MatSE443:
Introduction to the Materials Science of Polymers
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All paragraph and pages numbers refer to the primary text (Painter & Coleman) Study Guide (chapter 7)
Concepts that you must know:
Review -also from previous courses material- the following: phase
transition, first order phase transition, types of intermolecular
interactions (van der Walls, electrostatic, dipole-dipole, hydrogen bonding)
Bond rotations, bond rotation potential, trans / gauche for sp3 carbon.
Crystalline materials and X-Ray Diffraction. Crystal unit cell for
small molecules and polymers. Polymeric crystals:
fringed micelles, spherulites, chain folds, tie molecules.
Polymer crystals from solution, from the melt, shear-induced.
Exercises:
* Go through the 'random walk' derivations of 7.D, esp. the relations
on the mean square end-to-end distance (eq. 7.14) and the associated
probability distribution P(R) or W(R) (eq. 7.23, fig. 7.14).
* Explain rubber elasticity based on the concept of end-to-end
probability distribution W(R).
* Go through study question 5 (pg. 256), esp. on how mechanical
properties and optical transparency depend on the polymer state.
Interactive Module:
You need the
latest plugin
(Flash Player version 6) (which can be obtained free from here)
The files are extremely small (typically half a minute with a modem) and
can be run directly from this web-page.
Start by a 1 step RW (set the step to a large number, e.g. 90) and
plot 150 RWs. Notice how the ends are arranged. Change to 2 steps and
comment on how the distribution of ends changes. How many runs do you need
to start approaching the statistical average of the mean square end-to-end ?
Make 900 RW of 2 steps and comment on the existence of RWs that end
near the starting point (i.e. end-to-end close to zero)
Choose 100 steps of RW (set the step to a small number, e.g. 10) and
make 10, 20, 30, ..., 100 RWs. Comment on the RW end distribution and the
running mean square end-to-end average.
Choose a small step length (e.g. 5) and make increasingly longer RWs:
10, 20, 100, 200, ..., 999. Is RW an effective trajecory to get away from the
starting point? Comment on how your qualitative observation can be
quantified through the average mean square end-to-end distance.
