[xshadow]

Hi!I don't understand the  definition of  the degree of polymerization that my textbook says....
The definition I have is:


[size=78%]degree of polymerization, X[/size]n[/size][size=78%]= number (avarage)  of repeat units of the polymeric chains [/size]
X_n = number of monomer molecules/ number of polymer molecules = c₀/ (c₀-c₀p = 1/(1-p)

where:
c₀= n° of functional group at t=0
c= n° of functional group at a certain time "t"
c₀-c=pc₀ =  n° of functional group extinguished at the "t" time.
p= extent of reaction

Now my doubt is about these definition and the definition of degree of polyerization X_n

How can is possible that the expression: number of monomer molecules/ number of polymer molecules = c₀/ (c₀-c₀p = 1/(1-p)
can give X_n ?  IF X_n is the avarage number of repeat unit of a polymeric chain in my polymeric material how can that expression give that avarage number?!


Is impossible written like this...
Some help??
Thanks

[Hunter2]

In words the degree of polymerization tells you the percentage of monomer molecules to the built up polymer molecules at certain times. At start point you have only monomers, after some time the amount of monomers decrease and the amount of polymers increase. If you take samples between and stop the polymerization you get after analysis the degree of polymerization. If everithing has react then you have only polymers, The percentage is 100% then.

[xshadow]

In words the degree of polymerization tells you the percentage of monomer molecules to the built up polymer molecules at certain times. At start point you have only monomers, after some time the amount of monomers decrease and the amount of polymers increase. If you take samples between and stop the polymerization you get after analysis the degree of polymerization. If everithing has react then you have only polymers, The percentage is 100% then.

So the degree of polymerization is  the percentage of the starting  monomer converted in polymer OR the avarage  lenght of polymeric chains created??

Because my textbook says that "the percentage of the starting  monomer converted in polymer" is the extent of polymerization reaction, "p"

Thanks

[mjc123]

Because my textbook says that "the percentage of the starting  monomer converted in polymer" is the extent of polymerization reaction, "p"

The validity of that statement depends on the mechanism of polymerisation. Which reaction (if any) were you thinking of?

So the degree of polymerization is  the percentage of the starting  monomer converted in polymer

That can't be right, as it would be a number less than 1.

OR the avarage  lenght of polymeric chains created??

The formula you quoted gives the average length of all the molecules present, including unreacted monomer. This may or may not be reasonable, depending again on the type of polymerisation.

[xshadow]

Thanks!!!

My textbook uses thar formula in order to discuss the kinetics of Polycondensation at equilibrium.
Is a reasonable thing??

BECAUSE your answer "The formula you quoted gives the average length of ALL  the molecules present, including unreacted monomer." let me think that is only corret to predict the avarage lenght of (only) the Polyemer chains (so the degree of polymerization X_n) only when all monomer has reacted...


N.b:
I think it says that lika a general things....but later:
It considers the  polycondensation reaction :
---COOH + ---OH   <<< >>>  ---COO--- + H₂O

And says that:
[---COOH] , [---OH]= c₀   (where c₀ is the number of functional groups at t=0)
[ ---COO---], [H₂O] = p*c₀    (where p is the extent of reaction)

Than it says:
K_eq= k/k'= [ ---COO---] [H₂O] / [---COOH] [---OH]  =  (pc₀)²/(c₀-pc₀)² = p²/(1-p)²

So  p= K-K^1/2/ (K-1)   (where K is the equilibriu constant)
Than says:  X_n= 1/1-p  so X_n= K-1/K^1/2-1

[mjc123]

So  p= K-K^1/2/ (K-1)   (where K is the equilibriu constant)
Than says:  X_n= 1/1-p  so X_n= K-1/K^1/2-1

Brackets! You are saying something other than what you intend to say!
It is simpler to say p = K^1/2/(K^1/2-1) and X_n = K^1/2+1

let me think that is only corret to predict the avarage lenght of (only) the Polyemer chains (so the degree of polymerization Xn) only when all monomer has reacted...

When all monomer has reacted, p = 1 and you get X_n = ∞. Theoretically (you never achieve it in practice) you would have a single polymer molecule of infinite length. If you have an equilibrium, p will never be 1.
For any p < 1, there is a broad, approximately exponential distribution of chain lengths, in which monomer is the most numerous kind of molecule present (highest number fraction, but not weight fraction). This is an important fact about condensation polymerisation, and justifies the use of the formula X_n = 1/(1-p), which includes monomer. For some other types of polymerisation, e.g. living polymerisation, there are relatively few growing polymer chains and a large excess of monomer (until you reach high p). That formula then does not give a good description of the degree of polymerisation of the polymer chains themselves.

[xshadow]

When all monomer has reacted, p = 1 and you get X_n = ∞. Theoretically (you never achieve it in practice) you would have a single polymer molecule of infinite length. If you have an equilibrium, p will never be 1.
For any p < 1, there is a broad, approximately exponential distribution of chain lengths, in which monomer is the most numerous kind of molecule present (highest number fraction, but not weight fraction). This is an important fact about condensation polymerisation, and justifies the use of the formula X_n = 1/(1-p), which includes monomer.

mmhh...
But  p=1  means that all monomer molecules have reacted...but I could have a certain number of oligomers (usually big) and not only ONE  polymer molecule ( at wich corresponds X_n =1)

Does The avarage degree of polymerization X_n,at a certain time "t" , consider  only the polymer molecules or  the polymer molecules + the monomeric one ??

In polycondensation reaction the monomer usually disappears from reactor quickly...is this the reason of the formula X_n= c₀/ c₀-pc₀

Where c_₀ is the number of functional group at t=0
Thanks!!

[mjc123]

X_n = 1 does not mean there is only one molecule. What is the definition of X_n?

But  p=1  means that all monomer molecules have reacted...but I could have a certain number of oligomers (usually big) and not only ONE  polymer molecule ( at wich corresponds X_n =1)

That is not how condensation polymerisation works. Oligomers react alongside monomer, and there is always less of them. It is not a matter of sequential addition of monomer to polymer chains. Monomers react to give dimer, trimer etc and these can react with each other to give longer chains, and so on. The result, as I said, is an approximately exponential distribution, as in the attached graph.

Does The avarage degree of polymerization Xn,at a certain time "t" , consider  only the polymer molecules or  the polymer molecules + the monomeric one ??

I have told you this twice. Are you paying attention at all?