# Homework 9

```Chem. 4595
Fall 1998
Problem Set #9
Due Tuesday, December 8
1. Consider the “bead and wire” model below to represent, approximately, a rigid rod of
total length L = 3000 &Aring; and diameter, d &lt;&lt; L.
1000 &Aring;
1000 &Aring;
1000 &Aring;
Assume the “wire” part scatters no light, but the beads scatter as small particles. In
the isotropic (freely tumbling) limit, compute the average form factor P() for  = 45o,
90o and 150o. Assume you have one of the snazzy new frequency doubled diode solid
state lasers that Santa gave me for Christmas a few years ago (= 5320 &Aring;). Take the
solvent refractive index as n = 1.55. You may wish to compare your results with the
true values for P() of rods, as tabulated in books such as “Light Scattering from
Polymer Solutions” M. B. Huglin, Ed. Or you could compute P(for many different
angles, obtain Rg from a Guinier plot, as above, and then compare that to the
expectation value for a rod of length 3000 &Aring;.
2. What precision must you have to determine the difference between trimers arranged
linearly and trimers arranged trigonally, using dynamic light scattering to measure the
translational diffusion coefficient? Hint: this is a Kirkwood-Riseman problem; the
necessary formula for the friction coefficients that govern the diffusion rate is in
Richards.
Linear Trimer
Trigonal Trimer
3. In this problem, you do a &quot;dry&quot; experiment to determine by &quot;straight&quot; GPC the
molecular weight distribution of some unknown polymer, referenced against
polystyrene standards. To calibrate the instrument, you run a bunch of polystyrene
standards, whose true molecular weights were determined already by the vendor using
osmometry or GPC/LS. Here are your calibration results.
Mn
Log10(Mn)
Elution Volume, Ve (mL)
773000
96200
15000
410000
19650
2535
110000
2.7E6
171000
51000
5.88818
4.98318
4.17609
5.61278
4.29336
3.40398
5.04139
6.43136
5.233
4.70757
13.44
16.35
20.235
14.88
19.065
21.51
16.095
12.165
15.678
17.808
Now you inject your unknown polymer and record its trace, as shown below:
str8GPC
0.05
DRI signal
0.04
0.03
0.02
0.01
0.00
10
15
20
V
e
&quot;DRI signal&quot; is a voltage level from the differential refractive index detector. It is
proportional to the concentration (the actual constant of proportionality isn't very
important in straight GPC). Your mission is to convert this plot into a DRI signal vs. M
plot, then determine Mn, Mw, and Mz, using the calibration data provided. You can solve
this problem graphically, with just a calculator and a ruler, or you can devise a
computerized approach (less tedious once you figure out how to do it).
If you choose to follow the computerized approach, you must get the data from the
website. It consists of a huge set of X,Y data pairs, the elution volume vs. voltage from
the DRI concentration detector. You can find these data at:
http://russo.chem.lsu.edu/4595web/worddocs/gpc.htm. There must be several ways to get
these data into a program where you can manipulate them. After viewing the file at the
address just listed, I recommend erasing the &quot;gpc.htm&quot;, then hit &quot;return&quot;. You should see
a list of files in the &quot;worddocs&quot; directory on my server. Right click on the GPC.htm file
to save it on your desktop. Start Excel and then open the gpc.htm file from within Excel.
Hints:
 You can use Origin or Excel to make a nice fit to the log10M vs. Ve data. This allows
you to quickly convert Ve data, point by point, to M. That will give you the plot as
DRI vs. M. Now you must subtract any baseline data underneath the curve. The
concentration at a given point is proportional to the difference between that point and
the baseline. Use standard relations to compute Mn, Mw, Mz.




You may wish to download the GPC &quot;HowTo&quot; file from the http://russo.chem.lsu.edu
website.
If you use Origin, and if the dataset has an appreciable baseline, try out its spiffy
baseline subtraction features
Also note Origin's nifty row and column statistics features.
Don't hesitate to ask for help! It's too late in the semester to struggle, but this is a
good problem with which to develop your computer skills.
4. Compute the hydrodynamic radius of a polymer that, at infinite dilution, diffuses at
1.35 x 10-7 cm2/s in a fluid of viscosity 1.08 cP at 35oC.
```