# What is the relationship between the molecular weight of a polymer and that of polystyrene?

So, I read in a similar chemistry thread that you can get Mn and Mw of the polymer of the interest by comparing the result of the sample obtained from GPC/SEC with the standard known molecule weight polymer like polystyrene. I don't understand how this works. You compare what of the polymer with what of the polystyrene to determine the molecular weight?? There has to be a constant factor when determining relative values between two things, and what is it in the case of polystyrene and the polymer of the interest?
What do you mean by polystyrene equivalent value? What is the point of determining the relative molecular weight of a polymer based on the polystyrene equivalent value??

Thank you!

You have to have something to calibrate the column with. Polystyrene is typically used since it can be made cheaply (well, relatively cheaply) with a pretty small molecular weight distribution.

Yes, there will be differences between the true molecular weight of a polymer and what the comparison to polystyrene gives you. But does that really matter? Why do you need to know the absolute molecular weight, when a relative comparison works just fine?

It's similar to how we determine the mass of something. At present, there is that infamous block of Pt/Ir in Paris that is the standard kilogram. All mass measurements are made through a series of comparison to that mass.

• The problem is that you have no idea what the difference is. We have a rather good idea how many atoms of Pt and Ir are in that block in Paris. – Karl Mar 31 '16 at 1:24

In size exclusion chromatography (SEC), the molecules elute in order of decreasing molecular weight (actually solvodynamic radius - we'll get back to that). The larger molecules (or polymer chains) do not fit into the pores in the stationary phase and thus spend more time in the mobile phase and elute faster. The smaller molecules can get stuck in the pores and thus elute slower.

Now, one of the most common detectors is a differential refractometer, which measures the concentration of analyte in the eluent since the refractive index $\eta$ of a dilute solution depends only on the molal concentration of the solution ($m$), the refractive index of the pure solvent $\eta_0$, and a constant $k_\eta$

$$\eta=k_\eta m +\eta_0$$

This relationship helps us figure out the amount of polymer that is eluting at any given time. However, the system needs to be calibrated so that we can related elution time to specific molecular weights. That's where polystyrene standards come in. Polystyrene is chosen because it can be prepared in low-polydispersity samples of known molecular weight by carefully controlling the polymerization.

We use "polystyrene-equivalent" value or "relative to polystyrene standards" because we know the molecular weights of the polystyrene standards.