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Di-block copolymer analysis: GPC

G el P ermeation C hromatography is a well known method of measuring molecular weight distribution of polymers. For di-block copolymers, a proper calibration curve can be constructed by using Mark-Houwink parameters of homopolymers ( see here ). Usually, di-block copolymers are obtained by synthesis one block first then "grow" the other block from the end of preceding block. The molecular weight distributions of final di-block copolymer and preceding block are accessible by GPC, the molecular weight distribution of the 2nd block, however, is hard to obtain. Here I present a simple method to calculate the molecular weight distribution of 2nd block by GPC data of preceding block and final di-block copolymer. Assuming that we already have the molecular weight distribution of the preceding block, $P_1(n)$, it is generally that the length of the 2nd block "grow" from the depends on the preceding chain length $n$, therefore, the pdf of the 2 blocks should be a joint pdf