Chemistry 4595
Problem Set #4
Fall 1998
Due: Thursday, September 24
Richards 4.1.
Richards 4.2.
1. A polystyrene of molecular weight 1,000,000 has an RMS end to end length of about
1000 Å. Estimate the radius of gyration.
2. Given the information in Problem 1, estimate the radius of gyration of a polystyrene
with molecular 46,000,000 (this is the largest PS I know). Assume theta conditions.
3. Now go back to problem 2 and assume good solvent conditions.
4. The book by Hiemenz lists Rg2 = 2R2/5 for a sphere of uniform density and radius R.
Does this make sense intuitively? Only use words in your answer--no equations!
5. Consider a thin solid disk of radius R and uniform thickness and uniform density.
What is its radius of gyration?
6. Discotic polymers of the type mentioned in Problem 4 may stack into large cylinders,
leading to liquid crystal formation. Obtain an expression for Rg of such a stack in terms
of the radius of each disk, R, and the number of disks, N, each of thickness t.
7. Aggregation of polymers is important in biological and many commercial systems.
Suppose two spheres bond together side-by-side. By how much does Rg of the aggregate
exceed Rg of the individual sphere? (Hint: you have derived the solution to this problem
in the first set).
8. Show that the expression for the mean square dimension of a wormlike chain
<r2> = 2a[L - a + aexp(-L/a)]
is valid in the rodlike limit, L << a.