13.4 The Reaction Kinetics of Polymer Formation 589
a single curve, called alimit cycle. There is also a simplified mechanism with five
steps called theoregonator, developed by Noyes’ group at the University of Oregon.^21
This mechanism also leads to oscillatory behavior that simulates the BZ reaction fairly
accurately.PROBLEMS
Section 13.3: Autocatalysis and Oscillatory Chemical
Reactions
13.24 a.By differentiation of Eq. (13.3-10), find an expression
for the rate of the autocatalyzed reaction of
Eq. (13.3-1).
b.Find an expression for the time at which the rate has
its maximum value.13.25 a.Construct an accurate graph ofxas a function oft
for the function of Eq. (13.3-10). Take the case that
[A] 0 1 .000 mol L−^1 , [F] 0 0 .100 mol L−^1 , and
kapp 1 .00 L mol−^1 s−^1.
b.Construct an accurate graph of the rate of the reaction
for the case of part a.
13.26 a.Plot the curve in phase space representing the
solution of Eq. (13.3-14) forC 1 .00 mol L−^1 ,
[A] 1 .00 mol L−^1 ,k 1 1 .00 L mol−^1 s−^1 ,
k 2 0 .5 L mol−^1 s−^1 , andk 3 0. 1 .00 s−^1. One way
to proceed is to solve Eqs. (13.3-13a) and (13.3-13c)
numerically by writing a computer program using
either Euler’s method or the Runge–Kutta
method.^22
b.Construct plots of [X] and [Y] as a function of time,
using the program of part a.13.4 The Reaction Kinetics of Polymer Formation
The wordpolymercomes frompoly, meaning “many,” andmeros, meaning “parts.”
Polymer molecules are formed from small molecules (monomers) that react to form
covalently bonded chains or networks. Synthetic polymers such as polyethylene, nylon,
and polyesters are found in many manufactured products. There are also many natu-
rally occurring polymers, including natural rubber, proteins, starches, celluloses, and
nucleic acids. The properties of polymers are determined by their molecular struc-
tures, and the properties of synthetic polymers can be tailored to specific applica-
tions. The “Macrogalleria” website http://www.psrc.usm.edu/macrog maintained by
the Polymer Science Department of the University of Southern Mississippi provides
a great deal of information about polymers, including a video of the action of the
Zeigler–Natta catalyst that is used to form synthetic rubber that is identical to natural
rubber.
Some polymers, such as polyethylene, polystyrene, and polypropylene, have
chainlike molecules. These polymers usually soften when heated and are sometimes
calledthermoplastic polymers. Other polymers are made up of networks instead of
chains. Some of the network polymers have long chains with short chains (cross links)
fastening two or more chains together, and others, such as Bakelite, have networks
that are bonded in two or three dimensions. These polymers are sometimes called
thermosetting because they are usually formed at high temperatures.(^21) R. J. Field and R. M. Noyes,J. Chem. Phys., 60 , 1877 (1974). If you search for “oregonator” in Google or any other search engine, you will find links to
programs that will solve the kinetic equations for you.
(^22) See R. G. Mortimer,Mathematics for Physical Chemistry, Elsevier/Academic Press, San Diego, 2005, p. 260ff, or any numerical analysis textbook.