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I am extremely new to both polymer chemistry and NMR. I am struggling with the following question: A proton NMR is used to attempt to quantify the molecular weight of a poly(ethylene oxide) molecule with methyoxy end groups at each terminus. If the integration of the methyl protons relative to the methylene protons gave a ratio of 1:20, what can you say about the molecular weight?

Thank you. All help is appreciate including resources for me to be able to read up on my lacking knowledge.

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  • $\begingroup$ Note that "all" NMR does in this case is provide you with the relative amounts of methyl and methylene group hydrogen atoms, so while NMR is particularly useful for such a determination, it's really a question about understanding molecular structure and some math. $\endgroup$ – Buck Thorn Feb 2 at 8:43
  • $\begingroup$ The longer the polymers, the more challenging they can be in NMR, because of their relaxation and diffusion times. You absolutely need to talk to your NMR specialist, expose the molecules you are studying and ask him/her: "Can I use the standard proton settings? If not, how can I make sure the spectra lines are actually quantitative?" $\endgroup$ – SteffX Feb 2 at 13:07
  • $\begingroup$ @SteffX It's not so much about the size, but the solubility. Diffusivity is largely irrelevant, and relaxation times don't change once you are in the range of actual macromolecules. In all cases, I would however run a short saturation recovery $T_1$ experiment. Takes little extra time, and then you know where you are with respect to quantitativeness. $\endgroup$ – Karl Feb 2 at 17:39
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I hope this is not a homework question. Suppose your polymer has $n$ reapeating units and capped with methyl groups at the end as you described. Thus, it should looks like following figure: PEO

Thus it has $n$ $\ce{(-CH2CH2-)}$ units and $2$ $\ce{(-CH3)}$ units. Thus your $\ce{(-O-CH2-)}$ signal is accounted for $4n$ protons while $\ce{(-O-CH3)}$ signal accounted for only $6$ protons. Thus, $$\frac{4n}{6} = \frac{20}{1}$$ You may find the value of $n$ from this equation and you can calculate the molecular weight of the polymer in hand.

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    $\begingroup$ Importantly, almost all polymer samples are a mixture of molecules with different chain lengths, and quantification by NMR provides an average value for the whole sample, more specifically the number-average chain length/molecular weight. $\endgroup$ – Nicolau Saker Neto Feb 2 at 4:42
  • $\begingroup$ Also important, it might not be the case tough, but polymers tends to have different dynamics and respond differently to nmr, to the point that quantitative evaluation of this kind might be fallacious. Not sure in this case. Sure with polymers having pendants attached. The latter can be seen while the backbone no, for instance. $\endgroup$ – Alchimista Feb 2 at 9:04
  • $\begingroup$ @Alchimista Very unlikely in solution. If you use standard recycle delay settings for 1H NMR (20 s or so), the end groups will definitively give a quantitative response, and the less mobile middle part of the polymer chain has an even shorter $T_1$. What do you mean by "pendants"? $\endgroup$ – Karl Feb 2 at 9:21
  • $\begingroup$ Pendants as functional groups consisting of mobile alchyl chains terminated with big groups. My comment might over emphasises the situation in solution but it is what I have observed at least with conjugated polymers. Might also be related to the fact that true solutions are hard to attain with many polymers in general. But I am just suggesting a possibility and I do not think is strictly related to the Q. @Karl $\endgroup$ – Alchimista Feb 2 at 11:08
  • $\begingroup$ @Alchimista I can imagine conjugated backbones to be a problem. Might be so stiff even in solution that their nuclear spins don't find the way back to equillibrium. I'd love to see T1-correlated spectra on such stuff. $\endgroup$ – Karl Feb 2 at 11:51

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