Without performing experimental characterization such as GPC based on the known quantities such as moles of monomers and monofunctional reactant (end-capper) can i assume the following is correct to calculate the number average (Mn)?
r = N_a / (N_b + 2 N^m_b) where N_a and N_b are stoichiometrically equal and the monofunctional reactant is N^m_b
X_n = (1 + r)/(1-r)
thus M_n = X_n(M_0) where M_0 is the mean molecular mass of the repeat unit
For instance, if the moles of monomer A and B are 0.045 mmol and the mono functional reactant is 0.002 mmol and i divide all values by Avogadro's number
r is then approximately 0.9 and such X_n is approximately 20.2
11 multiplied by the mean molecular mass (1708 g/mol)
therefore the M_n is approximately 34.5 kDa
Assuming that you are dealing with difunctional monomers for both A & B, that A&B are present in stochiometric amounts, and assuming 100% conversion of all reactants (never happens, by the way!):
Two of the monofunctional reactant (endcapper) would be required for every polymer chain. So in your example, you have 0.002/2 = 0.001 mmol of polymer chains. Then, if you have 0.045 mmol each of A & B monomers, you'll have (0.045 + 0.045) / 0.001 = 90 units of monomers (A + B combined) + two units of monofunctional reactant molecules per polymer chain. Ignoring the monofunctional reactant (since it wasn't provided in the question - maybe it's a short chain alcohol for example?), the estimated M_n is (90 mol monomer / mol polymer ) * 1708 g/mol monomer = 153 720 g/mol polymer.
That said, in reality I would expect the values to be very different:
1) 100% conversion is rarely reached, and so your M_n would be expected to deviate (partly depends on how reactive the endcapper molecules are relative to the monomers)
2) If the endcapper molecules are of substantial molecular weight, then clearly your M_n values would have to be adjusted accordingly.
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