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SCIENCE CHINA Chemistry, Volume 61, Issue 3: 319-327(2018) https://doi.org/10.1007/s11426-017-9146-6

Can Flory-Stockmayer theory be applied to predict conventional free radical polymerization of multivinyl monomers? A study via Monte Carlo simulations

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  • ReceivedAug 9, 2017
  • AcceptedSep 15, 2017
  • PublishedDec 26, 2017

Abstract

The conventional free radical polymerization (FRP) of multivinyl monomers (MVMs) inevitably leads to gelation even at low monomer conversion resulting in difficulties to control and monitor the reaction process. Flory and Stockmayer (F-S theory) studied it based on two fundamental assumptions: (1) independent and equivalent vinyl groups; (2) no intramolecular cyclization. However, until now its applicability to FRP of MVMs (especially regarding the extent of intramolecular cyclization) is still controversial. In this paper, Monte Carlo simulations are used to study FRP of divinyl monomers by two kinetic models: with/without cyclization models. The results of the simulations are compared with the calculated gel points based on F-S theory and the experimental data. It is found that the intramolecular cyclization has a negligible impact on the polymerization process and the gel point before gelation, which are in agreement with the prediction by F-S theory, but the effect becomes significant above the gel points.


Funded by

National Natural Science Foundation of China(51573129)


Acknowledgment

This work was supported by the National Natural Science Foundation of China (51573129), Science Foundation Ireland Principal Investigator Award (13/IA/1962), Investigator Award (12/IP/1688) and Health Research Board (HRA-POR-2013-412). This work was carried out at National Supercomputer Center in Tianjin, and the calculations were performed on TianHe-1 (A). The authors are very grateful to Prof. Krzysztof Matyjaszewski, Carnegie Mellon University, for his valuable comments and advice on this work.


Interest statement

The authors declare that they have no conflict of interest.


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  • Figure 1

    Effect of the system size (Xm) on the predictions of gel point. The growth of reduced degree of polymerization (RDP) [23] against divinyl monomer conversion in FRP of divinyl monomers (cyclization included) (color online).

  • Scheme 1

    Schematic presentation of the simulated FRP of divinyl monomers. If intramolecular crosslinking is allowed (with cyclization, lower part) the macromolecules contain closed loops marked as blue open circles (color online).

  • Figure 2

    FRP of divinyl monomers. The growth of (a) number average chain length (Pn), (b) weight average degree of polymerization (Pw), (c) dispersity (Đ) with divinyl monomer conversion. The initial ratio [X]0/[Ini]0=100:1 (color online).

  • Figure 3

    FRcP of monovinyl and divinyl monomers. The growth of number average chain length (Pn) with monovinyl monomer conversion for (a) w.c. model and (d) wo.c. model. The growth of weight average degree of polymerization (Pw) with monovinyl monomer conversion for (b) w.c. model and (e) wo.c. model. The growth of dispersity (Đ) with monovinyl monomer conversion for (c) w.c. model and (f) wo.c. model (color online).

  • Figure 4

    FRP of divinyl monomers. The growth of RDP with divinyl monomer conversion. The initial ratio [X]0/[Ini]0=100:1 (color online).

  • Figure 5

    FRcP of monovinyl and divinyl monomers. The growth of RDP with monovinyl monomer conversion for (a) w.c. model and (b) wo.c. model (color online).

  • Figure 6

    FRP of divinyl monomers. Effect of an intramolecular cyclization in w.c. simulation. Ratio of intermolecular crosslinks per chain to all crosslinks per chain versus divinyl monomer conversion. Arrows indicate gel points.

  • Figure 7

    FRcP of monovinyl and divinyl monomers. Effect of an intramolecular cyclization in “with cyclization” simulation. Ratio of intermolecular crosslinks per chain to all crosslinks per chain versus monovinyl monomer conversion. Arrows indicate gel points (color online).

  • Figure 8

    Illustration of the three polymerization stages in FRP of MVMs. (a) Linear propagation; (b) intermolecular crosslinking; (c) gelation (color online).

  • Table 1   Summary of all parameters used in the simulation for FRP of divinyl monomers

    Parameters

    Value

    Ref.

    [X]0/[M]0/[Ini]0 a)

    100:0:1

    [26]

    [X] (M) a)

    1.45

    [26]

    Number of monomer elements (Xm) b)

    107

    this work

    Number of initiator elements (Xa) b)

    105

    this work

    kd (s−1) c)

    9.8×10−6

    [18,30]

    kpm (L/(mol s)) d)

    150

    [21,31]

    kpp (L/(mol s)) e)

    75

    [13,21]

    kt (L/(mol s)) d)

    106

    [21,31]

    The simulation system ([X]0/[M]0/[Ini]0 and [X]) corresponds to Ref. [26]. X represents divinyl monomers or crosslinkers, M represents monovinyl monomers, Ini represents initiators; b) the value of Xm (the system size) was estimated in this work, the value of Xa was calculated based on Xm, 100:1; c) the value of kd was chosen according to the typical value for azo initiators (around 10−5) which was calculated based on Refs. [18,30]; d) kpm and kt were chosen based on the values used both in the universal simulation work (Ref. [31]) and the work specifically for methacrylate monomers (Ref. [21]); e) the value of kpp was set twice smaller than that of kpm as used in Ref. [13]. According to the mean-field feature of F-S theory and the equal reactivity of all double bonds, the ratio of kpm and kpp used in this work can be picked according to the number of double bonds on corresponding reactants (divinyl monomers and pendent vinyls).

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