To Infinity and Beyond

How can measurements of an infinitely dilute polymer have any meaningful purpose at all, especially since nobody works with such dilute solutions in the real world?   It turns out that the intrinsic viscosity can be related to the molecular weight by the Mark-Houwink equation: [η] = K M^α  [η] is the intrinsic viscosity, K is a constant, M is the molecular weight and α is another constant.  You can do some theoretical development of this equation and find that α should be 0.5, which is usually not the case.  But it is still an important value.

 

Polymers in solution do not exist as long straight molecules, but instead are coiled up in a random coil.  The size of this coil can be related to α with larger values of α indicating that random coil is larger than would be expected. A larger coil will interact with more solvent molecules and drag these along in the flow field creating a larger viscosity.  So a quick look at the value of α will tell you how good the solvent is that you are working with. α = 0.8 means it’s a terrific solvent, α =0.5 means that it’s a lousy solvent.  α less than 0.5 means that the polymer will soon be coming out of solution.

 

In an incredibly mind-blowing relationship, these values determined at infinite dilution can in fact be related to a pure polymer.  Molten polymers also exist as a random coil, and the size of this coil is the exact same size as when α = 0.5. How cools it that? An infinitely dilute solution and an 100% pure polymer have something in common.