Theoretical Determination of Molecular Weight of AB 2 Dendrimers

The Molecular weight of any AB2 type dendrimers were calculated by suggested theoretical equation. The results were compared with the data reported by others. It was found that there are no remarkable differences between the calculated and reported data.


Introduction
Dendrimers are highly branched macromolecules, obtained by an interactive sequence of reaction steps, having precisely defined molecular structures 1,3,5 .These aesthetically appealing synthetic macromolecules distinguish themselves from normal polymers in two critical ways.Firstly, they are constructed from AB n monomers which produce linear polymers.Thus, they contain hyper branched structures.Secondly, they are synthesized in an interactive fashion.The combination of these two features lead to a nonlinear, stepwise synthetic growth where in the number of monomer units incorporated in each successive interaction roughly doubles (AB 2 ) or triples AB 3 .
That in the previous cycle, each repetition cycle lead to the addition of one more layer of branches which is a generation to the dendrimer from work.The generation number of the dendrimer is equal to the number of repetition cycles performed, and can be easily determined by counting the number of branch points as one proceeds from the core to the periphery 2,4,6 .

Results and Discussion
PPI is an AB 2 type polymer, in which the core is diaminobutane.The core has two active sites (Z 0 = 2), which can construct four branches for generation 1(G1), eight branches for generation 2(G2) and twelve branches for generation 3(G3 The molecular weight of a dendrimer is the sum of the molecular weight of branches and the molecular weight of core (M core ). Mw (4) Molecular weight of the generation 1 and 3 of MNBA has reported 7 which is 1052 and 5712 gmol -1 , respectively.By using the equation (3) and by replacing Z 0 = 3 for generation 1, the amount of molecular weight would be 1026 which has 1% of deviation from the experimental data.
M r =133, M Core =228 Mw n =228, + (6x133) = 1026 Also the molecular weight for the generation 3 by using the equation ( 4) would be 5814 which has a 2% deviation.
Figure 4.The molecular structure of dendrimers TAZ, PPI, MNBA, PAMAM are in according to the structures in Figure 1-4 respectively.Also, the same calculation of molecular weight was carried out for TAZ, PPI, MNBA and PAMAM and the results were summarized in Table 2. Table 2.The reported and calculated molecular weights and percentage of error for TAZ, PPI, MNBA,PAMAM dendrimer As it is apparent from the table the inaccuracy of the molecular weight by comparing with those of Table 2 are trivial.It is interesting that with taking out of two continues LMNCz 0 from the Table 1, one can find out the surface branch of the higher generation according to those reported by Newkome 1,9,10 .The surface branches are shown in Table 3.

Table 3 .
The number of surface branches for AB 2 dendrimers.