Polyfunctional monomers, modelization

Modelization of the System. Theoretical treatment of polyfunctional monomers condensation polymerization has been firstly proposed by Flory and Stockmayer (22.23 and later by Gordon, Bruneau, Macosko and others (24-26. These theories lay out the basic relation between extent of reaction and average molecular weight of the resulting non linear polymers. 

The mathematical model of network formation in the pregel stage will focus on the prediction of the gel conversion and the evolution of number-and mass-average molar masses, Mn and Mw, respectively. For chainwise polymerizations, calculations will be restricted to the limit of a very low concentration of the polyfunctional monomer (A4 in the previous example). Thus, homogeneous systems will always be considered. 

The above example gives us an idea of the difficulties in stating a rigorous kinetic model for the free-radical polymerization of formulations containing polyfunctional monomers. An example of efforts to introduce a mechanistic analysis for this kind of reaction, is the case of (meth)acrylate polymerizations, where Bowman and Peppas (1991) coupled free-volume derived expressions for diffusion-controlled kp and kt values to expressions describing the time-dependent evolution of the free volume. Further work expanded this initial analysis to take into account different possible elemental steps of the kinetic scheme (Anseth and Bowman, 1992/93 Kurdikar and Peppas, 1994 Scott and Peppas, 1999). The analysis of these mechanistic models is beyond our scope. Instead, one example of models that capture the main concepts of a rigorous description, but include phenomenological equations to account for the variation of specific rate constants with conversion, will be discussed. 

Figure 3.58. Problem of bond and node percolation a model of gel formation during polymerization of a polyfunctional monomer in solution (Stanley et al., 1980 Efros, 1982 ) [Reprinted with permis.sion from Dynamics of Synergetic Systems Proc. Int. Symp. on Synergetics, Butlfeld, Germany, September 2f-29, 1979 Ed. M.Haken. Copyright by Springer-VerlagJ...

On the other hand, despite the fact that equations (3.I1)-(3.I5) are widely used for the description of the polymerization of polyfunctional monomers up to the high conversion state and satisfactory describe the experimental data, their physical sense has not been discovered yet. That is why results obtained via the autocatalytic model do not offer the possibility to explain the chemical mechanism of a process and theoretical grounds of the constants 1 and 2-... 

Functionally terminal polymers are valuable material intermediates. The di- and polyfunctional varieties (telechelic polymers) have found theoretical (e.g., model network) and commercial (e.g., liquid rubber) applications (1, ). On the other hand, macromolecules with a functional group at one chain end (semitelechelic polymers) have been used to prepare novel macromolecular monomers (Macromers ), as well as block and graft copolymers ( -8). 

Practical Aspects. The foregoing theoretical relationships are difficult to apply to the curing of ultraviolet light-cured printing inks for several reasons. First, the polymerization kinetics of the complex monomers and prepolymers used in flie ink formulations have not yet been investigated under conditions that can be correlated with theory (i. e., low concentrations of reactants, constant temperature, simple model formulations). Second, the ultraviolet light-cured inks are polymerized in bulk to high conversion tiie polyfunctional nature of the... 

Raman fibre optics has been used to study the emulsion homopolymerisations of styrene and n-butyl acrylate (35). An IR spectroscopic technique for the examination of radical copolymerisations of acryl and vinyl monomers was developed. A comparative study of the copolymerisation of model monomer pairs was made using monofunctional and polyfunctional compounds. The data established the role of structural-physical transformations, involved in the formation of crosslinked polymers, on the copolymerisation kinetics and on the nonuniformity of distribution of crosslinks in the copolymers formed (151). Raman fibre optics of polymerisation of acrylic terpolymers was also used to monitor as well as an on-line measurement of morphology/composition (66). The high temperature (330 °C) cure reaction of 4-phenoxy-4 -phenyl-ethynylbenzophenone was monitored using a modulated fibre optic FT-Raman spectrometer (80). 

Equivalent phase diagram for a gelating system in semi-dilute solutions with a good solvent, is the monomer concentration (and each monomer is polyfunctional). is an equivalent temperature, which decreases from infinity to low values when the chemical reaction progresses. The particular model used in the text assumes instant reaction between monomers which are in contact. But the qualitative features of the diagram are more general. 

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