Premium
Step‐Growth Polymerized Systems of General Type “AfiBgi”: Generating Functions and Recurrences to Compute the MSD
Author(s) -
Hillegers L. Tom,
Slot Johan J. M.
Publication year - 2015
Publication title -
macromolecular theory and simulations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.37
H-Index - 56
eISSN - 1521-3919
pISSN - 1022-1344
DOI - 10.1002/mats.201400091
Subject(s) - polynomial , constant (computer programming) , mathematics , differential equation , type (biology) , function (biology) , degree (music) , generating function , monomer , order (exchange) , polymerization , mathematical analysis , computer science , chemistry , physics , ecology , organic chemistry , finance , evolutionary biology , economics , biology , programming language , polymer , acoustics
General step‐growth polymerization systems of order 2 are considered, i.e. systems of type “AfiBgi”. We describe an algorithmic method to calculate the molecular size distribution (MSD). Input to the algorithm is the “recipe”: a list of the monomers involved stating their A and B functionalities and their molar amounts, and the degree of conversion. Output is the MSD and its moments. Three main steps lead from input to output: (i) setting up a polynomial equation for the generating function that generates the MSD, (ii) transforming this polynomial equation to a differential equation, and (iii) transforming the latter one further to a recurrence equation. The recurrence yields the MSD and is of constant order.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom