Currently Taught Courses

CHEM 1303 General Chemistry I 

CHEM 1304 General Chemistry II

Previously Taught Courses

CHEM 5383 Physical Chemistry I 

CHEM 5384 Physical Chemistry II 

CHEM 6114 Chemical Kinetics 

CHEM 5396 Advanced Physical Chemistry   

Last taught Fall 2013

Text 

Recommended texts: (i) P. Atkins and J. de Paula: Physical Chemistry, 9th ed., (W. H. Freeman and Company, New York, 2010); and (ii) I. R. Epstein and J. A. Pojman: An Introduction to Nonlinear Chemical Dynamics (Oxford University Press, New York, 1998). 

Course Grade 

Three homework assignments and a term paper on a topic related to the Belousov-Zhabotinsky reaction or the Chlorite-Iodide-Malonic Acid reaction.

Course Description: This course covers transport and chemical kinetics, with special emphasis on temporal and spatial pattern formation in nonlinear chemical systems. The class will acquaint students with the basic theoretical ideas and experimental tools of chemical pattern formation.

Background: Patterns are ubiquitous in nature, ranging from the spiral structure of galaxies to banded rocks to the stripes of the zebra to the one-cellular algae Acetabularia. Though temporal and spatial patterns in chemistry were sporadically reported in the literature during the first half of the last century, the field of chemical pattern formation only took off in 1968. At a conference in Prague that year, the work of Belousov and Zhabotinskii on oscillating chemical reactions, done in Moscow in the fifties and early sixties, became widely known to western scientists. It was realized at that time that their work could be understood in the framework of dissipative structures, whose theory was being developed by the Brussels school. Also, Turing's seminal 1952 article "The Chemical Basis of Morphogenesis" was "rediscovered". In this work, Turing proposed a theory of chemical spatial pattern formation and its application to biological patterns. The field of oscillating reactions received a further boost in 1972, when Noyes and coworkers at the University of Oregon elucidated the chemical mechanism of the Belousov-Zhabotinskii reaction. In the mid-seventies, the Bordeaux group pioneered the use of the CSTR (continuous-flow stirred tank reactor) for the study of chemical oscillations and chaos. This tool has become an invaluable device in the field of oscillatory reactions. Then in the early eighties, Epstein, De Kepper, and coworkers at Brandeis University discovered systematic ways to design new oscillating chemical reactions. In 1987, the Austin group developed the CFUR (continuous-flow unstirred reactor) as the spatial analogue to the CSTR. Chemical patterns persist in a CFUR as long as the feed of the reactor is maintained. Turing patterns, stationary spatial chemical patterns, were first observed in a CFUR in 1990 by the Bordeaux group. 

Web Sites, Literature, Etc.

Movies:

"Never Say Never":  The history of the BZ reaction produced by Moscow State Television in 1982 (dubbed in English).

Brandeis group: Various movies of pattern formation in reaction-diffusion systems.

Some good introductory articles are: 

• I. R. Epstein, K. Kustin, P. De Kepper, and M. Orban: Oscillating Chemical Reactions, Scientific American, March 1983, 112–123 

• I. R. Epstein: Patterns in Time and Space - Generated by Chemistry, Chemical & Engineering News, March 30, 1987, 24–36 

• J. D. Murray: How the Leopard Gets Its Spots, Scientific American, March 1988, 80–87 

• I. R. Epstein and K. Showalter: Nonlinear Chemical Dynamics: Oscillations, Patterns, and Chaos, J. Phys. Chem. 100 (1996) 13132–13147

Classic articles: 

• R. Luther: II. Sitzung am Dienstag, den 22. Mai, vormittags 9 Uhr, im grossen Auditorium des chemischen Laboratoriums der Technischen Hochschule. Räumliche Fortpflanzung chemischer Reaktionen, Z. f. Elektrochemie 12, 596 (1906) [translation by R. Arnold, K. Showalter, and J. J. Tyson: J. Chem. Ed. 64, 740 (1987)]

• A. J. Lotka: Contribution to the Theory of Periodic Reactions, J. Phys. Chem., 14, 271-274 (1910)

• J. S. Morgan: XXX. —The periodic evolution of carbon monoxide, J. Chem. Soc., Trans., 109, 274-283 (1916)

• A. J. Lotka: Undamped oscillations derived from the law of mass action J. Am. Chem. Soc., 42, 1595-1599 (1920)

• R. S. Lillie: The Recovery of Transmissivity in Passive Iron Wires as a Model of Recovery Processes in Irritable Living Systems: Part I, J. Gen. Physiol., 3, 107-128 (1920)

• R. S. Lillie: The Recovery of Transmissivity in Passive Iron Wires as a Model of Recovery Processes in Irritable Living Systems: Part II, J. Gen. Physiol., 3, 129-143 (1920)

• W. C. Bray: A Periodic Reaction in Homogeneous Solution and Its Relation to Catalysis, J. Am. Chem. Soc., 43, 1262-1267 (1921)

• B. P. Belousov: A Periodic Reaction and Its Mechanism in Field, R. J. and Burger, M. (eds.), "Oscillations and Traveling Waves in Chemical Systems," Wiley, 605-613 (1985)

• A. M. Turing: The Chemical Basis of Morphogenesis, Phil. Trans. R. Soc. Lond. B, 237, 37-72 (1952)

• A. M. Zhabotinsky: A history of chemical oscillations and waves, Chaos, 1, 379-386 (1991)

Chemical Kinetics with R

R is not only a powerful environment for statistical analysis and graphing data, it also provides a high-level programming language for scientific computing. R is an excellent tool for solving kinetic rate equations and for modeling nonlinear chemical systems. R is open source and is available free-of-charge for all three major platforms: Macintosh, Windows, and Linux.

Installation:

1. Download and install the appropriate R binary from The Comprehensive R Archive Network (CRAN).

2. Download and install the free and open-source front end RStudio, a powerful editor and superb integrated development environment for R.

3. The R binary installs only the base system. To solve kinetic rate equations and to model nonlinear phenomena in chemistry, biology, ecology, etc., you need to install additional packages using the R application. Go to the menu item "Packages," and click "Install package(s)." The wording of the menu items may differ slightly, depending on the platform and version. Make sure that "Install dependencies" is checked. You can also use RStudio to install packages. Do not download package binaries directly from CRAN using the package URL provided below.

Useful Packages for Chemical Kinetics and Nonlinear Dynamics:

• deSolve: General solvers for initial value problems of ordinary differential equations (ODE), partial differential equations (PDE), differential algebraic equations (DAE), and delay differential equations (DDE). deSolve entry at CRAN

• rootSolve: Nonlinear root finding, equilibrium and steady-state analysis of ordinary differential equations. rootSolve entry at CRAN

• ReacTran: Modeling reacting systems with diffusive or advective transport in one, two or three dimensions. ReacTran entry at CRAN

• bvpSolve: Solvers for boundary value problems of ordinary differential equations. bvpSolve entry at CRAN

• GillespieSSA: Gillespie's Stochastic Simulation Algorithm (SSA) for simulating internal fluctuations due to small copy numbers in chemical systems; provides Gillespie's exact stochastic simulation algorithm (Direct method) and several approximate methods. GillespieSSA entry at CRAN

• adaptivetau: Adaptive tau leaping method; an approximate method of Gillespie's Stochastic Simulation Algorithm (SSA) for simulating internal fluctuations. adaptivetau entry at CRAN

• sde: Simulation and inference for stochastic differential equations; modeling external fluctuations. sde entry at CRAN

• ggplot2: Enhanced graphics capabilities. ggplot2 entry at CRAN; ggplot2

Many additional packages for a variety of tasks are available at CRAN and at Bioconductor. 

Literature for Scientific Computing and Mathematical Modeling with R:

• Soetaert, K. and Meysman, F.: Scientific computing in R (2013); an excellent tutorial to get started with R

• Soetaert, K.; Cash, J. and Mazzia, F.: Solving Differential Equations in R (Springer, 2012)

• Bloomfield, V.: Computer Simulation and Data Analysis in Molecular Biology and Biophysics: An Introduction Using R (Springer, 2009)

• Soetaert, K. and Herman, P. M. J.: A Practical Guide to Ecological Modelling: Using R as a Simulation Platform (Springer, 2009)

• Stevens, M. H. H.: A Primer of Ecology with R (Springer, 2009)

• Chang, W.: R Graphics Cookbook (O'Reilly, 2013)

• Adler, J.: R in a Nutshell (O'Reilly, 2012)