Polymerization depropagation

It is known that the ring-opening polymerization of lac-tides is an equilibrium process and some monomers are present in the reaction mixture even at the very end of polymerization. Depropagation (like side reactions if they do occur) results in broadening of the molecular weight distribution. Thus, the value of the dispersity close to 1 indicates that at the moment when the above-described dispersion polymerization of D,L-lactide was stopped, the system was still far from equilibrium. 

The mechanism of anionic polymerization of cyclosiloxanes has been the subject of several studies (96,97). The first kinetic analysis in this area was carried out in the early 1950s (98). In the general scheme of this process, the propagation/depropagation step involves the nucleophilic attack of the silanolate anion on the sUicon, which results in the cleavage of the siloxane bond and formation of the new silanolate active center (eq. 17). 

With most common monomers, the rate of the reverse reaction (depropagation) is negligible at typical polymerization temperatures. However, monomers with alkyl groups in the a-position have lower ceiling temperatures than monosubstituted monomers (Table 4.10). For MMA at temperatures <100 °C, the value of is <0.01 (Figure 4.4). AMS has a ceiling temperature of <30 °C and is not readily polymerizable by radical methods. This monomer can, however, be copolymerized successfully (Section 7.3.1.4). 

Increasing the temperature may also increase the rate of depropagation resulting in equilibrium monomer concentrations well above an acceptable residual monomer concentration (Sawada (1976)). It seems there exists an optimum temperature of polymerization that will reduce the time of polymerzation but will avoid the problems of depolymetization and of initiator depletion. 

In this paper we present a meaningful analysis of the operation of a batch polymerization reactor in its final stages (i.e. high conversion levels) where MWD broadening is relatively unimportant. The ultimate objective is to minimize the residual monomer concentration as fast as possible, using the time-optimal problem formulation. Isothermal as well as nonisothermal policies are derived based on a mathematical model that also takes depropagation into account. The effect of initiator concentration, initiator half-life and activation energy on optimum temperature and time is studied. 

None of the above efforts considered depropagation effects in combination with the optimal reactor problem. When a polymerization is carried out at high temperature to reach a fmal monomer concentration which is low, the thermodynamic (depropagation) effects may become more important than the kinetic ones. 

We emphasize that the conditions subscripted with a zero (time, initiator and monomer concentration) are not the beginning of a reaction, but rather some point well advanced in the polymerization process when the remaining amount of monomer is small in absolute terms but large compared to the desired end state of the polymerization (Mg M ). The amount of initiator Ig is to be achieved by addition to any present immediately before time zero, and the final monomer concentration, M, is set by production specifications. We do not set any predetennined bounds on upper and lower temperature limits. In practice the upper limit will be detennined by either reaction variables (depropagation and initiator depletion) or by process variables (heat exchange), while the lower temperature limit will be determined by process variables (solubility, heat exchange). We do not here consider the process variables to be constraints. 

Ito, K., and Yamashita, Y., Propagation and depropagation rates in the anionic polymerization of e-caprolactone cyclic oligomers, Macromolecules. Ij., 68-72, 1978. 

Polymerization Equilibria. As mentioned earlier, esters of strong acids, e.g. trifluoromethane sulfonic acid ("triflates"), are excellent initiators for the polymerization of THF. With such initiators, however, a complication arises. In addition to the normal propagation i depropagation equilibria of oxonium ions, Smith and Hubin postulated that the macroion ( ) may also convert into a corresponding nonpolar macroester ( ) by attack of the anion (14). ... 

Recall the discussion in Sec. 2-3 concerning the competition between linear polymerization and cyclization in step polymerizations. Cyclization is not competitive with linear polymerization for ring sizes greater than 7 atoms. Further, even for most of the reactants, which would yield rings of 5, 6, or 7 atoms if they cyclized, linear polymerization can be made to predominate because of the interconvertibility of the cyclic and linear structures. The difference in behavior between chain and step polymerizations arises because the cyclic structures in chain polymerization do not depropagate under the reaction conditions that is, the cyclic structure does not interconvert with the linear structure. 

In addition to the usual polymer-monomer propagation-depropagation equilibrium that may he present, trioxane polymerization proceeds with the occurrence of a polymer-formaldehyde equilibrium ... 

Polymerization of 1,3,5-trioxepane involves more complicated propagation-depropagation equilibria. The initially formed oxycarbocation XX loses formaldehyde to yield oxycarbocation XXI, which in turn loses 1,3-dioxolane to regenerate XX ... 

Some cationic ring-opening polymerizations take place without termination and are reversible. Oxirane and oxetane polymerizations are seldom reversible, but polymerizations of larger-sized rings such as tetrahydrofuran are often reversible. The description of reversible ROP is presented below [Afshar-Taromi et al., 1978 Beste and Hall, 1964 Kobayashi et al., 1974 Szwarc, 1979]. It is also applicable to other reversible polymerizations such as those of alkene and carbonyl monomers. The propagation-depropagation equilibrium can be expressed by... 

A typical example showing that we are able to build macromolecules at will is given by C. P. Pinazzi and co-workers in the first chapter of the second section, Chapter 27. They report how model polyenes can be built and how they react. In Chapter 28 K. F. O Driscoll illustrates the limitations in polymerization. For every vinyl monomer, a ceiling temperature exists, above which depropagation exceeds polymerization. If two vinyl monomers are copolymerized at a temperature at which one depropa-gates, the polymer formed will have an unusual composition and sequence distribution. 

The same reason (depropagation of dioxolane-dioxolane blocks) which prevents formation of long dioxolane sequences in solution also applies to polymerization in the crystalline phase. This supports the assumption that most of the dioxolane incorporated into the crystalline copolymer is present as single units and not as longer blocks. 

There must therefore exist some conditions where the rate of propagation is just equal to the rate of depropagation, i. e. where AG = 0. The temperature at which the rates of reaction (2) are equal in both directions is of special importance for polymerizations. 

Fig. 1 Tc. The difference in the rates of propagation and depropagation (curve 1) determines the temperature range where long chains can be generated. In the hatched section, polymerization does not occur.

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