Chapter 8 Measurement of Molecular Weight and Size
For instance, the COOH group in a condensation polymerization or a vinyl group in an addition polymerization. Methods including NMR, IR or chemical titration.
The limitation of this method is 1) some end-group are unknown, especially an addition polymerization 2) insensitive when the molecular weight are so high (> 25,000 for example)
We are going to focus on membrane osmometry
where p are osmotic pressure
The principle of membrane osmometry
will be illustrated at the class.
A general equation for calculating molecular weight by colligitive property measurement:
It is usual to plot p/RTc vs c. In general, a straight line results whose intercept at c=0 is 1/Mn.
Units: c (g/ml), R= T (K),
Typical data and figure as shown in figure 8.5 and 8.6.
The two compartments of an osmometer are separated by a semi permeable membrane, through which only solvent molecules can penetrate. The thermodynamic drive toward equilibrium results in a difference in liquid level in the two capillaries. The resulting hydrostatic pressure increases the solvent activity on the solution side until, when the applied pressure equals the osmotic pressure, equilibrium is achieve.
Two types of osmometers are described
A simple set-up that you can make.
Membranes: The usual materials include
· collodion (nitrocellulose of 11-13.5% nitrogen);
· regenerated cellulose, made by denitration of collodion;
· gel cellophane that has never been allowed to dry after manufacture;
· bacterial cellulose, made by the action of certain strains of bacteria;
· rubber;
· poly(alcohol);
· polyurethane;
· poly(vinyl butyral);
· and polychlorotrifluoroethylene.
Light scattering is the most common way of measuring weight average molecular weight.
Polymers make the solution viscous, why?
The higher the molecular weight, the more viscous the polymer solution will be.
For most every polymer there's a definite relationship between molecular weight and viscosity. So, measure the viscosity, and we can get the molecular weight. And that's just what we're going to talk about next, measuring the viscosity of a polymer solution.
As shown in the picture, we could measure how long it takes for a given volume of the solution to flow through a tube.
Two methods can be used to calculate intrinsic viscosity: h = (hsp)c=0
1. from specific viscosity
hsp is to denote the specific viscosity hsp =(t-t0)/t0, t and t0 are the efflux time of polymer solution and solvent, respectively.
2. from reduced viscosity (hred or hr)
hr is to denote the reduced viscosity hr = hsp / c , ln hr is also called inherent viscosity (hinh).
the intercept is intrinsic viscosity, h
Another way to tell if you've done everything right is that k' - k'' should equal 0.5
the intrinsic viscosity h to calculate molecular weight. We calculate it with a simple little equation:
This is called the Mark-Houwink equation. M is what we call the viscosity average molecular weight and K' and a are the Mark-Houwink constants. There is a specific set of Mark-Houwink constants for every polymer-solvent combination. So you have to know these for your polymer-solvent combination in order to get an accurate measure of molecular weight. This means that you can't get a good measure if you're measuring a polymer that you've just invented and there are no calculated Mark-Houwink constants available. But it still can give you a qualitative idea of whether molecular weight is high or low. The mere fact that you get an intrinsic viscosity can tell you a lot, too. Sometimes that's the only way you can tell that what you have made is indeed a polymer.
note: You have to use dilute solutions to do this kind of experiment. If the solutions are too concentrated, the polymer molecules might get close enough together to interact with each other. This causes the viscosity to increase in ways that our equations here don't describe very well, so accurate measurements can't be made. That's why this technique is called dilute solution viscosity.
Principle of size exclusion chromatography
The beads are normally a rigid, porous, highly corsslinked polystyrene.
A sample of a dilute polymer solution is introduced into a solvent stream flowing through the column. As the dissolved polymer flow past the porous beads, they can diffuse into the internal pore structure of the gel to an extent depending on their size and the pore size distribution of the gel. Small polymer molecules penetrate a larger fraction of the interior of the gel.
The larger molecule, therefore, the less time it spends inside the gel, and the sooner it flows through the column. The different molecular species are eluted from the column in order of their molecular size as distinguished from their molecular weight.
So, we can make a plot of time on the x-axis and the number of polymer molecules coming out at a given time on the y-axis, like this:
Because we can calculate molecular weight from elution time. we can turn this plot into a plot of molecular weight on the x-axis and the number of molecules with a particular weight on the y-axis, like this:
In SEC, we're really not measuring mass so much as the hydrodynamic volume of the polymer molecules, that is, how much space a particular polymer molecule takes up when its in solution. We can approximate the molecular weight from SEC data because we know the exact relationship between molecular weight and hydrodynamic volume for polystyrene, and we use polystyrene as a standard. But the relationship between hydrodynamic volume and molecular weight isn't the same for all polymers, so we get only an approximate measurement.
G. MALDI -- matrix-assisted laser desorption/ionization mass spectrometry.
MALDI is a new method that can measure molecular weight averages and molecular weight distributions very exactly.
Normally we get a picture like this:
Creel, Howard, Trends in Polymer Science, Elsevier, 1993, vol.1, no.11, pp.336-342 "Prospects for the Analysis of High Molar Mass Polymers Using MALDI Mass Spectrometry".
Homework:
2. Which methods would you use to obtain the molecular weight and distribution of a polymer on a routine basis, as in process control? why?
3. Which methods would you use to obtain this information for a new polymer type not previously studied? why?
12. What kind of information does one obtain from measuring [η]? How can you make the best guess at M from measurement of [η] on an entirely new kind of polymer?
13. A polymer with M=100,000 obeys the mark-Houwink equation with K=1x10-4 and a=0.8. Huggins's constant (k' in equation 1) is 0.33. Calculate the specific viscosity at c=0.30g/dl.
21. (just give it a try) The following data were obtained by membrane osmometry of solution of a polyethylene sample in xylene at 90 oC. At this temperature the density of xylene is 0.8014 and that of polyethylene is 0.8173. Calculate the molecular weight of the sample and the second virial coefficient. (R=8.314 J/mol.K)
C (g/liter): 2.00 4.00 6.00 8.00
p(cm xylene): 2.585 5.965 9.66 13.935