For the software given bellow, it was programmed based on eq (5):
Most of these parameters’ definitions can be found from the passage. The “Weight Constraint” sets the confine of the molecular weight coordinate for both displaying and calculating. The “Monomer Weight”, defined as its name, may affect the height and the horizontal position of a bar in the chart. If one wish to compare the generated chart with experimental data that uses mass concentration as unit, the molar concentration must be changed according to the “Monomer Weight” as well. Kd, Pf and Pc are automatically generated after inputting other parameters (Kd and Pf affect each other). Click “Generate Chart” to obtain the theoretical outcome from eq (5). Click “Use log” to change these bars’ horizontal position for comparing it with Adjusting Pa_d, Pb_d and Pf according to your experimental data to find a similar point. The optimized value of Pa_d and Pb_d would be the indicator of hindrance or recruiting.
The strategy shown below is based on the gelation theory by Flory[ “Monomer Size Distribution Obtained by Condensing A-R-Bf-1 Monomers”. Chapter IX. Flory, Paul J. Principle of Polymer Chemistry. 1953.].
Consider there are two kinds of monomers ‘A’ and ‘B’ in the system, one with fA functional groups ‘a’ and the other with fB functional groups ‘b’. With the principle of equal reactivity, we can say an arbitrary ‘a’ selected from the system have a probability “Pa” of having reacted. And the assumption that reactions between ‘a’ and ‘b’ groups on the same molecule are forbidden (no intracellular reaction) enable us to enumerate the probable shape of a certain molecule with cA number of A and cB number of B from a root to all the molecule’s branches.
Fig. 4. The functional groups on a monomer are classified into parent-connecting ones and branchers.
The definition of parent is the same as that one of tree, which means the monomer’s neighbor nearest to the root. Select cB ‘a’ from a1 to an shown in the picture. That is the number of ‘ab’ and ‘ba’ pairs substrates the number of ‘a’ connected to parents, which equals the number of reacted ‘a’ branchers. The same goes for ‘b’. Notice that all the parent connecting ‘b’ should be paired with branching ‘a’ and all the parent connecting ‘a’ should be paired with branching ‘b’. The number of combinations here is
The worry of not that loops may occur in such combinations can be eliminated if the expression given above is understood like this:
