chemical engineering education
VOLUME 38 NUMBER 4 FALL 2004
GRADUATE EDUCATION ISSUE
.t Featuring articles on graduate courses...
STeaching Coupled Transport and Rate Processes (p.254)
SDemirel
SA Computational Model for Teaching Free Convection (p.272)
Il Goldstein
A Graduate Course on Multi-Scale Modeling of Soft Matter ip.242)
Hung, Gubbins. Franzen
t Reflections on Project-Based Learning in Graduate Courses (p.262)
SParulekar
< Teaching and Mentoring Training Programs: A Doctoral Student's Perspective (p.250)
E ,Baber, Bfriedis. Worden
5 Relating Abstract Chemical Thermodynamic Concepts to Real-World Problems (p.268)
.0 CCastaldt, Dorao, Assaq-Anid
.4 ... and articles of general interest.
a Random Thoughts: An Educator for All Seasons (p.?280). .................. ... .. ................. Felder
S a JAVA-Based Heat Transfer Visualization Tools ip.282)................ .......... .......... ..... .. ... Zhen Keith
3 High-Performance Learning Environments ip.286) ............... .. .. . .. .... ..... rce. Schreiber
5 a Deseloping Metacognitive Engineering Teams (p 316) ... .. ............... .......... Newell. Dahm. Harvey, Newell
S *' Pillars of Chemical Engineering: A Block-Scheduled Curriculum (p.292) ............. ...... ....... McCarth. Parker
SDevelopment of Cross-Disciplinary Projects in a ChE Undergraduate Cumculum (p.296' ................. Glennon
Deeloping Communication Skills in Engineering Students ip 302) .....Roeckel. Parra. Donoso, Mora, Garcia
Put Your Intuition to Rest: Write Mole Balances Systematically (p 308) ................ Gadewar. Doherty, Malone
'p
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Chemical Engineering Education
Volume 38
Number 4
Fall 2004
> GRADUATE EDUCATION
242 A Graduate Course on Multi-Scale Modeling of Soft Matter,
Francisco R. Hung, Keith E. Gubbins, Stefan Franzen
250 Teaching and Mentoring Training Programs at Michigan State Univer-
sity: A Doctoral Student's Perspective,
Tylisha M. Baber Daina Briedis, R. Mark Worden
254 Teaching Coupled Transport and Rate Processes,
Yasar Demirel
262 Reflections on Project-Based Learning in Graduate Courses,
Satish J. Parulekar
268 Relating Abstract Chemical Thermodynamic Concepts to Real-World
Problems,
Marco Castaldi, Lucas Dorazio, Nada Assaf-Anid
272 A Computational Model for Teaching Free Convection,
Aaron S. Goldstein
> RANDOM THOUGHTS
280 An Educator for All Seasons, Richard M. Felder
> WEB-BASED TOOLS
282 JAVA-Based Heat Transfer Visualization Tools,
Haishan Zheng, Jason M. Keith
> CLASSROOM
286 High-Performance Learning Environments,
Pedro E. Arce, Loren B. Schreiber
316 Developing Metacognitive Engineering Teams,
James Newell, Kevin Dahm, Roberta Harvey, Heidi Newell
> CURRICULUM
292 Pillars of Chemical Engineering: A Block-Scheduled Curriculum,
Joseph J. McCarthy, Robert S. Parker
296 Development of Cross-Disciplinary Projects in a ChE Undergraduate
Curriculum,
Brian Glennon
302 An Innovative Method for Developing Communication Skills in
Engineering Students,
M. Roeckel, E. Parra, C. Donoso, O. Mora, X. Garcia
308 Put Your Intuition to Rest: Write Mole Balances Systematically,
Sagar B. Gadewar, Michael F Doherty, Michael F Malone
279 Positions Available
CHEMICAL ENGINEERING EDUCATION (ISSN 0009-2479) is published quarterly by the Chemical Engineering
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Fall 2004
Graduate Education
A Graduate Course on
MULTI-SCALE MODELING OF
SOFT MATTER*
FRANCISCO R. HUNG, KEITH E. GUBBINS
Chemical Engineering Department, North Carolina State University Raleigh, NC 27695-7095
STEFAN FRANZEN
Department of Chemistry, North Carolina State University Raleigh, NC 27695-8204
Theory and simulations play an important role in chemi-
cal engineering, chemistry, and physics. They provide
a link between the microscopic features of a system
and its macroscopic properties. Molecular simulations can
be used as "computational experiments" to get information
that would be very difficult or impossible to get in a labora-
tory, and they can also assist in the analysis of experimental
results. Moreover, simulations provide a way to test theories
and thus determine their range of validity.' 21
A number of problems of current interest require insight
on many length scales, ranging from angstroms (subatomic
and atomic scales: electron rearrangement, bond breaking and
formation) up to macroscopic scales (bulk material proper-
ties). For example, intermolecular interactions have length
scales on the order of nanometers, and the microscopic struc-
ture of some phases can involve length scales on the order of
tens of nanometers, microns, millimeters and even larger, de-
pending on the nature of the molecules present in the system.
In a similar way, the corresponding time scales of the dy-
namic processes associated with these phenomena can range
from femtoseconds to milliseconds, reaching seconds or even
hours in some cases. Examples of systems exhibiting such a
wide range of length and time scales are polymeric and col-
loidal systems, self-assembly of surfactants on surfaces, bio-
logical systems, and chemical reactions in nonideal or nano-
structured environments (liquid solutions, supercritical flu-
ids, porous media, micelles, composites, etc.).
Problems such as these require a multi-scale approach in
which ab initio, atomistic, and meso-scale methods are com-
bined. No single model or simulation algorithm can cover
this range of length and time scales. Figure 1 illustrates the
length and time scales presently accessible to the main groups
of computational methodologies. This figure was constructed
SCourse website: http://gubbins.ncsu.edu/che597b/
assuming that calculations are performed for a maximum of
one week on the Blue Horizon (IBM SP3) supercomputer at
the San Diego Supercomputer Center (SDSC), which has a
maximum speed of 1.728 Tflops.31 More and more approxi-
mations are introduced as we move from ab initio algorithms
to the continuum level: larger length and time scales are
handled efficiently, but at the cost of reduced accuracy and
loss of fine structure. Electronic structure is lost in atomistic
simulations, and atomistic detail is lost in meso-scale simu-
lations. An important challenge and an active area of research
in modeling of soft matter is how to link the different meth-
ods available to cover the whole range of length and time
Francisco R. Hung received his BS (1996) and
MS (1999) in chemical engineering at Universidad
Simon Bolivar in Venezuela. He was Assistant
Professor in the Department of Thermodynamics
and Transport Phenomena at Universidad Sim6n
.Bolivar before coming to North Carolina State Uni-
versity, where he is currently a chemical engineer-
ing PhD candidate.
Keith E. Gubbins is the W H. Clark Distin-
guished University Professor at North Carolina
State University, where he has been since
1998. He obtained his PhD at the University of
London and has been a faculty member at the
University of Florida and Comell University prior
to joining North Carolina State University.
Stefan Franzen is Associate Professor of
Chemistry at North Carolina State University. He
has a BS degree from University of California,
Berkeley, and a PhD from Stanford University.
He was a Peace Corps Volunteer Teacher in
Kenya, EMBO Fellow at Ecole Polytechnique
in Palaiseau, France, and Director's Fellow at
Los Alamos National Laboratory, prior to joining
the faculty at NCSU.
Copyright ChE Division of ASEE 2004
Chemical Engineering Education
Graduate Education
: llm ^ TII --- T --- -- ^ ^
scales of interest (see, e.g., 1481 and references therein). In addition, a common criti-
cism from industry is that our PhD graduates are too specialized and have insuffi-
cient knowledge of modeling methods outside of their own specialization. In an
industrial setting, the researcher is expected to be able to choose the most appropri-
ate method for studying and solving a new problem and to apply it and get results
quickly. Therefore, students need to have familiarity with the full range of tools
available for theoretical and modeling work.
In the Spring Semester of 2004 we offered a new graduate course in multi-scale
modeling of soft matter. Most of the students taking the course were from chemistry
and chemical engineering, and the course was also offered via video transmission to
students from the University of North Carolina at Chapel Hill. The aim of this course
is to provide a background on the computational methods available at the different
scales, at a level suitable for graduate students whose primary research interests are
experimental as well as theoretical. Students in the class are asked to work problems
using web-based modules illustrating the different theoretical and simulation ap-
proaches for a variety of problems. This paper presents an overview of the most
important features of the course, including the basis, applicability, and strengths
and weaknesses of the methods. Examples of some of the computational exer-
cises are presented and discussed. The course material is posted on the course
website at and includes PowerPoint slides
and videos of the lectures, as well as links to the web modules containing the
computational exercises proposed.
COURSE STRUCTURE
The course syllabus is presented in Table 1. The course is suitable for students
who are already familiar with classical thermodynamics, and differential and inte-
Times
100
(ms) 10-3
(s) 10-6
(ns) 10-9
(ps) 10-12
Based on SDSC Blue Horizon (SP3)
1.728 Tflops peak performance
CPU time = 1 week I processor
Atomistic
Simulation
Methods
SSemi-e
S method
(fs) 1015 -
10-10 10-9
(nm)
Continuum
Methods
J LTight-binding
MNDO, INDO/S
10-8 10-7 10-6 10-5 10-4
(pm)
Length/m
Figure 1. Length and time scales accessible to different molecular simulation meth-
ods. We assume that the calculations are performed for a maximum of one week on
the Blue Horizon IBM SP3 supercomputer at the San Diego Supercomputer Center
(SDSC), which operates at a maximum speed of 1.728 Tflops.
TABLE 1
Course Syllabus
Lecture Topic
1. Introduction; electronic, atomistic,
mesoscale modeling; examples
2. Ab initio methods; Schrodinger equation;
Born-Oppenheimer approximation
3. Ab initio methods; Hartree-Fock method;
density functional theory (DFT)
4. Ab initio methods; density functional
theory (DFT) and applications; semi-
empirical methods
5. Introduction to semiclassical statistical
mechanics
6. Canonical ensemble; partition function,
thermodynamics
7. Factoring the partition and distribution
functions
8. Distribution functions and correlation
functions
9. Uniqueness theorem; reverse Monte Carlo
10. Statistical mechanics in the grand
canonical ensemble
11. Intermolecular forces
12. Composite pair potentials and force fields
13. Force field parameterization
14. General features of molecular simulation;
Monte Carlo algorithm: Metropolis
method
15. Monte Carlo simulation: canonical
ensemble, isothermal-isobaric ensemble,
grand canonical ensemble
16. Monte Carlo simulation and phase
equilibria (I): Gibbs ensemble Monte
Carlo; determination of chemical
potentials: thermodynamic integration
17. Monte Carlo methods and phase equilibria
(II); Gibbs-Duhem integration method;
overview of other Monte Carlo methods
18. Molecular dynamics
19. Molecular dynamics; calculation of
dynamic properties: constraint dynamics
20. Mesoscale methods; lattice Monte Carlo
21. Mesoscale methods; Langevin dynamics,
coarse graining, and Brownian dynamics
22. Mesoscale methods; Brownian dynamics
and dissipative particle dynamics
23. Statistical mechanics of inhomogeneous
fluids: interface, surface tension.
adsorption
24. Density functional theory (DFT) of
interfaces
25. Adsorption, fluids in pores, phase
equilibria in confined systems
26. Colloids
27. Biological systems (I)
28. Biological systems (II)
29. Special topics; multiscale molecular
modeling of chemical reactivity (I)
30. Special topics; multiscale molecular
modeling of chemical reactivity (II)
Fall 2004
)
gral calculus. The course has no formal exams. The students
are asked to work on the proposed computational modules,
and to complete a term paper project on a free topic related to
the course. The course consisted of four groups of lectures:
1. Electronic (subatomic) scale: ab initio and semi-empirical
methods (lectures 1-4)
2. Atomistic scale: semiclassical statistical mechanics,
intermolecular forces, Monte Carlo and Molecular Dynam-
ics methods (lectures 5-19)
3. Meso-scale: Lattice Monte Carlo, Langevin Dynamics,
coarse graining, Brownian Dynamics and Dissipative
Particle Dynamics (lectures 20-22)
4. Applications: phase equilibria of bulk and confined
systems, adsorption and interfaces, colloids, biological
systems and chemical reactions (lectures 23-30)
Since there is presently no suitable text for such a course,
Methods
Main Idea
material was taken from several sources. The text by Leach19'
covers parts of the material in Section 1, much of Section 2,
and parts of Section 4. Additional references for Section 1
(ab initio and semi-empirical methods) include the books by
Jensen,l'o Szabo and Ostlund,1l" Parr and Yang, 12' and Koch
and Holthausen.'31 The section on semiclassical statistical me-
chanics is covered in Gray and Gubbins"14] and McQuarrie,"l5
and more advanced aspects of Monte Carlo and Molecular
Dynamics methods are covered in the monographs of Allen
and Tildesley1ll and Frenkel and Smit.121 Meso-scale meth-
ods (Section 3) are covered briefly in Frenkel and Smit,121
and in more detail in monographs by Zwanzig1161 and Mazo.1171
The first three groups of lectures covered the theoretical
basis of the methods, followed by a description of the most
relevant theoretical and modeling tools, their strengths and
Electronic scale: Calculate properties from first
ab initio principles solving the Schrrdinger
equation numerically
* Can handle processes that involve bond breaking/formation,
or electronic rearrangement (e.g., chemical reactions)
* Methods offer ways to systematically improve on the
results, making it easy to assess their quality
* Can (in principle) obtain essentially exact properties
without any input but the atoms conforming the system
* Can handle only small systems,
on the order of 102 atoms
* Can only study fast processes,
usually on the order of 10 ps.
* Approximations are usually
necessary to solve the equations
Electronic scale: Use simplified versions of equations Can also handle processes that involve bond breaking or *Difficult to assess the quality of the
semi-empirical from ab initio methods (e.g., treating formation, or electronic rearrangement results
explicitly only the valence electrons); Can handle larger and more complex systems than ab initio Need experimental input and large
include parameters fitted to methods, often of the order of 103 atoms parameter sets
experimental data Can be used to study processes on longer timescales than can
be studied with ab initio methods, on the order of 10 ns
Classical atomistic Use empirical or ab initio derived Can be used to determine the microscopic structure of more Results depend on the quality of the
scale: Molecular force fields, together with semi- complex systems, on the order of 105 106 atoms force field used to represent the system
Dynamics (MD), classical statistical mechanics to Can study dynamical processes on longer timescales, on the Many physical processes happen on
Monte Carlo (MC) determine thermodynamics (MC, order of 1 ps length- and timescales inaccessible by
MD) and transport (MD) properties these methods, e.g., diffusion in solids,
of systems. Semi-classical statistical many chemical reactions, protein
mechanics equations are solved folding, micellization
"exactly"
Meso-scale Introduce simplifications to atomistic Can be used to study structural features of complex systems Can often describe only qualitative
methods to remove the faster degrees
of freedom, and/or treat groups of
atoms ("blobs of matter") as
individual entities interacting
through effective potentials
on the order of 108 10' atoms
* Can study dynamical processes on timescales inaccessible
to classical methods, up to seconds
tendencies; the quality of quantitative
results may be difficult to ascertain
* In many cases, the approximations
introduced limit the ability to physically
interpret the results
Continuum
(not covered in this
course)
Assume that matter is continuous and
treat the properties of the system as
field quantities. Numerically solve
balance equations coupled with phe-
nomenological equations to predict
the properties of the systems
* Can in principle handle systems of any macroscopicc) size
and dynamic processes on longer time scales
* Require input (viscosities, diffusion
coefficients, parameters required in
equations of state, etc.) from experiment
or from a lower-scale method; they can
be difficult to obtain in some cases
* Cannot explain results that depend on
the electronic or molecular level of
detail
Chemical Engineering Education
TABLE 2
Pros and Cons of the Different Modeling Tools Described in this Course
Pros C(
~F~C-~C*I* --~;--- ---- ---- - -
" -~~'I'~~' ~~'-'-`'i ~ '-"-"-' ~-~-- --- ~-L'~- -- -
f
i- :-
-~
weaknesses, and the kind of problems studied with them. In
addition, ways to link results obtained using methods at dif-
ferent scales are described and discussed when appropriate.
The last section of the course covers the use of the different
methodologies in various applications. The main idea of each
one of the group of methods described in this course, as well
as their most important advantages and disadvantages, are
summarized in Table 2. We included continuum methods in
Table 2 for completeness, although these modeling tools are
not covered in this course. These methods are applied at the
macroscopic scale and usually involve solving the equations
of material and energy balance, coupled with phenomeno-
logical (constitutive) equations, to predict the properties of
the systems assuming that matter is continuous. The most
important continuum methods are usually studied in detail in
a number of courses in chemical engineering.
At the electronic (subatomic) scale, we discussed both ab
initio and semi-empirical methods. The purpose of the ab
initio methods (Table 2) is to calculate properties from first
principles using quantum mechanics.[5,9- l] The nature of the
atoms comprising the system is provided as input, and the
time-independent Schridinger equation is then solved numeri-
cally for a given many-atom system
H=O=E< (1)
where q$ represents the wave function of the many-atom sys-
tem, E is the total energy, and H is the Hamiltonian operator.
For the general case of a system of N electrons and M nuclei,
the Hamiltonian operator ists15
SN 1 M I N M N-1 N 1 M-l M ZZ
i H=-1 1 -I Yv I 1 X Z (2)
i=l 2 1=1 2M I i= ll= i i=1 ji+lrij I=1 J=I+1 R
where the indices i,j,... refer to the electrons and the indices
I,J,... refer to the nuclei. The symbol V2 is a Laplacian op-
erator with respect to the coordinates of electron i, and VI is
a Laplacian operator with respect to the coordinates of the
nucleus I. The first term in Eq. (2) represents the electronic
kinetic energy; the second term is the nuclear kinetic energy.
The remaining three terms are the Coulomb interactions be-
tween the nuclei and the electrons, between electron pairs
and between nucleus pairs, respectively. Equation (2) is writ-
ten in atomic units.[5,"1
Some of the basic elements common to most ab initio meth-
ods are introduced during the lectures. We also briefly ex-
plore some of the most common approaches to finding ap-
proximate solutions to Eq. (1), and discuss their advantages
and limitations (Table 2). Density functional theory (DFT) is
an alternative approach covered in class that permits one to
obtain reasonably accurate results for complex systems. The
main difference between DFT and the methods mentioned
before is that the fundamental variable is not the wave func-
tion ( but the electronic density p(r).[5,10,12,131 The energy
functional E[p] in DFT includes terms accounting for the ki-
netic and potential energy of both electron-nucleus and elec-
tron-electron interactions. The latter accounts for the poten-
tial energy of the Coulomb interaction and the so-called ex-
change-correlation potential energy.5, 10'12.131 Applications, ex-
amples, advantages and limitations of DFT are discussed.
An alternative and less rigorous approach to the electronic
problem is provided by the semi-empirical methods (Table
2), which are briefly discussed. In these algorithms,[5,9,"" the
many-electron problem is simplified in some way (e.g., by
treating explicitly only the valence electrons), and then some
parameters obtained from experiment or higher quality ab
initio calculations are included in order to get good results.
The main advantages and disadvantages of such methods
(Table 2) are discussed. Semi-empirical methods are particu-
larly useful for dealing with large systems (e.g., biomolecules,
chemical reactions in complex systems) where the more
computationally demanding ab initio methods are impos-
sible to apply due to limited computing power. On the
other hand, the semi-empirical methods are not truly ab
initio methods, since they make use of experimental in-
formation to obtain their results.
Before introducing the two main classical atomistic simu-
lation methods (Molecular Dynamics and Monte Carlo; see
Table 2), we include some lectures discussing semiclassical
statistical mechanics, intermolecular forces and commonly
used force fields and models to describe intra- and intermo-
lecular interactions. In atomistic simulation methods,'12'91
empirical or ab initio derived force fields are used, together
with semiclassical statistical mechanics, to determine ther-
modynamic and/or transport properties of the system of in-
terest. In general, the (mechanical) properties of a system,
such as internal energy, pressure and surface tension, depend
on the positions and moment of the N particles that form the
system. In Molecular Dynamics (MD), the molecules move
naturally under their own interaction forces; the positions and
velocities of each atom or molecule are followed in time by
numerically solving Newton's equations of motion
d2xi Fx
i (3)
dt2 mi
which describe the motion of a particle with mass mi along
one coordinate xi, Fxi being the force acting on the particle in
that direction (due to the presence of other molecules, or ex-
ternal forces). The average of a (mechanical) property A can
be determined as
average = lim 1 A[pN(t), r (t)]dt
"t-- 1:
Fall 2004
Ir ~ ii
Graduate Education
where pN(t) and rN(t) represent the N moment (p,, p,, .... pN)
and positions (r,, r,,..., r,), respectively, at time t. In Monte
Carlo, we determine average properties from an ensemble,
rather than a time, average
(A)= JfdpNdrNA(pN,rN)P(pN,rN) (5)
where P(pN,rN) is the probability density of finding a mo-
lecular configuration with moment pN and positions rN. The
probability density is given by the statistical mechanics of
the system.11,2'9 In MC, a random number generator is used to
stochastically perturb a system (by randomly moving the
molecules, changing the volume of the system, etc.). In order
to generate an ensemble of configurations distributed accord-
ing to P(pN,rN), only a fraction of these perturbations are ac-
cepted. According to the ergodic hypothesis,[1'2'9 the time
average and ensemble averages are equal, so Aaverage = (A).
The main features of MD and MC are introduced in this group
of lectures, together with their extension to different en-
sembles, derivation of the acceptance criteria, a description
of some of the more advanced MD and MC techniques, and
some typical applications of these methods.
Soft matter often consists of large, massive particles (e.g.,
polymers, colloids, surfactants, proteins, etc.) in a sea of small,
light particles (solvent). In such systems the time scales in-
volved for the large and small particles are very different. In
the meso-scale methods (Table 2), simplifications to classi-
cal atomistic methods are introduced (coarse-graining) to re-
move the faster degrees of freedom and/or treat groups of
atoms as individual entities interacting through effective po-
tentials. One example of such methods is lattice Monte Carlo
simulations,'2'9'18] in which molecules or groups of atoms oc-
cupy discrete positions on a lattice; the simulations are
computationally more efficient than those using atomistically
detailed continuum models. Other meso-scale methods cov-
ered are Brownian Dynamics and Dissipative Particle Dy-
namics,'1'21 which are based on the Langevin equation for the
dynamics of the large particles"1617'
mai(t)= Fi(t)= X Fi yvi(t)+ oGi(t) (6)
where m is the mass of the particles, ai(t), vi(t), and F (t) are
the acceleration, velocity and force, respectively, for particle
i, Fi is the conservative (solvent-mediated) force acting on
the large particle i due to another large particle j, and y is the
friction coefficient on the big particles due to the presence of
small particles. The last term in Eq. (6) is a "random force"
introduced to account for the Brownian motion due to colli-
sions between the small particles and the large particle, and
must be included to ensure that the equipartition theorem is
obeyed at long times.1'2,16,'71 The noise amplitude is oa, and
;i(t) is a Gaussian random variable. The noise amplitude (T
and the friction coefficient y are related via the fluctuation-
dissipation theorem.1'2'16'.171
The connection between results from modeling methods in
different scales via upscalingg" or downscalingg" approaches
are introduced. The upscalingg" approach is deductive: re-
sults from a lower-scale calculation are used to obtain poten-
tials and parameters for a higher-scale method. Examples
mentioned in class are the calculation of properties from ato-
mistic and/or meso-scale simulations, such as phenomeno-
logical coefficients (e.g., viscosities, diffusivities), for later
use in a continuum model; fitting of force-fields using ab
initio results, for later use in atomistic simulations; deriving
the potential energy surface for a chemical reaction, to be
used later in atomistic MD simulations; deriving coarse-
grained potentials for "blobs of matter" from atomistic simu-
lation, to be used in meso-scale simulations. In contrast, the
downscalingg" approach is inductive and involves using
higher-scale information (often experimental) to build param-
eters for lower-scale methods. This is more difficult, due to
the non-uniqueness problem. For example, atomistic simula-
tion results lack any electronic detail, and meso-scale simu-
lations do not contain atomistic detail; thus, there is no unique
way to reintroduce such detail and go to the lower level. Some
examples of downscaling are the fitting of two-electron inte-
grals in semi-empirical electronic structure methods to ex-
perimental data (ionization energies, electron affinities, etc.)
and fitting of empirical force fields to reproduce experimen-
tal thermodynamic properties, e.g., second virial coefficients,
saturated liquid density and vapor pressure.
PROBLEM SETS AND WEB MODULES
A practical approach to the instruction of modern topics in
theory and simulation must rely on hands-on experience with
computers and software, illustrating the application of some
of the methods covered in class to a number of practical prob-
lems. We have used commercial software from Accelrys Inc.,
with a graphical user interface (Insight II) for the setup and
analysis of most of the simulations. This approach decreases
the amount of time required on software-specific issues. In
addition, some of the simulation exercises are based on home-
made programs done by members of our research groups.
We have defined two groups of applications, one based in
methods at the electronic scale and the other studying appli-
cations at classical atomistic scales. So far we have not in-
cluded any group of applications in meso-scale simulations,
but we are working in order to include some of them in fu-
ture offerings of this course. In each module, the students run
a small calculation that takes approximately 10 minutes (or
less) of CPU time, which helps them understand the process
of setting up a calculation and submitting the job on a com-
Chemical Engineering Education
Graduate Education
puter with a batch queue. The elementary (starting) modules
can be tackled in less than 2 hours, even for students who
lack basic computer skills. The advanced modules can take
three hours or longer. Since some students were not famil-
iar with UNIX operating systems (or even with command-
line computing), we provided a help menu on the course
website describing basic operations such as file transfer,
editing and storing data.
Quantum chemistry applications
We chose to focus on density functional theory (DFT) [-"10,2.13
since it is widely used and provides reasonably accurate re-
sults with fair computational costs for complex systems. Some
of the proposed DFT modules include
Water (starting module)
Polymers
Surface adsorption
In the water module, the students are asked to determine
the values of properties such as bond lengths and angles,
charges and dipole moment, and force constants for stretch-
ing and bending. These are parameters required in typical
force field parameterizations and can also be compared to
experimental values. Moreover, these results can be compared
later with those obtained from simulations of water using
classical force fields, which is included in the atomistic
group of applications. The form of the molecular orbitals
for water can also be examined from the DFT calculations.
Beyond water, the students can progress to more advanced
calculations including geometry optimization for polymers
and surface adsorption.
In the polymer module, the elastic constants such as the
bulk and Young's modulus can be calculated for crystal-
line polymers such as polyethylene.[19'20 The surface ad-
sorption module involves calculation of the adsorption
energy of small molecules (diatomics, amines, thiols,
etc.), on a range of metals (Au, Ag, Pt, Pd, Ru, etc.)."211
The suggested example is the adsorption of carbon
monoxide on Ni( 111),122,231 which is depicted in Figure
2. In addition, the vibrational frequencies of adsorbed
CO can be compared to those exhibited by a free mol-
ecule of carbon monoxide.
Classical atomistic applications
Some of the proposed modules in this group of applica-
tions include
MD and MC simulation of Lennard-Jones argon (starting
module)
MD simulation of liquid water
Reactive Monte Carlo (RxMC) study of the ammonia
synthesis reaction (bulk fluid phase)
Quench dynamics of cyclic peptide analog of Leu-
enkephalin
In the starting module, the students are asked to per-
form both MD and MC simulation of Lennard-Jones (LJ)
argon in the canonical ensemble. The students perform
simulations at different temperatures, calculate typical fluid
properties (e.g., internal energy, pressure, heat capacity,
radial distribution function), and compare the results from
both methods. The self-diffusion coefficient is also deter-
mined from the MD simulations using both the velocity
autocorrelation function and the mean square displacement,
and the results from both methods are compared.
In the water module, the students are asked first to equili-
brate two hydrogen-bonded water molecules, using the
transferable intermolecular potential TIP3P, in a very low-
density gas phase, and then to estimate the energy of for-
mation of the hydrogen bond and the angle between the
two associated water molecules. These two results can be
compared with experimental values. Following this, the
students perform MD simulations of liquid TIP3P water
at room temperature and determine properties such as in-
ternal energy, heat capacity, self-diffusion coefficient, di-
Fall 2004
Figure 2. DFT applied to surface adsorption. Depiction of
adsorption of carbon monoxide (CO) on Ni(1 11). (a) Lateral
view, and (b) top view. The distance between the adsorbate
layer of CO and the Ni surface is 1.2 A.
( GradufW Eucation
pole autocorrelation function, and the radial distribution
functions 0-0, O-H, and H-H, comparing to experimental
values when possible.
The constant pressure version of the Reactive MC
(RxMC) method1241 is used in one of the modules to deter-
mine the equilibrium state of a mixture of N2, H2 and NH3
in the bulk, reacting according to N2 + 3H2 <=> 2NH3, at
high temperatures and pressures. The typical trial moves
attempted in a RxMC simulation are summarized in Fig-
ure 3(a). The molecular models were the same as those
used recently by Turner, et al.,[251 and are depicted in Fig-
ure 3(b). The molecular constants used to calculate the par-
tition function for this reactive mixture (N2, H2 and NH3)
are all found in McQuarrie's text.""1 Close agreement with
the experimentally measured conversions of ammonia in
the bulk phase is expected to be achieved with RxMC.[251
The protein folding problem is one of the central issues
in bioscience and biotechnology today. While the problem
is enormously complicated, a simple demonstration of the
thermodynamic and statistical issues is exemplified by the
application of quench dynamics in the study of the folding
transition of a cyclic hexamer peptide, which is shown in
Figure 4. This molecule is hydrophobic and can penetrate
cell membranes; then, the cyclic peptide is hydrolyzed and
drugs such as Leu-enkephalin'26-281 can be released inside
the cell. Therefore, such a system can be used as a drug
delivery system model. To understand the peptide relative
membrane permeability, we must first search the thermo-
dynamically accessible states. To accomplish this, the pep-
tide is heated and equilibrated at high temperatures (e.g.,
500 K) to overcome any isomerization barriers. A number
of peptide conformations are selected, quenched (progres-
sively cooled to lower temperatures) and equilibrated. The
resulting structures represent local minimum conforma-
tions, and their relative energies map out the thermally ac-
cessible conformations of the peptide. Three families of
structures are expected to be found: folded, unfolded and
intermediate. The folded structure (Figure 4) has two hy-
drogen bonds, shown in Figure 4 as the N-H O=C dis-
tances of 2.07 A and 2.09 A. The folded structure has a 3-
sheet fold, as shown by the side view. The unfolded struc-
ture (Figure 4) has no hydrogen bonds (N-H O=C distances
of 4.35 A and 4.42 A), has a crowned morphology, and the
side view shows that the structure is more similar to an
extended chain, rather than to a 3-sheet. The intermediate
structure has only one hydrogen bond and combines fea-
tures of both of the previously described structures. This
particularly simple example illustrates how computational
modeling of folding transitions is possible using a relatively
simple model. The structures obtained from quench dynam-
ics simulations can then be used to compute vibrational
248
frequencies using density functional theory methods, obtaining
results in agreement with experimental trends.[29)
CONCLUDING REMARKS
The main objective of this course is to make students familiar
with the most important computational methods available at dif-
ferent scales (electronic, atomistic and meso-scale), and to illus-
trate how they can be applied to some problems of current inter-
est. The course was offered for the first time in Spring 2004, and
we plan to further develop it for future offerings. We are cur-
rently working to include a group of computational exercises on
meso-scale simulations in the course, and thus provide practical
examples of modeling at all the different scales covered in this
course. In addition, we plan to include practical exercises linking
the results from methods at different scales, via upscaling or
downscaling. This is an active research area at present, and it is
important for a course of this kind to be up to date. Both the
course outline and computational modules need to be continu-
ally updated in order to cover the most recent and interesting
methodologies and applications.
ACKNOWLEDGMENTS
We are grateful to the students from North Carolina State Uni-
A,--B+C
*o 00 go 00
0 0 0 O
O 00* 0 000 Particle
SOo 0 Volume
0/000 000
o. sto volume
S* A o change
d () reaction ,repe reaction
e. Noe w tep a step
A-BC B+C- A
(a) (b)
Figure 3. Reactive Monte Carlo (RxMC) module: (a) illustration
of the RxMC typical moves for a reaction A <- B + C: particle
move, volume changes, forward and backward reaction steps;
and (b) schematic representation of the model molecules stud-
ied. Nitrogen was represented by a two-site LJ molecule, with
the addition of three point charges chosen to account for its
quadrupole. The hydrogen molecule was treated as a single LJ
sphere, and the model for NH, consisted of one LJplus negative
point charge site to represent the nitrogen, and three positive
point charges to represent the three hydrogens. No LJ sites were
used to account for the hydrogens on the ammonia molecules.
Chemical Engineering Education
7 :
--
- = L-- ~ ~ ~ 1-11- _.
Graduate Educatfion
versity and the University of North Carolina at Chapel Hill
who took this course, for their patience, support, feedback and
motivation. We gratefully acknowledge Professors David A.
Kofke (University at Buffalo, The State University of New
York) and Sharon C. Glotzer (University of Michigan), for
kindly providing us full access to their respective course ma-
terials. We thank Erik E. Santiso, who prepared the material
and lectured the classes about chemical reaction modeling. We
also would like to thank Henry Bock, Naresh Chennamsetty
and Supriyo Bhattacharya, for their help in the preparation of
the lectures about meso-scale simulations. It is a pleasure to
thank Professors Ken Thomson (Purdue University) and C.
Heath Turner (University of Alabama), for kindly providing
the data for Figures 1 and 3 of this paper.
REFERENCES
1. Allen, M.P., and D. J. Tildesley, Computer Simulation of Liquids,
Clarendon Press, Oxford (1987)
2 Frenkel, D., and B. Smit, Understanding Molecular Simulation 2"d Ed.,
Academic Press, San Diego, CA (2002)
3. Information taken from http://www.npaci.edu/BlueHorizon/. 1 Tflop =
1012 floating point operations per second.
4. de Pablo, J.J., and F. A. Escobedo, "Molecular Simulations in Chemical
Engineering: Present and Future," AIChE J., 48, 2716 (2002)
Side
Folded Unfolded
Figure 4. Quench Dynamics module. Depiction of the folded
and unfolded structures obtained from quench dynamics
simulations of a model cyclic hexamer peptide. Two hydro-
gen bonds are observed in the folded structure (N-H O=C
distances of 2.07 A and 2.09 A, top view), which has a 63-
sheet fold (side view). The unfolded structure exhibits a
crowned morphology with no hydrogen bonds (N-H O=C dis-
tances of 4.35 A and 4.42 A, top view), and an extended-
chain morphology (side view). The structures obtained from
quench dynamics simulations can be used to compute vibra-
tional frequencies using density functional theory methods.
The trends in the vibrational frequency of the folded and
unfolded structures agree with experimental results.
Fall 2004
5. Santiso, E.E., and K. E. Gubbins, "Multi-Scale Molecular Modeling of
Chemical Reactivity," Mol. Simul., in press (2004)
6. Maroudas, D., "Multiscale Modeling of Hard Materials: Challenges and
Opportunities for Chemical Engineers," AIChE J., 46, 878 (2000)
7. Glotzer, S.C., and W. Paul, "Molecular and Mesoscale Simulation Meth-
ods for Polymer Materials," Annu. Rev. Mater Res., 32, 401 (2002)
8. Abraham, F.F., J. Q. Broughton, N. Bernstein, and E. Kaxiras, "Span-
ning the Length Scales in Dynamic Simulation," Comp. Phys., 12, 538
(1998)
9. Leach, A.R., Molecular Modelling. Principles andApplications 2nd Ed.,
Prentice-Hall, Harlow (2001)
10. Jensen, F., Introduction to Computational Chemistry, John Wiley and
Sons, Chichester (1999)
11. Szabo, A., and N. Ostlund, Modem Quantum Chemistry: Introduction
to Advanced Electronic Structure Theory, Dover, New York (1996)
12. Parr R.G., and W. Yang, Density-Functional Theory ofAtoms and Mol-
ecules, Oxford University Press, Oxford (1989)
13. Koch, W., and M.C. Holthausen, A Chemist's Guide to Density Func-
tional Theory, Wiley-VCH, Weinheim (2000)
14. Gray, C.G., and K.E. Gubbins, Theory of Molecular Liquids, Clarendon
Press, Oxford (1984)
15. McQuarrie, D.A., Statistical Mechanics, University Science Books,
Sausalito (2000)
16. Zwanzig, R., Nonequilibrium Statistical Mechanics, Oxford University
Press, New York (2001)
17. Mazo, R.M., Brownian Motion, Clarendon Press, Oxford (2002)
18. Panagiotopoulos, A.Z., "On the Equivalence of Continuum and Lattice
Models for Fluids," J. Chem. Phys., 112, 7132 (2000)
19. Miao, M.S., M.L. Zhang, V.-E. van Doren, C. van Alsenoy and J.L. Mar-
tins, "Density Functional Calculations on the Structure of Crystalline
Polyethylene at High Temperatures," J. Chem. Phys., 115, 11317 (2001)
20. Bruno, J.A.O., N.L. Allan, T.H.K. Barron, and A.D. Turner, "Thermal
Expansion of Polymers: Mechanisms in Orthorhombic Polyethylene,"
Phys. Rev. B, 58, 8416 (1998)
21. Franzen, S., "Density Functional Calculation of a Potential Energy Sur-
face for Alkane Thiols on Au( 111) as Function of Alkane Chain Length,"
Chem. Phys. Lett., 381, 315 (2003)
22. Doll, K., "Density Functional Study of Ni Bulk, Surfaces and the Adsor-
bate Systems Ni( 111)('3 x i3)R30o-C1, and Ni(111)(2x2)-K,", Surf. Sci.,
544, 103 (2003)
23. Shah, V., T. Li, K.L. Baumert, H.S. Cheng, and D.S. Sholl, "A Compara-
tive Study of CO Chemisorption on Flat and Stepped Ni Surfaces Using
Density Functional Theory," Surf Sci., 537, 217 (2003)
24. Johnson, J.K., A.Z. Panagiotopoulos, and K.E. Gubbins, "Reactive Ca-
nonical Monte Carlo: A New Simulation Technique for Reacting or As-
sociating Fluids," Mol. Phys., 81, 717 (1994)
25. Turner, C.H., J.K. Johnson, and K.E. Gubbins, "Effect of Confinement
on Chemical Reaction Equilibria: The Reactions 2NO tr>(NO)2 and
N2+3H, <2NH, in Carbon Micropores," J. Chem. Phys., 114, 1851
(2001)
26. Wang, B., K. Nimkar, W. Wang, H. Zhang, D. Shan, O. Gudmundsson,
S. Gangwar, T. Siahaan, and R. T. Borchardt, "Synthesis and Evaluation
of the Physicochemical Properties of Esterase-Sensitive Cyclic Prodrugs
of Opioid Peptides Using Coumarinic Acid and Phenylpropionic Acid
Linkers," J. Pept. Res., 53, 370 (1999)
27. Dudowicz, J., K.F. Freed, and M. Y. Shen, "Hydration Structure of Met-
Enkephalin: A Molecular Dynamics Study," J. Chem. Phys., 118, 1989
(2003)
28. van der Spoel, D., and H.J.C. Berendsen, "Molecular Dynamics Simula-
tions of Leu-Enkephalin in Water and DMSO," Biophys. J., 72, 2032
(1997)
29. Maness, S.J., S. Franzen, A.C. Gibbs T.P. Causgrove and R.B. Dyer,
"Nanosecond Temperature Jump Relaxation Dynamics of Cyclic p-Hair-
pin Peptides," Biophys. J., 84, 3874 (2003) J
249
cGraduate Education
TEACHING AND MENTORING
TRAINING PROGRAMS
AT MICHIGAN STATE UNIVERSITY
A Doctoral Student's Perspective
TYLIHA M. BABER, DAINA BRIEDIS, R. MARK WORDEN
Michigan State University East Lansing, MI 48824-1226
any new faculty enter the academic world with
minimal teaching experience or training in peda-
gogy. In fact, a majority of engineering professors
have never had a formal course in education."' This defi-
ciency can easily be addressed through implementation of
teaching programs targeted at doctoral students who aspire
to an academic career. The rationale behind a formal teach-
ing program is that new professors who study educational
methods will likely be better prepared to teach and will be
more efficient during their first years in academia." 1 Benefits
of graduate training in teaching include
Helping confirm whether the student is well suited for and
would enjoy an academic career
Providing both conceptual knowledge and significant
experience in college-level teaching
Giving a significant advantage over other candidatesfor an
academic position.'12
A College Teaching Certificate (CTC) program was estab-
lished in the College of Engineering at Michigan State Uni-
versity (MSU) to help provide such training. It was initiated
in 1998 in response to a request from several graduate stu-
dents for training in college teaching methods. A planning
committee of faculty and graduate students was formed to
develop such a program. During the 1998-1999 academic year,
the committee submitted a proposal to establish the CTC pro-
gram, and it was successfully initiated in the spring of 2000.
A total of 23 engineering doctoral students have now suc-
cessfully completed the program and received certification
in college teaching.[3' The College of Natural Science had
previously established a similar program.'41
CTC PROGRAM FORMAT AND EVALUATION
Theory and Practice of Teaching Engineering Students
The overall purpose of the CTC program is to provide
graduate students with valuable experience in college-level
teaching and to prepare them for careers in academia. To
achieve this goal, the program requires successful comple-
tion of two courses. The first course, "Theory and Practice of
Teaching Engineering Students," introduces students to peda-
gogical theories and effective methods used in teaching en-
gineering. The theory and practice component of the program
is similar to many courses at colleges of engineering around
the country.51 Learning objectives for the course include: 1)
applying fundamental theories of cognitive processes in the
practice of teaching engineering students, 2) designing ef-
Tylisha M. Baber is a doctoral candidate in
chemical engineering at Michigan State Univer-
sity. She graduated from North Carolina State
University with honors in December of 1998 with
a Bachelor of Science degree in chemical engi-
neering (bioscience option).
Daina Brledis is Associate Professor in the De-
partment of Chemical Engineering and Materi-
als Science at Michigan State University. She
has conducted research in bioadhesion and is
currently studying development of effective
learning tools for the multidisciplinary class-
room. She is active nationally and internation-
ally in engineering accreditation, and is a mem-
ber of the ABET Board. She leads the assess-
ment and evaluation efforts in her program.
R. Mark Worden, Professor of Chemical Engi-
neering, bridged to chemical engineering after
earning a Bachelors' degree with a double ma-
jor in chemistry and cell biology. His research is
in the area of biochemical engineering, and he
has been active in development of multidisci-
plinary training programs.
Copyright ChE Division of ASEE 2004
Chemical Engineering Education
250
Graduate Education
^ ^________ __ _____ _ __ ^_ _ -^ ^ - --
TABLE 1
Course Topics
* Attributes of a Professional
* Student Learning Styles and
Assessment
* Starting the Academic Career
* Diversity and Gender Issues
* Teaching Assessment
* Mentoring
* Course Proposal
* Accreditation
* Dealing with Hostile Students
* Understanding "Class Personality" And
Student Perspectives
* Delivering Course Content: The Lecture
* Delivering Course Content: Active
Learning And Cooperative Learning
* Delivering Course Content: The Use
of Technology
* Designing Effective Laboratories
* Designing Effective Homework
Assignments
* Incorporating Design Into Engineering
Courses
* Faculty And Student Rights And
Responsibilities
* How To Be An Effective Junior
Faculty
TABLE 2
List of Projects
Statement of Teaching Philosophy
This entails a clear and concise, but personal statement of one's philosophy about
teaching. It is considered a living document, so as one's experience grows, it also
changes. This assignment is graded on the basis of the depth of thought presented.
Teaching Toolbox
This includes materials that can help and support the participant's teaching. The
teaching toolbox has two compartments. The first compartment deals with items
pertinent to the theory and practice of teaching and the second compartment includes
items that support the teaching of a specific topic in the student's discipline. Both
compartments are organized collections of papers, exams, projects, notes, physical
models, etc., that the student can use as a reference for future teaching assignments.
The Toolbox is graded for completeness with respect to the essential components
presented in the course, the richness of development the student added beyond the
course materials, and its overall organization.
Journal
This is the participant's reflection on the theory and practice of teaching engineering
students and an exploration of one's own philosophy of teaching. It is allowed to be in
the form of a diary, a collection of essays, a record of conversations, letters to
colleagues, or a mixture of these. The Journal is graded on the basis of the depth of
thought presented.
Mini- Lecture
This is a 15- to 20-minute lecture on a scientific subject area that is given by the
participant during the normal two-hour class period. The grade is based on a standard
oral presentation grading form that is given to the students in advance.
Course Web Page
Participants design and implement a web page based on the topics covered in the mini-
lecture. The web page must have at least one download and one link to another website.
This project is graded on the basis of its layout, utility, and overall organization.
Assignment
Based on the topics covered in the mini-lecture, the participant prepares an assignment.
which could take the form of an examination, quiz, homework, or project. The grade is
based on the attributes of the Assignment.
Course Proposal
The participants submit a proposal for a course that includes all the administrative
details for a new course proposal at Michigan State University. A course description in
ABET format accompanies the proposal. The Course Proposal is graded for
completeness and innovative thought.
Fall 2004
fective lectures, laboratories, and assignments, 3) using ap-
propriate methods to deliver course content, 4) designing
and applying assessment tools, 5) writing a proposal for a
new course, and 6) developing a website as an engineering
educational tool."' A list of topics facilitated in the course
is shown in Table 1. In addition to the text'" used in this
course, supplemental reading is provided, including articles
from Prism, Journal of Engineering Education, and pro-
ceedings of the ASEE Annual Conference.
I (author TB) felt that the course provided an excellent
background on the theories and methods used to effectively
teach engineering students. The assigned projects, listed in
Table 2, taught me how to organize and present course ma-
terial and encouraged me to think critically about how to
reach engineering students through innovative teaching
strategies. The class, which met once a week for 2 hours,
was interactive and thus allowed participants to engage in
discussions about teaching and to exchange personal expe-
riences involving education and teaching styles.
Mentored Teaching of Engineering Students
In the second course, "Mentored Teaching of Engineer-
ing Students," participants gained experience in teaching
under the close guidance and supervision of an engineer-
ing faculty member of their choice. Typically, participants
chose their research advisors as the teaching mentor. I chose
my research advisor because of our well-developed rela-
tionship and his expertise in the subject matter. Faculty men-
tors participate in the program without special compensa-
tion and are largely motivated by their commitment to de-
veloping academicians of the future. The mentored teach-
ing experience allows participants to cultivate their own
teaching styles by taking full responsibility for developing
lecture presentations, delivering course materials, prepar-
ing assignments (homework and examination problems),
and conducting office hours, typically over 2-to-4 weeks.
In order to prepare for the mentored teaching experience, a
contract between the faculty mentor and the graduate stu-
dent is established that details the duties and responsibili-
ties of both parties. The mentor is mainly responsible for
attending all class sessions, for which the participant is the
instructor, and evaluating the participant's teaching. Fur-
thermore, CTC participants are required to compile a teach-
ing portfolio that includes all of their teaching aids and ma-
terials (e.g., lecture notes, homework assignments, exami-
nation problems), examples of student work, student and
faculty evaluations, and a statement describing their teach-
ing philosophy. Additional information contained in the
portfolio includes a listing of service contributions to Michi-
gan State University or to the profession, such as participa-
tion on teaching committees, work on curriculum revision,
( Graduate Education
attendance at professional meetings in education, evidence
of contribution to the larger community through Service
Learning Activities, and teaching honors or recognition. The
portfolio is evaluated on its organization, presentation, and
completeness. Grading for this course is based on the comple-
tion of both the graduate student's contractual duties and
evaluation of the teaching portfolio. Upon successful comple-
tion of this course, participants receive a College Teaching
Certificate notation on their transcripts.
In the second course described above, I had an opportunity
to teach a portion of an undergraduate thermodynamics
course. Through this experience, I gained an appreciation of
the challenges that faculty members face when balancing
teaching and research. Over a three-week period, I taught three
chapters from Introductory Chemical Engineering Thermo-
dynamics.'6 Content included Departure Functions (Chapter
7), Phase Equilibrium in a Pure Fluid (Chapter 8), and React-
ing Systems (Chapter 14). I chose these topics because of my
previous experience as a teaching assistant for this course
and my familiarity in these areas.
As a first-time instructor, I found that the time required to
prepare for lecture was much greater than expected. This is a
common issue for many faculty members and has been ad-
dressed by Reis,12' who suggests that the real time for class-
room preparation is three times the original estimation. Careful
preparation of handouts, meticulous attention to accuracy, and
thorough structuring of numerous example problems con-
sumed a significant amount of time. In the end, some of this
material wasn't covered in class due to time constraints. This
incident was an excellent lesson on the balancing of fervent
preparation with the pace of a typical classroom lecture.
As part of the requirements for the teaching portfolio, the
students provided feedback, suggesting strengths and weak-
nesses for my style of teaching. Most students expressed ap-
preciation for the detailed example problems worked in class
because it helped solidify concepts. Three chemical engineer-
ing faculty members (Carl Lira and coauthors DB and MW)
also provided valuable feedback.
CTC PROGRAM RECOMMENDATIONS AND
FUTURE DIRECTIONS
I felt that the first course provided an excellent background
on the theories and methods used to effectively teach engi-
neering students, and the second course allowed me to imple-
ment these principles by having the same teaching responsi-
bilities as faculty members. My main recommendation for
enhancing the CTC program is to improve the recruitment of
participants. Recruitment efforts of both faculty and gradu-
ate students were originally done through email, but this
method was an informal and non-interactive way of promot-
)
ing the program. I recommend broader advertising to better
inform faculty and graduate students of this training oppor-
tunity, such as a general seminar or an informational session
scheduled each semester. During the session, the rationale
and benefits of the program could be explained, detailing the
success and areas of improvement of the program. This type
of session would allow both faculty and students to ask ques-
tions and to interact. It could also motivate graduate students
to pursue an academic career and encourage faculty mem-
bers to become mentors.
Currently, the CTC program is being jointly taught with
the College of Natural Science, specifically through the Di-
vision of Science and Mathematics Education (DSME). The
DSME is co-administered by the Colleges of Natural Sci-
ence and Education and its mission is to improve science and
mathematics education, from kindergarten through the un-
dergraduate years, through the professional development of
pre-service and in-service teachers and faculty members.'"
Academic specialists and faculty members with partial ap-
pointments in various departments and other colleges (includ-
ing the College of Engineering), graduate and undergraduate
students, and professional and clerical staff work together in
DSME to conduct a variety of courses, degree programs, and
other activities in support of its mission. In addition to con-
nections with the College of Natural Science, links to the NSF-
sponsored Center for the Integration of Research, Teaching
and Learning (CIRTL) are being established. The objective
of CIRTL is to create a model interdisciplinary professional
development program that will prepare graduate students,
post-doctoral researchers, and current faculty to meet the fu-
ture challenges of national Science, Technology, Engineer-
ing and Mathematics (STEM) higher education.18'
OTHER TEACHING AND MENTORING
TRAINING PROGRAMS AT MSU
MSU offers numerous teaching and mentoring opportuni-
ties, through programs, seminars, and workshops that are di-
rected at faculty development, many of which are also open
to graduate students. As a doctoral student with a passion for
teaching, I tried to take advantage of all of them! I served as
a teaching assistant for the undergraduate introductory ther-
modynamics course during my first semester at MSU. In this
role, I was responsible for attending lectures, preparing and
facilitating recitation sessions, proctoring examinations, con-
ducting office hours, and preparing solutions to homework
problems. These tasks familiarized me with the essential tan-
gential responsibilities of a professor.
For the two consecutive summers of 2002 and 2003, I
served as a chemistry instructor for a summer enrichment
program conducted through the College of Human Medicine.
Chemical Engineering Education
_
Graduate Education)
The Pre-Health Professions Preparation Institute (PPPI) is a
six-week residential summer program designed to provide
students from under-represented minority and/or disadvan-
taged backgrounds with preliminary education to enhance
their preparation and probability for successful completion
of college-level course work. I taught the first four chapters
of the course material covered in the freshmen general chem-
istry course.'91 In addition to teaching and tutoring, I had the
opportunity to mentor these students. Mentoring included
leading discussions about the expectations of college-level
work and the importance of conducting research, even at the
undergraduate-level. I also assisted these students in week-
end community-based service learning activities.
MSU has developed a relatively new graduate program,
the Multidisciplinary Graduate Training Program on Tech-
nologies for a Biobased Economy (TBE), that promotes in-
terdisciplinary scholarly interactions between students and
faculty in various scientific disciplines. I am a participant of
this graduate program. It's purpose is to produce a diverse
group of PhD scientists and engineers who have broad train-
ing related to biobased industrial product formation, have
strong research skills, and are able to work effectively in mul-
tidisciplinary teams. The program addresses the increasing
need to conduct basic and applied research requiring the con-
tributions of two or more disciplines and yielding new areas
of inquiry and application.2' Furthermore, multidisciplinary
programs and centers allow graduate students to think "out-
side the box" through exposure to philosophies of other sci-
entists and engineers not in their immediate discipline. Work-
ing with a range of individuals who have differing perspec-
tives and skills is excellent training for the interdisciplinary
opportunities that await students as new professors.21
One requirement of the TBE program was participation in
the College Teaching Certificate Program described above.
As a TBE participant, I was also required to complete the
Multidisciplinary Bioprocessing Laboratory (MBL) course.
The goal of this course is to teach students how to work ef-
fectively in multidisciplinary teams in a research environ-
ment.1 01 The students, both undergraduate and graduate, are
divided into multidisciplinary teams that conduct a semes-
ter-long, mentored research project in a participating faculty
member's research lab. To prepare students to carry out their
projects efficiently, the MBL course also incorporates inno-
vative teaching practices to help students to develop commu-
nication and critical thinking skills; these include collabora-
tive and problem-based learning, project-management con-
cepts, peer assessment, and ethics. I also served as a research
mentor for this course, in which I was responsible for guid-
ing three students to complete a research project. This men-
toring role provided experience in another essential duty of a
professor-serving as a research advisor. The TBE program
Fall 2004
is an innovative training venue that allows graduate students
to participate in contemporary research problems and to de-
velop and enhance essential skills to effectively teach techni-
cal concepts. Detailed information on the institutionalization
of the CTC and TBE programs and the MBL course at MSU
is provided in several papers.E4,-1""0. They can assist colleges
or departments interested in developing similar programs and
courses at their institution.
CONCLUSIONS
I found the teaching and mentoring training programs of-
fered at MSU to be an effective and valuable program for
preparing future educators. As a result of participating in these
programs, I am a better-prepared, more competitive, and mar-
ketable engineer, researcher, and professor. My extensive
teaching and mentoring experiences have improved my or-
ganizational and communication skills. Furthermore, my ex-
perience explaining technical and abstract concepts has de-
veloped my critical-thinking skills. My experience suggests
that, although participation in these types of programs takes
time away from research, the time invested in graduate teach-
ing and mentoring experiences is worthwhile and has en-
hanced my preparation for a career in academia. Similar pro-
grams at other universities can provide the same benefits to
engineering graduate students.
ACKNOWLEDGMENT
Fellowship for author TB was provide by the Graduate
Assistance in Areas of National Need (GAANN) through the
United States Department of Education.
REFERENCES
1. Wankat, P.C., and F.S. Oreovicz Teaching Engineering. Purdue Uni-
versity at
Publications/teaching_engineering>
2. Reis, R. M., Tomorrow's Professor: Preparing for Academic Careers
in Science and Engineering, IEEE Press, New York, NY (1997)
3. Personal communication with Dr. C. W. Somerton
4. Somerton, C.W., Bohl, D., and M.J. Crimp, "Development of an En-
gineering Teaching Certificate Program," Proc. 2000 ASEE North
Central Section Ann. Meet., East Lansing, Michigan, April (2000)
5. Somerton, C.W., Davis, M., and R.Y. Ofoli, "A Teaching Certificate
Program at Michigan State University," Proc. 2001 ASEE Education
Ann. Conf., Albuquerque, NM (2001)
6. Elliot, J.R., and C.T. Lira, Introductory Chemical Engineering Ther-
modynamics, Prentice Hall PTR, Upper Saddle River, NJ (1999)
7. Division of Science and Mathematics Education at
www.dsme.msu.edu/>
8. CIRTL Strategic Plan at
9. Kotz, J.C., and P. Treichel, Jr., Chemistry & Chemical Reactivity, 4*
ed., Saunders College Publishing, New York, NY (1999)
10. Worden, R.M., and D. Briedis, "Institutionalizing the Multidisciplinary
Lab Experience," Proc. 2003 ASEEAnn. Conf., Nashville, TN (2003)
11. Preston, C., Briedis, D., and R.M. Worden, "Training Chemical Engi-
neers in Bioprocessing," Proc. 2001 ASEE Ann. Conf, Albuquerque,
NM (2001) n
_._ ___
-zi..-
(
OraduiatSdcateon
TEACHING COUPLED
TRANSPORT AND RATE PROCESSES
YASAR DEMIREL
Virginia Polytechnic Institute and State University Blacksburg, VA 24061
Coupling refers to a flux occurring without its primary
thermodynamic driving force; for example, mass flux
without a concentration gradient called the thermal
diffusion is a well-known coupled process. Coupling also
refers to a flux occurring in a direction opposite to the direc-
tion imposed by its driving force; for example, a mass flux
can occur from a low to a high concentration region and is
called the active transport or uphill transport, such as potas-
sium and sodium pumps coupled to chemical energy released
by the hydrolysis of adenosine triphosphate (ATP) in bio-
logical systems. Although the coupled processes seem to be
in conflict with the principles of second law of thermody-
namics, interestingly, the second law allows the progress of a
process against its driving force and hence with a decrease in
entropy ASj< 0, but only if it is coupled with another process
with larger positive entropy change, i.e., ASk >> 0, thus pro-
ducing a positive total entropy change (AS + ASk) > 0. This is
consistent with the second-law statement that a finite amount
of organization may be obtained at the expense of a greater
amount of disorganization in a series of coupled spontaneous
processes. This can have important implications in describing
the coupled phenomena and organized structures in complex
systems, such as biological energy conversion cycles.( 7)
Some examples of coupled processes follow. Thermoelec-
tric phenomena have the Seebeck and the Peltier effects; in
the Seebeck effect, a temperature difference between two junc-
tions of dissimilar metals produces an electromotive force;
in the Peltier effect, the two junctions are maintained at the
same constant temperature, and a current applied through
the system causes a heat flux from one junction to another.
The uniform junction temperatures are maintained under a
steady heat flux."'
In heat and mass transfer, thermal diffusion (Soret effect)
and the Dufour effect are the coupled transport processes. In
the Soret effect, a mass flux occurs due to a temperature gra-
dient without a corresponding concentration gradient, while
in the Dufour effect, a heat flux occurs due to chemical po-
tential gradient, without temperature gradient. Thermal dif-
fusion is a critical separation process for isotope mixtures
and is of great interest in oceanographic problems. Another
well-known coupled process is the B6nard instability where
a critical temperature gradient in a fluid induces a structured
convection in the forms of cells or rotated flows (left and
right) and contributes to an effective coupling between hy-
drodynamic and thermal forces.'2 In living systems, the res-
piration system is coupled to the oxidative phosphorylation,
and ATP is produced.'45'7) The change from a simple to a com-
plex behavior is the order and coherence within a system that
leads to coupled processes and organized dissipative struc-
tures."'3 Such structures are not necessarily far from local
equilibrium and can only be maintained by a constant supply
of mass and/or energy fluxes. They have long been confined
only to biological systems, but this is changing and research-
ers from diverse disciplines are studying the occurrences and
implications of coupled processes."2,313)
Teaching of coupled processes in a first-year graduate class
should cover the approximate contents presented in Table 1,
which also lists some possible textbooks and their present
coverage. Textbooks for transport phenomena by Bird, et al.,
and Deen'9' describe some of the coupled phenomena with-
out the nonequilibrium thermodynamic (NET) theory, while
the texts for thermodynamics by Kondepudi and Prigogine,(1)
and Demirel(7' describe some of the coupled transport and
reaction processes with the postulates and formulations of
NET. The concept of nonequilibrium systems and the NET
theory would provide students with the basic fundamentals
of coupling (see Table 2). This study presents the use of NET
in teaching various coupled processes from physical and bio-
logical systems in the transport phenomena II graduate course
at Virginia Tech.
Yasar Demirel is a visiting professor in the Department of Chemical En-
gineering at Virginia Tech. He received his PhD from the University of
Birmingham, UK. He teaches senior design, thermodynamics, transport
phenomena, and simulation. His research focuses on coupled transport
and rate processes in physical and biological systems. He is the author of
a book titled Nonequilibrium Thermodynamics: Transport and Rate Pro-
cesses in Physical and Biological Systems, published by Elsevier, and
over 90 journal articles and conference proceedings.
Copyright ChE Division of ASEE 2004
Chemical Engineering Education
L
NONEQUILIBRIUM SYSTEMS
Transport and rate processes are open, nonequilibrium, and
irreversible systems with temperature, concentration, pres-
sure gradients, and affinities. Figure 1 shows a stationary-
state nonequilibrium system with coupled and uncoupled
fluxes. Although the system is not at global equilibrium, ther-
modynamic properties such as temperature, concentration,
pressure and internal energy are well-defined in an elemental
volume surrounding a given point. These volumes are small
enough that the substance in them can be treated as uniform,
and yet they contain a sufficient number of molecules so that
the principles of statistics and the methods of phenomeno-
logical thermodynamics are applicable. Therefore a local equi-
librium in any elemental volume exists, and the thermody-
namic properties are related to the state variables in the same
manner as in equilibrium.'"'1 Mostly, the internal relaxation
processes in the fluid or material are much faster than the
rate of change imposed upon the state variables, and the lo-
cal equilibrium concept is valid for a wide range of transport
and rate processes of usual fluid systems." l-9 For example,
TABLE 1
Contents and Coverage for
Coupled Transport and Rate Phenomena
Bird, Stewart Kondepudi &
Contents & Lightfootl" Prigogine"' Deen'"
Nonequilibrium systems Ch 1.2
Local equilibrium Ch 24.1 Ch 3.4. 15.1
Dissipative structures Ch 19
Nonequilibrium thermodynamics Ch 15
Balance equations & entropy balance Ch 19.2, 24.1 Ch 15.3 Ch 11.8
Dissipation (entropy production) Ch 24.1, B7 Ch 15.2 Ch 11.8
Minimum entropy production Ch 17.2
Identification of fluxes and forces Ch 24.3 Ch 15.5
Phenomenological equations Ch 16.1 Ch 11.4
Phenomenological coefficients Ch 16.1 Ch 11.8
Onsager's reciprocal relations Ch 24.1 Ch 16.2 Ch 11.4
Curie-Prigogine principle Ch 24.1 Ch 16.2
Degree of coupling
Coupled systems
Multicomponent diffusion Ch 24.2. 22.9 Ch 11.8
Diffusion in electrolyte systems Ch 11.7
Heat and mass transfer Ch 24.2 Ch 16.8 Ch 11.4
Thermoelectric phenomena Ch 16.3
Chemical reactions Ch 16.5
Electrokinetic phenomena Ch 16.7
Membrane transport Ch 24.5
Biological systems Ch 19.3. 19.6
Second law analysis
Lost work, exergy loss
Extended nonequilibrium
Thermodynamics
Network thermodynamics
Mosaic in nonequilibrium
thermodynamics
Rational thermodynamics
Example problems & questions Ch 24 Ch 15, 16 Ch 11.4
Fall 2004
Graduate Education)
the relaxation time for heat conduction for gases at normal
conditions is 10-2s, and for typical fluids 10-"-10-'3 s."" Lo-
cal equilibrium is not valid in highly rarefied gases where
collisions are too infrequent, however, and hence the relax-
ation times are much higher. The extension of equilibrium
thermodynamics to nonequilibrium systems with the local
equilibrium assumption is possible in terms of entropy s[T(x),
ni(x)] and energy u[T(x), ni(x)] densities, which are a func-
tion of the temperature and species mole number densities at
location x, when a well-defined local temperature T(x) ex-
ists. Consequently, the total entropy and energy can be ob-
tained from the integrals over the volume of system
S= s[T(x),ni(x)]dV U= fu[T(x),ni(x)]dV
v v
and using the s(x) and u(x), we obtain the local variables of2-6)
(as/au)ni =/T(x) and (as/ni)u =- i(x)/T(x)
The level of distance from the global equilibrium may be
treated as a parameter of a process, and is called the thermo-
dynamic branch as shown in Figure 2."' Near global equilib-
rium, there are linear relations between the driving forces in
the process and the fluxes that result; examples are Fourier's
and Fick's laws. Processes occurring far from global equilib-
rium, however, such as most chemical reactions, lead to non-
linear force-flux relations, and in some cases to the sponta-
Y
UW
Figure 1. Nonequilibrium distribution of components in a
stationary-state coupled system: Flux of species Uis coupled
with the flux of Y through an enzyme in a cell. Species of Y
do not take part in any chemical reaction. Neither the flux
of U nor the flux of Y is coupled to the flux of W, however.
TABLE 2
General Procedure for Teaching Coupled Phenomena with
Nonequilibrium Thermodynamics Approach
Step Procedure
1. Start with the Gibbs relation in terms of the relevant thermodynamic
variables
2. Establish the conservation laws for the variables
3. Establish an entropy balance equation and derive the rate of entropy
production or dissipation function to identify a set of conjugate fluxes
and thermodynamic forces
4. Use these fluxes and forces in linear phenomenological equations
5. Calculate total fluxes in terms of forces or forces in terms of driving forces
6. Calculate the transport coefficients using Onsager's reciprocal rules
7. Calculate the dissipations due to individual processes
8. Quantify the effects and degree of coupling on transport and rate processes
7-I
r -~*r j,
Cz 11m D
--------
neous formation of self-organized dissipative structures.'4"6)
NONEQUILIBRIUM THERMODYNAMICS (NET)
Change of total entropy of a system is
dS deS diS (1
+ (1)
dVdt dVdt dVdt
where the dS/dVdt is the rate change of total entropy, the
first term on the right is the entropy exchange through the
boundary that can be positive, zero, or negative, and the sec-
ond term is the rate of entropy production due to irreversible
processes within a system, and is always positive. We deter-
mine the volumetric rate of entropy production
S= (diS/dVdt) = YJkXk 0
or the rate of local dissipation of Gibbs free energy in terms
of a product of a flux, Jk and a thermodynamic force, Xk,
y = I JkXk = T 2> 0
For a multicomponent fluid system with n species and z
number of chemical reactions, the dissipation function can
be derived by incorporating the entropy balance into the gen-
eral balance equations of mass, momentum, and energy, and
the Gibbs relation7,10'
'P-=JX=TO=
T IJu V i[TV( --]-Fi +- :(Vv)-- AjJrI L>0
T T i=1 T T T =1 'Jr
where
J and J
IRi
Fi
A
V
.1,
vectors of heat and mass fluxes respectively
chemical potential of species i
force per unit mass of component i
viscosity part of stress tensor
velocity
affinity (A=- vivi)
stoichiometric coefficients
reaction flux, which is a scalar.
In Eq. (2), the dissipation function consists of four separate
contributions of heat transfer, mass transfer, momentum trans-
fer, and chemical reactions (without electrical and magnetic
effects); their conjugate fluxes and forces are summarized in
Table 3. The relationship between the heat flux, J and the
conduction heat flux, J, is
n_
Jq =Ju -hiJi
i=l
where hi is the partial specific enthalpy.
In the dissipation-phenomenological equation (DPE) ap-
proach,(12) Eq. (2) identifies a set of independent conjugate
fluxes and forces to be used in the following linear phenom-
enological equations in the form of a conductance formulation
J,= LikXk (3)
k=l
If the fluxes are easy to determine or relate to measurable
properties, then the following resistance formulation is pre-
ferred
m
Xi= 2 KikJk (4)
k=l
The phenomenological coefficients, Lik or Kk (i,k =
1,2,...,m) are related to the transport coefficients, such as ther-
mal conductivity, k, and mass diffusivity, D, and can be de-
termined experimentally; Kk = ILlk/ILI, ILI is the determinant
of the matrix of the coefficients Lik, and ILlik is the minor for
Lk. According to Onsager's reciprocal relations, the cross co-
efficients are symmetric Lik = Lki; (isk) for a set of indepen-
dent conjugate fluxes and forces identified by the dissipation
function or the rate entropy production. Onsager's relations
are based on microscopic reversibility, and are independent
of the state of a system or any other microscopic assump-
tions.",'0 The cross coefficients, Lik, describe the degree of
coupling, qik,,, of processes(4,12)
u Thermodynamic branch
I-
Organized
structures
Xs
Linear region Nonlinear region
Xc X
Figure 2. Thermodynamic branch indicating the linear and
nonlinear regions; X shows the force and Xc is the critical
force or distance from equilibrium state, where no force
exists. After a critical distance from global equilibrium the
system may move to an organized structure that needs con-
stant supply of matter and/or energy.
TABLE 3
Conjugate Fluxes and Forces Identified by the Dissipation
Function (DPE) Approach"'"
Process Flux Force
Heat flux Ju=L Xq Xq =TV
Mass flux Ji=LXi X =Fi-TV 2
Viscous effect Jv=LvXv X,=(Vv)
k
Reaction velocity Jr =LrX, Xr =A-- ivij
i=i
where
VaI-v(tim +hiV( -
T-T T- TT
Chemical Engineering Education
Lik (5)
(LiiLkk)1/2
which can be determined using the transport coeffi-
cients."2'13,16)
From Eqs. (2) and (3), the dissipation is expressed by
m
'P=LikXiXk >0
i,k
and the matrix form of it shows that the dissipation function
is quadratic in form
T=XTLX= TKJ>0
for all forces and fluxes, where XT and JT are the transpose of
the respective vectors. Table 4 shows the four main postu-
lates in the linear NET approach.
COUPLED TRANSPORT AND RATE
PROCESSES
Equation (2) consists of scalars of tensor rank zero YO,
vectors with tensor rank one ,', and a tensor of rank two TP2
0O =T(V.v)- Jr,jAj 0 (6)
j=1
Y;= JuTV I + il JiFi- TV(r ] 0 (7)
'2 = T':(Vv)'s >0 (8)
where T:(Vv)=T':(Vv)'+T(V-v) (the double dot product of a
symmetric and antisymmetric tensor is zero). According to
the Curie-Prigogine principle, in isotropic macroscopic sys-
tems, a scalar process cannot produce a vectorial change and
vice versa; for example chemical affinity cannot cause a di-
rected heat flux, and more generally, fluxes and forces whose
tensorial rank differ by an odd number cannot couple in an
isotropic medium. Such fluxes can be coupled at the system
boundaries (which are not isotropic) by the boundary condi-
TABLE 4
Four Main Postulates of the Linear Nonequilibrium
Thermodynamics (NET) Approach
Global form of the flux-force relations is linear, and the propor-
tionality constants in these relations are the phenomenological
coefficients
In an isotropic system, according to the Curie-Prigogine principle,
no coupling of fluxes and forces occurs if the tensorial order of the
fluxes and forces differs by an odd number
In an isotropic system, any flux is caused by all the forces that
satisfy the Curie-Prigogine principle, and any force is caused by
all the fluxes
Matrix of the phenomenological coefficients is symmetric
provided that the conjugate fluxes and forces are identified from a
dissipation function equation or an entropy production equation
tions, however.
The fluxes and forces in Eq. (2) can be defined in various
ways, for example, definitions of mass fluxes change with
the choice of reference velocity. The entropy production re-
mains invariant under certain transformations, however;1,14)
for example, for a system in mechanical equilibrium
S(ciFi ciV))= 0
(from the isothermal Gibbs-Duhem equation and mechani-
cal equilibrium equation), and for the transformation
Ji Ji + vci
where c is the concentration of component i, and v is an arbi-
trary average velocity. Equation (7) can be transformed fur-
ther by introducing the total potential
9i = i i+Wi
where is the specific potential energy, the isothermal gra-
dient of the total potential VwLi* and the heat flux J in the
following expression
VT VT
T -Fi = Vg -gi +Vvi =VTi-h, (9)
T T T
where Vq, = F,. Using Eq. (9) in Eq. (7), we have for n-1
independent diffusion fluxes
n-1
't= -JqVlnT- I JiVT (g-I 0 (10)
This procedure eliminates an arbitrary choice of fluxes and
forces, and ensures that the cross phenomenological coeffi-
cients obey the Onsager's relations for linear phenomeno-
logical laws.
In the next section, some examples of transport and rate
processes from physical and biological systems are presented
to show the utility of NET in teaching coupled processes.
Heat and Mass Transfer For a fluid under mechanical
equilibrium with no chemical reaction, the dissipation func-
tion of heat and independent diffusion fluxes from Eq. (10)
is(7.12,14)
n-l n-l1
T = -JqV In T i Jiaik n j V TP, (11)
i,k=l j=1 j TPwi
where ak = 8k + wk/w and 86k is the unit tensor, w is the
mass fraction of species j. In a binary liquid mixture, a set of
independent forces identified by the dissipation function of
Eq. (11) for heat and mass fluxes is X = -VlnT and X, =
-(1/w2)(l/fwl)TP Vw,, respectively. Then the linear phe-
nomenological equations are
-Jq = LVln T+L 1 Vw (12)
'4 W2 (aWi )T,P
Fall 2004
. ,, -- -- - '?3
-q = VlnT+LVIn T + l Vwl (13)
w2 a )T,P
Here, by the Onsager reciprocal relations, L = Lql. From
Eq. (12), heat flux due to primary coefficient Lq is expressed
by Jq = -LqqVn T = -LqqTV( / T); after comparing with
Fourier's law Jq = -kVT the Lq is related to the thermal
conductivity k:L = kT. When no volume change occurs due
to the diffusion flows (no volume flow), the mass flux J, is:
J =-L11(1+ ViC /V2c2)(aVi1 /aci)Vc,
where c. and Vi are the concentration and partial molar vol-
ume of component i, respectively; comparing it with Fick's
law, J, =-DVc,, the L,, is related to the diffusion coefficient
of component 1 D,: LI = D[(1 +Vici /V2c2)(ag1 /3ac)] .
The heat of transport Q, of species 1 is defined by Q, = L q/
L,; it is the heat carried by a unit flux of species 1 when
there is no temperature gradient and no diffusion of other
species and can be measured experimentally.!5' Equations (12)
and (13) can be expressed in terms of heat of transport Q,
and the transport coefficients-7.121
-Jq = kVT +pD1QIVw, (14)
-J1 = pDT V ln T + pD1Vwl (15)
where DT is the thermal diffusion coefficient for species 1
and p is the density. The second term on the right side of Eq.
(14) shows the Soret effect, also known as thermal diffusion,
while the first term on the right side of Eq. (15) shows the
Dufour effect. Comparing Eqs. (13) and (15) with vanishing
concentration gradients yields Lq = pDT .The degree of cou-
pling can be expressed in terms of Q, and the other transport
coefficients from Eq. (5) (13)
S pDMIM2WlW2
qQkMaRT 2(1+r)
(16)
where M. and Mv show the molecular mass of species i
and mixture, respectively, R is the gas constant, and
F1 = (a In i /3 In xI )TP is called the thermodynamic factor,
and can be determined from experimental data or an activity
coefficient, y, model. As heat and mass fluxes are both vec-
tors, the sign of q indicates the direction of fluxes of a spe-
cies; if q > 0, the flow of a species may drag another species
in the same direction, while the flux may push the other spe-
cies in the opposite direction if q < 0.7,12) Using Eqs. (14) to
(16), effects of concentration and temperature on the coupled
heat and mass fluxes in liquid mixtures can be studied.(',13
Membrane Transport The dissipation equation for an
isothermal, nonelectrolyte transport in an ideal binary sys-
tem of solute (s) and water (w) through a membrane is(14'161
S= -JsA^s- JwA^w >0 (17)
With Onsager's relations, Lpd = Ldp, the transport through
the membrane can be described by the three coefficients in-
stead of four. The coefficient L is the mechanical coefficient
of filtration, the Ld has the characteristics of a diffusion coef-
ficient, the cross coefficient Ldp is the ultrafiltration coeffi-
cient, and Lpd is the coefficient of osmotic flux. The ratio -
L pd/L is called the reflection coefficient cr, which is always
smaller than unity. With these coefficients, the degree of cou-
pling is obtained from q = Ldp/(L Ld)112
Transport in Ion-Exchange Membrane For the diffu-
sion of a single electrolyte and water in an ion-exchange mem-
brane, the dissipation due to the fluxes of ions (1 and 2) from
a neutral salt and water across the boundary is(14,16
S= -JiAi J2A2 JwAug > 0 (24)
where pi is the electrochemical potential of ion i, and ex-
pressed by i-i=.i+ziFE; here z; is the charge and F is the
Faraday constant. For a pair of electrodes interacting revers-
ibly with one of the ions in the solution, the electromotive
force AE can be related to the electrochemical potential dif-
ference of the ith ion AE=Aji/ziF. By assuming that the ion
2 reacts reversibly with the electrode, and since ion 1 is not
produced or consumed, then the flux of ion 1 is the flux of
salt, and given by Js = J,/v,, where v, is the number of ions
decomposed per molecule of salt, which obeys the
Chemical Engineering Education
Equation (17) leads to the following general forms of the
fluxes
Js = -Lss As LswAgw (18)
Jw = -Lws A[s LwwAgw (19)
where the forces Ais, ALiw are the differences of chemical
potentials, and J and J are the fluxes for the solute and wa-
ter across the membrane, respectively. It is customary to re-
place A~i with more easily measurable quantities, such as
AgLi = ViAP + RTA ln ci = ViAP + RTAc / c, and Eq. (17) be-
comes
= -Js(VsAP+AI /cs)-Jw(VwAP- AHn/cw) O (20)
where Vs and Vw are the partial volumes, c and c are the
concentrations of solute and water, respectively, AH is the
osmotic pressure difference Al = RTAcs. Equation (20) is
further transformed by defining the total volume flux Jv across
the membrane as J, = JV, + JsVs, and the flux of the sol-
ute Jd relative to the water Jd =J /c J /c
'= -JAP- JdAnI 0 (21)
With the forces of AP and All identified by Eq. (21), the
commonly used phenomenological equations that describe
the transport through a membrane are
J = -LpAP LpdAH (22)
Jd = -LdpAP LdA (23)
electroneutrality condition v,z1 + vz, = 0. With the electric
current flux I = F(Jz, + Jz,), Eq. (24) becomes
T = -JsAps JwAp IAE > 0 (25)
It may be advantageous for certain cases to transform Eq.
(25) further by using the volume flux J instead of water flux
Jw, and by introducing the relationships Aps = VsAP + AH / cs
for a nonelectrolyte solute and A w = V (AP AHs) into
V = -J,(AP As)- JsAFs / cs IAE > 0 (26)
The related phenomenological equations are then
Jv =-Lv(AP- AHs)- LvsAHs/c, LveAE (27)
J, = -L,,(AP Anl)-LssAlls / cs LseAE (28)
I= -Lev (AP A )-LesAHsn/c LeeAE (29)
In Eqs. (27) to (20) six coefficients characterize the mem-
brane transport due to Onsager's relations. The coefficients
can be determined by measuring conductivity of the mem-
brane, transport numbers, and the fluxes due to electro-os-
motic, osmotic, diffusional, and pressure.
The thermodynamic efficiency of energy conversion q can
be defined as
s )+_Jw^ lw (30)
= IAE IAE )
where IAE represents the driving process, and JALs and JwAw
are the driven processes. The degrees of coupling are the ion-
water qsw, ion-current qse, and water-current qw,, which are
Lsw
q sw w )1/2
S(L ss ww
Lse
qse Lss e/2
(LssLee
Lwe
qwe (LwwLee)l/2
Graduate Education )
the net oxygen consumption, and the out flux Jp is the net rate
of ATP production.
Based on Eq. (32), the linear phenomenological relations are
Jp =LpXo+LpXp (33)
Jo =LopX +LpXp (34)
Here, Lo is the influence of substrate availability on oxy-
gen consumption rate and Lp is the feedback of the phosphate
potential on ATP production rate. The cross-coupling coeffi-
cient Lop is the phosphate influence on oxygen flux, while Lpo
shows the substrate dependency of ATP production. Experi-
ments shows that Onsager's reciprocal relations hold for OP,
andL =L .L 5
op po
Thermodynamic efficiency of the coupled systems of res-
piration (driving, N >> 0) and OP (driven, P < 0) is defined
as the ratio of output power (Tp = JpXp) to the input power
(to = J0X0)(4.6)
n=- (35)
JoXo
By dividing Eq. (33) by Eq. (34), and by further dividing the
numerator and denomerator by Xo(LoL )l2, we obtain the effi-
ciency in terms of the force ratio x and the degree coupling q
n = jx +q (36)
q+l/x
where
Jp XZ ( aL n )2 L
j= x= Z= Lo and q= Lop with 0
JZ' X" Lo (LoLp)1/2
(31)
Oxidative Phosphorylation (OP) Experiments and
empirical analyses of cellular processes show that linear re-
lations exist between the rate of respiration and growth rate
in many organisms, and for some of the steps in OP.'5.616' In
mitochondria, the respiration system is coupled to the OP,
and the electrochemical potential gradient of protons across
the inner membrane drives the synthesis of ATP from ad-
enosine diphosphate (ADP) and phosphate (Pi). The theory
of NET has been used to describe the thermodynamic cou-
pling, and how the mitochondria can control the efficiency
of OP by maximizing ATP production, the cellular phosphate
potential, or the cost of ATP production. ,6" For this coupled
system a representative dissipation expression is
Y = JoX, +JpXp > 0 (32)
where the input force X. is the redox potential of oxidizable
substrates, and X is the output force representing the phos-
phate potential, Xp = [AG p + RT ln(cATP / CADPCpi)], which
drives the ATP utilizing functions in the cell; the AGO is the
standard Gibbs free energy. The associated input flux Jo is
Fall 2004
The ratio J /J is the conventional phosphate-to-oxygen con-
sumption ratio P/O, the term Z is called the phenomenologi-
cal stoichiometry. For the biphasic function in Eq. (36), opti-
mal thermodynamic efficiency qopt is the function of q only,
as shown in Figure 3.
r2
_opt + j (37)
The sequence of coupling is controlled at switch points
where the mobility, specificity, and the catalysis of the cou-
pling protein are altered in some specific ways, such as shifted
equilibrium. Equations (32) to (37) offer a phenomenologi-
cal description of respiration and oxidative phosphorylation,
and the NET approach does not require a detailed mecha-
nism of the coupling.
Chemical Reactions NET theory provides a linear re-
lation between the rate of reaction Jr and the affinity A of
reaction (A=- vili where the v, are the stoichiometic co-
efficients, which are positive for products and negative for
reactants) when IAI **
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