The Schulz-Zimm distribution has the following form:
p(x) = [k/Mn]^k x^(k-1) exp(-k*x/Mn)
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gamma(k)
Where x is the molecular weight and Mn is the number-average molecular weight. The constant k is defined by 1/(PD - 1) where PD is the polydispersity index ==> Mw/Mn (Mw = weight average molecular weight). For PD 2, k is less than 1, and hence x^(k-1) would give large values for small x, resulting in a monotonically decreasing p(x). Has anybody dealt with this before and is it logical to expect this type of monotonically decreasing p(x) for PD > 2? I know for sure that many naturally occurring biopolymers have PD > 2. So, any insights guys?
Hello Peter, would you mind explaining your comment because I've seen cases where PD > 2.
This distribution function was proposed to describe the two theoretical limits considered for radical chain (or addition) polymerization: terminated by disproportion (k=0) and terminated by combination (k=1) (also asuming that k/Mn is approximately lnp) where p is the probability of a further addition step. Radical polimeration reactions use to have a mixture of these two terminations and the empiral Shultz distribution function can nicely desbribe their real molecular weight distributions. Greater polydispersity means that these simple theoretical kinetic schemes are not applicable to your reaction.
Hello Juan, thanks for your answer. In that case, what type of theoretical distribution can be used to cover greater polydispersity? Mind to give me some suggestions?
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