Size Exclusion Chromatography (SEC)

Size Exclusion Chromatography (SEC) jls164

SEC helps us answer the question, what is the molar mass distribution of the polymer? In general, to analyze the sample, you pass a solution (polymer plus solvent) through a column that is packed with porous beads. A detector “watches” when polymer comes out the other end of the column (often by change in refractive index or UV absorption). The software generates a plot of polymer concentration vs. time, which gives you an indication of the molar mass dispersity of the polymer.

General description of the principles of SEC
Figure 11.5: General description of the principles of SEC
Source: Wikipedia: Size-exclusion chromatography

Importantly, as shown in the figure above, larger polymers exit the column (i.e., elute) faster than smaller polymers. This is a bit counterintuitive for most people. It has to do with the fact that larger molecules have a shorter path length in the column than the smaller polymers. The packing material in the column has a range of pore sizes; the larger polymers cannot fit into the smaller pores, and hence they are more limited in the paths that they can take through the column, and elute faster. Smaller polymers that can go into the smallest pores will ultimately travel greater distances within those pores and hence elute more slowly.

Often, SEC data is not plotted as a function of time, but rather as a function of elution volume. Elution volume (Ve) is the volume of solvent required to move the polymer from the point of injection (one end of the column) to the detector (other end of the column). A small elution volume means that little solvent is required to flush the polymer out of the column (this would correlate to “fast” elution) while a large elution volume means that more solvent is required (correlating with a “slower” elution). Data you collect might look something like this:

Bell curve showing Elution volume on the x-axis and amount of polymer on the Y-axis
Figure 11.6: Generic elution volume plot
Source: Lauren Zarzar

Now even though we say SEC can be used to measure molar mass distributions, in fact, as you may have noticed, it actually is separating polymers by their “size” rather than mass. More precisely, SEC is separating polymers by their hydrodynamic volume or hydrodynamic radius – which is affected by various things, in particular the polymer (chemistry and structure), solvent, solvent/polymer interactions, and temperature.

Diagram showing a tightly coiled (small hydrodynamic volume) and a more elongated (larger hydrodynamic volume)
Figure 11.7: Representation of hydrodynamic volume
Source: Lauren Zarzar

Unfortunately, molar mass does not always correlate with polymer hydrodynamic volume. After all, when we were considering polymer conformations in solution, the polymer “size” could vary widely depending on whether it was coiled or extended. These considerations of polymer conformations in solution are relevant when we try to interpret data from SEC experiments. This means a polymer with the smaller hydrodynamic radius will require a higher elution volume than a polymer with a larger hydrodynamic radius, even if the sample with small hydrodynamic radius has the higher molar mass!

PROBLEM

Consider polystyrene of the same molar mass in methanol, chloroform, and n-hexane. Which would you expect (using the table below) to have the largest hydrodynamic volume, of the options given?

Table 11.1: Solubility Parameters
Polymerδ (cal/cm3)1/2Solventδ (cal/cm3)1/2
Poly(tetraflouroethylene)6.2n-Hexane7.3
Poly(dimethylsiloxane)7.4Cyclohexane8.2
Polyisobutylene7.9Carbon tetrachloride8.6
Polyethylene7.9Toluene8.9
Polyisoprene8.1Ethyl acetate9.1
1,4-Polybutadiene8.3Tetrahydrofuran9.1
Polystyrene9.1Chloroform9.3
Atactic polypropylene9.2Cadbon disulfide10.0
Poly(methyl methacrylate)9.2Dioxane10.0
Poly(vinyl acetate)9.4Ethanol12.7
Poly(vinyl chloride)9.7Methanol14.5
Poly(ethylene oxide)9.9Water23.4
Source: E.A. Grulke in Polymer Handbook, Brandrup, J. and Immergut, E. H. (Eds.), 3rd ed., Wiley, New york, 1989.

ANSWER

Chloroform

A smaller difference in solubility parameters means better solvent for the polymer → more polymer-solvent interactions, more elongated polymer.

Now that we know that SEC is actually separating polymers by their hydrodynamic volume, how do we go about actually correlating that with the molar mass? The best way to do this is with a calibration curve made using standards which are expected to behave like your sample. To make such a calibration curve, you get a series of low dispersity polymers of known molar mass and run them through the SEC to yield a plot that could look something like the top plot of the figure below, where each peak corresponds to the elution of one of the standards:

Calibration curve showing X-axis elution volume and Y-axis amount of polymer.
Figure 11.8: Elution volume curve correlating with callibraation curve
Source: Lauren Zarzar

Since you know the molar mass of each of your standards, you can correlate each of those peaks with a specific elution volume. This allows you to make the calibration curve (bottom plot of the figure above). Now you can use this calibration curve to correlate the elution volume to molar mass for any sample that you expect to elute similarly in the SEC column (i.e., sample chemistry of polymer, same solvent).

So we can figure out now how to correlate elution volume to molar mass, but how do we get the molar mass distribution of the sample?

diagram showing ageneric elution plot and a generic molar mass plot
Figure 11.9: Correlating an elution plot to a molar mass plot
Source: Lauren Zarzar

First, we normalize the area under the SEC data curve to 1, because presumably all our polymer is somewhere on that plot. Then we can slice it into sections of arbitrarily small widths (vi). Each slice has a weight fraction (wi) associated with it, according to the area within that slice. Each slice also has a molar mass which you can figure out using the calibration curves we just learned about:

Diagram showing the same plots in figure 11.9 but the elution plot has been divided with verticle lines
Figure 11.10: Normalizing the area under the SEC data curve
Source: Lauren Zarzar

Therefore, if you know the weight fraction of polymer with a specific molar mass, we can use that to create our molar mass distribution curve.

PROBLEM 2

Here are two calibration curves for two standards of a polymer with the same chemical composition, same (good) solvent, and same temperature... But different shapes! Which polymer is branched and which one is linear?

Plot of two lines. X-axis is Elution volume and the Y-axis is log(M). Line 1 lies below line 2.

ANSWER

2 is branched and 1 is linear.

They are in a good solvent, so the linear polymer will have the larger hydrodynamic volume. (Branching will make the polymer more compact as compared to a linear polymer with the exact same mass, all else equal). The linear polymer will therefore elute faster, with lower Ve, for a given molar mass

Summary of strengths and weakness of SEC

Strengths of SEC

  • Can be used for a pretty wide range of polymers and solvents systems – can be used for sensitive biological systems in aqueous solutions as well as synthetic polymers in organic solvents.
  • Can get information about molar mass, distribution of molar mass, and dispersity (and also Mn).

Limitation of SEC

  • We are using hydrodynamic volume as an analog to molar mass. Depending on your polymer system, you may or may not be able draw an accurate correlation between the two.
  • If there is interaction between the column packing material (the stationary phase) and your polymer, this will cause longer elution times and will mimic smaller polymers.