[hm389]

I have a question regarding polymerisation that I need some guidance with.  Here is the question:

'Step reaction polymerisation of lactide gives polylactide. A sample of polylactide was prepared by bulk polymerisation of lactide. Ignoring any contribution of end groups to molecular weight, calculate what conversion would be needed for the reaction to give a polymer with M_n (number average molecular weight) of 495 000 g mol^-1, and estimate M_w (weight average) if you assume a most probable distribution. Molar mass of lactide is 144g mol^-1.'

I understand what the terms M_n and M_w mean, but am unsure about what it means by 'calculate what conversion would be needed', does this mean conversion between M_n and M_w? Any help would be greatly appreciated.

[mjc123]

No, it means conversion of monomer to polymer. Suppose a fraction p of the monomers have reacted to become part of polymer molecules. Do you know (or can you work out) an equation relating M_n to p?

[hm389]

No, it means conversion of monomer to polymer. Suppose a fraction p of the monomers have reacted to become part of polymer molecules. Do you know (or can you work out) an equation relating M_n to p?

Thank you for your reply. I have just looked over my lecture notes and I am still unsure/ can't work out an equation relating M_n to p.

[wildfyr]

Look up the Carothers equation.

[hm389]

Look up the Carothers equation.

Ok, so if I use M_w/ M_n= 1 + p, to solve for p and I only know M_n, how would I go about working out the value of M_w?

[wildfyr]

The Carothers equation is Xn=1/(1-p) where Xn is the degree of polymerization (aka the number of monomer units in a chain). You don't need Mw for it, only Mn and the molecular weight of a monomer unit.

What do we know about the polydispersity of step-growth polymerization? What is a reasonable value for Mw to make the PDI=Mw/Mn equation true?

Or, you could look at the wikipedia page for Carothers equation (shocking, I know) and scroll down and see how to solve for Mw directly just knowing p and the monomer unit in a equimolar step growth polymerization.