Chemistry 4595
Midterm #1
Fall 1998
October 15, 1998
1. Soap bubbles are filled with air and enclosed by a thin liquid membrane, which is
mostly water. Write an approximate expression for the radius of gyration, Rg, of a
soap bubble having total radius R.
2. Make a table of as many common shapes (polymers are common shapes to you now!)
as you can, containing the shape, the mass fractal dimension, df, and the exponent  as in
size ~ M. The first row of the table is done for you. 
SHAPE
ROD
Mass Fractal Dimension
df
1
Exponent

1
3. On the plot below, make a qualitative sketch of Smix for the ideal solution case (use a
full line) and for the Flory-Huggins calculation (use a dotted line, or a different color if
you have it). Note that the mole fraction is to be used as the x-coordinate for both curves.
+
Smix
0
0
xsolute
1
4. Discuss in a few sentences the kinds of non-ideality we can have in small particles,
linear polymers, and globular polymers (like proteins).
5. What are some of the differences between addition and condensation polymers? Give
one example of each by writing a chemical formula.
6. Your classmate, J. Willard Wannabe, has measured an osmotic pressure plot, shown
below, for a protein known to behave as a globular solid.

c
0
c
Of course, the behavior is described by the virial equation:

16R 3 
 1

 RT 
 A2 c  ...  and we showed that: A2 
where  is
c
3M 2
M

Avogadro’s number. Clearly, A2 is negative in the plot. J. Willard Wannabe has
asked you to decide if this plot and these equations mean the radius is negative or
the mass is negative, or both. What’s your answer?
7. In the rotational isomeric state model, a proposed statistical weight matrix for a
typical vinyl polymer has the following form:
u
t
1
t
g 
g 
g g



0

0
Each term (1, 0 or ) in the matrix represents a Boltzmann factor for the energy of
neighboring conformations (t for trans and g for gauche).
A)
B)
C)
D)
For typical vinyl polymers, is  less than 1 or greater than 1?
Why are some terms set to zero?
What was the main reason that the RIS model had to be developed?
What is the big computational advantage to it?
8. We have said that <r2> = C nl22 and we showed (in two different ways!) that
n0.2 . This is for polymers in three dimensions. For a polymer confined to a
surface (i.e., two dimensions) ny where y is some exponent. Do you expect y to
be more than 0.2 or less than 0.2? Defend your reasoning.
9. Tell in your own words, with pictures if you like, what the persistence length of a
polymer is.
10. Suppose you are a Ph.D. in industry, and your boss tells you to do a rotational
isomeric state calculation to estimate mean square end to end lengths for some new
wormlike polymer the company is trying to market as a high-strength replacement for
Kevlar. These days, that’s easy—just get the Biosym program. But as you walk out
of the office, he suddenly calls you back in and says, “Oh, by the way—marketing
wants a plot of persistence length vs. mass, too.” You have already decided to leave
this company because your boss clearly did not have the benefit of a Polymer
Physical Chemistry course and is, therefore, an idiot. What should you reply?
Oh…and marketing
wants a plot of
persistence length vs.
molecular weight, too!
11. Your rude comments to the idiot boss in the previous problem go over his head, and
he fails to fire you. Darn! Instead, he assigns you to determine the weight percent at
which the new “wonder rod” polymer makes liquid crystals. Dutifully, you make
solutions up at various compositions. You find by polarizing light microscopy that
the solution becomes liquid crystalline at 12.6% by weight. The boss is delighted,
and tells you that he will show these results at a sales meeting on the French Riviera
next month. You point out that, perhaps, a technical expert should accompany him,
and you volunteer for the assignment. He explains that corporate cutbacks have
eliminated non-essential personnel from traveling to meetings located near topless
beaches in the Mediterranean. And besides, he failed to buy his tickets early and had
to pay a premium for the last seat available on the Concorde. He returns angry
because you did not anticipate that he would require the volume fraction of the LC
transition, not weight fraction. He doesn’t even know the difference, but wants to be
educated. (It is always the privilege of the underpaid to educate). Write a short
report (include equations to confuse the boss) to explain how we convert from weight
fraction to volume fraction. Invent symbols as you need them. If the partial specific
volume is known to be 0.932 mL/g for this polymer, and the density of solvent is
1.033 g/mL, make the conversion for your boss. Also, discuss any approximations
you had to make.
12. The curves below represent the free energy of mixing at a particular temperature.
Graphically estimate the equilibrium concentrations of the coexisting phases. I must
see your graphical process—don’t just guess an answer!
Gmix

polymer
