Survivor as the preferred learners preferred the article discus sions. Overall, sensory learners preferred article discussions while intuitive learners preferred Survivor. The stronger visual learners had a slight preference for Survivor over article discussions. Overall, global learners preferred article discussions while sequential learners preferred Survivor. One individual chose lectures as the favorite class activity and their strongest preference was toward sequential. Lectures tended to be quite sequential in concept progression, while the article topics were undirected due to students freedom of choice to obtain an article. In addition, the Survivor game questions were purposefully randomized. Students were also asked to score how much they learned during each activity on a scale from 1 to 10 with 10 being demonstrated in Table 3, the students felt they learned the
Chemical Engineering Education 196 most from their concept development project followed by their favorite activityarticle discussions. The students learned the least from the Survivor game, but it should be noted that the average score here is still greater than neutral (5). This critique of their own learning was cross-correlated with their learning style and is shown in Figure 4. Trend lines using a least squares method are added to guide the eye for an overall tendency. As shown, active learners felt they learned more from the project, article, and lecture learned more from Survivor than the active learners, which is surprising given the learning mechanism this modality sug gests. In all cases, all types of learners rated Survivor lowest as a learning tool. Such trends can also be captured using a cross-correlation scheme such as the normalized covariance in a more concise three learning styles and the data is in Table 4: sensory/intui tive (row 2), visual/verbal (row 3), and sequential/global (row 4). Students learning style, l, was correlated with their course activity preferences, a, as follows: C ll aa ll aa la () 2 2 6 where l and a denote average learning-style preference and activity preference, respectively. This linear correlation provides an indicator normalized between -1 where the two data sets demonstrate a perfectly linear negative correlation, 0 where the data sets are uncorrelated, to +1 where the two data sets demonstrate a perfectly linear positive correlation. The results are presented in Table 4. Learning style vs. activity correlations are not particularly strong and given the population size (13 respondents), the numbers could have been skewed by the response of an in dividual or two. Negative correlations in this case indicate a modality, while positive correlation numbers indicate a pref erence towards the second dimension. For example, intuitive learners and sequential learners equally liked the projects. Other notable trends include that visual learners felt they learned more than verbal learners from the lectures. Students were also asked if there was a particular combi nation of learning activities that was instrumental in helping them learn. The two most common combinations mentioned were lecture / Survivor (by 4 of 13) and article / project (by 4 of 13). This result is not surprising given that lecture served to provide a foundation and the Survivor game was a mechanism for students to practice applying this knowledge. Similarly, use their article presentation to read and present on articles of use to their team concept design project. Newells Survivor paper  discussed a model where stu dents had four primary types of motivation. The original work describing this was Biggs and Moore in 1993.  They summarized the four types as: Intrinsic learning because of natural curiosity or interest in the activity itself; Social learning to please the professor or peers; Achievement learning to enhance position relative to others; and Instru mental learning to gain rewards beyond the activity itself (better grades, increased likelihood of getting a high-paying these four motivators on a scale from 1 to 10 with 10 being cally motivated (8.8 2), fairly neutrally socially motivated (5.0 2.2), a little more strongly motivated by achievement (6.5 1.9), and even more strongly instrumentally motivated (7.8 1.5). It should be noted that by directly asking students to rate their motivation, the results might be biased to higher numbers because of the tendency to consciously or subcon sciously rate higher. Students motivation, m, was correlated with their prefer ences for each course activity, a, using the normalized covari ance as follows: C aa mm aa mm am () 2 2 7 where a and m denote average of each activity and motiva tion, respectively. The results are presented in Table 5. Intrinsically motivated students equally preferred Survi vor and the concept development project. This preference is similar in instrumentally motivated students. Intrinsically motivated students, however, showed a slight preference for the article discussions with no correlation for the lectures while the instrumentally motivated students were the opposite. Most students felt they were not strongly motivated by social factors, which is likely the reason that negative correlations were observed for these against Survivor, article discussions, and the projects. The most surprising dimension of this is the negative correlation between socialand achievement-based motivations and Survivor, which suggests that those with a higher desire to please others and those who want to advance relative to others disliked Survivor. While the Survivor game T ABLE 4 Correlation of Students Learning Style (l) With Preferred Class Activity (a)l \ a Lecture Survivor Article Project ACT/REF -0.29 0.32 -0.32 -0.42 SEN/INT 0.01 -0.14 0.17 0.23 VIS/VRB -0.41 -0.27 -0.14 0.16 SEQ/GLO -0.11 -0.10 0.08 -0.22
Vol. 44, No. 3, Summer 2010 197 provides immediate feedback from the professor and peers, it also tends to favor extroverted individuals (personal observa tion) and extroversion/introversion is likely not correlated with a desire to please others. SUMMARYA research-focused special topics course on Analytical Mi 2008 with four different class-learning activities. The activi ties were lectures, a Survivor game, article discussions, and a concept development project conducted in teams. While the students showed a strong preference towards the article dis cussions, most felt they learned the most from the projects. Correlations with student learning styles were compiled and demonstrated that while students have a preference for certain activities, learning is possible with all activities as demonstrated by quantitative learning rankings greater than neutral. Overall, the students rated themselves as intrinsically and instrumentally motivated. Grades were de-emphasized in this course, yet student participation by all except one student was greater than the professor has seen in core chemical engineering courses she has taught. The population size was rather small (13 completed the surveys), yet interesting trends suggest learning merits in each of the four class activities. Any individual interested in implementing these strategies or who would like course preparation materials may contact implementations of this course by increasing time dedicated to those activities that most promote student learning. In order, they are projects,  articles, [2,3] and lecture. While the Survi vor game was not rated as high in terms of learning merit, it was still rated higher than average (6.5 on a 10-point scale) and should remain included to complement the lectures and to introduce an element of fun into the course. In general, the inclusion of diverse learning tools into a single course students of all learning styles. ACKNOWLEDGMENTSThe author would like to acknowledge funding support from the National Science Foundation (CBET 0644538) as well as the hard work and enthusiasm of the students enrolled in this course. REFERENCES 1. Newell, J.A., Survivor: Classroom. A Method of Active Learning That Chem. Eng. Ed. 39 (3), 228 (2005) 2. Minerick, A.R., Journal Club: A Forum to Encourage Graduate and New Engineering Educators Division American Society of Engineer ing Education Proceedings (June 2006) 3. Hill, P.J., Teaching Entering Graduate Students the Role of Journal Chem. Eng. Ed. 40 (4), 228 (2006) 4. Minerick, A.R., and G.T. Thibaudeau, Use of Concept Development Engineering Education Southeast Section Proceedings (April 2009) 5. Maase, E.L., and K.A. High, Active Problem Solving and Applied Chem. Eng. Educ. 42 (1), 23 (2008) 6. Harrison, R.G., M.U. Nollert, D.W. Schmidtke, and V.I. Sikavitsas, The Research Proposal in Biomechanical and Biological Engineering Chem. Eng. Ed. 40 (4), 228 (2006) Chem. Eng. Ed. 38 (2), 94 (2004) 8. Lipscomb, G.G., A Compendium of Open-Ended Membrane Problems Chem. Eng. Ed. 37 (1), 46 (2003) 9. Newell, J.A., S.H. Farrell, R.P. Hesketh, and C.S. Slater, Introducing Emerging Technologies into the Curriculum Through a Multidisci Chem. Eng. Ed. 35 (4), 296 (2002) 10. Felder, R.M., and L.K. Silverman, Engr. Education 78 (7) 674 (1988) 11. Soloman, B.A., and R.M. Felder, Soloman-Felder Learning Styles html> Accessed Sept. 22, 2008 12. Israelachvili, J., Intermolecular and Surface Forces: Second Edition Academic Press, San Diego (1992) 13. Probstein, R.F., Physicochemical Hydrodynamics: An Introduction 2nd Ed., Wiley-Interscience Publication, New York (1994) 14. Rathore, A.S., and A. Guttman, Electrokinetic Phenomena Marcel Dekker, New York (2004) 15. Bird, R.B., W.E. Stewart, and E.N. Lightfoot, Transport Phenomena 2nd Ed., Wiley, New York (2002) 16. Fournier, R.L., Basic Transport Phenomena in Biomedical Engineering Taylor & Francis, Philiadelphia (1999) 17. Truskey, G.A., F. Yuan, and D.F. Katz, Transport Phenomena in Biological Systems Pearson Prentice Hall, Upper Saddle River, NJ (2004) 18. Li, D., Technology V. 2 Elsevier, Amsterdam (2004) 19. Morgan, H., and N.G. Green, AC Electrokinetics: Colloids and Nanoparticles in Microtechnologies and Microsystems Series Research Studies Press, Baldock (2003) 20. Delgado, A.V., Interfacial Electrokinetics and Electrophoresis in Surfactant Science Series V. 106 Marcel Dekker, New York (2002) 21. Webster, J.G., Bioinstrumentation John Wiley & Sons (2004) 22. Krathwohl, D.R., B.S. Bloom, and B.B. Masia, Taxonomy of Educa II: Affective Domain New York: David McKay Co., Inc. (1973) 23. Blackboard Learning Systems,< http://www.blackboard.com/>, Accessed Nov. 5, 2009 24. Herr, A.H., J.I. Molho, J.G. Santiago, M.G. Mungal, T.W. Kenny, and M.G. Garguilo, Electroosmotic Capillary Flow Analytical Chemistry 72 (5) 1053 (2001) ASEE Prism 6 (4) 18 (1996) 26. National Effective Teaching Institute (NETI), in cooperation with American Society of Engineering Education,
Chemical Engineering Education 198 Course projects are an effective way to focus students attention  as students learn best when they become actively involved in solving problems.  Properly cho sen projects can serve to prepare engineering undergraduates for industrial settings where specialized process simulators ( e.g. Aspen Plus, CHEMCAD, HYSIM, and PROSIM) are used extensively. [3-6] Steady-state process simulators in separa tions and/or design courses are already used in most chemi cal engineering departments.[7, 8] Recently, programs such as Aspen Chromatography allow students to model and solve liquid-phase ion exchange systems that are often operated as unsteady-state processes. Commercial simulators model these sorption processes through the solution of partial differential equations governing heat and mass transfer and algebraic equations describing equilibrium and pressure drop.  biotechnology and bioprocessing where they are confronted ies represent a large percentage of new biopharmaceuticals and those currently in clinical trials. This important class of proteins often requires several downstream processing steps exchange chromatography followed by hydrophobic interac tion chromatography (or cation exchange chromatography),  reduce operating costs. The recent use of weak partitioning chromatography (WPC) in the downstream processing of antibodies by Wyeth BioPharma [10-12] In that process, WPC is employed to purify monoclonal antibodies in anion exchange systems as part of a two-column separa tion platform (with Protein A chromatography) as compared to traditional three-column separation platforms. WPC is an isocratic chromatographic protein separation method performed under mobile phase conditions where the product A CASE STUDY IN WEAK P ARTITIONING CHROMA T OGRAPHY ChE STEVEN T. EVANS, 1 XINQUN HUANG, 2 AND STEVEN M. CRAMER 1 1 Rensselaer Polytechnic Institute Troy, NY 12180 2 Covidien St Louis, MO, 63132 Copyright ChE Division of ASEE 2010
Vol. 44, No. 3, Summer 2010 199 operations  where no binding of the product protein occurs.  In addition, product losses are reduced by loading larger amounts of product. Finally, a short wash step can also be employed to attain even higher purity and resin capacity using WPC. In this paper we describe a project that was used in an ad vanced chromatographic separations course (15 weeks long, offered every Spring term) taught to senior undergraduate students and graduate students for the past three years. The biotechnology-related separations challenge was derived from the WPC work presented by S. Vunnum  at the 2006 national American Chemical Society conference and recently published in several papers. [11-16] Many of the details of using the commercial simulator employed (Aspen Chromatogra phy) and teaching courses with simulators integrated into lectures have been reported previously.[3, 8] The course project described in this paper was designed to instruct the students in basic simulator operation and to enable them to apply course material to an important separation challenge from the biotechnology industry. 2. THE PROJECT 2.1 Learning Objectives: tives  for this project were as follows: At the end of this project students should be able to 1) gener plots, 2) use a simulation tool for chromatographic modeling, 3) explain the subtleties of a novel mode of chromatography (WPC) through varying calculations and simulations, 4) il for directing experiments, and 5) apply their chromatographic simulation and optimization experience to modeling other separation processes. 2.2 Project Goal: The students were instructed that their goal was to optimize the product yield (recovery) associated with the anion exchange step while satisfying several constraints. The feed mixture for this system consisted of a therapeutic monoclonal antibody (product) and two compounds representing typical impurities in these biological mixtures ( e.g. nucleic acids, endotoxins, viruses, or host cell proteins). These impurities are in general more strongly bound than the product of interest under anion exchange chromatographic conditions.[12, 18, 19] The process must result in a product yield greater than 90% while satisfying a 95% purity constraint. Further, the process must maximize the production less than eight hours (typical work shift). 2.3 Overview: This project is based on a recent publication describing the WPC process.  Students were introduced to key WPC concepts, provided with batch adsorption data, instructed to plot adsorption isotherms, and then required to column simulations (varying feed loading volume and salt counter-ion concentration). Students were then charged with the open-ended task of optimizing this separation through simulations varying parameters of their choosing (factorial simulation). 2.4 Introducing Students to the Problem: The students were given extensive equilibrium adsorption data for the prod uct and the impurities at three different salt concentrations, some of which are shown in Figure 1 as symbols. They were isotherm with counter-ion dependence [Eq. (1)]. This isotherm is readily available in Aspen Chromatography and was chosen for its ability to represent nonlinear chromatographic behavior at different salt concentrations. Q IP IP cI P IP c i i bi i 1 1 2 3 4 ex p e xp b bi i k k kb nc IP C IP IP 5 3 1 1e xp 4 4 5 1 k bk k cI P C () In this isotherm equation Q i is the amount of solute i bound to the stationary phase and C i is the amount of solute i in the by IP 1i through IP 5i for each solute i, c b is the salt counter-ion Figure 1. Adsorption isotherms for the prod uct ( ), impurity 1 ( ), and impurity 2 ( ). Isotherms are given for varying NaCl concen trations of 190 (dotted lines), 200 (dashed lines) and 225 mM (solid lines).
Chemical Engineering Education 200 concentration in the mobile phase, and C k in the denominator summation is the mobile phase solute concentration for all solutes (except the salt counter-ion, b). Once the isotherm plots were generated and the isotherm pa rameters of the product and the two impurities were obtained, the students were then instructed to determine the effect of varying salt concentration (counter-ion, c b) upon these iso therms. Adsorption isotherms for counter-ion concentrations of 190 (dotted lines), 200 (dashed lines) and 225 mM (solid lines) are shown in Figure 1. The diamonds represent the product, the circles represent impurity 1, and the squares rep resent impurity 2. The students were asked to comment upon of each solute changes with the salt concentration, and what their initial thoughts on possible separation strategies might be. Additionally the students were asked to comment on the salt concentration at which the isotherms of all of the solutes begin to overlap corresponding to conditions that would make For the data given in this problem a salt concentration of typical student work. Chromatography: The generation of partition or distribution phase (Q) to that in the mobile phase (C) as the concentration in the mobile phase approaches zero (corresponding to the linear regime of the isotherm). The calculation of partition K Q C P C 0 2 () p vs. C salt  A representative student-generated plot is shown in Figure 2 for the product and most highly retained impurity (note: in this plot the salt concentration ranged from 150 to 300 mM). To help the students interpret this plot they were informed that protein ion exchange separations are typically operated bind-elute separations the product K p is high under the column tions the product K p is low (usually <0.1). WPC separations p values for WPC range from 0.1 to 20. and WPC) has distinct advantages and disadvantages. The choice of chromatographic operation depends upon the solutes in a particular system. Students were instructed to comment both high and low counter-ion salt concentrations. They were also asked to rate the potential utility of these three separa tion modes for this particular feed mixture. This enabled the students to learn about the behavior of WPC as compared learning objective 3. 2.6 Preliminary Project Student Reports: Prior to em ploying Aspen Chromatography the students were required to write preliminary reports that included the following: plotted written responses to the various fundamental and applied questions mentioned above. These reports should have a de tailed discussion of the isotherm and include the following observations: i) the product is always the least strongly bound component of the feed mixture under all salt conditions, ii) as the salt concentration was increased, the relative decrease in the amount of product bound was less than that ob served for the impurities, iii) superior separations may be possible at higher Figure 2. A representative parti tion coefcient plot  of log K p ver sus log C salt for the product ( ) and the most highly retained species, impurity 2 ( ) for NaCl concentra tions ranging from 150 to 300 mM.
Vol. 44, No. 3, Summer 2010 201 chromatography may result in improved ion exchange chro matographic processes. These exercises served to meet the Isotherm parameters (Table 1) were then given to students to compare with their obtained values and for use in Aspen Chromatography. Data and insight gathered were then used in the Aspen Chromatography simulation platform for optimizing this anion exchange separation. From this point forward, each student was told to use the isotherm parameters provided by the instructor (note: the use of inappropriate isotherm parameters could result in simulator non-convergence since isotherms ). Students were then introduced to the commercial simulator through a hands-on computer laboratory lecture. Example problems were reviewed with the students under the guidance of the instructor. In this classroom environment the instructor was able to visit with each student and address the individual questions raised. 3. ASPEN CHROMA T OGRAPHY 3.1 Process Flowsheet: The Aspen Chromatography software was used to generate a model using the isotherm parameters and column properties given below along with appropriate Solver Properties (note: representative solver properties are given in the appendix for those unfamiliar with Aspen). While the com mercial simulator has been described in detail elsewhere[3, 8] it The Templates and Demonstrations given in the Aspen software package are useful for gaining familiarity with the problems already stored within the Aspen chromatography sheet. After runnings the simulation, results can be viewed by get acquainted with the simulation platform and are easily adapted to a range of other separation problems. responding models (Figure 3) they were also instructed on how to use the Cycle Organizer. By clicking on appropriate T ABLE 1 Extended Langmuir With Counter-Ion Dependence Isotherm ParametersIsotherm Parameters Product Impurity 1 Impurity 2 1 33.87 66.09 70.55 2 25.56 3.13 3.02 3 7.58 1.16 1.13 4 0.48 2.39 2.40 5 0 1.08*10 -3 9.93*10 -4 Figure 3. Aspen Chromatography graphical user interface and representative owsheet.
Chemical Engineering Education 202 assign appropriate models ( e.g. ionx_r_feed, ionx_r_column, and ionx_r_product) to the column. 3.2 Simulation Parameters: For the purpose of the simula for generating the batch adsorption data and determining the isotherm parameters) having the following properties was used: inter-particle voidage of 0.40, intra-particle voidage of 0.70, bed capacity of 30 M, and 50 micron radius spherical particles. The following simulation assumptions were used: liquid viscosity of 1 cP, spherical stationary phase resin particles -1 for the solutes, material balances assuming convection with disper sion based upon plate numbers (400 plates for the counter-ion and a linear lumped resistance kinetic model assumed. The simulations were set to allow varying pressure with constant differential equation discretization method with 100 nodes Initially the students were instructed to use a feed load 2 column volumes). The concentrations of the product and impurities in the feed mixture were set to 8 mM product, 1 mM impurity 1, and 1 mM impurity 2. While it is a good as sumption that the product comprises between 90-95% of the WPC feed, the product and impurities concentration values were chosen for ease of illustration during instruction. The feed stock counter-ion concentration was always set equal to that of the column running buffer for each WPC simulation as these separations are carried out under isocratic conditions. Through this hands-on computer laboratory lecture the stu dents were then able to independently run Aspen, satisfying learning objective 2. Figure 4, A through E. Simulated chromatograms for separations with varying feed volumes at constant inlet NaCl concen tration of 210 mM (dash dot line), ow rate (10 ml/min), and feed concentrations [8 mM product (solid line), 1 mM impurity 1 (dashed line), 1 mM impurity 2 (dotted line)]. Feed loading varied from a) 25, b) 40, c) 50, d) 100, and e) 200 minutes. A. B. C. D. E.
Vol. 44, No. 3, Summer 2010 203 3.3 Factorial Simulations: optimize the separation. Factorial simulations allow for the study of a given factors effect upon a response variable as well as interactions between factors. If the number of experi ments for a full factorial design is too high, a fractional facto rial design may be performed in which some of the possible combinations (usually at least half) are omitted. or greater product recovery (yield) with at least 95% purity. The optimal separation processes should maximize the product shift limitation. The students were required to perform facto rial simulations using the Aspen Chromatography simulator to vary the feed loading volume and salt concentration in the col umn running buffer. Further parameters (feed concentration as an extra-credit option in the present form of this project. Students were initially instructed to approach the problem in an explicitly outlined manner and later asked to optimize the 3.3.1 Varying Column Loading Volume: The following simulations were aimed at instructing the students of WPC process variable the students were asked to study was the ef fect of the feed loading volume upon the product production feed concentrations (8 mM product, 1 mM of each of the two impurities) were used. For each simulation the salt concentra tion in the loading buffer was set equivalent to the running buffer. Simulations using feed loading times of 25, 40, 50, 100, and 200 minutes were required of the students. Results from the concentration (mM) of the product (solid line), impurity 1 (dashed line), and impurity 2 (dotted line) are given on the left hand y-axis, the salt (dash-dot line) concentration (mM) is given on the right hand y-axis, and the separation time is given on the x-axis (minutes). Figure 4A shows the WPC separation for a feed loading time of 25 minutes. In this plot an induced salt wave is observed early in the chromatogram due to the desorption of salt during solute binding. The product does not reach its plateau concen and each of the two impurities that would allow the process engineer to further increase the feed loading time while still satisfying the constraints on the process. As the feed loading times increased (Figures 4 B-E) the product peak began to broaden (Figure 4B, 40-minute feed load) and develop a spike (Figure 4C, 50-minute feed load). This spike is due to the competitive binding of the induced salt wave and the product.  Further increases in the feed loading time to 100 minutes resulted in broadening of the concentra tion spike into a two-step concentration breakthrough of the product (Figure 4d). Under these conditions, however, the product began to overlap with the impurities adversely affect ing the yield and productivity. A further increase in the feed loading time to 200 minutes (Figure 4e) resulted in greater product losses due to overlap with the impurities. From this set of simulations the students should have noted that there exists an optimum WPC feed loading time for a given salt concentration. Loading times that were too small under-utilize the column capacity available while larger load ing times eventually suffer from product losses. 3.3.2 Varying Salt Concentration: The students were instructed to study the effect of varying the salt concentration under which the WPC separations are performed. Simulations NaCl) were required of the students. Figures 5 A-D (next page) show chromatograms for these simulations that were performed using a feed loading time of 100 minutes (note: this feed load corresponded to the conditions where the product began to overlap with the impurities in Figure 4). Students were asked to comment on the changes observed for these parametric WPC simulations (breakthrough times of the product and impurities, time required for the entire separation, shapes of the peaks obtained, etc). As the salt concentration is increased to 220 mM (Figure operation with product yield diminished due to early eluting impurities. In fact, this illustrates the potential advantage of As the salt concentration is decreased (Figures 5 B-C) WPC becomes the dominate mode of separation with increased resolution between the product and impurities. At 200 mM salt complete separation is achieved between the product and the impurities even at this elevated feed load of 100 minutes. Further decrease in salt concentration to 170 mM (Figure 5D) resulted in even greater separation between the product and A typical shift time for workers in a manufacturing plant (eight hours) would make such long separation processes impractical. Further decrease in the isocratic operating salt concentration would result in product K p values characteristic of bind and elute separations. Clearly, as with the feed loading time, there exists an optimum salt concentration for perform ing WPC separation of a given feed stock. tions and enabled students to learn about the behavior of WPC as compared to more traditional modes of chromatography, satisfying learning objectives 3 and 4. 3.3.3 Fractional Factorial Simulations: Data from pre liminary project reports along with the parametric simulations carried out (Figures 4 and 5) now positioned the students to solve the open-ended task of optimizing this separation. The
Chemical Engineering Education 204 students were asked to use the Aspen Chromatography simulator to determine the optimum separation conditions (maximized product yield per unit time for a given purity constraint) for this system which did not exceed an eighthour shift limitation typical in industrial settings. Results from a systematic fractional factorial design approach varying the feed loading volume (11 discrete values) and salt concentration (5 discrete values) are outlined below. The maximum productivity for the system is given by Eq. (3) where T Total is the total run time for a given column separation, M is the amount of product protein loaded ( i.e. V times C, where V is the volume and C is the concentra tion of protein loaded). Regeneration and re-equilibration times are not included in this since it is expected that these will be the same for all WPC processes for a given feed/column system. Eq. (3) can be rewritten in the form loading is the feed loading time. f M T Tota l () 3 ma x: f TF C T loadin g Tota l () 4 The decision variables that can be used to maximize concentration of the feed components, and the salt con centration used for the separation. The students were not given explicit separation conditions for these separations Simulations performed under these various conditions were then used by the students to produce graphs of the productivity (mass of product per time) as a function of feed loading volume and salt concentration (Figure 6). In this representative productivity bar graph, the data time) did not satisfy the constraints, while the other data (full bars) did. From this analysis, the students were then asked to select product from the impurities. For example in Figure 6 the optimum result would correspond to a salt concentration Figure 5, A through D (all, left). Simulated chro matograms for separations with varying NaCl con centrations (dash dot line) at constant feed loading time (100 min), ow rate (10 ml/min), and inlet feed concentrations [8 mM product (solid line), 1 mM impurity 1 (dashed line), 1 mM impurity 2 (dotted line)]. Salt counter ion concentrations were: a) 220, b) 210, c) 200, and d) 170 mM NaCl. D. C. B. A.
Vol. 44, No. 3, Summer 2010 205 of 200 mM and a feed load time of 250 minutes. Students were also required to submit representative simulations results illustrating the trends observed in their data and to comment upon how the optimal conditions were obtained. Additionally the students were asked to comment upon the separation conditions for which the constraints were not met. Finally, inspired students were encouraged to take their analysis further by investigating the effect of varying the concentration of the feed components (keeping the relative WPC separations. 4. PROJECT ASSESSMENT In this section we summarize how learning objectives were project, and provide guidance upon how instructors can assess tives  for this project were as follows: At the end of this project students should be able to 1) generate and interpret simulation tool for chromatographic modeling, 3) explain the subtleties of a novel mode of chromatography (WPC) through varying calculations and simulations, 4) illustrate directing experiments, and 5) apply their chromatographic simulation and optimization experience to modeling other separation processes. Project description handouts provided to the students contained information on current biotech nology separation challenges and taught them about WPC (objective 3). The tasks they were required to perform taught them how to generate and interpret adsorption isotherm and to the use of simulation tools for chromatographic modeling (objective 2). Further, as the students performed the required simulations under varying conditions ( e.g. feed load and salt concentration) the subtleties of WPC separations became ap parent (objective 3). The students were also able to observe trade-offs between maximizing productivity while minimizing the overall process time and satisfying process constraints. tions (objective 4) during the optimization of their processes. By the end of the project, the students were comfortable and indicated that they felt they had learned the necessary skills to model other separation processes (objective 5). The student response to the addition of this simulationbased project into the course was quite favorable. While the students had not previously used Aspen Chromatography they had some familiarity with Aspen software through pre project was used in the course, the students indicated that more experience with the Aspen simulator in general would have been useful prior to the assignment. This was addressed in the following year by including a hands-on computer laboratory in the lecture sequence. In this studio format, the students were able to get assistance from the instructor and students experience. Student enthusiasm was apparent, since the entire class stayed well after the instructional period had ended in order to continue learning how to properly use the chromatographic simulator. Students commented that they enjoyed visualizing the separations that they had been studying earlier in the course derstanding of chromatographic separations. They also com mented that this project enabled them to better understand the implementation of many of the course concepts and theories Figure 6. Representative productivity bar graph for varying feed loading time and NaCl concentrations. For each feed loading time shown on the x-axis results are given at 5 NaCl concen trations of 170, 200, 210, 220, and 250 mM from left to right. The data represented by unlled bars (purity) and half-lled (shift time) did not satisfy these particular constraints, while the other data (full bars) satised all constraints.
Chemical Engineering Education 206 for an actual separation process. Finally, several students commented that this simulation module was their favorite part of the course. Student assessment was based on two written reports that they were required to submit, one prior to using Aspen and one after. The students were assessed for their ability to generate e.g. isotherm plots, partition and simulations performed for the optimization of the pro cess) as well as for their understanding of these processes as evidenced by the discussions in these reports. 5. CONCLUSIONS The commercial simulator Aspen Chromatography was employed to study and optimize an important new industrial separation process, weak partitioning chromatography. This chromatographic separations course. Students initially were asked to manipulate adsorption data to determine adsorption isotherm parameters and to study the effect of salt on the isotherm behavior. A preliminary report was turned in at this point that also included their responses to a number of ques tions to probe their knowledge of the subject matter. The students were then requested to carry out detailed sets of parametric simulations to investigate the effect of operat ing parameters ( e.g. feed load, salt concentration) on the productivity and yield of this separation process. The course project served to teach students basic simulator operation, apply course material to a separation challenge from the biotechnology industry, and encourage open-ended problem exploration for process optimization. ACKNOWLEDGMENTS This research was supported by NIH Grant 5R01 GM047372. Helpful discussions with Alexander Freed are also gratefully acknowledged. REFERENCES Chem. Eng. Educ. p. 92 (2001) 2. Wankat, P.C., Learning Through Doing: A Course on Writing a Text Chem. Eng. Educ. p. 208 (1993) 3. Wankat, P., Using a Commercial Simulator to Teach Sorption Separa Chem. Eng. Educ. p. 165 (2006) 4. Ge, M., C. Li, and S. Ren, ChemCAD Software and Application in isuanji Yu Yingyong Huaxue 21 (5), 781 (2004) 5. Smith, C.A., and F.W. Villaescusa, Simulating Chromatographic Sepa J. of Chem. Educ. 80 (9), 1023 (2003) 6. Haddad, P.R., M.J. Shaw, J.E. Madden, and G.W. Dicinoski, A Computer-Based Undergraduate Exercise Using Internet-Accessible Simulation Software for the Study of Retention Behavior and Optimi J. of Chem. Educ. 81 (9), 1293 (2004) Chem. Eng. Educ. 39 (1), 68 (2005) 8. Wankat, P.C., Integrating the Use of Commerical Simulators in Lecture J. of Eng. Educ. 91 (1), 19 (2002) Biotechnology Progress 23 (5), 995 (2007) 10. Vunnum, S., M. Switzer, R. Godavarti, T. Iskra, P.R. Brown, S. Tobler, J. Coffman, B. Costigan, C. Kha, D. Wright, K. Sterl, and B. Kelley, Abstracts of Papers 232nd ACS National Meeting, San Francisco, CA (2006) 11. Tobler, S.A., A. Noyes, P.R. Brown, M. Switzer, and B. Kelley, Re moval of HMW Species Using AEX in the Weak Partitioning Mode Abstracts of Papers 234th ACS National Meeting, Boston, MA (2007) 12. Kelley, B.D., S.A. Tobler, P. Brown, J.L. Coffman, R. Godavarti, T. Iskra, M. Switzer, and S. Vunnum, Weak Partitioning Chromatog Biotechnology and Bioengineering 101 (3) 553 (2008) 13. Coffman, J.L., J.F. Kramarczyk, and B.D. Kelley, High-throughput screening of chromatographic separations: I. Method development Biotechnology and Bioengineering 100 (4) 605 (2008) 14. Kramarczyk, J.F., B.D. Kelley, and J.L. Coffman, High-Throughput Screening of Chromatographic Separations: II. Hydrophobic Interac Biotechnology and Bioengineering 100 (4), 707 (2008) 15. Wensel, D.L., B.D. Kelley, and J.L. Coffman, High-Throughput Screening of Chromatographic Separations: III. Monoclonal Antibod Biotechnology and Bioengineering 100 (5), 839 (2008) 16. Kelley, B.D., M. Switzer, P. Bastek, J.F. Kramarczyk, K.L. Molnar, T.N. Yu, and J. Coffman, High-Throughput Screening of Chromatographic Biotechnology and Bioengineering 100 (5), 950 (2008) Chem. Eng. Educ. 31 (3), 178 (1997) 18. Champion, K.M., J.C. Nishihara, I.S. Aldor, G.T. Moreno, D. Andersen, K.L. Stults, and M. Vanderlaan, Comparison of the Escherichia coli Proteomes for Recombinant Human Growth Hormone Producing and Proteomics 3 (7), 1365 (2003) 19. Van Dyk, D.D., D.R. Misztal, M.R. Wilkins, J.A. Mackintosh, A. of Cellular Changes Associated With Increased Production of Human Proteomics 3 (2), 147 (2003) 20. Gallant, S.R., A. Kundu, and S.M. Cramer, Modeling Nonlinear J. of Chroma tography A 702 (1-2), 125 (1995)APPENDIX DIAGNOSTICS (Solver reporting level: low; Properties reporting level: none; Watch group: 0; Watch torn sub-group: 0; Check procedure derives: off; Relative checking toler ance: 0.001; Absolute checking tolerance: 0.001; Check the list variables in equivalences for highest variable steps and residuals). TOLERANCES (Absolute variable tolerance: 1e-007; Rela tive variable tolerance: 1e-007; Absolute equation tolerance: 1e-007; Variable change tolerance: 1e-007; Numerical de rivative absolute perturbation: 1e-005; Numerical derivative relative perturbation: 1e-005; Explicit event tolerance: 1e005; Uncheck Solver scaling; Check Eliminate equivalence equations; Check Use Group Decompositions). TEARING (Procedure tearing: Update; Tear update strat
Vol. 44, No. 3, Summer 2010 207 egy: Direct; Relative tear tolerance: 1e-005; Absolute tear tol erance: 1e-005; Maximum number of tear iterations: 100). INTEGRATOR (Integration method: Gear; Maximum or der: 5; Absolute integration error tolerance: 0.0005; absolute tear error tolerance: 1e-005; relative integration error toler ance: 0.0005; relative tear error tolerance: 1e-005); Uncheck include sensitivity errors; Uncheck reconverge torn variables; Select that the integration error test includes States only; Variable Initial step size of 0.001; Minimum variable step size: 0.0001; Maximum variable step size: 0.1; Variable step reduction factor: 0.5; Uncheck Always enforce minimum step size; Check Interpolate communication time; Uncheck Locate model discontinuities; Uncheck Re-initialize after variable step-change; Check Use initial step size after variable stepchange; Show 0 highest integration errors; Show 0 highest tear integration errors). LINEAR SOLVER (Name: MA48; Drop tolerance: 0; Reanalyze threshold: 2; Pivot tolerance: 0; Re-analyze FLOPS window size: 0; Re-pivot every 0 factorizations; Solver searches 3 columns for pivots; Uncheck use transpose). NON LINEAR SOLVER (Mode: Standard; Method: Mixed Newton; Convergence criterion: Residual; Maximum diver gent steps: 20; Maximum step reductions: 20; Maximum iterations: 500; Maximum fast Newton steps: 8; Uncheck Dogleg method; Maximum range fraction tolerance: 0; Maxi mum approach to bound: 1; Absolute perturbation: 1e-005; Singularity perturbation: 0.01; Maximum variable step: 50; Clip factor: 1e-006; Highest variable steps: 0; highest residu als above tolerance: 0; Print linear algebra for groups of size > 0; Uncheck Enabled homotopy). ESTIMATOR (Estimator: Least Squares; Solver: NL2SOL; Reporting level: High; Solution convergence tolerance: 0.0001; Maximum iterations: 2000; Relative function toler ance: 0.0001; Absolute function tolerance: 0.0001; False convergence tolerance: 0). OPTIMIZER (Optimizer: FEASOPT; Reporting level: Medium; Maximum iterations: 100; Solution convergence tolerance: 0.0001; Maximum relative step: 10; Maximum absolute step: 10). HOMOTOPY (Initial homotopy step: 0.1; Maximum homotopy step: 1; minimum homotopy step: 0.01; Step size increment factor: 10; Step size decrement factor: 0.5).
Chemical Engineering Education 208 The traditional development presents the fugacity  of a pure substance as a mathematical translation to the Gibbs energy. fP GG G RT iR ii Ri T ex p ( 1) ) The most frequent expression is the equivalent implicit form or a variant thereof: GG GR T f P ii Ri T i R ln () 2 For example, Smith, Van Ness, and Abbott,  Tester and Modell,  and Kyle  use nomenclature of the form: GT RT f ii i ln () 3 The function of system temperature is: i i Ri T R TG GR TP ln () 4 The inclusion of the reference pressure term in the tempera infeasibility since fugacity has units of pressure and the argu ment of the logarithm must be dimensionless. Prausnitz, Lich tenthaler, and de Azevedo  use nomenclature of the form: GG RT f f ii R i iR ln () 5 The values at the reference point are: fP GG G iR R iR iR iT ,, () 6 Others (Winnick,  Kyle,  and Elliott and Lira  fugacity in differential form at constant temperature: dG RT df i i ln () 7 Integration from the arbitrary reference point at the system temperature gives the Prausnitz, et al. form. Sandler  the fugacity as a transformation to the residual Gibbs energy: fP G RT i iP ex p ( ) 8 All authors use this equation as the basis for computing the value of the fugacity. This equation does not contain the refer ence state or the ideal gas Gibbs energy change. A graphical representation of the rigorous mathematical fugacity and Gibbs energy for a pure substance. The graphical representation provides students with a visual interpretation methods for determining the value of the fugacity. PG DIAGRAM FOR A PURE SUBST ANCE A PG diagram demonstrates the physics underlying the diagram for argon. The PG diagram was developed using data from the NIST Chemistry WebBook (
Vol. 44, No. 3, Summer 2010 209 180 K and 236.9 bar with Gibbs energy of -15,280 Joule/mole is to be determined. G J oul e mole AR Kb ar ,, ( ) 180 236 9 15 280 9 GIBBS ENERGY FOR A SUBST ANCE BEHAVING AS AN IDEAL GAS The Gibbs energy of a substance behaving as an ideal gas can be determined at any temperature and pressure provided that: The absolute (or standard) entropy of the ideal gas is known at some reference state, and The ideal gas heat capacity is known over the range from the reference temperature to the system temperature. Gibbs energy is a state (point) function. As such, any con venient path between two states determines the difference in the Gibbs energy. Select a path from the ideal gas reference state to a hypothetical ideal gas state that is composed of: 1) an isobaric step at the reference state pressure from the reference state temperature to the ideal gas state temperature (details of the ideal gas reference state and the computation of the Gibbs energy change for the isobaric step are contained in the Appendix) and 2) an isothermal step at the ideal gas state temperature from the reference state pressure to the ideal gas state pressure. GG GG ii R i Ti P () 10 Rearranging: GG GG ii Ri Ti P () 11 The fundamental property relationship for the Gibbs energy is: dG Sd TV dP () 12 For the isothermal step, the Gibbs energy change is: GV dP RT P dP RT P P iP P P P P R R R ln () 13 Rearranging: ln P P G RT GG G R iP ii Ri T RT () 14 The isotherm for a pure substance behaving as an ideal gas Figure 1. PG diagram for argon.
Chemical Engineering Education 210 is a straight line with slope of 1/RT on the semi-logarithmic PG diagram. It is a fundamental axiom of thermodynamics that all substances behave as an ideal gas as the pressure approaches zero on an isotherm, therefore, every isotherm becomes asymptotic to a straight line with this slope as the pressure approaches zero. Note that the four isotherms on Figure 1 become asymptotic to a straight line at low pressure and that the slope of the line decreases with increasing tem perature. The dashed line, asymptotic at low pressure to the 180 K isotherm, is the 180 K isotherm for argon behaving as Suppose that the Gibbs energy for argon as an ideal gas at 180 K and 236.9 bar relative to the ideal gas reference state taken to be 120 K and 1.5 bar with an ideal gas absolute en tropy of 132.35 Joule/mole K and Gibbs energy of -13,444 Joule/mole is to be determined. The ideal gas reference state is not on the 120 K isotherm for argon. It is an ideal gas refer ence state, therefore it is located on the 120 K isotherm for argon behaving as an ideal gas that is asymptotic to the real isotherm as the pressure approaches zero. At the low pressure of the reference state, there is little difference between the real isotherm and the ideal gas isotherm. The two-step path is depicted on Figure 1 by a dashed line that begins at the reference state and proceeds horizontally (isobaric) to an intermediate state on the 180 K isotherm for the ideal gas and then proceeds from the intermediate state along The Gibbs energy of argon behaving as an ideal gas at 180 K and 236.9 bar is -14,070 Joule/mole. G J oul e mole Ar Kb ar ,, ( ) 180 236 9 14 070 15 Substituting for the isothermal step and rearranging: GG GG GR T P P ii R i Ti P i T R , ln GG GR T P P ii Ri T R ln () 16 RESIDUAL GIBBS ENERGY The residual Gibbs energy at constant pressure is the differ ence between the Gibbs energy of the system and the Gibbs energy of a system of the same chemical composition and at the same temperature and pressure but behaving as an ideal gas. GG G iP ii () 17 An important attribute of residual properties is that the calcula tion only requires PVT data and/or equations of state applicable on the system isotherm from a pressure that approaches zero to the system pressure. These calculations do not require heat capac ity or absolute entropy. On the PG diagram, the residual Gibbs energy for argon at 180 K and 236.9 bar represents a process from Gibbs energy for argon at 180 K and 236.9 bar is: GG G J oul e m iP ii ,, 15 280 14 070 1 210 o ol e () 18 PHYSICAL DEFINITION OF THE FUGACITY FOR A PURE SUBST ANCE The fugacity of a pure substance at a temperature and pres sure is the pressure at which the substance behaving as an ideal gas at the same temperature has the same Gibbs energy as the system. On Figure 1, the Gibbs energy of a system contain ing argon at 180 K and 236.9 bar is -15,280 Joule/mole. The pressure of argon behaving as an ideal gas at 180 K that has a Gibbs energy of -15,280 Joule/mole is 105.5 bar. This is the fugacity of argon at 180 K and 236.9 bar. The fugacity is easily determined on Figure 1 as the pressure where a vertical line through the point at 180 K and 236.9 bar intersects the G J oul e mole Ar Kb ar ,, ( ) 180 105 5 15 280 19 The fugacity is a point located on the ideal gas isotherm. The two-step path from the reference state gives the implicit GG GR T f P ii Ri T i R ln () 20 DETERMINING THE FUGACITY FOR A PURE SUBST ANCE Consider the Gibbs energy changes for a three-step process from the reference state to the system state that is composed of: 1) an isobaric step for the substance behaving as an ideal gas at the reference state pressure from the reference state temperature to the intermediate state at the system temperature, 2) an isother mal step for the substance behaving as an ideal gas at the system temperature from the reference state pressure to the system pres sure, and 3) an isobaric step from the ideal gas isotherm to the for the two-step process from the reference state to the ideal gas for a system at 180 K and 236.9 bar). The Gibbs energy change for the third step is the residual Gibbs energy. GG GR T P P G ii Ri T R iP ln GG GG GR T P P ii ii Ri T R ln G iP () 21
Vol. 44, No. 3, Summer 2010 211 GG RT f P G iR iT i R iR ln G GR T P P G RT f P iT R iP i ln ln G fP G RT iP i iP ex p () 22 This is the equation that is used to compute the value of the fugacity of a pure substance. The residual Gibbs energy at constant pressure is determined from PVT data and/or equations of state for the pure sub entropy at the reference state is not required. The isobaric ideal gas Gibbs energy change cancels and this eliminates the need for the ideal gas heat capacity. At 180 K and 236.9 bar, the residual Gibbs energy is -1210 Joule/mole. Substitution gives the fugacity: fP G RT ba r i iP ex p ex p 236 9 1 2 210 8 3143 18 J oul e mole J oul e mole K 0 0 105 5 23 K ba r () ) ln () P f G RT i iP 1 24 The slope of the 180 K isotherm for argon behaving as an ideal gas at 180 K and 236.9 bar is indicated on the diagram. The rise on the semi-loga residual Gibbs energy and the fugacity are measures of the deviation from ideal gas behavior. The fugacity is a measure of the vertical distance (on a logarithmic scale) from ideal gas behavior to the system state. The residual Gibbs energy is a measure of the horizontal distance (on a linear scale) from ideal gas behavior to the system state.PHASE COEXISTENCE FOR A PURE SUBST ANCEThe temperature, pressure, and Gibbs energy of a pure substance must be equal in each phase for two or more phases to coexist. GG ii () 25 equivalent requirement for fugacity. GG RT f P G iR iT i R ln i iR iT i R i GR T f P f ln f i () 26 Since the fugacity can be determined from PVT information for a substance, it is more convenient for phase coexistence calculations than Gibbs energy. Lewis  used this requirement coupled with the low concept of fugacity. STUDENT COMPREHENSION Lewis described the concept of fugacity that he intervening century would agree. The PG diagram tions and gives insight to the advantages of fugac ity over Gibbs energy. Students prefer the physical the diagram. It explains why two quantities with the same units but different values, pressure and fugac ity, are equal when two phases of a pure substance are in equilibrium. Fundamental comprehension applying fugacity. CONCLUSIONS The semi-logarithmic PG diagram for a pure substance with superimposed isotherms for the substance behaving as an ideal gas provides physi compute the value of the fugacity. The PG diagram clearly demonstrates that the fugacity of a pure sub stance at a temperature and pressure is the pressure at which the substance behaving as an ideal gas at the same temperature has the same Gibbs energy as  of the fugacity. NOMENCLA TURE C Pi Ideal gas heat capacity at constant pressure for the pure substance f i Fugacity of the pure substance at the system temperature and pressure f i,R Fugacity of the pure substance at an arbitrary reference point at the system temperature G i Gibbs energy of the pure substance at the system temperature and pressure G iI Gibbs energy for a hypothetical ideal gas at the intermediate state (system temperature and reference state pressure) G i,R Gibbs energy of the pure substance at the arbi trary reference point at the system temperature G iR Gibbs energy for a hypothetical ideal gas at the reference state for the Gibbs energy relative to the reference state for the enthalpy Gi ( ) Gibbs energy of pure substance in phase Gi ( ) Gibbs energy of pure substance in phase G i Gibbs energy of the pure substance as a hypo
Chemical Engineering Education 212thetical ideal gas at the system temperature and pressure G iP Ideal gas Gibbs energy change at constant temperature from the reference state pressure to the system pressure G iR Gibbs energy at the ideal gas reference state G iT Ideal gas Gibbs energy change at constant pressure from the reference state temperature to the system temperature G iP Residual Gibbs energy at constant pressure H iR Enthalpy for a hypothetical ideal gas at the reference state for the Gibbs energy relative to the reference state for the enthalpy P Absolute pressure of the pure substance P R Absolute pressure at the ideal gas reference state R Gas constant S iR Absolute entropy for a hypothetical ideal gas at the refer ence state for the Gibbs energy T Absolute temperature of the pure substance T R Absolute temperature at the reference state for the Gibbs energy i T A function of system temperature REFERENCES Proceedings of the American Academy 37 (4), 49, (1901) 2. Smith, J.M., H.C. Van Ness, and M.M. Abbott, Introduction to Chemi cal Engineering Thermodynamics 7th Ed., McGraw-Hill (2005) 3. Tester, J.W., and M. Modell, Thermodynamics and Its Applications 3rd Ed., Prentice-Hall (1996) 4. Kyle, B.G., Chemical and Process Thermodynamics 3rd Ed., PrenticeHall (1999) 5. Prausnitz, J.M., R.N. Lichtenthaler, and E.G. de Azevedo, Molecular Ther modynamics of Fluid-Phase Equilibria 3rd Ed., Prentice-Hall (1999) 6. Winnick, J., Chemical Engineering Thermodynamics John Wiley (1997) 7. Sandler, S.I., Chemical, Biochemical, and Engineering Thermodynam ics 4th Ed., John Wiley (2006) 8. Poling, B.E., J.M. Prausnitz, and J.P. OConnell, The Properties of Gases and Liquids 5th Ed., McGraw-Hill (2000) 9. Elliott, J.R., and C.T. Lira, I ntroductory Chemical Engineering Ther modynamics Prentice-Hall (1999) APPENDIX The value of the fugacity can be determined without speci fying the ideal gas reference state, however, development of the PG diagram requires a reference state where the absolute GH TS () 27 The Gibbs energy and the enthalpy are relative quantities however the temperature and entropy are absolute quantities. The absolute entropy (relative to the perfect crystalline state at a temperature of absolute zero) for the substance behaving as an ideal gas is required to determine the Gibbs energy at the ideal gas reference state. GH TS iR iR Ri R ,, () 28 Gibbs energy and enthalpy are relative quantities but are value of one to the arbitrary reference state for the other. In Helmholtz energy make all four quantities interdependent. The NIST database reports the absolute entropy of argon as an ideal gas at 298.16 K and 1 bar to be 154.84 Joule/mole K. Extensive tabulations of data for absolute entropies do not exist, thus, one of the driving forces to replace Gibbs energy with fugacity. Standard entropies may be reported for the pure substance as a solid or liquid. In principle, the absolute entropy at an ideal gas reference state can be determined from ity based on an ideal gas reference state general. Poling, Prausnitz, and OConnell  provide methods for estimating absolute entropies in the absence of data. ISOBARIC GIBBS ENERGY CHANGES FOR A PURE SUBST ANCE ideal gas is an isobaric process. The Gibbs energy change for the process is: GG G iT iI iR () 29 state is: GH TS iI iI iI ,, () 30 The ideal gas enthalpy at the intermediate state is deter mined from the ideal gas heat capacity: HH Cd T iI iR Pi T T R ,, () 31 Determination of the value for the absolute entropy at the intermediate state also requires a correlation for the ideal gas heat capacity. SS C T dT iI iR Pi T T R ,, () 32 Tabulations of parameter values for correlations of data for the ideal gas heat capacity of pure substances are extensive and there are several group contribution methods  to estimate the heat capacity in the absence of correlations.
Vol. 44, No. 3, Summer 2010 213RECAP OF P ART 1  Research productivity is the dominant criterion for tenure and promotion at most research universities in the United States, and its becoming increasingly important at institutions that used to have only teaching mis sions. This policy has hurt the quality of education at many universities by denying some outstanding teachers tenure, and it has also led to a lot of mediocre research. research and teaching are inextricably linked, to an extent that only active researchers can be effective teachers. While teaching and mentoring graduate students, its connection to undergraduate education is far from obvious. Prince, et al.  recently surveyed the literature on the connection and found that while disciplinary research can support teaching in correlations have not been found between individual faculty research productivity and teaching effectiveness, or between institutional research productivity and student learning and satisfaction. (In fact, most correlations of both types have been negligible and sometimes negative.) Most faculty members do not integrate their research into their undergraduate courses, and many who attempt it waste valuable class time on mate rial irrelevant to the course objectives or too advanced for the students backgrounds. Undergraduate research does provide THE LINK BETWEEN RESEARCH AND TEACHING RICHARD M. FELDER North Carolina State UniversityAs a rule, however, only a small subset of the student body participates in research, the participants often function more like unpaid lab assistants than real researchers, and research learning and skill development. (See Reference 2 for citations STRENGTHENING THE LINKPrince, et al.  offer several proposals for strengthening the research-teaching nexus, including these: Encourage faculty members to use inductive teach ing methods ( e.g. inquiry-based, problem-based, and project-based learning). An instructor may effectively promote learning by teaching in a manner that emulates elements of the research process. Inductive methods such as inquiry-based, problem-based, and project-based learning do that. When implemented correctly, Copyright ChE Division of ASEE 2010 Random Thoughts
Chemical Engineering Education 214they facilitate students attainment of high-level thinking and problem-solving skills  and can reach more students at a lower cost than undergraduate research can. Engage a substantial percentage of the student body in meaningful research. The impact of undergraduate research is limited if only a relative handful of students participate in it, while involv ing many students can add considerably to the quality of a departments teaching program. Simply giving students projects is not enough, however; for undergraduate research to be effective, the advisor must really mentor the students and not just treat them as additional pairs of hands to help out in the lab. Formally recognize and reward faculty members who successfully integrate teaching and research. Successful integration might involve relevant incorporation of the instructors research into course lectures, assignments, and exams; using inductive teaching methods and demonstrat ing their effectiveness; and guiding students through wellconducted research projects. If such activities are explicitly included in annual faculty performance evaluations and they count in tenure and promotion decisions, they will eventually become part of the academic culture.STRENGTHENING BOTH RESEARCH AND TEACHING Strengthening the linkage between research and under graduate teaching can improve the latter, but only to a limited extent. As long as excellence in research is routinely rewarded with tenure and promotion and excellence in teaching is oc casionally recognized with an award, teaching quality will be well below what it could be. The following two steps should improve an institutions teaching program dramatically with Make sure each department has some faculty members (at least 10%) who specialize and excel in teaching and educational scholarship. Treat performance in teaching/educational research and disciplinary research identically when tenur ing, promoting, and rewarding faculty members. The idea is not to reverse the positions of research and teach ing in the faculty reward system to make teaching dominant. Frontier research is critical to the future of our society, and it is vitally important for universities to keep doing it since industry has largely abandoned research that doesnt promise a quick payoff. But just as not every teacher has the aptitude to be an excellent researcher, not every researcher is capable of being an excellent teacher. Some professors manage to excel at bothalmost every department has a fewbut there are not nearly enough of them to populate all department faculties. So, in addition to hiring and promoting people who are outstanding disciplinary researchers and adequate teachers, every academic department should make room for some outstanding teachers and educational scholars who do little or no disciplinary research. Those individuals will keep up with innovations in pedagogy and instructional technology and share their knowledge with interested colleagues to help them improve their teaching. They will teach important un dergraduate courses (such as the engineering lab and capstone design course) that most research-oriented faculty members have little interest in teaching, and help students acquire critical professional skills (communication, teamwork, ethical awareness, etc.) that traditional faculty are often reluctant to include in their courses. There is also a somewhat self-serving argument. Being outstanding teachers, the specialists will mo tivate their students to learn and inspire them to grow. Alumni tend to remember such teachers fondly throughout their lives, and when they are asked for discretionary donations or en dowments of scholarships, named chairs, and new labs and buildings for their alma mater, those memories often lead to generous responses. (All universities have such stories.) Administrators commonly fear that hiring and promoting education specialists will cause a reduction in institutional research productivity, but that doesnt have to happen. Some traditional faculty members freed from unwanted responsi the education specialists should bring in some of the mil lions of dollars of funding awarded every year for research on teaching and learning. Having education specialists on the faculty will allow most research and teaching to be done enthusiastically and expertly by people who enjoy and excel in those activities. As long as the specialists are held to the same high performance standards for tenure and promotion that are applied to traditional research faculty and they are rewarded equally for success, everybody wins. REFERENCES 1. Felder, R.M., The Link Between Research and Teaching. 1. Chem. Eng. Ed. 44 (2), 109
Vol. 44, No. 3, Summer 2010 215 The majority of students pursuing undergraduate de grees are digital natives (sometimes called the Net Generation). These men and women are characterized by being born in the 1980s or 1990s and by having grown up from a very young age. The ubiquity of laptops, cell phones, digital music players ( e.g. iPods), and other electronic devices has this generation plugged into technology continuously throughout a typical day. The advantages enjoyed by tech nology-savvy students are numerous. The near instantaneous access to course-related information can be used to look up tion within seconds. The integration of technology in the classroom, e.g. using Tablet PCs to promote student engage ment,  is almost expected by the digital natives. There are many technology-driven behaviors that challenge faculty in higher education today, however. For example, communicate (and sometimes cheat ), including the wide availability of solutions manuals for textbooks that are only intended for instructors. Also, handheld technologies allowing to shorter student attention spans. Text messages truncate the are limited to just 140 characters (about the length of this sen tence). Myriad books, blogs, and wikis discuss topics related to the growing population of digital natives [4-7]; however, this paper focuses on a simple classroom exercise to encourage students to use the seemingly endless information around them to enhance their college educations. Active learning is a key component of many different teach ing techniques used to engage students.  The use of multimedia ( e.g. audio, video, PowerPoint presentations) is one way to maintain student interest throughout a class period and during the duration of a quarter or semester. Student participa active-learning strategies. Therefore, for an activity to truly qualify as active learning, students enthusiasm is needed. YouTube Fridays began as a way to show the students Thermodynamics. The fact that a professor is both teacher and researcher is important to emphasize to undergraduate students. YOUTUBE FRIDAYS: MATTHEW W. LIBERATORE Colorado School of Mines Golden, Colorado 80004 Copyright ChE Division of ASEE 2010 ChE classroom
Chemical Engineering Education 216 Seeing the interesting problems their professor works on piques their interest and motivates them to get the most out of their studies. After watching a video of people walking worked and if they could build one.  I chose another video,  the second week of class, and the students wanted to know if there would be videos every week. I consented, on the condition that the students do the YouTube Fridays started its transition from a fun way to start class at 8 a.m. on Fridays (and to bolster Friday attendance) IMPLEMENT A TIONYouTube Fridays have been piloted as part of two courses (Table 1). Introduction to Engineering Thermodynamics, a sophomore-level class for students in chemical engineer ing, engineering physics, and civil engineering, was where YouTube Fridays began. A more formal YouTube Fridays pilot was completed the next semester as part of a Material and Energy Balances class, a sophomore-level course for chemical engineering students. The students were required to relate their chosen video to the topic of the course, namely engineering in the second. The evolution of the topics of the will be discussed in the context of each pilot. A section on how YouTube Fridays were evaluated precedes the conclud ing remarks and summary of how to adopt YouTube Fridays in other courses. Pilot 1: The Birth of Y ouTube Fridays Introduction to Engineering Thermodynamics introduces basic concepts including units conversion, reading steam and the second law of thermodynamics (entropy). During the of three or four students (of the 40 total students), which primarily used to work problems during class. The active learning exercises of working problems in Thermo Teams constitute approximately half of the class time throughout the semester, and many groups work together inside and outside of class. The videos chosen by the Thermo Teams covered a range of thermodynamics-related topics; the most popular topics included phase changes and blowing things up. Relating the selected videos was a series of clips showing water condensing behind a jet engine (sometimes called a contrail).  Concur rently, the students were learning about phase diagrams of the video, a sketch of a pressure-temperature diagram was placed on the board. The starting condition of the water in the air was labeled ( i.e. independent intensive variable that changed were quickly the board (Figure 1). The video and accompanying discussion were a perfect lead-in to the class material for the day. Using the videos to create quantitative homework problems great way to overcome the perceived irrelevance of textbooks by the technology-centric students. One example video was an at-home experiment performed by two young siblings, estimated to be about 11 and 7 years old.  Here, a plate of green-dyed water has a candle sitting in the center. Three P CP Liquid P Solid Waterleaving Visibleice TP Water leaving airplane engine Visible ice particles trail airplane Vapor T T ABLE 1 Outline of the Two Pilots of YouTube Fridays Pilot Course (n=number of enrolled students) Semester StudentSelected Videos Written Report University Course Evaluation YouTubeEvaluation 1 Introduction to Engineering Thermodynamics Fall 2008 Yes No Yes No 2 Material and Energy Balances Spring 2009 Yes Yes Yes Yes Figure 1. Schematic of a pressure-temperature phase diagram of a pure uid. Overlaid points represent the two phases of water present in the videos.
Vol. 44, No. 3, Summer 2010 217 pennies are placed on the plate, the candle is lit (with parental supervision), and a glass cup is placed over the candle. The the cup. As the cup was placed over the lit candle, I stopped the video and asked the class what they expected to happen. The overwhelming consensus was that the water level in the cup would rise. The video continued and the classs intuition was proven to be correct. A quantitative engineering estimate problem based on the video (Figure 2) required the students to complete a force balance. demonstrated a way to engage students of the Net genera tion. Videos were used to reiterate recent class material, and even introduce the students to advanced topics beyond a topic was the idea of nucleation. The video involves some young people with a clear glass bottle of beer subcooled to a temperature below the freezing point.  They show the to initialize nucleation. The entire bottle of beer freezes in just seconds to the wonder of the people in the video and the class. (I think many of the students attempted this trick the following weekend.) P ilot 2: Y ouTube F ridays and Chemical Engineering core course in the chemical engineering curriculum at Colorado School of Mines. The Spring 2009 class contained 55 students The formal YouTube Friday assignment was given during the second week of class. Students were asked to select videos related to chemical engineering (jobs, products, the video and giving a short oral description in class, the students were now required to complete a short written assignment as well. The written document provides an avenue for the students to analyze their chosen video. The objective of the written report was to address one or more of the following ques tions: How does the video relate to chemi cal engineering, biochemical engineering, or large-scale chemical production? What is the chemical reaction involved? How is the chemical reaction or product scaled up? What company produces the chemical(s) in the video? Does the video involve a chemi cal engineering job you would like to have? our daily activities? The written document needed to be signed by each member of the group. Overall, the quality of writing and depth of thinking demonstrated was better than I had anticipated. To give the students an idea of the length (less than 5 minutes) and content of the video, I chose a student-created  The various scenes of produced medicines, etc., would not exist without chemical engineers. Based on the example video, the student-selected being a chemical engineering student, and the jobs that a chemical engineer might perform. The mix of information on chemical engineering with humor was common throughout the semester. In total, videos created by chemical engineer ing students were very popular (including those from South Dakota School of Mines and Technology, Brigham Young University, University of Minnesota, the students in the pilot class at Colorado School of Mines, Tufts University, and Northwestern University). Detailed discussions of a few of of the students undergraduate education. Figure 2. Screenshots of a video made of an at-home experiment (a. and b.) and the course-related problem derived from the video (c.).
Chemical Engineering Education 218 One of the more humorous videos of the semester also proved to be one of the most instructive of the semester. cal engineering-centric lyrics (Figure 3).  While the whole class enjoyed the video and likely picked up one or two clearly learned even more, as they wrote a detailed report containing information that was not even in the video. First, actor. Obviously CSTR is not part of the texting vernacular. Next, the basic assumptions of perfect mixing, steady state operation, constant density, isothermal, and irreversibility were stated as conditions needed to understand the function of a CSTR. In addition, current course content was reiterated rate in as out, which is important so that the reactor does not the author of Elements of Chemical Reaction Engineering a book that we use for one of the classes we must take during Six of the 11 videos focused on education and jobs related to chemical engineering. Having an understanding of math ematics, physics, chemistry, and biology was mentioned in multiple videos as well as several of the written reports. The uitous and one video was quoted as saying half of the students was that chemical engineers are problem solvers. The many eos and by the students. Most prevalent areas of future need for chemical engineers were clean energy, nanotechnology, and biotechnology. The excellent pay of chemical engineers chemical engineering degree. The problem-solving skills of law, management, and entrepreneurial positions. The central themes of a chemical engineering education and the profes sion of chemical engineering were certainly covered over the course of one semester. The educational value for the students will be discussed in the evaluation section below. ment was open-ended, it was not surprising a subset of the videos were related to chemical reactions and physiochemical changes. Two videos were segments from the show Myth Busters involving the combustion of non-dairy creamer  and walking on a corn-starch pool.  The corn-starch pool and the concept of shear thickening (also covered during the cusses applying a force quickly, which causes thickening, vs. Figure 3. CSTR hand/body motions (parody of the song YMCA).  C S C S R T R T
Vol. 44, No. 3, Summer 2010 219 example of kinetics (another advanced topic covered later in the curriculum) outside of a reaction engineering setting. The concept of kinetics was also prevalent in a video of a recorded lecture contrasting the rate of reaction and the heat of reaction. During the middle of the semester, a group of students in the class took the initiative and made their own video and posted it to YouTube.  The enthusiastic group naturally chose to group mimicked other videos on YouTube by combining toilet bowl cleaner ( i.e. concentrated hydrochloric acid) and aluminum foil. The reaction created hydrogen gas. First, a plastic soft drink bottle was destroyed by the reaction in less than a minute. Then, a Nalgene bottle was used as a sealed reactor. The bottle did not explode; the top was simply blown off. The students report noted the different strengths of two when producing aluminum chloride on an industrial scale. Overall, the breadth of chemical engineering was captured the videos was included in the written reports.EVALUA TIONThe assignments were graded at the conclusion of both pilot courses, and the points were added to the participation/webbased quiz portion of their grade (5% of total grade for the semester). Overall, the selection and discussion of the video contributed between 0.5 and 1% of the semester grade. During the second semester, the grading rubric was broken down into four categories: 1. length and content appropriateness of the video; 2. video provides new and/or interesting information about chemical engineering or being a chemical engineer; 3. length and content appropriateness of the written document; and 4. the written document addresses one of the questions in the assignment or related information. With few exceptions, the students did an excellent job selecting appropriate, inter esting, and entertaining videos. In the future, a peer-review component will also be added to the grade. The peer evalua tion will hopefully circumvent the problem of just one or two assignment. I expect more uniform participation throughout the semester with the peer review component making up 20% of the assignments grade. on the back of the universitys course evaluations. One student commented that YouTube promoted his learning. The curious comments on another students evaluation; as someone with no text-messaging experience, I went to class the day after reading the evaluation (which was from the previous semester) and naively asked the students what the statement meant. A after laughing at their professor for a minute, assured me that FTW is a very positive statement, basically saying that YouTube Fridays were great. In addition to the universitys course evaluation, a one-page evaluation of YouTube Fridays was given at the end of the second pilot. The evaluation was completed during class and the students names were required. The multiple-choice sec tion allowed for four levels of response. Two free-response questions and an area for additional thoughts/questions/com ments/concerns completed the evaluation form. The assess ment of students opinions, both positive and negative, will lead to a more student-centered activity in future semesters. Overall, the students gave YouTube Fridays favorable re marks, which are summarized below. The evaluations should be taken in context. The goal of pilot 2 was to introduce the students to chemical engineering and what chemical engineers do, which was very successful based on the written reports and the data collected from the evaluations. YouTube Fridays were not designed to improve their learning of material and energy balances during pilot 2, which also was corroborated by the evaluations. Five multiple-choice questions were ranked on a scale of The questions focused on whether YouTube Fridays promoted learning new things about chemical engineering and jobs for chemical engineers, the effectiveness of videos vs. websites, and the value of the class time throughout the semester. The T ABLE 2 Students Percentage Responses to Five Survey Statements at the End of the Second Pilot CourseStatements Strongly Agree Agree Disagree Strongly Disagree in YouTube Fridays. 11 69 20 0 I know more about the jobs available to chemical engineers from participating in YouTube Fridays. 9 73 18 0 YouTube videos teach me more about chemical engineering than websites about chemical engineering. 7 32 61 0 time) to watch YouTube and not cover class material. 24 56 18 2 I think YouTube Fridays helped me learn the material in ChEN 201 this semester. 0 18 71 11
Chemical Engineering Education 220 about chemical engineering, learning about chemical engineering jobs, and using a small fraction of class time for YouTube instead of class material (Figure 4). The students believed, however, that they learn more about chemical engineering from websites ( e.g.
Vol. 44, No. 3, Summer 2010 221 T ABLE 3 Samples of Written Comments from Students Upon Completion Of Pilot 2I heart YouTube Fridays. YouTube Fridays were very valuable and helped to give a reason for some people to come to class on Fridays. Ive learned that mixing chemicals can cause dangerous explosions. Good to work in groups so we can meet the other students in our class. and most people dont know what a chemical engineer does on a day-to-day basis. The whole group summary thing was not really helpful because one person usually did it. I learned that there are a lot more careers available for chemical engineers than I thought there were. people often devote their degrees to other work). these videos helps to remind us all why we are going through this. It shows our future worth. More work than it needs to bevery hard to get four people T ABLE 4 Summary of Implementing YouTube Fridays for a Semester (16-week) Course Week 1 Show a video appropriate for the topic of the semester, form groups of three or four stu dents, distribute assignment with timeline, expectations, and grading rubric. Weeks 3-15 Watch videos once per week. Collect written reports. Weeks 15-16 Grade all videos and reports. Collect student feedback. Post-Semester activity for future semesters.reactions in the middle of the term, and energy balances at the end of the semester.CONCLUDING REMARKSYouTube Fridays only take a small fraction of class time and are an effective way to engage the Net generation and to expand the content of the course in a dynamic way. The organization and execution of this activity are summarized in Table 4. All of the student selected videos from both pilots are included on the authors faculty webpage.  Technology in the classroom will continue to change in the coming years and technology that is readily assimilated by current and future generations, however, is necessary to continually engage the increasingly technology-savvy student.ACKNOWLEDGMENTSThe author would like to acknowledge Ron Miller for help with evaluation and manuscript preparation.REFERENCES 1. CSTR. [cited July 14, 2009]; Available from:
Chemical Engineering Education 222 One of the fundamental challenges in teaching a poly mer science course is to develop the students intu ition regarding how this class of materials behaves. Professors often describe polymers as entangled masses of spaghetti or kite string to explain the unique behavior of poly mers. The reason this is commonly done is that if students can visualize how polymer chains interact and function through tangible examples, then they are better able to understand many of the basic concepts in polymer science and engi neering. Near the end of my graduate polymer engineering a more didactic fashion, students must be able to visualize and understand the models used in polymer science in order to interpret microstructures, predict effects on properties, and derive the corresponding equations. One important topic in polymer science is the kinetics of polymerization reactions. Modeling polymerization reactions does not typically require a detailed knowledge of the organic chemistry involved, since most polymerization reactions fol low one of several motifs. For instance, in a typical stepwise growth polymerization, there are two monomer types such monomers. Each type B monomer will react with two type A monomers, and each monomer does not react with its own type. A stoichiometric reaction at high conversion will result in long polymer chains of alternating monomer types. A clas sic example of this reaction is the synthesis of polyester from a monomer with two alcohol groups and a second monomer with two carboxylic acid groups. Modeling the kinetics of the molecular weight development does not require knowing the details of the chemistry, except for knowing the aforemen tioned bonding rules. With these thoughts in mind, two polymerization simula tors were developed for two different polymerization types: stepwise growth and free-radical chain polymerizations. In these simulators, the details of the chemistry are neglected, and computer models of polymerization are created by POLYMERIZA TION SIMULA T OR WILLIAM M. CHIRDON University of Louisiana at Lafayette Lafayette, LA 44130 Copyright ChE Division of ASEE 2010 ChE classroom
Vol. 44, No. 3, Summer 2010 223 considering monomers as simple spheres of different types students to quickly obtain an understanding of how these po lymerization reactions occur and the differences between the two. For instance, at moderate conversions, the step-growth polymerization will result in a variety of oligomers, while the free-radical chain polymerization will result in a few long polymers along with unreacted monomers, as seen in Figure 1. An instructor can demonstrate these concepts more effectively and expeditiously with a computer simulation rather than with a blackboard. The simulators featured in this article are also convenient for instructors and institutions because they are free to use for academic, noncommercial purposes. TARGET AUDIENCE This simulator is an ideal tool for introducing polymeriza tion reactions or simply the concept of a polymer. It has been found to be useful for at least two student groups. First, this module has been found to be effective in a basic materials science/engineering class to introduce polymer materials. In polymers with the use of this simulator allows for the students to quickly develop an appreciation for what polymers are and how they are made. The full potential of the simulator, however, can be real ized in a graduate-level introductory polymers course, where basic polymer concepts and formulae can be quantitatively analyzed by the students by exporting their acquired data into spreadsheets. Students are likely to become more engaged in a class when there are live demonstrations of polymerizations,  or if they can use processing or characterization equipment themselves. These simulators offer much of the visual stimulus of a live demonstration with the convenience of a PowerPoint presentation, and they allow students to conduct their own simulated experiments. From the students perspective, the simulators represent an easier mechanism for learning the material that is more that this method of instruction allows students with different learning styles that are less receptive to lectures to grasp the key concepts by executing their own model experiments. Surveys conducted at the end of my graduate polymer students visualize and understand polymerization reactions section. Most professors have known some individuals who were rather lackluster students, yet they excel in more handson activities such as laboratory work, independent research, or future employment in industry. Similarly, instructors may ing in lectures may have a chance to excel if they are given an opportunity to perform their own model experiments and analyze the data that they collect. MOLECULAR SIMULA TION MODELS The simulators demonstrated in this paper were developed as an Etomica molecular simulation module. These modules are available online, coded in Java, and free for purposes of academic research and instruction. The modules are publicly available at
Chemical Engineering Education 224 In these models, the average speed of the particles is de termined by the system temperature. The temperature can be speeds to obtain the set temperature for the system. The user is able to set adiabatic or isothermal conditions and change the temperature while the simulation is running. This allows the students to see the effects of temperature on polymeriza tion reactions. The bond energy is also programmable, which affects both the strength of the bond and the heat released during reaction. Users can then monitor the numberand weight-average molecular weights, chain-length histogram, temperature, and conversion over time. STEPWISE GROWTH SIMULA TION Stepwise growth polymers are created by reacting at least two different monomer types. In the simplest case, there will be a type A and a type B monomer, where each monomer will react and bond twice with the other type but not its own type. Monomers that form two bonds are known as di-func simulation, but the monomers are given names for clarity. The type A monomers are di-functional alcohols, annotated as di-ols. The type B monomers are di-functional carboxylic acids, annotated as di-acids. Mono-ols and Mono-acids are mono-functional groups that act as end-capping agents. A tri-functional acid is also available as a cross-linking agent. The di-ols, di-acids, and cross-linking agents are represented as red, blue, and green dots, respectively. Using this simple model, a variety of basic concepts in stepwise growth polym erization can be demonstrated as discussed in the Student F R EE R A D I C AL CHAIN ADD I T ION S IMULA T IONFree-radical chain addition is an entirely different mecha nism of polymerization that has completely different reaction kinetics and results in a different distribution of molecular tion is known as the initiation step, where an initiator molecule forms free radicals. In this simulation, the initiator is consid ered to behave as a typical peroxide initiator, which splits to form two free radicals when heated. This simulation models each initiator as two particles that are not reactive when they energy, however, so that as the temperature is increased, more bonds are spontaneously broken by the thermal energy. When an initiator splits, it forms two free radical species, each of which can react with a monomer. Once the free radical reacts with a monomer, the formerly reactive particle permanently bonds to the monomer, which then becomes reactive towards other monomers, and the initiation step is complete. The initiation step results in the nucleation of a growing polymer chain and leads to the second stage in this polymer ization: propagation. In the propagation stage, monomers are added one by one to the growing chain. Each time a monomer is added, the radical (reactive) nature of the chain is passed to the newly added monomer so that the unit on the end is the only chemically active unit in the chain. The last stage of this polymerization is termination, where the propagation is terminated in one of two ways when the active ends of two propagating chains collide. In termination by combination, the active ends will bond with each other, effectively doubling the average molecular weight in this step. Alternatively, the chains can terminate by disproportionation, where the radical is transferred from one chain to the other, killing the reactiv ity of both chains and resulting in two polymer chains with the same average molecular weight as before the termination step. The probability of combination vs. disproportionation is an input parameter. STUDENT ACTIVITIES These computer simulations can serve to teach students over a range of levels from a sophomore materials science course through a graduate-level introduction to polymers. Since the detailed reaction mechanisms have been replaced by simple bonding rules, the level of chemistry included in objectives of the course. For a materials science course where the students have never been formally exposed to polymer science or organic chemistry, the details of the chemistry can be neglected and only the bonding rules of the monomers need to be discussed. This may be particularly advisable if the course includes a chemistry or chemical engineering. These simulations will is a polymer and how they are formed. After a demonstration in front of the class, which may take less than 30 minutes, the students should be able to describe how initiator concen weight of a polymer, the three basic steps of a free-radical chain polymerization, effects of termination mechanism on molecular weight, effects of temperature, the importance of stoichiometry in stepwise growth polymerizations, the effect of mono-functional groups, and the concept of gelation. These critical concepts can be covered quickly and effectively by using this simulation as a visual aid. After this brief tutorial, students will be better prepared for polymer work in under graduate research projects, industrial internships, or graduatelevel polymer courses. The students can then be referred to the website if they wish to learn more about polymerization reactions. The full potential of the simulation can be used in a graduatelevel polymers course. The simulations are not ideal for ad vanced graduate work or for research purposes since they are two-dimensional, contain a small number of molecules (with respect to the statistics of large numbers of polymers), and the
Vol. 44, No. 3, Summer 2010 225 however, makes the simulations ideal for illustrative purposes for an introductory polymer science or engineering course, because most of the fundamental polymer formulae still ap ply. The students can then use the simulations to collect their own data, copy the data to a spreadsheet, analyze the data, interpret the results, and discuss how their results agree or disagree with theoretical predictions. Students in a polymer science course should be able to quantitatively predict the results of the given polymerization from the concentrations of the reactants. For instance, in an unbalanced step-wise growth polymerization consisting of two di-ols for each di-acid monomer, a student should predict that the maximum number-average degree of polymerization thermore, the simulation would also help the student visual ize that while the number-average degree of polymerization should also be able to quantitatively predict the effect of mono-functional groups. The numberand weight-average molecular weights can be pasted into a spreadsheet, plotted as in Figure 2, and compared to theoretical predictions from the following equations.  Xn p Xw p p PD Ip 1 1 1 1 11 () where Xn Xw PDI, and p represent number-average degree of polymerization, weight-average degree of polymerization, polydispersity index, and conversion, respectively. In a free-radical chain polymerization, the students should for a polymerization reaction if the initiator-to-monomer ratio and termination mode are given. Gelation can be modeled by using the step-wise growth simulator. Gelation occurs when the polymer network reaches visualized with the periodic boundary condition by pressing functionality, f, is greater than two for a stoichiometric mixture of reagents, then gelation will typically occur at a high conversion. The critical conversion at which gelation predicted as pf c 1 1 2 for a large number of monomers in a stoichiometric, 3-D system.  Since the simulator features a relatively small number of monomers in a 2-D system for visualization purposes, however, this equation only works as an approximation. The effects of temperature on the polymerization can also be observed. The simulations can be run under isothermal or adiabatic conditions, and students can plot the conversion over time for both conditions. Under adiabatic conditions, the heat of reaction will raise the temperature during the polymerization reaction, resulting in faster reaction rates. In the stepwise growth simulator, however, the reactions are reversible, so the larger temperatures generated in the reaction molecular weight. This auto-acceleration is a real effect as is the thermal degradation which can result at high temperatures. One unrealistic aspect, however, is that the thermally broken polymer chains are able to reform bonds. In reality, thermally degraded polymers typically result in chain ends that are not reactive with monomers or other polymer ends. A student can copy the conversion data over time by rightclicking on the plot and then pasting the data into a spreadsheet where the reaction rate kinetics can be analyzed. A reaction rate equation for the consumption of monomer can be pro posed such as dM dt kM n where M, t, k, and n are the monomer concentration, time, rate constant, and order of reaction, respectively. The student can perform his/her own analysis to then determine the values for the rate constant and the order of reaction. The student can also investigate the effect of temperature on the rate constant. 18 0 0.5 1 1.5 2 2.5 3 3.5 00.050.10.150.188.8.131.520.40.450.5 Conversion Degree of Polymerization Xw Xw(theory) Xn Xn(theory) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 0.050.10.150.184.108.40.2060.40.450.5 Conversion Polydispersity Index PDI PDI(theory) Figure 2 a) Simulation results for number and weight-average degrees of polymerization plotted vs. conversion and compared to theory. b) Polydispersity index of simulation plotted vs. conversion and compared to theory.
Chemical Engineering Education 226 Acid catalysis causes the reaction order for many stepwise  Since acid cataly sis is not included in the simulation mechanism, however, a second-order reaction is expected, which has a solution of the form: 11 0 MM kt where M 0 is the initial monomer concentration.  From this equation, k can be readily calculated by taking the slope of 1/M plotted over time as shown in Figure 4a. A model of assuming a reaction order. For a multidisciplinary polymer engineering course, a minimum amount of organic chemistry may be included in the I remind the students that alcohols react with carboxylic acids to form esters, which leads to showing how a di-ol and a diacid can react to form a long chain of polyester. At minimum, this amount of chemistry is required to understand polymer understanding what a polyester is and how it is made without should similarly be able to identify common polymers and the types of monomers used to synthesize them. This will help the students become conversant in polymer terminology so that they may better comprehend research papers and presentations relevant to polymers later in their careers. In a graduate-level polymer chemistry course with an organic chemistry prerequisite, the chemistry mechanisms would be an essential element of the corresponding lectures. In such a course, the students might be asked to critique this 19 a) b) 20 y = 0.0021x + 0.0103 0 0.005 0.01 0.015 0.02 0.025 1 2 3 4 5 Time (picoseconds) 1 / (Number of unreacted bonds) 0 10 20 30 40 50 60 70 80 90 100 12345 Time (picoseconds) Number of unreacted bonds Simulation 2nd order fit Figure 3. a) Simulation of gelation caused by tri-function al monomers. b) View of the simulation with the periodic boundary condition showing 3 3 unit cells. Note that the chain continues from one unit cell to the next and is of innite size after gelation. Figure 4. a) The inverse of the number of unreacted monomer bonds is plotted vs. time to nd k. b) The tted reaction constant can be used to compare the 2nd order kinetics equation to the simulation data.
Vol. 44, No. 3, Summer 2010 227 polymerization model by discussing some of the unrealistic instance, the students may predict how the removal of the affects the order of the reaction. An instructor might also explain how polymer chains may thermally degrade through a beta-scission mechanism or discuss other unfavorable side reactions. RESUL TS The use of these simulations had a positive impact on the effectiveness of instruction. As an instructor, I found this was an enjoyable variation from the usual PowerPoint and chalkboard lectures. The students welcomed this change in the medium of instruction even more so. This alternation in medium alone can help an instructor avoid Death by Pow  Furthermore, the lated experiments, analyzing their own data with spreadsheets, and performing the critical thinking required to interpret the results and compare them to theoretical predictions. Incorpo rating these tasks is also valuable for achieving accreditation outcomes and improving course evaluations. that some theoretical equations will work exactly, some ap proximately, and others not at all due to the assumptions and approximations of the model and how it fails or succeeds in representing reality. One unrealistic aspect of the simulation is that all of the monomers in the simulation were given a molecular weight of 1 g/mole. Therefore, the degree of po lymerization is equal to the molecular weight. This was done for the sake of simplicity; however, it was found that it could be confusing to the students when the terms degree of po ably. Emphasizing this caveat early in the introduction of the work as approximations in this simulation. Equations derived based strictly on stoichiometry and extent of conversion should work exactly, however. Allowing students to predict which equations will work or fail with this model exercises their critical-thinking skills and will give them a deeper un derstanding of the equations and their implied assumptions. Beyond my anecdotal observations, an anonymous survey consisting of 49 questions (38 multiple choice and 11 open response) was taken by an independent party to evaluate the effectiveness of this model for the CHEE 417(G): Polymer the questions is shown in Table 1 for brevity. The class only had seven students, which is excellent for instruction and discussion, but poor for survey statistics even with all seven students responding. Regardless, the feedback was very positive for all of the students. The survey data for the ques tions in Table I was collected again in the Fall of 2009 with 12 out of the class of 18 students responding with similarly positive results. In addition to the quantitative survey data, the students were asked open-ended questions regarding the simulation and its implementation. These results were similarly favor able. Many of the students found the simulations aided their ability to visualize the polymerization reactions and found the simulator easy to use. Some students also appreciated the opportunity to practice spreadsheets skills in the analysis of the kinetics. While most students found the interface easy to understand and use, especially with the supporting documen tation and examples on the website, it was recommended that the instructor take time at the start to explain the features to be controlled using the interface. Some students have suggested T ABLE 1 Survey Results of the Simulation Module for CHEE 417(G): Polymer Engineering # Statements Fall 2008 Average Fall 2009 Average 1 The computer simulation was an effective use of my time. 4.14 4.25 2 4.43 4.50 3 This simulation was a valuable experience. 4.43 4.25 4 This computer simulation allowed me to study a problem in a way not possible with a conventional experiment. 4.14 4.13 5 The use of this module aided in my understanding of the material. 4.43 4.08 6 I believe this module should be used next year. 4.71 4.25 7 The use of this simulation module was a valuable use of class time. 4.43 4.00 8 The content covered in the simulation was appropriate to the course. 4.71 4.17 9 The computer simulation provided me insights I had not had before. 4.29 4.25 10 I feel the computer simulation was effective in increasing my understanding of molecular motion. 4.29 4.25 are shown.
Chemical Engineering Education 228the model should be more complex, featuring more realistic chemical mechanisms, larger numbers of monomers, and mak ing the simulation three-dimensional. This would necessarily make the simulator more complicated to setup and slower to run, however. There was a fair balance of comments that the simulator was too simplistic vs. being too complicated to set up, which seems to indicate that a good balance has been achieved for students at this level. A trial version of a 3-D simulator was partially developed, but it was not used, because the molecules and interactions were harder to see, even though it was more aesthetically impressive. Some students would prefer the assignments be assigned to small groups; however, an equal number of students pre ferred working individually. Running multiple simulations to high conversions can take a considerable amount of time, so allowing data sharing among groups might be a reasonable option if large take-home projects are assigned. Instructors, as in any experiment or assignment, are advised to conduct the simulations themselves before assigning them to make sure that the time demands are reasonable and that the expected results are produced. This simulator was primarily used in individual take-home assignments to ensure that each student had an equal opportunity to use the simulator and received an individual assessment of their work. The ability to work in teams is an important career skill and accreditation outcome, however, and this could be an opportunity to implement a team-based project in a polymer course. CONCLUSIONS strations, and laboratory experiments. Unfortunately, many of these course supplements are not implemented due to the mate rial cost, preparation time, safety considerations, or laboratory space required. The simulations presented here allow students as they set experimental parameters, collect and analyze data, exercise spreadsheet skills, and then interpret their own results. The only investment required is a small amount time by the instructor to become familiar with the simulator and to make sure that the students have access to a computer. Overall, the simulations were found effective in explaining the fundamentals of polymerization in a 30-minute demon stration for a materials science and engineering course. The simulations were also successful for teaching a polymer engineering graduate course over the course of the month in which lecture topics, demonstrations, and assignments were conducted and reviewed using the simulations and spreadsheets. An instructor can use these simulators as a brief qualitative introduction to polymer science or as an opportu nity for rigorous derivation, analysis, and testing of polymer equations, or any intermediate between these extremes that ACKNOWLEDGMENTS The development of this and other molecular-simula tion-based education modules  was supported by grant DUE-0618521 from the National Science Foundation to the CAChE (Computer Aids for Chemical Engineering) Cor poration.  The author proposed the polymerization module including the basic algorithm and developed the supporting documentation. Prof. David Kofke of the University at Buf falo manages the module development project with algorithm implementation and coding provided by Dr. Andrew Schultz. Additional software support has been provided by Robert Rassler. Phil McLaury conducted the assessment of the simulation under the supervision of Prof. George Bodner of Purdue University. REFERENCES 1. Painter, P.C., and M.M. Coleman, Fundamentals of Polymer Science 2nd Ed., Technomic Publishing, Pennsylvania (1997) 2. Sperling, L.H., Introduction to Physical Polymer Science 4th Ed., Wiley-Interscience, New Jersey (2006) 3. Odian, G., Principles of Polymerization 3rd Ed., Wiley-Interscience, New York (1991) 4. Sun, S.F., Physical Chemistry of Macromolecules Wiley-Interscience, New York (1994) 5. Noggle, J.H., Physical Chemistry HarperCollins Publishers, USA (1989) Chem. Eng. Ed. 39 (1), 28 (2005) 7. Etomica: Molecular Simulation API,
Vol. 44, No. 3, Summer 2010 229EHRENFESTS LOTTERY TIME AND ENTROPY MAXIMIZA TIONHENRY S. ASHBAUGH Tulane University New Orleans, LA 70118 Copyright ChE Division of ASEE 2010 The conservation of energy dictated by the First Law of Thermodynamics is an intuitively appealing concept. Simply put, energy is neither created nor destroyed, but is just transformed from one form to anotherkinetic energy transformed into potential energy, electrostatic energy transformed into gravitational energy, etc. The challenge of applying the First Law of Thermodynamics then reduces to an accountants job, maintaining a balance sheet for energy in its different forms. Tracking down apparent discrepancies having played a vital role in the development of relativity, quantum mechanics, and particle physics. Despite the power of the First Law, it does not tell us how systems change with time when they are freely allowed to evolve ( e.g. a locking pin is removed from a piston or an ice cube is placed in a hot (the piston moves to equate pressures and the ice cube melts). to determine equilibrium. Thermodynamic equilibrium is determined by the intro duction of the concept of entropy, which unlike the energy is not a conserved property but obeys a maximization principle encapsulated by the Second Law of Thermodynamics. Ac cording to this law, the entropy change of an isolated system is greater than or equal to zero for any spontaneous process, and the entropy is maximized at thermodynamic equilibrium. tion by equating time spontaneously moving forward as the direction in which entropy increases. In difference to other natural laws which are time reversible, like Newtons laws of motion, the arrow of time is unique to the Second Law of Ther modynamics. Indeed, it has been asserted that all phenomena that behave differently in one time direction can ultimately be linked to the Second Law of Thermodynamics.  It is usually at this point in an introductory thermodynamics class that reversible and irreversible processes are introduced, and the differential change in entropy (dS) is equated with the reversible heat that crosses a closed systems boundaries (dQ rev) divided by the absolute temperature (T), dS dQ T re v ( ) 1 following Clausius historical development. While this clas sical statement of the entropy change is true, the connection amount of time to complete and real observable changes abstract. To help solidify this concept, it is helpful to provide physically motivated examples of the entropy in action and the approach to equilibrium. From his studies of gas dynamics and equilibrium, Ludwig Boltzmann proposed an alternate entropy formulation that draws connections between macroscopic observables and the ChE Why dont you call it entropy? ... no one understands entropy very well, so in any discussion you will be in a position of advantage. John von Neumanns name suggestion to Claude Shannon for missing information in information theory. 
Chemical Engineering Education 230 molecular nature of matter. Boltzmanns entropy formula, Sk ln ( ) 2 is famously engraved above his bust at his grave marker in Vienna.  The macroscopic entropy in this expression is iden A is Boltzmanns constant, and is equal to the ratio of the ideal gas constant to Avagodros number. Interestingly from a historical point of view, Planck was the problem, building upon Boltzmanns earlier work on the con nections between entropy and probability.[4, 5] Following Eq. (1), Boltzmanns entropy formula directly links the addition of heat to an increase in the number of accessible molecular states. Boltzmanns entropy formula underlies the popular conceptualization of entropy as disorder or randomness. A literal interpretation of entropy as disorder can be problematic, however, due to gut feelings of what constitutes disorder,[6, 7] and alternate interpretations that equate entropy with energy dispersal.  empirical, resting on its predictive power. A better understanding of the Second Law of Thermo dynamics necessarily requires students to work through examples and thought experiments. To familiarize students with the connections between their personal expectations for equilibrium and maximization of the entropy with increas ing time, I describe a series of games that can be played out in class or on a computer. The student assumes the role of a Bingo-like caller transferring numbered marbles between urns based on the outcomes of spins of a lottery wheel. The relationships between entropy, time ( i.e. spins of the wheel), and increases in the number of states are shown to be applicable to engineering concepts like diffusion and the derivation of equations-of-state. By establishing entropy maximization in terms of familiar concepts, I hope to form a stronger foundation for explaining the connection between the Second Law of Thermodynamics and equilibrium, and show how this principle pervades problems outside the traditional thermodynamics curriculum. EHRENFESTS LOTTERY Paul and Tatiana Ehrenfest proposed a simple thought experiment to explore the connections between probability, entropy, and time.  The experiment is played out as a lottery obeying the following rules (Figure 1): You are given two urns and N sequentially numbered 1 remaining n 2 wheel is spun, randomly producing a number between 1 and N. The randomly selected marble is then located, taken from the urn it is in, and placed into the other urn. The wheel is then spun again and the process is repeated On the molecular level the marbles can be thought of as repre senting individual gas molecules, while the urns correspond to discrete volume units. While the correspondence between the lotterys random-transfer dynamics and molecular motions may appear tenuous, this model has been shown to provide an accurate description of gas mixing.  After describing the lottery, the class may already have a number of intuitive expectations about the evolution of urn occupancy trends, including: number of marbles in both urns will average N/2. 2) The relative time sequence of different occupational states can be, roughly, worked out given the number of marbles in each urn. For example, say you are told N = n 1 = 100 marbles, and that at one point in the spin sequence there are n 1 = 47 and n 2 = 53 marbles distributed between the urns, while at another point there are n 1 = 84 and n 2 = 16 marbles in the two urns. It is most reasonable to expect the sequence. fair game so that each marble has a 50/50 chance of being in either urn. The second expectation, while perfectly reason able, is not as easy to justify based only on gut feelings. In the long time limit, the probability distribution of urn occu pational probabilities approaches a binomial distribution. For large N, the binomial distribution is sharply peaked about the 50/50 occupational probability, but it does not rule out the observation of a heavily skewed distribution such as 84 and a well-mixed system is approximately 10 -12 These skewed distributions become exceedingly rare with increasing N, so that in practice they can be neglected. We note that this omission provides a potential entry for Maxwells demon to wreak havoc, getting usable work by waiting for unlikely events. While outside the scope of this article, it may be useful to segue into a discussion of Maxwells demon after introducing Ehrenfests lottery.  The relationship between Boltzmanns entropy and the urn occupational states can be evaluated by counting the number of ways of randomly choosing n 1 marbles to be placed in urn 1 and n 2 of the individual marbles. To calculate the number of ways of divvying up the marbles between the two urns we draw a hypothetical random sequence of all the marbles, and then 1 marbles in urn 1 and the remaining n 2 marbles in urn 2. The number of ways of arranging all the marbles in a random sequence is N! following standard combinato 1 marbles are in each urn but not their identities. The number of ways of
Vol. 44, No. 3, Summer 2010 231 choosing n 1 marbles to be placed in urn 1 is therefore over counted by the number of ways of randomly selecting this subset of marbles, n 1!. A similar over counting holds for the marbles designated for urn 2. The number of ways of randomly dividing n 1 and n 2 marbles between the two urns is then N nn !! .( ) 12 3 A perceptive student may notice that Eq. (3) implies that each marble is indistinguishable from one an other, but in fact we have indicated that the marbles are numbered from 1 to N. When the marbles are dis tinguishable the number of ways of urn is exactly one. For example for a 4-marble system we could specify urn and marbles 2 and 3 are in the second, and there is only one way to achieve this distribution. The numbering scheme, however, is only a matter of convenience for the purpose of choosing a marble to move, and we are free after each spin to renumber the marbles for the next spin without changing the probabilistic distribution of marbles in the lottery. So, returning to our 4-marble example we could renumber the marbles 1 and 2 in the game. From the games point of view, only the number of ways of distributing the n 1 and n 2 marbles matters, not the numbered identities of the individual marbles. The same can be said for mixing identical molecules in a volume, where only separations manipulating the vastly smaller number of macroscopic thermodynamic state variables like temperature and pressure.  substituting Eq. (3) into Boltzmanns entropy formula, yielding Sk N nN kn n N n n N ln !! ln ln 12 1 1 2 2 ( ) 4 mation, i.e. ln XX XX !l n  When all the marbles reside entirely in either urn 1 or 2 (n 1 is zero. When the marbles are evenly distributed between the urns (n 1 2 entropy is a maximum and equal to that S max entropy is a monotonically increasing function. The expectation that the entropy of the system increases on average with each spin of average change in the entropy as the result of a lottery spin is determined by summing over all possible transfer moves the probability of choosing to transfer a marble from one urn to the other ( i.e. p(urn1 urn 2) or p(urn 2 urn 1) multiplied by the change in the entropy associated with each move ( i.e. Su rn ur no ru rn ur n 12 21 ) S pu rn ur nS ur nu rn pu rn ur nS 12 12 21 u ur nu rn 21 5 .( ) The angled brackets, denote an average. The probability of choosing to move a marble from an urn is equal to the number of marbles in that urn divided by the total number of marbles, e.g. p(urn 1 1/N. Expanding Eq. (4) in terms of n 1 and substituting into Eq. (5), an accurate expression for the average change in the entropy between successive spins of the wheel can be derived, S k nn N n n 12 1 2 0 6 ln ( ) This average entropy change is positive when the occupation numbers differ and approaches zero as the occupations of each urn approach one occupational state about the equilibrium average. Starting with n 1 the outcomes for two independent, random lotteries simulated using MAT LAB As the game plays out, the number of marbles in urn 1 decreases for occupational state (Figure 2a). The entropy concurrently increases as the marbles become more evenly distributed between the urns (Figure 2b). The the stochastic nature of Ehrenfests lottery. The relative magnitude of these -1/2 in accordance with the central 2 9 6 1 5 7 8 10 3 4 4 9 3 5 2 6 7 1 10 8 urn 1 urn 2 Figure 1 Figure 1. Schematic illustration of the two-urn lottery with 10 marbles.
Chemical Engineering Education 232 limit theorem, so that on a per-marble basis excursions from the average diminish as the number of marbles increases (Figure 3). For a macroscopic number of molecules/marbles are manifested experimentally in measurable quantities like the heat capacity and isothermal compressibility.  While the 50/50 state, these deviations are manifested as spontaneous decreases in the entropy below the maximum value (Figure entropy point to the statistical nature of the Second Law of Thermodynamics. In particular, the Second Law of Thermo dynamics is more appropriately thought of as a statement about the equilibrium distribution rather than a property of a single snapshot of molecular positions.  The average urn occupancy can be solved analytically from a master equation for the discrete lottery spin dynamics. Given an average of ns 1 marbles are in urn 1 for spin s, the prob ability a marble in urn 1 is chosen to be moved into urn 2 is the number of marbles in urn 1 divided by the total number of marbles. Similarly, given ns 2 marbles are in urn 2, the probability a marble in urn 2 is chosen to be moved into urn 1 is ns N 2 The change in the average occupancy of urn 1 between spin s and s+1 is the probability a marble is added to urn 1 less the probability one is taken away, ns ns ns N ns N ns N 1 1 2 1 1 1 12 7 .( ) The long time equilibrium state for which the average occupancy does not change between successive spins, ns ns 1 1 1 0 is ns N 1 2 8 ( ) as expected for a fair lottery. Conservation of the number of marbles dictates the average occupation of urn 2. For an initial occupation of 0 n 1 (0) N in urn 1, the solution of Eq. (7) yields ns N n N N 1 1 2 0 2 1 2 s .( ) 9 by back substitution. The occupation dynamics and entropy evolution described by Eq. (9) are compared to the simulated example discussed in Figure 2. The agreement between the random lotteries and master equation results is excellent, al since it only describes the mean behavior. A PPLI C A T ION T O M UL T IPL E U RNS A M O DE L FOR DIFFUSION Ehrenfests lottery can be extended to an arbitrary number of urns numbered from 1 to i max. In difference to the twourn lottery, the marbles are moved following the spins of moved as in the two-urn game. The second wheel chooses whether the marble is moved to the urn above or below the starting urn in the sequence, i.e. from urn i to either urn i+1 the sequence, i.e. from urn 1 to urn 0 or from urn i max to urn i max+1, the marble is returned to its starting urn. The combinatorial counting of states described by Eq. (3) can be extended by replacing the denominator with the product of factorials of the occupancy of each urn. The entropy in this case is Sk N n kn n N i i i i i i i ln ln ,( ) ma x ma x 1 1 10 where Stirlings approximation has again been used to sim plify the factorials. It is worthwhile to consider the limits of Eq. (10) to assure ourselves the entropy follows intuitive expectations for the marble distribution as the lottery is played out. When all the marbles sit in urn j, substituting n j n ij 0 into Eq. (10) there is only one way to achieve this distribution and the entropy is zero. In the other extreme, the entropy is maximized when the occupancies Figure 2 Figure 2. Outcomes of two random simulations of the two-urn lottery with 100 marbles and the master equation description of the mean behavior. Plots a and b show the occupation of urn 1 and the entropy, respectively.
Vol. 44, No. 3, Summer 2010 233 of each urn are the same and equal to N/i max  The entropy maximum in this case is S max max, which is a generalization of the entropy maximum obtained for the two-urn lottery where i max While a derivation of the mean change in the entropy, S following each spin is more involved for the multi-urn lottery, each spin of the lottery wheel results in an exchange between only two urns. The mean entropy change is then expected to follow an equation comparable to Eq. (6). The entropy of the multi-urn lot tery should therefore increase as the game is played out following the same logic as for the two-urn lottery. Figure 4 shows the outcome of a multi-urn game with i max the lottery is played out, and the marbles disperse among the remaining urns (Figure 4a). After approximately 10,000 spins, the distribution of marbles is essentially uniform and equilibrium is attained within the statistical tuations about the occupation averages decrease as the number of marbles in the game increases. The entropy of the lottery increases as the game is played, and ap pears to asymptotically approach the equilibrium value of S max the equilibrium occupational state where all urns have of marbles ( e.g. to be evenly distributed between all the urns is lower for the multiurn case than compared to the two-urn lottery, resulting in entropies below the maximum when each urn has equal numbers of marbles. occupational state have a larger relative effect on the fractional oc cupations used to calculate the entropy [Eq. (10)] as the number of urns increases. These spurious deviations from the monotonic increase in the entropy dictated by the Second Law diminish as the number of marbles increases, in agreement with the two-urn lottery. A discrete master equation for the mean multi-urn occupation dynam ics can be developed analogous to the two-urn equation [Eq. (7)]. In the present case, the change in the number of marbles in urn i as the result of a lottery spin is equal to the probability a marble from either urn i-1 or i+1 is chosen to be added to ns ns N i i 1 1 2 less the probability a marble from urn i is removed, ns ns ns ns N ns i i i i i 1 2 1 1 N N .( ) 11 When a marble is chosen to move to an urn outside the sequence, max reduces Eq. (11) to ns ns ns N io ri io ri or i ma x m ax ma x 1 2 21 ns N io ri ma x .( ) 2 12 Figure 3 N = 4 N ( ) 1 / 2 2 = n 1 2 n 1 2 Figure 4 Figure 3 (above). Relative uctuation, / N, in the occupation number of urn 1 in the two-urn lottery as a function of the total number of marbles. Figure 4 (right). Results for a 10-urn lottery with all 100 marbles initially placed in the rst urn. Occupational distributions after s spins for a random lottery and by numerical solution of the master equation description are plotted in a and b, respectively. The calculated entropies are plotted in c.
Chemical Engineering Education 234 If the urns are considered as being evenly spaced apart paring Eq. (11) with Ficks Second Law in one dimension, nt Dn x 22 the change in the average occupation of urn i after the spin on the left-hand sign of the equals sign corresponds to a dimensionless time derivative, while the difference in mean urn occupations between neighboring urns on the right-hand side corresponds to a dimensionless spatial D x Nt 2 2 13 ( ) the number of marbles increases since the marbles are moved only one at a time, while molecules truly move simultane ously. Equilibrium is achieved for Eqs. (11) and (12) when the mean occupation of all the urns is the same, at which point the entropy [Eq. (10)] is maximized. This lottery can be readily generalized to multi-dimensional diffusion depending on the spatial arrangement of urns. The occupational distribution evolution predicted by Eqs. (11) and (12) and correspond ing entropies are shown in Figure 4. The agreement with the random lottery is excellent. A TECHNICAL ISSUE REGARDING THE CONVERGENCE OF THE TWO-URN LOTTERY It was recently pointed out that Ehrenfests two-urn lottery technically does not converge to the binomial distribution in between two distributions whose average is the binomial distribution.  Perhaps the simplest demonstration of this non-convergence is if we consider a two-urn lottery with a will be moved to urn 2, and subsequently relocated to urn 1 after the second spin. As the lottery progresses, the marble will oscillate back an forth between the urns, occupying urn 1 after even numbers of spins and urn 2 after odd numbers of spins. After an even number of spins then, the marble will occupy urn 1 with a probability of one and urn 2 with a prob ability of zero. Similarly, after an odd number of spins the marble will occupy urns 1 and 2 with probabilities of zero and one, respectively. The occupational probability distribution then has not converged to a single distribution, but vacillates between two distinct distributions. If the even and odd spin probability distributions are averaged, however, we obtain a 50/50 probability distribution as dictated by the binomial distribution for a single marble. The nonconvergence of the two-urn probability distribution can be alleviated by breaking the even/odd symmetry by intro ducing spin outcomes where no marbles are moved, thereby opening up the possibility of the marble in the example above of being found in urn 1 (2) after an odd (even) number of breaks the even/odd symmetry of the two-urn lottery, allow ing the occupational probability distribution to converge. The two-urn lottery could converge to a single distribution, rather than an average of even and odd distributions, by enforcing performing a second move direction determining spin. In practice, however, the nonconvergence of the two-urn lot tery does not have any practical consequences on the results presented in Figures 2 and 3, since they track the evolution of states of individual spin sequences.  RELA TIONSHIP T O THE IDEAL GAS LAW The long-time equilibrium of the multi-urn lottery provides an inroad for deriving the ideal gas law as an outcome of entropy maximization. From standard thermodynamic rela tionships, the equation of state follows from the derivative of the equilibrium entropy with respect to volume at constant internal energy and number of marbles (molecules), i.e. PT SV UN ma x As pointed out above, the equilibrium entropy of the multi-urn lottery is S max max. Based on the of marbles could potentially be placed in an urn, making the energy effectively constant. If each urn has the same volume, v urn, the total volume of the system is given by the product of max v urn. To this point I have not discussed the temperature, T, within the context of the lottery. Since the temperature is directly related to the average is inversely related to the time between spins. Based on these considerations, the pressure is given by the increase in the equilibrium entropy associated with adding another urn (volume) increment to the lottery while keeping the number of marbles constant, By establishing entropy maximization in terms of familiar concepts, I hope to form a stronger foundation for explaining the connection between the Second Law of Thermodynamics and equilibrium, and show how this principle pervades problems outside the traditional thermodynamics curriculum.
Vol. 44, No. 3, Summer 2010 235 PT S V T Si Si i ma x ma xm ax ma xm ax ma x 1 1 v vi v kN T Vv v ur n u rn ur n ur n ma x ln ln ln V v v kN T Vv V ur n ur n ur n v kN T V nR T V ur n ( ) 14 A is the number of marbles/molecules in mole units. Thus, the ideal gas law follows from the dispersal of marbles among a collection of urns. Non-ideal contributions to the equation-of-state arise from the introduction of energetic interactions between marbles, e.g. excluded volume and dispersion interactions, which temper the urn occupancies. PROGRAM A VAILABILITY simulation. I have uploaded the MATLAB  This pro gram simulates the twoand multi-urn lotteries, solves the master equation spin dynamics, calculates entropies, and plots the results. DISCUSSION Ehrenfests Lottery can be used at multiple points throughout the thermodynamics curriculum to reinforce the role of the Second Law of Thermodynamics in determining equilibrium and to highlight the molecular nature of substances. In practice, ics class at Tulane University. The multi-urn lottery and the connection to the ideal gas law are introduced further along in the semester once thermodynamic partial derivative relationships have been discussed. I return to the multi-urn lottery in our second-semester thermodynamics class after our students have had transport phenomena to connect diffusion processes to the Second Law. This model can be readily extended to ideal mixing and the van der Waals equation of state by introducing between marbles in neighboring urns (van der Waals). An alternate formulation of this model, referred to as the Dog and Flea model, has also been developed to further explore transport phenomena for small systems and chemical reactions.  While not a panacea, Ehrenfests lottery provides a simple model that, when used in conjunction with other illustrative examples like the Carnot cycle, can shore up student appreciation of the Second Law of Thermodynamics. REFERENCES 1. Avery, J., Information Theory and Evolution 2.
Chemical Engineering Education 236 P subject with which many students never become fully comfortable. It is our opinion that the Gibbsian geo metrical framework, which can be easily represented in Excel spreadsheets, can help students to gain a better understanding of phase equilibria using only elementary concepts of high school geometry. Phase equilibrium calculations are essential to the simula tion and optimization of chemical processes. The task with these calculations is to accurately predict the correct number of phases at equilibrium present in the system and their com positions. Methods for these calculations can be divided into two main categories: the equation-solving approach (K-value method) and minimization of the Gibbs free energy. Isofugac ity conditions and mass balances form the set of equations in the equation-solving approach. Although the equation-solving approach appears to be the most popular method of solution, it does not guarantee minimization of the global Gibbs energy, which is the thermodynamic requirement for equilibrium. This is because isofugacity criterion is only a necessary but global Gibbs free energy can be equivalently formulated as the stability test or the common tangent test. The Gibbs stability condition is described and has been used extensively in many references.[1, 2] It has been more frequently applied in liquid-liquid equilibrium rather than vapor-liquid equilibrium calculations. Gibbs showed that a composition is that the Gibbs energy of mixing (g M) curve at no point be below the tangent line to the curve at the given overall composition. This is the case with the binary system in Figure 1(a); it is homogeneous for all compositions. The g M vs. composition curve is concave down, meaning that no split occurs in the global mixture composition to give two liquid two different points on the g M curve sharing a common tangent line. In contrast, the change of curvature in the g M function as shown in Figure 1(b) permits the existence of two conju gated points (I and II) that do share a common tangent line and which, in turn, lead to the formation of two equilibrium liquid phases (LL). Any initial mixture, as for example z i in g M curve, is intrinsically unstable (d 2 g M / dx i 2 <0) and splits VAPOR-LIQUID EQUILIBRIA Copyright ChE Division of ASEE 2010 ChE MARA DEL MAR OLAYA, JUAN A. REYES-LABARTA, MARA DOLORES SERRANO, ANTONIO MARCILLA University of Alicante Apdo. 99, Alicante 03080, Spain
Vol. 44, No. 3, Summer 2010 237 into two liquid phases having compositions x i I and x i II and a lower value for the overall Gibbs energy of mixing (M
Chemical Engineering Education 238 For liquid mixtures the ideal Gibbs energy of mixing (di mensionless) is gx x id L i i i ln () 5 where the reference state for each component i is the pure liquid at the temperature and pressure of the system. Many equations have been proposed to model the excess Gibbs energy and can be found in the literature. For example, the van Laar equation for binary systems: g AA xx Ax Ax EL () 12 21 12 12 12 12 6 where A 12 and A 21 are the binary interaction parameters of the model that must be obtained by equilibrium data cor relation. Guess parameters i p i 0 i i P x p y i i 0 i i 1 y n 1 i i END no yes Guess T b i ) ) T (T ) y (y ( Min NP 1 k 2 i exp i NP 1 k n 1 i 2 i exp i no yes Figure 3. Flowchart for the calculation of the activity coefcient model parameters by equilibrium data regres sion. The discontinuous line represents the algorithm for the bubble point equilibrium calculations. This activity is framed in the subject of Principles of Separation Processes in Chemical Engineering in a fourthconsists of: a) A lecture of the theoretical fundamentals of VLE, presen tation and analysis of T-x,y diagrams and sketch of Gibbs stability criterion. b) A guided classroom solution of different VLE problems non-azeotropic VLE binary system, and consequent solu tion of a binary homogenous azeotropic mixture, where students work on their own computers using Excel and Matlab. c) Development of a project in groups of students where an analogous analysis of VLE, but also of LLE, must be done for a heterogeneous azeotropic binary mixture. d) As optional projects, VLE for ternary or more compli cated mixtures could also be considered, but the visual ization becomes more complicated. THEORY The equilibrium condition for component i being simultane ously present as a liquid and vapor equilibrium phase can be written as the isofugacity condition ff i v i L () 1 i V ii oL i oL i c P P Py p v RT dP i o ex p ii x( ) 2 where i v the total pressure, y i and x i are the molar fractions of compo nent i in the vapor and liquid phases, respectively, p i oL is the vapor pressure of component i, i oL i is the activity v i c is the molar volume of the condensed phase as a function of pressure. The exponential correction is the Poynting factor which takes into account that the liquid is at a pressure P different from the liquid saturation pressure p i o At moderate pressures, i v i oL and the Poynting factor are near unity, and Eq. (2) can be rewritten as Py px ii o ii () 3 The constant pressure T-x,y diagram can be obtained by calculating the bubble temperatures (T b) of the various liquid mixture compositions (x i), and also by calculating the compo sition of the equilibrium vapor phase (y i). The calculation is On the other hand, the Gibbs energy of mixing (dimension less) is the sum of two contributions, the ideal and excess Gibbs energies: gg g Mi dE () 4
Vol. 44, No. 3, Summer 2010 239 Substituting Eq. (5) and Eq. (6) into Eq. (4), and consider ing the selected reference state, the expression obtained for the Gibbs energy of the liquid phase at the temperature of the system T is: gT gx xx x AA xx Ax L M L ln ln 11 22 12 21 12 12 1 12 12 7 Ax () The vapor phase is considered ideal and, therefore, the following equation is used for the Gibbs energy of mixing of the vapor phase: gg yy yy MV id V ,, ln ln () 11 22 8 To compare Gibbs energy curves for liquid and vapor phases both must be obtained from a common reference state. For VLE calculations at constant T and P a convenient reference state is the pure component as liquid at the same T and P of the system. In this case, the Gibbs energy of pure component i in the vapor and liquid phases are g i oV 0 and g i oL 0 respectively. The difference in the Gibbs energy between a pure vapor and a pure liquid can be approximated using the following equation: gg P p i oV i oL i o ,, ln () 9 Consequently the following equation is used for the Gibbs energy of the vapor phase, referred to the liquid aggregation state at the temperature of the system T: gT yg yg yy yy V o V o V 11 22 11 22 10 ln ln () According to Eq. (9), the sign of g i oV may be positive or negative; depending on the ratio between the total pressure of the system and the vapor pressure of component i, which, in turn, depends on the temperature: If Pp gg g If i o i oV i oL i oV ,, 0 is positive P Pp gg g i o i oV i oL i oV ,, 0 is negative After both the g V and g L isotherm curves have been calcu lated and represented, the Gibbs stability or common tangent plane test can be easily applied to them to ascertain which phases are most stable and what the equilibrium composi tions are. at constant T and P can be selected to be the liquid state at the temperature of the system for both components in both phases. If Gibbs energy surfaces for both p phases are gener ated to analyze the equilibrium as a function of temperature T, however, a reference state must be used in the calculations at a unique temperature T 0. gT gT RT Sd T RT Vd P p p T T P P 0 1 1 11 0 0 () For non-isothermal VLE, however, the Gibbs energy for both p phases (V and L) must be calculated as a function of temperature T using a reference state ( i.e. the pure liquid) at a unique reference temperature T 0 g p (T 0). In this case, the Gibbs energy for both vapor and liquid phases includes an entropic term from T 0 to T. For isobaric conditions, Eq. (11) becomes: gT gT RT Cp T dTdT p p T T L T T 0 1 12 00 () where Cp L is the heat capacity of the liquid. In the above expression g p PROBLEM ST A TEMENT For the binary homogeneous azeotropic system ethanol (1) + a) Calculate the parameters for the selected thermodynamic model regressing T-x,y experimental data. b) Build the temperature vs. composition (T-x,y) diagram with an Excel spreadsheet. c) Represent graphically in a 3-D diagram (for example, us ing Matlab) the g (vapor and liquid) vs. composition and temperature surfaces for this system. g curves in Excel for the vapor and liquid mixtures of the phases present and their compositions must be deduced using the Gibbs common tangent test. e) Show that the results obtained using the Gibbs stabil ity criteria are consistent with those obtained using the T-x,y diagram. The Van Laar equation can be used to represent the excess Gibbs energy (g E i) of the liquid mixtures. The vapor phase can be considered as ideal. SOLUTION The A ij parameters for the Van Laar model [Eq. (6)] calculated for the ethanol (1) + benzene (2) binary system [8-10] according to shows an example of the possible spreadsheet distribution to obtain the model parameter values and the T-x,y diagram by successive bubble temperature calculations with Solver function in Excel using various liquid mixture compositions (x i) and calculating the equilibrium vapor phase composi tion. The parameter values obtained are A 12 A 21 homogeneous azeotropic point occurs for this system at a minimum boiling temperature.
Chemical Engineering Education 240 Figure 5 shows the 3-D graph used to represent the Gibbs energy surfaces of the liquid (g L) and vapor phases (g V) as a function of temperature and composition. The selected refer ence state for each one of the components is the liquid state at the azeotrope boiling point (T 0). The Gibbs energy surfaces for L and V have been calculated using Eq. (12) where g P(T) is calculated with Eq. (10). The values for g i oV are calculated with Eq. (9), where the vapor pressures for ethanol and ben zene have been obtained using the Antoine equation, with the constants given in Table 1.  The entropy changes of Eq. (12) are calculated with Cp L(T) given in Table 2. As can be seen in Figure 5, the g surfaces cross each other so that the vapor phase is the stable phase at high temperatures (g V lower than g L) and the liquid phase the stable aggregation state at lower temperatures (g L lower than g V). For a more detailed Figure 6 shows the Gibbs energy curves plotted for the vapor and the homogeneous liquid mixtures at each one of these temperatures. After students have completed these representations, an analysis of Figure 6 is done, taking into account the Gibbs stability criteria: p o 2 < p o 1 ; therefore, taking into account Eq. (9), g i oV < g i oL V vs. composition curve is lower than g L [Figure 6(a)], showing that the vapor phase is the stable aggregation state over the entire composition space at this temperature. p o 2 p o 1 ; therefore, for the ethanol component, g oV 1 < g oL 1 but for benzene, g oV 2 > g oL 2 The g V and g L curves have two points sharing a common tangent line, corresponding to the VL equilibrium y 1 and x 1 1 the liquid is the stable aggregation state, and at values higher than z 1 [Figure 6(b)]. Any global mixture between those values will split in the VLE. p o 2 < p o 1 g oV 2 > g oL 2 for both ethanol and benzene components. Two regions of the g V and g L curves each contain one point of VL equilibrium: [y 1 1 1 x 1 Figure 4 (right). Spreadsheet ex ample of the Van Laar parameters calculation re gressing T -x,y ex perimental data for the ethanol (1) + benzene (2) binary system at P=760 mmHg. Figure 5 (below). Gibbs energy surfaces for vapor g V (ideal) and liquid g L (Van Laar) mixtures as a function of the temperature and composition for the ethanol (1) + benzene (2) binary system at P=1 atm.
Vol. 44, No. 3, Summer 2010 241 the conjugated y-x equilibrium compositions, as can be seen in Figure 6(c). The vapor is the stable aggregation state at in termediate concentrations and the liquid is the stable phase near each pure component. The g V curve rises as the tem perature decreases until the azeotropic temperature (68.01 V and g L curves are tangent in one point [Figure 6(d)]. This point corresponds to the homo geneous azeotrope, for which the vapor and liquid phases in equilibrium have identical compositions (y 1 1 L curve lies below the g V curve over the entire composition space, demonstrating that a homoge neous liquid phase is the most stable aggregation state for any global mixture composition [Figure 6(e)]. It must be highlighted that all of the above, deduced from the Gibbs energy curves, is obviously consis tent with the T-x,y diagram shown in Figure 4. Treatment of the VLE calculation using the Gibbs common tangent plane criteria provides stu dents with a deeper understanding of the problem, however, because the insight into the reasons for the V or L phase stability or the VLE splitting is much more evident than with using the isofugacity condition. Although solving the isofugacity condition together with the mass balance equa tions (K-value method) constitutes the most popular method of calculation, our experience has shown that the Gibbsian geometrical framework is a very useful tool for educational purposes. Students state that the geometric analysis of chemi cal equilibrium, with an available and easy to use program such as Excel, permits a clear understanding of the VLE split ting in terms of Gibbs energy minimization. EXTENSION T O HETEROGENEOUS AZEOTROPIC MIXTURES An extension of this exercise is proposed where the VLE is studied for a heterogeneous instead of a homogeneous azeotropic system. The binary system (a) T=90C -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.00.20.40.60.81.0 x 1 y 1 g (b) T=79C (c) T=72C (d) T=68.01C (calculated azeotrope) (e) T=60C -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 00.20.40.60.81 x 1 y 1 g Tangent line Equilibrium compositions g L g V -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 00.20.40.60.81 x 1 y 1 g -0.18 -0.14 -0.10 -0.06 -0.02 00.020.04 x 1 y 1 g M y 1 x 1 -0.70 -0.50 -0.30 -0.10 0.10 0.30 00.20.40.60.81 x 1 y 1 g x 1 y 1 y 1 'x 1 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 00.20.40.60.81 x 1 y 1 g x 1 =y 1 Figure 6. Analysis of the Gibbs energy curves for vapor (g V ) and liquid (g L ) mixtures at different temperatures for the ethanol (1) + benzene (2) binary system at P=1 atm showing the common tangent equilibrium condition. T ABLE 1 Antoine Equation Constants for Ethanol and Benzene  log(p o o A B C Ethanol 5.33675 1648.220 230.918 Benzene 3.98523 1184.240 217.572 T ABLE 2 Heat Capacity Constants of Liquid for Ethanol and Benzene  Cp L A B C D Ethanol 59.342 0.36358 -0.0012164 1.803-6 Benzene -31.662 1.3043 -0.0036078 3.8243-6
Chemical Engineering Education 242 sitions. Figure 9(a) shows the isotherm corresponding to L curve (x 1 L1 x 1 L2 that a liquid phase splitting is the most stable situation for any global mixture composition z comprised between them, x 1 L1
Vol. 44, No. 3, Summer 2010 243 have a common tangent line. The existence of this VLL equilibrium is consistent with the T-x,y representation of this system (Figure 7). With this example, the students demonstrate the reason for the VLL splitting in terms of stability or the minimum Gibbs energy of the system. CONCLUSIONS Dealing with the VLE calculation in terms of the Gibbs common tangent criteria provides students with a deeper under standing of the problem than using the isofugacity condition. An exercise of application of the Gibbs common tangent criteria to VLE has been proposed for a homogeneous azeo tropic binary system at a constant pressure using simple tools such as Excel spreadsheets and Matlab graphics. The Gibbs energy surface and curves at different temperatures have been analyzed to compare distinct situations that are consistent with the T-x,y diagrams. This graphical analysis proves that the vapor is the stable phase at high temperatures, the liquid phase is the stable aggregation state for lower temperatures, and that the azeotrope (VLE) corresponds to a temperature where both liquid and vapor Gibbs energy curves are tangent in one point. Students use this previous spreadsheet to develop an extension to consider the VLLE of a heterogeneous azeotropic system, which is tackled as a project in groups. Their reports of results show that the reasons for the V or L phase stability or the VLE and VLLE splitting is much more evident with the Gibbsian framework than using the isofugacity condition. NOMENCLA TURE f i F Fugacity of component i in phase F P Pressure p phase f Degrees of freedom (Phase Rule) Figure 9. Analysis of the Gibbs energy curves for vapor (g V ) and liquid (g L ) mixtures at different temperatures for the water (1) + n-butanol (2) binary system at P=1 atm, showing the common tangent equilibrium condition. (a) T=91C (b) T=94C (c) T=92.7C (calculated azeotrope) Tangent line Equilibrium compositions g L g V T = 92.7C -0.25 -0.2 -0.15 -0.1 -0.05 0 00.20.40.60.81 x 1 y 1 g x 1 x 1 y 1 L1 L2 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 00.20.40.60.81 x 1 y 1 g x 1 y 1 x 1 y 1 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 00.20.40.60.81 x 1 y 1 g x 1 x 1 L1 L2
Chemical Engineering Education 244 T b Boiling temperature n Number of components i v i oL p i o v i c Molar volume of the condensed phase as a function of pressure p i o Vapor pressure of component i y i Molar fraction of component i in the vapor phase x i Molar fraction of component i in the liquid phase i A ij Binary interaction parameter between species i and j (van Laar or NRTL equation) ij Non-randomness factor (NRTL equation) g id Ideal Gibbs energy of mixing (dimensionless) g E Excess Gibbs energy (dimensionless) g M Gibbs energy of mixing (dimensionless) g Gibbs energy (dimensionless) g V, g L Gibbs energy (dimensionless) of the vapor and liquid phase, respectively. g i oV g i oL Gibbs energy of pure component i (dimensionless) in the vapor and liquid phase, respectively. id Ideal E Excess M Mixture L, L1,L2 Liquid phase, Liquid phase 1, Liquid phase 2 V Vapor phase ACKNOWLEDGMENTS the Vicepresidency of Research (University of Alicante) and Generalitat Valenciana (GV/2007/125). REFERENCES 1. Wasylkiewicz, S.K., S.N. Sridhar, M.F. Doherty, and M.F. Malone, Global Stability Analysis and Calculation of Liquid-Liquid Equilib Ind. Eng. Chem. Res. 35 13951408 (1996) 2. Baker, L.E., A.C. Pierce, and K.D. Luks, Gibbs Energy Analysis of Soc. Petrol. Eng. AIME. 22 731-742 (1982) 3. Sandler, S.I., Models for Thermodynamic and Phase Equilibria Cal culations Marcel Dekker, New York (1994) Ind. Eng. Chem. Res. 47 4973-4987 (2008) 5. Castier, M., XSEOSan Open Software for Chemical Engineering Chem. Eng. Ed. 42 (2) 74 (2008) 6. Lwin, Y., Chemical Equilibrium by Gibbs Energy Minimization on Int. J. Eng. Ed. 16( 4) 335-339 (2000) 7. Prausnitz, J.M., R.N. Lichtentaler, and E. Gomes De Azevedo, Mo lecular Thermodynamics of Fluid-Phase Equilibria 3rd Ed., Prentice Hall PTR, Upper Saddle River (1999) 8. Gmehling, J., and U. Onken, Vapor-Liquid Equilibrium Data Collec tion. Alcohols, Ethanol and 1, 2-Ethanediol, Supplement 6 Chemistry Data Series, DECHEMA (2006) 9. Wisniak, J., Azeotrope Behaviour and Vapor-Liquid Equilibrium AIChE M.I. Series D. Thermodynamics V.3, AIChE, 17-23 (1982) 10. Lide, D.R., CRC Handbook of Chemistry and Physics 2006-2007: A Ready-Reference Book Of Chemical and Physical Data CRC Press (2006) 11. Poling, B.E., J.M. Prausnitz, and J.P. OConnell, The Properties of Gases and Liquids McGraw Hill (2001) 12. Yaws, C.L., Chemical Properties Handbook: Physical, Thermody namic, Environmental, Transport, Safety, and Heath-Related Properties for Organic and Inorganic Chemicals McGraw-Hill (1999) 13. Gmehling, J., and U. Onken, V apor-Liquid Equilibrium Data Collec tion. Aqueous System Supplement 3. Vol. I, part 1c. Chemistry Data Series, DECHEMA, (2003) 14. Iwakabe, K., and H. Kosuge, A Correlation Method For Isobaric Va Fluid Phase Equilib. 192 171186 (2001)
ChE book review Heat Transfer Reviewed by Copyright ChE Division of ASEE 2010